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APPLICATIONS OF THE DIFFERENTIAL REFLECTIVITY RADAR TECHNIQUE: FOCUS ON ESTIMATION OF RAINFALL PARAMETERS AND MICROWAVE ATTENUATION PREDICTION

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A pplications o f the differential reflectivity radar technique:
Focus on estim ation o f rainfall param eters and microwave
attenuation prediction
Direskeneli, Haldun, Ph.D .
The Ohio State University, 1987
UMI
300 N. Zeeb Rd.
Ann Arbor, MI 48106
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APPLICATIONS OF THE DIFFERENTIAL REFLECTIVITY RADAR TECHNIQUE:
FOCUS ON ESTIMATION OF RAINFALL PARAMETERS
AND MICROWAVE ATTENUATION PREDICTION
DISSERTATION
Presented in Partial Fulfillment of. the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of the Ohio State University
By
Haldun Direskeneli, B.S., M.S.
The Ohio State University
1987
Dissertation Committee:
Approved by
Richard N. Boyd
Walter E. Mitchell, Jr.
David L. Moffatt
Advisor (J
•
Department of Electrical Engineering
To My Family
ii
ABSTRACT
This study explores the application of the differential
reflectivity radar method to estimate rainfall parameters by comparing
radar-derived estimates with ground-based disdrometer and raingage
measurements.
The derivation of the empirical relationships linking
the rainfall parameters rainfall rate (R), water content (M) and
median volume diameter
(Dq )
to the radar observables horizontal
reflectivity factor (Zjj) and/or differential reflectivity
are
described based on simulations employing disdrometer measurements made
during a 1982 field experiment in central Illinois.
Three case
studies are described utilizing these relationships to compare radar
estimates with ground-based measurements.
For the Ohio State Precipitation Experiments (OSPE, 1982) a
systematic approach to select the appropriate radar volume to be
compared with the disdrometer is described including a cross­
correlation analysis between the (Z^
Z_jj) pairs obtained from the
radar measurements and disdrometer-derived values.
The empirical (Zjj,
Zj^) relationship for R resulted in 9% and 24% for' the normalized bias
and standard error, respectively, compared to 31% and 36% for the best
conventional single parameter Z-R relationship.
The MAYPOLE '83 experiment involved the transformation of dis­
drometer measurements to the radar altitudes to account for drop size
iii
sorting due to different fall velocities within a narrow radar beamwidth and resulted in a very good agreement between the radar- and
disdrometer-derived parameters.
MAYPOLE '84 comparisons involved high raingage
rainfall rates (R
> 120 mm h ^
max
estimates.
which were compared with the radar
r
After fall time and wind transport of raindrops were
accounted for, errors of 7% for the bias and 30% for the standard
error were obtained, considerably better than the results using Z-R
relationships.
The work also examines application of the
method to predict
C-band reflectivity profiles from S-band measurements and compares the
results with actual C-band measurements.
This test includes the
estimation of C-band specific attenuation and reflectivity factor from
S-band (Zjj
Z_„) measurements.
Potential applications of the Z^^
method to scavenging of aerosols and estimation of vertical air
velocities are also considered, based on simulations derived from a
disdrometer data base.
iv
ACKNOWLEDGMENTS
I wish to express my appreciation and thanks to my advisor, Dr.
Thomas A. Seliga.
His guidance, suggestions and assistance are deeply
appreciated.
I also extend my appreciation to Dr. Kftltegin Aydin for his
numerous invaluable suggestions throughout the course of this work.
Additional gratitude is extended to Dr. Viswanathan N. Bringi of
Colorado State University, Mr. Richard E. Carbone, Dr. Paul Herzegh,
Dr. Jeff Keeler and Ms. Cindy Mueller of the National Center for
Atmospheric Research for their assistance during the MAYPOLE field
projects and to Dr. Eugene A. Mueller of the Illinois State Water
Survey for his help during the Ohio State Precipitation Experiments
field project.
I wish to thank the College of Engineering at The Pennsylvania
State University for providing me the support and opportunity to
reside at Penn State to complete my research.
I extend my thanks to The Ohio State University for providing
tuition support for one year while in residence at Penn State.
Appreciation is extended to the staff of the Communications and
Space Sciences Laboratory for their assistance during my stay at Penn
State.
v
Finally, special thanks to Ms. Barbara Webb for her time and
efforts, particularly during the final stages of this work.
Ms. Helen
Clark's patience and competence in typing the dissertation have been
especially helpful.
This research was supported by the Atmospheric Research Section,
National Science Foundation, the Air Force Office of Scientific
Research, the Army Research Office, and the National Aeronautics and
Space Administration under NSF Grant ATM-80033767, and by the Army
Research Office through the University Corporation for Atmospheric
Research under subcontract NCAR S3025.
vi
TABLE OF CONTENTS
A B S T R A C T ........................................................
iii
ACKNOWLEDGEMENTS ................................................
v
V I T A ............................................................
xi
LIST OF T A B L E S .................................................
xiv
LIST OF FIGURES................................................... xviii
LIST OF SYMBOLS.................................................... xxix
CHAPTER
1.
INTRODUCTION............................................
1.1
1.2
1.3
2.
1
General Nature of the Problem....................
Previous Related Studies ........................
Research Objectives and Approach ................
1
4
8
DIFFERENTIAL REFLECTIVITY RADAR METHOD AND
EXPERIMENTAL FACTORS...................................
11
2.1
Differential Reflectivity Method ................
11
2.1.1
2.1.2
2.1.3
2.1.4
2.1.5
11
14
16
16
2.1.6
2.1.7
2.2
Radar Observables .........................
Rainfall Parameters ......................
Specific Attenuation......................
Drop Size Distribution....................
Single Parameter Estimationof Rainfall
Parameters...............................
Differential Reflectivity Radar Technique .
Statistical Considerations................
18
19
23
Experimental Facilities..........................
28
2.2.1
28
Radars.....................................
2.2.1.1
2.2.1.2
2.2.1.3
CHILL Radar (OSPE)................
CP-2 and CP-4 Radars (MAYPOLE
•83, ' 8 4 ) .......................
Antenna Performance..............
vii
28
29
29
2.2.2 Ground Facilities
2.2.2.1
2.2.2.2
3.
Disdrometer .....................
Portable Automated Mesonet(PAM) .
30
31
DISDROMETER-BASED RAINFALL SIMULATIONS.................
32
Disdrometer Measurements ........................
Relationships between RainfallParameters and
Radar Observables...............................
32
3.2.1
3.2.2
Rainfall Rate and Water C o n t e n t ..........
Median Volume Diameter....................
35
42
Error Computations ...............................
46
3.3.1
48
3.1
3.2
3.3
3.3.2
4.
30
Simulated Comparisons of Rainfall
Parameters...............................
Choice of Relationships..................
DIFFERENTIAL REFLECTIVITY RADAR MEASUREMENTS OF
RAINFALL................................................
4.1
OSPE Case Study...................................
4.1.1
4.1.2
4.1.3
Cell Selection.............................
Swath S e l e c t i o n ..........................
Radar-Disdrometer Comparisons ............
4.1.3.1
4.1.3.2
4.1.3.3
4.1.3.4
60
61
65
77
91
95
97
98
R e m a r k s ...................................
100
Radar-Disdrometer Comparisons: 4 June 1983
MAYPOLE '83 Experiment .........................
101
4.2.1
4.2.2
4.2.3
4.2.4
4.3
48
Rainfall Rate.....................
Liquid Water Content ............
Median Volume Diameter ..........
Reflectivity Factor and Differ­
ential Reflectivity............
4.1.4
4.2
35
Radar and Disdrometer Measurements........
Transformation of Disdrometer Time Records
to Radar Altitudes.......................
Disdrometer-Radar Comparisons ............
R e m a r k s ...................................
Radar-Raingage Comparisons: 15 June 1984
MAYPOLE Experiment .............................
4.3.1
4.3.2
4.3.3
4.3.4
Raingage Measurements ....................
Radar Measurements........................
Raingage-Radar Comparisons................
R e m a r k s ...................................
viii
99
102
108
Ill
129
129
130
131
137
143
5.
PREDICTION AND COMPARISONS OF C-BAND REFLECTIVITY
PROFILES FROM S-BAND MEASUREMENTS ...............
5.1
5.2
Introduction.....................................
Simultaneous Operation of CP-4 (5.45 cm) and
CP-2 (10.7 cm) Radars...........................
C-Band Specific Attenuation and Reflectivity
Factor from S-Band Measurements.................
Prediction Procedure .
........................
S-Band Predictions and C-Band Measurements . . . .
Summary...........................................
160
173
176
182
OTHER APPLICATIONS......................................
186
6.1
186
5.3
5.4
5.5
5.6
6.
Aerosol Scavenging Rates ........................
6.2
145
147
Scavenging Rates...........................
Simulations ...............................
189
193
Vertical Air Velocities..........................
199
6.1.1
6.1.2
6.2.1
6.2.2
6.2.3
6.2.4
7.
145
Previous Studies...........................
Doppler Velocity Components ...............
Model Computations.........................
Proposed Experiment .......................
201
203
206
209
SUMMARY AND CONCLUSIONS ................................
213
7.1
7.2
213
215
Review of the Problem............................
Simulated and Experimental Results ..............
7.2.1
7.2.2
Disdrometer Simulations ...................
Case Studies...............................
215
216
7.2.2.1
7.2.2.2
216
7.2.2.3
7.2.3
7.2.4
7.3
OSPE Disdrometer Comparisons . . .
MAYPOLE '83 Disdrometer
Comparisons.....................
MAYPOLE '84 Raingage Comparisons .
217
218
C-Band P r o f i l e s ...........................
Other Applications.........................
218
219
Recommendations for Future Research..............
220
7.3.1
7.3.2
7.3.3
7.3.4
Rainfall Studies...........................
Hydrology, Flash Flood Forecasting and
Weather Modification.....................
Prediction of (Z„, Z_.„) Profiles at
Attenuating Wavelengths .................
Cloud Physics, Scavenging, Earth Energy
and Radiation Budget.....................
ix
220
221
221
222
APPENDIX
Radar Specifications
LIST OF REFER E N C E S ............................................
x
224
228
VITA
13 September 1955.................Born - Cihanbeyli, Turkey
1978 , ...........................
B.S., Electrical Engineering
Middle East Technical University,
Ankara, Turkey
1978 .............................
Graduate Teaching Associate,
Physics, Middle East Technical
University
1979-1981......................... Graduate
Research/Teaching
Associate, Atmospheric Sciences
Program and Electrical Engineering
Department, The Ohio State
University, Columbus, Ohio
1981 .............................
M.S., Electrical Engineering,
The Ohio State University
1981-1985......................... Graduate
Research Associate,
Atmospheric Sciences Program,
The Ohio State University
1985-1987.
...
.................
Research Assistant, Communications
and Space Sciences Laboratory,
The Pennsylvania State University,
University Park, Pennsylvania
PUBLICATIONS
Direskeneli, H . , 1981: Effective Propagation Characteristics in
Random Medium Using Multiple Scattering Medium. Atmos. Sci.
Prog. Rep. No. AS-S-113, The Ohio State University, Columbus.
Direskeneli, H . , T. A. Seliga, and K. Aydin, 1983: Differential
Reflectivity (Zq r ) Measurements of Rainfall Compared with Ground
Based Disdrometer Measurements.
Preprints 21st Conf. Radar
Meteor., Edmonton, Alberta, Canada, AMS, A75-A78.
xi
Seliga, T. A., K. Aydin, and H. Direskeneli, 1983: Disdrometer
Measurements During a Unique Rainfall Event in Central Illinois
and Their Implication for Differential Reflectivity Radar
Observations. Preprints 21st Conf Radar Meteor., Edmonton,
Alberta, Canada, AMS, 467-474.
Seliga, T. A., K. Aydin, and H. Direskeneli, 1983: Possible Evidence
for Strong Vertical Electric Fields in Thunderstorms from
Differential Reflectivity Measurements. Preprints 21st Conf.
Radar Meteor., Edmonton, Alberta, Canada, AMS, 500-502.
Seliga, T. A., K. Aydin, and H. Direskeneli, 1984: Comparison of
Disdrometer-Derived Rainfall and Radar Parameters During MAYPOLE
'83. Preprints 22nd Conf. Radar Meteor., Zurich, Switzerland,
AMS, 358-363.
Seliga, T. A., K. Aydin, and H. Direskeneli, 1986: Disdrometer
Measurements During an Intense Rainfall Even in Central
Illinois: Implications for Differential Reflectivity Radar
Observations.
J. Climate and Appl. Meteor., 25(6), 835-846.
Direskeneli, H . , K. Aydin, and
T. A. Seliga, 1986:Radar Estimation
of Rainfall Rate Using Reflectivity Factor and Differential
Reflectivity Measurements Obtained During MAYPOLE '84:
Comparison with Ground-Based Raingages. Preprints 23rd Conf.
Radar Meteor., Snowmass, Co., AMS, 116-120.
Aydin, K., T. A. Seliga, and H. Direskeneli, 1987: Rainfall
Parameters Derived from Dual Polarization Radar Measurements
Compared with a Ground-Based Disdrometer in Central Illinois.
1987 International Geoscience and Remote Sensing Symposium
(IGARSS '87).
IEEE/URSI, Ann Arbor, Michigan.
Direskeneli, H., T. A. Seliga, and K. Aydin, 1987:
Prediction of
C-Band Reflectivity Profiles in Rainfall Using S-Band Dual Linear
Polarization Measurements and Comparisons with Simultaneous
C-Band Measurements.
1987 International Geoscience and Remote
Sensing Symposium (IGARSS '87). IEEE/URSI, Ann Arbor, Michigan.
Aydin, K., H. Direskeneli, and T. A. Seliga, 1987: Dual Polarization
Radar Estimation of Rainfall Parameters Compared with GroundBased Disdrometer Measurements: 29 October 1982, Central
Illinois Experiment. Accepted for publication in IEEE Trans.
Geosc. Remote Sensing.
FIELDS OF STUDY
Major Field:
Electrical Engineering
Studies in Electromagnetic Theory:
L. Peters, Jr., C. A. Levis
Studies in Communications:
Moffatt
Professors R. G. Koujoumjian,
Professors C. E. Warren, D. L.
xii
Fields of Study (continued)
Studies in Atmospheric Sciences:
Arnfield, M. R. Foster
Studies in Mathematics:
Studies in Statistics:
Professors T. A. Seliga, A. J.
Professors H. D. Colson, S. Drobot
Professor J. C. Hsu
xiii
LIST OF TABLES
PAGE
TABLE
3.1.
3.2.
3.3.
Estimated fractional standard deviations (FSD) of
rainfall rate (R), horizontal reflectivity factor
(Zfl) and differential reflectivity (Zq r ) in
thunderstorms at R = 1, 10_and 100 mm h-^-. Here
ZR is in mm6m“3 and Zd r = Z^/Zy where Zy is the
vertical reflectivity factor .......................
36
(R/Zfl)- and (M/Zr J-Zd r relationships derived from'
regression analyses. The estimated constants for
these power law relationships and the corresponding
95% confidence limits are given. Correlation
coefficients (p) for [log (R/Zr ) and log Z q r ] and
[log (M/Zr) and log Z q r ] are also listed. R is the
rainfall rate, M water content, Z r reflectivity
factor and Z r r differential reflectivity ........
AO
(R/Zh)“ and (M/Zh)-Do relationships derived from
regression analyses. The estimated constants for
these power law relationships and the corresponding
95% confidence limits are given. Correlation
coefficients (p) for [log (R/Zh) and log Do] and
[log (M/Zr) and log Do] are also listed. R is the
rainfall rate, M water content, Dq median volume
diameters and Z r reflectivity f a c t o r ..............
A1
Zj)R(dB)-Do(mra) relationships derived from
regression analyses. The estimated constants for
these relationships and the corresponding 95%
confidence limits are given. Correlation
coefficients (p) for the linear (Z r r and Do) and
power law (log Z DR and log D q ) relationships are
also listed. Results were obtained from data in the
ranges 0.2 < Zp^ < 2.6 and 0.7 < D q < 3.0. Zj>r is
the differential reflectivity and D q median volume
d i a m e t e r ...........................................
A5
xiv
Rainfall rate errors for the heavy rainfall event
of October 6, 1982 in central Illinois in terms of
NB, NSED, AD and AAD (see Eqs. 3-19 through 3-2A).
Reflectivity factor and differential reflectivity
data are simulated from disdrometer measurements of
raindrop size distributions, and the relationships
given in Table 3.2 and Eqs. (3-5, 7, 9, 25, 26, 27)
are used in obtaining rainfall rates from the
simulated radar measurements. The disdrometerderived rainfall rates are treated as reference
values ............................................
Water content errors for the heavy rainfall event
of October 6, 1982 in central Illinois in terms of
NB, NSED, AD and AAD (see Eqs. 3-19 through 3-24).
Reflectivity factor and differential reflectivity
data are simulated from disdrometer measurements
of raindrop size distributions, and the relation­
ships given in Table 3.2 and Eqs. (3-6, 8, 10, 28,
29) are used in obtaining water contents from the
simulated radar measurements. The disdrometerderived water contents are treated as reference
values ............................................
Median volume diameter errors for the heavy rain­
fall event of October 6, 1982 in central Illinois
in terms of NB, NSED, AD and AAD (see Eqs. 3-19
through 3-24). Differential reflectivity data
are simulated from disdrometer measurements of
raindrop size distributions, and the relationships
given in Table 3.4 and Eqs. (3-17, 18) are used
in obtaining median volume diameters from the
simulated radar measurements. The disdrometerderived median volume diameters are treated as
reference values .................................
Rainfall rate errors for two independent rainfall
events that occurred on June 8 and 13, 1982 near
Boulder, Colorado, in terms on NB, NSED, AD and
AAD (see Eqs. 3-19 through 3-24). Reflectivity
factor and differential reflectivity data are
simulated from disdrometer measurements of rain­
drop size distributions, and the relationships
given in Table 3.2, and Eqs. (3-5, 7, 9, 25-27)
are used in obtaining rainfall rates from the
simulated radar measurements. The disdrometerderived rainfall rates are treated as reference
values ............................................
Water content errors for two independent rainfall
events that occurred on June 8 and 13, 1983 near
Boulder, Colorado, in terms of NB, NSED, AD and
AAD (see Eqs. 3-19 through 3-24). Reflectivity
factor and differential reflectivity data are
simulated from disdrometer measurements of
raindrop size distributions, and the relationships
given in Table 3.2 and Eqs. (3-6, 8, 10, 29) are
used in obtaining water contents from the
simulated radar measurements. The disdrometerderived water contents are treated as reference
values ............................................
Median volume diameter errors for two independent
rainfall events that occurred on June 8 and 13,
1983 near Boulder, Colorado, in terms of NB, NSED,
AD and AAD (see Eqs. 3-19 through 3-24). Reflec­
tivity factor and differential reflectivity data
are simulated from disdrometer measurements of
raindrop size distributions and the relationships
given in Table 3.4 and Eqs. (3-17 through 3-18) are
used in obtaining median volume diameters from
the simulated radar measurements. The disdrometerderived median volume diameters are treated as
reference values .................................
Cell D4 radar-disdrometer comparisons of rainfall
rate, water content, median volume diameter,
reflectivity factor and differential reflectivity
for the 29 October 1982 rainfall event. Rg, Rgfj,
Rg , Mp, M q employ
radar observed
(ZR , ZDR) whereas
RZR» RMS* rMP» rJW and mD0 use ZH only. Doe and
D q q are estimated from ZpR . Disdrometer values
are the reference values for all entries .........
Swath radar-disdrometer comparisons as in Table
4.2, except the results are for the swath averages
of cells (B4, C4, D4, E4) shown in Fig. 5.2. Rg^
and Rgjflj employ (ZH » ZDR) for rainfall rate
estimation with different averaging considerations
(see Section 4.1.3). ZR is the reflectivity factor
and ZpR differential reflectivity.................
Statistical summary of radar- and disdrometerderived parameters including mean values (x),
standard deviations (s), correlation coefficients
( ), and the slope (A) and the intercept (B) of
the linear regression coefficients. The super­
scripts D and R for ZR , ZpR and Dq and the
subscripts D and R for R refer to disdrometerand radar-derived values, respectively, where Zg
is the reflectivity factor, ZpR is the differential
reflectivity. R is the rainfall rate, D q is the
median volume diameter ...........................
5.1.
Description of radar measurements...................
148
5.2.
Disdrometer-derived specific attenuation empirical
formulas for 5.45 cm specific attenuation - 10.7
cm reflectivity factor and differential reflec­
tivity relationships ...............................
167
Disdrometer-derived reflectivity factorempirical
formulas for 5.45 cm reflectivity factor - 10.7 cm
reflectivity factor and differential reflectivity
relationships.......................................
172
Empirical formulas to estimate precipitation
scavenging rates A from both (Zjj, Z^r) and (R, D q ).
Relationships were derived from multiple regression
analyses using disdrometer data and for different
aerosol radii. Correlation coefficients (p) for
the regression relation relating the logarithms of
the parameters are also shown. R is the rainfall
rate, D q is the median value diameter, Zjj is the
reflectivity factor, Zj)R is the differential
reflectivity .......................................
191
Empirical formulas to estimate precipitation
scavenging rates A from both ZH and R. Relation­
ships were derived from regression analyses using
disdrometer data and for different aerosol radii.
Correlation coefficients (p) for the regression
relationship relating the logarithms of the
parameters are also shown. R is the rainfall rate
and ZH is the reflectivity factor...................
192
Constants of the <vt>- Z DR relationship derived
from a linear regression analysis of the relation­
ship expressed in base 10 logarithms. Correspond­
ing 95% confidence limits and correlation
coefficients (p) are also given,
is the
reflectivity weighted fall velocity and Z^R is the
differential reflectivity...........................
208
5.3
6.1.
6.2.
6.3.
xvii
LIST OF FIGURES
FIGURE
2.1.
2.2.
2.3.
2.4.
2.5.
3.1(a).
3.1(b).
PAGE
Raindrop distortion model:
an oblate spheroid is the
body of revolution formed when an ellipse is rotated
about its minor axis...................................
15
Rain parameter diagram for exponential drop size
distribution model. Radar reflectivity factor versus
rainfall rate with isopleths of median volume
diameter Dq and parameter N q . Data points represent
estimates inferred from radar measurements (Seliga
et al., 1981), and MP signifies the Marshall-Palmer
Z-R relationship........................................
20
Raindrop canting angle (a), (a) in the plane of
incidence with an angle of incidence(9), and (b) per­
pendicular to the plane of incidence
22
Variation in Z d r with canting angle a (a) in the plane
of incidence, and (b) perpendicular to the plane of
incidence. Zero canting angle (a = 0) results in
maximum Z jjr where Z jjr is the differential reflectivity
(Al-Khatib et al., 1979)...............................
24
Standard deviation (dB) of the square law estimator
as a function of sample size m and cross-correlation
coefficient p (Bringi and Seliga, 1980) ..............
27
Time records of R and M during the 6 October 1982
rainfall event in central Illinois. Solid lines are
actual disdrometer measurements representing 2 min
running average of 30 s recordings. Crosses are the
simulated radar estimates of R and M computed for
Eq. (3-5) using disdrometer-derived (Z jj, Z q r ). Zero
time indicates values averaged over 1513:30-1515:30.
R is the rainfall rate, M water content, Z h reflec­
tivity factor and Z q r differential reflectivity . . . .
33
Time record of Do during the 6 October 1982 rainfall
event in central Illinois. Solid lines are actual
disdrometer measurements representing 2 min running
averages of 30 s recordings. Crosses are simulated
radar estimates of D q computed from Eq. (3-15) using
the disdrometer-derived Z q r . D o is the median volume
diameter and Z ^ differential reflectivity............
34
xviii
3.2.
3.3.
3.A.
3.5.
3.6.
3.7.
3.8.
3.9.
4.1.
4.2.
Scatter plot of R/Z h versus Z q r for the data set
shown in Fig. 3.1(a). The fitted curve corresponds to
Eq. (3-5). R is the rainfall rate, Zg reflectivity
factor and Z q r differential reflectivity...............
37
Scatter plot of M/Zu versus Z q r for the data set
shown in Fig. 3.1(b). The fitted curve corresponds
to Eq. (3-6). M is the water content, Zjj reflectivity
factor and Z q r differential reflectivity..............
37
Scatter plot of R/Zj, versus D q . The fitted curve
corresponds to the 2-section relationship given in
Table 3.3. R is the rainfall rate, Zg reflectivity
factor and D q median volume diameter...................
38
Scatter plot of M/Z™ versus D q . The fitted curve
corresponds to the 2-section relationship given in
Table 3.3. M is the water content, ZH reflectivity
and D q median volume diameter .........................
38
Scatter plot of D q versus Zq ,> on (a) logarithmic and
(b) linear scales obtained from the data set shown in
Fig. 3.1. The fitted curve corresponds to Eq. (3-15).
D q is the median volume diameter and ZH differential
reflectivity............................................
44
Scatter plot of Re derived from the empirical
relationship given in Eq. (3-6) versus disdrometerderived where R is the rainfall rate..................
49
Scatter plot of Me derived from the empirical
relationship given in Eq. (3-6) versus disdrometerderived where M is the water content...................
49
Scatter plot of D q £ derived from the empirical
relationship given in Eq. (3-15) versus disdrometerderived
where D q is the median volume diameter . . .
50
The relative locations of the CHILL radar and the
disdrometer for the 29 October 1982 rainfall event in
central Illinois. Z# contours of a rain cell obtained
from three different PPI scans are also shown which
were used to estimate storm speed and direction. The
times indicate beginning of the scans. Zjj is the
reflectivity factor ...................................
64
The spatial cell network used in the cross-correlation
analysis of the radar versus disdrometer data for the
central Illinois rainfall event (see Section 4.1).
Columns 1-7 are along the storm track, whereas rows
(A-E) are along the radar rays at the indicated azimuth
angles. The numbers in each cell correspond to the
first of the six range gates to be averaged.
Disdrometer is located at the center of cell A4 . . . .
66
xi x
A.A.
A.A(c).
A.5.
A.6.
A.7.
A.8(a).
Cross-correlation coefficients for (a) ZH and (b )
time series data obtained from radar and disdrometer
measurements shown for optimum delay times for radar
measurements. Z h is the reflectivity factor and ZpR
differential reflectivity .............................
69
Cell DA scatter plots of (a) Rg derived from the
radar (ZR , Z DR) using Eq. (3-5) versus disdrometerderived Rp ana (b) Mg derived from the radar (ZR , ZDR)
using Eq. (3-6) versus disdrometer-derived Mg. R is
the rainfall rate, M water content, ZH reflectivity
factor and Z DR differential reflectivity...............
71
Cell DA scatter plot of Dgg derived from the radar
^DR' using Eq, (3-15) versus disdrometer-derived D o d »
where D q is the median volume diameter.................
72
Cell DA scatter plots of radar measured (a) Z h and
(b) Z d r versus their corresponding values derived
from disdrometer measurements. Zh is the reflectivity
factor and ZDR is the differential reflectivity . . . .
73
Horizontal distance X traveled by raindrops of
different sizes during their fall to the ground
versus terminal velocity v t of the raindrops. Results
are shown for different boundary layer depths
and
for raindrops originating from upper, mid and lower
beam heights h. The horizontal extent of the radar
swath and the disdrometer drop diameter corresponding
to the Vf. axis are also superimposed...................
77
Time of impact on the disdrometer of the raindrops
originating from lower, mid and upper beam heights, h
plotted for raindrops with different terminal
velocities, v t and disdrometer drop diameters. The
direction of the disdrometer time sample with respect
to radar sampling time and the percentage of
disdrometer sample observed by radar for different v t
are also shown.
....................
79
Time records of R and M during the 29 October 1982
rainfall event in central Illinois. The solid lines
represent 2.5 min running averages of 30 s disdrometer
samples with zero time corresponding to values
averaged over 0018-0020:30. The points indicate
radar estimates derived from (Zh » ZpR) using Eqs.
(3-5) and (3-6) delayed by 2 min. R is the rainfall
rate, M water content, Z h reflectivity factor and
Zj)R differential reflectivity.........................
80
xx
A.8(b).
A.9.
A.10.
A.10.
A.11.
A.12.
A.13.
Time record of Do during the 29 October 1982 rainfall
event in central Illinois. The solid lines represent
2.5 min running averages of 30-s disdrometer samples
with the zero time corresponding to values averaged
over the time interval 0018-0020:30. The points
indicate radar estimates derived from (ZR , ZpR ) using
Eq. (3-15) delayed by 2 min. D q is the median volume
diameter, ZR reflectivity factor and ZpR differential
reflectivity............................................
81
Time records of ZR and ZpR for the rainfall event
shown in Fig. A.8. The points are obtained from the
radar measurements and the solid lines are the
disdrometer-derived values. ZR is the reflectivity
factor and ZpR differential reflectivity...............
82
Swath scatter plots of (a) Rg derived from the
empirical relationship of Eq. (3-5) and (b) R q
derived from the gamma model relationship of Eq. (3-9)
using radar (ZR , ZpR) versus Rp obtained from the
disdrometer [see next page for (c) and (d)]. R is
the rainfall rate, ZR reflectivity factor and ZpR
differential reflectivity .............................
83
Swath scatter plots of (c) R z r derived from the
empirical Z-R relationship of Eq. (A-6) and (d) RMS
derived from the Mueller-Sims (1966) relationship of
Eq. (A-5) using radar Z h versus Rp obtained from the
disdrometer [see previous page for (a) and (b)].
R is the rainfall rate and Z R reflectivity factor . . .
87
Swath scatter plots of (a) M g derived from the
empirical relationship of Eq. (3-6) and (b) M
derived from the gamma model relationship of Eq.
(3-10) using radar (Zp» Z p R) versus M d obtained from
the disdrometer. M is the water content, Z R reflec­
tivity factor and Z ^ differential reflectivity . . . .
85
Swath scatter plots of (a) D q g derived from the
gamma model relationship of Eq. (3-18) and (b) D q e
derived from the empirical relationship of Eq. (3-15)
using radar ZpR versus D o d obtained from the
disdrometer. D q is the median volume diameter and
Z DR is the differential reflectivity...................
86
Swath scatter plots of radar measured (a) Zp and
(b) Z p R versus their corresponding values derived
from the disdrometer measurements.
Z R is the
reflectivity factor and Z p R is the differential
reflectivity............................................
87
xxi
A.1A.
A.15.
A.16.
A.17.
Relative locations of the CP-2 radar and the
disdrometer during the A June 1983 rainfall event
in Boulder, Colorado. The trajectory of the rain­
drops, the location of the radar volumes used for
different elevation angles and the radar rays and
the range gates used for averaging are also shown . . .
106
Time records of the computed radar observables
(a) Zh and (b) Zq R corresponding to the disdrometer
measurements for the A June 1983 event in Boulder,
Colorado. Also shown are (c) R and (d) Dq measured
by the disdrometer for the same event. Zj$ is the
reflectivity factor, Zjj differential reflectivity,
R rainfall rate and D q median volume diameter ........
107
Vertical distributions of raindrops with different
terminal velocities and their corresponding
disdrometer size categories at 15 s intervals to
determine the raindrops contributing to the radar
sampling volumes at the six elevation angles. Pairs
of drop size distributions averaged to obtain 30 s
disdrometer samples and the radar beamwidth at
different elevation angles are also indicated ........
110
Time records of the transformed rainfall parameters
(a) ZH , (b) ZDR, (c) R and (d) D q derived from the
disdrometer measurements corresponding to 1° radar
elevation angle. ZR is the reflectivity factor,
ZD£ differential reflectivity, R rainfall rate and
D q median volume diameter ...............................
A.18.
A.19.
A.20.
112
Time records of the transformed rainfall parameters
(a) Z jj, (b) Z DR, (c) R and (d) D q derived from the
disdrometer measurements corresponding to 2° radar
elevation angle. ZR is the reflectivity factor,
Z q R differential reflectivity, R rainfall
rate and
D q median volume diameter ...............................
113
Time records of the transformed rainfall parameters
(a) Zh» (b) ZdO> (c ) R and (d) D q derived from the
disdrometer measurements corresponding to 3° radar
elevation angle. Zu is the reflectivity factor,
ZDR differential reflectivity, R rainfall
rate and
D^ median volume diameter .............................
114
Time records of the transformed rainfall parameters
(a) ZH , (b) ZDR, (c) R and (d) D q derived from the
disdrometer measurements corresponding to A° radar
elevation angle. Z jj is the reflectivity factor,
Zpjj differential reflectivity, R rainfall
rate and
D q median volume diameter .............................
115
xxii
A.21.
Time records of the transformed rainfall parameters
(a) ZR , (b) ZDR, (c) R and (d) D q derived from the
disdrometer measurements corresponding to 5° radar
elevation angle.
ZR is the reflectivity factor,
ZDR differential reflectivity, R rainfall rate and
D median volume diameter .............................
116
Time records of the transformed rainfall parameters
(a) Z , (b) Z , (c) R and (d) D q derived from the
disdrometer measurements corresponding to 6 radar
elevation angle. Z R is the reflectivity factor,
Z p R differential reflectivity, R rainfall rate and
D q median volume diameter .............................
117
Scatter plots of radar-observed (a) Z ^ a n d
(b) Z§R versus their corresponding value Z R and
ZD,, obtained from the results shown in Figs. A. 17A.23(a) and A.17-A.23(b), respectively.
ZR is the
reflectivity factor and Z DR is the differential
reflectivity............................................
118
Scatter plots of radar-derived rainfall rates computed
from (a) the empirical (ZR , ZDR> relationship and
(b) Marshall-Palmer relationship versus disdrometerderived rainfall rates shown in Figs. A.17-A.23(c).
ZH is the reflectivity factor and ZDR differential
reflectivity............................................
119
Scatter plot of D q derived from the radar measure­
ments of ZDR versus disdrometer-derived values shown
in Figs. A.17-A.23(d) where D q is the median volume
diameter................................................
120
The relative locations of the CP-2 radar and the two
PAM stations during the 15 June 198A rainfall event
in Boulder, Colorado...................................
126
Constant altitude (2.A km MSL) PPI's of (a) ZR and
(b) Z n_ generated from the value scan between
1705:3b-1707:31 MDT during the 15 June 198A event.
Z is the reflectivity factor and ZR differential
reflectivity..........................................
128
A.27(c). Constant altitude (2.A km MSL) PPI of R generated
from the volume scan between 1705:36-1707:31 MDT
during the 15 June 198A event where R is the
rainfall r a t e ........................................
129
A.22.
A.23.
A.2A.
A.25.
A.26.
A.27.
A.28.
Constant altitude (2.A km MSL) PPI's of (a) Z R
and (b) ZDR generated from the volume scan between
1716:A0-1718:31 MDT during the 15 June 198A event . .
xxiii
132
A.28(c).
A.29.
A.30.
A.31.
A.32.
A.33.
A.3A.
5.1.
Constant altitude (2.A km MSL) PPI of R(mm h )
generated from the volume scan between 1716:AO1718: 31 MDT during the 15 June event where R is the
rainfall r a t e .......................................
133
RHI's of (a) Z jj and (b) ZDR generated from the
volume scan between 1705:36-1707:31 MDT during the
15 June 198A event which shows a North-South
vertical cross-section of (ZR , Z..R ) passing through
the PAM 15 site located 27.8 km east of CP-2. Zh .
is the reflectivity factor and ZDR differential
reflectivity..............
13A
Time record of R obtained from PAM 15 raingage
measurements. Also shown are the radar estimates
R~ d r derived from the empirical relationship using
(ZR , Zj)R) and (a) Rjyjp derived from the MarshallPalmer relationship and (b) Rj derived from the
Jones (1956) relationship of Eq. (A-8). Zero time
corresponds to 1700 MDT. R is the rainfall rate,
ZR is the reflectivity factor and ZpR is the
differential reflectivity ...........................
138
Time record of R obtained from PAM 11 raingage
measurements. Also shown are the radar estimates
R Zd r derived from the empirical relationship using
(ZR , ZDR) and (a) R^p derived from the MarshallPalmer relationship and (b) Rj derived from the
Jones (1956) relationship of Eq. (A-8). Zero time
corresponds to 1700 MDT. R is the rainfall rate,
Z ji is the reflectivity factor and ZpR is the
differential reflectivity
......................
139
Scatter plot of R z d r derived from the empirical
relationship using (Z^, ZDR) versus R obtained
from the measurements of both PAM 11 and 15 raingages. R is the rainfall rate......................
1A1
Scatter plot of Rj^p derived from the MarshallPalmer relationship versus R obtained from the
PAM 11 and 15 raingages where R is the rainfall
rate..................................................
1A2
Scatter plot of Rj derived from the Jones (1956)
relationship of Eq. (A-8) versus R obtained from
the PAM 11 and 15 raingages where R is the rain­
fall r a t e ............................................
1A2
Demonstrating the applicability of using CAPPI's
for deriving CP-A reflectivity fields affected
by attenuation along ray paths.......................
150
xx iv
5.2(a).
5.2.
5.3.
5.4.
5.5.
5.6.
5.7.
5.8.
Constant altitude (3.0 km MSL) PPI of Zu ^q generated
from the CP-2 volume scan between 1418*.52-1422:02
during the 30 June 1984 event. Z jj^ q *-s the S-band
reflectivity factor .................................
152
Constantaltitude (3.0 km MSL) PPI's
of (b) ZpR
and (c) R generated from the CP-2 volume scan
between 1418:52-1422:02 during the 30 June 1984
event. ZDR is the differential reflectivity and
R is the rainfall rate...............................
153
Constant altitude (3.0 km MSL) PPI of Zjj5 generated
from the CP-4 volume scan between 1418:33-1421:12
during the 30 June 1984 event.
ZR 5 is the C-band
reflectivity factor .................................
154
RHI's of (a) Z jjiq generated from the CP-2 volume
scan between 1418:52-1422:02 and (b) Zjj5 generated
from the CP-4 volume scan between 1418:33-]421:12
during the 30 June 1984 event showing an East-West
vertical cross-section of (Zr ^q , Zr j ) at y = 20 km.
Zrio end Z R 5 are the S-band ana the C-band
reflectivity factors,respectively....................
155
RHI's of (a) ZDR and (b) R generated from the CP-2
volume scan between 1418:52-1422:02 during the
30 June 1984 event showing an East-West vertical
cross-section of (R, ZDR) at y = 20 km. Zpp is the
differential reflectivity and R is the rainfall
rate..................................................
156
RHI's of (a) Z r i q generated from the CP-2 volume
scan between 1418:52-1422:02 and (b) Z R 5 generated
from the CP-4 volume scan between 1418:33-1421:12
during the 30 June 1984 event showing an East-West
vertical cross-section of (Zjjio* ^h 5) at y = 22 km.
Zflio and Z R 5 are the S-band and the C-band
reflectivity factors, respectively..................
158
RHI's of (a) ZDR and (b) R generated from the
CP-2 volume scan between 1418:52-1422:02 during
the 30 June 1984 event showing an East-West
vertical cross-section of (R, ZDR) at y = 22 km.
Z DR is the differential reflectivity and R is the
rainfall r a t e .......................................
159
Scatter plot of ZR versus ZDR obtained from the
CP-2 volume scan between 1418:52-1422:02 during the
30 June 1984 event. The solid line is the rainfall
boundary defined by Aydin et al. (1986). Both
negative and large values of Z jjR at low Z jj are
thought to be due to ground clutter. ZR is the
reflectivity factor and Z DR differential reflec­
tivity................................................
161
xxv
Variation of (a) A h s /Zh IO and (b) Ah 5/Zv 10 versus
ZDR for disdrometer-derived distributions (see next
page for (c) and (d)]. AH^ is the C-band specific
attenuation at horizontal polarization and ZR i q ,
Z v i o (S-band) horizontal and vertical reflectivity
factors, respectively. ZDR is the differential
reflectivity........................................
Variation of (c)
and (d) Ayg/Zyjn versus
ZDR ^or disdrometer-derived distribution [see
previous page for (a) and (b)J. A V 5 is the C-band
specific attenuation at vertical polarization and
ZH10* ZV10 S-band horizontal and vertical reflec­
tivity factors, respectively. Zj)R is the
differential reflectivity . . . ...................
Variation of predicted A^5 / Z v e r s u s Znp for
the disdrometer-derived distributions where A£5 is
derived from the empirical relationship given in
Table 5.2 in the form of Eq. (5-1). Aj*c is the
predicted C-band specific attenuation at vertical
polarization, S-band horizontal reflectivity
factor and ZDR differential reflectivity..........
Errors between the actual and the predicted values
of the attenuation (AR 5 /AR 5 ) versus Zdr for
disdrometer derived distributions. a ]|5 is
derived from the empirical relationship given in
Table 5.2 in the form of Eq. (5-1). A R 5 is the
C-band specific attenuation and Z q R differential
reflectivity. ................................. . .
Variation of (a) Z ^ / Z ^ g an<i (b) ZH5^ZV10 versus
ZDR for disdrometer-derived distributions [see
next page for (c) and (d)]. Z-^5
t^ie C-band
horizontal reflectivity factor and ZR i q » Zyio S-band
horizontal and vertical reflectivity factors,
respectively. ZDR is the differential reflec­
tivity. .
........ ...............................
Variation of (c) Z ^ / Z ^ o anc* (<*) ZV5^ZH10 versus
Z DR for disdrometer-derived distributions [see
previous page for (a) and (b)]. Z ^ is the C-band
vertical reflectivity factor and Z r i q , Zy^g S-band
horizontal and vertical reflectivity factors,
respectively. ZDR is the differential reflec­
tivity..............................................
xxv i
5.13.
5.14.
5.15.
5.16.
5.17.
5.18.
5.19.
5.20.
6.1.
Variation of predicted Zr j /Zh IO versus Zd r for
the disdrometer-derived distributions where Z^j isderived from the empirical relationship given in
Table 5.3 in the form of Eq. (5-2). Zg^ is the
predicted C-band horizontal reflectivity factor,
Zh i o S-band horizontal reflectivity factor. Zd r
is the differential reflectivity.....................
171
Predicted CP-4 reflectivity values derived from
CP-2 (Zr i o » Zd r ) measurements. The azimuth angles
and the gate spacing used in the prediction scheme
for rays along paths originating from CP-4 are
also indicated. Azimuth angles are measured CCW
from north. Zr i o
the S-band reflectivity
factor and Z d r differential reflectivity............
175
The predicted C-band CP-4 reflectivity factor
contours (Fig. 5.14) superimposed as an overlay
on the actual CP-4 measurements (Fig. 5.3) for the
15 June 1984 e v e n t . .................................
178
Spatial variation of reflectivity factors at
S-band measured by CP-2 compared with the pre­
dicted and the measured reflectivity factors at
C-band along the CP-4 rays with azimuth angles
(a) 35° and (b) 40° CCW from north...................
180
Spatial variation of reflectivity factors at S-band
measureed by CP-2 and the simulated reflectivity
factors at C-band along the same ray originating
from CP-2 at an azimuth angle of 38.2° CCW from
north. C-band reflectivity values without
accounting for attenuation ( Z ^ ) are also shown . . .
181
Scatter plot of the predicted and measured
reflectivity factors for the CP-4 radar at C-band
for the ray with the azimuth angle 35° CCW from
n o r t h ................................................
183
Scatter plot of the predicted and measured
reflectivity factors for the CP-4 radar at C-band
for the ray with the azimuth angle 40° CCW from
north
.....................................
183
Scatter plot of the predicted and actual reflec­
tivity factors for the CP-4 radar at C-band for
even rays with the aximuth angles between 3 0 0 -45 °
CCW from n o t h ........................................
184
Computed scavenging rate A and rainfall rate R
scatter plot for aerosols of radius 0.2 ym
corresponding to disdrometer measurements from the
rainfall event of 6 October 1982.....................
194
xxvii
6.2(a).
6.2(b).
6.2(c).
6.2(d).
6.3.
6.A.
6.5.
Computed and simulated time history of A for
aerosols of radius 0.2 ym corresponding to
disdrometer measurements from the rainfall event of
6 October 1982 where A is the scavenging rate . . . .
195
Computed and simulated time history of A for
aerosols of radius 0.5 ym corresponding to
disdrometer measurements from the rainfall event
of 6 October 1982 where A is the scavenging rate.
..
196
Computed and simulated time history of A for
aerosols of radius 1.0 ym corresponding to
disdrometer measurements from the rainfall event
of 6 October 1982 where A is the scavenging rate.
..
197
Computed and simulated time history of A for
aerosols of radius 2.0
corresponding to
disdrometer measurements from the rainfall event
of 6 October 1982 where A is the scavenging rate.
..
198
Computed scavenging rates Ashowing their
variability with aerosol size in the range 0.2
- 2 ym
ym
200 .
Reflectivity weighted fall velocity dependence
on
derived from disdrometer simulations ........
207
Reflectivity weighted fall velocity dependence on
Zfj derived from disdrometer simulations, including
empirical <vt> - Z relationships due to Rogers
(1964), Sakhan and Srivastava (1971), Joss and
Waldvogel (1970) and this work, indicated as R,
SR, JVJ and D, respectivelyv where Z is the
reflectivity factor .................................
210
xxviii
LIST OF SYMBOLS
Description
Symbol
Unit
A
Specific attenuation
a
Semi-minor axis of a raindrop
AAD
Average absolute difference
AD
Average difference
^H5
C-band specific attenuation at horizontal
polarization
(dB km
^5
C-band specific attenuation at vertical
polarization
(dB km
b
Semi-major axis of a raindrop
CAPPI
Constant altitude plan position indicator
CCW
Counter-clockwise
CW
Clockwise
CST
Central standard time
D, De
Equivolume diameter
(mm)
Median volume diameter
(mm)
D
max
Maximum equivolume diameter
(mm)
dB
Decibels
dBZ
Decibels of the reflectivity factor
DSD
Drop size distribution
E
Scavenging efficiency
f
Radar frequency
FSD
Fractional standard deviation
D0
(dB km
(mm)
(mm)
-1
(mm
(Hz)
xx ix
-3
m
)
GOES
Geostationary Operational Environmental
Satellite
H
Horizontal polarization
ISWS
Illinois State Water Survey
|k |2
Refractivity factor at S- and C-bands (=0.93)
K
Direction of propagation
M
Liquid water content
M
Complex index of refraction for water
m
Parameter of the gamma model DSD
MAYPOLE
MAY POLarization Experiment
MDT
Mountain daylight time
MSL
Mean sea level
NB
Normalized bias
NCAR
National Center for Atmospheric Research
N(D)
Raindrop size distribution
N
m
Parameter of the gamma model DSD
No
Parameter of the exponential model DSD
NSED
Normalized standard error of the difference
OSPE
Ohio State Precipitation Experiment
P, Pr
Total average backscattered power
PAM
Portable automated mesonet
PPI
Plan position indicator
R
Target range
R
Rainfall rate
r
Axial ratio (a/b)
RHI
Range height indicator
SB
Sample bias
S(v)
Doppler velocity spectrum
(W m ^ s)
Sn (v)
Normalized Doppler velocity spectrum
(m-1 s)
u,
Horizontal wind velocity
(m s_1)
v
Doppler velocity
(m s-1)
<v>
Reflectivity weighted Doppler velocity
(m s-1)
v
Terminal velocity
(m s 1)
<vfc>
Reflectivity weighted terminal velocity
(m s 1)
w
Mean vertical air velocity
(m s 1)
Z
Reflectivity factor
(dBZ)
Z_D
Differential reflectivity
(dB)
uq
DK
S-band horizontal reflectivity factor
(dBZ)
C-band horizontal reflectivity factor
(dBZ)
Apparent C-band horizontal reflectivity
factor
(dBZ)
Zy,
S-band vertical reflectivity factor
(dBZ)
Zyj
C-band vertical reflectivity factor
(dBZ)
a
Canting angle
(deg)
A<(>
Differential phase shift
(deg)
6
Boundary layer depth
(m)
n
Reflectivity cross-section density
(mm
A
Parameter of the DSD
(mm ^)
A
Scavenging rate
(s_1)
X
Radar wavelength
(mm)
p
Correlation coefficient
Pw
Water density
(kg m -3)
o
Surface tension
(J m“2)
a
Extinction cross-section at horizontal
polarization
(mm2)
^H’ ZH10
Zjj,j
Z
'
xxxi
2
m
-3
)
Extinction cross-section at vertical
polarization
Backscatter cross-section at horizontal
polarization
Backscatter cross-section at vertical
polarization
Fall time of raindrops
xxxii
CHAPTER 1
INTRODUCTION
1.1
General Nature of the Problem
Radar has been an important tool for remote sensing of the
atmosphere, since interactions between atmospheric particles and radio
waves are significant in the microwave and millimeter wave bands.
Backscattered power at these wavelengths can be interpreted to give
information about these atmospheric particle scatterers, specifically
for detection and characterization of rain and cloud particles
consisting of snow and ice crystals, all commonly referred to as
hydrometeors.
Radar information also has important applications in
communication systems and propagation studies, especially along
earth-satellite paths, since the communication channels employing
these wavelengths are affected by hydrometeors causing cross-talk when
orthogonal polarizations are used and attenuation that can signifi­
cantly degrade channel quality.
Radar is unique in the remote sensing of atmospheric scatterers
because of its inherent ability to cover large areas from a single
location in real time.
To approach the same capability otherwise
would require installation of a dense network of ground stations,
aircraft and other aerial sensing devices which in turn would result
in much greater costs and delays in data transmission and analysis.
1
The most recent developments in radar remote sensing include the
use of multi-parameter radar measurements (MPRM) to provide
independent information about the atmospheric medium and scatterers
from polarization, phase, frequency and statistical characteristics of
the received echoes in addition to their backscattered power.
These
measurements usually employ dual polarization, dual wavelength and
Doppler spectrum techniques.
More than one radar may also be involved
in transmitting and receiving various signals, operating either simul­
taneously or sequentially.
One of the most promising techniques among the MPRM's utilizes a
dual polarization radar receiving the backscattered returns in two
linear, orthogonal polarizations, horizontal and vertical.
This
scheme relies on measuring the differential reflectivity
which was
introduced by Seliga and Bringi (1976) and is defined as the differ­
ence (in dB) in radar reflectivities between returns at these two
orthogonal polarizations.
hydrometeors:
is the result of three properties of
(1) their non-spherical shape; (2) their high degree of
mutual orientation; and (3) representation of raindrop size distribu­
tions by models dominated by two independent parameters.
assortment of raindrops, Z ^
For an
is measured by illuminating the volume at
vertical polarization which is aligned along the symmetry axis and
horizontal polarization which is aligned along the major axis of the
generally oblate-shaped raindrops.
The backscattered power is
received with the same polarization as the transmitted one.
Raindrops
tend to be deformed into nearly oblate spheroidal shapes with their
axes of symmetry aligned dominantly along the vertical and larger
drops are uniformly more deformed than the smaller ones (Pruppacher
and Pitter, 1971).
This raindrop behavior results in polarization-
dependent backscattering properties.
When differential reflectivity
is combined with the effective reflectivity factor at either hori­
zontal (Zjj) or vertical (Zy) polarizations, the two parameters of a
given raindrop size distribution can be determined.
Rainfall
parameters such as rainfall rate (R), liquid water content (M) and
median volume diameter (Dq ) and propagation characteristics such as
specific attenuation (A) and relative phase shift (A<J>) can also be
estimated accurately from these polarimetric measurements, resulting
in considerable improvement over other radar techniques developed to
estimate these parameters using a single radar observable such as
reflectivity factor (Z) (Battan, 1973; Atlas et al., 198A).
Thus far, the Zqjj method has proven to be useful in several
applications.
(1)
These include:
estimation of drop size distribution (DSD) which yields the
spatial and temporal evolution of rainfall rate, liquid
water content and median volume diameter;
(2)
discrimination of regions of water, ice and mixed phase
hydrometeors and the detection of hail; and
(3)
other applications such as prediction of cumulative micro­
wave attenuation, differential attentuation and differential
phase shift in rainfall using both attenuating and non­
attenuating wavelengths.
Combined, these applications clearly have major implications for
cloud physics, hydrology, weather modification and communications.
4
This study, therefore, was undertaken to examine further the use
of the
method for rainfall rate measurement and other related
applications.
It includes:
a review of relevant assumptions and
theory; three studies comparing radar with ground-based measurement of
rainfall; a successful demonstration of using the method to predict
specific attenuation and reflectivity at attenuating microwave wave­
lengths; and simulations which show that the method has potential for
rainfall scavenging of aerosols and for determining vertical air
motions.
1.2
Previous Related Studies
The relationships between the reflectivity and attenuation of
microwaves and rainfall rate were first examined by Ryde (1941, 19A6)
who was mainly concerned with precipitation as unwanted clutter as
noted by Atlas et al. (198A).
Wexler and Swingle (19A7), Marshall et
al. (1947) and Atlas (1947, 1948) were the first to interpret Ryde's
work for radar meteorological applications, and Marshall and Palmer
(1948) proposed an exponential size distribution for raindrops to
obtain an empirical relationship between the reflectivity factor (Z)
and rainfall rate (R)
Z = ARb = 200 R 1,6
6 ~3
"1
where Z is in mm m
and R is in mm h .
(1-1)
To arrive at this, they
assumed N q in the exponential distribution
N(D) = N q exp -(AD) (mm *m ^)
(1-2)
to have a specific value independent of rainfall (Nq = 8x10
3
mm
“1 -3
m ).
Marshall et al. (1947) and Austin and Williams (1951) conducted the
first experiments on the relation between echo intensity and rain
rate.
Austin and Richardson (1952) and Blanchard (1953) reported the
first signs that there was not a universal relationship between Z and
R.
Atlas et al. (1953) were the first to demonstrate quantitatively
the extent to which particle shape, orientation, phase state, and the
polarization and angle of incidence of the transmitted wave affects
the reflectivity of precipitation as indicated by Rogers (198A).
And,
by the mid-1950s, strong evidence had already been gathered (Twomey,
1953) that a satisfactory estimate of R cannot be determined from Z
alone through a simple Z-R relationship.
Nevertheless, extensive
investigations to obtain empirical Z-R relationships continued where
the values of the parameters A and b varied widely according to rain
type, geographical location, space and time.
The result was that by
1970, Battan (1973) reported 69 Z-R relations for different locations
around the world.
A physical basis for this multitude of relations
was given by Atlas and Chmela (1957) in a rain-parameter diagram
involving the four basic parameters Z, R, M (liquid water content) and
D q (median volume diameter).
More recently, Ulbrich and Atlas (1978)
extended the same work by adding N q and
(optical extinction).
They
showed the extent of the errors which is possible in estimating any of
these parameters using Z alone and recognized the fact that remote
measurements of R required at least two independent parameters.
indicated that the region spanned by the Z-R relations listed by
They
6
Battan extends over three orders of magnitude for N q and more than one
order of magnitude for R.
The Z ^ method, introduced by Seliga and Bringi, promises to
improve the estimation of precipitation parameters to a greater
accuracy.
Simulations derived from disdrometer measurement, by
Ulbrich and Atlas (1984) showed that assuming a gamma DSD model with
m = 2 reduced the bias in R, M and D q estimates when compared with
results derived using the exponential model of Eq. (1-1).
Similar
simulations by Seliga et al. (1986) indicated that the technique
promises to produce a normalized standard error of better than 13%
over the range R from 0.1 to 260 mm h
A number of field tests of the
method have been performed
producing very encouraging results as noted in a review article by
Ulbrich (1986).
First field experiments by Seliga and Bringi (1978)
and Seliga et al. (1979) reported that D q and
were in their
expected ranges of 0.5-4 mm and 0-4 dB, respectively.
Seliga et al.
(1980a) and Bringi et al. (1982) constructed a time profile of R from
ground-based disdrometer measurements and, after comparing them with
the radar estimated values, found good qualitative agreement for a
1978 storm near Chicago, Illinois.
Al-Khatib et al. (1979) and Seliga
et al. (1980b, 1981) performed radar-raingage comparisons over a dense
network of raingages and reported an improvement in estimation of R of
around a factor of two for the Z^^ method over Z-R relationships.
Clarke et al. (1983) also reported good agreement for this method when
comparing radar and raingage derived R.
Direskeneli et al. (1983)
showed that Z-- derived R and Dn tracked the spatial and
temporal variability of disdrometer-derived values very well.
Seliga
et al. (1984) employed a transformation technique to account for
changes in DSD with altitude to demonstrate the agreement between
radar and disdrometer derived (Z^, Z ^ ) .
Direskeneli et al. (1986) in
a preliminary report, used a Cartesian interpolation technique to
transform the radar volume
into
constant altitude plan position
indicators (CAPPI's) and compared the radar and raingage-derived R's
by accounting for the wind transport and fall time of raindrops in a
1984 Colorado storm with high R.
They reported improvements of 14%
and 23% in normalized standard error with respect to two other Z-R
relationships (see Section 4.3).
The above experimental studies outline research by the Ohio
State/Penn State radar meteorology group for quantitatively estimating
rainfall parameters by the Z ^ method.
Experiments have also been
carried out by the Rutherford Appleton Laboratory employing the
Chilbolton radar in Southern England (Hall et al., 1980).
comparison between
A
and disdrometer-derived D q values led Goddard
et al. (1982) to propose a modified relationship between the axial
ratio and the equivalent diameter of the raindrops.
Goddard and
Cherry (1984a) obtained radar-derived rainfall rates from a sample
volume 200 m above a disdrometer without accounting for drop size
sorting or wind transport of raindrops.
They suggested the need for a
DSD other than exponential to account for a systematic overestimation
of R of 33%.
Subsequently, Goddard and Cherry (1984b) employed a
gamma model of m = 5 and obtained a standard deviation of 33% between
the radar- and raingage-derived R.
Cherry et al. (1984) reported
general agreement between radar and airborne disdrometer measurements
8
of rainfall parameters; they attributed differences in radar and
aircraft deduced
(Nq,
Dq)
of the DSD on the method of measuring the
aircraft spectra which placed greater emphasis on the large diameter
drops.
Although the focus of this work is on rainfall rate, water
content and drop size estimation, several other important topics are
also included.
They are:
- application of
to predict and compare C-band reflectivity
profiles from S-band measurements by estimating C-band
attenuation and reflectivity factors from S-band (Z^,
measurements (Chapter 5);
- simulations on how to estimate aerosol scavenging rates from
(Zjj,
measurements (Chapter 6);
- the potential role of Zqjj as an estimator for reflectivityweighted fall velocity (Chapter 6).
Previous related work in
these areas is considered within the context of these chapters.
1.3
Research Objectives and Approach
This work deals primarily with the applications of the
differential reflectivity radar technique to estimating rainfall
parameters and predicting microwave attenuation.
Case studies,
derived from the 1982 Ohio State Precipitation Experiment (OSPE) in
Central Illinois and the 1983 and 1984 MAY POLarization Experiment
(MAYPOLE) field programs provide the data for the research.
Rainfall
rate results also include comparisons with estimates from single
parameter Z-R methods.
In order to make observation volumes of radar
and ground measurements compatible, careful attention was paid to
spatial and temporal factors due to the large separation and
resolution differences between these systems.
Potential applications
of Z^R in two new areas, namely scavenging by rain washout of aerosols
and fall velocity of raindrops are also examined.
The results of the
study are organized as follows:
Chapter 2--Differential Reflectivity Radar Method and
Experimental Factors.
The theory of the Z^R method is outlined with
special emphasis on how the radar measurements can be used to
determine rainfall parameters.
Major assumptions of the technique and
their physical basis are discussed.
The specifics of the experimental
facilities from which the dual polarization radar data and ground
based measurements were obtained are outlined as well as a review of
relevant statistical measures.
Chapter 3— Disdrometer Based Rainfall Simulations.
The findings
of the simulations by Seliga, Aydin and Direskeneli (1986) are
reviewed to establish the relationships between the radar observables
(Zjj.Zp^) and the rainfall parameters R, M and D q .
The estimates of
the errors in these simulations are described and results are compared
to other estimation methods.
Chapter 4--Differential Reflectivity Radar Measurements of
Rainfall.
The major emphasis in this chapter is to demonstrate that
the Zq R method results in improved estimation of rainfall parameters.
Results obtained from case studies from three different field programs
are presented, comparing radar and ground-based measurements.
These
studies differ experimentally and, consequently, require special
10
techniques to account for volume sampling differences, drop size
sorting and wind transport.
Chapter 5— Predictions and Comparisons of C-Band Reflectivity
Profiles from S-Band Measurements.
Simulations to estimate C-band
reflectivity factors and attenuation using S-band (Z„
described.
» ZDR) are
These results are employed to predict successfully the
apparent reflectivity factor profiles of a C-band radar employing the
S-band radar measurements made at a different site during the MAYPOLE
*84 field experiment.
Chapter 6— Other Applications.
Potential use of Z ^ measurements
in two other applications are discussed.
These are the determination
of the scavenging rates of aerosols by precipitation and a proposed
scheme to recover the vertical air motion component of the
reflectivity weighted Doppler velocities from Z ^ radar observations.
Chapter 7--Conclusions and Recommendations.
research are summarized in this chapter.
Results of the
Recommendations for possible
improvements in future studies and a brief discussion of other
applications based on the (Z„» Zq ^) radar measurements conclude the
study.
CHAPTER 2
DIFFERENTIAL REFLECTIVITY RADAR METHOD AND EXPERIMENTAL FACTORS
The purpose of this chapter is to outline the basic concepts in
radar remote sensing, focusing on the differential reflectivity radar
method and its applications for estimating rainfall parameters and
microwave attenuation.
A review of the relevant radar observables as
well as a discussion of the underlying physical basis for these are
presented.
The experimental facilities that supplied the radar and
ground truth data for the studies given in Chapters 4-6 are
described.
Possible sources of error that can affect comparisons of
the radar estimated parameters with ground-based measurements are also
discussed.
2.1
2.1.1
Differential Reflectivity Radar Method
Radar Observables
In this research, radar meterological measurements are obtained
by illuminating a medium containing randomly positioned hydrometeors
with a finite length electromagnetic pulse and sampling backscattered
energy at fixed time intervals or gates (Battan, 1973; Doviak and
Zrnic, 1984).
The two incoherent radar parameters employed in dual
polarization measurements are the effective reflectivity factors at
11
12
horizontal (Zjj) and vertical (Zy) polarizations (Seliga and Bringi,
1976):
^max
~
V ^
TT |k|
where A(mm):
|
0„ ,,(D)N(D)dD
H ’V
(mm6 m~3)
(2-1)
radar wavelength (mm)
2
CM
6
-
1
+
2
m
IkI2
I
2
= 0.93 ;
refractivity factor
at S-band C-band frequencies with m being the complex index of
refraction for water
a„ ,,(D):
H, V
bacxscattering cross-sections at horizontal and
2
vertical polarizations (mm )
D:
Zjj
y
equivolume diameter (mm)
N(D):
raindrop size distribution (mm
D
maximum drop size,
r
max
:
-1
m
-3
)
is related to the total backscattered power P from this ensemble of
distributed targets through
C Iv I2
? =
Zh,V
(W)
(2_2)
where C is a constant which depends on the radar characteristics.
When Rayleigh scattering applies, the backscattering cross-section of
an individual, spherical scatterer is
1)6
c™"2)
and the reflectivity factor for an ensemble of raindrops becomes
C2"3)
13
Z =
I
max
A
-1
D N(D)dD
(mm
m
-3
(2-4)
)
0
Differential reflectivity ( Z ^ ) can be defined as the difference (in
dB) between
and
Zy
(2-5)
The differential reflectivity radar method for estimating
rainfall parameters utilizes the deformation of raindrops into nearly
oblate spheroidal shapes as they fall through the atmosphere.
The
vertically and horizontally polarized backscattering cross-sections of
raindrops differ considerably for raindrops of sizes larger than 0.5
mm, and this difference increases as the raindrop size increases
because of the axial ratio dependence of the oblate drops with size
(equivalent diameter).
For computing Eq. (2-1), the backscattering cross-sections
a„ ,,(D) may be determined using Waterman's (1965) (1969) T-matrix
method and the axial ratios (r) given by Green (1975).
The latter
approximation, relating r to D, agrees well with the theoretical and
experimental results of Pruppacher and Pitter (1971) and has the
analytical form
(mm)
where
pw = 10
a -
3
kg m
-3
7.275 x 10
g = 9.8 m s ^
-2
(water density)
-2
Jm
(surface tension)
(2-6)
14
r =
a/b;
axial ratio where a is the semi-minor and b is the
semi-major axis of an oblate spheroidal drop.
Fig. 2.1 illustrates the geometry of the oblate' spheroidal raindrops as
well as the horizontally and vertically polarized electric field
incident on it.
Since r depends on D, a radar measurement based on r
can in turn yield an estimate of the size of the raindrops.
In practice, the maximum drop size D
max
is assumed to be 8 mm
which is based on experimental studies of the critical sizes above
which breakup of raindrops occursduring their steady state fall
through the atmosphere (Pruppacher and Klett, 1978).
2.1.2
Rainfall Parameters
The rainfall parameters to be estimated using radar observables
are rainfall rate (R), liquid water content (M) and median volume
diameter
( D q .).
R and M are given by
D
max
D v (D)N(D)dD
(mm h
)
(2-7)
0
max
(2-8)
D N(D)dD
0
where vfc(D) is the terminal velocity of the raindrops (Gunn and
Kinzer, 1949).
A good approximation to v
is given by Atlas et al.
(1973) as
vfc(D) = 9.65 - 10.3 e"°'6D (m s"1)
(2-9)
15
Minor Axis
Major Axis
(Vertical Polarization
E,,JHorizontal Polarization)
~HO
Incident Fields
Figure 2. 1* Raindrop distortion model:
an oblate spheroid is the body
of revolution formed when an ellipse is rotated about its
minor axis.
16
D q is the diameter such that half the water content is contained in
drops with diameters smaller than D q and can be obtained from,
fD°
3
1
D N(D)dD - j
fDmax
0
2.1.3
3
D N(D)dD
(2-10)
0
Specific Attenuation
Specific attenuation for propagation of radio waves through the
rainfall within the radar volume is defined as
D
2
f max
Ajj^v = A.343 x 10
i
(dB km"1)
aER v (D)N(D)dD
(2-11)
0
where
O otl
Uai>V
: extinction cross-sections at horizontal and vertical
polarizations.
2.1.4
Drop Size Distribution
Many drop size distributions (DSD) within the radar volume have
been generally assumed to have an exponential form,
N(D) = Nn exp(-AD) (0 < D <
U
—
—
_1
where ^ ( m m
Dmax
)
(mm"1 m'3)
(2-12)
_^
m
) and A(mm
) are the parameters of N(D).
This form
of the DSD was suggested by Marshall-Palmer (1948), based on their
analysis of the drop size spectra obtained by Laws and Parsons (1943).
Once DSD is determined, the other rainfall parameters R, M and D q can
be obtained from Eqs. (2-7), (2-8) and (2-10).
Experimental results
indicate that Eq. (2-12) is a good approximation when sufficient
spatial and temporal averaging is performed on the drop size spectra
17
(Ulbrich, 1983).
More recent studies also indicate that the N q
parameter of this model is
different times
subject to large and sudden changes during
within the same stormfor similar rainfall rates
(Waldvogel, 1974; Donnadieu, 1982).
Since these changes in N q are
independent of A» it is necessary to specify both parameters (Nq , A)
of the DSD in order to account for rainfall variations during and
within a storm.
This in turn implies the necessity for using at least
two radar observables to obtain an estimate of these parameters.
Sekhon and
Srivastava (1970) have shown that, for D
/Drt> 2.5,
max 0 —
*
the approximation A ® 3.672/Dq is within 2% of its limiting value.
This indicates that the exponential model DSD is insensitive to
changes in D
for large D
/Dft.
°
max
°
max 0
Another improvement in DSD modeling can be achieved by assuming a
gamma model DSD (Ulbrich and Atlas, 1984) as
N(D) = N Dm exp (-AD)
m
0 < D < D
— — max
(2-13)
In this model, N^ is used rather than the notation Nq as proposed by
Ulbrich and Atlas, since N
(mm
-1
m
-3
) as for Nq.
m
has units of (mm
" 1 “ in
m
“3
) rather than
Note that, when m = 0, N(D) reduces to the
exponential form of Eq. (2-12) so the exponential model DSD is a
special case of the gamma model DSD.
that, for D
max
Ulbrich and Atlas also indicated
/Dn > 2.5, A converges to A = (3.67 + m)/Dn for m > -3.
0
°
0
Thus, the gamma model DSD is relatively insensitive to changes in D^ y
for large D
/Dn .
*
max 0
Simulations of Ulbrich and Atlas (1984) and Seliga et al. (1986)
have shown that estimations based on the exponential model tend to
18
overestimate (R, M) and underestimate
Dq .
A gamma model DSD with
m * 2 greatly reduces the bias in these estimates (see Chapter 3).
Simi-larly, Goddard and Cherry (1984b) found that a gamma model of
m ■ 5 reduced their bias and standard deviation of radar-raingage
comparisons.
In this research, the empirical relationships to obtain
R, M and D q from radar observables do not assume any a priori
analytical form for the DSD, although computations of the same
rainfall parameters based on a gamma model DSD with m « 2 are also
performed for the comparisons.
2.1.5
Single Parameter Estimation of Rainfall Parameters
While suggesting the exponential form of Eq. (2-12), as noted
earlier, Marshall-Palmer (M-P) assumed N q as a constant and A = A(R).
Based
on
these
assumptions, N(D) and all the integral quantities
defined in Sections 2.1.2 and 2.1.3 involving N(D) depend only on a
single DSD parameter and can be estimated from any one of the other
defined quantities.
form Eq. (1-1) [Z(mm
For R, they developed a Z-R relationship of the
m
) * 200 R ' ].
Other investigators also used
the empirical form,
Z = ARk
(mm^ m ^)
(2-14)
to estimate R from Z, but derived or assumed different values for A
and b depending on the precipitation type and location.
Battan (1973)
listed 69 Z-R relationships from around the world and selected the
following as being the most typical for classification according to
storm type:
- stratiform rain:
Marshall-Palmer
(A = 200, b = 1.6)
19
- orographic rain:
Blanchard (1953) (A = 31, b = 1.71)
- thunderstorm rain:
Jones (1956)
(A = 486, b ■ 1.37).
These typical and other Z-R relationships are also employed in
this study in the simulations of Chapter 3 and in the experimental
comparisons of Chapter 4.
Power law expressions have also been
extended to Z-M and A-R and A-Z relationships to estimate M and A in
the microwave region (Douglas, 1964; Wexler and Atlas, 1963;
McCormick, 1970).
To demonstrate the physical basis for the wide range of
variations of the empirical Z-R relationship parameters, rain
parameter diagrams were introduced by Atlas and Chmela (1957) and
Ulbrich and Atlas (1978) for related radar and rainfall parameters.
Figure 2.2 shows the possible variations in Z, R, N q and D q for
different Z-R relationships in a rain parameter diagram along with a
group of radar-derived data points.
The wide range of variations of
these parameters illustrates the need for estimation methods based on
at least two observables to account for the two parameter DSD's.
Seliga and Bringi (1976) introduced Zq ^ in addition to
second radar observable to provide this additional information.
2.1.6
Differential Reflectivity Radar Technique
The Zqjj technique of estimating rainfall parameters derives from
the following three assumptions:
1.
Falling raindrops are not spherical, but assume an
approximately oblate spheroidal shape as their shapes are modified by
surface tension, gravitational and aerodynamic forces.
Also, their
oblateness increases with increasing drop size (Section 2.1.1).
Radar
Reflectivity
Factor, Z H(dBz)
20
10°
10'
Rainfall Rate ( m m / h r )
Figure 2.2.
Rain parameter diagram for exponential drop size
distribution model. Radar reflectivity factor
versus rainfall rate with isopleths of median
volume diameter Do and parameter No. Data points
represent estimates inferred from radar measure­
ments (Seliga et al., 1981), and MP signifies the
Marshall-Palmer Z-R relationship.
21
Therefore, their equilibrium axial ratios are a unique function of
drop size.
Theoretical calculations of Pruppacher and Pitter (1971)
and wind tunnel experiments of Pruppacher and Beard (1970) support
this argument.
However, Jameson and Beard (1982) and Jameson (1983)
found the relationship between the axial ratios and D to be different
from their equilibrium values after analyzing ground-based
photographic measurements of raindrops (Jones, 1959) and attributed
the result to oscillations of raindrops due to the energy created by
collisions.
Johnson and Beard (1984) and Rasmussen et al. (1984)
indicated that an existing ice core in melting raindrops would cause
greater dampening of these oscillations and result in equilibrium
shapes dominating their description.
In situ aircraft measurements by
Cooper et al. (1983) and Chandrasekar et al. (1984) indicated good
agreement between the predicted and experimental equilibrium values
of the axial ratios.
Thus, there is strong evidence to support the
hypothesis that the shapes of raindrops is well-approximated by their
equilibrium axial ratios given by Pruppacher and Pitter (1971) and
empirically related to drop size by Green's (1975) formula (Eq. 2-6).
2.
The symmetry axes of the falling raindrops are mutually
aligned along the vertical direction.
For raindrops deviating from
the symmetry axes, the canting effects can be analyzed in two
categories:
raindrop canting in the plane of incidence, and perpen­
dicular to the plane of incidence.
Fig. 2.3 demonstrates these
propagation conditions in terms of the canting angle a.
The
corresponding effects of radar elevation angles different than 0° are
shown in Fig. 2.4(a), taken from Al-Khatib et al. (1979) who used the
22
S y m m e t r y Axis
(a)
Figure 2.3.
Raindrop canting angle (ft), (a) in the plane of
incidence with an angle of incidence (6) .and
(b) perpendicular to the plane of incidence.
23
scattering formulation of Evans et al. (1978), to compute the results.
For canting angles less than 10° Z^R is underestimated by only 5-6%.
Available measurements of raindrop canting angles indicate that mean
10°.
a
Furthermore, supporting the hypothesis that hydrometeors fall
with preferred orientation (McCormick and Handry, 1976).
Beard and
Jameson (1983), in their theoretical investigations, obtained a mean
1.5° due to wind shear and an rms a <. A
general, canting effects on
due to turbulence.
Thus, in
measurements should be negligible for
most applications.
3.
Raindrop size distributions are dominated by two independent
parameters.
Previous simulated and experimental results outlined in
Chapter 1 and the results of this research (see Chapter A) support
this argument.
The assumed gamma model of Eq. (2-13) employs three
parameters, but Ulbrich and Atlas (198A) indicated a general
correlation between N
m
and m which would reduce that model to a
two-parameter one.
Based on these assumptions, the polarimetric Z^R method
introduces a second radar observable in addition to
DSD of raindrops.
to estimate the
The form of the relationships between parameters
are given in Eqs. (3-5) and (3-6); these were computed from
disdrometer measurements without any a priori assumptions about the
analytical form of the DSD.
Eqs. (3-7) through (3-10) are similar
relations based on the exponential and gamma model assumptions for
DSD.
<.
ZOR(a)DB
a =5
a-0
a =5
CD
O
a
a iO'
oc
Q
N
a =l5
(a)
Maximum ZOR (DB)
(b)
Maximum ZDR (DB)
Figure 2.4. Variation in
with canting angle a (a) in the plane of incidence, and (b) perpendicular
to the plane of incidence. Zero canting angle (a = 0) results in maximum Zjjr where Zd r
is the differential reflectivity (Al-Khatib et al., 1979).
ISJ
2.1.7
Statistical Considerations
is expected to have values between 0.5-4 dB in natural
rainfall.
As seen from Eqs. (3-5) and (3-6), for accurate rainfall
parameter estimation
has to be measured with a standard error of
less than around 0.2 dB.
This accuracy is possible, since a high
degree of correlation exists between
and Zy if rapidly switching H
and V polarizations on a pulse-to-pulse basis are employed by the
radar.
For this research, Z ^ was measured using polarization agile
radars (CP-2 and CHILL) transmitting alternate highly-correlated H and
V polarized pulses.
A single channel receiver was used for co-polar
reception, thereby minimizing effects due to differential drift which
might occur with different receivers.
The major source of error in Z ^
is due to the nature of the
narrow band noise signal associated with randomly moving hydrometeors
in the scattering volume and their subsequent locations in space over
time.
For optimum estimation, three estimators of Z ^ have been
defined (Bringi and Seliga, 1980).
These are
1 - Square-Law Estimator
-
-
m
n
- Jl ^
( 2 - 1 5 )
m i=i
^
where A ^ y^, i = l,m for a pairwise set of independent samples.
2 - Log-Ratio Estimator
26
3.
Ratio Estimator .
.
m
Aj,. 2
** ■ - Jx
(2-17)
The results of Doviak and Zrnic (1984) indicate that, although
both the square-law and the log-ratio estimators are unbiased, the
square-law estimator results in slightly lower standard errors.
example, for a cross-correlation of p = 0.97 between
For
and Zy, Z ^
can be measured with standard errors in the range 0.1-0.2 dB at a
single gate using 40-60 pairs of independent correlated samples.
Their results are in agreement with those of Bringi and Seliga which
are shown in Fig. 2.5 for different p and
m.
A square-law estimator
is used by the CHILL radar while the CP-2 radar employs a log-ratio
estimator which produces a slightly greater error.
When the sampling
rates used by these radars in the experiments described in Chapters 4
and 5 are combined with additional spatial averaging, statistical
variations in Z ^
(and Zjj) are predicted to be of little consequence
to the results.
Another possibly important source of error for Z ^
absolute (and relative) calibration of (Z^, Zy).
in Zpp is minimized by calibrating Z ^
is the
The relative error
in misty rain or by pointing
the radar along the zenith (resulting in Zp^ ;0).
CP-2 Z^^
calibrations additionally used solar measurements.
Sources of error
for Zy include statistical errors similar to those described above for
Zp£, errors due to quantization and uncertainties in the radar
constant.
A description of these error sources were outlined by
Al-Khatib et al. (1979).
Specific estimates of these errors for the
27
Standard
D e v i a t i o n , dB
Square Law
20
40
Cross Correlation =0
.0.90
,0.92
,0.94
0 .9 6
0.98
100
80
60
Number of Sam ples, m
Figure 2.5. Standard deviation (dB) of the square law
estimator as a function of sample size m and
cross-correlation coefficient p (Bringi and
Seliga, 1980).
28
, Zpfl) measurements during the OSPE and MAYPOLE field experiments
are given in Chapter A.
2.2
Experimental Facilities
2.2.1
Radars
The field experiments outlined in Chapters A and 5 employed the
S-band (CHILL and CP-2) and C-band (CP-A) radar systems.
In this
section, the operation of these radars is briefly described.
Complete
specifications of these radar systems are given in the Appendix.
2.2.1.1
CHILL Radar (OSPE)
The 10.9 cm CHILL radar, operated by the Illinois State Water
Survey (ISWS), was employed during the Ohio State Precipitation
Experiment (OSPE) in 1982.
It operated in a fast polarization
switching mode on a pulse-to-pulse basis as required to reduce the
standard error in
DK
estimation.
The polarization transmission and
reception control on the CHILL system were made possible through
electronic control of a high-power switchable waveguide circulator
(Seliga and Mueller, 1982).
This circulator had four ports with
energy propagating in either a clockwise (CW) or counterclockwise
(CCW) direction depending on the switching state of the circulator.
Circulator switching time was less than 5 ys and resulted in loss of
data for targets within 750 m of the radar which was not important for
this study.
29
2.2.1.2
CP-2 and CP-A Radars (MAYPOLE »83. *84)
The CP-2 and CP-4 radar systems with wavelengths of 10.7 cm and
5.A5 cm, respectively, were operated by the National Center for
Atmospheric Research (NCAR) during the 1983 and 198A MAY POLarization
Experiments (MAYPOLE).
The CP-2 radar, similar to the CHILL, employed
a high power, pulse-to-pulse switching between linear, orthogonal,
horizontal and vertical polarizations.
The switch- as vith the CHILL
radar, was provided by the Ohio State research group for implementa­
tion by NCAR or the CP-2 radar.
2.2.1.3
Antenna Performance
One of the major factors for both the CHILL and CP-2 radars is
the influence of the antenna illumination function characteristics on
Zpjj measurements.
Herzegh and Carbone (198A) examined these for CP-2
and reported that, although a very good symmetry for the illumination
patterns at orthogonal polarizations was obtained in the main lobes,
the top and bottom sidelobes are stronger in horizontal with respect
to vertical polarization and left and right sidelobes are stronger at
vertical with respect to horizontal polarization, respectively.
Their
simulations of this mismatch of illumination patterns resulted in a
positive bias for
in regions of vertical reflectivity gradients
and a negative bias in regions of horizontal gradients.
These effects
are also present with the CHILL radar, since the antenna and feeds are
of identical design (Johnson, 198A).
exercised in using
Consequently, care must be
measurements in regions of strong reflectivity
gradients with these radars.
Fortunately, this problem does not
appear to be important in the case studies considered in this study.
30
2.2.2
Ground-Based Facilities
2.2.2.1
Disdrometer
The disdrometer which was used in the simulations and
experimental studies was an electromechanical instrument developed by
Joss and Waldvogel (1967).
It sorts drops into 20 size ranges, the
smallest range being 0.3 < D(mm) < 0.4 and the largest being D(mm) >
2
5; its sampling cross-section area is 50 cm .
N(D) averaged over
30 s is derived by,
N
( 2- is )
' ^ AD±
> « V = A.........
At v^(D'i)
where
N(D^) : the size distribution of the i'th range
: number of drops counted during the time interval At in
the i'th range
At : averaging interval (30 s)
v t^i^
: term*na^ velocity of the drops in the i'th range
: size interval of the i'th range.
The discrete relationships for R, M and D q estimation from these
are given by Seliga et al. (1986), and additional information on the
operational characteristics were reported by Joss and Waldvogel (1970)
and Waldvogel (1974).
The estimated fractional deviations (FSD) for
disdrometer-derived values of (H, Zjj,
are outlined in Table 3.1.
31
2.2.2.2
Portable Automated Mesonet. (PAM)
The PAM system was operated by NCAR to provide surface mesoscale
data during MAYPOLE '83 and '84.
data with an accuracy of
of meteorological data.
It provided rainfall accumulation
±0.25 mm and 19 other surface measurements
The data were also available in real time
using the GOES satellite that linked the remote stations to a base
station in Boulder, Colorado, which collected and archived the data
and generated graphic displays for system control and scientific
analysis.
A detailed description of the PAM system is given by Brock
et al. (1986).
CHAPTER 3
DISDROMETER BASED RAINFALL SIMULATIONS
In order to use differential reflectivity ( Z ^ ) as an additional
radar parameter to obtain improved estimates of the rainfall
parameters, rainfall rate (R), liquid water content (M) and median
volume diameter (Dq ), relationships between the radar observables
(Z„, Z-r,) and these parameters are required.
n
UK
These relationships were
derived by Seliga, Aydin and Direskeneli (1986) from numerical simula­
tions linking rainfall drop size distributions (DSD) to the rainfall
parameters and'radar observables.
This chapter reviews these findings
in detail, since they establish the expected lower bounds on errors of
the radar estimates presented in Chapter 4 for three case studies
which compare radar estimates of R with ground-based raingage and
disdrometer measurements.
3.1
Disdrometer Measurements
The DSD's used by Seliga et al. (1986) were obtained during an
intense rainfall event that occurred on 6 October 1982 in Central
Illinois during the Ohio State Precipitation Experiment (OSPE).
plots of R, M and D q for this event are shown in Fig. 3.1.
continuous plots at 30-s
Time
The
time intervals represent 2 min running
averages of the disdrometer data.
This averaging was used to obtain a
large enough number of drops per DSD sample to reduce the variance in
32
0
M (gm '3 )
-1
o'
0
o
-2
0
0
Content,
0
Wat er
Rai nf a l l Rat e,
R ( m m h " 1)
0
-3
O -1
I0
0
20
40
60
80
Tim e
Figure 3.1(a).
I00
I20
I40
I60
I80
(min)
Time records of R and M during the 6 October 1982 rainfall event in central Illinois.
Solid lines are actual disdrometer measurements representing 2 min running average
of 30 s recordings. Crosses are the simulated radar estimates of R and M computed
for Eq. (3-5) using disdrometer-derived (Zr , Zr r ). Zero time indicates values
averaged over 1513:30-1515:30. R is the rainfall rate, M water content, Zr
reflectivity factor and Zr r differential reflectivity.
u>
u>
Do (mm)
Median Volume Diameter,
3.5
3.0
2.5
2.0
0.5
20
40
60
80
100
120
140
160
180
Time (min)
Figure 3.1(b).
Time record of D q during the 6 October 1982 rainfall event in central Illinois. Solid
lines are actual disdrometer measurements representing 2 min running averages of 30 s
recordings. Crosses are simulated radar estimates of D q computed from Eq. (3-15)
using the disdrometer-derived Z ^ .
Dq is the median volume diameter and ZpR differ­
ential reflectivity.
u>
■S'
35
the derived radar and rainfall parameters to acceptable levels.
Zero
time in these plots corresponds to the measurements averaged over the
period 1513:30 to 1515:30.
A
deviations (FSD) of
^
The estimated fractional standard
A
a
A
an(* a Z D R ^ D R at ^ =
an(*
1,11,1
h ^ for these DSD sampling conditions were computed, based on the
approach of Joss and Waldvogel (1969) and Gertzman and Atlas (1977)
and are given in Table 3.1.
3.2
3.2.1
Relationships between Rainfall Parameters and Radar Observables
Rainfall Rate and Water Content
For two-parameter DSD models such as the truncated exponential or
gamma, the Z ^ technique can be employed to estimate R and M from
(Zr » Zjjr) measurements, since R/Z^ and M/Z jj are unique functions of
Zp^ in these models (Chapter 2).
When the variation of the DSD
parameters such as the order of the gamma model (m) or the maximum
drop size C®max) are insignificant.
To determine the applicability of
the aforementioned ratio relationships with Z^^ under natural rainfall
conditions, Seliga et al. (1986) used simulations derived from the
wide ranging, highly variable Illinois rainfall event to examine and
determine the empirical dependence of R/Z^ and M / o n
Z^.
These
results are plotted in Figs. 3.2 and 3.3 for R/Zg and M/Z jj,
respectively.
Corresponding plots versus D q , instead of Z^^, are
given in Figs. 3.4 and 3.5. The strong correlations between the
variables on these graphs suggest power law relationships of the form:
36
Table 3.1.
Estimated fractional standard deviations (FSD) of
rainfall rate (R), horizontal reflectivity factor (Zjj)
and differential reflectivity (Zd r ) in thunderstorms
at R = 1, 10 and 100 mm h“l. Here Zjj is in mm^m--* and
Zd r = Zji/Zy where ZV is the vertical reflectivity factor.
Rainfall Rate (mm h“l)
FSD
8 r /r
%
r /Zd r
1
10
100
0.15
0.09
0.06
0.50
0.24
0.12
0.06
0.06
0.06
R ( m m h 'V Z M t m n r ^ m 3 )
1-2
i-«
I0'1
Figure 3.2.
Scatter plot of R/Zjj versus ZpR
for the data set shown in Fig.
3.1(a). The fitted curve
corresponds to Eq. (3-5). R is
the rainfall rate, Zp reflectivity
factor and Zp^ differential reflec­
tivity.
Figure 3.3.
Scatter plot of M/ZH versus ZpR for
the data set shown in Fig. 3.1(a).
The fitted curve corresponds to
Eq. (3-6). M is the water content,
Zfl reflectivity factor and Zpjj
differential reflectivity.
io-;
ICT
10
'6
*E
E
I0':
N
Z
N
1i
0
E
o»
10-’
10°
10*
10-’
Median Volume Diameter, C\,(mm)
Figure 3.4.
Scatter plot of R/Zg versus Do- The
fitted curve corresponds to the
2-section relationship given in
Table 3.3. R is the rainfall rate,
Z|i reflectivity factor and Do median
volume diameter.
Median Volume Diameter, (}, (mm)
Figure 3.5.
Scatter plot of M/Zh versus D q The fitted curve corresponds to
the 2-section relationship given
in Table 3.3. M is the water con­
tent, Zfl reflectivity factor and
D q median volume diameter.
0
39
R/ZH -
aR (ZD R )bR
(>1)
M/ZH ’
R/Z„ -
m/ zh
(>2)
cR (D0 )dR
(3-3)
= <« (Do)dM
(3' 4)
where the corresponding units are R(mm h
6 -3
Z^(mm m ) and ZpR (dB).
“1
”3
), M(g in ).
Tables 3.2 and 3.3 summarize the results of
regression analyses based on the standard method of linearizing the
relationships with logarithms to the base 10 (Yevjevich, 1972).
The
tables give the estimated value of the coefficients (a^, bR , c^, b^,
CR*
CM*
anc* ^ e i r
confidence limits for two cases, one for
the entire range of parameters and the other for two regions separated
by high and low values of ZpR and D q as indicated in the tables.
The
latter two-section piecewise linear approach is preferred since it
better accounts for the variations between the parameters than the
relationship derived over the entire range.
The resultant
relationships were assumed to apply for even higher values of Z^R and
D q than those indicated, since the regression analysis results (not
shown), obtained from the original 30-s disdrometer data with maximum
(Zq ^, D q ) values of (2.9 dB, 3.2 mm), produced nearly the same
empirical relationships.
An interesting observation is that the
dependence of the ratios on D q exhibits more scatter than their
corresponding Z^R
dependence.
This shows that Zq R that Zq R , when used
with Z„, is a better estimator of R than even an a -priori knowledge of
V
Table 3.2.
(R/ZR )- and (M/Zh )-Zd r relationships derived from regression analyses. The estimated con­
stants for these power law relationships and the corresponding 95% confidence limits are
given. Correlation coefficients (p) for "log (R/Zr ) and log ZpR ] and [log (M/Zr) and log
ZDR] are also listed. R is the rainfall rate, M water content, ZR reflectivity factor
and ZpR differential reflectivity.
R/ZH
aRZDR
l
A
A
/\
SR
aRl
A
P
PS
D a t a Range (dB)
"
bR2
0.2 < ZDR < 2.6
1.51 • 10-3
1.49
10-3
1.52 • 10-3
-1.55
-1.52
-1.57
-0.99
0.2 < ZDR < 0 . 7
1.95 • 10-3
1.84 • 10-3
2.07 • 10-3
-1.04
-0.94
-1.14
-0.95
0.7 < ZpR < 2.6
1.59 • 10-3
1.57 • 10-3
1.61 • 10-3
-1.67
-1.64
-1.70
-0.99
bM2
P
•
aR2
bR
bM
M/ZH = aMZDR
A
aM
A
aMl
aM2
A
A
bM
bMl
0.2 < ZgR < 2.6
7.38 • 10“ 5
7.26 • 10-5
7.49 • 10-5
-1.92
-1.88
-1.95
-0.99
0.2 < Zq R < 0.7
1.04 • 10~4
9.43 • 10-5
1.14 • lO-4
-1.29
-1.13
-1.44
-0.92
0.7 < Z^R < 2.6
7.81 • IQ”5
7.64 • IQ-5
7.98 • 10“5
-2.04
-2.00
-2.09
-0.98
o
Table 3.3.
(R/Zjj)- and (M/Zjj)-Dq relationships derived from regression analyses. The estimated
constants for these power law relationships and the corresponding 95% confidence limits
are given. Correlation coefficients (p) for [log (R/Zfl) and log Do! and [log (M/Zh ) and
log Do] are also listed. R is the rainfall rate, M water content, Do median volume
diameter and ZR reflectivity factor.
dR
r /z h
■
c rd o
A
/A
A
dR
dRl
dR2
P
-2.29
-2.23
-2.34
-0.98
4.85 • 10~3
-2.20
-2.00
-2.40
-0.91
5.86 • 10"3
-2.45
-2.36
-2.53
-0.96
A
/V
A
CR
CRl
CR2
0.7 < DQ < 3.0
4.80 • 10“3
4.62 • 10~3
5.00 • 10-3
0.7 < D0 < 2.1
4.54 • 10-3
4.26 • 10~3
2.1 < DQ < 3.0
5.47 • 10"3
5.11 • 10"3
Date Range (mm)
m
/z h -
cm d o
A
/\
A
A
CM
CM1
CM2
dM
dMl
dM2
P
0.7 < D q < 3.0
3.16 • 10"*
3.02 • 10"4
3.29 • 10"4
-2.86
-2.80
-2.92
-0.98
0.7 < D0 < 2.4
3.01 • 10“4
2.80 • 10-4
3.24 • 10“4
-2.82
-2.59
-3.04
-0.93
2.4 < D q < 3.0
3.54 • 10~4
3.29 • 10“4
3.80 • 10~4
-3.00
-2.90
-3.09
-0.97
42
To illustrate use of the empirical relationships, the estimated R
and M values in the Illinois rainfall event from the two-section
(Zjj, ZpR ) relationships.
R =
1.95 x lO^ZjjZjjn"1,04^
h"1),
0.2 <
ZDR < 0.7
R -
1.59 x 10"3 ZHZD R -1*67(mm h'1), 0.7 < ZDR < 2.6
M =
1.04 x 10"4 ZjjZpn"1 *29(g m~3),
0.2 <
^
M *
7.81 x 10_5 ZHZ])R"2,0A(g m'3),
0.7 <
ZDR < 2.6
are superimposed on the time plots of Figure 3.1.
(3-5)
< 0.7
(3-6)
For reference
purposes, these relationships may be compared with those derived by
Ulbrich and Atlas (1984), given by
R/Zjj =
1.93
x
10“3ZDR“1,5(mmh ^ / a n A a " 3)
(3-7)
M/Zjj =
1.28
x
10‘4ZDR"1,94(gm"3/mm6m"3 )
(3-8)
for the exponential model DSD, and
R/Zh =
1.70
x
10"3ZDR"1,5(mmh_1/mm6m"3)
(3-9)
M/Zjj =
9.90
x
10_5ZDR‘1,94(gm ‘3/mm6m'3)
(3-10)
for the gamma model DSD where Z^R is in dB.
3.2.2
Median Volume Diameter
One of the hypotheses of the Z^R method is that Z^R = ZjjR (Dq ) ar*d
is relatively independent of the other DSD parameters such as Dmay and
43
m.
To test this hypothesis, Seliga et al. (1986) examined Z ^ ( d B )
versus DQ(mm) as shown in Fig. 3.6 on both linear and logarithmic
scales.
The high correlation between Z q R and D q is evident;
therefore, by using linear and power law relationships, D q may be
estimated from Z^R and vice versa as originally proposed by Seliga and
Bringi (1976).
Regression analyses, applied to the Illinois DSD data
set, were performed to determine coefficients for both the linear and
logarithmic relationships, giving
(3-11)
ZDR(dB) " aLD0 (nm) + bL
ZDR(dB) = ap (D0(mm))bP
(3-12)
DQ(mm) - cLZQR (dB) + dL
(3-13)
D 0(mm) = cp(ZDR(dB))dP
(3-14)
where subscripts L and P indicate linear and power law relationships,
respectively.
In Eqs. (3-11) and (3-12), D q is the independent
parameter, and in Eqs. (3-13) and (3-14), Zq R is used as such.
The
results of these regression analyses are summarized in Table 3.4.
Different relationships for employing Z^R and D q as the independent
parameters are used rather than obtaining one and deriving the other,
since in linear regression analysis the coefficients which are
obtained using mean square estimation are different from the
corresponding reciprocal coefficients.
D q values, estimated from Z^R
using the form of Eq. (3-14) in Table 3.4,
D q = 1.68
Zdr° ’6A Cn®»)
(3-15)
2.5
-
i.
2.0
©
©
E
10°
o
Q
©
E
,2
3
c
g
T3
Median
Volume D iam eter,D 0 (mm)
3.0
©
2
0.5
10-'
(a)
Figure 3.6.
0.5
1.0
2.0
2.5
(b)
Scatter plots of D q versus
on (a) logarithmic and (b) linear scales obtained from the
data set shown in Fig. 3.1. The fitted curve corresponds to Eq. (3-15).
D q is the median
volume diameter and Zq r differential reflectivity.
30
Table 3.4.
ZpR(dB)-Do(nnn) relationships derived from regression analyses. The estimated constants for
these relationships and the corresponding 95% confidence limits are given. Correlation
coefficients (p) for the linear (Zpg and Do) and power law (log Z^r and log Do) relation­
ships are also listed. Results were obtained from data in the ranges 0.2 < Zj)p < 2.6 and
0.7 < Dq < 3.0. Zjjg is the differential reflectivity and D q median volume diameter.
Regression Parameters
ZDR * aLD0 + bL
ZDR *
A
A
aL
aLl
/\
aL2
0.902
0.934
D0 ■ C',ZDRdP
A
A
bL
bLl
bL2
0.966
-0.511
0.444
-0.577
P
0.96
A
A
A
A
aP
3P1
aP2
bp
bPl
bp2
P
0.505
0.469
1.43
1.38
1.48
0.95
0.487
/V
CL
D0 = CLZDR + dL
A
0.983
A
A
CL1
CL2
0.949
1.02
A
A
CP
CP1
/s
CP2
1.68
1.66
1.69
A
A
A
dL
dLl
dL2
P
0.617
0.715
0.96
0.666
A
A
dP
dPl
dP2
P
0.613
0.659
0.95
0.636
•p*
in
46
are superimposed in the time plot of D q in Fig. 3.1(b) to illustrate
the performance of the relationship.
Other relationships of the same
form were derived by Seliga et al. (1983),
Z ^ = 0.54 D0 1,39
(dB)
(3-16)
and by Ulbrich and Atlas (1984),
ZDR = 0.76
D q 1,55
(dB)
(3-17)
Zq R « 0.58 D0 1,55
(dB)
(3-18)
for the exponential and gamma model DSD's, respectively, and where
D q is in mm.
3.3
Error Computations
In order to quantify the comparisons between radar estimates of
rainfall parameters and ground-based measurements, a number of error
measures are available.
These include Sample Bias (SB), Normalized
Bias (NB), Normalized Standard Error of Difference (NSED), Average
Difference (AD) and Average Absolute Difference (AAD).
These are
defined as follows:
Sample Mean
X -
I
f
X
(3-19)
” i=l
Sample Bias
A
/\
SB = *R - *D
(.3-20)
47
Normalized Bias
NB * B/Xp
(3-21)
A
X^ - radar-derived parameters
A
Xp - disdrometer-derived parameters
Normalized Standard Error of Difference
N
N S E D - - - [ “ I (Xr - X
- B)2]1/2
Xp N i=l
i
i
(3-22)
Average Difference
ad
■ - jx
Average Absolute Difference
N
(3-24)
AAD
i'
J
1. X
NB and AD are closely related while NSED is considered a more useful
measure of the scatter of the estimators than AAD, since the effects
of the bias are removed with NSED while AAD incorporates the bias in
the measurements as an overall error figure.
Thus, AAD does not
significantly differ from AD for large bias values.
Ulbrich and Atlas
(1984), Goddard and Cherry (1984a), Seliga et al. (1986) and Ulbrich
(1986) used various combinations of these measures in their
simulations and radar-ground-based rainfall comparisons.
This work
emphasizes use of NB and NSED for the error analyses, since they are
relative measures commonly used in statistics.
48
3.3.1
Simulated Comparisons of Rainfall Parameters
The rainfall rates obtained by the
method using the
disdrometer-derived radar observables (Zg» ^q ^) are compared with the
actual rates in Fig. 3.7.
The scatter is very low throughout the
entire range of R indicating a very good theoretical applicability of
the two-section empirically-derived relationship of Eq. (3-5).
Liquid
water content estimates for the same rainfall event employing the
empirical relationship of Eq. (3-6) are shown in Fig. 3.8, also
demonstrating a very good agreement with the actual disdrometer values.
Fig. 3.9 shows the comparison of the disdrometer-derived median volume
diameter estimates with the actual measurements.
that
The figure indicates
is a good estimator of D q and can be used to determine this
important DSD parameter.
3.3.2
Choice of Relationships
Since a number of relationships for estimating rainfall
parameters from (Z„, Z ^ ) measurements are available, it is important
to establish the most appropriate ones for use in the case studies
presented in Chapter 4.
The intercomparisons given by Seliga et al.
(1986) provide an excellent criteria for this choice:
first, by
comparing the errors produced by various relationships in simulations
using the Illinois rainfall data of 6 October 1982, and second, by
observing the performance of the same relationships when applied to
two independent rainfall events in Boulder, Colorado, on June 8 and
13, 1983.
Tables 3.5, 3.6 and 3.7 present these findings for the 6
October 1982 event and include results for seven rainfall relation-
10°
o>
IO«
10-*
R tmrnh'1)
Figure 3.7.
Scatter plot of Re derived from the
empirical relationship given in
Eq. (3-6) versus disdrometer-derived
where R is the rainfall rate.
Figure 3.8.
Scatter plot of Me derived from the
empirical relationship given in
Eq. (3-6) versus disdrometerderived where M is the water content.
VO
50
4
3
( UUUJ) ®°Q
m•
2
4m.
0
D0 (mm)
Figure 3.9. Scatter plot of DQe derived from the empirical rela­
tionship given in Eq. (3-15) versus disdrometerderived where D q is the median volume diagemeter.
51
ships, six water content relationships and six median volume diameter
relationships, respectively.
The R relationships include the one- and
two-sectional empirical relationships of Seliga et al. (1986), the
exponential and gamma model relationships of Ulbrich and Atlas (1984)
and three Z-R relationships.
The latter includes:
the Marshall-Palmer (1948) relationship which is commonly used
for characteristic stratiform rain
Z - 200 Rjjp6 (mm6m ‘3)
(3-25)
the.Joss and Waldvogel (1970) widespread rain relationship
Z - 300 Rjy1 '5 (mm6m -3)
(3-26)
and the empirical relationship derived from the Illinois data set
Z = 388 Rzr1,36 (mm6m -3)
(3-27)
The results for R in Table 3.5 are given for three ranges of R:
R <. 5, 5 < R <. 50 and R > 50 mm h
These show that, overall, the
two-section empirical relationships yield the best results.
That is,
they produce the smallest NB and NSED of NB = 1.3%, -1.3% and 2.9%
and NSED = 7.6%, 5.7% and 4.2% within the ranges outlined above.
Examination of Table 3.6 shows that the two-section empirical
relationships for M are the preferred choice yielding NB = 1.5%, 0.1%
and 2.9% and NSED - 12.6%, 11.8% and 8.0% within the same ranges.
In
addition to the empirical relationships, these comparisons include the
exponential and gamma relationships of Eqs. (3-8) and (3-10) and
Table 3.5
Rainfall rate errors for the heavy rainfall event of October 6, 1982 in central Illinois
in terms of NB, NSED, AD and AAD (see Eqs. 3-19 - 3-24 ). Reflectivity factor and
differential reflectivity data are simulated from disdrometer measurements of raindrop
size distributions, and the relationships given in Table 3.2 and Eqs. (3-5, 7, 9, 25, 26,
27) are used in obtaining rainfall rates from the simulated radar measurements. The
disdrometer-derived rainfall rates are treated as reference values.
R(nn/h) < 3
5 < R(mm/h) < 50
R - 2.12 mn/h
NSED(Z)
AD(Z)
50 < R(mm/h) < 220
R - 19.5 un/h
AAD(Z)
NB(Z)
HSED(Z)
AD(Z)
R - 102.6 mm/h
AAO(Z)
NB(Z)
NSED(Z)
AD(Z)
AAO(Z)
Rainfall Race Estimation Method
NB(Z)
Two section empirical (Zjj, Zpp)
(Eq. 3-5)
1.3
7.6
0.6
6.1
-1.3
5.7
-1.1
4.9
2.9
4.2
2.1
3.5
Caoma model (Eq. 3-9)
11.8
11.4
12.1
14.6
13.6
13.5
11.7
12.3
23.9
12.5
23.0
23.0
Marshall-Palmer (Eq. 3-25)
38.6
49-.0
48.7
55.4
2.1
16.1
1.5
17.5
-24.9
23.3
-20.5
20.7
5.6
44.5
9.3
37.9
4.3
21.6
1.3
20.4
-0.9
16.3
3.0
11.5
One section empirical (Zjj, ZDR)
(Table 3.2)
-0.2
8.7
0.2
7.7
-1.3
5.6
-2.4
4.7
6.3
5.4
5.5
6.0
Exponential model (Eq. 3-7)
27.1
17.8
27.5
28.4
29.2
23.5
27.0
27.0
60.9
19.7
. 39.8
39.8
Joss-Waldvogel (Eq. 3-26)
14.6
44.1
21.4
40.3
-7.8
16.3
-6.9
20.2
-23.2
22.0
-19.3
19.5
Empirical Z-R (Eq. 3-27)
Ln
NJ
Table 3.6
Water content errors for the heavy rainfall event of October 6, 1982 in central Illinois
in terms of NB, NSED, AD and AAD (see Eqs. 3-19 - 3-24 ). Reflectivity factor and
differential reflectivity data are simulated from disdrometer measurements of raindrop
size distributions, and the relationships given in Table 3.2 and Eqs. (3-6, 8, 10, 28,
29) are used in obtaining water contents from the simulated radar measurements. The
disdrometer-derived water contents are treated as reference values.
M(g/m3) < 0.1
M • 0.066 g/m3
Water Content Estimation Method
Two section empirical (Zg,
(Eq. 3-6)
zd r )
Gamma model (Eq. 3-10)
Douglas (Eq. 3-29)
DapIrleal Z-M (Eq. 3-28)
One section empirical (Zjj, ZDR)
(Table 3.2)
Exponential model (Eq. 3-8)
0.1 < M(g/m3) < 1
1 < M(g/m3) < 9
fi " 0.37 g/m3
M " 2.88 g/m3
NB(Z)
NSED(Z)
AD(Z)
AAD(Z)
NB(Z)
NSED(Z)
AD(Z)
1.5
12.6
0.9
11.0
0.1
11.8
0.4
36.9
21.2
37.5
40.3
30.1
23.0
122.6
84.9
124.7
124.7
22.0
28.7
57.3
27.8
54.0
1.6
13.4
2.0
76.8
31.9
77.6
AAD(Z)
NB(Z)
NSED(Z)
AD(Z)
8.6
2.9
8.0
0.9
5.0
31.0
31.5
39.8
30.8
36.8
36.8
36.6
34.2
42.3
-9.6
27.2
-0.6
14.8
-6.0
35.4
-3.2
36.6
4.1
18.6
8.7
14.1
12.0
-2.8
10.5
-2.3
8.8
6.1
9.8
3.6
6.3
78.4
68.1
44.9
69.2
69.2
80.5
56.8
76.6
76.6
AAD(Z)
Ui
54
the empirical Z-M relationship derived from the Illinois data set
Z - 2.83 x 10A M zm1,47
(3-28)
plus Douglas1 (1964) equation
Z - 2.4 x 10A Mp1 ’82
(3-29)
The D q comparisons in Table 3.7 show little difference between
the NB and NSED of any of the empirical relationships, each of which
has a comparable NB and a significantly lower NSED than the expo­
nential DSD model (Eq. 3-17) and the gamma DSD model (Eq. 3-18).
The results of the above comparisons support the use of Eqs.
(3-5), (3-6) and (3-15) for the case studies in Chapter 4.
To test
these assumptions, the two independent disdrometer-measured rainfall
events in Colorado of June 8 and 13, 1984, provided a convenient test.
The R, M and D q simulations for these cases produced the error mea­
sures given in Tables 3.8, 3.9 and 3.10, respectively.
showed
that the choice of the two-section
R and M are the
best
These conclusively
empirical relationships for
choices and that either
of the empirical Zq R -Dq
relationships outlined in Table 3.4 is preferred over the exponential
and gamma model relationships.
Thus, the following set of relation­
ships were chosen to perform the case studies presented in Chapter 4:
R
= 1.95 x 10-3 ZjjZq ^ 1,04 (mm h'1) ,
0 . 2 < Z D R <0.7
R
* 1.59 x 10-3 ZRZDR"1,67 (mm h"1) ,
0 . 7 < Z D R <2.6
(3-30)
Table 3.7
Median volume diameter errors for the heavy rainfall event of October 6, 1982 In central
Illinois in terms of NB, NSED, AD and AAD (see Eqs. 3-19 - 3-24). Differential reflec­
tivity data are simulated from disdrometer measurements of raindrop size distributions,
and the relationships given in Table 3.4 and Eqs. (3-17, 18) are used in obtaining median
volume diameters from the simulated radar measurements. The disdrometer derived median
volume diameters are treated as reference values.
Median Volume Diameter
Estimation Method
D0(mm) < 1.5
1.5 < Dp/on) < 2.5
2.5 < I>0(a») < 3.0
Dq - 1.18 in
D0 - 2.05 am
DQ - 2.67 am
NB(Z)
NSED(Z)
AD(Z)
NB(Z)
NSED(Z)
AD(Z)
Bnplrlcal (Table 3.4, Eq. 3-11)
4.6
13.1
4.8
9.3
-2.4
8.5
-2.5
Baplrlcal (Table 3.4, Eq. 3-12)
2.1
15.6
2.1
11.9
-0.8
8.2
Empirical (Table 3.4, Eq. 3-13)
9.9
12.1
10.2
10.6
-2.4
Daplrlcal (Table 3.4, Eq. 3-14)
6.3
14.8
6.3
10.8
Gamma model(Eq. 3-18)
-10.3
12.7
-10.2
Exponential model (Eq. 3-17)
-24.9
10.9
-24.8
AAD(Z)
AAD(Z)
AAD(Z)
HB(Z)
NSED(Z)
AD(Z)
7.3
2.1
4.0
2.1
3.4
-0.8
6.5
1.5
3.4
1.5
2.9
7.8
-2.3
6.7
-0.1
3.7
-0.2
2.8
-1.3
7.4
-1.2
6.0
-1.5
3.0
-1.5
2.8
15.0
-16.1
6.8
-16.0
16.3
-16.0
2.7
-16.0
16.0
25.7
-29.7
6.8
-29.7
29.7
-29.6
2.5
-29.6
29.6
Ln
Table 3.8. Rainfall rate errors for two independent rainfall events that occurred on June 8 and 13,
1983 near Boulder, Colorado, in terms of NB, NSED, AD and AAD (see Eqs. 3-19 - 3-24).
Reflectivity factor and differential reflectivity data are simulated from disdrometer
measurements of raindrop size distributions, and the relationships given in Table 3.2,
and Eqs. (3-5, 7, 9, 25-27) are used in obtaining rainfall rates from the simulated
radar measurements. The disdrometer derived rainfall rates are treated as reference values.
June 8 Event
June 13 Event
R = 1.17 mm/h-^
R = 2.42 mm/h-l
Rainfall Rate Estimation Method
NB(%)
Two section empirical (Z^, Zp^)
(Eq. 3-5)
-0.1
11.8
-5.7
8.1
-3.5
8.5
-2.2
6.3
Gamma model (Eq. 3-9)
12.4
16.0
25.6
28.3
4.8
7.8
5.9
7.5
Marshall-Palmer (Eq. 3-25)
-2.2
28.1
19.6
27.4
43.5
22.5
65.7
66.2
1.9
12.4
16.3
22.5
-7.5
8.9
-6.5
7.4
27.8
33.0
42.9
43.8
19.2
13.9
20.4
20.4
-21.9
40.2
-11.8
20.9
19.9
21.2
35.6
39.6
One section empirical (Zjj, Zp^)
(Table 3.2)
Exponential model (Eq. 3-7)
Joss-Waldvogel (Eq. 3-26)
NSED(%)
AD(%)
AAD(%)
NB(%)
NSED(%)
AD(%)
AAD(%)
Ln
ON
Table
3.9. Water content errors for two independent rainfall events that occurred on June 8 and 13,
1983 near Boulder, Colorado, in terms of NB, NSED, AD and AAD (see Eqs. 3-19 - 3-24) .
Reflectivity factor and differential reflectivity data are simulated from disdrometer
measurements of raindrop size distributions, and the relationships given in Table 3.2 and
Eqs. (3-6, 8, 10, 29) are used in obtaining water contents from the simulated radar
measurements. The disdrometer-derived water contents are treated as reference values.
June 13 Event
June 8 Event
_3
M = 0.106 gm J
Water Content Estimation Method
NB(%)
Two section empirical (Z^, Zpj^)
(Eq. 3-6)
-1.3
Gamma model (Eq. 3-10)
Douglas (Eq. 3-29)
One section empirical (Zjj,Zj)^)
(Table 3.2)
Exponential model (Eq. 3-8)
M = 0.064 gm-3
AD(%)
AAD(%)
NB(%)
17.9
-10.5
14.1
-3.3
12.8
-1.3
9.3
40.8
43.3
57.3
59.5
23.6
18.3
25.9
26.2
20.5
27.5
42.9
46.4
100.1
38.4
140.2
140.2
3.4
17.9
14.4
24.0
-7.7
13.0
-6.0
9.3
81.8
85.6
103.1
103.8
59.6
37.7
62.6
62.6
NSED(%)
NSED(%)
AD(%)
AAD(%)
Table 3.10. Median volume diameter errors for two independent rainfall events that occurred on June 8
and 13, 1983 near Boulder, Colorado, in terms of NB, NSED, AD and AAD (see Eqs. 3-19 3-24).
Reflectivity factor and differential reflectivity data are simulated from dis­
drometer measurements of raindrop size distributions and the relationships given in Table 3.4
and Eqs. (3-17 - 3-18) are used in obtaining median volume diameters from the simulated
radar measurements. The disdrometer-derived median volume diameters are treated as
reference values.
Median Volume Diameter
Estimation Method
June 8 Event
June 13 Event
72 mm
5o = 1 -
DQ = 1. 01 mm
NB(%)
NSED(%)
AD(%)
AAD(%)
NB(%)
NSED(%)
AD(%)
AAD(%)
(Table 3.4, Eq.
3-11)
-1.1
8.4
-0.5
7.1
3.1
11.7
4.7
9.4
Empirical (Table 3.4, Eq.
3-12)
0.9
8.5
1.5
7.2
-6.5
14.5
-7.4
14.3
Empirical
(Table 3.4, Eq.
3-13)
0.3
8.3
1.1
7.0
10.8
11.7
13.2
14.0
Empirical (Table 3.4, Eq.
3-14)
1.8
8.3
2.5
7.2
-0.9
13.9
-1.2
11.3
Gamma model(Eq. 3-17)
-13.6
8.2
-13.1
13.7
-16.5
12.1
-16.9
19.5
Exponential model(Eq. 3-18)
-27.6
8.4
-27.2
27.2
-30.1
11.6
-30.4
31.2
Empirical
Ui
00
59
M = 1.04 x 10-A ZHZDR"1,29 (8 m "3 ) » °-2 ^ ZDR ^ °-7
N = 7.81 x 10"5 Zh Zd r "2 *04 <8 m ”3) . 0.7 < ZDR < 2.6
(3-31)
D q = 1.68 Zdr°*6A (ram)
(3-32)
6 *3
where the corresponding units are ZR(mm m ), Z^R (dB) and DQ(mm).
CHAPTER A
DIFFERENTIAL REFLECTIVITY RADAR MEASUREMENTS OF RAINFALL
The preceding chapter showed that comparisons of rainfall
parameters obtained from disdrometer measurements with the same
parameters estimated by the disdrometer-derived radar observables (Zjj,
Zpjj) gave encouraging results for the applicability of the differ­
ential reflectivity radar rainfall estimation technique.
This chapter
presents the results of case studies from three different field
programs to test the aforementioned simulated results.
The first
occurred in central Illinois on 29 October 1982 during the Ohio State
Precipitation Experiments (OSPE), and the two others in Boulder,
Colorado during the MAYPOLE '83 and '84 field programs on 4 June 1983
and 15 June 1984.
The studies consisted of comparisons between
ground-based measurements and radar estimates of rainfall parameters.
A brief description of these case studies follows:
(1)
OSPE:
Comparisons of the rainfall parameters R, M, and D q ,
estimated from the radar observables (Z^
^DR
were made with in-situ
measurements using a disdrometer located at a site 47.1 km away from
the radar.
(2)
This study is given in Section 4.1.
MAYPOLE *83:
Similar disdrometer comparisons
site that was only 6.35 km away from the radar.
are made for a
This case differed
from the Illinois case in that the width of the radar beam was
60
61
considerably smaller and the rainfall event was of short duration and
transient in nature.
(3)
the
MAYPOLE *84:
The results are given in Section A.2.
Comparisons of rainfall rates estimated using
method are made with measurements from two ground-based rain
gauges located at distances of 28.6 km and 35.2 km from the radar.
These data were from the same storm and differed from the other case
studies in that they are for heavier rainfall rates than the other two
cases.
Each of the studies required special techniques to account for
sampling differences between the radar and the ground truth
measurements.
Temporal to spatial transformations as well as schemes
accounting for effects of advection and drop size sorting are included
in the analyses.
A .1
OSPE Case Study
This experiment took place on 29 October 1982 during the Ohio
State Precipitation Experiments (OSPE).
The rainfall event of 6
October 1982 consisted of only disdrometer measurements whereas on 29
October both the CHILL radar and the disdrometer were operational.
Descriptions of the CHILL radar and the disdrometer are given in
Chapter 2.
The radar was located in Central Illinois at the airport
of the University of Illinois near Champaign-Urbana, and the disdrommeter was located at the Clinton site (227 m MSL) at a distance of
A7.1 km away from the radar and an azimuth angle of 285.6° from
relative to the radar.
One degree E- and H-plane half power beam
widths of the radar antenna corresponded to an approximately 820
north
m beam diameter at the disdrometer site.
During this rainfall event,
CHILL radar operations began from 2220 PM CST on 28 October and
continued for nearly 8 h until 0630 on the 29th.
A tipping-bucket
rain gauge verified the total rainfall amount at the disdrometer site.
The disdrometer recorded several rainfall events throughout this
period, and, since the radar was calibrated at 0135 CST, the period
0018-0054 was chosen for analysis.
radar errors affecting the results.
This reduced the probability of
During this period, the radar
operated in the plan-position indicator (PPI) mode performing narrow
sector scans between the azimuth angles 280.7°-290.5° at a fixed
elevation angle of 0.9° with an angular velocity of l°s
The large
number of sector scans over the 36 min time period of interest
provided an excellent radar data base from which comparisons with
disdrometer measurements could be made.
The CHILL radar was operating
in a pulse-to-pulse fast switching mode between the alternating H and
V polarizations every 1 ys, and the data were recorded after power
averaging of 32 pulses at each polarization.
The drop size distributions (DSD's) producing the rainfall
parameters were recorded by the disdrometer every 30 s.
For this
analysis, the disdrometer data were averaged over 5 recording periods
which extended the sampling periods to 2.5 min; this procedure
produced 2.5 min running average samples every 30 s.
It was used to
reduce the standard error in the rainfall parameters and also made the
averaging period of the disdrometer records more compatible with the
vertical extent of the radar beam.
This is seen by considering the
fall speed of the event's mean median volume diameter, D q , of 1.7 mm.
63
These raindrops would
traverse the radar beamwidth in around 1A0 s
which matches closely
the 150 s disdrometer averaging period.
Thus, a
single radar sample at the range of the disdrometer is compatible with
a 2.5 min average ground-based observation.
The fractional standard
deviation (FSD) of rainfall rate under these circumstances is about
0.13 for R ■ 1 mm h *
1969).
and 0.10 for R ■ 5 mm h * (Joss and Waldvogel,
The radar scanned the sector in approximately 10 s, so every 3
consecutive radar scans were averaged and compared with the 30 s (2.5
min averaged) disdrometer recordings.
The fall time of the raindrops
introduced a delay .time which caused the disdrometer data to lag the
radar measurements.
This delay tiri** was defined to be the difference
between the time of the second scan in each radar triad and the
mid-point of the 2.5 min averaging period of the disdrometer data.
In
order to determine the corresponding spatial location of the radar
data for comparison, the speed and the direction of the storm had to
be accounted for by using the PPI scans of the reflectivity factor
contours.
A track of the 30 and 35 dBZ contours of
at a 0.9°
elevation angle during the rainfall event is shown in Fig. 5.1.
This
indicates that the storm was moving in the NE direction at about A5 °
from the north with a speed of around 30 ms
In addition to the
bulk motion of the storm, frictional effects in the atmospheric
boundary layer can cause the wind direction and speed to change with
height in the lower atmosphere, deviating counter-clockwise with a
decreasing speed as height decreases.
The comparisons depend on the
accurate prediction of the location of those raindrops aloft which
eventually were recorded by the ground-based instruments.
A
64
0.0*o 3* I3
DISDROM ETER
00:20:26
CHILL R A D A R
Okm
00:12:32
Figure 4.1.
The relative locations of the CHILL radar and the
disdrometer for the 29 October 1982 rainfall event in
central Illinois.
contours of a rain cell obtained
from three different PPI scans are also shown which were
used to estimate storm speed and direction. The times
indicate beginning of the scans.
Zjj is the reflectivity
factor.
65
cross-correlation scheme of comparing the radar-observed and the
disdrometer-derived
is used to determine the location of
the appropriate radar volume for the comparisons; details of this
procedure are outlined in Section 4.1.1.
The radar data were
organized into an equivalent surface network of cells forming
parallelograms as shown in Fig. 4.2.
The axes, defined by the numbers
1 through 7 in each row, are in the radial direction from the radar
with the first range gate in each cell noted.
The axes, represented
by the letters A-D in each column, are aligned in the direction of the
storm track with the corresponding azimuth angles shown along the
track.
Spatial averaging within each cell site corresponds to 3 radar
rays and 6 range gates, forming cell sizes of around 1 km (3 rays
spanning 1.28° at 47.1 km range) by 900 m (6 gates of 150 m length per
gate).
This choice of spatial averaging created non-overlapping radar
cells having comparable dimensions along both axes.
The ray averaging
was accomplished by averaging each ray with its two adjacent rays.
The azimuth angle represents the middle ray, and the numbers in the
cells designate the first of six range gates averaged within that
cell.
The disdrometer was located at site A4.
This averaging pro­
duced standard errors of (Zg» 2 ^ ) within each cell of (0.5 dB, 0.1
dB).
During the 36 min of this rainfall event, 179 radar scans were
analyzed.
4.1.1
Cell Selection
Since the columns of the radar cell network (numbered 1-7) are
aligned with the estimated storm track (45° from the north) and
IKm
Ra n g e
340
344
3 48
35 2
35 6
330
334
33 8
342
320
32 4
326
3 32
3 36
300
30 4
308
32 2
3 26
290
29 4
298
- 284.4
284
288
285.6
2 8 3.2
- 282. 0
30 2
306
.280,
292,
296
- 2 80.8
Figure 4.2. The spatial cell network used in the cross-correlation analysis of the radar versus
disdrometer data for the central Illinois rainfall event (see Section 4.1). Columns
1-7 are along the storm track, whereas rows (A-E) are along the radar rays at the
indicated azimuth angles.
The numbers in each cell correspond to the first of the
six range gates to be averaged. Disdrometer is located at the center of cell A4.
On
O'
67
assuming that the effects of wind shear and advection were negligible,
column 4 would be the expected path through which the raindrops would
fall from the observed radar volume onto the disdrometer.
However, if
wind shear and advection are important, then an analysis based on
these claims might possibly result in comparisons between unrelated
drop size distributions (DSD's).
Also, choice of the section of the
column that contributed to the ground data depends on the averaging
time of the disdrometer and the estimate of the average storm speed
over the path of descent.
Sampling time governs the section length,
while storm speed governs the location of the section.
Complete
information on the vertical and horizontal wind profiles was not
available, although ground observations, consistent with frictional
effects, showed the surface wind speed to be considerably less than
the 30 ms * estimated speed of the storm scan obtained from radar at a
height of 740 m.
Each of the parallelogram cells shown in Fig. 4.2,
representing the corresponding radar observation cells, was considered
for the cell selection.
The procedure requires examination of the
cross-correlation coefficients (p^^* ^z d r ^ between the radar-averaged
and the disdrometer-derived (Zjj, Z ^ ) time series for all the sites at
different time delays.
(Pz h > ^ZDR^ were chosen for this purpose since
(Z„, ZnD) are the independent radar parameters of interest.
n
UK
Also, if
the correlation procedure for choosing the radar cells is correct,
then
Pz d r ) should both exhibit maxima in the same cells.
Thus,
a test of the methodology results from cross-correlating both
, Zj^) as opposed to selecting either one of these or another
single parameter such as rainfall rate.
Considering the different
68
delay times between the radar and the ground measurements was necessary, since the fall time of raindrops from the radar beam height of
740 m can cause a significant delay between the radar and disdrometer
observations.
The problem may be further complicated by the terminal
velocity dependence on drop size and vertical winds (updrafts and
downdrafts).
To implement the process, the maximum (Pz h * ^ZDR^ were determined
for each cell.
The lag times at which these maxima occurred were
taken to represent the optimum time delay between the radar and
disdrometer observations.
for all cells in Fig. 4.2.
Fig. 4.3(a ) shows the maximum values of
In calculating p ^ ,
the time delays were
limited in range from 0.5 min to 3.5 min by physical considerations.
The disdrometer-measured DSD's were not expected to contribute to
radar observations outside the time window due to computations based
on beam height, beamwidth and raindrop fall speeds.
For example, a
spatially uniform distribution of raindrops in the radar volume would
contribute to a measured DSD only between the times represented by the
minimum fall time of the largest raindrops from the lower section of
the beam and the maximum fall time of the smallest raindrops from the
upper section of the beam.
As expected, optimum time delays increased
for the radar cells located farther away from the disdrometer.
Also,
for each row peaks along a single column (4), supporting the storm
track analysis which showed the general storm direction to be toward
the Northeast at 45°.
Column 4 p ^ values were high and ranged
between 0.94 to 0.95.
Fig. 4.3(b) shows the corresponding cross­
correlation values of P™™, for all the cells.
£DK
The delay times for the
69
0.9
x
N
0.8
0.7
Range
(a)
0.9
ZDR
D/
/E,
0.8
0.7
(b)
Figure 4.3.
Range
Cross-correlation coefficients for (a) Zjj and (b) Z^ r time
series data obtained from radar and disdrometer measure­
ments shown for optimum delay times for radar measurements.
Zji is the reflectivity factor and ZpR differential
reflectivity.
70
peak values of
and P2DR
fro*“ each other in only two out
of 35 cells, thereby confirming the procedure of radar cell selection
for comparisons with the disdrometer measurements.
Note that PgpR
exhibits less uniformity in range than Pgg* hut its peak values
(0.84-0.86) again concentrate along column 4.
Columm 4 cells, although having different optimum delay times of
0.5, 1.0, 1.5, 2.0 and 3.0 min for the sites A4, B4, C4, D4 and E4,
respectively, have all comparable (P^h *
maximized both the
Pa*rs t^ie
cell
and p ^ ^ ; its delay time matching the result of
the swath analysis presented later in this section.
The difference in
p_„and p_n_ in the ranges 1-7 are significantly higher than the
ZH
ZUK
differences along the storm tracks A-D, indicating greater variability
normal to the storm track than along the storm track.
The optimum
time delay (highest correlation) at site D4 is 2 min.
This is
consistent with an estimate based on the fall speed of drops of 1.7 mm
diameter which was assumed while determining the averaging period of
the disdrometer giving an average lag time of 126 s, consistent with
the time lag of the D4 site.
The cross-correlation analysis was also
extended to p^, p^ and p^Q with the rainfall parameters (R, M, D q )
estimated using the 2-region relationships of Tables 3.2 and 3.3.
Maximum p^, p^ and
tively.
p^ q
were 0.90, 0.87 and 0.83 for site D4, respec­
Figs. 4.4(a)(b)(c) and 4.5(a)(b) show comparison scatter
plots for the radar and the disdrometer-derived parameters for site
D4 (see also Section 4.1.3 and Tables 4.1 and 4.2).
0.21
0.18
R e (mmh
3
-
0.15
fI
O
0.12
E
2 -
O'
ixi 0.09
♦♦ **♦ * +
♦+
♦ +
♦♦
♦
0.06
I 0.03
*
±±.
0.03
R d (mmh
)
(b)
0.06
0.09
0.12
_L
0.15
_L
0.18
M0 (gm‘ 3)
Figure 4.4. Cell D4 scatter plots of (a) Rg derived from the radar (Zh , Z^r ) using Eq. (3-5) versus
disdrometer-derived Rj) and (b) Mg derived from the radar (Zh , Zjjr) using Eq. (3-6) versus
disdrometer-derived MD . R is the rainfall rate, M water content, Zh reflectivity factor
and ZpR differential reflectivity.
0.21
72
2.8
2.4
++
^
++
D0e (mm)
2.0
0.8
0.4
0 .4
0.8
2.0
2.4
2.8
DoD (mm)
Figure 4.4(c). Cell D4 scatter plot of D q e derived from the radar Zd r
using Eq. (3-15) versus disdrometer-derived D q d where
D q is the median volume diameter.
RADAR
Z H (dBZ)
40
35
.6
30
.4
♦ + +
25
V* v
♦ : ♦*
*«*
XJ
O'
Q
N
CC
20
.2
<
Q
< 0.8
VC
I5
♦♦
10
0.6
5
5
(a)
10
20
25
30
DISDROMETER Z H (dBZ)
15
35
40
0.4.
0.4
0>)
0.6
0.8
1.0
1.2
1.4
1.6
DISDROMETER Z DR (dB)
Figure 4.5. Cell D4 scatter plots of radar measured (a)
and (b) Zjjr versus their corresponding values
derived from disdrometer measurements. Zjj is the reflectivity factor and ZpR is the
differential reflectivity.
74
4.1.2
Swath Selection
In order to improve on the results using cell D4, consideration
must be given to the path length of the radar sample along the storm
track which contributes to the disdrometer measurements.
That is, the
spatial extent of the storm track that contributed to the ground
measurements must be matched to the averaging time of the disdrometer
(150 s).
Each of the cells cover 1.2° in azimuth angle and about 1.1
km along the storm track; ranges to the disdrometer change from 47.1
km for the cell A4 to 49.5 km for the cell E4.
The exact horizontal
speed of the raindrops along their descent is not known, and, instead
of initially estimating their transit time from the radar volume to
the ground from the storm speed of 30 ms * and other assumed wind
behavior, swaths of different extents were analyzed using the same
cross-correlation procedure.
All the possible contiguous swath
combinations extending over a various number of sites were analyzed to
find the maximum cross-correlation coefficients between the (Zjj,
time series of the radar volumes and the corresponding disdrometer
values.
The best match occurred for sites (B4, C4, D4, E4) with an
optimum delay time of 2 min which was identical to the delay time of
the single cell D4 and consistent with the earlier single cell
correlation results.
The cross-correlation values for this swath are
0.95, 0.89, 0.94, 0.92 and 0.88 for P ^ ,
PZDR» P^» Pj^ and P^q ,
respectively.
It is of interest to test the physical consistency of this
result.
A disdrometer sampling time of 150 s and a constant
horizontal wind speed of 30 m s * would imply a swath length of around
75
A.5 km.
4.2).
Swath (B4, C4, D4, E4) is approximately 4.4 km wide (Fig.
Assuming the radar swath represents a sample from a steady
state storm being advected across the earth's surface, the 4.4 km
length is then consistent with the sampling time transformed to a
spatial scale of 30 m s * x 150 s * 4.5 km.
The correlation results may also be examined in terms of raindrop
trajectories to determine what portion of each disdrometer size
category emanates from the radar swath.
This is done by considering
the delay time between radar and disdrometer sampling, the duration of
the disdrometer sample, the storm velocity and the terminal velocity
of each drop size.
Assume the storm moves at the wind speed u which
varies with height z according to
u(z) =
u q [1
- exp(-z/6)] (m s 1)
(4-1)
where uQ(ms *) is the horizontal wind velocity above the boundary
layer and 6(m) is depth of the boundary layer where u(z) = 0.632
[e.g., see Stern (1968)].
uq
If the terminal velocity of the drop does
not change very much with z, the height of the raindrops originating
at z = z
o
z =
after time t would be
(z q
- vt t)
(m )
(4-2)
These approximations lead directly to an estimate of the horizontal
distance traveled by the raindrops during their fall to the ground.
x (t )
=
u(z)dt
(m)
(4-3)
76
x(t) =
t-j + exp(-ZQ/6)-l]
where r = z /v„ is the fall time.
o t
Fig.
4.6
for
(4-4)
The results for x(x) are plotted in
parameters most likely representative of the
experimental conditions:
u
o
= 30 m s *
zq
* 330, 740, 1150 m (lower, mid and upper beam heights)
v
“ 3, 4, . . . , 9 m s *
(corresponding to drop diameters of
0.75-5 mm)
6 = 100, 200, 300, 400 m
The choice of the boundary layer depths model data given in
Stern for night time conditions.
Also shown in the figure are the
horizontal extent of the swath and selected disdrometer drop size
categories superimposed on the terminal velocity axis.
The plots
indicate the expected approximate horizontal distance of origin of the
raindrops within the radar swath that arrived at the disdrometer site
without any sampling period considerations.
greatly with 6.
The results do not vary
In this experiment, the drop sizes of greatest
interest center around D q « 1.7 mm and have velocities between around
4-7 m s * .
Fig.
4.6
s hows
that the disdrometer sampled raindrops
in this range come from all parts of the radar beam's vertical extent
over most of the 4.4 km wide swath.
Also, note that the swath
contains over 50% of the disdrometer samples for raindrops of all
sizes represented by v
in the range 3-9 m s * .
77
8(m)
h ■ 740m
h ■ 330m
100
10
200
9
300
a
400
7
100
6
£
200
X
\
5
300
+ E4
400
4
+ 04
\
3
100
+ C4
2
200
300
400
+ B4
0
0
2
3
4
5
6
7
8
9
V t ( m s * 1)
i_________ l_____________ i_________ i_______i---- 1
0.75
1.50
2.25
3.15 4.75
0.35
0,(m m )
Figure 4.6.
Horizontal distance X traveled by raindrops of
different sizes during their fall to the ground versus
terminal velocity v t of the raindrops. Results are
shown for different boundary layer depths 6 and for
raindrops originating from upper, mid and lower beam
heights h. The horizontal extent of the radar swath
and the disdrometer drop diameter corresponding to
the Vt axis are also superimposed.
78
Fig.
4.7
shows
the time of impact on the disdrometer of drops
originating from within the radar beam.
The duration of the
disdrometer time sample relative to the equivalent radar sampling
period (vertical transit time through the radar beam) is indicated for
the lower, mid and upper beam heights.
As expected, the time delay
increases for smaller drops due to smaller fall velocities.
From Fig.
4.6 and 4.7, the disdrometer sample duration and the radar swath
length are shown to be highly comparable for 6 % 200-300 m.
The
percentage of disdrometer sample observed by radar is above 55% for
all drop sizes, and greater than 74% for drops between 1.0-2.5 mm in
equivalent diameter.
The results of the analysis of drop trajectories relative to the
disdrometer sampling times and radar sample swath and the comparative
results indicate that choices of the swath length and the disdrometer
sample period are compatible.
In addition, they corroborate the
correlation analysis used originally to determine the swath size and
its location.
The time series plots of the swath/disdrometer R, M and D q values
are shown in Fig. 4.8 while Fig. 4.9 gives the corresponding radar
Scatter plots of the radar and disdrometer
values for these are given in Figs. 4.10 through 4.13.
In these
figures, the radar observations were shifted 2 min in time to account
for the fall time of the disdrometer-sampled raindrops.
Gaps in the
time records resulted from periods where the radar performed wider
sector scans than normal.
The corresponding time plots follow the
I20(s)
DISDROMETER TIME SAMPLE
PERCENTAGE of
DISDROMETER SAMPLE
OBSERVED BY RADAR
— — 5 5.3%
I50(s)
4.75 -
9
3.1 5 -
D .lm m )
2.25 i/>
h=330m
(LB)
h=740m
(BC>
h= I I50m
(VB)
8
66 .0 %
7
78.0%
6
9 1.3%
5
86 .0 %
4
74.7%
1.50 -
0.75 -
3
200
100
RADAR SAMPLING
TIME
Figure 4.7.
300
56.7%
T IM E (s)
Time of impact on the disdrometer of the raindrops originating from lower, mid
and upper beam heights, h plotted for raindrops with different terminal
velocities,
and disdrometer drop diameters. The direction of the dis­
drometer time sample with respect to radar sampling time and the percentage
of disdrometer sample observed by radar for different v t are also shown.
0.08
0.04
2.5
R(mmh
I
0.5
0
4
8
I2
I6
20
24
28
32
36
TI ME( mi n )
Figure 4.8(a). Time records of R and M during the 29 October 1982 rainfall event in central
Illinois. The solid lines represent 2.5 min running averages of 30 s disdrometer
samples with zero time corresponding to values averaged over 0018-0020:30. The
points indicate radar estimates derived from (Zjj, Zp^) using Eqs. (3-5) and (3-6)
delayed by 2 min. R is the rainfall rate, M water content, Zjj reflectivity
factor and ZpR differential reflectivity.
oo
°
2.4
2.0
E
E
■ s ■\ y
o
O
0.8
0
4
8
12
16
20
24
28
32
36
TIME(min)
Figure 4.8(b). Time record of D q d u r i n g
the 29 October 1982 rainfall event in central Illinois. The
solid lines represent 2.5 min running averages of 30-s disdrometer samples with the zero
time corresponding to values averaged over the time interval 0018—0020:30. The points
indicate radar estimates derived from (Zg, Zdr) using Eq. (3-15) delayed by 2 min. Do is
the median volume diameter, Zjj reflectivity factor and Z^r differential reflectivity.
(mm)
2.4
2.0
o
Q
0.8
0
4
8
12
16
20
24
28
32
TIME(min)
Figure 4.9. Time records of Zjj and Zjjr for the rainfall event shown in Fig. 4.8. The points are
obtained from the radar measurements and the solid lines are the disdrometer-derived
values. Zjj is the reflectivity factor and Zjjjj differential reflectivity.
36
0
0.5
(a)
Figure 4.10.
I
1.5
2
R o l m m h * 1)
2.5
3
3.5
0
(b)
0.5
1.0
1.5
2.0
2.5
3.0
Rolmmh'1 )
Swath scatter plots of (a) Rg derived from the empirical relationship of Eq. (3-5) and
(b) Rg derived from the gamma model relationship of Eq. (3-9) using radar (Zh , Z^r ) versus
Rj) obtained from the disdrometer [see next page for (c) and (d)]. R is the rainfall rate,
Zh reflectivity factor and Zj)R differential reflectivity.
3.5
4.0
3.5
---- r—r
t
1---------- 1--------- r
t
r
3.5 *
-i
3.0 -
2.5 -
25
-C
(mmh
i 20
n
E
oc
1.5
m
r-1
-
" «
- If
»««
■
0.5 -
O5
05
(c)
■
1.5 -
1.0
><'•1
•*
■
I
15
R0 ( m m h *1 )
2.5
3.5
O
(d )
0.5
1.0
J_____ I
_____ I_____ L
1.5
2.0
2.5
3.0
3.5
4.0
R jjtm m h '1 )
Figure 4.10. Swath scatter plots of (c) RZR derived from the empirical Z-R relationship of Eq. (4-6) and
(d) Rm s derived from the Mueller-Slms (1966) relationship of Eq. (4-5) using radar Zr versus
Rj) obtained from the disdrometer [see previous page for (a) and (b)]. R is the rainfall
rate and ZR reflectivity factor.
00
4S
0.21
0.18
-
o.i 5 -
(gm*3)
ro 0.12
i
E
UJ
^
-
0 09
O'
o 0.09 -
0.06
0.06 -
0.03
0.03
0
(a)
Figure 4.11.
0.03
0.06
0.09
M d ( g m ' 3)
0.12
0.15
-
0.06
0.09
0.12
0 .2 I
M0 (gm '3 )
Swath scatter plots of (a) Mg derived from the empirical relationship of Eq. (3-6) and
(b) Mg derived from the gamma model relationship of Eq. (3-10) using radar (Zg, Zpg) versus
Mg obtained from the disdrometer. M is the water content, Zg reflectivity factor and Zd r
differential reflectivity.
00
Ui
2.4
2.4
2.0
2.0
Dqg (mm)
K K
E
E
XX
X
Lxi
o
*****
X *
*
0.8
0.8
(a)
Figure 4.12.
1.2
Q
**
1.6
D oD (mm)
2.0
2.4
0.8
0.8
a)
1.2
I .6
2.0
2.4
D oD (mm)
Swath scatter plots of (a) DoG derived from the gamma model relationship of Eq. (3-18) and
(b) D q £ derived from the empirical relationship of Eq. (3-15) using radar
versus D0j)
obtained from the disdrometer. D q is the median volume diameter and Zjjr is the differential
reflectivity.
00
O'
35
m
RADAR
Z u (dBZ)
30
GO
*o
25
tr 1.0
o
N
cr
20
< 0.8
Q
<
or
0.6
I5
I0
(a)
20
25
30
DISDROMETER Z H (dBZ)
Figure 4.13.
35
0.4
0.4
(b)
0.6
0.8
1.0
1.2
1.4
DISDROMETER Z DR (dB)
Swath scatter plots of radar measured (a) Zjj and (b) Zp^ versus their corresponding values
derived from the disdrometer measurements. Zjj is the reflectivity factor and ZDr is the
differential reflectivity.
00
-vj
88
same peaks and valleys and are also comparable in their values as seen
in the scatter plots.
The rainfall rate scatter plots are given in Fig. A.10.
In
addition to showing results for the (Zg, Z^g) 2-region empirical
relationship (Eq. 3-5) and gamma model
Rg
Rg
relationship (Eq. 3-9),
they also include results for the Mueller and Sims (1966) Z-R (R^g)
relationships
Z
derived for Champaign-Urbana
(A-5)
= 372 I^gA7 (mm6m~3)
and an empirical
R^g
relationship derived from the entire rainfall
event of 28-29 October 1982 as
„
Z
._c 0 l.A5 , 6 -3 n
= A25 R^
(mm m )
(A-6)
The liquid water content scatter plots in Fig. A.11 utilized the
empirical
Mg
relationship (Eq. 3-6) and gamma model
relationship (Eq. 3-10).
Dg scatter plots in Fig. A.12 used the
logarithmic relationship (Eq. 3-15) for the empirical
gamma model
Dgg
Mg
of Eq. 3-18.
Dgg
and the
The time series and scatter plots show
good comparisons between the radar- and disdrometer-derived rainfall
parameters.
These are discussed in greater detail in the following
sections along with a comparative examination of different schemes of
estimating selected parameters.
A.1.3
Radar-Disdrometer Comparisons
From an original 179 radar scans taken at approximately 10 s
intervals, 59 (Zg, Z^g) values were obtained for comparison with the
89
disdrometer samples.
These data produced the results given in Tables
4.1, 4.2 and 4.3 where the disdrometer values were taken as the
ground-truth reference.
Tables 4.1 and 4.2 relate to single cell A4,
and Table 4.3 is for the swath.
The errors were analyzed in terms of
NB, NSED, AD and AAD as defined by Eqs. (3-19), (3-20), (3-21) and
(3-22).
The parameters AD and AAD are given primarily for comparison
with previously reported results in the literature.
In this
discussion emphasis will be on the use of the NB, NSED pair, since
NSED is a measure of the scatter of the data with the bias effects
removed, and NB is a direct measure of bias.
The sample means of
6 *3
and Zy are obtained using linear averaging in units of mm m , and Z ^
from the difference of Z^(dBZ) and Z^(dBZ).
The spatial and temporal averaging of the radar data leads to
several schemes of interpreting rainfall parameters.
These depend on
whether Z^ ^ are power-averaged over space and time to final values
from which (R, M, D q ) are derived or whether the space and/or time
partitioned values of Z„ .. are used to estimate their respective
n, v
rainfall parameters from which the overall averages are obtained.
These procedures are illustrated by considering how, for example, Z^
is derived from spatial and temporal averaging:
^ O m n V 3) > ^
(mm6m~3)
(4-7)
where (i,j) correspond to time and space indices, respectively,
representing the N sample scans occurring in each 30 s period and the
M cells making up the swath.
As noted previously, for this experiment
90
N ranged between 2-A, and M = A (cells BA, CA, DA and EA).
Eq. (A-7)
may be expanded into its parts; this results in
ZH " M *N
E ^iil + N E ^ 1 2 + ’ ' • + N
^MiA^
i=l
i=l
i-1
ZH “ M *N ^ 1 1
(4“8)
+ ^ 2 1 + • • * ^ N l ^ + N [ZM12 + ^f22
+ * ’ ' + ^1N2^ + • * * + N t^MlA + ZM2A + * * * ^IN A ^
(A—9)
For. each
Z^
term in the above expressions there is a corresponding
Zy
and Z ^ .
Similarly, each (Z^, Zj^) pair may be used to estimate (R,
M, D q ).
Thus, there are at least three possible averaging schemes to
estimate these parameters.
For example, R may be found from either of
the following:
»E = W
ZDR>
(4 - 10)
M
h n m S j , RJ
3
M
(4-u )
N
where the R. and R. , values are derived from their corresponding (Z„,
J
ij
n
Zp^) values as illustrated in Eqs. A-8 and A-9.
Note that when
dealing with a single cell such as DA, the above reduces to two
alternative schemes,
91
^ " W
and
*» - 1
X
ri
( 4 -
In order to determine
i 3 )
which procedure is mostappropriate for
this experiment, comparisons between the disdrometer measurements of
rainfall rate R^ and Rg, Rg^ and
which are given in Table 4.3.
were performed, the results of
Rg clearly gave the least errors as
measured by NB, NSED, AD and AAD and therefore is chosen as the
preferred radar parameter throughout the rest of this case study.
A
comparison between R^ and Rg and Rg^ for cell D4 (Table 4.2) yielded
similar results with Rg being the preferred radar estimate.
Since R
is considered the most important parameter of interest, all other
radar-derived rainfall parameters were obtained using the same scheme
as for Rg, that is
M = MCZg, Zjjg)
(4-14)
D q - D0 (ZnR)
(4-15)
Similarly, all other radar estimated rainfallparameters,
such as
those computed from Z-R and Z-M relationship and gamma model (Zg, Z^g)
relationships for (R,M,Dq ), are derived using the same averaging
technique.
The cross-correlation procedure which was used to match the radar
volume to ground based measurements can also be tested using the
results of Table 4.1.
When the NB and NSED from column 4 are compared
Table 4.1. Radar-disdrometer comparisons of rainfall rates for the 29 October 1982 event. The error
rates NB (Eq. 3-21), NSED (Eq. 3-22), AD (Eq. 3-23) and AAD (Eq. 3-24) are given for
selected cells shown in Fig. 4.2. The disdrometer is located at the center of cell A4.
Rainfall rate, R (mm h ^), R = 1.03 mm h ^
Duration = 35 min
Range
3
4
5
Azimuth
NB
%
NSED
%
AD
%
AAD
%
NB
%
NSED
%
AD
%
AAD
%
NB
%
NSED
%
AD
%
A
28.3
44.6
34.3
50.0
17.7
31.7
14.6
27.7
16.9
49.6
9.1
32.8
B
13.4
30.5
12.9
28.8
13.9
35.2
10.0
29.5
13.0
52.4
4.4
35.6
C
21.7
35.0
16.7
30.5
13.8
34.0
6.6
31.9
7.1
45.9
1.6
36.4
D
19.4
34.8
13.0
29.2
6.9
35.9
0.1
29.6
7.2
52.0
-0.1
39.4
E
22.2
39.8
15.6
36.8
11.0
39.9
3.6
35.9
-7.8
41.5
-14.5
38.5
AAD
%
VO
N>
93
with values in adjacent columns (3 and 5) at all sites, column 4 is
seen to produce the smallest errors with column 3 results being
slightly better than those in column 5.
Among the single radar sites,
D4 gave the overall best result, although all the adjacent sites in
column 4 are comparable, demonstrating the earlier conclusions about
the storm track, optimum column and site choices.
4.1.3.1
Rainfall Rate
Tables 4.2 and 4.3 present the comparisons for cell D4 and the
swath consisting of cells (b 4, C4, D4, E4), respectively.
In addition
to the empirical and Mueller and Sims (1966) Z-R relationships, the
tables include results for the Z-R relationships of Joss and Waldvogel
(1967) (Eq. 3-26) which is used for widespread rain and the M-P
relationship (Eq. 3-25).
Also listed are results from the gamma model
for interpreting (Zg» ZpR ) radar measurements (Eq. 3-9).
Comparing the Rg results of Tables 4.2 and 4.3 shows that the
swath averaging of (B4, C4, D4, E4) significantly reduces NSED by around
11.5% when compared to the results obtained for cell D4, although NB
is slightly greater by around 2%.
The gamma model relationships
showed very similar relative behavior.
For the Z-R relationships,
denoted by RgR , R ^ , R^p and R_j, swath averaging improves NSED by
5-8% while NB increases by 3-5%.
These results show that all
the R estimates benefit from smaller standard errors when comparable
spatial averaging of the radar volumes with the disdrometer time
averaging is used.
This improvement is more significant in the (Z^,
ZpR ) relationships than for the Z-R relationships.
As a consequence
94
Table 4.2.
Cell D4 radar-disdrometer comparisons of rainfall rate,
water content, median volume diameter, reflectivity factor
and differential reflectivity for the 29 October 1982
rainfall event. Rg, Rgjj, Rq, Mg, Mq employ radar observed
(ZH» ZDR) whereas Rgg, R ^ , Rtfp, Rjy and Mpo use ZH only.
D0g and Dqq are estimated from Zdr. Disdrometer values
are the reference values for all entries.
Cell IM
Duration (35 min)
Estimation Method
Rainfall rate
AD
%
AAD
%
(Eq. 3-5)
6.9
35.9
-0.2
29.6
ren
(Eq. 4-13)
9.1
38.5
1.5
30.8
rg
(Eq. 3-9)
15.6
40.4
7.8
31.8
rzr
(Eq. 4-6)
26.4
40.5
21.4
31.0
(Eq. 4-5)
37.5
46.2
32.6
39.4
(Eq. 3-25)
93.7
72.5
92.6
92.6
RJW (Eq. 3-26)
56.9
56.6
52.5
56.7
(Eq. 3-6)
14.0
41.1
6.5
32.8
(Eq. 3-10)
46.2
60.1
27.3
51.7
(Eq. 3-29)
165.0
102.8
171.6
171.6
(Eq. 3-15)
-3.3
10.0
-3.4
8.6
(Eq. 3-18)
-18.0
8.9
-18.1
18.5
-1.6
7.3
-2.6
6.3
8.5
15.9
10.2
15.0
r ms
r mp
me
M = 0.049 gm“^
Mg
m do
Median volume
diameter
D q = 1.65 mm
NSED
%
Re
R ■ 1.03 mm h-^
Water content
NB
^
doe
dog
Zy = 26.6 dBZ ZH (radar measurement)
Z„R - 0.87 88 ZDR (radar measurement)
Table 4.3.
Swath radar-disdrometer comparisons as in Table 4.2,
except the results of for the swath averages of cells
(B4, C4, D4, E4) shown in Fig. 5.2. RgM and R g ^
employ (Zg, Zjjr) for rainfall rate estimation with
different averaging considerations (see Section 4.1.3).
Zg is the reflectivity factor and Zpg differential
reflectivity.
Swatch Averaging of Cells $4, C4, 04, E4)
Duration (35 min)
Estimation Method
NB
^
NSED
Rg
9.1
24.4
6.2
25.6
R e m (e 9* 4-11)
11.5
25.9
8.6
25.9
Re M n (e 9- 4-12)
14.2
28.2
10.5
28.6
Rq
(Eq. 3-9)
17.8
28.6
14.0
29.2
RZR (e 9* 4-6)
30.0
35.8
31.3
33.4
RjlS (Eq • 4-5)
41.4
40.9
43.6
44.3
(Eq. 3-25)
99.3
65.0
108.6
108.6
Rjjj (Eq. 3— 26)
61.4
50.3
65.1
65.1
Mg
(Eq. 3-6)
15.9
28.5
12.2
29.1
Mq
(Eq. 3-10)
48.0
44.4
43.1
50.5
Md0 (Eq. 3-25)
172.9
94.0
192.2
192.0
Median volume
diameter
D q * 1.65 mm
D q e (e 9* 3—15)
-2.5
7.4
-2.3
6.4
Doc (Eq. 3-18)
-17.3
7.0
-17.2
17.2
ZH “ 26.6 dBZ
(radar measurement)
0.6
4.9
0.6
4.2
9.5
13.2
12.1
14.8
Rainfall rate
R ■ 1.03 mm h-^
Rm p
Water content
M - 0.049 gm"3
ZDR - 0.87 dB
(Eq. 3-5)
(radar measurement)
Z
AD
%
AAD
%
96
of these swath versus cell comparisons, all the remaining results will
focus on the swath findings.
The small increases in dB for the swath
are not considered as important as the larger improvements in NSED.
If the empirical Rg and the gamma model Rg estimates are
compared, Rg is better by 8.7% in NB and A.2% in NSED which are
similar to the results of the simulations in Chapter 3 which indicated
an expected 10.5% reduction in NB and 3.8% in NSED for R < 5 mm h
The empirical Rg had an NB of 9.1% and an NSED of 2A.A%.
The only
comparable experiment employing (Zg, Z^g) was performed by Goddard and
Cherry (1984b) which produced a similar bias and a 33% standard
deviation, which is about 9% more than NSED obtained here.
Their
results required them to assume a Zg bias of 1.5 dBZ and a gamma model
of m ■ 5.
Rg errors can also be compared to Z-R relationships
utilizing the same Zg time series.
The improvements of the Rg over
the empirical Z-R relationship derived for this event (Eq. 5-2) are
20.9% in NB and 11.4% in NSED.
These improvements are consistent with
the simulation results of Chapter 3 which predicted an improvement of
4.1% in NB and 36.9% in NSED.
The improvements of Rg over R computed
from the other Z-R relationships are 32.3%, 90.2% and 52.3% in NB and
16.5%, 40.6% and 25.9% in NSED for the R^g (Mueller-Sims), R^p
(Marshall-Palmer) and Rj^ (Joss-Waldvogel) rainfall rates,
respectively.
Again, the simulations in Chapter 3 predicted similar
improvements:
37.3% and 13.3% in NB and 41.4% and 36.5% in NSED for
Rgp and
respectively.
Rg errors of 9.1% in NB and 24.4% in NSED
differ considerablly from the simulated results of Chapter 3 which are
1.3% and 7.6% in NB and NSED, respectively.
The increase in these
97
experimental errors over those predicted from the disdrometer-derived
simulations may be due to a number of reasons, including
(a)
the large difference in the radar and the disdrometer
sampling volumes (about 3 x 10
9
m
3
for the radar versus 4.5
o
m
(b)
for the disdrometer);
statistical and measurement errors such as bias and
calibration in both the radar and disdrometer;
(c)
errors in determining and accounting for the horizontal
and vertical wind motion;
(d)
other factors such as higher order DSD effects which
might require more than two radar parameters to estimate
R; and effects of spatial and temporal gradients on the
measurements.
4.1.3.2
Liquid Water Content
In addition to R, Tables 4.2 and 4.3 give the liquid water
content comparisons for cell D4 and the swath (A4, B4, C4, E4). The
swath averaging improves NSED by 12.6% and 15.7% for the empirical Mg
(Eq. 3-6) and the gamma model Hg (Eq. 3-10), respectively, while NB
increases slightly by about 2% for both.
This result, as for R, again
suggests using the swath results for comparisons.
The swath Mg computations resulted in 15.9% and 28.5% in NB and
NSED, respectively, while the gamma model Mg resulted in 48.0% and
44.4%.
These show improvements
of 32.1% in NB and 15.9 in NSED for Mg
over Mg which are comparable to the improvements shown in the
simulations of Chapter 3.
The simulated results are 1.5% and 12.6%
98
for
VL
and 36.9% and 21.2% for Mg in NB and NSED, respectively, for
_3
M < 0.1 g m
.
The differences, when compared with the simulations,
are 14.A% and 15.9% for Mg and 11.1% and 23.2% for Mg.
The
differences between the simulated and experimental results are most
likely due to the same factors outlined in Section 4.1.3.1.
The
single M-Z relationship used for comparison here is due to Douglas
(1964) [the only one reported by Battan (1973)] and resulted in
excessive errors of 165.0% in NB and 102.8% for NSED.
4.1.3.3
Median Volume Diameter
Comparative results for the median volume diameter D q at cell D4
and the swath are also included in Tables 4.2 and 4.3.
The swath
shows improvements of only 0.8% and 2.5% for the empirical relation­
ship (Dqe, Eq. 3-15) and 0.7% and 1.9% for the gamma model (Dq G > Eq.
3-18) in NB and NSED, respectively.
Although the improvements are not
as great as those for R and M, for consistency the comparisons which
follow again use the swath results.
The NB and NSED results for the swath are -2.5% and 7.4% for D^g
and -17.3% and 7.0% for D q q » respectively, indicating comparable NSED
errors while D^g shows an improvement of 14.3% in NB over D ^ .
Goddard and Cherry (1984b) reported a bias of -5% and a standard
deviation of 15% in their radar-disdrometer comparisons assuming a
gamma model of m = 5.
Their bias errors are comparable to those of
Dgg while their standard error (presumably similar to NSED) is twice
as large.
The simulated results in Chapter 3 were -1.3% and 7.4% for
DQg and -16.1% and 6.8% for Dqq in NB and NSED, respectively, for
99
1.5 mm < D q .£.2.5 mm which holds for nearly all the data of this
event.
The experimental results for D0E are very comparable to their
simulated counterparts which contrasts with the empirical Rg and Mg
results which both showed significant differences of around 16% in
NSED and slight increases in NB when the simulated and the actual
radar-disdrometer resuts are compared.
If the relationships derived
for Rg, Mg and D^g in Tables 3.2 and 3.3 are representative, R and M
are dependent on both (Zg, Zgg), whereas Dq is in principle only
related to Z^g.
Whether this one-to-one relationship between Z^g and
Dq accounts for the very similar experimental and simulation results
cannot be directly ascertained, but the results are very encouraging.
One possible explanation may be found in the form of the DSD which may
be approximated by the gamma model given in Chapter 2.
If this form
is representative, for a given m, R and M are dependent on both N^ and
Dq.
Large spatial and temporal variations in Nm within a storm have
been reported by Joss and Waldvogel (1970); such variations in the
storm would produce large changes in Zg (or R and M) but not
necessarily in Z^g (or
D q ).
Nevertheless, utilizing (Zg, Z^g)
resulted in significant improvements for R, M and
Dq
estimates over
single parameter relationships under experimental conditions.
4.1.3.A
Reflectivity Factor and Differential Reflectivity
Radar measured and disdrometer-derived (Zg, Z^g) are in very good
agreement as seen in Tables 4.2 and 4.3.
The swath averaging improved
NSED by only 2.7% in Z^g and 2.4% in Zg with respect to cell D4 while
NB's were comparable.
These correspond to (0.64 dBZ, 0.023 dB)
100
reductions in NSED for the mean (Zg, Zpjj) which in turn translate into
a decrease (3%, 16%) in NSED for (Rg, Mg) computed using the empirical
relationships of Eqs. (3-5) and (3-6).
The Zg error improvements were
6 —3
computed using units in mm m
(power averaging) while computations
for Zjjg were made in dB.
These improvements are comparable to the
improvements of about 16% found for swath averaged Rg and Mg outlined
in Sections 4.1.3.1 and 4.1.3.2.
4.1.4
Remarks
The simulations of the (Zg , Zgg) two parameter estimation method
for R, M and D q rainfall parameters in Chapter 3 were tested in the 29
October 1982 central Illinois experiment.
The radar derived rainfall
parameters were compared with disdrometer measurements located 47.1 km
away from the radar.
The results of 179 radar scans at a constant
elevation angle of 0.9° produced very good agreements between radar
estimates and disdrometer measurements.
The empirical Rg and
relationships utilizing both radar parameters showed significant
improvements over both gamma model (m « 2) and Z-R or Z-M relation­
ships.
Rg produced errors of 9.1% for the normalized bias (NB) and
24.4% for the normalized standard error of difference (NSED), whereas,
the best of the Z-R relationships, empirically derived from the same
rainfall event, gave 30.0% for NB and 35.8% for NSED.
These results
strongly support use of Z^g as an additional estimation parameter in
radar rainfall rate and water content measurements.
In order to
perform the comparisons correctly, a systematic approach to select the
appropriate radar volume was undertaken.
This analysis included
101
performing a cross-correlation to optimize the matching of the
disdrometer temporal averaging with the radar spatial averaging.
This
approach was confirmed through an examination of raindrop trajectories
which demonstrated that the disdrometer samples were derived from the
radar swath which maximized the cross-correlation coefficients of the
radar-measured and disdrometer-derived (Z„ , Zj^) values.
This
approach is considered useful for future radar rainfall comparisons
with the ground based measurements as well.
4.2 Radar and Disdrometer Comparisons:
Experiment
4 June 1983 MAYPOLE
The MAY POLarization Experiment in 1983 (MAYPOLE '83) in Boulder,
CO provided additional opportunities to test the differential
reflectivity method of estimating rainfall parameters using the CP-2
radar.
MAYPOLE was a collaborative research program between The Ohio
State University, National Center for Atmospheric Research (NCAR) and
Colorado State University.
Its main objective was to perform
experiments with the CP-2 radar in the newly modified multiple
polarization mode including S-band reflectivity factor (Z^) and
differential reflectivity
X-band reflectivity factor
linear depolarization ratio (LDR) in addition to S-band Doppler
velocity measurements.
A description of the CP-2 radar is outlined in
Chapter 2 and the Appendix.
The disdrometer was in operation
throughout this program and supplied a continuous record of rainfall
events in the Boulder area.
One of the main objectives of MAYPOLE '83
was to evaluate the Z ^ method of estimating rainfall rates and
area-wide cumulative rainfall.
To realize this, the CP-2 radar made
measurements whenever a rainfall event had been detected in the
vicinity of the disdrometer.
In this section, the 4 June 1983
rainfall event was selected for comparisons between the radar
estimated rainfall parameters and the same parameters measured by the
ground-based disdrometer.
The main characteristic of this event was
the short range of the radar to the disdrometer resulting in a smaller
radar volume compared with the other events discussed in this study.
Thus, the rainfall parameters measured by the disdrometer were trans­
formed to the corresponding radar altitudes to make meaningful
comparisons.
Because of the nature of the rainfall event, in addition
to transport, this transformation had to account for drop size sorting
which occurs as the raindrops descend from the radar height to the
disdrometer.
4.2.1
Radar and Disdrometer Measurements
The rainfall event occurred between 1948-2008 MDT.
The
disdrometer was the same one used in the Central Illinois study and
was located in the vicinity of the Boulder Atmospheric Observatory
(BAO) meteorological tower.
The CP-2 radar was 6.35 km away from the
disdrometer at an azimuth of 173° from true north.
Both the radar and
the disdrometer was at 1540 m MSL elevation which alters the empirical
, Zj^)-R relationship which was derived previously in Chapter 3.
The considerable elevation increases the fall velocities of the
raindrops and affects the analysis in two different respects.
The
disdrometer is an electromechanical instrument estimating the
equivalent diameter of the raindrops from their momentum assuming a
103
mean sea level elevation.
The increase in raindrops fall speeds
results in a different set of equivalent drop sizes due to increased
momentum for each drop size.
Therefore, a new set of horizontal and
vertical backscattering cross-sections and other disdrometer drop size
coefficients were used to analyze the disdrometer data.
Another
effect of the increased terminal velocities is the resultant
modification of the empirical relationship which is used to estimate
the rainfall rate from (Z„ ,
The rainfall rate as defined by Eq.
(3-5) is dependent on the terminal velocity v
of the raindrops, and
an adjustment is necessary as these velocities increase.
The pressure
dependence of v^ (Eoote and du Toit, 1969) and an assumed mean
atmospheric pressure of 827 mb for the radar and the disdrometer
location gives
v
t
* 1.085 v.
to
(4-3)
where vfc and vfc are the terminal velocities for this experiment and
for MSL, respectively.
Since R is proportional to vfc and since all
drops would increase their terminal velocities by the same percentage,
the empirical relationships are simply multiplied by the factor 1.085.
For example, the 1-section empirical relationship which was used for
this rainfall event [Eq. (3-1), Seliga et al. (1983)] becomes
R « 1.79 x 10"3 Zjj Z ^ " 1,52
(mm h"1)
(4-4)
The rainfall event at the disdrometer site began at 1945 MDT and
developed rapidly, reaching 45 dBZ Z^ and an 8 mm h * rainfall rate
intensity within 2 minutes.
The intensity of the event continued
104
until 1952 MDT after which time the cell moved away from the dis­
drometer site and began dissipating.
The radar performed 28
sector
PPI scans between the azimuth angles 342°-10°, covering the volume
over the disdrometer location with the elevation angles changing
between 1° to 6° in 1° steps with an angular velocity of 2° s * between
1951-2007 MDT.
The CP-2 radar was operating with a PRF of 960 in a
pulse-to-pulse fast switching mode, and the data were recorded after
pulse averaging of 256 pulses in each polarization resulting in 2
records per second.
Horizontal and vertical wind profiles were
obtained from the BAO tower (300 m in height) measurements and by an
examination of the Doppler velocities corresponding to the same radar
scans.
The event most likely consisted of only rainfall, in that the
vertical structure of (Z^, Z_„) indicated that the melting layer was
at a height of 1.2 km.
In order to compare the ground-based measure­
ments with the corresponding radar volumes at different elevations,
the horizontal wind speed and direction were estimated from the BAO
tower measurements and were found to be nearly constant at approxi­
mately 12 ms *7205° over the tower height of 300 m.
For heights above
300 m the winds were taken to be 15 ms Vl80°, same as the highest
measurement on the BAO tower.
The radar Doppler velocity measurements
were in agreement with the tower and also showed very little change in
winds with heights above 300 m in the region of interest.
The disdrometer measurements indicated that a
diameter of 1.5 mm is representative of the event.
median volume
This implies a
terminal velocity of around 6 ms * which, together with the wind
speed, was used to determine the approximate radar elevation
105
angle-dependent location of the radar volumes from which the
disdrometer-sampled raindrops originated.
This analysis indicated
that the disdrometer samples originated from radar volumes at eleva­
tion angles 1°, 2°, 3°, 4°, 5° and 6° which in turn translate into
height/range locations of 100 m/6.55 km, 250 m/6.875 km, 400 m/7.20
km, 550 m/7.575 km, 700 m/7.95 km and 850 m/8.325 km, respectively,
from the CP-2 radar.
The path of the raindrops, the location of the
radar volumes to be used for different elevation angles and the radar
rays and the range gates which were used for averaging are illustrated
in Fig. 4.14.
Three successive rays and two range gates were averaged
resulting in a 420 m x 400 m horizontal extent of the radar volume at
6° elevation, the linear dimensions of which compared favorably with
the transformed range resolution of the 30 s disdrometer samples
(12-15 m s ^ x 30 s * 360-450 m).
Six radar volume scans produced 33
data samples corresponding to six elevation angles (l°-6°) which were
used to compare with the ground-based measurements.
The disdrometer time records, showing the variations of the
computed radar observables (Z„, Z™), plus R and D q , are shown in Fig.
4.15.
Time t = 0 corresponds to 1948:45 MDT.
The variation in these
plots indicates that the rainfall event was locally transient and may
have been a dissipative stage with strong gradients in all the
rainfall parameters.
Over the period of 20 min shown in these plots,
the peak values of 45 dBZ, 2.7 dB, 12 mm h
and 3.5 mm for Z„,
^DR’ R
and D q decreased to 2 dBZ, 0.3 dB, 0.1 mm h * and 1.0 mm, respec­
tively.
The high rate of change in these rainfall parameters, coupled
with a narrow radar beamwidth, necessitated the transformation of the
106
352*
354*
356*
358*
0*
I0 km
ELEVATION
•
I*
■
2*
A
•
3*
3*,4*
•
•
m
4*
5*
5*.6*
•
6*
TRAJECTORY
RANGE GATE
39
BAO TOWER
DISDROMETER
34
CP-
S km
Figure 4.14.
Relative locations of the CP-2 radar and the disdrometer
during the 4 June 1983 rainfall event in Boulder, Colo­
rado. The trajectory of the raindrops, the location of
the radar volumes used for different elevation angles
and the radar rays and the range gates used for averaging
are also shown.
o
N
— «n
O
—
O
I
”
N
o
o
16
TIME IMIN.) •
TIME IMIN.I
o
V
E
J
c
K
TIME IMIN.I
20
TIME (MIN.)
Figure 4.15. Time records of the computed radar observables (a) Zh
and (b) Zjjr corresponding to the disdrometer measurements
for the 4 June 1983 event in Boulder, Colorado. Also
shown are (c) R and (d) D q measured by the disdrometer
for the same event.
ZH is the reflectivity factor, Zdr
differential reflectivity, R rainfall rate and Do median
volume diameter.
108
ground-based measurements to the radar measurement heights as
explained in the next subsection.
A.2.2
Transformation of Disdrometer Time Records to Radar Altitudes
The half power beamwidth of the CP-2 radar is 0.96°, resulting in
a beam diameter of 140 m at the radar volume of interest at 6°
elevation angle (range
8.325 km).
The vertical beam-crossing time of
raindrops of 1.7 mm in diameter would be 23 seconds which is
comparable to the disdrometer sampling period.
But unlike the
previous rainfall study in central Illinois where the descent time of
the raindrops was less than the disdrometer averaging period (150 s),
in this event raindrops in different size categories having different
fall velocities were sampled during different disdrometer periods.
For example, 2.5 mm drops, originating from 850 meters in height at 6°
elevation angle
reach the surface 104 s later, whereas 1.3 mm drops
take 160 s to reach the surface.
The time difference between these is
of the order of two sampling periods.
Even for the drops originating
at the height corresponding to the 3° elevation angle, the arrival
times for these same sizes differ by a full sampling period.
The
resultant differences in the arrival times of different size drops
indicate that the rain drop size distribution, which filled the radar
volumes during the successive scans, changed during their descent and
were sampled as different DSD's by the disdrometer.
This phenomenon,
which is generally described as being due to drop size sorting, must
be accounted for when the disdrometer records are compared with the
radar measurements.
This is accomplished hereby transforming the
109
ground-based measurements to their respective radar elevation heights.
The steps in this transformation are outlined below:
(1)
Upper and lower height limits for the radar beam at
different elevation angles are computed using the locations
of the radar volumes determined in Section 4.2.1 (43-157 m
for 1°, 190-310 m for 2°, 337-463 m for 3°, 484-616 m
4°, 630-770 m for 5°,
(2)
for
777-923 m for 6°).
For a particular time of interest T
during the rainfall
event, the heights in the atmosphere of the raindrops
within
each size category for all the disdrometer record are
computed.
The transformation consists of mapping each drop
size category, recorded during each 30 s disdrometer
sampling period and assumed to occur at the midpoint of this
period, into heights determined by the product of the
appropriate terminal velocity and time interval between T
and the disdrometer sample times.
In order to ensure
adequate spatial coverage of the disdrometer measurements
within the vertical limits of the radar volumes, each drop
size category vertical distribution was replicated at T + 15
s.
This procedure is illustrated in Fig. 4.16 which indi­
cates the height of the raindrops in each size category
contributing to the radar sampling volumes at the 6 eleva­
tion angles.
(3)
The drop size categories within the beamwidth limits of
different radar elevation angles are determined from those
samples which intersect the vertical extent of the radar
no
ELEVATION
ANGLE
04
io o o r
900
04
RADAR
BEAMWIDTH
800
03
HEIGHT(m)
700
03
600
500
D2
400
D2
300
200
100
Vj (ms*1)
I____________ I____________________ I_________________ I------- 1
0.34
0.74
1.66
3.08
5.36
De(mm)
Figure 4.16. Vertical distributions of raindrops with different terminal
velocities and their corresponding disdrometer size cate­
gories at 15 s intervals to determine the raindrops con­
tributing to the radar sampling volumes at the six elevation
angles. Pairs of drop size distributions averaged to obtain
30 s disdrometer samples and the radar beamwidth at
different elevation angles are also indicated.
Ill
volumes.
If two or more disdrometer samples in any size
category are contained in the volume, the average of the
samples are used to represent that size.
(A)
In order to obtain the time history of the event correspond­
ing to the radar volumes at the six elevation angles, the
disdrometer records were transformed to height profiles at
30 s intervals according to the procedures outlined in (2)
and (3).
The resultant DSD1s were then used to compute
rainfall and radar parameters R, M, D q ,
and
as
functions of time for comparison with the radar measure­
ments .
A.2.3
Disdrometer-Radar Comparisons
Disdrometer records of the transformed rainfall parameters are
shown in Figs. A.17 through A.22. corresponding to successive
elevation angles of 1°-6°(1°).
Disdrometer derived (Zjj, Zq r ) as well
as (R, D q ) are identified as (a) through (d), respectively, in each
figure.
Radar measurements are indicated'by the discrete data points.
Note that the transformation process accounts for the delay times
between radar and disdrometer samples at each of the elevation angles,
and that the radar parameters are separated by approximately 2 min and
AO s which is the duration of each volume scan.
ments (Z^,
For radar measure-
are the observed parameters where (R^, D q ) are
estimated using Eqs. (A-A) and (3-15), respectively.
In general, good
agreement between the time plots of the disdrometer and the radar
parameters are obtained.
The radar parameters follow closely the
occ
•IEWUIflH • I OEC
*
n w
—
«
£4
SC
N to
1
n
IB
TIME (MINJ
TIME IMIN.I-
OEC
OEC
1
E
C
K
T F ^
TIME IMIN.I
io
TIME IMIN.I
Figure 4.17* Time records of the transformed rainfall parameters
(a) Zg, (b) Zjjp, (c) R and (d) Do derived from the
disdrometer measurements corresponding to 1° radar
elevation angle.
Zh is the reflectivity factor, Z^r
differential reflectivity, R rainfall rate and D q
median volume diameter.
113
K cwmioh
• g'otc
occ
N
aa
x
N
a
TO
re
TIME (MIN.)
I
(C )
Rn(mm/hr)
'LCVAUON • 2 OEC
ItlVBTtON * 2 OEC
.
\
1
1
TIME
Ml
IMIN.I
TIME IMIN.I
Figure 4.18. Time records of the transformed rainfall parameters
(a) Zh, (b) ZD R , (c) R and (d) D q derived from the
disdrometer measurements corresponding to 2° radar
elevation angle. Zh is the reflectivity factor, ZpR
differential reflectivity, R rainfall rate and D q
median volume diameter.
oce
o ec
N
at
a
x
N
M
1
12
TIME (MIN.)
TIME (MIN.)
XEVBTIBW « 3 OEC
DEC
in*
«Qo«q
«
K
cu
N
O
O0
TIME IMIN.I
TIME IMIN.I
Figure 4.19. Time records of the transformed rainfall parameters
(a) Zh , (b) Z d r » (c ) R and (d) D q derived from the
disdrometer measurements corresponding to 3° radar
elevation angle.
Zh is the reflectivity factor, Z^p
differential reflectivity, R rainfall rate and D q
median volume diameter.
■LEVATIiON • 4
oec
OEC
c
_ e
n
r* *
a
Is
"" o
le
N «
TIME [MIN.I
TIME IM IN.I
:
le»»tibh . n oec
OEC
RR(mm/hr)
'LEVAT
« Oc
o ft
20
TIM E
IMIN.I
20
TIME IMIN.I • .
Figure 4.2 0. Time records of the transformed rainfall parameters
(a) ZH , (b) Zdr, (c) R and (d) Do derived from the
disdrometer measurements corresponding to 4° radar
elevation angle.
ZR is the reflectivity factor, Zj)R
differential reflectivity, R rainfall rate and D q
median volume diameter.
ore
ore
TIME (MIN.)
TIME (MIN.)
ELEVBTjOH . j OEC
ILEVHTOOH . S OEC
H E YU I I OH « S
n
in
«
SE
e
o
TIME IMIN.1
Figure 4. 2L
TIME IMIN.I •
Time records of the transformed rainfall parameters
(a) ZH , (b) ZD R , Cc) R and (d) Do derived from the
disdrometer measurements corresponding to 5° radar
elevation angle. ZH is the reflectivity factor, ZpR
differential reflectivity, R rainfall rate and D q
median volume diameter.
IbJ
1
ELfvflT HON . t OCC
d
occ
n
eS
d
i
( Z Q Q ) **Z
m
1
TT
/I
r
•
V
•
•
o
. V
ei
Q. w---
TIM E (M IN )
OEC
qevBTiBM . » ote
( J i | / u i u i ) Mtj
in
E
E
mcz
p)
TIM E
IMIN.I
TIME
IMI N.I
Figure i.22. Time records of the transformed rainfall parameters
(a) Zr , (b) Zd r , Cc ) R and (d) D q derived from the
disdrometer measurements corresponding to 6° radar
elevation angle.
Zr is the reflectivity factor, Zd r
differential reflectivity, R rainfall rate and Do
median volume diameter.
50
40
N
30
rsi
rsi
20
0
(a)
10
20
30
Z°(dBZ)
40
50
(b)
H
R
D
Figure 4.23. Scatter plots of radar-observed (a) ZR and (b) ZgR versus their corresponding values ZH
and z [jR obtained from the results shown in Figs. 4.17-4.23(a) and 4.17-4.23(b), respectively.
ZR is the reflectivity factor and Zjjr is the differential reflectivity.
10
£
45
0£
0.1
0.1
M-P
aoi
0.01
0.01
(a)
0.1
10
R (mm/hr)
o.oi
(b)
o.i
i
10
RJmm/hr)
Figure 4.24. Scatter plots of radar-derived rainfall rates computed from (a) the empirical (Zg, Z]jR)
relationship and (b) Marshall-Palmer relationship versus disdrometer-derived rainfall rates
shown in Figs. 4.17-4.23(c). ZH is the reflectivity factor and ZDR differential reflectivity.
D 0 (mm)
120
2
D n(mm)
T>
Figure 4.25. Scatter plot of D q derived from the radar measurements of
ZDR versus disdrometer-derived values shown in Figs. 4.174.23td) where D q is the median volume diameter.
121
dissipating trend of the rainfall event as observed with the disdrometer.
In Fig. 4.23, radar-observed and disdrometer-derived
are compared.
Radar estimated R and D q are also compared
with their disdrometer derived counterparts in Figs. 4.24 and 4.25.
These scatter plots are obtained using the data in the time plots of
the same parameters, by matching each radar value to the best fit
disdrometer value within one disdrometer sampling period away from the
radar sampling time (±30 s).
The superscripts R and D refer to
disdrometer and radar, respectively.
The scatter plots of the radar
and disdrometer rainfall parameters indicate a very close agreement
between measurements.
It is also of interest to compare the (Z^,
derived estimates with R obtained from the Marshall-Palmer (1948)
relationship of Eq. 3.25.
The latter results are shown in Fig. 4.24(b)
and, when compared with Fig. 4.24(a), indicate that a much greater bias
(overestimate) in R results when using the Marshall-Palmer relation­
ship.
Table 4.4 is a statistical summary of the results.
For each
radar and disdrometer-derived rainfall parameter, the mean value (X)
and the standard deviation cr^, given by,
<v24
are computed.
? *2 - *2
<4- 5>
i=l
The linear, least-squares fit parameters of the
corresponding data points are also given in Table 4.4, including the
correlation coefficient (p) and the slope (A) and the intercept (B) of
the linear regression coefficients.
The results
show that using
122
Table 4.4.
Statistical summary of radar- and disdrometer-derived
parameters including mean values (x), standard deviations
(s), correlation coefficients (p), and the slope (A) and
the intercept (B)* of the linear regression coefficients.
The superscripts D and R for Zjj, Zq r and D q and the
subscripts D and R for R refer to disdrometer- and radarderived values, respectively, where Zji is the reflec­
tivity factor, ZpR is the differential reflectivity, R
is the rainfall rate and D q is the median volume diameter.
Linear Regression Parameters
s
p
A
2? (dBZ)
cl
21.77
11.69
21.29
11.38
zjJR (dB)
0.85
0.43
zL
“DR
0.79
0.44
1.33
1.61
Rr (Eq. 4-4)
1.35
1.65
R^
2.10
2.67
4
Rjj (mm h
-i
)
(Eq. (3-25)
D q (mm)
1.56
0.49
D q (Eq. 3-13)
1.32
0.52
0.985
0.959
0.41
0.864
0.885
0.040
0.973
0.996
0.023
0.950
1.577
0.006
0.834
0.874
-0.040
123
, 2-^) results in significantly improved estimates of radar
estimated rainfall rates over conventional Z-R methods.
A .2.4
Remarks
Simultaneous CP-2 radar and disdrometer measurements were
compared during the rainfall event of 4 June 1983.
The short distance
between the radar and the disdrometer resulted in a narrow beamwidth
making the effects of different fall velocities of the drops in a
radar volume important.
The transformation of the disdrometer
measurements to radar altitudes was used to account for this drop size
sorting.
Effects of horizontal wind transport of the raindrops were
also approximately accounted for using the known wind speed to
estimate the region where the radar measurements were most representa­
tive of the disdrometer measurements.
The comparisons between the
radar-estimated and disdrometer-derived rainfall parameters were very
good, supporting
4.3
method of rainfall estimation.
Radar-Raingage Comparisons:
15 June 1984 MAYPOLE Experiment
During MAYPOLE 1984, evaluation and further development of the
differential reflectivity technique for precipitation measurements
continued.
The CP-2 radar made measurements over the Portable
Automated Mesonet (PAM) network whenever rainfall occurred over the
network which was established to supply ground observations of rain­
fall rate and other atmospheric parameters for comparison with radar
observations.
The rainfall event of 15 June 1984 provided an
excellent opportunity for such comparisons and was unique in that the
12A
rainfall rates were considerably higher peak (R > 120 mm h *) than the
other case studies and since raingages, rather than disdrometers,
furnished the ground truth.
In this study, time changes of rainfall rate over two PAM
stations are compared with the radar estimates of the same parameter
obtained from the volume scans spanning an approximately 35 min time
period.
The comparisons are performed by using a spherical to Carte­
sian interpolation technique to obtain constant-altitude PPI's
(CAPPI's) at different heights.
Consideration of the wind speed and
direction, mean fall velocity of the raindrops,height of
the CAPPI's
and the appropriate radar volumes to be compared with the
raingage
sampling period yielded ground-based raingage measurements.
The
analysis is done for both the two-parameter Z„ -Zd r estimation method
and the single parameter Z-R method utilizing two commonly used
relationships.
A.3.1
Raingage Measurements
During this event the PAM stations supplied the wind vector, air
temperature, humidity, barometric pressure and other atmospheric
parameters in addition to the rainfall rate.
The precipitation gages
at each site were of the tipping bucket type where the accumulation is
measured in increments of 0.25 mm.
The resolution of the wind speed
is 0.1 m s * and the wind direction is 0.1 .
The time diagrams of all
the parameters are recorded in 1 min intervals.
the PAM stations is given in Chapter
2.
More information on
125
The PAM stations selected for analysis in this case study were
the two which received the most amount of rainfall (stations 11 and
15).
Their locations relative to the radar are shown in Fig. 4.26.
PAM 15, at the Brighton site, was co-located with the CP-4 radar where
personnel confirmed that the event consisted of heavy rain as opposed
to mixed phase hydrometeors or hail.
The altitude of both stations
were at 1.49 km MSL whereas the CP-2 radar location was at 1.75 km.
The gage measurements are given in Section 4.3.3.
4.3.2
Radar Measurements
During this event the CP-2 radar operated continuously in a
volume scan mode with the measurements broken into two portions.
From
1703-1726 the sequence consisted of PPI sectors of 52° between azimuth
angles of 42°-94°, an angular velocity of 4° s * and elevation angle
increments of 1.1° between the angles 0.5°-8.2°.
This observational
time period produced 10 volume scans with each volume scan lasting
around 1 min 50 s and comprising 8 elevation angles.
During the time
period 1727-1735, 9 other volume scans were completed when the radar
operated between the azimuth angles of 52°-74° with an angular
velocity of 2° s * and covering the elevation angles between 0.5°-2.0°
in 3 steps.
The radar was in the similar pulse-to-pulse fast
switching mode as during the MAYPOLE '83 case study with a PRF of 960.
Data were recorded after pulse averaging 128 pulses in each
polarization during the first 15 volume scans and 256 pulses in each
polarization during the last 5 scans.
PAM I I S T A T I O N
( 3 5 .2km ,64.6°)
P AM
I 5 STATION
( 2 8 .6km ,77.4°)
C P - 2 RADAR
I Okm
Figure 4.26. The relative locations of the CP-2 radar and the two PAM stations during the
15 June 1984 rainfall event in Boulder, Colorado.
The radar data were obtained in the Universal Format (Barnes,
1980) which was suitable for processing using SPRINT and CEDRIC
software (Mohr et al., 1981; Mohr and Miller, 1983).
SPRINT is an
interactive program that transforms the data values from radar space
to 3-dimensional Cartesian coordinates.
For each selected Cartesian
grid point (x, y, z) with the spherical coordinates (R,
6,<p),
four
radar beams surrounding its location in space from successive PPI
scans are determined.
A sequence of bilinear interpolations of the
eight surrounding data points from the adjacent constant elevation
angle planes leads to an interpolation of the radar data to each of
the selected (x, y, z) grid points.
CEDRIC enables the user to
perform various functional operations on the Cartesian data sets
generated by SPRINT.
Since radar scattering or reflectivity factor measurements are
6 "3
only linear when in units of mm m
rather than in dBZ, the preferred
method of interpolation should employ
^
6 —3
(mm m ) after which Z^R
is derived from Z^R = 10 log Z^/Zy as opposed to interpolating
Zjj ^(dBZ) and ZpR (dB).
Thus, in this study all (Z^, Z^R ) Cartesian
data points were obtained using the preferred method, that is, the
6 "3
(Zjj, Z ^ ) spherical data points were transformed to (Z^, Z^) in mm m
and interpolated to Cartesian grid points at 200 m intervals in the
(x, y) planes located at constant altitudes (z) separated by 300 m,
ranging from 2.1 to A.5 km MSL.
Fig. A.27 shows
CAPPI's obtained
from the volume scan between 1705:36-1707:31.
the areas where Z^
In Fig. 4.27(a) note
50 dBZ indicating high reflectivities and Z^R > 2
128
ZHldB Z I
20
liiilij'!.
30
•
40
30
E
20
> *.-
20
OJ
i
CL
O
10
0
1
IQC
O
Z
I
_
/'•‘v *c1
20
25
35
30
EAST of CP-2 (km)
(a)
Zqr (dB)
K
TniniiiiiM
::!:::ioi:iii:::::::
slilil> il!!!!l!!!& i1
iiHmiMSh
h
jiiS?!:
L Ift
\
nnifTTU
J
20
r
25
..........
. . . . T.:::
30
EAST of CP-2 (km)
Figure 4.27. Constant altitude (2.4 km MSL) PPI's of (a) Zjj
and (b) Z])r generated from the value scan
between 1705:36-1707:31 MDT during the 15 June
1984 event. Zr is the reflectivity factor and
Zd r differential reflectivity.
Rlmmh' )
20
50
I5
I0
NORTH
of
CP-2
(km)
10
:::::::::
::::::
V :K :I.
I5
20
25
30
35
E A S T of C P - 2 (km)
129
Figure 4.27(c). Constant altitude (2.4 km MSL) PPI of R generated from the
volume scan between 1705:36—1707:31 MDT during the 15 June
1984 event where R is the rainfall rate.
130
dB which shows that the event consisted of rainfall containing drops
of large diameter.
To compute the R field (Fig. 4.27(c)),
corresponding to the same area, the 1-section empirical relationship
of Table 3.2, modified to account for the decreased atmospheric
pressure in Colorado and corresponding increased terminal velocities,
was used.
Radar- estimated rainfall rates were obtained for all the
CAPPI's between 2.1 km-3.0 km in 300 m increments using the CEDRIC
software.
Based on the vertical profiles of the (Zy, Z^^) fields,
heights above 3.0 km most likely contained mixed phase hydrometeors,
including hail and graupel particles as opposed to rainfall.
Consequently, the average height of the CAPPI rainfall computations is
2.55 km which has a corresponding mean atmospheric pressure of 742 mb.
This reduced pressure alters the terminal velocities of raindrops
(Foote and du Toit, 1969) by,
v t = 1.12
v tQ
(4-6)
(m s ' 1 )
where v is the velocity of interest and
vq
is the velocity at MSL.
This changes the 1-section empirical relationship of Table 3.2 (used
for convenience to accommodate CEDRIC) to
(4-7)
R « 1.69 x 10"3 Zjj Zj^"1 *55 (mm h"1)
This is the relationship used to obtain the rainfall rates shown in
Fig. 4.27(c) at the height of 2.4 km.
area of R
The figure describes a wide
50 mm h 1 surrounding PAM station 15.
The series of
CAPPI's derived from the volume scans provide a time history of the
131
were obtained for the 19 volume scans, each consisting of A heights
which contain Cartesian grid points in 200 m (x, y) increments.
A.28 shows (Z-j,
Fig.
, R) 2.A km CAPPI's for a later volume scan which
occurred during the times 1716:A0-1718:31.
By comparing the CAPPI's
in Figs. A.27 and A.28 storm motion and development can be tracked.
For example, the storm area described by the high R values in Fig.
3.27 over PAM 15 moved over the PAM 11 station resulting in the heavy
rainfall rates recorded by this gage.
Thus the same region of the
storm was responsible for the event as recorded by both PAM stations.
Fig. A.29 shows a North-South vertical cross-section of the radar
observables (Zr *
passing through the PAM 15 location during the
volume scan between 1705:36-1707:31.
This and other RH1 scans
indicate that the regions below 3 km consisted primarily of rainfall.
This information was used to establish the CAPPI's to be used for
radar-rain gage comparisons.
As seen in this figure, although the
high 55 dBZ Z^ core of this storm extends up to A km in height, low
Zp^ ( 0.5 dB) values above 3.5 km indicate that hydrometers other than
rainfall, most likely dominated throughout the storm.
The estimation of the wind vectors, needed to locate the radar
volumes at different elevations for comparison with ground-based
measurements, was achieved in two ways.
First, the surface wind speed
and direction data are obtained from the two PAM stations.
Their time
records indicate a significant shift in both parameters during the
event.
The surface wind speed V(m s *) and direction 6(deg) were
found to be
132
20
20
CM
5
QO
I0
a:
25
30
35
EAST of CP-2 (km)
(a)
Zq r (dB)
ft
m
\
,:X®.
N'
^
V
20
({
Cv*
*& A ' \
*X*'
rA J , ,
25
.........r>V; 'ft (£)
- 1'? 1 ( 0 *
30
EAST of CP-2 (km)
Figure 4.28. Constant altitude (2.4 km MSL) PPI's of (a) Zr
and (b) Zjjr generated from the volume scan
between 1716:40-1718:31 MDT during the 15 June
1984 event. Zr is the reflectivity factor and
Zd r differential reflectivity.
20
V «
50
of CP-2
(km)
10
I5
:S:-' A :
10
NORTH
50
20
25
30
35
E A S T of C P - 2 (km)
Figure 4.28(c).
133
Constant altitude (2.4 km MSL) PPI of R(mm h -1) generated from
the volume scan between 1716:40-1718:31 MDT during the 15 June
event where R is the rainfall rate.
134
Z M (dBZ)
ffi
1111 k"'il i1111!
5
7 .5
10
NORTH of CP-2 (Km)
(a)
4 .5
i
0.5
3.5
0.25
liiil?
:
0
(b)
2 .5
5
7 .5
10
I 2 .5
I5
NORTH of CP-2 (km)
Figure 4.29. RHI's of (a) Zjj and (b) Zjjr generated from the volume
scan between 1705:36-1707:31 MDT during the 15 June
1984 event which shows a North-South vertical crosssection of (Zjj, Zd r ) passing through the PAM 15 site
located 27.8 km east of CP-2. ZH is the reflectivity
factor and Zd r differential reflectivity.
135
V * 5.7 m s"1
;
0 - 202°
for t < 1728
MDT
V = 3.3 m s'1
;
0 - 101°
for t >_ 1728
}
MDT J
V * 9.4 m s ^
;
0 = 173°
for t <. 1713
MDT
V - 5.5 m s"1
;
0 -
for t > 1713
MdT
for PAM 11
and
86°
after averaging once the Indicated time periods.
}
J
for PAM 15
The results were also
compared with the wind vectors obtained from the movement of the storm
cell as seen in the time history of the CAPPI's at different heights.
For PAM 11, the storm speed and direction were estimated to be 5.8-6.1
m s * at 197°.
This result compares very favorably with early portion
of the average surface estimation for PAM 11.
Applying the same
approach to PAM 15 produced a wind speed of 9.6-10.1 m s * at 190°-200°
which again matched very closely the radar-derived storm motion
estimates and provided evidence to support use of the PAM wind
measurements in the analysis.
The comparisons between the time records of the radar and rain­
gage data involved estimating the delay times of the raindrops,
corresponding to CAPPI's at different heights.
The method of
averaging the PAM rainfall rate data also affects the choice of the
volume from which the radar data comes.
Representative values of
for each CAPPI height in the vicinity of the PAM stations led to
estimatesof corresponding median volume drop sizes (Eq. 3-15) from
which approximate bulk terminal velocities are obtained (Eq. 4-6).
Expected fall time of raindrops are then computed and added to the
radar observation times in order to match the radar estimated rainfall
136
estimates from different CAPPI's with the PAM rainfall rates.
For
example, for CAPPI data at 3.0 km, a representative Z ^ of 2 dB indi­
cates that D q * 2.62 mm.
This leads to a bulk terminal velocity of
8.5 m s * and an estimated time for the raindrops to reach the surface
(1.5 km MSL) of 176 s, a delay time of nearly 3 min for this CAPPI.
Horizontal wind speed and direction indicate the grid points where the
radar data from this CAPPI should be selected.
This process was
repeated for every volume scan and CAPPI height of interest.
As in
was chosen
Section A.2, the horizontal resolution of the radar data
to accommodate the spread of the expected fall velocities
caused by different drop sizes.
was found to be 8.5 m s *
Since the expected bulk fall velocity
for a 2.A km CAPPI (mean height), this
would correspond to a representative fall time of around 105 s.
A
fall velocity spread of A m s * would then result in a horizontal
resolution of around A20 m which compares favorably with the 200 m x
200 m square grid from which the radar data are derived for comparison
with the gage.
The radar and PAM data are both averaged to decrease their
variability and to obtain comparable spatial (radar) and temporal
(raingage) resolutions.
After the initial interpolation, the radar
data at four adjacent Cartesian grid points on the constant-z plane
were spatially averaged;
the overall radar averaging procedure is
estimated to yield standard errors for
and Z^^
and 0.1 dB, respectively (Sirmans et al., 198A).
of less than 0.5 dBZ
To establish an
appropriate PAM data averaging time duration, the vertical resolution
of the interpolated radar data was taken into consideration.
The
137
combined vertical angular width of the interpolated elevation scans
and the radar beamwidth is around 2.1
, corresponding to a vertical
resolution of 1.3 km at the range of PAM 11.
Taking 8.5 m s * as the
representative terminal velocity for the raindrops, gives a transit
time of around 153 s.
This analysis led to a choice of using running
averages displayed every minute for both PAM station raingage data
sets to compare with the radar estimates.
4.3.2
Raingage-Radar Comparisons
A comparison of the radar estimated rainfall rates with those
obtained from the rain gages is shown in Figs. 4.30 and 4.31 for the
PAM 15 and PAM 11 stations, respectively.
Radar estimates include the
Marshall-Palmer (1948) (Eq. 3-25) and the Jones (1956) thunderstorm
Z-R relationships,
Z - 486 R 1,37 (mm6m'3 )
(4-8)
in addition to those obtained from the 1-section empirical Z^
relationship.
As for the (Z„ , Zp^)-R relationship of Eq. 4-7, the Z-R
relationships should also be modified for increased fall velocities of
raindrops due to altitude.
However, this was not done in this study,
since it would have increased the estimated rainfall rates (by about
7%) which are already overestimated using the unaltered Z-R
relationships (see Table 4.5).
Rain gage data are 3 min running
averages of the 1-min PAM rainfall data.
The rainfall event spans
different time periods for the PAM 11 and 15 stations.
For PAM 15,
the rainfall rate reaches a peak value of 122 mm h * at 1708 within 3
10
15
20
TIME(min)
(a)
150---
A.
; \
4* PAM 15
* RZ0(*
O Rj
R(mmh
100--
50--
0--0
(b)
5
10
IS
20
TIME(min)
Figure 4.3G. Time record of R obtained from PAM 15 raingage measurements.
Also shown are the radar estimates R z d r derived from the
empirical relationship using (Zjj, Zpp) and (a) R^p derived
from the Marshall-Palmer relationship and (b) Rj derived
from the Jones(1956) relationship of Eq. (4-8). Zero time
corresponds to 1700 MDT. R is the rainfall rate, Zjj is
the reflectivity factor and Zpp is the differential
reflectivity.
ao-r-
Muiiujy
40---
20-
-
20
40
TIME(min)
(a)
00-r-
+ PAM I
* rid*
O Rj
60--
(( tjujuj)y
40---
20--
O;
20
(b)
25
30
40
TIME(min)
Figure 4.31. Time record of R obtained from PAM 11 raingage measurements.
Also shown are the radar estimates R z d r derived from the
empirical relationship using (Zr , Zjjr) and (a) Rj^p derived
from the Marshall-Palmer relationship and (b) Rj derived
from the Jones (1956) relationship of Eq. (4-8). Zero time
corresponds to 1700 MDT. R is the rainfall rate, Zjj is the
reflectivity factor and Zpp is the differential reflectivity.
1A0
min after the beginning of the event.
accumulated a total of 9.9 mm.
_
h
It lasted around 14 min and
For PAM 11, the peak R reached 60 mm
i
at 1729 after a slower, more steady increase of around 12 min.
The event lasted around 23 min and also accummulated 9.9 mm.
Examination of the plots show that R^ d r f ° H ° ws the variations in the
surface data more closely than do the Z-R relationship estimates.
Similarly, the NSED result of 30.6% for R^DR indicates an
improvement of 14.8% and 23.3% over R^p and Rj which are 45.4% and
53.9%, respectively.
Regarding the PAM 15 comparisons in Fig. 4.30,
the significant Z-R overestimates in the beginning of the storm
deserve special examination.
This result is believed to be
attributable to the presence of very large raindrops in the radar
scattering volume which are not accounted for through an averaging
procedure of rainfall estimation as is represented by use of a Z-R
relationship.
In this case, Z^p accommodates for this large drop size
and accordingly modifies the rainfall rate estimation by reducing the
Zpp dependent proportionately constant between R and Zp.
a Zg of 55dBZ at
Z^p = 2 . 5 and 3.2
R(55,
2,5) - 129 mm h"1 and
R(55,
3.2) - 88 mm h'1
compared to R^p
= 100 and Rjy =
For example,
dB would give
146 mm h
At the beginning of this
event, Z^p was quite large and exceeded 3.0 dB.
Thus, the data and
sample computations support the explanation given here to explain the
behavior of Z-R relationships relative to the Z^p method of rainfall
141
150
100
-C
E
E
cr
o
M
CL
50
0
50
100
150
R ( m m h " ')
Figure 4.32. Scatter plot of RgjjR derived from the empirical rela­
tionship using (Zfl, Zd r ) versus R obtained from the
measurements of both PAM 11 and 15 raingages where R
is the rainfall rate.
150-r-
1 0 0 --
100---
(mmh
(mmh
150 -T-
a_
2
a:
oc
5 0 ---
50---
ir
0
100
50
150
R l m m h ' 1)
Figure 4.33. Scatter plot of
Marshall-Palmer
R obtained from
raingages where
rate.
Rjjp derived from the
relationship versus
the PAM 11 and 15
R is the rainfall
0
100
50
150
R l m m h ' 1)
Figure 4.34. Scatter plot of Rj derived from
the Jones (1956) relationship of
Eq. (4-8) versus R obtained from
the PAM 11 and 15 raingages where
R is the rainfall rate.
N)
143
rate estimation.
Interestingly, this same phenomenon may be
applicable to the time centered around 20 min in the data for PAM 11
in Fig. 4.31.
It can be argued from the time plots of R^p and Rj that the
raingage measurements lagged R^p and Rj by an interval of around 1
min.
Accordingly, R^p and Rj were moved forward by 1 min in time, but
their standard error results improved only slightly (43% for R^p and
51% for Rj in NSED), while NB, as expected, remained the same.
Therefore, adjusting the Z-R results to match better an apparent
discrepancy in timing did not significantly affect the conclusions.
4.3.3
Remarks
The results obtained in this experiment illustrate that the
(Zjj-Zpp) method of estimating rainfall rates works very well in heavy
rainfall and also improves the estimates obtained from Z-R relation­
ships employing a single radar parameter.
This experiment differs
from the other case studies described previously, since it employs
raingages for ground truth and presents results for significantly
higher rainfall rates.
The rainfall rates are comparable to the
simulated Central Illinois event, the conclusions of which are also
tested in this case study.
Those simulations predicted an improvement
in the normalized standard error between the Z^p technique and the M-P
relationship of more than 10% in the range 5 <. R (mm h *) < 50 and 12%
in the range 50 £ R (mm h *) < 220 as opposed to the 15% improvement
found in this case study.
The results of this experiment are also comparable to other case
studies.
The 29 October 1982 Central Illinois experiment described in
Section A .1 resulted in a 9.1% NB and 2A.A% NSED for
and 35.8% NSED for the best Z-R rainfall estimation.
and 30.0% NB
Goddard and
Cherry (198Ab) obtained 11% bias and 32% standard deviation for their
RgQ£ computed from a gamma model relationship with M * 5 and A0% in
standard deviation for their best fit Z-R relationship.
As expected,
all of these results are higher than the errors found in the
simulations of Seliga et al. (1986) [A-6% in NSED for 5
220].
R (mm h *)
Factors affecting the experimental results and the possible
error sources were outlined in Section A.1.3.1.
CHAPTER 5
PREDICTION AND COMPARISONS OF C-BAND REFLECTIVITY PROFILES
FROM S-BAND MEASUREMENTS
5.1
Introduction
The reflectivity factors measured by a radar operating at an
attenuating wavelength can be adequately predicted by using the
reflectivity factors at horizontal and vertical polarizations measured
at a non-attenuating wavelength (Goddard and Cherry, 1981, 1984a;
Leitao and Watson, 1984; Aydin et al., 1983a; Bring! et al., 1986).
This capability has important ramifications for understanding rainfall
effects on microwave communication systems when propagation through
storms occurs.
In this chapter, the predicted and measured reflec­
tivity profiles of a C-band radar (5.45 cm wavelength) are compared to
test this hypothesis.
The prediction employs the horizontal reflec­
tivity factor (Zjjiq ) and differential reflectivity (Zj^) obtained from
the dual polarization measurements of an S-band radar (10.7 cm wave­
length) combined with an approximate geometry describing the problem.
C-band radars are currently used in many cloud physics and
precipitation studies and also as part of multiple-Doppler radar
systems.
At this wavelength, attenuation effects often have to be
taken into consideration, since the observed reflectivity factor at a
given range gate includes effects due to the two-way attenutation
experienced by the propagating electromagnatic wave along the path
within the storm to that gate.
For this reason, it is convenient to
145
146
denote the observed C-band reflectivity factor, including attenuation
effects, as "apparent."
Thus,
is defined as the apparent or
measured C-band horizontal reflectivity factor in contrast to the
unattenuated Z^,..
Attenuation effects at C-band are significant for high rainfall
rates while at S-band they are negligible, typically less than 0.1 dB
km
at R ■ 100 mm h ^ (Battan, 1973).
Radar studies of attenuation
were considered extensively by Battan and Doviak and Zrnic (1984).
Following the pioneering work of Hitschfeld and Bordan (1953), Joss et
al. (1974) and Atlas and Ulbrich (1974) reported on comparisons of the
theoretical and experimental results of radar attenuation within
rainfall cells.
Prediction of reflectivity factors at different
wavelengths using an attenuation-correction technique was considered
in various dual wavelength studies to distinguish hail from rainfall
within a storm.
For example, Eccles (1975, 1979), Jameson (1977),
Jameson and Heymsfield (1980) and Tuttle and Reinhart (1981) employed
empirical techniques using either the returned powers at an
attenuating and a non-attenuating wavelength or a single
attentuation-reflectivity relationship to compensate for attenuation
and correct the hail signal.
S-band polarization measurements were utilized in a rayprediction technique for 3.2 cm radar reflectivities by Aydin et al.
(1983b, 1984) to confirm the presence of hail along the ray.
Other
attenuation studies using dual polarization were reported by Leitao
and Watson (1984), Goddard and Cherry (1984), Goddard et al. (1981)
and Bringi et al. (1986) at 3 cm and smaller wavelengths.
147
This chapter outlines and tests a generic approach to obtain the
complete reflectivity profile of a storm cell at an attenuating
wavelength from non-attenuating
The procedure
is demonstrated at 5.45 cm wavelength, but is also applicable to other
attenuating wavelengths such as at X-band and possibly K -band.
5.2 Simultaneous Operation of CP-4 (5.45 cm) and CP-2 (10.7) cm
Radars
During the MAYPOLE '84 project in Boulder, Colorado, on 30 June
1984, a storm cell had been synchronously tracked by the CP-2 S-band
radar which is capable of dual polarization measurements and the CP-4
C-band radar operating in horizontal polarization at a location 28.6
km nearly due East of CP-2.
Both radars operated simultaneously
during the time period 1400-1443 MDT from which a single volume scan
from each radar was chosen for analysis.
The storm cell was fully
mature, having reflectivity factors above 50 dBZ during the selected
time period.
in Table 5.1.
A listing of the measurements for both radars are given
Note that CP-2 was operating in a pulse-to-pulse fast
switching mode where the number of pulses averaged for each record was
128 at each polarization.
Other radar specifications are given in
Chapter 2 and the Appendix.
Since the CP-2 and CP-4 radars were at different locations, the
data from these radars can't be compared in their radial coordinate
systems.
The elevation for the data from each radar changes
independently from the other as the range varies, and, although both
radars have comparable half-power beamwidths (0.96° for CP-2, 1.06°
for CP-4), the storm volumes corresponding to each radar beam differ
148
Table 5.1. Description of radar measurements
Volume scan period
Total volume scan time
Range of sector PPI
azimuth angle (deg)
Angular velocity (deg s
Elevation angles (deg)
CP-4 (5.45 cm)
CP-2 (10.7 cm)
1418:33-1421:12
1418:52-1422:02
2 min 39 s
3 min 10 s
268°-32°
12°-60°
15
4
o
0
1
-ts
o
Radar
0.5°-23°
Elevation steps (deg)
2°
l°-3°
Number of pulses averaged
(each polarization)
64
128
PRF
1667
960
Elevation (km)
1.49
1.75
Location:
Date:
Project:
Boulder, Colorado
30 June 1984
MAYPOLE '84
149
considerably due to differences in their ranges from the storm cell
and the elevation scan patterns.
Therefore, to compare the radar data
within the same volume along the path originating from CP-4, data from
both radars are analyzed using the interactive software CEDRIC (see
Section 4.3) for transformation from radar space to 3-dimensional
Cartesian coordinates, using the code's successive bilinear
interpolation scheme.
Linear values of Z ^
employed with this technique, and
interpolated Z ^
q
and Z ^
q
values.
q
,
an(* ^H5 are
values are obtained from the
After the transformation, the
processed data are described in CAPPI's at chosen grid locations.
From the original radar space data, the volume between the
heights 2.1 km-4.5 km was processed in 300 m elevation steps.
Two
hundred m horizontal grid spacings in each constant altitude plane
were chosen to make the interpolation compatible with the radar range
gate resolution.
CAPPI's for both radars can then be used for
comparison.
This is a reasonable approach, since the propagation paths of
CP-4 rays (at 4° elevation angle) within the chosen CAPPI (z ■ 3 km)
for this storm are such that the CP-z radar data, as described in this
CAPPI, are representative of what these CP-4 rays experience as they
propagate through the storm.
This experimental condition is
illustrated in Fig. 5.1 which indicates that the region of interest is
dominated by a single CP-4 elevation angle (4 ) PPI scan.
Note that
most of the 3 km CP-4 CAPPI is interpolated by CEDRIC from this scan.
The applicability of this approach was verified by comparing CP-2
CAPPI's at different heights around 3 km which were found to be very
similar.
Thus, using a more sophisticated approach (see Section 4.2)
(Km)
3 .5 -
MSL
4 .0 -
ALTITUDE
4 .5 -
CP-4 E L ^ = 2
CAPPI
3.0
2 .5 -
2. 0 «— STORM LOCATION— J
(CP-4J
O
10
20
30
40
50
RANGE FROM CP-4 (km)
150
Figure 5.1. Demonstrating the applicability of using CAPPI's for deriving CP-4
reflectivity fields affected by attenuation along ray paths.
151
for predicting attenutation effects along CP-A rays in this storm was
deemed necessary.
Figure 5.2(a) shows the CAPPI of Z ^
obtained from the CP-2 radar.
q
at a height of 3.0 km MSL
All radar plots in this chapter are
shown in a coordinate system taking the CP-2 radar as their origin.
This enables the data from both radars to be compared without
additional spatial transformations.
The contour lines for every 10
dBZ are indicated, and a high reflectivity core with values exceeding
50 dBZ and a peak value of 55.5 dBZ is also visible.
3.0 km is chosen to compare Z ^
q
with Z ^
The height of
and Z^^' as this height is
high enough not be affected by the ground clutter but lower than the
melting layer where the phase change from raindrops to mixed phase
hydrometeors occurs, since the attenuation effects deal with the
rainfall effects only.
In order to verify that the storm cell
consisted of only rainfall at this height, an examination of the
CAPPI's of Z^£ and R at this height, RHI scans of CP-2 data through
the storm cell and ground observations was performed.
shows the Z ^ contours for the same CAPPI.
Fig. 5.2(b)
A wide area of Zp^ values
exceeding 2 dB gives the indication that the central core of the cell
consisted of raindrops of large diameter (Z^^ = 2 dB implies D q = 2.62
mm from Eq.
3-15).
The R contours of this data shown in Fig. 5.2(c)
which are computed using the empirical (Z^, Z ^ ) relationship of Eq.
(3-5) and indicate a heavy rainfall core of R > 50 mm h ^ within the
storm.
The maximum R in this core was computed to be R ■ 1A0 mm h
Fig. 5.3 shows the apparent horizontal reflectivity Zjj,.' contours as
derived from the CP-A measurements.
Although both CP-2 and CP-A
35
50
30
30
20
25
NORTH
of
CP-2
( km)
40
v
20
5
20
E A S T o f C P - 2 ( k m)
25
30
152
Figure 5.2(a). Constant altitude (3.0 km MSL) PPI of Zh i q generated from the
CP—2 volume scan between 1418:52-3 422:02 during the 30 June
1984 event. ZHio is the S-band reflectivity factor.
153
35
05
E 30
_x:
OJ
I
CL
Z 25
o
X
f-
tr
o
z
20
I5
10
15
20
25
30
EAST of CP-2 (Km)
(b)
35
50
<\J
l
CL
O
25
o
X
h-
cn
O
Z
20
10
(c)
I5
20
25
30
EAST of CP-2 (km)
Figure 5.2. Constant altitude (3.0 km MSL) PPI's of (b) Zd r and
(c) R generated from the CP-2 volume scan between
1418:52-1422:02 during the 30 June 1984 event.
Zjjr
is the differential reflectivity and R is the
rainfall rate.
35
30
30
20
v • * *V
Q_
30
O
*.v •
25
X
o
jUinnc|j3rpi
Z 2 0
5
10
15
20
E A S T of C P - 2
25
30
( k m)
Figure 5.3. Constant altitude (3.0 km MSL) PPI of Zjj5 generated from the CP-4 volume
scan between 1418:33-1421:12 during the 30 June 1984 event. Zjj5 is the
C-band reflectivity factor.
.
!j£
4.8
50
40
:':K
30
X
Ul
^
20
'P.-.Or
x’.'i
'«:
2
I0
i-Ot
20
25
30
EAST of CP-2 (km)
E
4.
50
JXl
40
x
30
CO
20
LiJ
2.
I0
20
25
30
EAST of CP-2 (km)
Figure 5.4. RHI's of (a) Zhio generated from the CP-2 volume scan between 1418:52-1422:02 and (b) ZH 5
generated from the CP-4 volume scan between 1418:33-1421:12 during the 30 June 1984 event
Ui
showing an East-West vertical cross-section of (Zflio* ZH5) at y = 20 km. ZjjlO aiM* Zjj5
m
are the S-band and the C-band reflectivity factors, respectively.
4.8
Zonfe®)
-i—
i— i—
i— i— i— i— i—
i—
|— i— i— i—
i— i— i—
i— i—
i—
|— i— i—
i— i—
r
%.
0 .5
•
..........................
p i C p i i
« » ■ » »
I5
20
30
EAST of CP-2 (km)
(a)
4 .8
50
10
5
(b)
10
I5
20
25
30
EAST of CP-2 (km)
156
Figure 5.5. RHI’s of (a) ZDR and (b) R generated from the CP-2 volume scan between 1418:52-1422:02
during the 30 June 1984 event showing an East-West vertical cross-section of (R, Zjjr)
at y = 20 km. Zjjr is the differential reflectivity and R is the rainfall rate.
157
reflectivities exceed 50 dBZ, the high reflectivity contour area is
greatly reduced in the CP-A C-band reflectivity profile indicating
that the attenuation effects on Z ^ '
are significant.
Additional information on the structure of the storm cell is
described in the RHI plots of the radar parameters from both radars.
Fig. 5.4(a) is an RHI plot for Z ^
q
at y ■ 20 km for the storm cell.
Figs. 5.5(a) and (b) show the Z ^
and R fields for the same data set.
showing a vertical cross-section
Within the storm volume where the
high reflectivities ( Z ^ q > 50 dBZ) are observed, Z^^ > 2 dB and heavy
rainfall rates can be observed in the same region.
dB at x * 16.5 km corresponds to a region where Z ^
likely is in a region of melting graupel.
The dip of Z^^ < 2
< 40 dBZ and most
q
This should not affect the
analysis very much since it is a very small region within the storm
and since melting graupel is expected to behave similarly to rainfall
in its scattering properties (Aydin and Seliga, 198A).
the Zjjg1 corresponding to the same RHI plots.
Fig. 5.4(b) is
Note that the Z ^ ' > 50 dBZ
region is significantly reduced in size from the Z ^
q
contours
described in Fig. 5.4(a), although occurring at the same location.
Fig. 5.6(a) is an RHI plot of Z ^
at y ■ 22 km and the Z ^
q
q
showing the vertical cross-section
> 50 dBZ core above the surface.
The plot
outlines a wider section of the storm where the 3.0 km altitude
contains the Z^ > 40 dBZ region throughout most of the cell.
Z ^ and
R plots in Figs. 5.7(a) and (b), corresponding to the same plot,
indicate high Z ^ values and heavy rainfall rates throughout much of
this same height.
These results support the premise that the storm at
z ■ 3.0 km consisted primarily of rainfall.
Fig. 5.6(b) is the
.8
Cf
50
40
hX
30
O ;!
20
CD
LlJ
»;=v-•|-8-|-S-8t»-i|«-W'
X
20
10
(a)
25
30
EAST of CP-2 (km)
Z h 5WBZ)
I5
(b)
Figure 5. 6.
20
EAST of CP-2 (km)
RHl's of (a) ZH io generated from the CP-2 volume scan between 1418:52-1422:02 and
(b) Zjj5 generated from the CP-4 volume scan between 1418:33-1421:12 during the 30
June 1984 event showing an East-West vertical cross-section of (ZHio» ZH 5 > at y =
22 km. ZH io and ZH 5 are the S-band and the C-band reflectivity factors, respectively.
Ln
00
Zno(dB)
4 .8
0 .5
CD
Ll I
=1=2
S:
/
;
:-Sc
n.
7:
20
10
(a)
25
30
EAST of CP-2 (km)
R(mmh’ )
4.8
50
na -
10
ZE
CD
Ll I
=^2
20
10
(b)
EAST
25
30
CP-2 (km)
159
Figure 5.7. RHI's of (a) Zjjr and (b) R generated from the CP-2 volume scan between 1418:52-1422:02
during the 30 June 1984 event showing an East-West vertical cross-section of (R, Zjjr)
at y = 22 km.
Z^r is the differential reflectivity and R is the rainfall rate.
160
corresponding Z^,.' RHI plot deduced from CP-A measurements indicating
the decreased horizontal reflectivities due to attenuation.
the
> 50 dBZ core does not exist and that the Z ^ 1
is considerably smaller in extent.
Note that
> 40 dBZ core
Fig. 5.8 shows the ( Z ^ q , Zjjr)
scatter plot from the CP-2 radar for this volume scan.
The solid
curve in the figure is taken from Aydin et al. (1986) who described an
hail signal to differentiate rain and hail phase hydrometeors from
(Zh i q > Zpp) measurements.
region
The radar measurements are all in the lower
of the curve, suggesting the presence of rainfall as based on
their findings from disdrometer simulations.
Thus, the CP-2 radar
data strongly support the presence of rainfall throughout the entire
3.0 km CAPPI.
5.3
C-Band Specific Attenuation and Reflectivity Factor from S-Band
Measurements
The prediction of the C-band reflectivity profiles from S-band
utilizes empirical relationships relating the C-band specific
attenuation
Ajjg
and the reflectivity factor
Zjj^) measurements.
Z^,.
to S-band ( Z ^ q ,
The relationships used here were derived from drop
size distributions (DSD) collected during the field projects in
central Illinois in 1982 (OSPE) and in Boulder, Colorado, in 1983 and
198A (MAYPOLE).
More than 1800 DSD's with R > 0.1 mm h * were
employed for these derivations using 2 min running averages of 30 s
samples in order to reduce sampling errors in the DSD-derived
parameters.
The radar observables Z ^ g , Zy^g, Z ^ , Zjj,.,
Zy,., Ajj,. and
Ayj are computed from the DSD's utilizing the backscatter and extinc­
tion cross-sections for each drop size at 10°C.
The technique is
(dBZ)
70 C
Figure 5.8.
161
Scatter plot of ZR versus Zj)R obtained from the CP-2 volume scan between
1418:52-1422:02 during the 30 June 1984 event. The solid line is the
rainfall boundary defined by Aydin et al. (1986). Both negative and
large values of ZDR at low ZR are thought to be due to ground clutter.
ZH is the reflectivity factor and Zd r differential reflectivity.
162
similar to the simulations used to compute the empirical R/Zy, M/Z jj
and D q versus
relationships described in Chapter 3.
Although the
prediction procedure in this study involves only A^,., Z^,. and
in
relation to Zj^, other combinations of horizontal and vertical
polarizations for the same parameters were also obtained and are
presented here for possible future reference.
Fig. 5.9 shows the variation of A ^ / Z ^ g , A ^ / Z ^ q , ^ 5 ^ 1 0
versus Z^^ where
(dB).
^
are in (dB/km),
y^g in (mm^ m ^ and Z^^ in
The variations of these plots suggest that a least squares
polynomial fit in the form
V v 5 " ^ . V I O ^ O + al^DR + • • • +
ajfon
) (dB/km)
(5-1)
would suffice to describe the relationship between parameters.
The
order of the polynomial was decided after fitting polynomials of
increasing order to the actual plots, computing the fitted values for
each data point and examining the difference between the empirical
fits and the actual data.
The results of the polynomial fit of order m = A are tabulated in
Table 5.2 which gives the coefficients of the polynomials for each of
the Ay
versus
Z ^ relationships.
Fig. 5.10 shows the
fitted curve for A ^ / Z ^ g versus Z^^ used in the predictions.
The
curve follows very closely the plot of Fig. 5.9(a) showing
the actual
disdrometer simulations.
the error
Fig. 5.11 shows the magnitude of
between the actual and the predicted values of the attenuation
A jj,. ) for a polynomial fit of order m = A.
This procedure
(A^.-
was used
for different m values, and the errors were found to decrease as m
0 1 K)
0.9
0.9
0.8
0.8
0.7
0.7
0.6
Ji 0.6
(c Ui g U J U J j O I H z / j u i ^ / g p )
in
0.5
0.5
0.4
>0.4
0.3
CD 0 -3
«
0.2
0.2
0.5
(a)
Figure 5 . 9 .
2.5
I5
2.0
D I S D R O M E T E R Z 0R (dB)
.0
3.0
3.5
0.5
(b)
.0
1.5
2.0
2.5
3.0
D I S D R O M E T E R Z 0 r (<1B)
Variation of (a) A h s / Z j h o a n d
A H 5 / z v l O versus ZDR for disdrometer-derived distributions
[see next page for (c) and (d)]. Ajj5 is the C-band specific attenuation at horizontal
polarization and Z m g , Zy^g S-band horizontal and vertical reflectivity factors, respec­
tively.
is the differential reflectivity.
0.9
0.9
o .e
O.S
0.7
0.7
£
£
0.6
0.6
A V3(dB/km)/Zmo(mm6 m
io
0.5
<0
0.3
0.4
> 0.4
3
CD 0.3
0
in
0.2
0.2
0.1
0.5
(c)
1.0
2.0
D I S D R O M E T E R Z DR (dB)
3.0
3.3
0.5
(d)
0
1.3
2.0
2.3
30
D I S D R O M E T E R Z 0„ ( d B )
164
Figure 5.9. Variation of (e) Av s /Zjj^q and
A y S ^ ^ l O versus Zp^ for disdrometer-derived distribution
[see previous page for (a) and (b)]. Ayj is the C-band specific attenuation at vertical
polarization and Zh ^q » ZV10 S-band horizontal and vertical reflectivity factors, respec­
tively. Zp^ is the differential reflectivity.
165
0.9
0.8
0 .7
Z 0.6
rO
0.5
x 0 .4
Q-X
0.2
0.5
0
1.5
2.0
2 .5
3 .0
DISDROMETER ZnR (dB)
p
Figure 5.10.
Variation of predicted Ah 5 /Zhj_q versus ZpR for the
P
disdrometer-derived distributions where Ajj5 is derived
from the empirical relationship given in Table 5,2 in
the form of Eq. (5-1).
Ajj5 is the predicted C-band
specific attenuation at vertical polarization, S-band
horizontal reflectivity factor and Zqr differential
reflectivity.
166
to-I
.
+
:* 2 ? %
W
M 8P) ( s2 v - SHV)
>"3
^ iju
+#** ± +
*♦
M
-*i-4
10
*
&
M
T^fr‘^3§t^35Er
f
y s ^ + +.
+
++ +
*
< ii5 p fs & fs £ ?
+
'
fit*
v *-t
'
* *;{
^
0.5
+
+
+• jCu^ri-«"*L •f> + +
10
*
+H-
+
a.*
1.0
1.5
2.0
2.5
3.0
D ISD R O M E TE R Z 0R (dB)
Figure 5.11.
Errors between the actual and the predicted values of
the attenuation (Ah5 -A§ 5 > versus Zjjr for disdrometer
derived distributions. aJj5 is derived from the
empirical relationship given in Table 5.2 in the form
of Eq. (5-1). Afl5 is the C-band specific attenuation
and Zp£ differential reflectivity.
167
Table 5.2. Disdrometer-derived specific attenuation empirical
formulas* for 5.45 cm specific attenuation - 10.7 cm
reflectivity factor and differential reflectivity
relationships.
Coefficients
al
ao
a 2
a4
a3
(I)
6.460xl03
1.109xl05
3.441xl05
-2.117xl0S
3.325xl04
(II)
-7.559xl0 2
1.636xl05
1.895xlOS
-1.557xlOS
2.754xl04
(III)
7.494xl03
1.042xl05
3.861xlOS
-2.017xl0S
2.902xl04
(IV)
7.690xl02
1.528x105
2.424xlOS
-1.654xlOS
2.702xl04
Fig. 5.8(a):
(II)
Fig. 5.8(b):
(III)
Fig. 5.8(c):
(IV)
Fig. 5.8(d):
^H5 = ZH10/(a0+alZDR+a 2ZDR+a3 ZDR+a4 ZDR^
^ 5 = ZvlO/(aO+alZDR+a2ZDR+a3ZDR+a4ZDR)
\5
" ZH l 0 ^ a0+alZDR+a2ZDR+a3 ZDR+a4 ZDR^
ii
m
(I)
Zvl0/(a0+alZDR+a2ZDR+a3ZDR+S4ZDR)
168
increases to A after which they remained relatively stable.
2
% of the predicted values exhibit errors of more than
0.01
Less than
dB/km with
p
the highest error being 0.0A dB/km for
•
The error rates of the
fitted curves for m ■ A are outlined in Table 5.2, using Eq. (3-21)
and Eq. (3-22) for NB and NSED.
the predicted A a r e
For A^,. (dB/km) > 0.05, the errors in
1.8% in NB and 3.3% in NSED.
For 0.01 < Ajj,.
(dB/km) < 0.05, the errors are 0.1% in NB and 6.9% in NSED.
the empirical polynomial fit procedure predicts A ^
p
Clearly,
very closely to
actual A^^.
The prediction of C-band profiles also necessitated a scheme for
deriving
from Zjj
values from observed ( Z^g* Z^^), since Zjj
y^
differs
due to raindrop shape and possible Mie-region (large
electrical size) effects.
Effective reflectivity factors for the 5.A5
cm and 10.7 cm measurements can differ by more than 1 dB for large
drop diameters as observed from the ratio plots given in Fig. 5.12
which are plots of the ratios Zjjj/Zj^q, ^
Zys/ZviQ versus Z^^.
5 ^ 1 0
’ ^
and
5 ^ 1 0
A polynomial similar to Eq. (5-1) in the form
^H,V5 " ^H,V10^0 + biZDR + • • • +
is suggested from these DSD-derived simulations.
^mm
m
)
(5-2)
The results of the
polynomial fit of order m * A for these relationships are tabulated in
Table 5.3; as with the previous results, m s A was found sufficient to
describe the curves.
The Z^ ^
polynomial fits to these curves
resulted in smaller errors than the previous attenuation relationships
due to the less complex behavior and spread of the curves.
For
reference, the fitted curve of Zjjj/Zjjjq versus ZDR is shown in Fig.
5.13.
169
ZV5 (mm6 m 3)/Zv 10(mm6 m'3)
1.4
1.2
1.0
0.8
HH-
0.6
0
0.5
Zvs (mm6 m'3)/Zn i olmm6 m"3)
<a>
1.0
1.5
2.0
2.5
3.0
3.5
3.0
3.5
DISDROMETER Z0R(dB)
0.8
0.6
0.4
0.2
0
(b)
Fipure 5.12.
0.5
1.0
1.5
2.0
2.5
DISDROMETER ZDR (dB)
Variation of (c) Zvs/Z^iq and (d) 2v5/^KlO versus Zrip
for disdrometer-derived distributions [see previous
page for (a) and (b)]. Zy 5 is the C-band vertical
reflectivity factor and Zjjiq» ^VlO S-band horizontal
and vertical reflectivity factors, respectively.
Zpp
is the differential reflectivity.
170
.4
fO
I
<0
E
E
.2
~o
>
N
.0
ro
I
tf>
E
E
0.8
in
>
N
0.6
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
3.0
3.5
DISDROMETER ZDR(dB)
(c)
ro
'E
E 0.8
E
u>
"o
X
N
\
0.6
in'
*E
E
E
<0
m
>
N
0.2
0
(d)
Figure 5.12.
0.5
1.5
2.0
1.0
DISDROMETER Z 0R
2.5
(dB)
Variation of (a) Zj^/Zhio and (b) Zns/Zyio versus Z^r
for disdrometer-derived distributions [see next page
for (c) and (d)]. zH 5 is the C-band horizontal reflec­
tivity factor and
^VlO S-band horizontal and
vertical reflectivity factors, respectively. ZpR is
the differential reflectivity.
1.25
ro
i
E
ID
E
1.0
E
o
'"H H +
*H- -H+
+
vl 0.75
ro
'e
CD
| 0.5
in
CL X
N
0.25
0.5
0
1.5
2.0
2.5
3.0
3.5
D I S D R O M E T E R Z np ( d B )
p
Figure 5.13.
Variation of predicted Zh 5/Zh 10 versus Zjjr for the disdrometer-derived
p
distributions where Zr 5 is derived from the empirical relationship given
p
in Table 5.3 in the form of Eq. (5-2).
Zj^ is the predicted C-band horizontal
differential reflectivity.
is the
171
reflectivity factor, ZRl0 S-band horizontal reflectivity factor.
172
Table 5.3. Disdrometer-derived reflectivity factor empirical formulas*
for 5.45 reflectivity factor - 10.7 cm reflectivity factor
and differential reflectivity relationships
Coefficients
bo
bl
b2
b3
b4
(I)
1.011
-2.548xl0"2
1.150xl0-1
-4.749xl0~2
7 .067xl0~3
(II)
1.008
-2.362xl0-1
1.033X10**1
-3.823xl0“2
5.356xl0~3
(III)
1.005
2.368X10”1
1.009xl0_1
-1.503xl0“2
6.499xl0“3
(IV)
1.004
1.786xl0"2
4.712xl0-2
-1.083xl0-2
2.305xl0~3
(I)
Fig. 5.11(a):
(II)
Fig. 5.11(b):
(III)
Fig. 5.11(c):
(IV)
Fig. 5.11(d):
ZH5
ZHl0/(b0+blZDR+b2ZDR+b3ZDR+b4ZDR)
^ 5 " Zvl0/(b0+blZDR+b2ZDR+b3ZDR+b4ZDR)
Zv5 " W
(b0+blZDR+b2ZDR+b3ZDR+b4ZDR)
Zv5 " ZvlO/(bO+blZDR+b2ZDR+b3ZDR+b4ZDR)
173
5.A
Prediction Procedure
This section describes the procedure to predict the 5.A5 cm
reflectivity factor profiles from the 10.7 cm ( Z^g,
measurements.
(1)
Z^)
This procedure is performed in five steps:
For each ray, Z ^
is estimated using Eq. (5-12) (Table 5.3)
for pre-selected range gates from the S-band ( Z^p, Z ^ )
measurements.
(2)
The C-band specific attenuation A jj,. for the same range gates
are estimated using Eq. (5-1) (Table 5.2).
(3)
Once Z^,. and
are computed for all gates, the
computations to find Z^
1
are initiated at the leading edge
of the storm cell defined as Z ^ q “ 20 dBZ.
Z^'
is then
computed at each range gate using the equation
^n'
" ZH5n “ 2r
\
i*k
*1151 ' r *H5n
(5‘3)
where,
r * the path length of the range gate
k = the leading range gate
Zjj,j " C-band reflectivity factor as predicted from ( Z^g* Z ^ )
before attenuation (mm
6
m
“3
)
Zjjj1 = apparent C-band reflectivity factor differing from
because of attenuation along the ray path in the storm
, 6-3.
(mm m )
(A)
The process is then repeated for all rays of interest propa­
gating through the storm cell.
174
(5)
Reflectivity profiles can then be obtained by determining
the contours of Z ^ '
from the individual range gate values.
In order to test the procedure, ^
5
' values, corresponding to
rays originating from CP-4 and separated by 2.5° in azimuth throughout
the core of the storm (30°-45° wide) and 5° at the edges, were
determined from the CP-2 predictions.
Fig. 5.14 illustrates this
procedure as applied to the storm of interest.
The contours outline
the predicted C-band apparent reflectivity factors ( Z ^ 1) using the
CP-2 S-band measurements.
In order to compare these to the actual
measurements from the CP-4 radar, the Z^,.' values at all range gates
were grouped in increments of 10 dBZ as noted in the legend.
values in this figure were obtained from the (Zj^q,
The Z^,.'
values
corresponding to nearest neighbor CAPPI grid points to the pre­
selected range gate locations of the CP-4 rays chosen for the
analysis.
For rays passing through the storm's core, CP-2 grid point
data within around
200
m of the gate locations were averaged to arrive
at (Zjj^q, Zjj^) profiles along the simulated CP-4 rays.
for these rays were taken to be 400 m apart.
Gate locations
For rays outside the
core, a similar procedure was performed except that the gate spacing
was 600 m and data were averaged from grid points within around 300 m
of the gate location to obtain the (Z^g, Z ^ ) profiles along the
simulated CP-4 rays.
Typically, the procedure required averaging 2-4
CAPPI grid points for every gate value along the CP-4 rays.
Fig 5.14 includes the resultant storm cell features of Z^,.'.
These are outlined in 10 dBZ increments within an area bounded by the
o
175
X
Zhs
(dBZ)
predicted from C P - 2 (S-band)
x < 2 0 dBZ
• 2 0 dBZ
A 3 0 dBZ
4 0 dBZ
5 0 dBZ
CP -4
(C-bond)
Figure 5.14.
Predicted CP-4 reflectivity values derived from CP-2
(^HlO* Zdr) measurements. The azimuth angles and the
gate spacing used in the prediction scheme for rays
along paths originating from CP-4 are also indicated.
Azimuth angles are measured CCW from north. Zjjio Is
the S-band reflectivity factor and Zdr differential
reflectivity.
176
20 dBZ contour corresponding to where the cumulative attenuation
computation was initiated.
5.5
S-Band Predictions and C-Band Measurements
Due to uncertainties in the absolute bias and the calibration of
CP-2 and CP-A radars, the Z^
1
values predicted from CP-2
values have to be matched before the comparisons.
The possible
sources of errors in the radars are explained in Chapter 2.
Two
methods have been used to determine the necessary calibration:
(1)
The predicted and measured Z ^ '
the range 20
Z^
1
(dBZ)
are compared for all rays in
30 in all rays since the attenua­
tion effects within this range are negligible.
The bias is
determined from,
~
B - ZH5
pi
^
Ml
'hs
(dB)
( 5 ’ A)
/n p'
~ m1
where Z^^
and Z ^
are the mean predicted and measured
Zjjj', respectively, assuming that the relative calibrations
of the radars are correct.
The computed B = 3.5 dB indi­
cates that CP-A reflectivity factor measurements under­
estimate the reflectivity factors obtained from CP-2 by this
amount.
(2)
This method applies a linear regression between all the
predicted and measured Z^ , . 1 values for the rays intersecting
the core of the storm (30°
<_ 0
<. A5°).
The regression
equation of the form
Zjj^' = m Z ^ * ' + B
(dBZ)
(5-5)
177
is used to determine the bias B.
In this form, a slope m
sufficiently different from unity would have indicated a
bias error for the Zj^q measurements as well, since this
would lead to erroneous attenuation predictions.
The
regression analysis resulted in a slope of unity and a bias
of 4.0 dB, in good agreement with the previous estimation.
The measured, results presented here for Z^
1
were corrected
by increasing the radar values by 3.5 dBZ.
Fig. 5.15 shows the predicted 5.45 cm reflectivity factor (Z^^1)
as an overlay on the actual CP-4 measurements.
The boundaries of the
predicted contours are in very good agreement with the measurements,
duplicating most of the features.
reflectivity areas, Z ^ '
The size and magnitude of the high
> 50 dBZ, are well matched.
Two two-way
accumulated attenuation is highest along the rays through the core of
the storm reaching 2.5 dB for the 35° CP-4 ray (see Fig. 5.14).
that ray the maximum Z ^
q
is 55.5 dBZ with
Along
= 2.56 dB, indicating a
one-way specific attenuation of 0.84 dB * km and a rainfall rate of
140 mm h ^ from Table 5.2 and the empirical relationship, Eq. (3-5).
For reference purposes, it is of interest to compare this result from
A-R and A-Z relationships.
The closest any A-R relationship listed by
Battan (1973) comes to the (Ztt.q , Zpjj)-predicted value of 0.84 dB km ^
is due to Wexler and Atlas (1963).
predicts a value of A ^
Their relationship (A = 0.004R)
= 0.56 dB km * which is 33% less than the
polarimetric-predicted value.
The A-Z relationship [A ■ 1.12 x 10
-4
A
Z
] of McCormick (1970) which assumes a M-P distribution results in
Ajjg ■ 0.31 dB/km which is 63% smaller.
The maximum Z^^ of 3.12 dB is
3 5 r —
-i—i— ■— n — r— |— i— i—i—i— n — i i i
Zh5 (dBZ)
(PRED.) (MEAS.)
20
40
30 -
V.
..
Hill,
50
NORTH
of
CP-2
( k m)
30
2 5 7
m
20
;
.........I
I
10
5
i i . i i i I i i i ■ i i i i » I i » .i.«» i i i i I i i i i i i i i j_
15
20
25
30
EAST of CP-2 (km)
5.
The predicted C-band CP-4 reflectivity factor contours (Fig. 5.14)
superimposed as an overlay on the actual CP-4 measurements (Fig. 5.J)
for the 15 June 1984 event
178
Figure 5.
179
along the 40° ray from north (with a corresponding Z ^ g ■ 53.4 dBZ)
indicating that Dq * 3.48 mm from Eq. (3-15).
These CP-2 values of
(Zhiq» Zj)r) map into a Z^,. of 52.3 dBZ which 1.07 dB lower than Z ^ q .
The corresponding one-way A^,. ■ 0.53 dB km *.
These results show that
cumulative attenuation and non-Rayleigh scattering effects on Z^^ can
result in significant differences between Z ^ q and Z ^ 1, especially
near the core of the storm when Z ^ q > 40 dBZ.
The method outlined
here estimates these effects using ( Z^g, Z ^ ) measurements.
Figs.
5.16 and 5.17 show Z ^ q compared to predicted and measured Z^,.' for
CP-4 rays with azimuth angles 35° and 40° CCW from north, respec­
tively.
The leading edge of the cell is at the range of 16 km for
both rays which extends to around 28 km.
corrected for the bias of 3.5 dBZ.
The measured Z^
1
is
The results indicate accurate
prediction of the apparent Z^,.' using this correction technique.
The
discrepancies in the trailing edges of Fig. 5.17 are most likely due
to ice contamination in the CP-4 CAPPI's which are derived primarily
from a PPI scan at 4° (see Fig. 5.1).
for the lower measured Z ^ '
This ice would readily account
°f around 2-4 dB between 24-27 km.
Fig. 5.18 shows the simulated results for Z^,.' had the CP-4 radar
been co-located with CP-2.
Since the core of the storm cell is elon­
gated in the CP-2 direction resulting in a longer path of high Z ^
through the cell, the maximum accummulated two-way attenuation at an
azimuth angle of 38.2° CCW from north is 3.3 dB, higher than the
earlier predictions for the current CP-4 location.
For a peak (Zj^g,
Zpp) of (54.5 dBZ, 2.96 dB), the peak A^^ is 0.94 dB/km.
The shape
G O - t-
t-HIO
-------------- Z H3 (pred)
+ + + + Z HS (CP-4 1
Reflectivity
(dBZ)
50
40 —
3 0 -
20
--
16
20
(a)
24
22
Range
from
CP-4
26
26
(Km)
00 - r -
Z hio
--------------Z H5 (pred)
4- + + + Z hs ( C P - 4 )
Reflectivity
(dBZ)
5 0 ---
40-
DO -
20 -
10
14
16
(b)
Figure 5.3
16
20
Range
6
.
from
26
24
22
CP-4
20
30
(km)
Spatial variation of reflectivity factors at S-band
measured by CP-2 compared with the predicted and the
measured reflectivity factors at C-band along the CP-4
rays with azimuth angles (a) 35° and (b) 40° CCW from
north.
GO
"
"
^H5
+ + + + ZH5 (pred)
Reflectivity
(dBZ)
50
-
40
30
20
-
22
24
26
28
30
Range from CP-2
32
34
36
(km)
181
Figure 5.17. Spatial variation of reflectivity factors at S-band measured by CP-2 and
the simulated reflectivity factors at C-band along the same ray originating
from CP-2 at an azimuth angle of 38.2° CCW from north. C-band reflectivity
values without accounting for attenuation (Zjjs) are also shown.
182
non-Rayleigh scattering
effects of the raindrops result in values of
Zjjg (dashed curve in the figure) being somewhat less than
and
The scatter plot of
the 35° and 40° rays are shown in Figs. 5.19
5.20, respectively.
Since the attenuation effects are more
pronounced for higher reflectivities, an equal or better match of the
predicted Z ^ ' with the measurements at these levels compared with the
lower reflectivities indicates that the prediction procedure works
satisfactorily.
A scatter plot of the data from all the rays within
the storm's core (Zj^
q
> 40 dBZ), corresponding to the 7 rays between
azimuth angles 30°- 45°, is shown in Fig. 5.21.
An error analysis of
these rays resulted in 2.4 dBZ in NSED with a mean Z^^ of 36.4 dBZ for
values of Z ^ '
Z^'
> 20 dBZ.
The error analyses for Z^^' > 30 dBZ and
> 40 dBZ gave similar results demonstrating that the attenuation
effects were accounted for satisfactorily.
5 .6
Summary
In this chapter, the apparent reflectivity profiles of a radar
operating at C-band were predicted using S-band (Zjj^q , Z ^ )
measurements at S-band at a different location.
relationships between (Zj^
q
The scheme used
, Z^^) and (Zj^, A ^ ) obtained from
simulations derived from disdrometer data.
The comparisons resulted
in good agreement between the measured and predicted apparent
reflectivity profiles at C-band for rainfall.
This was demonstrated
by a standard error of 2.4 dBZ for reflectivities in the range between
20 dBZ-55 dBZ.
The results support the use of the dual polarization
(ZfliQ* Zpjj) technique to predict scattering and attenuation effects of
o
20
40
60
ZH5(pred) (dBZ)
Figure 5.18. Scatter plot of the predicted and
measured reflectivity factors for
the CP-4 radar at C-band for the
ray with the azimuth angle 35° CCW
from north.
0
20
40
60
Z H5 (pred) (dBZ)
Figure 5.19. Scatter plot of the predicted and
measured reflectivity factors for the
CP-4 radar at C-band for the ray with
the azimuth angle 40° CCW from north.
00
u>
184
60
Z H5<CP-4)
(dBZ)
+
-h
40
20
20
Z H5 (pred)
Figure 5.20.
40
60
(dBZ)
Scatter plot of the predicted and actual reflectivity
factors for the CP-4 radar at C-band for even rays with
the azimuth angles between 30°-45° CCW from north.
185
narrow beam microwaves propagating through rain-filled media along
paths originating from other possible radar locations.
CHAPTER 6
OTHER APPLICATIONS
In this chapter the potential use of
tions is considered.
in two other applica­
These are the determination of the scavenging
rates of aerosols by precipitation and the possible role of (Z„,
radar observations in the measurement of vertical air velocities.
6.1
Aerosol Scavenging Rates
Precipitation scavenging dominates the aerosol removal processes
from the atmosphere and has been estimated to be responsible for as
much as 80% of total aerosol removal (Junge, 1963; Robinson and
Robbins, 1971; Reiter, 1971).
Although many studies have been done to
identify pollutant sources and their dispersal in the atmosphere,
limited research has been directed towards obtaining realistic removal
rates by precipitation.
Accurate estimation of the interaction of
aerosols and rainfall is becoming more important for their effects on
visibility, material damage to property, human health and welfare and
in climatic studies for their effect on the Earth's radiation balance.
Precipitation scavenging consists of two major processes (Semonin
and Beadle, 1974).
"Washout" occurs during the fall of hydrometeors
whose growth has substantially terminated whereas "rainout" refers to
the removal process within clouds that occursduring the formation and
growth of cloud particles.
The aerosol particles affected by
186
precipitation scavenging range from
0.001
ym to
10
ym in radius, and,
at different size categories, the effective scavenging mechanisms also
differ.
For aerosols less than 0.1 y m in radius, Brownian diffusion
causes the aerosol particles to coagulate with hydrometeors.
range of aerosols between
0.1
and
1
For the
ym, there is a significant minimum
in scavenging effects which is referred to as
the "Greenfield gap"
(Greenfield, 1957; Pruppacher and Klett, 1978), although field
measurements by Graedel and Frany (1974) indicated larger than
expected scavenging in this range which was attributed to electro­
static attraction.
Radke et al. (1980) also reported on airborne
measurements that scavenging effects were an order higher for
submicron particles.
Interestingly, the largest mass of aerosols
reside in this region, coinciding with a relative maximum in the
retention efficiency of the human lung (Beard, 1974a). Phoretic forces
(thermo- and diffusio-phoresis, motion of particles arising from
non-uniform heating and by concentration gradients, respectively) are
more effective in this region.
Aerosol particles in this size
category also serve as cloud condensation and ice nuclei and may
subsequently be removed through precipitation of the raindrops and ice
particles they formed.
Raindrops containing these nuclei are also
efficient by Brownian diffusion, phoretic forces, inertial impaction
and electrical forces (Grover et al., 1977).
1
For particles larger than
ym in radius, removal caused by inertial impaction with hydrometeors
dominates the scavenging process.
External electric fields also cause
the aerosols to collide with the hydrometeors resulting in their
removal from the atmosphere at these size ranges.
188
An overall scavenging coefficient for the below-cloud processes
or washout rate,
A(r) (s *) has been defined to incorporate different
mechanisms of removal of aerosol particles of radius r by rainfall
from the atmosphere to compute the fractional decrease in time of the
particle concentration (Chamberlain, 1953; Engelmann, 1970).
fDmax
A(r) =
A(D) N(D) vfc(D) E(r,D) dD
(s
-i
)
(6-1)
0
where E(r, D) is the dimensionless scavenging efficiency of raindrops
of equivolume diameter D for particles of radius r and A(D) is the
horizontal cross-sectional area of raindrops.
A(D) vfc(D) E(r, D) is
the volume swept out per second by a raindrop of diameter D falling
with the terminal velocity vfc.
Hence, for a raindrop size
distribution N(D), A(r) is the fractional number of particles of size
r removed in one second.
The particle mass concentration remaining in
the air at a particular time t after initiation of the washout process
is given by
M = Mq exp(- A(t - tQ )) (g m 3)
where Mq is the initial mass concentration at time tg.
(6-2)
Eq. (6-2)
shows that removal of aerosol particles from the atmosphere is an
exponential decay process where the scavenging rate, A determines the
half-life of the scavenged particles, (t - tg) = 0.693 A *(r).
Eq.
(6 -1 ) shows the dependence of the scavenging rate, A on the drop size
distribution (DSD).
189
While determining A, Dana and Hales (1974) and Hill and Adamowicz
(1977) employed the DSD given by Best (1950) in their scavenging
models.
Slinn (1974) reviewed the various empirical DSD's used in the
scavenging studies and evaluated Eq. (6-1) as a function of mean
volume drop diameter D through an assumed empirical relationship
between R and D.
In all of these, as in most scavenging studies, A is
given as a function of R and the aerosol particle size.
DSD effects
are often ignored even though they can cause large discrepancies in
aerosol precipitation scavenging rates as pointed out by Slinn (1974).
6.1.1
Scavenging Rates
Since the
method estimates N(D) from (Z^,
it can
conveniently be employed to obtain the scavenging rate of aerosols
under different rain storm conditions.
Eq. (6-1) shows that for a
monodisperse aerosol size distribution, A ■ A(r, D) is a function of
DSD only.
For a particular N(D) and particle radius r, A should then
be related to the radar parameters as A * A(Z„ , Zj^) similar to the
estimation of the rainfall parameters R and M (Chapter 2).
The first step in computing A for different DSD's
is to obtain
the scavenging efficiency E(r, D) for a range of particle radii and
drop diameters.
Scavenging efficiencies are often taken to be equal
to numerical collision efficiencies of aerosols collected by water
drops.
This relationship assumes an adhesion efficiency of unity
which indicates that water drops retain all the particles colliding
with them as shown by the experimental findings of Weber (1969).
Determination of the numerical collision efficiencies have been
190
studied by various authors (Beard, 1974a,b; Beard and Grover (1974);
Grover et al., 1977; Wang and Pruppacher, 1977; Wang et al., 1978;
Radke et al., 1980).
In this section, scavenging efficiencies are
computed for the 20 drop size categories of the Joss-Waldvogel type
disdrometer and for particle radii of 0.2, 0.5, 1.0 and 2.0 y m based
on the tabulated numerical collision efficiencies of Beard (1974b).
Values for the necessary drop and particle sizes were found by
interpolation.
The drops and the particles were both assumed to be
unchanged, although computations are also possible for a moderately
charged case.
The simulated two-parameter relationships
A■A(v w -W l V 2
<6-3)
were determined employing the computed E(r, D) for each drop and
aerosol size from the central Illinois disdrometer measurements of
October 1982 (Seliga et al., 1986).
6
Results of a multiple regression
analysis, derived from the linear relationships of the logarithm to the
base 10 of the parameters, are given in Table 6.1 for four different
aerosol radii.
Similar relationships, employing the actual rainfall
parameters R and Dq as A = A(R, Dq), are also shown in the same table,
although they are not directly observable by radar.
The high
correlation coefficients (p = 0.90-0.99) presented in the table
indicate a very good fit for A using two parameters.
Since in other
scavenging studies, A is usually determined using a single estimator
and an assumed
DSD,
the regression analyses for A were also performed
using Zjj and R as the only estimators.
Table 6.2 summarizes the
191
Table 6.1
Empirical formulas to estimate precipitation scavenging
rates A from both (Zjj, Zqr) and (R, D q ) . Relationships
were derived from multiple regression analyses using
disdrometer data and for different aerosol radii.
Correlation coefficients (p) for the regression rela­
tion relating the logarithms of the parameters are also
shown. R is the rainfall rate, Do is the median volume
diameter,
is the reflectivity factor and Zdr is the
differential reflectivity.
A - a Z ai Z 3 2
A
a0 H
DR
Aerosol Radius, a(pm)
/N
A
ao
ai
0.2
1.51x1O'9
0.5
2
*2
P
0.886
-2.69
0.91
.2 2 xl 0 " 1 0
0.941
-2 . 1 1
0.98
1.0
2.72xlO~10
0.938
-1.87
0.99
2.0
7.85xl0~8
0.884
-2 . 2 1
0.97
A ■ bo Rbl D ob 2
Aerosol Radius, a (pm)
£ 0
A
A
bl
b 2
P
0.2
1.46xl0"6
0.969
-2.46
0.98
0.5
1.74xl0- 7
0.982
-1.24
0.99
1.0
1.71xlO-7
0.978
-0.820
0.99
2.0
4.93xl0" 5
0.935
-1.53
0.99
192
Table 6.2
Empirical formulas to estimate precipitation scavenging
rates A from both Zjj and R. Relationships were derived
from regression analyses using disdrometer data and for
different aerosol radii. Correlation coefficients (p)
for the regression relationship relating the logarithms
of the parameters are also shown.
R is the rainfall
rate and Zh is the reflectivity factor.
A -
‘0
*HC1
A
Aerosol Radius, r (vim)
so
C 1
P
0.2
8.07xl0“8
0.392
0.81
0.5
5.01xl0“ 9
0.554
0.94
1.0
4.33xl0~
9
0.594
0.96
2.0
2.07xl0~6
0.478
0.91
A - d„
r “1
A
Aerosol Radius, r(ym)
P
do
0.2
7.10xl0"
7
0.602
0.90
0.5
1
.2 1 xl 0 “
7
0.807
0.98
1.0
1.34xl0~
7
0.855
0.99
2.0
3.15xl0~5
0.707
0.97
193
results of these analyses.
The lower correlation coefficients (recall
that these are for the logarithmic relationships, and therefore small
changes are significant) when Z^ is used as the only estimator of A
indicate that using (Z^, Z ™ ) provides an improved estimation for A.
Although using R as the only estimator of A results in better
estimations than when using only Z^, Fig. 6.1 illustrates the
disdrometer-derived dispersion between R and A in a correlation
diagram for the aerosol size r ■ 0.2 pm.
mm h
From the figure, for R < 10
the difference in A for the same R can exceed a factor of 30.
This illustrates the need to account for DSD
6.1.2
when estimating A.
Simulation
The relationships described in Table 6.1 and 6.2 can be used to
estimate the scavenging rates for natural rainfall to determine the
applicability of the (Zjj, Z_^) method.
of A for four different aerosol radii
Fig. 6.2 shows the variability
between (0.2-2 Pm).
The solid
lines indicate the scavenging rates computed directly from Eq. (6 .1 )
for actual disdrometer measurements.
The crosses indicate the radar
estimates of A computed using the (Z^, Z_j^) relationships of Table
6
.1 , whereas the x's denote the estimates using Z^ as the estimator
using the regression formulas in Table 6.2.
Estimates of A using R
and/or Dq are not shown since they are not radar observables,
although these relationships may be useful for future applications.
The results of Fig. 6.2 indicate a very good agreement for
the
empirical (Z„, Z^^) estimation for all aerosol sizes.
largest
The
discrepancy is seen at the aerosol radius r = 0.2 p m for A
< 10 ^ s
194
SCAVENGING RATE, A (s'1)
r = 0 .2 /x
R(mmh’ ')
Figure 6.1.
Computed scavenging rate A and rainfall rate R scatter
plot for aerosols of radius 0 . 2 ym corresponding to
disdrometer measurements from the rainfall event of
6 October 1982.
SCAVENGING RA T E , A (s'
r * 0.2 /X
1-6
N
w
—
re
0
20
40
60
80
I 00
I20
I40
I60
I 80
TIME(min)
Figure 6.2(a).
Computed and simulated time history of A for aerosols of radius 0.2 Urn corresponding
to disdrometer measurements from the rainfall event of 6 October 1982 where A is the
scavenging rate.
VO
Ln
R A T E , A ( s ' 1)
SCAVENGING
r6
>-7
.-8
o
20
40
60
80
100
I20
I40
I60
I 80
TIME(min)
Figure 6.2(b).
Computed and simulated time history of A for aerosols of radius 0.5 ym corresponding
to disdrometer measurements from the rainfall event of 6 October 1982 where A is
the scavenging rate.
196
R A T E , A ( s ' 1)
SCAVENGING
I Cf 6
*7
O
20
60
80
I 00
I20
I40
I60
I80
TIME(min)
Figure 6.2(c).
Computed and simulated time history of A for aerosols of radius 1.0 ym corresponding
to disdrometer measurements from the rainfall event of 6 October 1982 where A is the
scavenging rate.
197
SCAVENGING
RATE, A (s'
r3
.-4
1-6
r7
0
20
40
60
80
I00
I20
I40
I60
I80
TIME(min)
Figure 6.2(d).
198
Computed and simulated time history of A for aerosols of radius 2.0 pm corresponding
to disdrometer measurements from the rainfall event of 6 October 1982 where A is
the scavenging rate.
199
The Z„ estimates greatly overestimate the actual A for smaller A and
H
underestimate
s
for large A.
For example, for r = 0.2 P m and A >
10 ^
the 2L, method underestimates A by as much as a factor of A,
for A < 10 ^ s * the maximum overestimation is around a factor of 10.
Fig. 6.3 shows the superimposed scavenging rate time plots for the
same aerosol sizes (0.2-2.0 Pm).
This figure illustrates
dependence of A on size as well as the marked
decrease in
the
large
A for
aerosol sizes in the submicron range in agreement with the "Greenfield
gap."
The overall A differs by around a factor of 10 for aerosol
radii r * 2 pm and r * 0.5 pm and
a factor of A between r
* 0 . 2 pm.
rates occur at r = 2.0 pm.
The largest scavenging
* 2
pm and r
The results of these simulations demonstrate that the (Z
method should serve as a useful tool to estimate A, similar to its
utility for estimating rainfall characteristics and specific
attenuation.
The method provides an improvement over the current
practices of approximating
distribution employing R.
DSD with an empirical, single parameter
Therefore, using
scavenging rates should improve our knowledge of how storms cleanse
the atmosphere of aerosols via the washout process.
An additional
improvement in studying the scavenging processes may also be achieved
by considering the aerosol size distribution N(r) and its effects on
the empirical relationships derived in this chapter.
6.2
Vertical Air Velocities
Several methods of employing a vertically pointing pulsed-Doppler
radar for determining vertical air velocities within the radar beam
RATE, A ( s ' 1)
SCAVENGING
IO ' 6
20
40
60
80
1 0 0
I 20
140
I60
80
TIME(min)
Figure 6.3.
Computed scavenging rates A showing their variability with aerosol size in the range
< r < 2 ym.
0.2
200
201
have been proposed (see Section 6.2.1).
Pulsed-Doppler radar provides
the Doppler velocity spectrum of particles within the scattering
volume.
During a rainfall event, this spectrum includes the effects
of different terminal fall velocities of raindrops as well as vertical
air motions in the column.
using
This section examines the possibility of
as an estimator for the terminal velocity contribution to
the mean Doppler velocity seen by a vertically pointing radar and the
subsequent estimation of vertical air velocities.
6.2.1
Previous Studies
In earlier studies, several components of the Doppler velocity
spectrum have been utilized for vertical air velocity determination.
Particularly emphasized in early work were the mean Doppler velocity <v>
and
the minimum and the maximum velocities in the spectrum, v ^
vma x ’
and
^ore recently, the complete Doppler spectrum in multiple
wavelengths are under consideration.
The first study to determine
vertical air velocities in the rain region employed maximum downward
velocity. vmt>y (Probert-Jones and Harper, 1961).They concluded
changes in vmav as a function of height were due
that
to changes in
vertical air velocity assuming that static fall velocities of the
largest drops do not change.
Battan (196A) and Battan and Theiss
(196-6) extended this technique by employing the lower end of the
velocity spectrum (indicating upward velocity).
They added 1 ms
this bound to account for the fall velocity of the smallest
*to
drops.
They also indicated that turbulence broadens the edges of the spectrum
and drop size sorting would complicate the results.
Rogers (196A)
202
assumed a Marshall-Palmer (M-P) exponential distribution form of the
DSD and derived an empirical relationship between the reflectivityweighted fall velocity and
(Eq. 6-10).
Atlas et al. (1973)
concluded that the methods of Battan and Rogers are subject to
significant errors.
Hauser and Amayenc (1981) assumed an exponential
DSD in their three parameter (3P) method which does a linear least
squares fit to the relation linking the DSD parameters and the
vertical air velocity to the Doppler spectrum.
This method also shows
a large variability due to spectral broadening and the particular DSD
assumption.
Grosh (1983) suggested using
to estimate terminal
fall velocities and improve multiple Doppler wind measurements.
His
<vfc- ZDR> relationship was based on the vfc(D) and D q (ZjjR ) expressions
by Rogers (1964) and Seliga et al. (1981), respectively, and is not
considered to be a satisfactory relationship for <vt> *
Sangren et al.
(1984) reported on the comparison of the dual-wavelength or ratio
method (Rayleigh versus Mie scattering) proposed by Walker and Ray
(1974) and the previous methods.
They concluded that this method,
while in theory being the most accurate one with no a priori
assumptions on air motions or DSD,is extremely sensitive to poor data
quality such as mismatched pulse volumes and spectral artifacts.
More
recently, Wakasugi et al. (1986) proposed a direct method employing VHF
Doppler radars using a least-squares fit of six parameters of the
Doppler spectrum assuming an exponential form for N(D) and a Gaussian
form for turbulence.
203
6.2.2
Doppler Velocity Components
Measured Doppler velocity is weighted with the power
backscattered from the particles moving in the radar volume (Battan,
1973).
00
|
v S(v) dv
(6-4)
<v> = Zf!----------00
I
S(v) dv
where S(v) is the Doppler velocity spectrum obtained from the Doppler
frequency spectrum (v ■ Xf/2 ) and is related to the total average
power
by,
00
Pr
=J S(v)
dv
(6-5)
•00
In this analysis, for simplification all velocities including
vertical air motion and fall velocity which would represent motion
toward a ground-based radar, are taken as being positive.
Neglecting turbulence effects, the Doppler velocity (v) in S(v)
has two main components, the fall velocity of raindrops
v
and the
mean vertical velocity w of the air containing the same raindrops.
Since a unique relationship between the equivalent drop size and the
fall velocity exists, the components of the normalized Doppler
204
spectrum (Sn (v) * S(v)/Pr ) are related to
DSD through (Doviak and
Zrnid, 1984),
S (w + v ) dv = au (D)N(D)dD/n
n
t
C
n
(6 - 6 )
where r| is the reflectivity or scattering cross-section density.
From
Eqs. (6-4) and (6 -6 ), the mean Doppler velocity in still air, which is
the reflectivity weighted fall velocity
r
can be found from
D
max
<v > .
t
r
D
v tCfH (D)N(D)dD
(6-7)
max
aR (D)N(D)dD
For Rayleigh scattering and spherical raindrops, <vfc> can be expressed
as
rDmax
<v > =
t
,
v tN(D)D dD
-2— -----------fDmax
(6 - 8 )
N(D)D dD
Conceptually, the vertical air motion can then be estimated from the
mean Doppler velocity
<v> and the reflectivity weighted fall velocity
<vt> *
w = <v> - <vt>
(6-9)
To estimate <vfc>, Rogers (1964) employed an empirical expression for
vfc(D) and the M-P DSD to arrive at
205
<vt> = 3.8 z0,071
(6-10)
Sekhon and Srivestava (1971), assuming a different DSD for a
thunderstorm, derived a similar expression,
<vt> = 4 . 3 Z0
(6-11)
'0 5 2
Joss and Waldvogel (1970b) for various types of rainfall, found
<vt> = 2 . 6 Z 0 , 1 0 7
(6-12)
Rogers (1967) expanded his results to a two-parameter DSD and arrived
at
<vt> = 0.46 (Z/M) 1 / 3
(6-13)
where M is liquid water content in g m
-3
.
Since fall velocity of raindrops is a unique function of the
raindrop size, ZjjR is expected to be a good estimator of <vt> in that
it also is a unique function of the raindrop size for
good estimator of Dq.
radar which scans
X J> 3 cm and a
To determine <vt> using ZpR , a dual polarization
in n e a r l y horizontal planes would be required.
Combining these
measurements
w i t h Doppler spectrum
from a pointing
radarcould thenconceivably lead
When the vertical air motion
inmeasurements
to a measure
of w.
w is known, the DSD can be estimated
from
o„(D)
J*
n
6
= JL
(6-14)
z
Sn (w + v t) dvt = D 6 N(D)dD/z
(6-15)
where Eq. (6-15) Indicates that, given w, N(D) can be obtained from Zjj
and Sr (v ) without any a priori assumptions about the form of N(D).
The difficulty in employing Eq. (6-15) is its sensitivity to small
uncertainities in w.
Atlas et al. (1973) indicated that errors of
±0.25 m s * can cause errors of 100% in N(D).
The estimation of w
from Eq. (6-9) by the use of empirical <vt>-Zjj relationships such as
Eqs.(6-10), (6-11), (6-12) and (6-13) is also subject to large errors
and therefore limits further the quantitative estimation of N(D)
(Rogers, 1967, 198A).
The next section shows that a very good estimation of <vt> from
ZnD measurements appears feasible which in turn should lead to more
DK
reliable estimations of w from vertical Doppler spectrum measurements.
6.2.3
Model Computations
In order to obtain an empirical relationship that enables Z ^
to
be used as an estimator of <vfc> , simulations were performed using the
6
October 1982 central Illinois disdrometer measurements.
shows a plot of the reflectivity weighted fall velocity
Zpj^ for all the DSD's during this 3-h rainfall event.
Fig.
6
.A
<vfc> versus
The plot
indicates a very strong correlation between <vt> and Z ^
for all drop
sizes and suggests a power law relationships of the form
(6-16)
The results of the regression analysis based on the linear
relationships between the base
10
parameters are shown in Table 6.3.
logarithm's values of these
Similar
< V t > z (ms-1)
207
Z DR (dB)
Figure 6.4.
Reflectivity weighted fall velocity dependence on
ZD£ derived from disdrometer simulations where Zjjr
is the differential reflectivity.
208
Table 6.3. Constants of the <vt>“ZDR relationship derived from a
linear regression analysis of the relationship expressed
in base 10 logarithms. Corresponding 95% confidence
limits and correlation coefficients (p) are also given.
<vt> is the reflectivity weighted fall velocity and Zq R
is the differential reflectivity.
<V
Data Range
A
a
bv
"
3v Z]DR
A
avli
*v 2
6.72
6.71
6.73
6.92
6.90
6.94
V
6V
A
A
vl
bv 2
P
0.367
0.364
0.369
0.999
0.249
0.244
0.254
0.992
0.2 < ZDR (dB)
< 1.3
1.3 < ZDR (dB)
<
2.6
209
relationships in Chapter 3, the table gives the estimated value of the
coefficients (av , bv ) and their 95% confidence limits for the two
regions, 0.2
<. Z DR
<
1.3
dB >. and Z DR >. 1.3 dB.
This two-section
piecewise linear approach is preferred, since it helps reduce the
variation between the measured and estimated parameters over the
entire range of Z^R .
A similar analysis was also performed for
between
Dq ,
but the correlation
<vt> and Dq was not found to be as strong as <vt>-
indicating that Z^R is a better estimator of <vt> than Dq.
A
relationship similar to Eqs. (6-10), (6-11) and (6-12) was also
obtained for the same data, using Z^ as the estimator for <vt> .
6.5 shows the scatter plot of <vfc> with respect to Z^.
Fig.
Although <vt>
and Zjj are well correlated, the spread in <vt> for a given Zjj is
excessive compared to Z^R (Fig.
6
similar to the one performed for
<v >
.A).
A regression analysis for
Z^,
resulted in
A.O Zjj0 , 0 6 1
(6-17)
the coefficients of which are within the range of the empirical
relationships obtained by Rogers (196A) and Sekhon and Srivastava
(1971) (Eq. 6-10) and (Eq. 6.11).
These three
>
-Z^
relationships
as well as the relationship of Joss-Waldvogel (1970b) (Eq. 6-12) are
also plotted in Fig. 6.5.
None of these relationships produce results
as good as <vt>-Zjjp relationship.
6
.2.A
Proposed Experiment
The above findings regarding potential use of Z^R as an estimator
210
9
JW
8
7
in
5
SR
4
JW
3
0
I0
20
30
40
50
60
ZH(dBZ)
Figure 6.5.
Reflectivity weighted fall velocity dependence on Z^j
derived from disdrometer simulations, including
empirical <vt> - Z relationships due to Rogers (1964),
Sakhan and Srivastava (1971), Joss and Waldvogel (1970)
and this work, indicated as R, SR, JW and D,
respectively.
Z is the reflectivity factor.
211
for <v^> suggests several possibilities for testing its utility,
especially in conjunction with vertical Doppler velocity spectrum
measurements for estimating of N(D) and w.
One such possible
experiment is described here.
- A vertically-pointing radar performs Doppler spectrum
measurements continuously at one or more range gates to
determine S(f) from which S(v) is derived.
performed with
Simultaneous
a second radar, narrow sector scanning in the horizontal
plane at different elevation angles over the verticalpointing radar or in the vertical plane containing the
vertical-pointing radar.
Attempts should be made to match
the resolution volumes of the radars through siting of the
radar, choice of antenna patterns and spatial averaging.
Also, the elevation angle of the Zp^ radar should not exceed
1 0
° in order to minimize any errors due to aspect angle
complications.
- Having chosen common scattering volumes for analysis, Z ^
is used to estimate <vt >.
- w is then obtained from w « <v>-<vt> where <v> is the
reflectivity weighted mean Doppler velocity seen by the
vertically-pointing radar.
- N(D) is approximated from S(v) and w from
N(D) - ZD ' 6 - g £
Sn (i + vt )
where S (w + v.) = S (v).
n
t
n
212
- From N(D), various rainfall parameters such as R, M, D q are
estimated and can be compared with the corresponding
method
- Disdrometer arrays on the ground at the vertically-pointing
radar site can provide ground truth data to compare with the
radar estimates.
This combined experiment should be performed as soon as possible
in order to test the ZDR“<vt> hypothesis developed in this section.
CHAPTER 7
SUMMARY AND CONCLUSIONS
7.1
Review of the Problem
Radar has the ability to provide information about the
atmospheric medium and scatterers over large geographical areas from a
single location in real time.
This capability represents an important
improvement over ground and aircraft-based systems, thereby reducing
costs and delays in information transmission and analysis.
Conven­
tional radar remote sensing techniques employ the backscattered
return power at a single linear polarization to estimate rainfall
parameters such as rainfall rate (R), liquid water content (M) and
drop size as well as the propagation-related parameters, specific
attenuation (A) and relative phase shift (A<J>) of rain-filled media.
Extensive studies using this technique of employing a single radar
observable indicated that the natural variability in raindrop size
distributions (DSD) often results in unsatisfactory estimations of
these parameters.
For example, rain-parameter diagrams, based on
exponential or gamma model distributions, show that errors of one to
three orders of magnitude in radar estimates of these parameters are
possible.
Current radar remote sensing techniques are beginning to employ
multi-parameter radar measurements to obtain additional information
213
214
about various characteristics of the atmospheric medium and
scatterers.
One of the most promising techniques is the differential
reflectivity or
method, introduced by Seliga and Bringi (1976),
which utilizes the backscattered returns at two orthogonal, linear
polarizations:
horizontal and vertical.
technique is based on three properties:
As applied to rainfall, this
(1 ) raindrops deform into
nearly oblate spheroidal shapes as they fall, and this deformation
increases with increasing drop size; (2 ) their symmetry axes are
mutually aligned along the vertical direction, and the deviation of
raindrops from these axes is negligible; and (3) the size distribution
of raindrops is reasonably dependent on two parameters.
Based on
these properties, a dual linear polarization radar measuring
the
difference between the reflectivity factors at horizontal and vertical
polarizations (in dB), introduces a second radar observable in
addition to Z^ to provide improved estimates of the rainfall
parameters R, M and Dq as well as the specific attenuation and
relative phase shift at either polarization.
(Chapter
6
Simulated results
) indicate that the Z^^ method also has the potential of
improving estimation of other parameters which are dependent on DSD
variations such as the scavenging rate of aerosols and reflectivity
weighted fall velocities of hydrometeors.
This study examined the application of the Z ^ method in the
estimation of rainfall parameters by comparing radar-derived estimates
with estimates of the same parameters obtained from ground-based
measurements using disdrometers and raingages.
The comparisons
accounted for the differences in resolution volumes and physical
locations of the radar- and ground-based systems.
The temporal
evolution of the rainfall parameters were then compared to verify the
validity of the Z ^ method.
To achieve these results, empirical
relationships describing the dependence of the rainfall parameters on
outlined based on simulations
derived from disdrometer measurements obtained during a field
experiment on
6
October 1982 in central Illinois.
The
method to
estimate rainfall parameters was applied for three case studies taken
from the 1982 Ohio-State Precipitation Experiments (OSPE) and the
MAYPOLE '83 and '84 projects.
This work also described the application of the Z ^ method to
predict C-band reflectivity profiles from S-band measurements and
compared the results with actual C-band measurements.
This task
included the estimation of C-band specific attenuation and
measurements.
Potential
applications of the Z ^ method to scavenging of aerosols and
estimation of vertical air velocities were also considered, based on
simulations derived from an existing disdrometer data base.
7.2
7.2.1
Simulations and Experimental Results
Disdrometer Simulations
In Chapter 3 the relationships linking rainfall parameters R, M
simulations of Seliga, Aydin and Direskeneli (1986).
These
simulations produced empirical, power-law relationships between the
216
radar and rainfall parameters.
Error analyses, based on these and
other (Zj. , Zjjr) rainfall relationships derived from exponential and
gamma model DSD's, are also presented.
The results for R are also
given for three Z-R relationships, including an empirically derived
relationship.
The errors for these relationships were computed in
terms of the normalized bias (NB) and normalized standard error of the
difference (NSED) in addition to two other commonly used error
measures, average difference AD and absolute average difference AAD.
The error values obtained from these simulations form the lower bound
for any estimate derived from these relationships for a typical
rainfall event, since no experimental error due to radar observations
are involved.
The error analyses indicated that the empirical
relationships, obtained from the simulations employing (Z^,
result in the lowest error estimates for the rainfall parameters
considered.
7.2.2
Case Studies
In Chapter 4 three case studies were undertaken applying the (Z^,
method of estimating rainfall parameters under diverse field
conditions.
The estimation of radar-derived parameters utilize the
empirical relationships obtained from the simulated results of Chapter
3.
The results pointed out significant improvements in R and M
estimation using (Z^, Zq „) radar observables compared to using Z^
alone.
Estimating D q from Z ^
also resulted in a satisfactory
comparison with disdrometer ground-based measurements.
217
7.2.2.1
OSPE Disdrometer Comparisons
The two-parameter estimation method employing (Zjj, Z ^ ) was
tested in the 29 October 1982 central Illinois case study.
The
results of radar-derived parameters obtained from 179 radar scans at a
constant elevation angle of 0.9° were compared with the disdrometer
which was located 47.1 km away from the radar.
A systematic approach
to select the appropriate radar volume to be compared with the
disdrometer is outlined.
This included a cross-correlation analysis
between the (Z^, Z^^) pairs obtained from the radar swath and
disdrometer-derived values.
This approach led to a definition of the
radar spatial averaging needed to match the temporal averaging of the
disdrometer.
Results of various (Z^, Z ^ ) averaging schemes for
deriving the radar rainfall parameters are also compared.
empirical (Z^,
NSED.
The
relationship for R produced 9.1% NB and 24.4%
These values were compared to a 30.8% NB and 35.8% NSED for
the best Z-R relationship, indicating that a significant improvement
in R was obtained with the Z ^ method.
This approach for making radar
and ground-based samples is also considered useful for future rainfall
parameter comparisons where significant distances between radar and
ground-based measurements are involved.
Several possible explanations
for the larger error estimates over the simulated results presented in
Chapter 3 are also outlined.
7.2.2.2
MAYPOLE *83 Disdrometer Comparisons
This field experiment on 4 June 1983 involved the CP-2 radar and
disdrometer measurements obtained from a site located a short distance
218
away from the radar (6.35 km), resulting therefore in a narrow radar
beamwidth.
Since the effects of different fall velocities for
different size drops become important in such a case, transformation
of the disdrometer measurements to the radar altitudes was employed.
By accounting for the horizontal wind transport effects, the regions
where the radar measurements were most representative of the
ground-based observations were estimated for each radar elevation
angle.
The time diagrams and the statistical analyses of radar- and
disdrometer-derived radar and rainfall parameters were in very good
agreement.
The results also pointed out the importance of accounting
for drop size sorting in similar studies in order to obtain
satisfactory results.
7.2.2.3
MAYPOLE '84 Raingage Comparisons
This field experiment involved considerably higher rainfall rates
(R
>120 mm h *).
max
The radar estimates were obtained from different
CAPPI's (Constant Altitude Plan Position Indicator) by transforming
the data from radar space to three-dimensional Cartesian coordinates
using successive bilinear interpolations.
This was done with the
CEDRIC computer code, developed by the National Center for Atmospheric
Research.
The fall time and wind transport of the raindrops were
accounted for in the comparisons with the ground observations.
Error
analysis, using the raingages as the reference, resulted in a 6.8% NB
for the empirical (Z„ , Zpg) relationship compared to 14.8% and 16.6%
for two Z-R relationships.
Similarly, NSED of the (Z^, Z^^)
estimation was 30.6% which was considerably better than the NSED's of
45.4% and 53.9% for the same two Z-R relationships.
219
7.2.3
C-Band Profiles
In Chapter 5 the predicted
and measured reflectivity profiles of
a C-band (5.A5 cm) radar (CP-4)
are compared using S-band ( Z ^ q , Zj^)
measurements (CP-2) obtained at a different site.
The comparison
scheme involved the determination of the relationships linking (Z^g,
Zg^) to (Zjjg, Ay,.).
Prediction of the observed C-band reflectivity
factors Zjj,.1 from ( Z^g, Z ^ ) to be compared with simultaneous CP-4
radar measurements involved first estimating ( Z ^ ,
) and then
accounting for the accumulated attenuation along rays originating from
CP-4.
Predicted
contours were then obtained by combining the
individual ray results.
These comparisons resulted in a good
agreement between the predicted
and apparent reflectivity profiles at
C-band for the rainfall event.
The standard error for the comparisons
was 2.4 dBZ for Zjj,.1 in the range of 20-55 dBZ.
This study demon­
strated that (Zg, Z^jj) rainfall measurements by a radar operating at a
non-attenuating S-band wavelength can be used to estimate the
attenuation and scattering of microwaves originating from a radar
which operates at an attenuating wavelength and is located at a
different site.
7.2.4
Other Applications
The potential use of Z ^
discussed in Chapter 6.
in two other applications have also been
Precipitation scavenging is responsible for
most of the total aerosol removed from the atmosphere, and the
scavenging rate A of the aerosols by the washout process is strongly
dependent on the size distribution of the raindrops.
The question of
whether the Z ^ method may serve as a useful tool to estimate A and
220
provide improvements over the current practice of relating A with R is
examined.
Conceptually, the scavenging rates for aerosol size
similar to its use for
distributions can be computed
rainfall parameter estimation, since the Z^R method accounts for
changes in DSD.
disdrometer
Simulated results from a rainfall event measured by
indicate that A can v a r y
for the same R.
by
as much as a factor of 30
Empirical relationships linking
(R, D q ) as well as using a single parameter R or D q were obtained.
Results of the regression analyses for these simulations show
significant improvements for using (ZR , ZDR) over R, indicating an
excellent potential of the Z^R method for remotely inferring aerosol
washout scavenging rates.
Estimation of vertical air velocities may also benefit from
improved estimates of raindrop characteristics.
Vertically pointing
Doppler radars measure the reflectivity weighted mean Doppler
velocities which include the weighted mean fall velocity component
<v^> of hydrometeors.
Simulations indicate that these fall velocities
can be estimated from Z^R which, when combined with Doppler
measurements, can yield the remaining vertical air motion component.
A
possible experiment which involves a dual polarization radar scanning
the volume over the vertically-pointing Doppler radar is described for
this purpose.
Simulation results relating ZpR and <vfc> are also given
along with a
-
relationships.
Z^R provides a significant improvement for fall
<vt > relationship for comparison with existing
velocity determination over the standard
method.
This implies that
the DSD can also be obtained more accurately from the spectrum, since
the vertical air velocities would be known more accurately.
221
7.3
Recommendations for Future Research
7.3.1
Rainfall Studies
The improvements obtained by the
method in estimating
rainfall parameters suggest that additional research in this area
employing dual polarization radar would provide detailed information
about the statistical nature as well as the spatial and temporal
variability of rainfall.
By employing dense disdrometer and raingage
networks, coupled with radar observations, higher resolution varia­
tions in R can be identified.
Longer periods of observation of
rainfall events will also be required to obtain statistical
information on R within an area.
These data would be important for
reliability studies of communication links, especially along groundbased and earth-satellite paths.
Additional comparisons of radar and
disdrometer. and/or raingage measurements, especially at high R's,
should also be performed at different locations throughout the world
in order to test the methodology more completely.
Such measurements
would also provide important information about the DSD characteristics
of these storms.
7.3.2
Hydrology, Flash Flood Forecasting and Weather Modification
The
method should be an important tool in hydrology for
estimating water resources over large areas; in flash flood
forecasting for more timely warnings and in weather modification by
providing accurate, quantitative estimates of rainfall parameters over
both short and long time durations.
The Z_.p method should also
222
contribute to these topics through improved characterization of
rainfall events by supplying measurements in areas without groundbased measurement systems or additional information in the presence of
such other observations.
7.3.3
Attenuating Wavelengths
Prediction
The scheme describing the estimation of reflectivity profiles in
Chapter 5 can also be extended to other attenuating wavelengths such
as X- or Ka -bands.
In addition, the prediction scheme allows for the
estimation of Z ^ profiles by a similar procedure involving
profiles.
and Zy
This has possibly important applications in attenuation
studies involving radars operating at attenuating wavelengths.
Characterization of storm cells and the presence of different
hydrometeor phases may also be possible by comparing the predicted and
measured profiles of apparent reflectivities at attenuating
wavelengths.
In studies involving more than a single radar, such as
in multiple-Doppler systems, accurate absolute and relative measure­
ments of radar observables should be achieved by intercomparing
predictions and measurements.
7.3.A
Cloud Physics. Scavenging. Earth Energy and Radiation Budget
Since Z ^
is an estimator of the drop size, processes involving
the evolution of hydrometeors can benefit from improved estimates of
size distributions at any stage during cloud formation.
Similarly,
scavenging processes involving the removal of aerosols and other
223
pollutants are expected to benefit from the improved estimation of
DSD's during precipitation.
This latter finding suggests that studies
aimed at estimating the scavenging rates for different types of
rainfall events should be undertaken.
Another important area of application is the effect of liquid
water contained within clouds and its ramifications for the energy and
radiation budget of the Earth.
Studies examining the effects of DSD
and liquid water content variations on the albedo characteristics of
storm systems should provide improved understanding of ecological
balance and climate modeling studies.
APPENDIX
Radar Specifications
224
225
Specifications of the CP-2 and CP-4 Radar Systems
Radars
Parameters
CP-2
CP-4
Doppler Capability
Yes
Yes
Antenna
Shape
Parabolic
Parabolic
Diameter
8.5
3.67
Half-Power Beamwidth (deg)
.96
1.06
43.9
41.2
System Gain (dB)
Radome on
43.8
Radome off
First Side Lobe
Level (one way) (dB)
-23 to -30
Radome on
-16 to -22
-22 to -25
Radome off
Polarization
dual
single
Rotation Rate (deg/sec)
0-15
0-25
Wavelength (cm)
10.67
5.45
Frequency (MHz)
2809
5500
Peak Power (kW)
1200
200-400
.2 to 1.5
1
Transmitter
Pulse Width (y sec)
Pulse Repetition Frequency (Hz)
480-1500
500-2000
600-700
(4.2)
750
(5.5)
1. 8
1. 8
Receiver
Noise temperature
(Noise figure dB)
K
Log video bandwidth (MHz)
226
Radars
Parameters_________
Linear channel bandwidth (MHz)
CP-2______
CP-A
1
0.9
(Adjustable)
Transfer Function
Doppler
Linear,
Limited
Linear,
Limited
Intensity
Log,
Linear
Log,
Linear
90
90
■116
-109
-18
-6
Dynamic Range
Log Channel (dB)
Sensitivity
Minimum detectable signal (dBm)
Equivalent reflectivity factor at
25 km (dBz) (Rain)
227
CHILL Radar System Specifications
(Seliga and Mueller, 1982)
10 cm Radar
Transmitter:
Peak Power
Frequency
Pulse Width
Pulse Repetition Frequency
600 kw
2700-2800 MHz
1.0 ys
950 Hz
Antenna:
Size
Gain
Beamwidth
Polarization
8.5 m parabolic reflector
A3.3 dB
l.(P E- and H-planes
H or V
Coherent Receiver:
Linearity
Noise Figure
Dynamic Range
Minimum Detectable Signal
±0.5 dB
11 dB
60 dB
-103 dBm
Incoherent Receiver:
Type
Noise Figure
Dynamic Range
Minimum Detectable Signal
Logarithmic
11 dB
60 dB
-103 dBm
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