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Observational analysis and retrieval of snowfall using satellite data at high microwave frequencies

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THE FLORIDA STATE UNIVERSITY
COLLEGE OF ARTS AND SCIENCES
OBSERVATIONAL ANALYSIS AND RETRIEVAL OF SNOWFALL
USING SATELLITE DATA AT HIGH MICROWAVE FREQUENCIES
By
YOO-JEONG NOH
A dissertation submitted to the
Department of Meteorology
in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
Degree Awarded:
Spring Semester, 2006
UMI Number: 3216526
Copyright 2006 by
Noh, Yoo-Jeong
All rights reserved.
UMI Microform 3216526
Copyright 2006 by ProQuest Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
ProQuest Information and Learning Company
300 North Zeeb Road
P.O. Box 1346
Ann Arbor, MI 48106-1346
The members of the Committee approve the Dissertation of Yoo-Jeong Noh defended on
December 6, 2005.
___________________________
Guosheng Liu
Professor Directing Dissertation
___________________________
Ruby Krishnamurti
Outside Committee Member
___________________________
T. N. Krishnamurti
Committee Member
___________________________
Sharon E. Nicholson
Committee Member
___________________________
Mark A. Bourassa
Committee Member
The Office of Graduate Studies has verified and approved the above named committee
members.
ii
ACKNOWLEDGEMENTS
I would like to express my gratitude to the following people for their support,
encouragement, and assistance in my research and my life.
Major professor: Dr. Guosheng Liu.
Committee members: Dr. T. N. Krishnamurti, Dr. Sharon Nicholson, Dr. Mark Bourassa,
Dr. Ruby Krishnamurti, and Dr. Henry Fuelberg.
All colleagues and staffs of the department of Meteorology, FSU.
My parents, sisters, brother in law, and lovely two nieces.
My precious friends in Korea and Tallahassee, USA.
And anybody I missed who definitely deserves a mention.
I cannot write all my thanks in words here.
I love you. God bless you.
iii
TABLE OF CONTENTS
List of Tables
.........................................................................................................
List of Figures
.........................................................................................................
Abstract
...............................................................................................................
v
vi
ix
1. INTRODUCTION ...................................................................................................
1
2. DATA AND RADIATIVE TRANSFER MODEL .................................................
7
2.1 Data
.........................................................................................................
2.2 Radiative Transfer Model ..............................................................................
7
16
3. OBSERVATIONAL ANAYSES.............................................................................
20
3.1 Temporal Variation of Precipitation ..............................................................
3.1.1 Detecting a diurnal cycle from surface radar precipitation...................
3.1.2 Satellite infrared brightness temperatures.............................................
20
20
23
3.2 Sensitivity of Microwave Frequencies to Falling Snow................................
29
3.3 Observed Snowfall Microwave Signatures....................................................
3.3.1 Satellite observations ............................................................................
3.3.2 Airborne observations...........................................................................
32
34
42
4. BUILDING THE A-PRIORI DATABASE..............................................................
48
4.1 Conversion of Radar Reflectivity to Snowfall Rate ......................................
4.2 Radiative Transfer Modeling of the Observed Snow Events ........................
4.3 Constructing the Database .............................................................................
50
53
57
5. BAYESIAN RETRIEVAL ALGORITHM .............................................................
59
6. APPLICATION OF AMSU-B SNOWFALL RETRIEVAL TO SNOWFALL CASES OVER
THE SEA OF JAPAN.............................................................................................
63
7. CONCLUSIONS......................................................................................................
75
REFERENCES
.........................................................................................................
79
BIOGRAPHICAL SKETCH .......................................................................................
85
iv
LIST OF TABLES
Table 2.1: MIR system parameters...........................................................................
10
Table 2.2: PR-2 system parameters. .........................................................................
11
Table 2.3: AMSR-E systems summary. ...................................................................
13
Table 2.4: AMSU-B systems summary. ...................................................................
15
Table 6.1: Correlation coefficients between snowfall retrievals and AMeDAS radar data.
.................................................................................................................
68
Table 6.2: Correlation coefficients between snowfall retrievals and AMSU-B channels.
.................................................................................................................
69
v
LIST OF FIGURES
Figure 1.1: Latitude - precipitation rate category diagram as derived from COADS dataset (the
Comprehensive Ocean - Atmosphere Data Set). ............................................
2
Figure 1.2: Snow crystal classification by Magono and Lee (1966). ..........................
4
Figure 2.1: Map of the Wakasa Bay and surrounding areas with aircraft flight tracks.
8
Figure 2.2: Accommodation of instruments on NASA P-3 for the Wakasa Bay experiment.
9
Figure 2.3: The dual frequency Precipitation Radar (PR-2). .......................................
10
Figure 2.4: The Advanced Microwave Scanning Radiometer - EOS (AMSR-E). ......
12
Figure 2.5: The Advanced Microwave Sounding Unit ? B (AMSU-B). .....................
14
Figure 3.1: Diurnal variations of the averaged precipitation (a) from 2 to 17 February 2001 and
(b) from 7 to 30 January 2003 over Wakasa Bay. ...........................................
21
Figure 3.2: Diurnal variations of precipitation from 7 to 30 January 2003 with the mean
removed. Solid lines represent the fitting curves. (a) Wakasa Bay, D1 (b) Offshore, D2
(c) Inland, D3 (d) Inshore, D4. ........................................................................
24
Figure 3.3: Normalized, frequency-weighted power spectral density of precipitation in the bay
(a) from 2 to17 February 2001 and (b) from 7 to 30 January 2003. ................
25
Figure 3.4: Diurnal variations of the averaged IR TBs and cloud fractions during the same
period of Fig.3.1 (2-17 February 2001). (a) D1 (b) D2 (c) D3. .......................
27
Figure 3.5: Same as Fig. 3.4 but for 7 to 30 January 2003. .........................................
28
Figure 3.6: Satellite IR brightness temperatures vs. radar precipitation over Wakasa Bay in
January 2003. ...................................................................................................
29
Figure 3.7: Sensitivity of brightness temperature to change in (a) liquid water path, (b) snowfall
(or ice water path), and (c) PCT vs. the polarization difference DP for liquid cloud and
snowfall at microwave frequencies of 37, 89, and 150 GHz.
.........................................................................................................
31
vi
Figure 3.8: Surface analysis maps combined with GMS IR images at 0300 UTC on (a) 29
January and (b) 30 January 2003. ....................................................................
33
Figure 3.9: Brightness temperatures of AMSR-E at 89 GHz and 37 GHz: (a) and (e) vertically
polarized TBs, (b) and (f) horizontally polarized TBs, (c) and (g) the polarization
difference, DP, and (d) and (h) the polarization-corrected temperature, PCT at 0333
UTC on 29 January 2003. ................................................................................
35
Figure 3.10: Vertically polarized TBs, horizontally polarized TBs, PCT, and the polarization
differences DP of AMSR-E at (a) 89 GHz and (b) 37 GHz along Line 1 shown in Fig.
3.9.
.........................................................................................................
36
Figure 3.11: Same as Fig. 3.10 but for along Line 2 shown in Fig. 3.9. .....................
37
Figure 3.12: Brightness temperatures of AMSU-B channels: (a) 89 GHz, (b) 150 GHz, (c)
183�GHz, and (d) 183�GHz at 0419 UTC on 29 January 2003. ..............
39
Figure 3.13: Brightness temperatures of AMSU-B at (a) 89 GHz, (b) 150 GHz, and (c) 183 GHz
along the line shown in Fig. 3.12. ....................................................................
40
Figure 3.14: Brightness temperatures of AMSR-E at 89 GHz and 37 GHz: (a) and (e) vertically
polarized TBs, (b) and (f) horizontally polarized TBs, (c) and (g) the polarization
difference, DP, and (d) and (h) the polarization-corrected temperature, PCT at 0414
UTC on 30 January 2003. ................................................................................
41
Figure 3.15: Vertically polarized TBs, horizontally polarized TBs, PCT, and the polarization
differences of AMSR-E at (a) 89 GHz and (b) 37 GHz along the line shown in Fig. 3.14.
.........................................................................................................
42
Figure 3.16: Comparisons of brightness temperature depressions from MIR and snowfall rate
from PR-2 at nadir for the flight track from 0316 UTC to 0333 UTC on 29 January
2003.
.........................................................................................................
44
Figure 3.17: Scatter diagrams between brightness temperatures from MIR and near surface
snowfall from PR-2 at nadir with regression lines. Squares are corresponding to the
center of the first cell, diamonds to the center of the third cell, triangles to the front part
of the fifth cell in the PR-2 cross section shown in Fig. 3.16. .........................
46
Figure 3.18: Vertical profiles of snowfall rate obtained from PR-2 by Ze-S relationship in each
cell indicated in Fig. 3.16. The fifth cell is divided into two parts (5 and 5?).
47
Figure 4.1: Two types of snowflakes used in the DDA computation. .........................
vii
49
Figure 4.2: Ze-S relationships for snow from calculations using DDA and several previous
studies. The calculated results for sector and dendrite snowflakes are represented
respectively by circles and inverted triangles at 13.4, 35.6, and 94 GHz.........
52
Figure 4.3: Snow particle size distribution and precipitation from ground observations at Fukui
airport during Wakasa 2003 Field experiment. ...............................................
55
Figure 4.4: Comparisons of brightness temperature depressions between MIR observations and
the radiative model results. ..............................................................................
56
Figure 5.1: Comparisons of PR-2 observations at 35 GHz (upper) and retrieved snowfall rate
(lower) along (a) leg1 and (b) leg3. .................................................................
61
Figure 5.2: Scatter plots between column-accumulated snowfall rates from PR-2 observations at
35 GHz and retrievals along (a) leg1 and (b) leg3. ..........................................
62
Figure 6.1: Comparisons of observations and retrieved results on 14 January 2001. (a-d)
Brightness temperature depressions from the AMSU-B at 89, 150, 183+3, and 183+7
GHz, (e-f) retrieved snowfall at 1.5 km and 2.0 km from the surface, and (g) hourly
accumulated snow data (3-hr averaged) from the AMeDAS radar data and (h) GMS IR
cloud top temperatures. ....................................................................................
65
Figure 6.2: Same as Fig. 6.1, but for 16 January 2001. ...............................................
66
Figure 6.3: Same as Fig. 6.1, but for 27 January 2001. ...............................................
67
Figure 6.4: Relations between the magnitude of brightness temperature depression of AMSU-B
and the column-accumulation of retrieved snowfall for three cases. ..............
70
Figure 6.5: Comparisons between retrieved snowfall rates and 3-hr averaged hourly
accumulated surface radar snow amounts at the nearest corresponding time, after 1 hour,
and after 2 hours respectively for 14, 16, and 27 January 2001. .....................
71
Figure 6.6: Comparisons between retrieved snowfall rates and AMSU-B brightness temperature
depressions at each frequency respectively for 14, 16, and 27 January 2001.
.........................................................................................................
72
Figure 6.7: Comparison between retrieved snowfall rates and hourly-accumulated snow data
from the AMeDAS radar data averaged for 14 snowfall cases during January and
February 2001. .................................................................................................
73
viii
ABSTRACT
In the high latitudes during cold seasons, a substantial portion of precipitation falls in the
form of snow. Measuring snow precipitation has many applications such as forecasting
hazardous weather, understanding hydrological water budget, and evaluating the cooling and
freshening effects of snow onto ocean surface. However, unlike rainfall, snowfall measurement
is extremely limited due to technical difficulties. Over ocean and in the uninhabited polar
regions, perhaps there is no snowfall observation of any kind. The goal of this study is to assess
the feasibility of measuring snowfall from satellite observations. In this study, snowfall
signatures over ocean are analyzed using satellite and airborne microwave radiometer
measurements at frequencies ranging from 37 to 340 GHz. Data used in the analysis include
satellite data from the Advanced Microwave Scanning Radiometer ? EOS (AMSR-E) and the
Advanced Microwave Sounding Unit ? B (AMSU-B), and airborne data from a millimeter-wave
radiometer and a dual-frequency precipitation radar during January 2003 over Japan Sea.
Through data analysis and radiative transfer modeling, a snowfall retrieval algorithm based on
Bayes? theorem is developed using high frequency satellite microwave data. The algorithm is
validated by independent surface radar/gauge data, subsequently applied to satellite AMSU-B
data for winter snowstorms near Japan. Specifically, the main results and findings from this
study are summarized as follows:
Through the temporal analysis of surface radar data, a diurnal variation of snowfall in
the Wakasa Bay (Japan) area is detected during winter, suggesting the effects of sea
breeze and topography. However, the clear diurnal variation of winter precipitation
cannot be identified by satellite infrared (IR) data. This finding eliminates the
possibility of using IR data to measuring snowfall. The sensitivity of microwave
channels to snowfall associated with shallow convective clouds is then investigated,
including the study of the optimal channel or channel combinations for snowfall
ix
retrievals. The results show that upwelling microwave radiation at frequencies higher
than 150 GHz has greater sensitivity to scattering by snow/ice, while radiation at
lower frequencies (e.g., 37 GHz) is not sensitive to snow scattering, but rather
sensitive to cloud liquid water.
A snowfall retrieval algorithm based on Bayes? theorem is developed using high
frequency microwave radiometry observations. In developing the Bayesian snowfall
retrieval algorithm, the a-priori database is the most important component.
Observational data from both airborne and surface-based radars are used to construct
the a-priori database of snowfall profiles in this study. These profiles are then used as
input to a forward radiative transfer model to obtain brightness temperatures at high
microwave frequencies. In the radiative transfer calculations, two size distributions
for snowflakes and ten observed atmospheric sounding profiles are used with
snowfall profiles from observations to diversify the database and therefore reduce
retrieval error. In addition, the single-scattering properties of the snowflakes are
calculated based on realistic nonspherical shapes using discrete dipole approximation.
The nonspherical treatment to snowflakes is a step forward in radiative transfer
modeling since ice and snow particles have so far been treated as spheres by most
investigators.
The snowfall retrieval algorithm is first validated by airborne microwave radiometer
and radar observations, and then applied to the AMSU-B satellite data. The results
are validated by surface radar-gauge network data over Japan. The retrieved snowfall
rates using AMSU-B data for three snowfall cases in the vicinity of Japan show good
agreement with surface radar observations with correlation coefficients of about 0.8,
0.6 and 0.96, respectively. The comparison results also suggest that the algorithm
performs better for dry and heavy snow cases, but is less accurate for wet and weak
snow cases due to insensitivity of the satellite microwave scattering. The snowfall
algorithm is used to calculate the mean snowfall distributions in the vicinity of Japan
x
from AMSU-B data for other 14 snowfall cases during January and February in 2001.
The retrieved snowfall is also compared with surface radar-gauge network data. The
retrieved mean snowfall during this period shows fairly good agreement in pattern.
The database used in the algorithm of the present study is derived from snowstorms near
Japan solely due to the data availability. Therefore, our snowfall retrieval algorithm is
considered suited the best for snowfall in this region. In order to apply this algorithm globally, it
is necessary to expand the a-priori database that is the critical component of this Bayesian
algorithm by including observations from other regions. As more snowfall radar observations
become available in the future such as the CloudSat radar (Stephens et al., 2002), a global
database can be constructed in a similar fashion, and the retrieval algorithm may be applied
globally. Moreover, deeper understanding of detailed structures of snow clouds in various
regions and more validations are also needed to improve the retrieval algorithm.
xi
CHAPTER 1
INTRODUCTION
In the high latitudes during cold seasons, a substantial portion of precipitation falls in the
form of snow. Measuring snow precipitation has many applications such as forecasting
hazardous weather, understanding hydrological water budget and evaluating the cooling and
freshening effects of snow onto ocean surface. But ground-based snowfall measurements are
difficult to make due to strong wind effects on snow gauges and melting/evaporating before
measuring, and observation sites are very sparse in remote regions. Thus, satellite measurements
have advantages for global snowfall observation. However, while satellite data have been
extensively used in many cloud and rainfall studies, existing satellite remote sensing techniques
have not been able to provide accurate snowfall retrievals. Visible and near-infrared methods
(e.g., Rossow and Schiffer, 1999; Rolland et al., 2000) can neither distinguish ice from liquid
water nor measure precipitation under a deep cloud. Also, visible method works only during the
daytime. Thermal infrared method (e.g., Giraud et al., 1997; Stubenrauch et al., 1999) can be
applied only to clouds with moderate optical depth. Compared to visible and infrared, microwave
observations are particularly useful for retrievals of precipitation since microwave senses not
only the cloud top but also deep into the cloud and precipitation layer.
Passive microwave instruments on satellites, such as the Special Sensor Microwave
Imager (SSM/I) and the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager
(TMI), have provided measurements of global rainfall over the past several decades. In particular,
the accuracy of rainfall retrievals has greatly improved in the tropical regions with the success of
TRMM (Kummerow et al., 2001). However, precipitation retrieval over the higher latitudes,
particularly snowfall retrieval, has not received as much attention. As reported by Mugnai et al.
(2004), a yearly precipitation average over the earth is about 690 mm, and ~5 % of that is
produced in the form of snowfall. Since snowfall has a significant portion of the total
1
precipitation amount, in Asia, northern regions of Europe, and North America, it becomes the
main driver of the regional and global water cycle process. In Fig. 1.1 (Mugnai et al., 2004), a
precipitation category diagram from the Comprehensive Ocean-Atmosphere Data Set (COADS,
a climatology of oceanic meteorological and sea surface observations recorded on ships)
illustrates the latitudinal distribution of cumulative percentage of light snowfall occurrence
(indicated as frozen precipitation) with light rain and mixed phase precipitation occurrence over
ocean.
Figure 1.1: Latitude - precipitation rate category diagram as derived from COADS (the
Comprehensive Ocean - Atmosphere Data Set) dataset. (From Mugnai et al., 2004).
2
It is evident from this figure how important particularly snowfall is to the water budget poleward
of the 30-degree parallels. Although falling snow is such an important component of global
precipitation in extratropical regions, an accurate satellite snowfall algorithm has not yet been
developed. It is believed that there are two major reasons for this lag. First, the ice signature is
indistinguishable from the liquid water signature at visible and infrared wavelengths, and the
radiative signature of snow particles (scattering signature) is weak at low microwave frequencies
(<90 GHz). This leaves high-frequency microwave as the best candidate for snowfall retrieval.
But satellite observations with reasonable spatial and temporal resolutions at these frequencies
were not available until recently when the Advanced Microwave Sounding Unit ? B (AMSU-B)
was launched onboard the NOAA-15 satellite by which this problem has been partially overcome.
The second reason for this lag is the nonspherical shape of ice particles and snowflakes as shown
in Fig. 1.2, whose radiative properties are much more complex than their liquid counterpart
(water drops). Due to the complexity in shape and orientation, ice and snow particles have been
treated as equal-mass spheres of solid ice or a soft sphere of a mixture of ice and air in many
physical retrieval algorithms. Additionally, the thermal emission by water vapor and cloud liquid
water has a masking effect on the snow scattering and reduces the snowfall signature (Liu and
Curry, 1998).
Liu and Curry (1996; 1997) studied the large-scale cloud and precipitation features in the
North Atlantic using satellite microwave data. They developed an ad hoc snowfall algorithm
using high frequency microwave data in order to separate the total precipitation into rain and
snow. The large-scale ice (snow) distribution retrieved by their algorithm qualitatively agreed
well with the snowfall frequency climatology from shipboard present-weather reports in spite of
a lack of directly adequate validation. Schols et al. (1999) studied snowfall signatures associated
with a North Atlantic cyclone. They emphasized the different responses of 85 GHz microwave
radiation to the cumulonimbus portion along the squall line and the nimbostratus portion north of
the low pressure center. They also showed low brightness temperatures at 85 GHz were observed
from cumulonimbus clouds as found in previous studies, but brightness temperatures at the
nimbostratus clouds north of the low center were significantly higher than anticipated.
Studies of the scattering signatures of snow particles by several investigators laid the
foundation for us to develop a snowfall retrieval algorithm. Evans and Stephens (1995) and Liu
(2004) studied the single-scattering properties of ice and snow particles at high microwave
3
frequencies using the discrete-dipole approximation (DDA, Draine and Flatau, (2000)). They
pointed out that the scattering properties of nonspherical ice and snow particles are substantially
different from spherical particles of equal-volume spheres.
Figure 1.2: Snow crystal classification by Magono and Lee (1966).
Based on the results of DDA simulations, Liu (2004) proposed parameterizations of the
scattering and absorption cross-sections and asymmetry parameters for rosettes, and sector and
dendrite snowflakes. Weng and Grody (2000) showed that the scattering due to ice clouds is
strongly dependent on frequency, and unlike the emission process, the scattering process is very
4
sensitive to the distribution of the ice particle size. After analyzing data observed over ocean by
an airborne radiometer and radar, Katsumata et al. (2000) reported that snow clouds can reduce
upwelling brightness temperatures at 89 GHz up to ~15 K while being hardly detectable by
radiometers at frequencies lower than 37 GHz. By radiative transfer modeling, Bennartz and
Petty (2001) and Bennartz and Bauer (2003) concluded that in the middle and high-latitudes, the
frequent occurrence of frozen precipitation makes it necessary to utilize high-frequency channels
(>100GHz) that are more sensitive to scattering by precipitation-sized particles. They pointed out
that a channel around 150 GHz contains significant useful information for identification and
retrieval of frozen precipitation at middle and high latitudes. The advantage of the scattering
information, especially at high microwave frequencies (greater than 89GHz), is that it is sensitive
enough to be detectable by satellites for frozen phase particles like snowflakes; it also can
provide information about precipitation over strongly emitting surfaces and hence is the primary
basis for estimating precipitation rates over land.
Using ice scattering signature at high microwave frequencies, algorithms to retrieve cloud
ice water path and snowfall have been developed by several investigators. Liu and Curry (1998)
and Deeter and Evans (2000) presented methods to retrieve ice water path using airborne
millimeter-wave radiometer data at 89, 150, 183� 183� 183�and 220 GHz. Liu and Curry
(2000) and Zhao and Weng (2002) developed ice water path algorithms using high frequency
microwave data from the Special Sensor Microwave Water Vapor Profiler (SSM/T2) and the
AMSU-B data. Skofronick-Jackson et al. (2003) investigated the combined use of radar and
radiometer data at high microwave frequencies to retrieve microphysical profiles in tropical
convective cloud. Also, Skofronick-Jackson et al. (2004) presented a physical method to retrieve
snowfall over land using AMSU-B data, and they applied the algorithm to a blizzard case that
occurred over eastern United States in 2001.
The goal of this study is to develop a snowfall retrieval algorithm based on Bayes?
theorem using high frequency microwave satellite data. An important component of the Bayesian
algorithm is the a-priori database that connects brightness temperatures to snowfall rates. In
constructing this database, first, we analyze satellite data and airborne measurements to
understand how microwave signals respond to snowfall with various conditions. Based on the
analyses, a large number of snowfall profiles obtained from observations over the vicinity of
Japan by both airborne and surface radars are used to construct the database, and these profiles
5
are related with brightness temperatures at the frequencies of satellite sensors by a radiative
transfer model (Liu, 1998). A new feature added to the radiative transfer model is that singlescattering properties parameterized for nonspherical snowflakes (Liu, 2004) are used while ice
and snow particles have been treated as equal-mass spheres of solid ice or a soft sphere of a
mixture of ice and air in many physical retrieval algorithms because of the complexity in shape
and orientation. To diversify the microphysical properties in the database, several particle size
distributions and atmospheric soundings measured over Japan during 2003 are used.
In situ data are desirable to validate and improve satellite retrieval algorithms, but
snowfall measurements are not easy due to technical difficulties; therefore, the lack of
observational data has been a serious problem hampering snowfall algorithm development.
Recently, the 2003 Wakasa Bay field experiment (Lobl et al., 2005) was conducted to validate
satellite retrieval products from the Advanced Microwave Scanning Radiometer ? EOS (AMSRE). It provides both remotely sensed and in situ data of snowfall events. The current study takes
full advantage of this rich dataset for the purpose of snowfall retrieval algorithm development
and validation.
The rest of the paper is arranged as follows. Chapter 2 describes the dataset and the
radiative transfer model used for the study. Analyses of various observations are shown in
chapter 3. Description of the a-priori database is given in chapter 4. The Bayesian retrieval
algorithm is presented in chapter 5. In chapter 6, the algorithm is applied to AMSU-B data for
snowfall events observed in the vicinity of Japan, and the results are compared with ground
based radar-raingauge network data. Conclusions are given in chapter 7.
6
CHAPTER 2
DATA AND RADIATIVE TRANSFER MODEL
2.1 Data
In this study, the Wakasa Bay and its surrounding areas (Fig. 2.1) near the Sea of Japan
are the main focus. In order to construct a database for snowfall retrievals, data collected during
the Wakasa Bay 2003 field experiment (Lobl et al., 2005) are used. This field experiment was
carried out near Japan for: validating precipitation products from AMSR-E, examining the
AMSR-E?s shallow rainfall and snowfall retrieval capabilities, and understanding the
precipitation structures through new remote sensing technology.
Of the various datasets collected in the experiment, the data from the following two
remote sensors onboard the NASA P3 aircraft (Fig. 2.2, Wilheit, et al., 2002) are analyzed: the
Millimeter-Wave Imaging Radiometer (MIR) and the dual frequency Precipitation Radar (PR-2).
The MIR is a total power, cross-track scanning radiometer that measures radiation at seven
frequencies: 89, 150, 183.3� 183.3� 183.3� 220, and 340 GHz (Racette et al., 1996). The
sensor has a 3-dB beam width of 3.5� at all channels. It can cover an angular swath up to �
degrees with respect to nadir. Each scan cycle is about three seconds (Wang, 2003). The PR-2
(Fig. 2.3) operates at 13.4 GHz (Ku-band) and 35.6 GHz (Ka-band), and uses a deployable 5.3-m
electronically scanned membrane antenna (Im, 2003). The details of theses instruments are
summarized in Table 2.1 and 2.2. Besides the airborne remotely sensed data, nine upper air
sounding profiles and in situ particle size distributions (explained in detail in section 4.2)
observed at Fukui airport (36.14癗, 136.22癊) during the Wakasa Bay 2003 field experiment are
used.
7
癗
癊
Figure 2.1: Map of the Wakasa Bay and surrounding areas with aircraft flight tracks.
In order to assess the sensitivity of microwave radiation to snowfall, satellite data from
microwave radiometers, AMSR-E and AMSU-B onboard two satellites, coincident with the field
experiment are also used. The AMSR-E (shown in Fig. 2.4) is one of the six sensors aboard the
Aqua satellite. This passive microwave radiometer has vertically and horizontally polarized 6, 10,
19, 23, 37, and 89 GHz channels and vertically polarized 50 and 53 GHz channels (refer to Table
2.3). It conically scans the Earth with an incident angle of ~55� to the normal of the Earth?s
surface. The swath width is about 1600 km. Spatial resolutions of the pixels are frequency
dependent. At 37 and 89 GHz, which are frequencies examined in this study, they are about 8�
km2 and 4�km2, respectively.
8
Figure 2.2: Accommodation of instruments on NASA P-3 for the Wakasa Bay experiment.
9
Table 2.1: MIR system parameters.
Frequency (GHz)
89, 150, 183.3� 183.3� 183.3� 220, 340
Accuracy
+/-2 K
Precision
0.5 K
Angular Swath
+/-50�
Beam width
~ 3 dB
Response Time
~40 msec
Weight
~82 kg
Power
~400 Watts
Figure 2.3: The dual frequency Precipitation Radar (PR-2).
10
Table 2.2: PR-2 system parameters.
Parameters
Ku-band
Ka-band
Frequency (GHz)
13.4
35.6
Polarization
HH, HV
HH, HV
Antenna Effective Diameter
0.4 m
0.14 m
Antenna Gain
34 dBi
34 dBi
Antenna Side Lobe
-30 dB
-30 dB
Antenna Scan Angle
��
��
Peak Power
200 W
100 W
Band Width
4 MHz
4 MHz
Pulse Repetition Frequency (kHz)
5
5
Vertical Resolution
37 m
37 m
Horizontal Resolution
800 m
800 m
Ground Swath
10 km
10 km
Sensitivity (at 10 km range)
10 dBZ
5 dBZ
Doppler Precision
0.3 m/s
0.9 m/s
11
Figure 2.4: The Advanced Microwave Scanning Radiometer - EOS (AMSR-E).
The snowfall retrieval algorithm is applied to the NOAA-16 AMSU-B data. The AMSUB (shown in Fig. 2.4) that is one of three separate cross-scanning units of AMSU has two highfrequency window channels at 89 and 150 GHz, and three split-bank channels at 183.3�
183.3� and 183.3�GHz (Zhao and Weng, 2002; Kramer, 2002). The AMSU-B crossly scans
� 47� from nadir, covering approximately a 2000 km wide swath. The spatial resolution at nadir
is ~15 km. The detailed descriptions of AMSU-B are given in Table 2.4. Five of the seven MIR
channels operate at the same frequencies as the AMSU-B. The AMSU-B data are provided by
NOAA National Environmental Satellite, Data, and Information Service (NESDIS).
12
Table 2.3: AMSR-E systems summary.
Frequency (GHz)
6.925
10.65
18.7
23.8
36.5
89.0
Bandwidth (MHz)
350
100
200
400
1000
3000
Sensitivity (K)
0.3
0.6
0.6
0.6
0.6
1.1
Mean Spatial Resolution
(km)
56
38
21
24
12
5.4
IFOV (km)
74 x 43
51 x 30
27 x 16
31 x 18
14 x 8
6x4
Integration Time (msec)
2.6
2.6
2.6
2.6
2.6
1.3
Main Beam Efficiency (%)
95.3
95.0
96.3
96.4
95.3
96.0
Beam Width
2.2
1.4
0.8
0.9
0.4
0.18
Dynamic Range
2.7 to 340 K
Incidence angle
55�
Polarization
Horizontal and vertical
Cross-polarization
Less than -20 dB
Swath
1445 km
Weight
324 � 15 kg
Power
350 � 35 Watts
To analyze the temporal characteristics of snowfall in the study area, data from two groundbased radars, AMeDAS (Automatic Meteorological Data Acquisition System) rain gauges, and
GMS (Geostationary Meteorological Satellite) infrared (IR) data are used. Radar observations
were conducted from 2 to 17 February 2001 and from 7 to 30 January 2003 in the vicinity of
Wakasa Bay, as part of the CREST (Core Research for Evolutional Science and Technology)
winter Mesoscale Convective Systems (MCSs) project and the US-Japan Aqua validation project.
A 3.2 cm Doppler radar was located at Obama (35.55癗, 135.74癊) in 2001 that are also used to
build the a-priori database, and a 5 cm Doppler radar was located at Mikuni (36.22癗, 136.14癊).
13
Figure 2.5: The Advanced Microwave Sounding Unit ? B (AMSU-B).
To convert equivalent radar reflectivity (Ze) of this radar to snowfall rate (S), we used the Ze-S
relationship of Aonashi et al. (2003), which is derived by comparing the near surface radar
reflectivity of this radar with the reading of a weighing snow gauge.
Finally, to validate the retrieved results, the AMeDAS radar precipitation data are used.
The AMeDAS (Makihara et al. 1995; Oki et al., 1997) consists of radar and automatic raingauge
stations located all over Japan. The radar-AMeDAS data are 1-hr accumulated precipitation
observations from gauge-calibrated radars. The data cover all of Japan and its coastal area.
14
Table 2.4: AMSU-B systems summary.
Frequency (GHz)
89
150
183.3�
183.3�
183.3�
RF Bandwidth
(GHz)
2x1
2x1
2 x 0.5
2x1
2x2
?T Temperature
Sensitivity
1.0 K
1.0 K
1.1 K
1.0 K
1.2 K
Calibration
Accuracy
1.0 K
(�2K
Random)
1.0 K
(�2K
Random)
1.0 K
(�2K
Random)
1.0 K
(�2K
Random)
1.0 K
(�2K
Random)
Linearity
0.3 K
0.3 K
< 0.33 K
0.3 K
0.36 K
Beam Efficiency
> 95%
> 95%
> 95%
> 95%
> 95%
Beam Width
1.1� � 10%
1.1� � 10%
1.1� � 10%
1.1� � 10%
1.1� � 10%
Beam Pointing
Accuracy
�10�
�10�
�10�
�10�
�10�
Cross Polarization
2%
2%
N/S
N/S
10%
Weight
60 kg
Power
90 Watts
Scan Angle
�.95�
Scan Period
8/3 sec
Resolution
~15 km
Swath
~2240 km
The spatial resolution is approximately 5 km x 5 km. Satellite infrared data from GMS
for February 2001 and January 2003 are also analyzed. The IR brightness temperature (TB) data
are obtained from the archives of the Goddard Distributed Active Archive Center. The spatial
resolution of pixels is 4 km, and the temporal coverage is every hour.
15
2.2 Radiative Transfer Model
In this study, the radiative transfer model based on the work of Liu (1998) for microwave
remote sensing and radiance data assimilation application is used. The basics of the model
formulation are briefly described in this section. The radiative transfer equation for polarized
waves in a plane-parallel and azimuthally-symmetric atmosphere with spherical particles can be
expressed by (Tsang and Kong, 1977):
�
d
d?
? I V (? , � ) ? ? I V (? , � ) ? ?0 1 ? PVV
? I (? , � )? = ? I (? , � )? ? 2 ??1 ? P
? H
? ? H
?
? HV
?1?
? (1 ? ?0 ) B(? ) ? ?
?1?
PVH ? ? IV (? , � ?) ?
d� ?
PHH ?? ?? I H (? , � ?)??
,
(2.1)
where I P (? , � ) is the radiance at optical depth ? (? = 0 at the top of the layer) in direction � (the
cosine of zenith angle) for polarization p (H or V), ? 0 is single-scattering albedo, and B(?) is
Plank function at ? that is expressed as a linear function of ?, i.e., B(?) = B0 + B1?, where B0 and
B1 are the Plank functions at the top and bottom of the layer. The four scattering phase functions
(PVV, PVH, PHV, and PHH) are the ones integrated over all azimuthal directions (Tsang and Kong,
1977). The exact solution of I P (? , � ) can be obtained by solving (2.1) using the discrete ordinate
method with sufficient streams. Liu (1998) used two approximations to develop a fast model.
First, it was assumed that the cross-polarization scattering in the scattering source term is
negligible and the scattering phase function can be expressed by the Henyey and Greenstein
(1941) scattering phase function that is expressed as:
P ( � , � ?) = ? Al pl ( � ) pl ( � ?) ,
(2.2)
l
where Al = (2l + 1) g l , g is asymmetry factor as given by Bohren and Huffman (1983), and
pl ( � ) is the lth order Legendre polynomial. A ?-function (Liou, 1992) was applied to the
calculations of g, Al , and ?.
16
Following Stamnes and Swanson (1981), the formal solution of (2.1) without inclusion of
polarization can be expressed as:
I (? , + � ) = I (? * ,+ � ) e ?(?
*
?? ) / �
?*
dt
?
�
+ ? J (t ,+ � ) e ?( t ?? ) / �
?
dt
0
�
I (? , ? � ) = I (0,? � ) e ?? / � + ? J (t ,? � ) e ? (? ? t ) / �
,
,
(2.3)
(2.4)
where � and -� represent upward and downward directions, respectively. ? * is the optical depth
of the layer. The source term J (? , � ) with the discrete ordinate approximation is
J (? , � ) =
n
1 2 n ?1
?0 ? Al pl ( � ) ? a j pl ( � j ) I (? , � j ) + (1 ? ?0 ) B (? ) ,
2 l =0
j=? n
(2.5)
where 2n is the stream number in discrete ordinate approximation, and a j is the quadrature
weight for jth quadrature point.
The solution at ith quadrature point can be expressed as
I (? , 礽 ) =
n
?L
j
W j ( 礽 ) e ?k j? + q( 礽 ) + B1? ,
(2.6)
j =? n
where kj and W j ( 礽 ) are eigenvalue and eigenvector, and Lj can be determined from continuity
of radiance between layers and boundary condition following the standard procedure as
described by Liou (1974). q( 礽 ) can be calculated by solving
?b
ij
q( � j ) = ?(1 ? ?0 ) B0 / 礽 ? B1 ,
(2.7)
j
where bij s have the same definition as those in Liou (1992). Substituting (2.6) into (2.5) yields
J (? , � ) =
n
? (1 + k � ) L W ( � ) e
j
j
j
j =? n
17
? k j?
+ Z 0 + B1? ,
(2.8)
where
1
?0 2 n ?1
n
2
W j (�) =
a j pl ( � j ) Wi ( � j )
? Al pl ( � ) j?
1 + k i � l =0
=? n
Z0 =
(2.9)
n
1 2 n ?1
?0 ? Al pl ( � ) ? a j pl ( 礽 ) q( � j ) + (1 ? ?0 ) B0 .
2 l =0
j =? n
(2.10)
Substituting (2.8) into (2.3) and (2.4) and performing the integral operations, the upward and
downward radiances at direction � can be written as
I (? , + � ) = I (? * ,+ � ) e ?(?
*
?? ) / �
+
n
?L
j
W j ( � )( e ?k j? ? e ?[ k j ?
*
+ (? * ?? ) / � ]
j =? n
+ Z 0 (1 ? e
?(? * ?? ) / �
I (? , ? � ) = I (0,? � ) e ?? / � +
) ? B1 [(? ? ? ) ? � (1 ? e
*
n
? L W (? � )( e
j
j=? n
? B1 [? ? � (1 ? e
?? / �
j
? k j?
? (? * ?? ) / �
)
,
(2.11)
)]
? e ?? / � ) + Z 0 (1 ? e ?? / � )
.
(2.12)
)]
In performing numerical calculations, the atmosphere is divided into many layers and
assumed that all microphysical properties (e.g., particle concentration, liquid/ice water content,
etc.) are uniform within each layer, but temperature varies linearly with optical depth. Ljs in (2.6)
are first obtained by solving a linear equation system that is resulted from applying boundary
conditions and the continuity of radiance between layers to (2.6). Thus, the radiances at
quadrature angles (礽) are obtained. To get radiance at any angle, �, (2.11) and (2.12) are then
applied. If ? = ? * in (2.12), the downward radiance at the bottom of the layer can be calculated
given the downward radiance at the top of the layer. Using the continuity of radiation at the
boundary of neighbored layers, this operation is continued until the downward radiation at
surface is derived. A boundary condition at surface allows calculating the upward radiation at
surface given the surface emissivity and temperature. Using the analogy of calculating
downward radiation from the top layer to surface by (2.12), upward radiation can be
continuously calculated from the bottom of a layer to the top of a layer by using (2.11) and
18
letting ? = 0 until the radiance at the top of a top layer is solved. The ?satellite observed?
radiance at the top of the atmosphere is obtained. Brightness temperature can be calculated then
from radiance using Plank function. Horizontally- and vertically-polarized radiances are
calculated separately because of the difference of their surface emissivity.
19
CHAPTER 3
OBSERVATIONAL ANAYSES
3.1 Temporal Variation of Precipitation
3.1.1
Detecting a diurnal cycle from surface radar precipitation
Understanding the temporal change of the precipitation statistics is essential not only in
predicting regional weather, but also in interpreting satellite precipitation retrievals. During the
winter months of 2001 and 2003, surface radar observations were conducted in the west coastal
area of Japan near Wakasa Bay, as part of the Japan CREST winter MCSs project and the USJapan Aqua validation project. The radar observation provided an excellent opportunity to
investigate the characteristics of snow precipitation in our focused area, which is often associated
with cold air outbreaks from the Eurasian continent.
Using data from the 16-day (02-17 February 2001) radar observations during 2001, the
radar-derived precipitation values are averaged over the entire bay area (Fig. 2.1) according to
the observation time in a day with 10-minute interval. The diurnal variation of these averaged
precipitation anomalies is shown in Fig. 3.1a by solid dots. The anomaly is defined by removing
the domain and whole-period averaged value. The average value is 0.193 mm h-1. Also, the
diurnal variation of radar-derived precipitation for ?undisturbed days? is plotted in Fig. 3.1a by
triangles. An undisturbed day is defined by the day without large-scale cyclonic cloud systems
visible in the domain from satellite images. Undisturbed days are subjectively picked up to avoid
changes induced by the passage of synoptic scale low-pressure systems. But they include locally
unstable conditions due to the cold air outbreaks. Seven days are found ?undisturbed? during the
16-day period, and the average is 0.224 mm h-1. Apparently, a morning high and an evening low
can be identified from both plots and the patterns are similar, although the amplitude of the
diurnal variation is slightly larger for undisturbed days. For all days, the maximum of the
20
anomalies is about 0.1 mm h-1, and the minimum is about ?0.09 mm h-1. For undisturbed days
only, the maximum is about 0.28 mm h-1, and the minimum is about ?0.14 mm h-1.
0.3
(a)
Feb. 2001
Undisturbed days
Precipitation (mm/h)
0.2
0.1
0.0
-0.1
-0.2
-0.3
0
Precipitation (mm/h)
0.4
2
4
6
8
10 12 14 16 18 20 22
(b)
Jan. 2003
Undisturbed days
0.2
0.0
-0.2
-0.4
0
2
4
6
8
10 12 14 16 18 20 22
Local Time (hour)
Figure 3.1: Diurnal variations of the averaged precipitation (a) from 2 to 17 February 2001 and
(b) from 7 to 30 January 2003 over Wakasa Bay.
21
Similarly, the results for January 2003 are shown in Fig. 3.1b. Fluctuations of the
anomalies are larger than those of February 2001, and the average values are respectively 0.434
mm h-1 and 0.165 mm h-1 for the total period and undisturbed days. On the whole, the positive
anomalies show in the morning and the negative anomalies in the evening, except for small
positive peaks found around 14 LST and 22 LST in the total period averages. For the 8
undisturbed days, the amplitude of the variation is smaller, and the negative anomalies appear
from 16 LST to 23 LST. In 2003, radar data covering much broader areas that are divided to all 4
domains (bay-D1, offshore-D2, inland-D3, inshore-D4) are available to us; a similar analysis is
done for each domain for comparison purpose using the January 2003 radar data (7-30 January
2003). Data are excluded of 23 and 27 January when very large synoptic systems dominated the
cloudiness in this total duration. In Fig. 3.2, the diurnal variations over four domains are
represented by hourly averaged precipitation anomalies. For illustration purpose, a sine curve
fitting is used to data. Again, it shows a late-night/early-morning high and an evening low in the
bay area (Fig. 3.2a). The phase of the variation in the bay area seems different from those of the
other three regions, which show a maximum near the local noon. Offshore over ocean (Fig. 3.2b),
there seem to be two peaks in the morning and afternoon. Over land area (Fig. 3.2c), while
significant, the diurnal cycle seems to be weak. Two minima in the evening and midnight are
also shown in Fig. 3.2c. The local noon maximum is particularly evident for the inshore area (Fig.
3.2d).
In summary, radar precipitation data from both 2001 and 2003 indicate an early morning
maximum and an evening minimum of precipitation within Wakasa Bay. There are also diurnal
cycles seen in surrounding areas (over ocean, over land, and along the coast), but the phases of
these cycles are different from the one in the Bay. Many features of the diurnal variation of
precipitation in the vicinity of Japan have been studied (Fujibe 1988, 1999; Oki and Musiake
1994; Misumi 1999). But most previous studies were mainly focused on heavy precipitations in
warm seasons. During winter in Japan, precipitation (including snowfall) distribution changes
largely by synoptic-scale and mesoscale circulations, although topographical features also play
an important role in varying the characteristics (Tachibana 1995). From this study, it is noticed
that the diurnal cycle is evident in this area even during winter and the maxima occur during the
day for the surrounding areas. The phase difference implies that the diurnal cycle in the Bay is at
22
least partially caused by mechanisms that do not exist in the other three regions, which is
possibly due to its geographical features.
Using radar precipitation data areally-averaged over the Bay during the period of 2 to 17
February 2001 and 7 to 30 January 2003, a spectral analysis is performed. The spectral analysis
is based on the fast Fourier transform (FFT). The power spectral density with 95% confidence
limits is calculated in order to find any regularity in the data. The Parzen window (Emery and
Thomson, 2001) is used for smoothing spectral estimates. Figure 3.3a is the variance-preserving
plot of the power spectral density of precipitation from 2 to 17 February 2001. It is normalized
by the variance and frequency-weighted. A clear peak with a period of one day is shown,
indicating a strong diurnal cycle. In Fig. 3.3b, the precipitation power spectrum of January 2003
is shown. While the diurnal signal is not as clear as the previous one, peaks near the period being
about 1 and 0.5 day are shown, indicating diurnal and semi-diurnal cycles. The diurnal signals
with small magnitudes over the other domains were also found in January 2003 (not shown).
Two peaks of the hourly averaged precipitation anomalies are seen over ocean (D2) in Fig 3.2b,
but a semi-diurnal signal is not clear in the spectral analysis.
3.1.2
Satellite infrared brightness temperatures
As the diurnal cycle of snow precipitation was identified in the bay area by surface radar
observations, it would be interesting to investigate whether a similar cycle exists for cloud
features, e.g., cloud top temperature and cloud fraction. Here, GMS IR brightness temperature
(TB) is used as cloud top temperature. Cloud fraction is defined by the ratio of the number of
pixels colder than a given threshold temperature to the total number of pixels. The threshold of
260 K is used.
In Figs. 3.4 and 3.5, the averaged cloud top temperature and the cloud fraction are shown
for the Bay (D1), offshore (D2) and inland (D3) areas. The averaged TBs are plotted by lines, and
cloud fraction by bar graph. In the bay area (Fig. 3.4a), the average TB has small variations, and
the minima are around 8-9, 18, and 23-0 LST. The 9 o?clock TB minimum does not correspond
with a cloud fraction maximum, which occurs at either 2 hours earlier around 7 LST or several
hours later around 12 LST. In all measures, the satellite IR data in 2001 do not show a clear
diurnal cycle in the bay area as shown by radar precipitation data.
23
Precipitation (mm/h)
0.5
(a)
0.4
Bay
(D1)
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
0
1
2
3
4
5
6
7
8
9
Precipitation (mm/h)
0.5
Local Time (hour)
(b)
0.4
10 11 12 13 14 15 16 17 18 19 20 21 22 23
Offshore (D2)
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
0
1
2
3
4
5
6
7
8
9
Precipitation (mm/h)
0.5
Local Time (hour)
(c)
0.4
10 11 12 13 14 15 16 17 18 19 20 21 22 23
Inland (D3)
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
0
1
2
3
4
5
6
7
8
9
Precipitation (mm/h)
0.5
Local Time (hour)
(d)
0.4
10 11 12 13 14 15 16 17 18 19 20 21 22 23
Inshore (D4)
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23
Local Time (hour)
Figure 3.2: Diurnal variations of precipitation from 7 to 30 January 2003 with the mean
removed. Solid lines represent the fitting curves. (a) Wakasa Bay, D1 (b) Offshore, D2 (c)
Inland, D3 (d) Inshore, D4.
24
Period (day)
10
4e-3
1
(a)
1 day
3e-3
Power
0.1
2e-3
1e-3
0
-4.0
-3.5
10
-3.0
-2.5
1
-2.0
-1.5
-2.0
-1.5
0.1
4e-3
(b)
Power
3e-3
1 day
2e-3
1e-3
0
-4.0
-3.5
-3.0
-2.5
Log frequency (cpmin)
Figure 3.3: Normalized, frequency-weighted power spectral density of precipitation in the bay
(a) from 2 to17 February 2001 and (b) from 7 to 30 January 2003.
25
However, as shown in Fig. 3.4b, in the offshore area of D2 the averaged TBs show a clear diurnal
cycle with the colder top temperature showing in the early afternoon and warmer top temperature
near midnight. In the inland area (Fig. 3.4c), a diurnal cycle is not identifiable from either cloud
fraction or cloud top temperature, but it is shown that the cloud fraction increases between 12
LST and 20 LST, although this trend is not clear in the brightness temperature variation.
In Fig. 3.5, several maxima and minima are found in the bay area (Fig. 3.5a), while TB
and cloud fraction do not show any apparent correlation. In the offshore area (Fig. 3.5b), while
the cloud fraction has small variations, the TBs seem to have a diurnal cycle with the coldest
value shown near noon. In the inland area (Fig. 3.5c), a semi-diurnal cycle is shown in TBs with
two lows in 10-11 and 19-20 LST. The first low might be related to the precipitation maximum
of Fig. 3.2c, and the second low seems to be related to the increasing trend in the late evening
after 17 LST of Fig. 3.2c. To find how different diurnal variations of IR TBs between all days and
undisturbed days are, two averaged TBs are also compared (not shown), but it is also hard to
identify a distinct pattern for the diurnal variation, especially in 2003.
From the descriptions given above, it appears that the diurnal variations of the
precipitation (derived by radar), and the clouds (derived by IR TBs) do not agree with each other.
In other words, the clear diurnal cycle in the bay area shown by radar precipitation does not show
up in the satellite cloud data, either by cloud fraction or by cloud top temperature. This implies
that cloud top temperature and fraction are not good indicators of surface precipitation for this
type of clouds (shallow convections). To further elaborate this point, the scatter plot of IR TBs vs.
radar precipitation is shown in Fig. 3.6 using data of January 2003 collocated over the bay area.
Since the surface radar grid is a finer than GMS pixel resolution, we averaged all radar
observations that fall within a GMS data grid (about 4 km) for the collocated data. As shown in
this figure, the correlation between the two quantities is very weak.
It is found that neither cloud top temperature nor cloud fraction derived from infrared
satellite observations can be used to produce the same diurnal cycle as derived from radar data.
Furthermore, there does not seem to be any clear correlation between cloud top temperature and
surface precipitation intensity for the type of clouds that were studied, which are mostly shallow
convections associated with cold air outbreaks. The correlation coefficients between IR TBs and
radar precipitation are?0.18 in February 2001 and ?0.06 in January 2003.
26
260
1.0
Tb (<=260K)
(a)
0.8
256
0.6
254
Cloud Fraction
Brightness Temperature (K)
Cloud fraction
258
0.4
252
250
0.2
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
260
1.0
(b)
Tb (<=260K)
0.8
256
0.6
254
Cloud Fraction
Brightness Temperature (K)
Cloud fraction
258
0.4
252
250
0.2
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
260
1.0
(c)
Tb (<=260K)
0.8
256
0.6
254
Cloud Fraction
Brightness Temperature (K)
Cloud fraction
258
0.4
252
250
0.2
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Local Time (hour)
Figure 3.4: Diurnal variations of the averaged IR TBs and cloud fractions during the same
period of Fig.3.1 (2-17 February 2001). (a) D1 (b) D2 (c) D3.
27
258
1.0
Tb (<=260K)
(a)
0.8
254
0.6
252
Cloud Fraction
Brightness Temperature (K)
Cloud fraction
256
0.4
250
248
0.2
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
258
1.0
(b)
Tb (<=260K)
0.8
254
0.6
252
Cloud Fraction
Brightness Temperature (K)
Cloud fraction
256
0.4
250
248
0.2
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
258
1.0
(c)
Tb (<=260K)
0.8
254
0.6
252
Cloud Fraction
Brightness Temperature (K)
Cloud fraction
256
0.4
250
248
0.2
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Local Time (hour)
Figure 3.5: Same as Fig. 3.4 but for 7 to 30 January 2003.
28
290
Brightness Temperature (K)
280
270
260
250
240
230
220
210
0
2
4
6
8
10
Precipitation (mm/h)
Figure 3.6: Satellite IR brightness temperatures vs. radar precipitation over Wakasa Bay in
January 2003.
Also, the values between cloud fractions with the threshold of 260 K and radar precipitation are
respectively 0.4 and ?0.18. For satellite observation of snow precipitation, high-frequency
microwave measurement may be an alternative because it measures the scattering signatures
caused by snowflakes.
3.2 Sensitivity of Microwave Frequencies to Falling Snow
Prior to developing a retrieval algorithm at microwave frequency, we first investigate
how microwave radiation responds to liquid and ice/snow water in the atmospheric column. A
radiative transfer model using 32-stream discrete ordinate method (Liu 1998; Liu and Curry,
29
1998) as described in Chapter 2 is used for the task. In this modeling study, a standard midlatitude winter atmosphere profile, and a Fresnel ocean surface model are used with the surface
temperature of 273 K. The single-scattering properties of the snowflakes in this model are
parameterized by Liu (2004), assuming that the snowflakes are comprised of equally mixed
sector-like and dendrite-like particles with random orientations. Brightness temperatures
emerging from the top of the atmosphere at AMSR-E viewing angle of 55� are calculated.
Figure 3.7 shows the brightness temperatures and their combinations at three microwave
frequencies (37, 89, and 150 GHz) in responding to the variation of liquid water path and
snowfall (or its corresponding ice water path). Two brightness temperature combinations are
considered: the polarization difference (DP=TB v - TB h) and the polarization-corrected
temperature as defined by Spencer et al. (1989), i.e.,
PCT = (1 + ? )TB v ? ? TB h,
(3.1)
where TB v and TB h are, respectively, the vertically and horizontally polarized brightness
temperatures at each frequency. A value of ? = 0.5 is used in (3.1), which is corresponding to the
value for January in the mid-latitudes suggested by Liu and Curry (1998). Since emission by
liquid water and gases in the atmosphere reduces the polarization difference of the radiation from
the highly polarized ocean surface, the DP is representative of the atmospheric emission. The
PCT is used to reflect the brightness temperature depression due to scattering by ice particles,
and it is designed to be less sensitive to the variations of water vapor and liquid water amount. In
other words, while the decrease in polarization difference largely responds to liquid water
increase in the atmosphere, the decrease of PCT represents the increase in the amount of
scattering ice/snow particles (Liu and Curry, 1998).
The left panel of Fig. 3.7 shows the model results when placing a liquid water cloud
between 1 and 1.5 km above the surface. The liquid water path (LWP) in the cloud varies from 0
to 1000 g m-2. The snowfall-only modeling results are shown in the mid panel of Fig. 3.7, in
which snowfall rate is varied from 0 to 5 mm hr-1, and the snow layer is assumed to be between
the surface and 4 km. The corresponding ice water path (IWP) of the snow layer is also shown in
the figure.
30
IWP (g/m2)
1000
2000
3000
80
PCT
200
40
TB v
DP
160
40
20
TB h
120
0
280
80
60
0
80
PCT
LWP=0
snow=0
PCT
TB v
TB h
TB v
DP
200
40
TB h
160
60
60
DP89 (K)
TB 89 (K)
240
20
LWP=1000
LWP
SNOW
40
20
120
0
280
80
20
snow=5
DP
DP89 (K)
TB h
snow=5
60
PCT
TB v
DP37 (K)
TB 37 (K)
240
80
LWP=0
snow=0
DP
DP37 (K)
0
280
LWP=1000
0
80
TB 150 (K)
60
PCT
TB v
TB h
200
40
TB h
160
DP
DP150 (K)
TB v
240
120
400
600
800
1000
0
1
snow=0
40
20
LWP=1000
0
200
60
20
DP
snow=5
0
LWP=0
2
3
4
5
DP150 (K)
PCT
180
200
220
240
LWP (g/m2)
Snowfall (mm/hr)
PCT (K)
(a)
(b)
(c)
260
0
280
Figure 3.7: Sensitivity of brightness temperature to change in (a) liquid water path, (b) snowfall
(or ice water path), and (c) PCT vs. the polarization difference DP for liquid cloud and snowfall
at microwave frequencies of 37, 89, and 150 GHz.
31
At 37 GHz, the brightness temperatures and the polarization difference are closely related to the
liquid water amount in the atmosphere. A larger amount of liquid water responds to a higher
brightness temperature at both polarizations and a smaller DP. There is little response of
microwave signals at 37 GHz to snowfall rate variation. At 89 and 150 GHz, as LWP increases,
brightness temperatures increase before saturating at about 1000 and 500 g m-2, respectively.
Brightness temperatures at these two channels show significant decreases as snowfall rate (or
IWP) increases, especially at 150 GHz. It is particularly noted that the variation of DP is more
sensitive to LWP changes, and the variation of PCT is more sensitive to snowfall rate or IWP
changes. To illustrate this observation, we re-plot the modeling results in DP-PCT space (the
right panel of Fig. 3.7), which show how the liquid water and snowfall induce DP and PCT
variations in the same chart. At 89 GHz, for example, as LWP increases from 0 to 1000 g m-2,
DP decreases by ~70 K while PCT decreases by ~20 K. But as snowfall rate increases from 0 to
5 mm h-1, DP only reduces by ~ 40 K compared to PCT reducing by ~ 60 K. The different
responses of DP and PCT to liquid and ice water are even clearer at 150 GHz. Therefore, more
information of LWP contained in DP is variations while PCT changes are more responsible to
the variation in snowfall rate (or IWP). Using these model simulation results as guidance,
satellite and airborne microwave radiometer data are examined in the following sections.
3.3 Observed Snowfall Microwave Signatures
To examine observed microwave snowfall signature, two snowfall cases were selected in
the region of the Sea of Japan during the Wakasa Bay 2003 field campaign on January 29 and 30,
2003. The surface weather analysis overlaid with GMS IR images for the two days are shown in
Fig. 3.8. On 29 January 2003, a low pressure system located near 50 癗, 140 癊 had moved
northwards and deepened to 976 hPa in Fig. 3.8a. Strong northwesterly flow is dominant over the
Sea of Japan and extensive snowfall areas were reported along the west coast of the main island
of Japan. An aircraft flight observing the snowfall over ocean was conducted; snow was seen
along the flight lines (A1 to B1 in Fig. 2.1, 36.5癗, 135.5癊 and 38.5癗, 135.5癊) around 0320
UTC. On 30 January 2003, the low seen in the previous day moved to the east, resulting in a
slightly reduced northwesterly flow across the Sea of Japan.
32
(a)
(b)
Figure 3.8: Surface analysis maps combined with GMS IR images at 0300 UTC on (a) 29
January and (b) 30 January 2003.
Snowfall was reported along the west coast of central Japan and predicted over the Sea of Japan.
Widespread clouds were observed over the Sea of Japan although from the IR image they
seemed not as deep as in the previous day. Aircraft flight experiments were performed along
several tracks including the line A2-B2 (36.33 癗; 134.5 癊 to 38.67 癗; 137.0 癊 in Fig. 2.1).
In the following, we examine satellite and airborne microwave radiometric signatures responded
to these two snowfall cases.
33
3.3.1
Satellite observations
The Aqua satellite passed over the experiment area at 0333 UTC on 29 January 2003.
Although there are frequencies from 6.6 to 89 GHz in AMSR-E, only 37 and 89 GHz are
examined in the study because other channels are almost transparent to the snow clouds. At 37
and 89 GHz, the emissivity of the ocean surface is lower than unity. As a result, cloud liquid
water will increase the satellite received brightness temperatures. Meanwhile, both cloud ice and
snow in the atmosphere will decrease upwelling radiation due to ice scattering.
Figure 3.9 shows the horizontal distributions of (a) and (e) vertically polarized brightness
temperatures, (b) and (f) horizontally polarized brightness temperatures, (c) and (g) the
polarization difference (DP= TB v ? TB h ), and (d) and (h) the polarization-corrected temperature
(PCT with ? = 0.5), at AMSR-E 89 GHz and 37 GHz. Fine features can be identified from
images of all the four variables. These features are induced by clouds and their associated
snowfall, since emission from ocean surface should be more uniform horizontally. It is seen that
there are several cloud cells between 37 癗 and 38 癗 over ocean with relatively low brightness
temperatures compared to their surrounding background values. It is also noticed that the
patterns of these cells are different for different channels or brightness temperature combinations.
The strongest emission signal of polarization difference (< 20 K) is found in the area around
37.2癗, 136.2癊. The centers of the lowest PCT are found slightly to the north of the center of
the lowest polarization difference.
To further elaborate, variations of the brightness temperatures along Line 1 and Line 2
(refer Figs. 3.9d and 3.9h) are shown in Figs. 3.10 and 3.11. Figure 3.10 represents brightness
temperatures at 89 GHz and 37 GHz along Line 1 that overlaps the aircraft flight track on 29
January 2003. To compare two frequencies with different resolutions, data from both frequencies
are first interpolated to a 0.025o� 0.025o grid. Then, the brightness temperature values along the
line are obtained by averaging values of the nearest five grids weighted by the inverse of the
distance between the grid center and the line. The results for 89 GHz are shown in Fig. 3.10a.
Several small cells seen in Fig. 3.9 along Line 1 correspond to the decreases of 89 GHz
brightness temperatures and PCT in Fig. 3.10a. Note that a peak in horizontally polarized
brightness temperatures is found at 37.2癗 just before the decrease of PCT, and another peak at
37.4癗 before the decrease of PCT near 37.58癗. The lowest depression of PCT from the cloudfree value of ~260 K is about 25 K near the cell centers. The largest decrease of the polarization
34
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure 3.9: Brightness temperatures of AMSR-E at 89 GHz and 37 GHz: (a) and (e) vertically
polarized TBs, (b) and (f) horizontally polarized TBs, (c) and (g) the polarization difference, DP,
and (d) and (h) the polarization-corrected temperature, PCT at 0333 UTC on 29 January 2003.
35
260
(a)
40
220
TBh
DP
200
37GHz Line1
PCT
240
TB (K)
30
20
180
220
50
(b)
70
TBv
200
80
60
DP
180
50
160
140
37.0
DP37 (K)
TB (K)
TBv
PCT
240
60
DP89 (K)
89GHz Line1
TBh
40
37.2
37.4
37.6
37.8
38.0
38.2
Latitude
Figure 3.10: Vertically polarized TBs, horizontally polarized TBs, PCT, and the polarization
differences DP of AMSR-E at (a) 89 GHz and (b) 37 GHz along Line 1 shown in Fig. 3.9.
difference is ~30 K near 37.2癗, and the location corresponds to the highest brightness
temperature at horizontal polarization. Figure 3.10b shows brightness temperatures at 37 GHz for
the same track (Line 1). The 37 GHz signals show less variations than those at 89 GHz, except
for a brightness temperature increase (the polarization difference decrease) near 37.2癗
corresponding to the first cell along Line 1 shown in Fig. 3.9d. Comparing 89 GHz and 37 GHz,
36
a slight shift in the pattern of the polarization difference could not only be caused by the different
resolutions of two channels, but also by the different response of brightness temperatures to
hydrometeors. The increase in 37 GHz brightness temperatures indicates a significant amount of
liquid water within the cell. However, either brightness temperature or PCT at 37 GHz does not
decrease corresponding to those decreases shown in Fig. 3.10a for 89 GHz, indicating lack of
response to scattering by cloud ice particles and snowflakes. In other words, cloud ice particles
and snowflakes produce measurable scatter signatures at 89 GHz, but are largely not detectable
at 37 GHz. The observational results are consistent with the radiative transfer model results
described earlier.
89GHz Line2
260
DP
PCT
40
TBv
30
220
200
TBh
180
PCT
240
TB (K)
20
10
37GHz Line2
220
DP89 (K)
(a)
(b)
70
TBv
200
60
DP
180
TBh
160
140
37.0
80
DP37 (K)
TB (K)
240
50
50
40
37.2
37.4
37.6
37.8
38.0
38.2
Latitude
Figure 3.11: Same as Fig. 3.10 but for along Line 2 shown in Fig. 3.9.
37
Figure 3.11 shows 89 GHz and 37 GHz data along another line that is shown as Line 2 in
Fig. 3.9. It is seen that this line crosses over a well-developed cell from Fig. 3.9. The lowest
depression of PCT observed at 37.43癗 is about 45 K at 89 GHz compared to those at the cloudfree regions (~260 K). The depressions of brightness temperatures in both polarizations are also
much larger than those in Line 1. Similar to what occurred in Line 1, the increase of horizontally
polarized brightness temperatures (and the decrease of the polarization difference) is shown
before (south of) the PCT depressions. This dislocation between the minima of PCT and
polarization difference suggests that the maxima of liquid water amount and snowfall rate occur
at different locations within a cell. At 37 GHz, the changes in vertically polarized brightness
temperature and PCT are small while horizontally polarized brightness temperature and
polarization difference show significant variations. The result further enforces our conclusion
that while 37 GHz channel is useful in determining liquid water path, it is incapable to detect
snowfall.
The NOAA-16 satellite passed the study area on 29 January 2003 at 0419 UTC. AMSUB data on the NOAA-16 are also analyzed to explore the response to snowfall at higher
frequencies. Figure 3.12 shows brightness temperatures at four channels of 89, 150, 183� and
183�GHz (the 183�GHz image is not shown. Its image appears to be between those of 183�and 183�GHz). Since AMSU-B channels contain only single polarization, it is not possible to
derive PCT or polarization difference as was done for AMSR-E channels. Additionally, because
of the coarser spatial resolution, the images appear lack of fine structures compared to those from
AMSR-E in Fig. 3.9. Nevertheless, low brightness temperature cells embedded on a long cloud
streak are clearly shown between 37癗 and 38癗. The signals are particularly clear at 150 and
183�GHz. In Fig. 3.13, brightness temperatures from the five AMSU-B channels are presented
along the line shown in Fig. 3.12, which corresponds to the aircraft flight track, Line 1 in Fig. 3.9.
The coarse spatial resolution reduced the sensitivity of radiation at 89 GHz, but significant
decreases in brightness temperatures at 150 GHz and 183�GHz are observed near the snowfall
cell at 37.7癗. The values of brightness temperature depression are about 15 K at 150 GHz and
25 K at 183�GHz compared to nearby cloud-free regions. Comparing to 89 GHz, the
sensitivity to snowfall is much higher at 150 and 183�GHz. The sensitivity at 183�and
183�GHz is not as large due to water vapor masking.
38
(a)
(b)
(c)
(d)
Figure 3.12: Brightness temperatures of AMSU-B channels: (a) 89 GHz, (b) 150 GHz, (c)
183�GHz, and (d) 183�GHz at 0419 UTC on 29 January 2003.
39
TB (K)
TB (K)
TB (K)
220
210
200
89
(a)
AMSUB (A1-B1)
230
150
220
210
(b)
250
183+-3
183+-1
240
230
(c)
36.5
183+-7
37.0
37.5
38.0
38.5
Latitude
Figure 3.13: Brightness temperatures of AMSU-B at (a) 89 GHz, (b) 150 GHz, and (c) 183
GHz along the line shown in Fig. 3.12.
The second case is meant to show the response of microwave radiation to snowfall with
much less intensity (the weak snowfall was reported by airborne radar observations). Figure 3.14
shows the brightness temperatures from AMSR-E at 0414 UTC on 30 January 2003. The
convective cells are aligned themselves along the streak clouds while they are much smaller and
weaker than those in the first case on 29 January 2003. In Fig. 3.14d, it is seen that several small
cells with low PCTs are orientated from northwest to southeast. At 37 GHz, no significant
signatures are identified along the track. The brightness temperature values along the aircraft
flight track (shown in Figs. 3.14d and 3.14h, or A2-B2 in Fig. 2.1) are shown in Fig. 3.15. The
lowest PCT depression at 89 GHz in a cell center is about 10 K near 135.2癊 compared to
surrounding cloud-free regions and the depression is much smaller at 37 GHz. Unlike in the first
case, in Fig. 3.15a, the maximum of the horizontally polarized brightness temperature of about
220 K, the lowest PCT of about 257 K, and the lowest polarization difference of 23 K occur at
40
Figure 3.14: Brightness temperatures of AMSR-E at 89 GHz and 37 GHz: (a) and (e) vertically
polarized TBs, (b) and (f) horizontally polarized TBs, (c) and (g) the polarization difference, DP,
and (d) and (h) the polarization-corrected temperature, PCT at 0414 UTC on 30 January 2003.
41
89GHz A2-B2
TBv
50
TB (K)
240
DP
40
220
TBh
200
30
20
180
37GHz A2-B2
240
TB (K)
220
DP89 (K)
PCT
(a)
80
PCT
(b)
TBv
200
DP
70
60
180
TBh
160
140
134.5
DP37 (K)
260
60
50
40
135.0
135.5
136.0
136.5
137.0
Longitude
Figure 3.15: Vertically polarized TBs, horizontally polarized TBs, PCT, and the polarization
differences of AMSR-E at (a) 89 GHz and (b) 37 GHz along the line shown in Fig. 3.14.
almost the same position, implying that the location of peak liquid water amount coincides with
the location of the strongest snowfall.
3.3.2
Airborne observations
The snow clouds on January 29 are observed by airborne radiometer MIR and radar PR-2.
One aircraft flight was carried out from 0319 UTC to 0333 UTC along the line of A1 to B1 as
shown in Fig. 2.1 (corresponding to Line 1 in Fig. 3.9). Figure 3.16 shows the aircraft nadir
42
observations of the brightness temperature depressions compared to the clear-sky values and the
time-height cross section of snowfall rate converted from PR-2 13.4 GHz radar reflectivity. For a
downward looking radiometer above the snow cloud, the scattering decreases the brightness
temperature compared to that from clear sky. In the brightness temperature depressions (?TB =
TB -TB0, where TB0 is the clear-sky brightness temperature), the clear-sky brightness temperatures
are derived from locations where no radar echo was observed; their values are 199.5, 218.7,
241.4, 250.6, 247.3, 243.8, and 255.7 K for 89, 150, 183� 183� 183� 220, and 340 GHz,
respectively. To obtain snowfall rate from radar reflectivity, a new reflectivity-snowfall rate (ZeS) relation are used that is developed for more realistic nonspherical snow particles (more details
given in the next chapter).
In Fig. 3.16, five convective cells can be identified in the radar cross section as indicated
by numbers 1-5. The depression of MIR brightness temperatures responds to these cells,
although the sign and the amplitude of the variation are channel-dependent. The depression of
brightness temperature at 220 and 340 GHz is greater than the other channels, and they reach
about 80 K for the first cell. Among the three 183-GHz water vapor channels, 183�GHz is the
most sensitive to the snowfall cells. It is notably seen from Fig. 3.16a that the 89-GHz brightness
temperatures at some convective cells are higher than clear-sky values, implying that rich cloud
liquid water exists in these cells, a result consistent with Katsumata et al. (2000) who studied
snow clouds in the same region. While the increase in brightness temperature occurs at 150 GHz
as well, the overall signature in this channel is the depression corresponding to snow cell. The
second cell seems to be weaker than the first one, and the brightness temperatures depression is
also smaller for all the channels. Note that at the starting point of the second cell a brightness
temperature peak appears at 89 GHz, suggesting that significant liquid water exists in front of the
center of the second snow cell. The third cell has rather different features, especially at 89 and
150 GHz; brightness temperatures are much greater than those values for the clear sky. It implies
that the third cell contains a great amount of liquid water, although heavy snowfall converted
from strong radar echo is shown from 1 to 4 km in Fig. 3.16c. The fifth cell is divided into two
parts indicated as 5 and 5? in Fig. 3.16c. The left region of the cell has the maximum snowfall
rate near the surface, but MIR brightness temperature depressions do not reach their minimum
until further into the middle of the cell as indicated by 5? in the figure.
43
40
TB (K)
20
0
-20
-40
-60
89
150
220
340
(a)
-80
20
TB (K)
0
-20
-40
-60
183+-1
183+-3
183+-7
(b)
-80
1
2
3
4
5 5?
(c)
Figure 3.16: Comparisons of (a and b) brightness temperature depressions from MIR at seven
frequencies and (c) snowfall rate from PR-2 at nadir for the flight track from 0316 UTC to 0333
UTC on 29 January 2003.
44
To quantitatively assess the relation between brightness temperature and near surface
snowfall rate, the brightness temperatures and radar reflectivity-derived snowfall rate at 1 km (to
avoid surface contamination) are averaged for every 10 seconds (corresponding to ~1000 m in
spatial scale) and plotted in Fig. 3.17. Brightness temperatures in all the channels decrease in
general as snowfall rates increase, although there is a significant large range of scatter. A
regression line for each channel is derived using the 10-sec averaged data and plotted in the
figure. The correlation coefficient is -0.2, -0.46, -0.65, -0.67, -0.66, and -0.68 for data at 89, 150,
220, 340, 183� and 183�GHz, respectively. Based on these data, the sensitivity of brightness
temperature to snowfall rate can be estimated as -4, -10, -16, -22, -10, and -14.4 K (mm h-1)-1 for
89, 150, 220, 340, 183� and 183�GHz channels.
In Fig. 3.17, it is found that some points, as denoted by squares, diamonds, and triangles,
do not follow the general trend in the relationships. The two squares come from the first cell; the
radar-derived snowfall profile corresponding to the profile 1 in Fig. 3.18. Strong radar returns are
observed in a very deep layer, suggesting the center of a very well developed convective cell.
The diamonds correspond to the third cell, which has the vertical radar profile 3 in Fig. 3.18. The
strongest echo occurs in the middle of the layer (about 2 km), and the large increase in 89 GHz
brightness temperatures implies a significant amount of liquid water in the cell. These results
suggest that cell 3 is in the early developing stage, and the bulk of the condensed water is still in
liquid form. The triangles correspond to the first part of the fifth cell that has its bulk of radar
returns near the surface (profile 5 in Fig. 3.18). It is seen from Fig. 3.16c that the patterns of
radar echoes for cells 4 and 5 are vertically tilted, possibly caused by vertical wind shear.
Although overall cell 5 has significantly decreased brightness temperatures, the first part of the
cell did not cause sizable brightness temperature reduction because of only a shallow snowfall
layer existing near the surface. The above discussion illustrates how the horizontal and vertical
structures of snow clouds influence the observed brightness temperatures, and emphasizes the
importance of further observational studies to characterize the three-dimensional structure of
snow clouds.
45
260
89 GHz
150 GHz
220 GHz
340 GHz
183+-1 GHz
183+-7 GHz
TB (K)
240
220
200
180
160
260
TB (K)
240
220
200
180
160
260
TB (K)
240
220
200
180
160
0.0
0.5
1.0
1.5
2.0
Snowfall (mm/hr)
0.0
0.5
1.0
1.5
2.0
Snowfall (mm/hr)
Figure 3.17: Scatter diagrams between brightness temperatures from MIR and near surface
snowfall from PR-2 at nadir with regression lines. Each data is the average for every 10 seconds
(~1000 m in spatial scale). Squares are corresponding to the center of the first cell, diamonds to
the center of the third cell, triangles to the front part of the fifth cell in the PR-2 cross section
shown in Fig. 3.16.
46
5
Height (km)
4
3
2
1
2
0.0
5'
3
4
0.5
1.0
1.5
5
1
2.0
2.5
Snowfall rate (mm/hr)
Figure 3.18: Vertical profiles of snowfall rate obtained from PR-2 by Ze-S relationship in each
cell indicated in Fig. 3.16. The fifth cell is divided into two parts (5 and 5?).
47
CHAPTER 4
BUILDING THE A-PRIORI DATABASE
An important component of a Bayesian retrieval algorithm is the a-priori database that
connects the observations (brightness temperatures) with the parameters to be retrieved (snowfall
rates); the probability density of a snowfall rate in the database should be consistent with the
likelihood of the same snowfall rate occurring in actual snow events. To build such a database,
we collect snowfall data from airborne and surface based radars.
In an effort to accurately calculate the scattering parameters of snowflakes in radar
equations and radiative transfer models, we performed DDA simulations using realistic snow
particle shapes. The DDA (Draine and Flatau, 2000) is a general method for computing the
scattering and absorption of arbitrarily shaped particles and has been used by many researchers
for studying the scattering by ice particles (e.g., Draine, 1988; Evans and Stephens, 1995). The
DDA is an approximation of the continuum target by a finite array of polarizable points that
acquire dipole moments to the local electric field. It has advantage in studies about the scattering
characteristics by complicated shaped particles like dendrites. The Draine and Flatau DDA
model approximates the targets by an array of polarizable points that are located on a cubic
lattice. Two types of snowflakes randomly orientated in space are considered in the DDA
computations as shown in Fig. 4.1. The ice volume is concentrated on the six main branches in
type-A (sector snowflake) and more uniformly spreads in the basal plane in type-B (dendrite
snowflake). Both types of snowflakes obey the following relations derived by Heymsfield et al.
(2002):
?0.377
Ar = 0.261Dmax
,
?1.0
? e = 0.015 Ar1.5 Dmax
48
(4.1)
where Dmax is the maximum dimension of the snowflakes, Ar is the area ratio (the projected area
of a snowflake normalized by the area of a snowflake with diameter Dmax), and ? e is the
effective density defined as the mass divided by the volume of a circumscribed sphere.
(a) Type-A (Sector Snowflake)
(b) Type-B (Dendrite Snowflake)
Figure 4.1: Two types of snowflakes used in the DDA computation.
49
4.1 Conversion of Radar Reflectivity to Snowfall Rate
The backscatter cross sections calculated from the discrete-dipole approximation (DDA)
for snowflakes is used to develop the Ze-S relationships. Vertical snowfall rate profiles used for
building the a-priori database are derived from data of PR-2 and a surface Doppler radar. To
convert equivalent radar reflectivity of the surface Doppler radar to snowfall rate, a Ze-S
relationship empirically derived by Aonashi et al. (2003) is used. This Ze-S relationship was
derived by comparing simultaneous observations of the near surface radar reflectivity of this
radar to the snowfall rate of a weighing snow gauge. However, since there are no simultaneous
Ze and S observations for PR-2, we need to obtain the Ze-S relations for PR-2. The new Ze-S
relationships are derived based on theoretical calculations. From the backscattering cross section
?(D) obtained from DDA calculations, the radar reflectivity can be calculated as follows:
?=
Dmax
? N ( D) ? ( D) dD ,
(4.2)
Dmin
where N(D) is the size distribution. The equivalent radar reflectivity factor Ze (mm6 m-3) can be
derived using
2
? 5 Kw Ze
,
?=
?40
(4.3)
2
where K w (= ~0.93 at 35 GHz) is a parameter related to the complex index of refraction of
water, and ?0 is the wavelength of the radar.
The following equation is used to obtain a melting diameter with equivalent liquid water
density from an observed maximum diameter.
3
3
4 ? Dmax ?
4 ?D?
??
? ?e = ?? ? ? w ,
3 ? 2 ?
3 ?2?
(4.4)
where ? w is the density of liquid water. The precipitation rate (S, snowfall rate) is calculated as
50
S = 0.6 ? ? v ( D ) N ( D ) D 3dD .
(4.5)
For the snowfall rate calculation, the following equation by Rutledge and Hobbs (1983) for
terminal velocity near ground is employed:
0.11
v ( D ) = 1.139 Dmax
,
(4.6)
where Dmax is the maximum dimension of snowflakes in m.
Figure 4.2 shows the so-derived Ze-S relationships by symbols for three frequencies (13.4,
35.6, and 94 GHz) together with several other relationships published in the literature for
comparison. The calculated results for sector and dendrite snowflakes (refer to Fig. 4.1) are
represented respectively by circles and inverted triangles in the figure. The Ze-S relations derived
in this study are generally within the envelope of previously published ones. It appears that the
difference of the Ze-S relations between the sector and dendrite snowflake types is small
compared to the difference among different frequencies. Therefore, we take the averaged
relationship of these two snowflake types, but use the separate equation for each of two PR-2
frequencies (13.4 and 35.6 GHz), i.e.,
Z e = 250S 1.083
at 13.4 GHz
(4.7a)
Z e = 88.97 S 1.04
at 35.6 GHz
(4.7b)
Z e = 38.06 S 1.057
at 94.0 GHz
(4.7c)
where Ze is the equivalent radar reflectivity in mm6 m-3, and S is the snowfall rate in mm h-1.
Here, the equation (4.7c) at 94 GHz is derived for the Airborne Cloud Radar (ACR) sensor that
is another airborne instrument mounted to the NASA P-3 aircraft together with MIR and PR-2
during the Wakasa Bay 2003 field experiment. Although the ACR data (Stephens and Austin,
2004) is not presented in this study, the equation and the data set would be useful for the future
research.
51
104
103
Ze (mm6m-3)
102
101
Sector Snowflake-13.4GHz
Sector Snowflake-35.6GHz
Sector Snowflake-94.0GHz
Dendrite Snowflake-13.4GHz
Dendrite Snowflake-35.6GHz
Dendrite Snowflake-94.0GHz
Wakasa snow (Aonashi,2003)
Snow_dry (Puhakka,1975)
Snow (Sekhon & Srivastaya,1970)
Snow_dry (Imai,1960)
Snow_plate, column (Ohtake & Henmi,1970)
Single crystals (Carlson & Marshall,1972)
Snow_dry (Fujiyoshi et al.,1990)
Snow (Boucher & Wieler,1985)
100
10-1
10-2
0.1
0.2
0.4
1
2
4
Snowfall Rate (mm/h)
Figure 4.2: Ze-S relationships for snow from calculations using DDA and several previous
studies. The calculated results for sector and dendrite snowflakes are represented respectively by
circles and inverted triangles at 13.4, 35.6, and 94 GHz.
52
4.2 Radiative Transfer Modeling of the Observed Snow Events
Since the a-priori database linking the brightness temperatures and snowfall rate will be
constructed by radiative transfer calculations, it is essential that the radiative transfer model can
produce brightness temperatures consistent with observations. This step is particularly important
for the radiative transfer modeling of snowfall because the scattering properties of nonspherical
snowflakes are not as well understood as those of raindrops. In this section, we simulate and
compare the model brightness temperatures with those observed by MIR during the Wakasa Bay
2003 field experiment to ensure the validity of the radiative transfer model. The radiative transfer
model used in the study solves the radiative transfer equation using discrete ordinate method (Liu,
1998) and calculates the single-scattering properties of nonspherical snowflakes using the DDA
based parameterization described by Liu (2004) assuming that the snowflakes are comprised of
equally (by mass) mixed sector and dendrite particles with random orientations as mentioned
above.
On 29 January 2003, strong northwesterly flow was dominant over the Sea of Japan, and
extensive snowfall areas were reported along the west coast of the main island of Japan. An
aircraft flight observing the snowfall over ocean was conducted along several different flight
legs; Figure 3.16 shows the well-developed convective cells, with echo tops up to 4 km,
observed on the first flight leg by the airborne radiometer MIR and the PR-2 radar. To take into
account the emission from cloud liquid water, a layer of cloud liquid water is assumed between 3
and 3.5 km. The liquid water path (LWP, g m-2) is determined by the brightness temperature
increase at 89 GHz using LWP = 0.84 ( ?TB 89 ) 2 that is derived by regressing radiative transfer
model simulation results. Due to the uncertainties for input variables such as atmospheric water
vapor profiles and snow particles size distributions, we choose to vary these variables in the
radiative transfer model simulations.
One of the most commonly used particle size distributions for snowflakes is in an
exponential form (Sekhon and Srivastava, 1970):
N ( D) = N 0 exp(??D) .
53
(4.8)
The parameters N0 and ? may be expressed either as constants or functions of snowfall rate. In
the radiative transfer simulations, we used the same form of the particle size distribution as (4.8),
but with two different parameterizations of the N0 and ?. First, the distribution of Sekhon and
Srivastava (1970) has been used, with N0 and ? are parameterized as functions of S. The second
size distribution is derived from data by Dr. Muramoto?s research team at Kanazawa University
(http://sharaku.eorc.jaxa.jp/AMSR/data_val/, referred to as the Muramoto size distribution
hereafter), who analyzed images of snow particles observed at Fukui Airport every 10 minutes
from 1600 LST 28 January to 0800 LST 29 January 2003. In Fig. 4.3, some examples of the
observed particle size distributions and their corresponding precipitation rates are presented. The
parameters for the exponential distribution equation are obtained from curve-fittings of these
observations. The Muramoto size distribution is used in the radiative transfer simulation together
with the size distribution of Sekhon and Srivastava (1970).
Simulations are conducted to examine the radiative transfer model and the specification
of the input parameters. In Fig. 4.4, the model results are shown for the 29 January 2003 snow
case (Fig.3.16). The x-axis represents the MIR observations and the y-axis the model results.
The black circles are the results of using the Muramoto size distribution (from observations) and
one Fukui sounding profile with the surface wind speed of 8 ms-1 that is the mean from surface
observations at the Fukui airport during the field experiment; the red triangles show the Sekhon
and Srivastava size distribution and the US standard winter mid-latitude atmosphere; the blue
triangles represent the Sekhon and Srivastava size distribution and one Fukui sounding profile.
Considering all the uncertainties related to the model inputs, the modeled ?TBs generally agree
well with the MIR observations. However, the modeled results at 340 GHz have relatively larger
depressions than observed in comparison. As expected, the 89 GHz channel responds more
sensitively to liquid water compared to the other channels; this results in positive ?TB values in
Fig. 4.4. From the other test simulations (not shown here), the surface temperature change (from
273 K to 267 K) in the model does not have any measurable effect on the results of brightness
temperature depressions.
54
400
200
0
1000
Jan 28 22:00-22:59
800
600
400
200
0
3000
2500
2000
1500
1000
500
0
1000
Precipitation (mm/h)
-3
-3
-1
Number (m mm )
-3
Precipitation (mm/h)
600
Jan 29 04:00-04:59
Precipitation (mm/h)
-3
00-09 min
10-19 min
20-29 min
30-39 min
40-49 min
50-59 min
-1
Number (m mm )
800
Jan 29 06:00-06:59
-1
Number (m mm )
Precipitation (mm/h)
Jan 28 18:00-18:59
-1
Number (m mm )
1000
800
600
400
200
0
0
2
4
6
8
Diameter (mm)
5
Jan 28 18:00-18:59
4
3
2
1
0
5
Jan 28 22:00-22:59
4
3
2
1
0
7
6
5
4
3
2
1
0
5
Jan 29 04:00-04:59
Jan 29 06:00-06:59
4
3
2
1
0
06:00
06:20
06:40
07:00
Time (min)
Figure 4.3: Snow particle size distribution and precipitation from ground observations at Fukui
airport during Wakasa 2003 Field experiment.
55
60
Model ?TB
30
60
89GHz
30
0
0
-30
-30
-60
-60
S-S & Standard winter
S-S & Fukui
Muramoto & Fukui
-90
-120
-120 -90
-60
-30
0
30
60
60
Model ?TB
30
-120
-120 -90
-60
-30
0
30
60
-30
0
30
60
-30
0
30
60
60
220GHz
30
0
-30
-30
-60
-60
-90
-90
-120
-120 -90
-60
-30
0
30
60
60
Model ?TB
-90
0
30
150GHz
340GHz
-120
-120 -90
-60
60
183+1GHz
30
0
0
-30
-30
-60
-60
-90
-90
-120
-120 -90
-60
-30
0
30
60
MIR ?TB
183+7GHz
-120
-120 -90
-60
MIR ?TB
Figure 4.4: Comparisons of brightness temperature depressions between MIR observations and
the radiative model results.
?: Sekhon and Srivastava distribution with US standard atmosphere winter profile
?: Sekhon and Srivastava distribution with a Fukui radiosonde sounding
?: Muramoto distribution with a Fukui radiosonde sounding
56
4.3 Constructing the Database
Now that the radiative transfer model produces reasonable brightness temperatures, we
next use this model to link snowfall rate with brightness temperatures at high microwave
frequencies. The snowfall profiles in the database are made using two sources: PR-2 data from
Wakasa Bay 2003 experiment and surface radar data from February 2001. The PR-2 snowfall
rate profiles are derived from PR-2 observations on 29 January 2003. Radar reflectivity is
converted to snowfall rate using the equations (4.7a and b), and a liquid water cloud layer is
inserted between 3 and 3.5 km with liquid water path calculated from 89 GHz ?TB. A total of
2201 snow profiles are generated from the PR-2 dataset.
Surface radar data from two snowy days, 13-14 February 2001, are also used to enrich
the database. Radar reflectivity was converted to snowfall rate using the Aonashi et al. (2003)
empirical Ze-S relationship. As mentioned earlier, the snow clouds in this region are rich in liquid
water. However, the surface radar observations do not contain information on cloud liquid water
because of the small size of cloud liquid water droplets, and there have been very few in situ
measurements of liquid water content profiles that are vertically concurrent in both time and
space. To obtain realistic snow cloud profiles for radiative transfer modeling, we add a liquid
water cloud layer to the snowfall profiles derived from surface radar. To determine how much
liquid water to include in each snowfall profile, we conducted an Empirical Orthogonal Function
(EOF) analysis on the database from the Wakasa Bay 2003 field experiment, in which both
snowfall profile and liquid water amount are available. The EOF method, as described by
Biggerstaff et al. (2005) and von Storch and Zwiers (1999), relates one-dimensional variable of
snowfall profiles to the scalar variable of liquid water content. Using this method, the
dimensionality of each snowfall profile can be reduced to the scalar values of the EOF
coefficients. Using these coefficients, the relationship between the vertical distribution of liquid
water contents and snowfall profiles was obtained. The derived liquid water contents of each
snowfall profile in 2001 are combined with surface radar data to construct about 10000 snow
cloud profiles.
The a-priori database are then constructed through radiative transfer model simulations
with all possible combinations of: about 2200 Wakasa Bay 2003 snow cloud profiles including
information of snowfall and liquid water, about 10000 surface radar (in 2001) snow cloud
57
profiles, a total of 10 atmospheric sounding profiles (from observations at the Fukui airport and
the US standard mid-latitude winter atmospheric profile), three different surface temperatures,
and two type of particle size distributions. The total number of datum points in this database is
about 260000. Using this a-priori database, the snowfall algorithm that is developed based on
Bayes theorem (described in the next chapter) retrieves snowfall profiles from the satellite
observations (e.g., AMSU-B).
58
CHAPTER 5
BAYESIAN RETRIEVAL ALGORITHM
A retrieval algorithm based on Bayes? theorem can be stated mathematically as follows
(e.g., Olson et al., 1996; Evans et al., 1995, 2002). Let vector x represents snowfall rate profiles,
and vector y0 represents available observations that are brightness temperature observations in
this study. In general, the best estimate of x, given the observations y0, is assumed as the
expected value,
E(x) =?? ...? x pdf (x) dx .
(5.1)
In Bayes? theorem, the probability density function, pdf (x) is written as
pdf ( x ) ? P( y = y 0 | x = x true ) P( x = x true ) ? POS [ y 0 ? y s ( x )] Pa ( x ),
(5.2)
where POS is the probability equivalent to the distance between observation y0 and simulations by
a radiative transfer model ys(x) for the atmosphere state x. Pa is the a-priori probability that x is
true. If we assume that the errors in the observations and the simulations are Gaussian and
uncorrelated, then POS can be written as
POS [y 0 ? y s (x)] ? exp{?0.5[y 0 ? y s (x)]T � (O + S) ?1 [y 0 ? y s (x)]} ,
(5.3)
where O and S are the observation and simulation error covariance matrices, respectively.
For a sufficiently large database, the integral in (5.1) can be approximated by the
summation for all xj. If we assume that the profiles in the database occur with the same relative
frequency as those in nature, or at least with the same frequency as those found in the region
59
where the retrieval method is applied, then the weighting by Pa is represented simply by the
relative number of occurrence of a given profile type xj. Then (5.1) may be written as
? (x) = ? x
E
j
exp{?0.5 [y 0 ? y s (x j )]T � (O + S) ?1 [y 0 ? y s (x j )]}
A?
j
,
(5.4)
where the normalization factor is
A? = ? exp{?0.5 [y 0 ? y s (x j )]T � (O + S) ?1 [y 0 ? y s (x j )]} .
(5.5)
j
In other words, the expected vector is from the normalized summation of multiplication of
atmospheric parameters xj and their corresponding weighting factor over a large ensemble of predefined snowfall-brightness temperature database. The weighting factors are determined by the
error covariance matrices (such as O and S) and a square of the vector distance
( [ y 0 ? y s ( x j )]T [ y 0 ? y s ( x j )] ) between the observed and simulated. In the present study, the
error covariance matrices, O and S, are set as follows similar to Olson et al. (1996) and Seo and
Liu (2005). The error covariance matrix, S, has no contribution if the model simulation, ys(x), is
assumed to be true. The observation error variances are set equal to the instrument error
variances with an assumption of zero-mean Gaussian distributed noise with a standard deviation
of 1.5 K to each channel except for 0.6 K to 150 GHz and 183�GHz. Due to a lack of
information on the correlation of errors between channels, only the diagonal terms of the matrix
O are estimated here, and off-diagonal terms are set to zero. The matrix (O+S)-1 for any in a
model database is inversely proportional to the value of a diagonal term of the error variance,
which determines the width (or spread) of the weighting function in terms of brightness
temperature distance. In the retrievals, we use [3 K, 1.2 K, 3 K, 3 K, 1.2 K] for ?TB ? 15 K and
[4.5 K, 1.8 K, 4.5 K, 4.5 K, 1.8 K] for ?TB ? 15 K, respectively, as observation plus simulation
uncertainties for each frequencies for AMSU-B. The algorithm is then applied to the case of 29
January 2003 as an assessment of the algorithm?s performance. Figure 4.5 shows the retrieved
snowfall by applying the algorithm to MIR data measured for two different flight legs. The
observed snowfall from PR-2 35 GHz (the upper panels) is compared with the retrievals. It
appears that the retrieval algorithm captures well the basic features of the snow cloud cells,
60
although differences exist in details between the observed and retrieved structures. Comparisons
between column-accumulated snowfall rates from these results are represented along leg 1 and
leg 3 in Fig. 5.2, which also shows reasonable agreements between observations and retrievals.
(a)
(b)
Figure 5.1: Comparisons of PR-2 observations at 35 GHz (upper) and retrieved snowfall rate
(lower) along (a) leg1 and (b) leg3.
61
100
100
Retrievals (mm/h)
(a) Leg1
(b) Leg3
80
80
60
60
40
40
20
20
0
0
0
20
40
60
80
100
Observations (mm/h)
0
20
40
60
80
100
Observations (mm/h)
Figure 5.2: Scatter plots between column-accumulated snowfall rates from PR-2 observations at
35 GHz and retrievals along (a) leg1 and (b) leg3.
62
CHAPTER 6
APPLICATION OF AMSU-B SNOWFALL RETRIEVAL TO
SNOWFALL CASES OVER THE SEA OF JAPAN
The snowfall retrieval algorithm is applied to the AMSU-B satellite data. Since there are
no 220 and 340 GHz channels in AMSU-B, the AMSU-B version of the retrieval algorithm only
uses data from five channels with frequencies from 89 to 183�GHz. Three snowfall cases are
studied from 14, 16 and 27 January 2001. These were located over Japan and its surrounding
areas, and coincided with the field experiment, ?Winter MCSs Observations over the Japan Sea 2001? (Murakami et al., 2001a, 2001b; Yoshizaki et al., 2001). During 12 to 19 of January, the
cold airmass with air temperature lower than ?35 癈 at 500 hPa stayed quasi-stationary over the
Japan Sea. Heavy snowfalls occurred on the western coastal areas of the Japan Islands. The
snowfall was mainly induced by quasi-stationary band-shaped snowfall systems elongated east
and west along the southern coast of Japan. Meanwhile, on 27 January a synoptic cyclone
developed and brought heavy snowfalls over the Kanto plain.
Since there are no intensive in situ observations to directly determine background
temperatures for theses cases in 2001, AMSU-B data are used for the statistical calculation of
background temperatures by analyzing the histograms over the 2-month period January through
February 2001. During this period, the brightness temperatures that are most frequently occurred
at 150 GHz at all AMSU-B scanning angles are used as the standard of clear sky. The focused
domain is then divided into four areas: land, coast, sea-1, and sea-2 (37.5-39 N, 133-136 E). The
coast is the region affected by the land contamination, and the sea-2 is the remote region much
farther from the coast compared to sea-1 area. At each channel, by averaging brightness
temperatures higher than the standard value for the clear-sky, the background temperature over
each area is derived.
Figures 6.1 through 6.3 show the brightness temperature depressions at four of the five
63
AMSU-B frequencies, the retrieved snowfall rates at 1.5 and 2.1 km, the hourly-accumulated
snow amount from the AMeDAS radar data, and the GMS infrared (IR) cloud top temperatures
for the three cases. Note that the AMeDAS radar snow amount is the hourly-accumulated snow
(in mm) averaged for 3 hours around the satellite passing time, not instantaneous snowfall rate.
Heavy snow bands are observed in the Wakasa Bay area on 14 and 16 January from the AMSUB observations (Fig. 6.1a-d and 6.2a-d). As stated by Bennartz and Bauer (2003), the reduction
of brightness temperature due to the scattering of snow appears much stronger at 150 GHz than
at 89 GHz. The snow bands are also clearly resolved at 183�GHz frequency. On 14 January
2001, the retrievals near the surface (Fig. 6.1e-f) are in good agreement with the AMeDAS radar
observations. In particular, strong snow bands northeast of the Wakasa Bay are clearly
reproduced in the retrievals. Despite the difficulty of directly quantitative comparison between
surface radar data and retrievals from the satellite, the maximum snowfall region shows a similar
magnitude and pattern. Meanwhile, in Fig. 6.1h IR signals for snowfall are not clearly
distinguishable; there is just an exceedingly blurred pattern of clouds. It is noteworthy that the
broad distribution of the depressions of brightness temperatures at 183�GHz is very similar to
that of low IR cloud top temperatures.
For the 16 January 2001 case, our retrieval algorithm detects two strong stationary snow
bands shown in Fig. 6.2b, although the maximum snowfall appears slightly behind in the west
side of the Wakasa Bay. The snow band in the 16 January case is a continuation of the snow
band shown earlier on 14 January, which lasted several days. However, the pattern of brightness
temperature depressions at 89 and 183�GHz channels become less similar to that of 150 and
183�GHz channels and differ significantly from the IR image. It is inferred that the
characteristics of these snow bands, including the change of the composition of liquid and
ice/snow in the clouds, have changed during 14 to 16 January.
In contrast to snow bands in the previous two cases, an organized snow cloud system
associated with a polar low on 27 January was observed. In the GMS IR image (Fig. 6.3h), we
can see that clouds covered most of the central Japan. The intense echo area was circular/spiral
in shape and corresponded to the maximum depression of brightness temperature of about 70 K
at 150 GHz (Fig. 6.3b). The AMSU-B snowfall retrievals show broad snow coverage over
central Japan that compares well with AMeDAS snow accumulation about 2 hours after satellite
64
passing time. In Fig. 6.4, retrieved snowfall and observed ?TB values of AMSU-B are shown in
each snowfall case.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure 6.1: Comparisons of observations and retrieved results on 14 January 2001. (a-d)
Brightness temperature depressions from the AMSU-B at 89, 150, 183+3, and 183+7 GHz, (e-f)
retrieved snowfall at 1.5 km and 2.0 km from the surface, and (g) hourly accumulated snow data
(3-hr averaged) from the AMeDAS radar data and (h) GMS IR cloud top temperatures.
65
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure 6.2: Same as Fig. 6.1, but for 16 January 2001.
66
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure 6.3: Same as Fig. 6.1, but for 27 January 2001.
67
Larger retrieved snowfalls are corresponding well to large depressions of brightness
temperatures, although in 16 January 2001 case the results are slightly more scattered and have
smaller values compared to the other cases.
Next, we examine the algorithm?s performance in a more quantitative manner using a
scatterplot of satellite retrieved snowfall rate versus AMeDAS radar observed hourly snowfall
accumulation (Fig. 6.5). The data pairs in the scatterplot are generated by averaging the satellite
retrievals and the AMeDAS radar hourly snow accumulations to a 1� latitude x 1� longitude grid.
In addition, for a satellite retrieval, AMeDAS hourly snowfall accumulations (3-hr averaged to
the center time) from 3 time periods are compared: the nearest hour to the satellite passage, 1
hour after, and 2 hours after satellite passage. The correlation coefficients between retrievals and
AMeDAS data at these times (refer to Table 6.1) are, respectively: 0.796, 0.834, and 0.790 for 14
January 2001 case; 0.625, 0.634, and 0.629 for 16 January 2001 case; and 0.915, 0.960, 0.971 for
27 January 2001 case. Although the correlation coefficients for the January 16 case are relatively
lower than the other cases, the highest correlation between the satellite retrievals and surface
radar measurements occurs 1 or 2 hours after the satellite passage. This phenomenon may reflect
the fact that satellite-measured quantities are snow particles floating in the atmosphere; it takes
time for the low-terminal-velocity snowflakes to reach surface.
Table 6.1: Correlation coefficients between snowfall retrievals and AMeDAS radar data.
Time
14 January 2001
16 January 2001
27 January 2001
At the nearest hour
0.796
0.625
0.915
+ 1 hour
0.834
0.634
0.960
+ 2 hours
0.790
0.629
0.971
The correlation coefficients shown above for the three cases are very different, ~0.8 for
January 14 case, ~0.6 for January 16 case, and ~0.96 for January 27 case. To get insight to this
68
difference, we investigate how brightness temperature at each frequency contributed to the
retrieval. Figure 6.6 shows the brightness temperature depressions at different channels versus
snowfall rate retrievals. The correlation coefficients (Table 6.2) are respectively ?0.590, ?0.869,
?0.526, and ?0.945 at 89 GHz, 150 GHz, 183�GHz, and 183�GHz for 14 January 2001 case.
For 16 January 2001 case, they are ?0.126, ?0.483, ?0.482, and ?0.830. For 27 January 2001
case, the values are ?0.841, ?0.945, ?0.751, and ?0.956. For all the cases, the correlations are
higher at 150 GHz and 183�GHz except for 150 GHz of 16 January case. Since they are more
sensitive to ice/snow scattering, higher weightings has been given to these two channels in our
snowfall retrieval algorithm.
Table 6.2: Correlation coefficients between snowfall retrievals and AMSU-B channels.
Channels
14 January 2001
16 January 2001
27 January 2001
89 GHz
?0.590
?0.126
?0.841
150 GHz
?0.869
?0.483
?0.945
183�GHz
?0.526
?0.482
?0.751
183�GHz
?0.945
?0.830
?0.956
It is interesting to notice that for the January 27 case the correlation coefficients between
snowfall rate and brightness temperature at all channels are high. In this case, the brightness
temperature depressions are much larger than the other cases. From these results for three
snowfall cases, it is found that the strong scattering signature leads the algorithm to perform the
best. On the other hand, on January 16 the brightness temperature depressions are small, and the
correlation for 89 GHz is even close to zero. It is interpreted that rich cloud liquid water exists in
this case, and the algorithm performs not as well under such conditions.
69
Column-accumulated snowfall
(a) 14 Jan 2001
102
101
100
10
20
30
40
50
60
70
Column-accumulated snowfall
Retrievals (mm/h)
(b) 16 Jan 2001
102
101
100
0
10
20
30
40
Column-accumulated snowfall
Retrievals (mm/h)
(c) 27 Jan 2001
102
101
100
0
20
40
60
80
100
Magnitude of ?TB (K)
Figure 6.4: Relations between the magnitude of brightness temperature depression of AMSU-B
and the column-accumulation of retrieved snowfall for three cases.
70
Observations (mm)
2.0
(a) 14 Jan 2001
1.5
1.0
0.5
?time=0hr
?time=+1hr
?time=+2hr
0.0
0.0
Observations (mm)
1.5
0.5
1.0
1.5
2.0
Retrievals (mm/h)
(b) 16 Jan 2001
1.0
0.5
0.0
0.0
6
0.5
1.0
1.5
Retrievals (mm/h)
(c) 27 Jan 2001
Observations (mm)
5
4
3
2
1
0
0
1
2
3
4
5
6
Retrievals (mm/h)
Figure 6.5: Comparisons between retrieved snowfall rates and 3-hr averaged hourly
accumulated surface radar snow amounts at the nearest corresponding time, after 1 hour, and
after 2 hours respectively for 14, 16, and 27 January 2001.
71
10
(a) 14 Jan 2001
5
?TB (K)
0
-5
-10
-15
-20
89GHz
150GHz
183+1GHz
183+7GHz
-25
-30
0.0
0.5
10
1.0
1.5
2.0
Retrievals (mm/h)
(b) 16 Jan 2001
5
?TB (K)
0
-5
-10
-15
-20
0.0
0.2
0.4
0.6
0.8
1.0
Retrievals (mm/h)
(c) 27 Jan 2001
20
?TB (K)
0
-20
-40
-60
-80
0
1
2
3
4
5
6
7
Retrievals (mm/h)
Figure 6.6: Comparisons between retrieved snowfall rates and AMSU-B brightness temperature
depressions at each frequency respectively for 14, 16, and 27 January 2001.
72
Figure 6.7: Comparison between retrieved snowfall rates and hourly-accumulated snow data
from the AMeDAS radar data averaged for 14 snowfall cases during January and February 2001.
To extend the algorithm validation beyond case studies, the snowfall algorithm is applied
to other 14 snowfall cases during January and February of 2001 in Japan region where is a more
northern part than the previous three snow cases, and the mean snowfall distribution for these 14
cases is derived from AMSU-B data (Fig. 6.7). To distinguish between snowfall and rainfall,
surface air temperature data from NCEP reanalysis data provided by the NOAA-CIRES Climate
Diagnostics Center (available at http://www.cdc.noaa.gov) are used. Only those precipitation
events with surface temperature below 0 癈 are chosen as snowfall cases, and the satellite data
coverage and radar data availability are also considered for the case selection. The retrieved
mean snowfall distribution is compared with AMeDAS radar data that are an hourlyaccumulation and averaged for three hours to the center time about one hour after the satellite
passage. From Fig.6.7, it is seen that the averaged snowfall retrievals show a fairly good
agreement with surface radar observation in pattern, especially showing well the snowfall
maximum over the west part of Japan. However, slightly strong retrieved snowfall signals of the
73
southwest part over land do not appear in the radar data. It can be the accumulated snow over
land influenced by the topographical effects. Additionally, snowfall signals appeared over ocean
in the retrievals may represent very low brightness temperatures due to the cold air temperature
in those areas, although there is no radar observation over the ocean so the exact comparison is
not possible.
74
CHAPTER 7
CONCLUSIONS
In this study, a snowfall retrieval algorithm has been developed based on Bayes? theorem
using high frequency satellite microwave data. In developing the Bayesian snowfall retrieval
algorithm, the a-priori database is the most important component. The database in our algorithm
is constructed using various observation data such as satellite, airborne microwave radiometer
measurements, and surface observations. Also, detailed observational analyses are performed for
more realistic and representative database. Our focus is the west coastal region of Japan near
Wakasa Bay and surrounding areas. The results can be summarized as follows:
First, through the temporal analysis of surface radar data, a diurnal variation of snowfall
in the Wakasa Bay (Japan) is detected in this area during winter, suggesting the effects of sea
breeze and topography in temperature contrast. However, the clear diurnal variation of winter
precipitation cannot be identified by satellite IR data. From these results, the possibility of using
IR data to measuring snowfall becomes weak, and we pay more attention to the great potential of
microwave measurements in studying winter precipitation and developing snowfall retrieval
algorithm. The sensitivity of microwave channels to snowfall is then investigated by a radiative
transfer model. The results show that upwelling microwave radiation at frequencies higher than
150 GHz is sensitivite to scattering by snow/ice, while radiation at lower frequencies (e.g., 37
GHz) is not sensitive to snow scattering, but rather sensitive to cloud liquid water.
Second, the scattering signals of snowfall are investigated in the areas at frequencies
ranging from 37 to 340 GHz using satellite and aircraft observations. The snow clouds
investigated in this study are associated with shallow convections caused by cold air outbreaks.
The cold air over warm ocean surface produces strong instability of the low atmosphere, and
often results in heavy snowfall. A significant amount of liquid water is often observed in the
75
convective cells as evidenced by the increase in 89 GHz brightness temperatures. At 37 GHz, the
snowfall scattering signature seems to be insignificant, while liquid water in some convective
cells increases brightness temperature (as much as ~30 K at 37 GHz horizontal polarization). At
89 GHz, the data show both the brightness temperature decreases due to ice scattering and
brightness temperature increases due to liquid water emission. Occasionally, these increases and
decreases occur at different locations of a convective cell. Observations using dual-polarization
clearly have advantage because we may use the polarization corrected temperature and the
polarization difference to separate, to a certain extent, the scattering and emission signatures.
Using AMSR-E data, the lowest PCT depression is about 25 K for the studied case. However,
the sensitivity to snowfall at 89 GHz is largely reduced for AMSU-B, which has a much larger
footprint and only a single polarization. At higher frequencies, the snowfall signatures become
evident even without the use of PCT. At the spatial resolution of AMSU-B pixels (~16 km at
nadir), we observed 15 ~ 20 K brightness temperature decrease at 150 and 183�GHz for the
studied case. At finer spatial resolution observed by airborne radiometers, the nadir view
brightness temperatures decrease as large as 40, 50, 60, and 80 K for 150, 183� 220, and 340
GHz channels, respectively. Furthermore, the influence by liquid water to channels of 183�GHz or higher frequencies is small. At 150 GHz, besides the brightness temperature decreases
induced by ice scattering, the brightness temperature increases caused by liquid water are also
evident, similar to but not as much as those at 89 GHz. Therefore, having a dual-polarization in
future instruments for this frequency is desirable for a better separation between liquid and ice
water signatures.
Third, the snowfall retrieval algorithm is developed. The algorithm is based on Bayes?
theorem using high frequency microwave radiometry observations. In developing the Bayesian
snowfall retrieval algorithm, the a-priori database is the most important component.
Observational data from both airborne and surface-based radars are used to construct an a-priori
database of snowfall profiles. These profiles are then used as input to a forward radiative transfer
model to obtain brightness temperatures at high microwave frequencies. Since the a-priori
database is an essential component of the Bayesian retrieval algorithm, special attention has been
paid in this study to its construction. First, the backscattering of radar reflectivity and the singlescattering properties used in the radiative transfer model are calculated using discrete dipole
approximation for realistic nonspherical ice particles. Using the scattering properties from
76
nonspherical particles, snowfall rates derived from radar reflectivities and brightness
temperatures calculated from radiative transfer models are expected to be more accurate than
those computed from (so far) widely used spherical approximations. The radiative transfer model
that is used to compute brightness temperatures for given snowfall rate profiles was tested
against airborne microwave radiometer data. Given the uncertainties of input variables, it appears
that the model results agree reasonably with observations except for a very high frequency 340
GHz channel. Second, the snowfall rate profiles used for building the database are from actual
radar observations. The usage of observational data instead of numerical model outputs ensures
that the statistics of snowfall rate profiles in the database are consistent with those occurred
naturally. To enrich the database, we included profiles from airborne radar and surface radar
observations. Third, the diversity of the database is further enhanced by using two different types
of particle size distributions: the widely used Sekhon and Srivastava (1970) distribution and the
Muramoto distribution that was derived in the Japan Sea region using in situ ice particle
measurements. Furthermore, embedded cloud liquid water layers and ten atmospheric sounding
profiles are used as input for computing brightness temperatures by a radiative transfer model.
Fourth, the snowfall retrieval algorithm is first validated by airborne microwave
radiometer and radar observations, and then applied to the AMSU-B satellite data and validated
by surface radar-gauge network data over Japan. The retrieved snowfall rates using AMSU-B
data for three snowfall cases in the vicinity of Japan show good agreement with surface radar
observations. The correlation coefficients between 1皒1� gridded results of retrieved snowfall
rate and AMeDAS radar snow accumulation varies from ~0.6 for a relatively light snowfall case
of snow bands with smaller scales to ~0.96 for a heavy snowfall case associated with a lowpressure system. It appears that the snow particles are relatively ?wet? for the low correlation
case with rich cloud liquid water in the clouds, but the snow particles are ?dry? for the high
correlation case, in which all AMSU-B channels show appreciable scattering signatures.
Therefore, further characterizing the vertical structure of hydrometeors through inclusion of
cloud liquid water layer, and through observation, and through developing the a-priori database
accordingly are highly desirable for improvement of accuracy of wet snowfall retrieval in the
future. Using the constructed database, the snowfall algorithm is applied to calculate the mean
snowfall distributions in the vicinity of Japan from AMSU-B data for other 14 snowfall cases
during January and February in 2001. Considering the satellite data coverage and radar data
77
availability, those snow cases for January and February in 2001 are chosen when the areaaveraged surface temperature from NCEP reanalysis data is below 0 癈. The retrieved snowfall
is compare with AMeDAS radar data. In comparison, the averaged snowfall retrievals show
fairly good agreement in pattern, especially in the west part of Japan, although the exact
validation for the snowfall retrievals over ocean is not possible due to the lack of radar data in
this area.
From the results of this study, the following future works are considered. The database
developed in this study is based on observations of snowfall events near the Japan Sea for the
sole reason of data availability. Therefore, our algorithm is considered best suited for snowfall in
this region. However, as more snowfall radar observations become available in the future such as
the CloudSat radar (Stephens et al., 2002), first, a global database can be constructed in a similar
fashion, and the algorithm may be applied globally. For this, deeper understanding of detailed
structures of snow clouds in each area and more validations also are needed. Next, developing a
more general discrimination method between snowfall, rain and snow cover signatures will be
necessary, although actual observations and surface temperatures from NCEP/NCAR reanalysis
data are used in this study. A few related studies have been performed. For example, Kongoli et
al. (2005) suggested an empirical method utilizing the unique combination of the AMSU
frequency, but it is still a challenging work. In addition, using dual-polarization observations are
preferable to clearly detect scattering signals and improve more accurate retrieval algorithm.
78
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84
BIOGRAPHICAL SKETCH
EDUCATION
Ph.D., Meteorology, (in progress), Florida State University, Tallahassee, FL, USA
M.S.,
Environmental Heat/Fluid Mechanics Program, School of Environmental Engineering, Pohang
University of Science and Technology, Korea, 1999
B.S.,
Astronomy and Atmospheric Sciences, Yonsei University, Korea, 1997
EXPERIENCE
Research Assistant, Dept. of Meteorology, FSU, Dr. Guosheng Liu?s Lab, Sept. 2001 ? Present
Research Associate, Global Environment Lab., Yonsei University, Oct. 1999 ? Aug. 2001
Instructor, Dept. of Atmospheric Sciences, Yonsei University, Sept. 2000 ? Dec. 2000
Researcher Associate, Remote Sensing Research Lab., Meteorological Research Institute/Korea
Meteorological Administration, April 1999 ? Oct. 1999
Research Assistant, Environmental Fluid Mechanics Lab., Pohang University of Science and Technology,
Sept. 2001 ? Feb. 1999
PUBLICATIONS
Noh, Y. J., G. Liu, E. K. Seo, J. R. Wang, and K. Aonashi, 2005: Development of A Snowfall Retrieval
Algorithm at High Microwave Frequencies. J. Geophys. Res. (Under review).
Noh, Y. J. and G. Liu, 2004: Satellite and Aircraft Observations of Snowfall Signature at Microwave
Frequencies. Rivista Italiana di Telerilevamento, 30, 101-118.
Noh, Y. J., G. Liu, N. Balas, K. Aonashi, and T. Koike, 2004: Diurnal variations of snow precipitation in
Wakasa Bay during winter. J. Meteor. Soc. Japan, 82, 1117-1128.
Varma, A. K., G. Liu, and Y. J. Noh, 2004: Sub-pixel scale variability of rainfall and its application to
mitigate the beam-filling problem. J. Geophys. Res. 109, D18210, 10.1029/2004JD004968.
MEMBERSHIP OF SOCIETIES
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85
ed themselves along the streak clouds while they are much smaller and
weaker than those in the first case on 29 January 2003. In Fig. 3.14d, it is seen that several small
cells with low PCTs are orientated from northwest to southeast. At 37 GHz, no significant
signatures are identified along the track. The brightness temperature values along the aircraft
flight track (shown in Figs. 3.14d and 3.14h, or A2-B2 in Fig. 2.1) are shown in Fig. 3.15. The
lowest PCT depression at 89 GHz in a cell center is about 10 K near 135.2癊 compared to
surrounding cloud-free regions and the depression is much smaller at 37 GHz. Unlike in the first
case, in Fig. 3.15a, the maximum of the horizontally polarized brightness temperature of about
220 K, the lowest PCT of about 257 K, and the lowest polarization difference of 23 K occur at
40
Figure 3.14: Brightness temperatures of AMSR-E at 89 GHz and 37 GHz: (a) and (e) vertically
polarized TBs, (b) and (f) horizontally polarized TBs, (c) and (g) the polarization difference, DP,
and (d) and (h) the polarization-corrected temperature, PCT at 0414 UTC on 30 January 2003.
41
89GHz A2-B2
TBv
50
TB (K)
240
DP
40
220
TBh
200
30
20
180
37GHz A2-B2
240
TB (K)
220
DP89 (K)
PCT
(a)
80
PCT
(b)
TBv
200
DP
70
60
180
TBh
160
140
134.5
DP37 (K)
260
60
50
40
135.0
135.5
136.0
136.5
137.0
Longitude
Figure 3.15: Vertically polarized TBs, horizontally polarized TBs, PCT, and the polarization
differences of AMSR-E at (a) 89 GHz and (b) 37 GHz along the line shown in Fig. 3.14.
almost the same position, implying that the location of peak liquid water amount coincides with
the location of the strongest snowfall.
3.3.2
Airborne observations
The snow clouds on January 29 are observed by airborne radiometer MIR and radar PR-2.
One aircraft flight was carried out from 0319 UTC to 0333 UTC along the line of A1 to B1 as
shown in Fig. 2.1 (corresponding to Line 1 in Fig. 3.9). Figure 3.16 shows the aircraft nadir
42
observations of the brightness temperature depressions compared to the clear-sky values and the
time-height cross section of snowfall rate converted from PR-2 13.4 GHz radar reflectivity. For a
downward looking radiometer above the snow cloud, the scattering decreases the brightness
temperature compared to that from clear sky. In the brightness temperature depressions (?TB =
TB -TB0, where TB0 is the clear-sky brightness temperature), the clear-sky brightness temperatures
are derived from locations where no radar echo was observed; their values are 199.5, 218.7,
241.4, 250.6, 247.3, 243.8, and 255.7 K for 89, 150, 183� 183� 183� 220, and 340 GHz,
respectively. To obtain snowfall rate from radar reflectivity, a new reflectivity-snowfall rate (ZeS) relation are used that is developed for more realistic nonspherical snow particles (more details
given in the next chapter).
In Fig. 3.16, five convective cells can be identified in the radar cross section as indicated
by numbers 1-5. The depression of MIR brightness temperatures responds to these cells,
although the sign and the amplitude of the variation are channel-dependent. The depression of
brightness temperature at 220 and 340 GHz is greater than the other channels, and they reach
about 80 K for the first cell. Among the three 183-GHz water vapor channels, 183�GHz is the
most sensitive to the snowfall cells. It is notably seen from Fig. 3.16a that the 89-GHz brightness
temperatures at some convective cells are higher than clear-sky values, implying that rich cloud
liquid water exists in these cells, a result consistent with Katsumata et al. (2000) who studied
snow clouds in the same region. While the increase in brightness temperature occurs at 150 GHz
as well, the overall signature in this channel is the depression corresponding to snow cell. The
second cell seems to be weaker than the first one, and the brightness temperatures depression is
also smaller for all the channels. Note that at the starting point of the second cell a brightness
temperature peak appears at 89 GHz, suggesting that significant liquid water exists in front of the
center of the second snow cell. The third cell has rather different features, especially at 89 and
150 GHz; brightness temperatures are much greater than those values for the clear sky. It implies
that the third cell contains a great amount of liquid water, although heavy snowfall converted
from strong radar echo is shown from 1 to 4 km in Fig. 3.16c. The fifth cell is divided into two
parts indicated as 5 and 5? in Fig. 3.16c. The left region of the cell has the maximum snowfall
rate near the surface, but MIR brightness temperature depressions do not reach their minimum
until further into the middle of the cell as indicated by 5? in the figure.
43
40
TB (K)
20
0
-20
-40
-60
89
150
220
340
(a)
-80
20
TB (K)
0
-20
-40
-60
183+-1
183+-3
183+-7
(b)
-80
1
2
3
4
5 5?
(c)
Figure 3.16: Comparisons of (a and b) brightness temperature depressions from MIR at seven
frequencies and (c) snowfall rate from PR-2 at nadir for the flight track from 0316 UTC to 0333
UTC on 29 January 2003.
44
To quantitatively assess the relation between brightness temperature and near surface
snowfall rate, the brightness temperatures and radar reflectivity-derived snowfall rate at 1 km (to
avoid surface contamination) are averaged for every 10 seconds (corresponding to ~1000 m in
spatial scale) and plotted in Fig. 3.17. Brightness temperatures in all the channels decrease in
general as snowfall rates increase, although there is a significant large range of scatter. A
regression line for each channel is derived using the 10-sec averaged data and plotted in the
figure. The correlation coefficient is -0.2, -0.46, -0.65, -0.67, -0.66, and -0.68 for data at 89, 150,
220, 340, 183� and 183�GHz, respectively. Based on these data, the sensitivity of brightness
temperature to snowfall rate can be estimated as -4, -10, -16, -22, -10, and -14.4 K (mm h-1)-1 for
89, 150, 220, 340, 183� and 183�GHz channels.
In Fig. 3.17, it is found that some points, as denoted by squares, diamonds, and triangles,
do not follow the general trend in the relationships. The two squares come from the first cell; the
radar-derived snowfall profile corresponding to the profile 1 in Fig. 3.18. Strong radar returns are
observed in a very deep layer, suggesting the center of a very well developed convective cell.
The diamonds correspond to the third cell, which has the vertical radar profile 3 in Fig. 3.18. The
strongest echo occurs in the middle of the layer (about 2 km), and the large increase in 89 GHz
brightness temperatures implies a significant amount of liquid water in the cell. These results
suggest that cell 3 is in the early developing stage, and the bulk of the condensed water is still in
liquid form. The triangles correspond to the first part of the fifth cell that has its bulk of radar
returns near the surface (profile 5 in Fig. 3.18). It is seen from Fig. 3.16c that the patterns of
radar echoes for cells 4 and 5 are vertically tilted, possibly caused by vertical wind shear.
Although overall cell 5 has significantly decreased brightness temperatures, the first part of the
cell did not cause sizable brightness temperature reduction because of only a shallow snowfall
layer existing near the surface. The above discussion illustrates how the horizontal and vertical
structures of snow clouds influence the observed brightness temperatures, and emphasizes the
importance of further observational studies to characterize the three-dimensional structure of
snow clouds.
45
260
89 GHz
150 GHz
220 GHz
340 GHz
183+-1 GHz
183+-7 GHz
TB (K)
240
220
200
180
160
260
TB (K)
240
220
200
180
160
260
TB (K)
240
220
200
180
160
0.0
0.5
1.0
1.5
2.0
Snowfall (mm/hr)
0.0
0.5
1.0
1.5
2.0
Snowfall (mm/hr)
Figure 3.17: Scatter diagrams between brightness temperatures from MIR and near surface
snowfall from PR-2 at nadir with regression lines. Each data is the average for every 10 seconds
(~1000 m in spatial scale). Squares are corresponding to the center of the first cell, diamonds to
the center of the third cell, triangles to the front part of the fifth cell in the PR-2 cross section
shown in Fig. 3.16.
46
5
Height (km)
4
3
2
1
2
0.0
5'
3
4
0.5
1.0
1.5
5
1
2.0
2.5
Snowfall rate (mm/hr)
Figure 3.18: Vertical profiles of snowfall rate obtained from PR-2 by Ze-S relationship in each
cell indicated in Fig. 3.16. The fifth cell is divided into two parts (5 and 5?).
47
CHAPTER 4
BUILDING THE A-PRIORI DATABASE
An important component of a Bayesian retrieval algorithm is the a-priori database that
connects the observations (brightness temperatures) with the parameters to be retrieved (snowfall
rates); the probability density of a snowfall rate in the database should be consistent with the
likelihood of the same snowfall rate occurring in actual snow events. To build such a database,
we collect snowfall data from airborne and surface based radars.
In an effort to accurately calculate the scattering parameters of snowflakes in radar
equations and radiative transfer models, we performed DDA simulations using realistic snow
particle shapes. The DDA (Draine and Flatau, 2000) is a general method for computing the
scattering and absorption of arbitrarily shaped particles and has been used by many researchers
for studying the scattering by ice particles (e.g., Draine, 1988; Evans and Stephens, 1995). The
DDA is an approximation of the continuum target by a finite array of polarizable points that
acquire dipole moments to the local electric field. It has advantage in studies about the scattering
characteristics by complicated shaped particles like dendrites. The Draine and Flatau DDA
model approximates the targets by an array of polarizable points that are located on a cubic
lattice. Two types of snowflakes randomly orientated in space are considered in the DDA
computations as shown in Fig. 4.1. The ice volume is concentrated on the six main branches in
type-A (sector snowflake) and more uniformly spreads in the basal plane in type-B (dendrite
snowflake). Both types of snowflakes obey the following relations derived by Heymsfield et al.
(2002):
?0.377
Ar = 0.261Dmax
,
?1.0
? e = 0.015 Ar1.5 Dmax
48
(4.1)
where Dmax is the maximum dimension of the snowflakes, Ar is the area ratio (the projected area
of a snowflake normalized by the area of a snowflake with diameter Dmax), and ? e is the
effective density defined as the mass divided by the volume of a circumscribed sphere.
(a) Type-A (Sector Snowflake)
(b) Type-B (Dendrite Snowflake)
Figure 4.1: Two types of snowflakes used in the DDA computation.
49
4.1 Conversion of Radar Reflectivity to Snowfall Rate
The backscatter cross sections calculated from the discrete-dipole approximation (DDA)
for snowflakes is used to develop the Ze-S relationships. Vertical snowfall rate profiles used for
building the a-priori database are derived from data of PR-2 and a surface Doppler radar. To
convert equivalent radar reflectivity of the surface Doppler radar to snowfall rate, a Ze-S
relationship empirically derived by Aonashi et al. (2003) is used. This Ze-S relationship was
derived by comparing simultaneous observations of the near surface radar reflectivity of this
radar to the snowfall rate of a weighing snow gauge. However, since there are no simultaneous
Ze and S observations for PR-2, we need to obtain the Ze-S relations for PR-2. The new Ze-S
relationships are derived based on theoretical calculations. From the backscattering cross section
?(D) obtained from DDA calculations, the radar reflectivity can be calculated as follows:
?=
Dmax
? N ( D) ? ( D) dD ,
(4.2)
Dmin
where N(D) is the size distribution. The equivalent radar reflectivity factor Ze (mm6 m-3) can be
derived using
2
? 5 Kw Ze
,
?=
?40
(4.3)
2
where K w (= ~0.93 at 35 GHz) is a parameter related to the complex index of refraction of
water, and ?0 is the wavelength of the radar.
The following equation is used to obtain a melting diameter with equivalent liquid water
density from an observed maximum diameter.
3
3
4 ? Dmax ?
4 ?D?
??
? ?e = ?? ? ? w ,
3 ? 2 ?
3 ?2?
(4.4)
where ? w is the density of liquid water. The precipitation rate (S, snowfall rate) is calculated as
50
S = 0.6 ? ? v ( D ) N ( D ) D 3dD .
(4.5)
For the snowfall rate calculation, the following equation by Rutledge and Hobbs (1983) for
terminal velocity near ground is employed:
0.11
v ( D ) = 1.139 Dmax
,
(4.6)
where Dmax is the maximum dimension of snowflakes in m.
Figure 4.2 shows the so-derived Ze-S relationships by symbols for three frequencies (13.4,
35.6, and 94 GHz) together with several other relationships published in the literature for
comparison. The calculated results for sector and dendrite snowflakes (refer to Fig. 4.1) are
represented respectively by circles and inverted triangles in the figure. The Ze-S relations derived
in this study are generally within the envelope of previously published ones. It appears that the
difference of the Ze-S relations between the sector and dendrite snowflake types is small
compared to the difference among different frequencies. Therefore, we take the averaged
relationship of these two snowflake types, but use the separate equation for each of two PR-2
frequencies (13.4 and 35.6 GHz), i.e.,
Z e = 250S 1.083
at 13.4 GHz
(4.7a)
Z e = 88.97 S 1.04
at 35.6 GHz
(4.7b)
Z e = 38.06 S 1.057
at 94.0 GHz
(4.7c)
where Ze is the equivalent radar reflectivity in mm6 m-3, and S is the snowfall rate in mm h-1.
Here, the equation (4.7c) at 94 GHz is derived for the Airborne Cloud Radar (ACR) sensor that
is another airborne instrument mounted to the NASA P-3 aircraft together with MIR and PR-2
during the Wakasa Bay 2003 field experiment. Although the ACR data (Stephens and Austin,
2004) is not presented in this study, the equation and the data set would be useful for the future
research.
51
104
103
Ze (mm6m-3)
102
101
Sector Snowflake-13.4GHz
Sector Snowflake-35.6GHz
Sector Snowflake-94.0GHz
Dendrite Snowflake-13.4GHz
Dendrite Snowflake-35.6GHz
Dendrite Snowflake-94.0GHz
Wakasa snow (Aonashi,2003)
Snow_dry (Puhakka,1975)
Snow (Sekhon & Srivastaya,1970)
Snow_dry (Imai,1960)
Snow_plate, column (Ohtake & Henmi,1970)
Single crystals (Carlson & Marshall,1972)
Snow_dry (Fujiyoshi et al.,1990)
Snow (Boucher & Wieler,1985)
100
10-1
10-2
0.1
0.2
0.4
1
2
4
Snowfall Rate (mm/h)
Figure 4.2: Ze-S relationships for snow from calculations using DDA and several previous
studies. The calculated results for sector and dendrite snowflakes are represented respectively by
circles and inverted triangles at 13.4, 35.6, and 94 GHz.
52
4.2 Radiative Transfer Modeling of the Observed Snow Events
Since the a-priori database linking the brightness temperatures and snowfall rate will be
constructed by radiative transfer calculations, it is essential that the radiative transfer model can
produce brightness temperatures consistent with observations. This step is particularly important
for the radiative transfer modeling of snowfall because the scattering properties of nonspherical
snowflakes are not as well understood as those of raindrops. In this section, we simulate and
compare the model brightness temperatures with those observed by MIR during the Wakasa Bay
2003 field experiment to ensure the validity of the radiative transfer model. The radiative transfer
model used in the study solves the radiative transfer equation using discrete ordinate method (Liu,
1998) and calculates the single-scattering properties of nonspherical snowflakes using the DDA
based parameterization described by Liu (2004) assuming that the snowflakes are comprised of
equally (by mass) mixed sector and dendrite particles with random orientations as mentioned
above.
On 29 January 2003, strong northwesterly flow was dominant over the Sea of Japan, and
extensive snowfall areas were reported along the west coast of the main island of Japan. An
aircraft flight observing the snowfall over ocean was conducted along several different flight
legs; Figure 3.16 shows the well-developed convective cells, with echo tops up to 4 km,
observed on the first flight leg by the airborne radiometer MIR and the PR-2 radar. To take into
account the emission from cloud liquid water, a layer of cloud liquid water is assumed between 3
and 3.5 km. The liquid water path (LWP, g m-2) is determined by the brightness temperature
increase at 89 GHz using LWP = 0.84 ( ?TB 89 ) 2 that is derived by regressing radiative transfer
model simulation results. Due to the uncertainties for input variables such as atmospheric water
vapor profiles and snow particles size distributions, we choose to vary these variables in the
radiative transfer model simulations.
One of the most commonly used particle size distributions for snowflakes is in an
exponential form (Sekhon and Srivastava, 1970):
N ( D) = N 0 exp(??D) .
53
(4.8)
The parameters N0 and ? may be expressed either as constants or functions of snowfall rate. In
the radiative transfer simulations, we used the same form of the particle size distribution as (4.8),
but with two different parameterizations of the N0 and ?. First, the distribution of Sekhon and
Srivastava (1970) has been used, with N0 and ? are parameterized as functions of S. The second
size distribution is derived from data by Dr. Muramoto?s research team at Kanazawa University
(http://sharaku.eorc.jaxa.jp/AMSR/data_val/, referred to as the Muramoto size distribution
hereafter), who analyzed images of snow particles observed at Fukui Airport every 10 minutes
from 1600 LST 28 January to 0800 LST 29 January 2003. In Fig. 4.3, some examples of the
observed particle size distributions and their corresponding precipitation rates are presented. The
parameters for the exponential distribution equation are obtained from curve-fittings of these
observations. The Muramoto size distribution is used in the radiative transfer simulation together
with the size distribution of Sekhon and Srivastava (1970).
Simulations are conducted to examine the radiative transfer model and the specification
of the input parameters. In Fig. 4.4, the model results are shown for the 29 January 2003 snow
case (Fig.3.16). The x-axis represents the MIR observations and the y-axis the model results.
The black circles are the results of using the Muramoto size distribution (from observations) and
one Fukui sounding profile with the surface wind speed of 8 ms-1 that is the mean from surface
observations at the Fukui airport during the field experiment; the red triangles show the Sekhon
and Srivastava size distribution and the US standard winter mid-latitude atmosphere; the blue
triangles represent the Sekhon and Srivastava size distribution and one Fukui sounding profile.
Considering all the uncertainties related to the model inputs, the modeled ?TBs generally agree
well with the MIR observations. However, the modeled results at 340 GHz have relatively larger
depressions than observed in comparison. As expected, the 89 GHz channel responds more
sensitively to liquid water compared to the other channels; this results in positive ?TB values in
Fig. 4.4. From the other test simulations (not shown here), the surface temperature change (from
273 K to 267 K) in the model does not have any measurable effect on the results of brightness
temperature depressions.
54
400
200
0
1000
Jan 28 22:00-22:59
800
600
400
200
0
3000
2500
2000
1500
1000
500
0
1000
Precipitation (mm/h)
-3
-3
-1
Number (m mm )
-3
Precipitation (mm/h)
600
Jan 29 04:00-04:59
Precipitation (mm/h)
-3
00-09 min
10-19 min
20-29 min
30-39 min
40-49 min
50-59 min
-1
Number (m mm )
800
Jan 29 06:00-06:59
-1
Number (m mm )
Precipitation (mm/h)
Jan 28 18:00-18:59
-1
Number (m mm )
1000
800
600
400
200
0
0
2
4
6
8
Diameter (mm)
5
Jan 28 18:00-18:59
4
3
2
1
0
5
Jan 28 22:00-22:59
4
3
2
1
0
7
6
5
4
3
2
1
0
5
Jan 29 04:00-04:59
Jan 29 06:00-06:59
4
3
2
1
0
06:00
06:20
06:40
07:00
Time (min)
Figure 4.3: Snow particle size distribution and precipitation from ground observations at Fukui
airport during Wakasa 2003 Field experiment.
55
60
Model ?TB
30
60
89GHz
30
0
0
-30
-30
-60
-60
S-S & Standard winter
S-S & Fukui
Muramoto & Fukui
-90
-120
-120 -90
-60
-30
0
30
60
60
Model ?TB
30
-120
-120 -90
-60
-30
0
30
60
-30
0
30
60
-30
0
30
60
60
220GHz
30
0
-30
-30
-60
-60
-90
-90
-120
-120 -90
-60
-30
0
30
60
60
Model ?TB
-90
0
30
150GHz
340GHz
-120
-120 -90
-60
60
183+1GHz
30
0
0
-30
-30
-60
-60
-90
-90
-120
-120 -90
-60
-30
0
30
60
MIR ?TB
183+7GHz
-120
-120 -90
-60
MIR ?TB
Figure 4.4: Comparisons of brightness temperature depressions between MIR observations and
the radiative model results.
?: Sekhon and Srivastava distribution with US standard atmosphere winter profile
?: Sekhon and Srivastava distribution with a Fukui radiosonde sounding
?: Muramoto distribution with a Fukui radiosonde sounding
56
4.3 Constructing the Database
Now that the radiative transfer model produces reasonable brightness temperatures, we
next use this model to link snowfall rate with brightness temperatures at high microwave
frequencies. The snowfall profiles in the database are made using two sources: PR-2 data from
Wakasa Bay 2003 experiment and surface radar data from February 2001. The PR-2 snowfall
rate profiles are derived from PR-2 observations on 29 January 2003. Radar reflectivity is
converted to snowfall rate using the equations (4.7a and b), and a liquid water cloud layer is
inserted between 3 and 3.5 km with liquid water path calculated from 89 GHz ?TB. A total of
2201 snow profiles are generated from the PR-2 dataset.
Surface radar data from two snowy days, 13-14 February 2001, are also used to enrich
the database. Radar reflectivity was converted to snowfall rate using the Aonashi et al. (2003)
empirical Ze-S relationship. As mentioned earlier, the snow clouds in this region are rich in liquid
water. However, the surface radar observations do not contain information on cloud liquid water
because of the small size of cloud liquid water droplets, and there have been very few in situ
measurements of liquid water content profiles that are vertically concurrent in both time and
space. To obtain realistic snow cloud profiles for radiative transfer modeling, we add a liquid
water cloud layer to the snowfall profiles derived from surface radar. To determine how much
liquid water to include in each snowfall profile, we conducted an Empirical Orthogonal Function
(EOF) analysis on the database from the Wakasa Bay 2003 field experiment, in which both
snowfall profile and liquid water amount are available. The EOF method, as described by
Biggerstaff et al. (2005) and von Storch and Zwiers (1999), relates one-dimensional variable of
snowfall profiles to the scalar variable of liquid water content. Using this method, the
dimensionality of each snowfall profile can be reduced to the scalar values of the EOF
coefficients. Using these coefficients, the relationship between the vertical distribution of liquid
water contents and snowfall profiles was obtained. The derived liquid water contents of each
snowfall profile in 2001 are combined with surface radar data to construct about 10000 snow
cloud profiles.
The a-priori database are then constructed through radiative transfer model simulations
with all possible combinations of: about 2200 Wakasa Bay 2003 snow cloud profiles including
information of snowfall and liquid water, about 10000 surface radar (in 2001) snow cloud
57
profiles, a total of 10 atmospheric sounding profiles (from observations at the Fukui airport and
the US standard mid-latitude winter atmospheric profile), three different surface temperatures,
and two type of particle size distributions. The total number of datum points in this database is
about 260000. Using this a-priori database, the snowfall algorithm that is developed based on
Bayes theorem (described in the next chapter) retrieves snowfall profiles from the satellite
observations (e.g., AMSU-B).
58
CHAPTER 5
BAYESIAN RETRIEVAL ALGORITHM
A retrieval algorithm based on Bayes? theorem can be stated mathematically as follows
(e.g., Olson et al., 1996; Evans et al., 1995, 2002). Let vector x represents snowfall rate profiles,
and vector y0 represents available observations that are brightness temperature observations in
this study. In general, the best estimate of x, given the observations y0, is assumed as the
expected value,
E(x) =?? ...? x pdf (x) dx .
(5.1)
In Bayes? theorem, the probability density function, pdf (x) is written as
pdf ( x ) ? P( y = y 0 | x = x true ) P( x = x true ) ? POS [ y 0 ? y s ( x )] Pa ( x ),
(5.2)
where POS is the probability equivalent to the distance between observation y0 and simulations by
a radiative transfer model ys(x) for the atmosphere state x. Pa is the a-priori probability that x is
true. If we assume that the errors in the observations and the simulations are Gaussian and
uncorrelated, then POS can be written as
POS [y 0 ? y s (x)] ? exp{?0.5[y 0 ? y s (x)]T � (O + S) ?1 [y 0 ? y s (x)]} ,
(5.3)
where O and S are the observation and simulation error covariance matrices, respectively.
For a sufficiently large database, the integral in (5.1) can be approximated by the
summation for all xj. If we assume that the profiles in the database occur with the same relative
frequency as those in nature, or at least with the same frequency as those found in the region
59
where the retrieval method is applied, then the weighting by Pa is represented simply by the
relative number of occurrence of a given profile type xj. Then (5.1) may be written as
? (x) = ? x
E
j
exp{?0.5 [y 0 ? y s (x j )]T � (O + S) ?1 [y 0 ? y s (x j )]}
A?
j
,
(5.4)
where the normalization factor is
A? = ? exp{?0.5 [y 0 ? y s (x j )]T � (O + S) ?1 [y 0 ? y s (x j )]} .
(5.5)
j
In other words, the expected vector is from the normalized summation of multiplication of
atmospheric parameters xj and their corresponding weighting factor over a large ensemble of predefined snowfall-brightness temperature database. The weighting factors are determined by the
error covariance matrices (such as O and S) and a square of the vector distance
( [ y 0 ? y s ( x j )]T [ y 0 ? y s ( x j )] ) between the observed and simulated. In the present study, the
error covariance matrices, O and S, are set as follows similar to Olson et al. (1996) and Seo and
Liu (2005). The error covariance matrix, S, has no contribution if the model simulation, ys(x), is
assumed to be true. The observation error variances are set equal to the instrument error
variances with an assumption of zero-mean Gaussian distributed noise with a standard deviation
of 1.5 K to each channel except for 0.6 K to 150 GHz and 183�GHz. Due to a lack of
information on the correlation of errors between channels, only the diagonal terms of the matrix
O are estimated here, and off-diagonal terms are set to zero. The matrix (O+S)-1 for any in a
model database is inversely proportional to the value of a diagonal term of the error variance,
which determines the width (or spread) of the weighting function in terms of brightness
temperature distance. In the retrievals, we use [3 K, 1.2 K, 3 K, 3 K, 1.2 K] for ?TB ? 15 K and
[4.5 K, 1.8 K, 4.5 K, 4.5 K, 1.8 K] for ?TB ? 15 K, respectively, as observation plus simulation
uncertainties for each frequencies for AMSU-B. The algorithm is then applied to the case of 29
January 2003 as an assessment of the algorithm?s performance. Figure 4.5 shows the retrieved
snowfall by applying the algorithm to MIR data measured for two different flight legs. The
observed snowfall from PR-2 35 GHz (the upper panels) is compared with the retrievals. It
appears that the retrieval algorithm captures well the basic features of the snow cloud cells,
60
although differences exist in details between the observed and retrieved structures. Comparisons
between column-accumulated snowfall rates from these results are represented along leg 1 and
leg 3 in Fig. 5.2, which also shows reasonable agreements between observations and retrievals.
(a)
(b)
Figure 5.1: Comparisons of PR-2 observations at 35 GHz (upper) and retrieved snowfall rate
(lower) along (a) leg1 and (b) leg3.
61
100
100
Retrievals (mm/h)
(a) Leg1
(b) Leg3
80
80
60
60
40
40
20
20
0
0
0
20
40
60
80
100
Observations (mm/h)
0
20
40
60
80
100
Observations (mm/h)
Figure 5.2: Scatter plots between column-accumulated snowfall rates from PR-2 observations at
35 GHz and retrievals along (a) leg1 and (b) leg3.
62
CHAPTER 6
APPLICATION OF AMSU-B SNOWFALL RETRIEVAL TO
SNOWFALL CASES OVER THE SEA OF JAPAN
The snowfall retrieval algorithm is applied to the AMSU-B satellite data. Since there are
no 220 and 340 GHz channels in AMSU-B, the AMSU-B version of the retrieval algorithm only
uses data from five channels with frequencies from 89 to 183�GHz. Three snowfall cases are
studied from 14, 16 and 27 January 2001. These were located over Japan and its surrounding
areas, and coincided with the field experiment, ?Winter MCSs Observations over the Japan Sea 2001? (Murakami et al., 2001a, 2001b; Yoshizaki et al., 2001). During 12 to 19 of January, the
cold airmass with air temperature lower than ?35 癈 at 500 hPa stayed quasi-stationary over the
Japan Sea. Heavy snowfalls occurred on the western coastal areas of the Japan Islands. The
snowfall was mainly induced by quasi-stationary band-shaped snowfall systems elongated east
and west along the southern coast of Japan. Meanwhile, on 27 January a synoptic cyclone
developed and brought heavy snowfalls over the Kanto plain.
Since there are no intensive in situ observations to directly determine background
temperatures for theses cases in 2001, AMSU-B data are used for the statistical calculation of
background temperatures by analyzing the histograms over the 2-month period January through
February 2001. During this period, the brightness temperatures that are most frequently occurred
at 150 GHz at all AMSU-B scanning angles are used as the standard of clear sky. The focused
domain is then divided into four areas: land, coast, sea-1, and sea-2 (37.5-39 N, 133-136 E). The
coast is the region affected by the land contamination, and the sea-2 is the remote region much
farther from the coast compared to sea-1 area. At each channel, by averaging brightness
temperatures higher than the standard value for the clear-sky, the background temperature over
each area is derived.
Figures 6.1 through 6.3 show the brightness temperature depressions at four of the five
63
AMSU-B frequencies, the retrieved snowfall rates at 1.5 and 2.1 km, the hourly-accumulated
snow amount from the AMeDAS radar data, and the GMS infrared (IR) cloud top temperatures
for the three cases. Note that the AMeDAS radar snow amount is the hourly-accumulated snow
(in mm) averaged for 3 hours around the satellite passing time, not instantaneous snowfall rate.
Heavy snow bands are observed in the Wakasa Bay area on 14 and 16 January from the AMSUB observations (Fig. 6.1a-d and 6.2a-d). As stated by Bennartz and Bauer (2003), the reduction
of brightness temperature due to the scattering of snow appears much stronger at 150 GHz than
at 89 GHz. The snow bands are also clearly resolved at 183�GHz frequency. On 14 January
2001, the retrievals near the surface (Fig. 6.1e-f) are in good agreement with the AMeDAS radar
observations. In particular, strong snow bands northeast of the Wakasa Bay are clearly
reproduced in the retrievals. Despite the difficulty of directly quantitative comparison between
surface radar data and retrievals from the satellite, the maximum snowfall region shows a similar
magnitude and pattern. Meanwhile, in Fig. 6.1h IR signals for snowfall are not clearly
distinguishable; there is just an exceedingly blurred pattern of clouds. It is noteworthy that the
broad distribution of the depressions of brightness temperatures at 183�GHz is very similar to
that of low IR cloud top temperatures.
For the 16 January 2001 case, our retrieval algorithm detects two strong stationary snow
bands shown in Fig. 6.2b, although the maximum snowfall appears slightly behind in the west
side of the Wakasa Bay. The snow band in the 16 January case is a continuation of the snow
band shown earlier on 14 January, which lasted several days. However, the pattern of brightness
temperature depressions at 89 and 183�GHz channels become less similar to that of 150 and
183�GHz channels and differ significantly from the IR image. It is inferred that the
characteristics of these snow bands, including the change of the composition of liquid and
ice/snow in the clouds, have changed during 14 to 16 January.
In contrast to snow bands in the previous two cases, an organized snow cloud system
associated with a polar low on 27 January was observed. In the GMS IR image (Fig. 6.3h), we
can see that clouds covered most of the central Japan. The intense echo area was circular/spiral
in shape and corresponded to the maximum depression of brightness temperature of about 70 K
at 150 GHz (Fig. 6.3b). The AMSU-B snowfall retrievals show broad snow coverage over
central Japan that compares well with AMeDAS snow accumulation about 2 hours after satellite
64
passing time. In Fig. 6.4, retrieved snowfall and observed ?TB values of AMSU-B are shown in
each snowfall case.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure 6.1: Comparisons of observations and retrieved results on 14 January 2001. (a-d)
Brightness temperature depressions from the AMSU-B at 89, 150, 183+3, and 183+7 GHz, (e-f)
retrieved snowfall at 1.5 km and 2.0 km from the surface, and (g) hourly accumulated snow data
(3-hr averaged) from the AMeDAS radar data and (h) GMS IR cloud top temperatures.
65
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure 6.2: Same as Fig. 6.1, but for 16 January 2001.
66
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure 6.3: Same as Fig. 6.1, but for 27 January 2001.
67
Larger retrieved snowfalls are corresponding well to large depressions of brightness
temperatures, although in 16 January 2001 case the results are slightly more scattered and have
smaller values compared to the other cases.
Next, we examine the algorithm?s performance in a more quantitative manner using a
scatterplot of satellite retrieved snowfall rate versus AMeDAS radar observed hourly snowfall
accumulation (Fig. 6.5). The data pairs in the scatterplot are generated by averaging the satellite
retrievals and the AMeDAS radar hourly snow accumulations to a 1� latitude x 1� longitude grid.
In addition, for a satellite retrieval, AMeDAS hourly snowfall accumulations (3-hr averaged to
the center time) from 3 time periods are compared: the nearest hour to the satellite passage, 1
hour after, and 2 hours after satellite passage. The correlation coefficients between retrievals and
AMeDAS data at these times (refer to Table 6.1) are, respectively: 0.796, 0.834, and 0.790 for 14
January 2001 case; 0.625, 0.634, and 0.629 for 16 January 2001 case; and 0.915, 0.960, 0.971 for
27 January 2001 case. Although the correlation coefficients for the January 16 case are relatively
lower than the other cases, the highest correlation between the satellite retrievals and surface
radar measurements occurs 1 or 2 hours after the satellite passage. This phenomenon may reflect
the fact that satellite-measured quantities are snow particles floating in the atmosphere; it takes
time for the low-terminal-velocity snowflakes to reach surface.
Table 6.1: Correlation coefficients between snowfall retrievals and AMeDAS radar data.
Time
14 January 2001
16 January 2001
27 January 2001
At the nearest hour
0.796
0.625
0.915
+ 1 hour
0.834
0.634
0.960
+ 2 hours
0.790
0.629
0.971
The correlation coefficients shown above for the three cases are very different, ~0.8 for
January 14 case, ~0.6 for January 16 case, and ~0.96 for January 27 case. To get insight to this
68
difference, we investigate how brightness temperature at each frequency contributed to the
retrieval. Figure 6.6 shows the brightness temperature depressions at different channels versus
snowfall rate retrievals. The correlation coefficients (Table 6.2) are respectively ?0.590, ?0.869,
?0.526, and ?0.945 at 89 GHz, 150 GHz, 183�GHz, and 183�GHz for 14 January 2001 case.
For 16 January 2001 case, they are ?0.126, ?0.483, ?0.482, and ?0.830. For 27 January 2001
case, the values are ?0.841, ?0.945, ?0.751, and ?0.956. For all the cases, the correlations are
higher at 150 GHz and 183�GHz except for 150 GHz of 16 January case. Since they are more
sensitive to ice/snow scattering, higher weightings has been given to these two channels in our
snowfall retrieval algorithm.
Table 6.2: Correlation coefficients between snowfall retrievals and AMSU-B channels.
Channels
14 January 2001
16 January 2001
27 January 2001
89 GHz
?0.590
?0.126
?0.841
150 GHz
?0.869
?0.483
?0.945
183�GHz
?0.526
?0.482
?0.751
183�GHz
?0.945
?0.830
?0.956
It is interesting to notice that for the January 27 case the correlation coefficients between
snowfall rate and brightness temperature at all channels are high. In this case, the brightness
temperature depressions are much larger than the other cases. From these results for three
snowfall cases, it is found that the strong scattering signature leads the algorithm to perform the
best. On the other hand, on January 16 the brightness temperature depressions are small, and the
correlation for 89 GHz is even close to zero. It is interpreted that rich cloud liquid water exists in
this case, and the algorithm performs not as well under such conditions.
69
Column-accumulated snowfall
(a) 14 Jan 2001
102
101
100
10
20
30
40
50
60
70
Column-accumulated snowfall
Retrievals (mm/h)
(b) 16 Jan 2001
102
101
100
0
10
20
30
40
Column-accumulated snowfall
Retrievals (mm/h)
(c) 27 Jan 2001
102
101
100
0
20
40
60
80
100
Magnitude of ?TB (K)
Figure 6.4: Relations between the magnitude of brightness temperature depression of AMSU-B
and the column-accumulation of retrieved snowfall for three cases.
70
Observations (mm)
2.0
(a) 14 Jan 2001
1.5
1.0
0.5
?time=0hr
?time=+1hr
?time=+2hr
0.0
0.0
Observations (mm)
1.5
0.5
1.0
1.5
2.0
Retrievals (mm/h)
(b) 16 Jan 2001
1.0
0.5
0.0
0.0
6
0.5
1.0
1.5
Retrievals (mm/h)
(c) 27 Jan 2001
Observations (mm)
5
4
3
2
1
0
0
1
2
3
4
5
6
Retrievals (mm/h)
Figure 6.5: Comparisons between retrieved snowfall rates and 3-hr averaged hourly
accumulated surface radar snow amounts at the nearest corresponding time, after 1 hour, and
after 2 hours respectively for 14, 16, and 27 January 2001.
71
10
(a) 14 Jan 2001
5
?TB (K)
0
-5
-10
-15
-20
89GHz
150GHz
183+1GHz
183+7GHz
-25
-30
0.0
0.5
10
1.0
1.5
2.0
Retrievals (mm/h)
(b) 16 Jan 2001
5
?TB (K)
0
-5
-10
-15
-20
0.0
0.2
0.4
0.6
0.8
1.0
Retrievals (mm/h)
(c) 27 Jan 2001
20
?TB (K)
0
-20
-40
-60
-80
0
1
2
3
4
5
6
7
Retrievals (mm/h)
Figure 6.6: Comparisons between retrieved snowfall rates and AMSU-B brightness temperature
depressions at each frequency respectively for 14, 16, and 27 January 2001.
72
Figure 6.7: Comparison between retrieved snowfall rates and hourly-accumulated snow data
from the AMeDAS radar data averaged for 14 snowfall cases during January and February 2001.
To extend the algorithm validation beyond case studies, the snowfall algorithm is applied
to other 14 snowfall cases during January and February of 2001 in Japan region where is a more
northern part than the previous three snow cases, and the mean snowfall distribution for these 14
cases is derived from AMSU-B data (Fig. 6.7). To distinguish between snowfall and rainfall,
surface air temperature data from NCEP reanalysis data provided by the NOAA-CIRES Climate
Diagnostics Center (available at http://www.cdc.noaa.gov) are used. Only those precipitation
events with surface temperature below 0 癈 are chosen as snowfall cases, and the satellite data
coverage and radar data availability are also considered for the case selection. The retrieved
mean snowfall distribution is compared with AMeDAS radar data that are an hourlyaccumulation and averaged for three hours to the center time about one hour after the satellite
passage. From Fig.6.7, it is seen that the averaged snowfall retrievals show a fairly good
agreement with surface radar observation in pattern, especially showing well the snowfall
maximum over the west part of Japan. However, slightly strong retrieved snowfall signals of the
73
southwest part over land do not appear in the radar data. It can be the accumulated snow over
land influenced by the topographical effects. Additionally, snowfall signals appeared over ocean
in the retrievals may represent very low brightness temperatures due to the cold air temperature
in those areas, although there is no radar observation over the ocean so the exact comparison is
not possible.
74
CHAPTER 7
CONCLUSIONS
In this study, a snowfall retrieval algorithm has been developed based on Bayes? theorem
using high frequency satellite microwave data. In developing the Bayesian snowfall retrieval
algorithm, the a-priori database is the most important component. The database in our algorithm
is constructed using various observation data such as satellite, airborne microwave radiometer
measurements, and surface observations. Also, detailed observational analyses are performed for
more realistic and representative database. Our focus is the west coastal region of Japan near
Wakasa Bay and surrounding areas. The results can be summarized as follows:
First, through the temporal analysis of surface radar data, a diurnal variation of snowfall
in the Wakasa Bay (Japan) is detected in this area during winter, suggesting the effects of sea
breeze and topography in temperature contrast. However, the clear diurnal variation of winter
precipitation cannot be identified by satellite IR data. From these results, the possibility of using
IR data to measuring snowfall becomes weak, and we pay more attention to the great potential of
microwave measurements in studying winter precipitation and developing snowfall retrieval
algorithm. The sensitivity of microwave channels to snowfall is then investigated by a radiative
transfer model. The results show that upwelling microwave radiation at frequencies higher than
150 GHz is sensitivite to scattering by snow/ice, while radiation at lower frequencies (e.g., 37
GHz) is not sensitive to snow scattering, but rather sensitive to cloud liquid water.
Second, the scattering signals of snowfall are investigated in the areas at frequencies
ranging from 37 to 340 GHz using satellite and aircraft observations. The snow clouds
investigated in this study are associated with shallow convections caused by cold air outbreaks.
The cold air over warm ocean surface produces strong instability of the low atmosphere, and
often results in heavy snowfall. A significant amount of liquid water is often observed in the
75
convective cells as evidenced by the increase in 89 GHz brightness temperatures. At 37 GHz, the
snowfall scattering signature seems to be insignificant, while liquid water in some convective
cells increases brightness temperature (as much as ~30 K at 37 GHz horizontal polarization). At
89 GHz, the data show both the brightness temperature decreases due to ice scattering and
brightness temperature increases due to liquid water emission. Occasionally, these increases and
decreases occur at different locations of a convective cell. Observations using dual-polarization
clearly have advantage because we may use the polarization corrected temperature and the
polarization difference to separate, to a certain extent, the scattering and emission signatures.
Using AMSR-E data, the lowest PCT depression is about 25 K for the studied case. However,
the sensitivity to snowfall at 89 GHz is largely reduced for AMSU-B, which has a much larger
footprint and only a single polarization. At higher frequencies, the snowfall signatures become
evident even without the use of PCT. At the spatial resolution of AMSU-B pixels (~16 km at
nadir), we observed 15 ~ 20 K brightness temperature decrease at 150 and 183�GHz for the
studied case. At finer spatial resolution observed by airborne radiometers, the nadir view
brightness temperatures decrease as large as 40, 50, 60, and 80 K for 150, 183� 220, and 340
GHz channels, respectively. Furthermore, the influence by liquid water to channels of 183�GHz or higher frequencies is small. At 150 GHz, besides the brightness temperature decreases
induced by ice scattering, the brightness temperature increases caused by liquid water are also
evident, similar to but not as much as those at 89 GHz. Therefore, having a dual-polarization in
future instruments for this frequency is desirable for a better separation between liquid and ice
water signatures.
Third, the snowfall retrieval algorithm is developed. The algorithm is based on Bayes?
theorem using high frequency microwave radiometry observations. In developing the Bayesian
snowfall retrieval algorithm, the a-priori database is the most important component.
Observational data from both airborne and surface-based radars are used to construct an a-priori
database of snowfall profiles. These profiles are then used as input to a forward radiative transfer
model to obtain brightness temperatures at high microwave frequencies. Since the a-priori
database is an essential component of the Bayesian retrieval algorithm, special attention has been
paid in this study to its construction. First, the backscattering of radar reflectivity and the singlescattering properties used in the radiative transfer model are calculated using discrete dipole
approximation for realistic nonspherical ice particles. Using the scattering properties from
76
nonspherical particles, snowfall rates derived from radar reflectivities and brightness
temperatures calculated from radiative transfer models are expected to be more accurate than
those computed from (so far) widely used spherical approximations. The radiative transfer model
that is used to compute brightness temperatures for given snowfall rate profiles was tested
against airborne microwave radiometer data. Given the uncertainties of input variables, it appears
that the model results agree reasonably with observations except for a very high frequency 340
GHz channel. Second, the snowfall rate profiles used for building the database are from actual
radar observations. The usage of observational data instead of numerical model outputs ensures
that the statistics of snowfall rate profiles in the database are consistent with those occurred
naturally. To enrich the database, we included profiles from airborne radar and surface radar
observations. Third, the diversity of the database is further enhanced by using two different types
of particle size distributions: the widely used Sekhon and Srivastava (1970) distribution and the
Muramoto distribution that was derived in the Japan Sea region using in situ ice particle
measurements. Furthermore, embedded cloud liquid water layers and ten atmospheric sounding
profiles are used as input for computing brightness temperatures by a radiative transfer model.
Fourth, the snowfall retrieval algorithm is first validated by airborne microwave
radiometer and radar observations, and then applied to the AMSU-B satellite data and validated
by surface radar-gauge network data over Japan. The retrieved snowfall rates using AMSU-B
data for three snowfall cases in the vicinity of Japan show good agreement with surface radar
observations. The correlation coefficients between 1皒1� gridded results of retrieved snowfall
rate and AMeDAS radar snow accumulation varies from ~0.6 for a relatively light snowfall case
of snow bands with smaller scales to ~0.96 for a heavy snowfall case associated with a lowpressure system. It appears that the snow particles are relatively ?wet? for the low correlation
case with rich cloud liquid water in the clouds, but the snow particles are ?dry? for the high
correlation case, in which all AMSU-B channels show appreciable scattering signatures.
Therefore, further characterizing the vertical structure of hydrometeors through inclusion of
cloud liquid water layer, and through observation, and through developing the a-priori database
accordingly are highly desirable for improvement of accuracy of wet snowfall retrieval in the
future. Using the constructed database, the snowfall algorithm is applied to calculate the mean
snowfall distributions in the vicinity of Japan from AMSU-B data for other 14 snowfall cases
during January and February in 2001. Considering the satellite data coverage and radar data
77
availability, those snow cases for January and February in 2001 are chosen when the areaaveraged surface temperature from NCEP reanalysis data is below 0 癈. The retrieved snowfall
is compare with AMeDAS radar data. In comparison, the averaged snowfall retrievals show
fairly good agreement in pattern, especially in the west part of Japan, although the exact
validation for the snowfall retrievals over ocean is not possible due to the lack of radar data in
this area.
From the results of this study, the following future works are considered. The database
developed in this study is based on observations of snowfall events near the Japan Sea for the
sole reason of data availability. Therefore, our algorithm is considered best suited for snowfall in
this region. However, as more snowfall radar observations become available in the future such as
the CloudSat radar (Stephens et al., 2002), first, a global database can be constructed in a similar
fashion, and the algorithm may be applied globally. For this, deeper understanding of detailed
structures of snow clouds in each area and more validations also are needed. Next, developing a
more general discrimination method between snowfall, rain and snow cover signatures will be
necessary, although actual observations and surface temperatures from NCEP/NCAR reanalysis
data are used in this study. A few related studies have been performed. For example, Kongoli et
al. (2005) suggested an empirical method utilizing the unique combination of the AMSU
frequency, but it is still a challenging work. In addition, using dual-polarization observations are
preferable to clearly detect scattering signals and improve more accurate retrieval algorithm.
78
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