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Spatially adaptive ocean surface wind retrievals using satellite microwave scatterometer measurements over tropical cyclones

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SPATIALLY-ADAPTIVE
OCEAN SURFACE WIND
RETRIEVALS USING
SATELLITE MICROWAVE
SCATTEROMETER
MEASUREMENTS OVER
TROPICAL CYCLONES
By
Lawrence Philipp Rice
A Dissertation Submitted to the Graduate School of the
Florida Institute of Technolog}’ in Partial Fulfillment of
the Requirements for the Degree of
Doctor of Philosophy
In
Electrical Engineering
Melbourne, Florida
May 1999
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9917479
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We the undersigned hereby recommend that the attached document be accepted as
fulfilling in part the requirements for the degree o f doctor o f philosophy in Electrical
Engineering
"Sparially-Adaptive Ocean Surface Wind Retrievals Using Satellite Microwave
Scatterometer Measurements over Tropical Cyclones," A Dissertation by
Lawrence Philipp Rice
Michael Thursby, Ph.D.
Associate Professor, Electrical Engineering
ifessor, Applied Mathematics
'rs Ph.D.
fessor
Division o f Electrical and Computer Science and Engineering
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Abstract
Title: Spatially-Adaptive Ocean Surface Wind Retrievals Using Satellite Microwave
Scatterometer Measurements over Tropical Cyclones
Author. Lawrence Philipp Rice
Major Advisor W. Linwood Jones Ph.D.
An algorithm is presented that extends the capabilities of the NASA Scatterometer
(NSCAT) Wind Retrieval Algorithm to include retrievals using 25 km wind vector
cells (SARA-25) and retrievals at individual normalized radar cross section
measurement cells (SARA-max). This Spatially Adaptive Retrieval Algorithm (SARA)
is shown to retrieve very high resolution and precise tropical cyclone wind fields when
using a model wind field with simulated (no noise, perfect model function)
measurements. Further, using NSCAT measurements, it is shown that the actual
SARA-25 retrievals are very close to the corresponding 50 km NSCAT retrievals for a
wide range of wind speeds and directions. The benefit from SARA is in cases where
higher spatial sampling is needed to fully describe the wind field. High gradient
regions such as the eyewall of a tropical cyclone, where measurements of peak winds
are a high priority, are well suited for SARA analysis. Using only one radar
backscatter measurement for a wind retrieval near an eyewall eliminates the effects o f
averaging used in SARA-25 and 50 km sampling. The SARA also provides a means to
test if adjacent radar backscatter measurements are self consistent. Non consistent
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measurements are most likely due to the effects o f rain; hence, SARA provides a
means to evaluate whether cells are affected by rain.
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Table O f Contents
TABLE OF CONTENTS
1 1S'I O f F!OUR£S *•••••■••••••••*••
»»»•• v n
*
LIST OF TABLES______________________________________________________________ X
ACKNOWLEDGEMENT_______________________________________________________XI
DEDICATION_______________________________________________________________ XH
CHAPTER ONE_______________________________________
1
INTRODUCTION AND WIND RETRIEVAL PRINCIPLES-----------------------------------------1
NASA Scatterometer D escriptio n ............................................................................................ 4
Wind R etrieval P rinciples and P ractice ............................................................................................7
CHAPTER TWO______________________________________________________________ 11
SARA DESCRIPTION__________________________________________________________ 11
CHAPTER THREE__________________________________________________
19
EVALUATION OF SARA CAPABILITIES AND PERFORMANCE IN SIMULATIONS... 19
CHAPTER FOUR_____________________________________________________________ 29
SARA COMPARED AND CONTRASTED TO NSCAT ALGORITHM-------------------------29
SARA C losely M atches NSCAT for non -TC F ields .................................................................... 29
SARA C ontrasted w it h N S C A T......................................................................................................... 46
Contrast B etween SARA R etrievals, and NSCAT R etrieva ls ..............................................57
CHAPTER FIVE.........
■................................ •«............................................ 76
IDENTIFYING <r0
CHAPTER SIX________________________________________________________________ 87
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APPENDIX A_________________________________________________________________ 92
In t r o d u c t io n T o T r o pic a l C y c l o n e C h a r a c t e r ist ic s ................................................................... 92
APPENDIX B_________________________________________________________________ 94
P h y sic s f o r Sc a tter o m eter M ea su r em en ts ........................................................................................ 94
Ocean Backscatter.....................................................................................................................95
NASA Scatterometer (NSCAT)................................................................................................. 96
D is tr ib u tio n o f Sam ples u s e d
in
C h a p te r F o u r ........................................................................... 108
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List of Figures
F igure 1 NSCAT A ntenna Illumination P attern .................................................................................5
F igure 2 T wenty -five km Sigma-0 cell ....................................................................................................6
Figure 3 NSCAT W ind R etrieval F unctional Diagram .................................................................... 13
Figure 4 F unctional D escription o f SA R A .......................................................................................... 14
F igure 5 N earest N eighbor G rouping B lock D ia g r a m ....................................................................16
F igure 6 G roupings for SARA-25: B eam 1 **’, Beam 3 ‘o ’, B eam 5 ‘x \ B eam 7 *+'..................17
F igure 7 NSCAT T racks for Rev ' s 478, 485, & 492 ........................................................................... 22
Figure 8 Oceanweather M odel for Rev 478........................................................................................ 27
F igure 9 O ceanweather M odel for Rev 4 8 5 ....................................................................................... 28
Figure 10 O ceanweather M odel for R ev 4 9 2 .....................................................................................28
F igure 11 Regions for A lgorithm C omparison data ........................................................................ 32
F igure 12 H istogram of SARA-25 S peeds Retriev ed ........................................................................ 33
Figure 13 H istogram of SARA-25 D irections Retrieved ................................................................. 34
F igure 14 H istogram of Speed D ifferences SARA - N S C A T ........................................................... 34
Figure 15 H istogram of D irection D ifferences SARA - N SC A T................................................... 35
F igure 16 Speed differences vs. incidence an g le .............................................................................. 36
F igure 17 D irection difference vs. incidence angle ........................................................................ 36
F igure 18 Speed differences vs. wind direction .................................................................................37
Figure 19 D irection differences vs. wind direction ........................................................................ 37
Figure 20 Speed differences vs. wind spe e d .........................................................................................38
F igure 21 D irection D ifference vs . wind speed ..................................................................................38
Figure 22 SARA-25 T w o Alias So lu tio n s .............................................................................................40
F igure 23 NSCAT 2 A lias Solutions ...................................................................................................... 40
F igure 24 SARA-25 T hree Allas Solutions ..........................................................................................4 1
Figure 25 NSCAT T hree A lias Solutio ns ............................................................................................. 41
F igure 26 SARA-25 F ou r Allas So lu tio ns ............................................................................................42
Figure 27 NSCAT F our A llas Solutions ............................................................................................... 42
F igure 28 NDBC Buoy W ind D irection C omparison H istograms M ike F reilich . O S U
45
F igure 29 NDBC B uoy W ind D irection C omparisons ........................................................................ 45
F igure 30 NDBC B uoy W ind D irection ..................................................................................................46
F igure 31 H istogram o f SARA-25 s pe e d s ............................................................................................. 48
Figure 32 H istogram o f SARA-25 directions ..................................................................................... 48
F igure 33 H istogram o f SARA-25 speed differences ........................................................................ 49
Figure 34 H istogram of direction differences , m ea n o .23°, standard deviation 14.9°........49
F igure 35 Speed differences versus incidence a n g le ....................................................................... 50
F igure 36 D irection differences vs . incidence angle ........................................................................50
Figure 37 Speed differences vs. wind direction .................................................................................51
Figure 38 D irection differences vs . wind direction ..........................................................................51
F igure 39 Speed differences vs. wind spe e d ........................................................................................ 52
Figure 40 D irection differences vs . wind speed .................................................................................52
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F igure 41 50 km WVC R etrieval o f R e v 478........................................................................................ 58
F igure 42 SARA-25 retrieval o f R ev 478.............................................................................................. 58
F igure 43 SARA-max R etrieval o f Rev 478.......................................................................................... 59
F igure 44 50 km WVC R etrieval of Rev 485........................................................................................ 59
F igure 45 SARA-25 Retrieval o f R ev 4 8 5 ............................................................................................. 60
F igure 46 SARA-max R etrieval o f Rev 485...........................................................................................60
F igure 47 50 km WVC R etrieval of R e v 492........................................................................................ 61
F igure 48 SARA-25 Retrieval o f R ev 492 ............................................................................................ 61
F igure 49 SARA-max R etrieval of Rev 492...........................................................................................62
F igure 50 Rev 478 with radial angle = 9 0 °..........................................................................................64
F igure 5 1 Rev 478 with radial angle = 3 0 ° ...........................................................................................64
F igure 52 Rev 478 wtth radial angle = -30°........................................................................................ 65
F igure 53 Rev 485 with radial angle = 9 0 ° ..........................................................................................65
F igure 54 Rev 485 with radial angle = 3 0 ° ..........................................................................................66
F igure 55 Rev 485 with radlal angle = -30°........................................................................................ 66
F igure 56 Rev 492 with radlal angle = 3 0 ° ..........................................................................................67
F igure 57 Rev 492 with radlal angle = 0 ° ............................................................................................67
Figure 58 Rev 492 with radial a n gle = 3 0 ° ..........................................................................................68
F igure 59 30° R adlal plot w ithout interpolation for R ev 485......................................................69
F igure 60 Speed C ontours fo r 50 km Sampling Rev 4 7 8 ...................................................................71
F igure 61 Speed C ontours for SARA-25 Rev 4 7 8 ............................................................................... 71
F igure 62 Speed Contours fo r SARA-max Rev 4 7 8 ............................................................................71
F igure 63 Speed C ontours f o r 50 km Sampling R ev 4 8 5 ...................................................................72
F igure 64 Speed C ontours fo r SARA-25 Rev 485............................................................................... 72
F igure 65 Speed C ontours fo r SARA-max Rev 485............................................................................. 73
F igure 66 Speed C ontours fo r 50 km Sampling R ev 492....................................................................73
Figure 67 Speed C ontours fo r SARA-25 Rev 492............................................................................... 74
F igure 68 Speed C ontours fo r SARA-max Rev 492............................................................................. 74
F igure 69 F low C hart for G O F t e s t ..................................................................................................... 78
F igure 70 Rev 478 SARA-max R etrievals failing 15% GOF t e s t ...................................................79
F igure 71 Rev 478 SARA-max R etrievals P assing the 15 % GOF t e s t ........................................79
F igure 72 Rev 485 SARA-max R etrievals F ailing 30% GOF test ...................................................80
F igure 73 R ev 485 SARA- max R etrievals P assing 30% GOF t e s t ................................................ 80
F igure 74 Rev 492 SARA- max R etrievals F ailing 15% GOF t e s t ................................................. 8 1
F igure 75 Rev 492 SARA-max R etrievals P assing 15% GOF t e s t ................................................. 81
F igure 76 Rev 485 with Ra d ia l Angle = 2 0 °.........................................................................................83
F igure 77 Rev 485 with Rad ial Angle = 10°.........................................................................................83
F igure 78 Rev 485 with Rad ial Angle = 0 ° ...........................................................................................84
Figure 79 Rev 485 with Rad ial Angle = -10°........................................................................................84
F igure 80 Rev 485 with R adia l Angle = -20°........................................................................................85
F igure 81 Rev 485 with Rad ia l Angle = -30°........................................................................................85
F igure 82 Speed contours fo r SARA-max Rev 485 without o u tliers ......................................... 86
F igure 83 Hurricane E lena . ...................................................................................................................... 92
F igure 84 NSCAT antenna illumination patterns on the o c e a n ................................................. 97
F igure 85 NSCAT 25 km sigma -0 cell g eo m etr y ................................................................................ 98
F igure 86 NSCAT 50 km sigm a -0 cell g eom etr y ............................................................................... 99
F igure 87 Wind Speed vs . D irection using G M F ................................................................................10°
F igure 88 Sample Fourier Series A pproximation to a GM F........................................................... 1°2
F igure 89 NSCAT 50 km resolution wind field ................................................................................. 105
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F igure 90 H igh resolution wind field .................................................................................................. 106
F igure 91 M aximum resolution wind field .......................................................................................... 106
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List o f Tables
T able 1 JTWC T rack Information for S uper T yphoon V iolet ......................................................21
T able 2 NSCAT Illumination o f Super T yphoon V io l e t ................................................................ 22
T able 3 Comparing 4,244 SARA-25 Solutions to C ollocated TC96 M odel Solutions 1.... 25
T able 4 C omparing 4,244 SARA-25 Solutions to Collocated TC96 M odel Solutions 2.... 26
T able 5 C omparing 16,896 SARA-max Solutions to C ollocated TC96 M odel Solutions . 26
T able 6 Statistics for E ntire D ata S e t ................................................................................................. 33
T able 7 P ercent o f Retrieval Locations w ith 2 ,3 , o r 4 A mbiguities ..........................................43
T able 8 SARA-25 R etrievals C ompared t o NSCAT Including a TC........................................ 47
T able 9 D ifferences between SARA-25 and SARA-max Retrievals for R ev 478..................... 54
T able 10 D ifferences between SARA-25 and SARA-max R etrievals for R ev 485................. 54
T able 11 D ifferences between SARA-25 and SARA-max R etrievals for Rev 492................. 54
T able 12 Sample size vs. Incidence An g l e ......................................................................................... 108
T able 13 Sample size vs. D irection w ith respect to S/C hea d in g .............................................. 108
T able 14 Sample S ize vs . M ean S peed ................................................................................................... 109
T able 15 Sample size vs. Incidence A n g l e ......................................................................................... 109
T able 16 Sample size vs . W ind D irection w r t S/C D ir ec tio n ...................................................... 109
T able 17 S ample size vs. mean speed ..................................................................................................... 110
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Acknowledgem ent
This research was supported by the Jet Propulsion Laboratory NASA Scatterometer
Project (NSCAT). Linwood Jones Ph.D., directed this research as my advisor. Josko
Zee helped validate this research. Oceanweather Inc. provided wind fields based on
their models.
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D edication
To Marion
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Chapter One
Introduction and Wind Retrieval
Principles
Use of active microwave remote sensing techniques (radar scatterometers) to measure
ocean surface winds is a mature science. Since 1978, satellite scatterometers have
been flown by the National Aeronautics and Space Administration (NASA) and later
by the European Space Agency (ESA) [1] for scientific and operational uses. For
research applications, satellite scatterometers provide global measurements of ocean
surface winds as inputs to atmospheric and oceanic models for climate research; and
for operational applications, scatterometer data have been used to improve numerical
weather prediction.
Also, an important, but not so well documented, application for satellite
scatterometers is to measure surface winds in tropical cyclones (TC’s) [2, 3, 4]. For
hurricanes in the Atlantic Ocean and Caribbean Sea, aircraft observations are made
when these storms threaten the US mainland; however, for most o f the world’s
oceans, only weather satellites provide observations of tropical cyclones. Visible and
infrared sensors on these satellites are used to track the position of hurricanes and to
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provide estimates o f their wind intensities. Unfortunately, visible and infrared
wavelength sensors can not penetrate the dense cloud cover surrounding the tropical
cyclone eye; therefore the ocean surface wind estimates are based upon indirect
statistical correlation between cloud patterns and surface winds that have large
uncertainty [5].
On the other hand, microwave scatterometers can penetrate the clouds (and even
light to moderate rain) and provide direct surface wind measurements. Unfortunately,
at Ku-band (14 GHz), these wind retrievals in tropical cyclones are degraded by
principally three effects:
1. The relationship between the ocean radar reflectivity (normalized radar cross
section, a 0) and the surface wind vector is not well known at speeds greater
than 20 m /s. The scatterometer wind vector algorithm uses this relationship,
known as the geophysical model function (GMF), to infer surface winds; but
when measured hurricane G0‘s are used, the retrieved winds are usually too
low.
2. The relatively low spatial resolution (typically 25 to 50 km) of satellite
scatterometer measurements produces wind field distortions, especially in high
wind-gradient regions. This results in incorrect wind direction solutions as
well as producing smoothed fields with reduced peak wind speeds.
3. Moderate to heavy precipitation contaminates the ocean backscatter
measurement [6]. Precipitation causes volume backscatter from rain droplets,
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it modifies the ocean surface reflectivity by droplets impacting the surface, and
it produces two-way atmospheric absorption. For light winds (< 7 m/s) the
combined effect is to increase the backscatter (cj0). For stronger winds, the
effect is predominately attenuation that reduce the ocean backscatter.
Unfortunately, both effects result in erroneous surface wind retrievals.
The purpose of this dissertation is to improve conventional wind retrievals in tropical
cyclones. This involves the development of a Spatial Adaptive Retrieval Algorithm
(SARA) to provide higher resolution wind fields in high wind gradient regions of
tropical cyclones and to identify ocean backscatter measurements affected by rain.
While SARA is validated using actual Ku-band scatterometer data (from the NASA
Scatterometer, NSCAT), it is nevertheless applicable to any scatterometer regardless
of its operating frequency or measurement geometry (e.g., European Remote Sensing
(ERS) scatterometer).
This dissertation consists of six chapters. Chapter one is the introduction which
focuses on a description o f the NSCAT satellite scatterometer and the mathematics
o f the scatterometer wind retrieval. Chapter two provides a functional description of
the Spatially Adaptive Retrieval Algorithm. Chapter three demonstrates SARA
tropical cyclone wind retrieval capabilities using simulated measurements. Chapter
four uses measured NSCAT ocean backscatter to provides a thorough comparison
(and contrast) of NSCAT and SARA retrievals. It is shown that SARA performs
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comparably to NSCAT over a wide range of oceanic wind fields except tropical
cyclones where SARA is superior. Chapter five describes a procedure for identifying
ocean G0 £s that may be affected by rain. Chapter six concludes the dissertation by
reviewing progress made, and providing suggestions for further research. Three
appendices are provided: the characteristics of TC’s are discussed in Appendix A, the
fundamentals for wind retrievals are presented in Appendix B, and an analysis of the
data used in Chapter four is presented in Appendix C.
N A SA Scatterom eter D escrip tion
An in-depth description o f the NSCAT instrument and its science data processing
system is given in [7]. A brief overview o f the NSCAT measurement geometry is
presented below. This will aid in the understanding o f our simulated and actual
results. The NSCAT is a radar system that measures the ocean normalized radar
cross section (a0) at multiple azimuths as illustrated in Figure 1. Each swath is
illuminated by four “fan beam” -antennas (beams) at three azimuths. The middle
azimuth has two antennas to measure dual polarized a 0’s at this position. The
instrument uses Doppler processing to subdivide each antenna fan-beam footprint
into 24 ar0 measurements. In each swath, the CT0 measurements from the four
antennas are collected into 25 km cr0 cells as shown in Figure 2-
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Beam - 2
Antenna
Beam - 1
Satellite
Subtrack
45'
Beams - 4
&-6
115
Beams - 3
‘ &- 5
-45
Beam - 8
Beam - 7
600 km
600 km
330 km
Figure 1 NSCAT Antenna Illumination Pattern
Four 25 km cells (16 C0’s) are combined to form a wind vector cell, WVC, where a
wind vector retrieval is produced. Thus, normal NSCAT geophysical processing
produces wind retrievals located on 50 km centers; while the inherent sensor
resolution is that o f each CT0 measurement (approximately 8 km x 35 km sampled on
25 km centers along and across the satellite track).
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Beam-1
Sigma-0 Centroid
Beam-3 (V-pol)
7 km
Beam-5 (H-pol)
Beam-7
25 km Sigma-0 Measurement Cell
Figure 2 Twenty-five km Sigma-0 cell
Tropical cyclones (TC’s) have high gradients in wind speed and direction. The 50 km
sampling provided by conventional NSCAT processing can miss the locations of peak
wind speeds and the high gradients. The motivation for SARA is to use the inherent
NSCAT sensor (a0) resolution for wind retrievals with the highest sampling possible
to describe the TC as accurately as possible using satellite scatterometry. Surface wind
measurements are of paramount importance to weather forecasters and scientists
studying TC’s, especially in regions where there are no other (in situ or airborne)
measurements available (e.g. most o f the Pacific and Indian Oceans).
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W ind R etrieval P rinciples and P ractice
Wind retrieval is a process of inverting remotely sensed radar backscatter
measurements to infer the geophysical ocean surface winds [8]. This technique uses a
group of radar cross section measurements and a geophysical model function to
produce a number (usually 2 to 4) of likely wind speeds and directions, or ambiguities,
for a given measurement location. To generate an unambiguous wind field, individual
ambiguities (wind directions) are selected at each retrieval location using a de-aliasing
technique such as a median filter [9]. This section describes how ambiguities are
generated using maximum likelihood estimation (MLE) and how an unambiguous TC
wind field can be generated using a spiral de-aliasing technique.
The wind estimation algorithm used in NISCAT is based on a MLE technique [10, 11,
12]. From basic probability theory, the purpose of the MLE is to provide a “best”
point estimate (versus a confidence interval) to a population parameter such as the
mean |i. or the standard deviation ct. To illustrate the MLE method [13]
... we assume that the population has a density function which
contains a population parameter, say 9, which is to be estimated by a
certain statistic [ any quantity obtained from a sample for the purpose
of estimating a population parameter]. Thus the density function can
be denoted by f(x,0). Assuming that there are n independent
observations, X1,...rXn, the joint density function for these
observations is
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L = f ( x t , 0 ) /( x , ,0)---f ( x n, 9)
which is called the likelihood. The maximum likelihood can then be
obtained by taking the derivative o f L with respect to 0 and setting it
equal to zero. For this purpose it is convenient to first take logarithms
and then take the derivative. In this way we find
1
/(* „ « )
df(xx,0)
3B
1
+ "
d6
From this we can obtain 0 in terms o f the xk.
The method is capable o f generalization. Thus in case there are
several parameters we take the partial derivatives with respect to each
parameter, set them equal to zero and solve the resulting equations
simultaneously.
The objective function for the NSCAT wind estimation MLE is given as follows [10]:
-V
AU,t) =Y.
a
1=1
+ ln<£2
where
U = wind speed
(f>= wind direction
A
cr0, = normalized radar cross section from measurements
cr0j = normalized radar cross sec tion from mod el f motion
S ' =Variance(jcr0i- a 0^j
N = number o f measurements in WVC
A description of the model function is in Appendix B.
8
R e p r o d u c e d with p e r m i s s io n o f t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n prohibited w ithout p e r m is s io n .
The NSCAT wind retrieval algorithm [14] inverts the model function, yielding several
wind speeds and directions for a given set of a 0 measurements combined with the
data corresponding to the measurements such as incidence angle, radar “look”
azimuth, and electromagnetic polarization. These retrievals are affected by model
function errors (e.g. failure o f model function to fully characterize the ocean a„ with
just two parameters —speed and direction) and measurement noise. The
measurement noise consists o f geophysical noise and communications noise. Finding
the “true” solution, or the solution closest to the actual wind speed and direction is
assigned to an ambiguity retrieval procedure. In the Spatially Adaptive Retrieval
Algorithm (SARA) ambiguity removal is performed using a spiral dealias technique.
The spiral dealias technique chooses the wind retrieval closest in direction to the
direction defined by a vector rotated an angle 0 towards the eye of the storm from
the tangent of the spiral. 0 is nominally 25 degrees1and decreases as storm strength
increases. The azimuth, A, is calculated as follows [15]:
sin AX
tan A = -------------— :— ----- Tr­
ees^ tan 5 - sm <pcos Ax
where
AX = difference in longitude = K ^ishnw vc ~ W )
<p= storm center latitude
5 - 25 km WVC latitude
1 Personal communication from Vmce Cardone, Oceanweather Inc.
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
After calculating the spiral direction, the algorithm selects the alias closest to
direction at each 25 km WVC location to define an unambiguous field.
10
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Chapter Two
Sara D escription
The foundation for SARA is the NSCAT Wind Retrieval Algorithm. SARA adds two
modifications to the NSCAT Algorithm. One is to regroup the measurements used
in a retrieval into 25 km wind vector cells or WVC (SARA-25 ) instead of a 50 km
WVC grouping2. Another is to use the directions from the 25 km WVC retrievals to
generate retrievals at each a 0 cell (SxARA-max). Using the wind direction from the 25
km WVC retrievals and the model function to search for a speed corresponding to
individual o0 measurements is the key feature for SARA. This technique yields wind
speed and direction for individual G0 sampling. The modified grouping is attached to
the input of the NSCAT algorithm while the higher resolution retrieval code is
attached to the output of the NSCAT algorithm. The heart of the algorithm using
MLE processing is untouched. As a result, any description o f SARA must start with a
description of the NSCAT Wind Retrieval Algorithm [14].
Figure 3 illustrates the NSCAT Wind Retrieval process. First sigma-0 measurements
are collocated into 50 km wind vector cells or WVC’s using knowledge of the
2 NSCAT now generates 25 Vm WVC winds. At the beginning o f this research the NSCAT 25 km WVC winds
were unavailable. Hence rhfo research compares SARA 25 km winds to NSCAT 50 km winds.
11
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
spacecraft orbit and NSCAT measurement geometry. Nominally sixteen
measurements are used for one grouping. All ancillary data needed to perform a
retrieval (e.g. incidence angle, radar look azimuth, and electromagnetic polarization)
are collected with the CT0’s. Once a series o f cr0’s have been grouped, a “first guess” or
an initial estimate o f the wind speed is made using measurements from fore and aft
beams. The MLE objective function (defined in chapter one) is calculated for every
wind direction. Next the wind speed is incremented, and the process is repeated to
build a MLE surface (MLE versus wind speed and direction). After the surface is
generated, a course search is made in two dimensions. - wind speed and wind
direction. The search tries to maximize the objective function. For every set o f wind
speed and direction there is a corresponding c 0 from the model function.
Maximizing the objective (or likelihood) function yields probable direction and speed
solutions called aliases or ambiguities. In normal NSCAT processing, dealiasing
selects a wind direction to make the field unambiguous [9]. Nominally two to four
aliases are returned from the “Sort WV Solutions by likelihood” step below. The flow
chart below is a closed loop such that wind retrievals are made continuously while
NSCAT is in operation to generate global winds. The start o f the procedure is when
data becomes available. The end of the procedure is when data is no longer available.
12
p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p ro d u c tio n p rohibited w ith o u t p e r m is s io n .
{ Sigma-0 Grouping
>1 (sigma-0 and related
j
data)
| Estimate Starting Wind
! Speed and Initialize
!
MLE Surface
Coarse "MLE Ridge'
Search
Locate Uopt at
directions 0-360 deg.
Sort WV solutions by
likelihood
|
Find Local MLE
| Maxima along 'ridge'
|
-> approximate
i
solutions
Wind Vector
i
Optimization Refine
approximate solutions
Figure 3 XSCAT Wind Retrieval Functional
Diagram
As described in appendix A, SARA selects the best wind vector or ambiguity based
on the spiral wind direction behavior known for TC’s. The center of the spiral is a
13
R e p r o d u c e d with p e r m i s s io n o f t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n proh ibited w ith o u t p e r m is s io n .
NSCAT
File
Does
'measurement Re
.within lat-lon box?
Y es
i/
'
i
Save all desired
measurements
j
!
!
Nearest neighbor
grouping of
measurements
/
Ai
Store data and /
pointer files from
grouping
/''R e a d next group
\ a n d test for E O F ? /
-Y es-
Use one group for a
SARA-25 retrieval
using MLE algorithm.
Select one solution
using spiral dealias.
/
-*j
\
/
V
End
A
Save each
\
SARA-25 j <
retrieval
_
i
________z_______
Use the SARA-25
retrieval for up to four
SARA-max retrievals
Save each
SARA-max
retrieval
Figure 4 Functional Description of SABA
14
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n proh ibited w ithout p e r m is s io n .
v
required input to SARA. The accuracy o f this dealiasing depends on the input center
of the spiral matching the center o f the storm.
As shown in Figure 4, SARA uses the NSCAT MLE processing to generate SARA-25
winds, and adds several features designed to provide higher sampling of wind fields.
The first step for SARA is to use a center o f storm location to collect data within a
given “box” centered on a storm with nominally ten degrees of latitude and fifty
degrees of longitude. This limits the number of points to be evaluated using the
nearest neighbor grouping procedure.
Next, the nearest neighbor grouping procedure generates two four column arrays.
There is one array for each side o f the spacecraft (S/C). Each row of the arrays
makes up nominally four pointers to the data collected in step one which makes up a
grouping suitable for SARA-25. One row points to four locations of data that are
spaced closer to each other than would any other grouping. See Figure 5.
This procedure generates groupings that cluster even numbered or odd numbered
beams that are closest to each other. A beam is numbered according to the sequence
at which measurements or made or the “firing order” for the measurements. Odd
beams are on the starboard (right) side o f the S/C, even beams are on the port (left)
side o f the S/C (see Fig. 1). A sample grouping o f the odd (or starboard) side o f the
S/C beams is shown below. Note that the diagonal empty swath in the upper left of
15
p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Process each side by
generating a 4 column array of
pointers to nearest neighbors
4 pointers define one group
generated as follows:
Read in km. (at. beam numbei
and record number. Sort into t
files for odd beams and 4 files
for even beams
L20 Data within latf
km box
I
End
y«
Choose longest of beam files
as an 'anchor” file. Anchor file
occupies column one of 4
column grouping array.
Locate nearest point to ancho
Anchor
and test for EOF?
No—W point from remaining 3 beam
files.
Add point to group by plating j
record number in column 2 of
grouping array
{
Add point to group by plating!
record number in column 4 of
beam array
|
J
Calculate centroid of the 3
selected points and locate
point in remaining beam
closest to centroid
| Calculate centroid of the 2 >
j selected points and locate I
I point in remaining two beams!
j
closest to centroid
Add point to group by plating j
record number in column 3 of
grouping array
Figure 5 Nearest Neighbor Grouping Block
Diagram
16
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
the diagram is due to a calibration cycle for the instrument. N o ocean backscatter
measurements are taken while the instrument is calibrating. Inspection of Figure 6
shows clusters of measurements from up to four beams (grouped near the circles)
that are later used to generate SARA-25 retrievals. Locations where beams are
missing are caused by: the nadir gap (Figure 1), measurements over land, or “bad” a 0’s
identified by several flags used in data processing.
+o
-P
-x
+
«P
*0
+
Gf
*
yo
+
+-X
V
*0
+
X
>
X
* o *■+ *o
X
+
+
X
-o
x
X
o
+x ~
*o
*o *
-x Xo+
X
<5 + x
*o * *o
_ ♦
* x+ / ( j O /
C?
*
27.5
%
^
t
*x°
* / &
o
/
* 4®
* +
dr
s'
*
2
f
18/ 4 &
* . *°
a
26.5 -
126
126.5
127
127.5
128
128.5
Longitude [degrees]
Figure 6 Groupings for SARA-25: Beam 1
Beam 3 co', Beam 5 ‘x’, Beam 7 *+’
17
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
After nearest neighbor collocation, each 25 km wind cell is processed using the
NSCAT Wind Retrieval Algorithm where the NSCAT code is modified to accept the
new grouping. After generating 25 km WVC ambiguities, the best alias is selected
using a spiral direction as described earlier. Using the spiral dealiased wind direction
(and the ancillary data), speeds are generated at each individual sigma-0 cell within the
25 km WVC, using Brent’s inverse parabolic interpolation algorithm [16] with the
model function. The speeds from this one dimensional search combined with the
directions from the SARA-25 retrieval comprise the SARA-max retrieval, which is the
ultimate resolution wind field generated by SARA.
18
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Chapter Three
Evaluation o f SARA Capabilities and
Performance using Simulation
Previously, microwave scatterometer wind retrieval measurement
performance in a TC environment has been evaluated using simulation
[17]. This chapter extends previous work by using a realistic tropical
cyclone surface wind model in a scatterometer simulation to evaluate
the performance o f the SARA algorithm. Since the geophysical model
function is known to have significant deficiencies at high wind speeds,
simulation provides an effective tool for evaluating the wind retrieval
algorithm with minimal influence of the model function. Previous
scatterometer simulations have shown the insensitivity of wind
retrieval accuracy to the choice of the GMF used.
Further, actual scatterometer measurements of TC’s have rain
attenuation effects which cannot be independently verified.
Also
NSCAT simulations [18,19] have shown that rain effects can produce
retrieved wind vector errors that could mask algorithmic errors. Thus
the simulations performed in this chapter can provide a meaningful
evaluation o f the SARA evaluation of the SARA algorithm
independent o f the effects of erroneous GMF’s and rain
contamination o f the ocean backscatter.3
The TC surface wind field used here is modeled. The radar measurement geometry
and CT0cell locations come from the actual NSCAT measurements of Super Typhoon
Violet in September o f 1996. As described in Appendix B, the model function relates
wind speed, relative azimuth (wind direction minus radar look azimuth), incidence
3 Personal communication from Linwood Jones Ph-D.
19
with p e r m i s s io n of t h e c o p yright o w n er. F u r th e r re p r o d u c tio n prohibited w ith out p e r m i s s io n
angle and beam polarization to ocean a r 0 . In the simulated typhoon surface wind
fields below, the wind speeds and directions come from a primitive equation,
planetary boundary layer surface wind model (hereafter called TC96 model) [20]. The
model function is then used to calculate a c 0 for each measurement location using the
TC96 speed and direction and using the corresponding NSCAT incidence angle,
beam polarization, and radar look azimuth. This creates a simulated NSCAT o 0 data
set for a “known” typhoon surface wind field.
SARA is then used to invert these data and to generate a simulated wind field
retrieval. These results are compared to the original TC96 model field to evaluate
SARA’s ability to infer the TC structure, especially in the high gradient region near the
TC eye wall. To provide some background to this simulation, a description o f Violet
and NSCAT sampling of Violet follows.
Typhoon Violet
Super typhoon Violet lasted from September 13* through the 23“*, 1996. A
description of Violet provided by the US Navy’s Joint Typhoon Warning Center,
(JTWQ is shown in Table 1. The “Type” column uses the abbreviations DEP for
depression, STO for storm, and TYP for typhoon. Maximum wind speeds and
typhoon track speeds are in knots, which is the convention used by the TC
meteorological community. JTWC maximum wind speeds are defined using one
20
p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
minute averaging. Further description o f the characteristics of tropical cyclones may
be found in Appendix A.
Table 1 JTWC Track Information for Super
Typhoon Violet
Year Month Day Julian Time UT Latitude Longitude E/W Course Speed
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
1996
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
11
12
12
13
13
13
13
14
14
14
15
15
15
15
16
16
16
16
17
17
17
17
18
18
18
18
19
19
19
19
20
20
20
20
21
21
21
21
22
22
23
23
24
24
255
256
256
257
257
257
257
256
258
258
259
260
260
260
261
261
261
261
262
262
262
262
263
263
263
263
264
264
264
264
265
265
265
265
266
266
266
266
267
267
268
268
269
269
18
6
18
0
6
12
18
0
12
18
0
6
12
18
0
6
12
18
0
6
12
18
0
6
12
18
0
6
12
18
0
6
12
18
0
6
12
18
0
6
0
12
0
12
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
UT
16
16
16
17
16
16
16
17
17
18
18
18
19
19
20
20
21
21
21
22
22
23
23
23
23
24
24
24
24
25
25
26
26
27
28
28
29
31
33
35
42
45
48
50
130
130.6
129.7
129.4
129.3
129
128.7
128.3
128.4
127.9
127.4
127
126.8
126.6
126.4
126.2
126.5
127.2
127.6
128.3
128.9
129.7
130.3
130.5
131
131.4
131.7
131.8
132.1
132.1
132.2
132.2
132.6
133.2
134.4
134.9
136
137.9
139.3
140.9
146.7
150.9
155.3
159.2
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
285
290
300
300
300
290
270
285
335
325
315
325
330
340
345
340
360
55
50
55
55
65
60
50
80
40
40
40
55
10
360
360
30
35
50
40
45
40
35
30
35
???
???
???
7
3
2
2
2
3
3
4
2
5
6
6
6
5
6
5
2
7
8
7
7
7
6
6
5
5
4
1
3
5
4
5
6
10
12
10
13
22
20
28
27
??
??
??
21
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Max.
Winds
25
30
35
45
65
75
75
80
90
90
100
105
115
125
130
125
125
115
105
100
95
90
90
90
80
80
90
90
90
90
90
90
85
80
80
80
75
70
75
80
65
b 06
b 06
b 05
Type
DEP
DEP
STO
STO
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
TYP
t ??
t ??
t ??
Table 2 NSCAT Illumination of Super
Typhoon Violet
NSCAT
Revolution
Number
Date of
Illumination
Time o f
Illumination
UTC
Center
Latitude (N)
Center
Longitude(E)
478
485
492
9/19/96
9/20/96
9/20/96
14:06
02:30
13:40
24.3
25.2
26.4
132.1
131.8
131.2
JTWC
Maximum
Winds
(knots)
80
90
90
50f
485
478
Japan
40 -
30 r
Violet Track
•
• •
492
I5 r
110
115
120
125
130
135
140
145
150
Figure 7 NSCAT Tracks for Rev's 478, 485,
& 492, and the JTWC track for Super
Typhoon Violet
NSCAT provided three passes over or near the eye of Violet. Much o f this work is
validated using these passes which occurred during Revolutions (or Rev’s) 478, 485
and 492 of NSCAT. Table 2 shows the time and location for NSCAT illuminations
R e p r o d u c e d with p e r m i s s io n of t h e cop y rig h t o w n e r. F u r th e r r e p ro d u c tio n p rohibited w ith o u t p e r m is s io n .
of Violet, and Figure 7 shows the subsatellite tracks of NSCAT and the JTWC track
of Violet.
Simulated Surface Winds
To generate collocated <J0’s and surface winds, actual NSCAT measurements provided
the cell locations for the simulated field. The speed and direction were interpolated
to these locations using the TC96 model.
The accuracy of Oceanweather models, demonstrated with earlier storms, provides a
convincing argument that the Oceanweather fields are realistic [21]. Oceanweather
models incorporate surface truth when possible; but for Violet, only estimates from
satellite visible and infrared sensors were available. These data were used to
determine the time history of the eye locations and estimates of the storm intensity
using the Dvorak scale.
A description of the Oceanweather model is presented below:
The TC96 model needs the following inputs in order to compute winds:
1. Central Pressure Po
2. Far Field Pressure Pfar
3. Radius o f Maximum Winds Rp
4. Holland B (a pressure profile parameter)
5. Track o f the system
23
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
The ambient flow in which the system is embedded (the synoptic
flow), Po, and the track are estimated by JTWC. and do have errors
associated with them.... Both Pfar and the ambient flow are
determined from synoptic pressure analysis and are generally well
known. The biggest unknown is in Holland's B and the radius of
maximum winds. For Violet, a B=1.00 was selected as the
climatological norm. As for Rp, it was determined by using pressure
profile fits to available ship data (which was sparse) and by using the
NSCAT data itself (assuming the instrument, while giving the
incorrect speed, could determine where the max was relative to the
center).4
The NSCAT data was used only to determine the eye location at the time of the
NSCAT passes.
Thus, it is reasonable to assume that the TC96 modeled winds reasonably
approximate the “true” speed and direction gradients, maximum speeds, and radial
profiles present in typhoon Violet. By generating a simulated cr0 data set using these
TC96 model speeds and directions and then retrieving the surface winds using SARA,
one can evaluate SARA ability for resolving TC winds down to the individual CT0
resolution (when the G0 measurements come from the NSCAT model function). In
this simulation, the <70 “measurements” are noise free and the model function relates
perfectly speed and direction to or0. Furthermore since the same model function is
used to retrieve the winds, it does not contribute to retrieval error. Thus, this
simulation provides optimistic results because the actual measurements are noisy and
the model function does not accurately represent higher wind speeds. Nevertheless,
.these results are useful to evaluate algorithmic errors introduced by SARA.
4 Personal communication from Andrew Cox, Oceanweather Inc.
24
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
The procedure for generating a simulated wind field and following with a SARA,
retrieval is as follows:
1. Assign the wind speed and direction at each NSCAT <T0 measurement cell location
from the TC96 model for revs 478, 485, and 492.
2. Use the model speed and direction with the ancillary data to calculate a simulated,
noise free, sigma-0 using the NSCATls model function.
3. Retrieve SARA-25 fields using the simulated data.
4. Perform the spiral dealias and assign the selected SARA-25 direction to nearby <70
cells.
5. Using the assigned direction, the model function, and ancillary NSCAT data for
the measurement, calculate the speed for each measurement cell
6. Compare the modeled and retrieved winds and calculate the mean and standard
distribution of the speed and direction differences.
The comparison between TC96 and SARA retrieved fields is shown in the tables
below:
Table 3 Comparing 4,244 SARA-25 Solutions to Collocated TC96 Model Solutions
Parameter
Speed Difference [knots]
Direction Difference [degrees]
Mean
Standard Deviation
0.003
0.003
0.4
4.3
5 Model functions were updated using NSCAT measurements during the NSCAT mission. NSCAT1 is the most
recent model function available at the time o f this research [22].
25
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
The wind direction standard deviation is largely due to the spiral dealias procedure not
selecting the NSCAT alias most closely aligned with the TC96 direction. In Table 4,
the standard deviation in direction drops down to two degrees after dealiasing the
SARA-25 field with the TC96 model field.
Table 4 Comparing 4,244 SARA-25
Solutions to Collocated TC96 Model
Solutions. Dealiased using TC96 directions
Parameter
Speed Difference [knots]
Direction Difference [degrees]
Mean
Standard Deviation
0.003
0.003
0.34
2.0
Table 5 Comparing 16,896 SARA-max
Solutions to Collocated TC96 Model
Solutions
Parameter
Speed Difference [knots]
Direction Difference [degrees]
Mean
Standard Deviation
0.07
0.1
1.5
4.5
The 4.5° standard deviation in direction for the SARA-max fields reflect the 4.3°
standard deviation o f the SARA-25 fields. The SARA-max retrievals are very close to
the TC96 fields, so SARA can measure TC winds down to the individual a 0 cell.
Noisy a 0 measurements, model functions that do not accurately translate measured
<J0’s into actual wind speeds, and rain backscatter and attenuation are the three main
26
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
reasons why SARA is not able to resolve actual TC’s with the same accuracy shown
with this simulation.
Examples o f the max sampling TC96 fields are shown in Figure 8 through Figure 10.
Quiver plots generate an arrow, with length proportional to speed, for every
measurement in the input field. The measurements here are for each a 0 measurement
location, hence these plots show the most detail available with the TC96 models used
and the SARA-max retrievals generated. Where a line o f measurements are missing,
the instrument has performed a calibration
Calibration Frame
Land
3
» -
126
127
128
129
130
131
132
133
Lorgitjd*
cycle.
Figure 8 Oceanweather Model for Rev 478
27
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
28
CoPyright
°Wner,
Either reProdt
uction
Pr°Hibitea
Wthout Perm/\
lssion
Chapter Four
SARA. Compared and Contrasted to
NSCAT W ind Retrieval Algorithm
There are two additional tasks needed to validate SARA as a wind retrieval algorithm.
First show that SARA closely matches NSCAT, and then apply a syllogism
connecting SARA retrievals to NSCAT validation as a wind retrieval algorithm. Since
the SARA algorithm uses a subset of the NSCAT algorithm one can expect similar
behavior from both. This close comparison is shown in the data discussed below.
SARA C losely M atch es N SC A T for non-T C F ield s
In order to compare SARA to NSCAT a large sample of NSCAT retrievals were
compared to the nearby SARA-25 retrievals. The SARA-25 fields were dealiased with
the NSCAT 50 km field. In other words, the SARA-25 solution closest to an NSCAT
solution was used for comparison. The NSCAT field was dealiased using a median
filter, the SARA-25 field was dealiased using the NSCAT field.
This comparison looked at SARA-25 speeds and directions compared to nearest
neighbor NSCAT solutions. Wind speed and direction were retrieved for over 25,000
29
p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
NSCAT locations. To introduce a statistical approach to this comparison, consider
two populations:
Population 1 = All NSCAT speeds or directions retrieved during NSCAT lifetime.
Population 2 = All 50 km WVC samples used here from Population 1 = 25,000
NSCAT retrievals from around the globe. Also included in this population are all o f
the SARA-25 samples taken from Population 1 corresponding to the NSCAT
retrievals used (100,000 SARA-25 retrievals). All sampling is done randomly using
replacement.
The statistics generated below are based on samples o f Population 2 using speed or
direction bins. Each SARA-25 retrieval is compared to its nearest neighbor 50 km
WVC retrieval. Outliers in direction result from having SARA-25 retrievals where the
nearest 50 km retrieval is too far away to make a valid comparison. For this reason,
and due to the possibility o f any data corruption, 2.8% of the measurements in
population 2 have been edited. The goal is to obtain a robust mean and standard
deviation for the experiments. The scheme for removing outliers is as follows:
1. Assume the direction difference pdf is Gaussian
2. Sort the signed differences in ascending order
3. Remove, or trim, the top and bottom x% o f the data. The x used here is 0.05.
4. Calculate the mean and standard deviation for the remaining data.
5. Accept the differences d that satisfy the following test.
\d \-/u < 1 * cr
30
p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
where
fl = mean o f trimmed measurements
ct = standard deviation of the trimmed measurements.
The reasons for assuming that Population 2 represents Population 1 are threefold.
First the population size N is large. Secondly, the sampling is random. Thirdly, the
sample statistics generated below do not vary significantly when using a population
size of 1,000 or 100,000.
Recall that the SARA algorithm uses a subset of the NSCAT algorithm for wind
retrieval. SARA essentially changes the grouping procedure, and modifies the MLE
Algorithm to handle a new set o f inputs. Since the SARA Algorithm uses a subset of
the NSCAT Algorithm one would expect similar performance. Over 100,000
comparisons are used here to make the comparison clear. Tables showing the
distribution of data used here can be found in appendix C.
Over 25,000 NSCAT Retrievals and the adjacent SARA-25 retrievals were collected
over the regions shown in Figure 11. For each 50 km retrieval there are nominally
four SARA-25 retrievals. To form speed differences, the speed o f the 50 km retrieval
was subtracted from each o f the four speeds from the SARA-25 retrievals. To form
direction differences, the direction of the 50 km retrieval was subtracted from each of
the four directions o f the adjacent SARA-25 retrievals. The smallest angle between
NSCAT and SARA retrievals is used as the difference in directions. Table 6 provides
the overall statistics for this data. With a mean speed difference o f less than half of
31
p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
one knot and a mean direction difference o f less than half o f one degree, it is clear
that SARA retrievals, in the average, match NSCAT Retrievals, but the standard
deviations show a slightly larger difference in the two retrievals. As shown in Figure
12, this sample contains a large number o f retrievals with speeds less than 10 knots.
These winds are considered light and variable. NSCAT wind direction performance is
degraded for light and variable winds. Further, as shown in Figure 21 Histogram o f
SARA-25 Speeds Retrieved, much o f the standard deviation in the wind directions in
the data used here is for low wind speeds.
Regions for Algorithm Comparison Data
100
to
o>
b)
CD
<d
h
33
(D
■o
3!
•C
<D
a
t
-100
-200
-50
0
50
Longitude [degrees]
Figure 11 Regions for Algorithm Comparison data
32
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Table 6 Statistics for Entire Data Set
Parameter
Speed Difference [knotsl
Direction Difference [degrees]
Mean
Standard Deviation
-0.11
0.31
1.10
9.38
Figure 12 and Figure 13 present histograms for SARA speeds and directions
respectively. The speed distribution parallels the distribution found in global
samplings [23]. Figure 14, and Figure 15 show the histograms of speed differences
and direction differences respectively. Because the sample taken is not a global
sample, the wind direction distribution does not resemble the global wind direction
distribution.
nsDQnm o*spoons nsn o ^n
0
5
10
15
20
25
30
35
40
Figure 12 Histogram of SARA-25 Speeds Retrieved
33
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
11
10
9
8
7
6
5
4
3
2
0
SO
ISO
200
Oirvctran [degrees}
100
250
300
350
Figure 13 Histogram of SARA-25 Directions
Retrieved
H t t a g a m o f S peed Dflerencea
I
23
«
-3
-2
•1
0
1
2
3
S08OdDffarerc»(S*RA-heCATfiroBl)
Figure 14 Histogram of Speed Differences
SARA - NSCAT mean -0.11 knots, standard
deviation 1.1 knots
34
R e p r o d u c e d with p e r m i s s io n o f t h e cop y rig h t o w n e r. F u r th e r re p ro d u c tio n p rohib ited w itho ut p e r m is s io n .
I la ogamdBrcctionOiflBq ie f tSARAGorTpafedlDN9CAr
-30
-10
0
10
20
30
Oi*cbcnDfcien» (SARA-NSCAT. degws)
Figure 15 Histogram of Direction
Differences SARA - NSCAT, mean 0.31°,
standard deviation 9.38°
In order to provide a detailed study of the mean differences, including standard
deviations, plots are generated for speed and direction differences vs. incidence angle
(Figure 16 & Figure 17), speed and direction differences vs. wind direction with
respect to S/C heading (Figure 18 & Figure 19), and speed and direction differences
vs. wind speed (Figure 20 & Figure 21). All o f these figures show that there are no
systematic errors with incidence angle, wind speed, or wind direction except Figure
20. The errors in Figure 20 show a small but statistically significant increase in speed
differences with speed. Since, SARA-25 has typically V* o f the G0 measurements
used for a 50 km NSCAT retrieval, it is expected that there should be some
differences at low wind speeds where the signal to noise ratio is low. At high speeds
(>20 knots) this trend can be attributed to the small number o f retrievals available at
35
p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n pro hibited w ith o u t p e r m is s io n .
higher wind speeds. The small number of samples leads to an inaccurate comparison
for the highest speeds (> 20 Knots), that could lead to less accurate comparisons.
•
.
.
J
-1.5(.
L
IS
-1
....................
20
2 S 3 0 3 S 4 0
45
_J
S 0 S 5 6 Q
tnodanc* Angte [4«grMS|
Figure 16 Speed differences vs. incidence
angle
i*r
5l
5 0
.
25
30
35
40
45
50
56
60
j n o d t c t Ang|« [<t y w i [
Figure 17 Direction difference vs. incidence
angle
36
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
M sanSpM d D rth m » (S A A A . NSCAT. M s )
1-5
«-o.s
k
0
so
100
ISO
200
250
300
350
Wind OirMtton * / L S C Oweflon [d sp w s|
Figure 18 Speed differences vs. wind
direction
Ml,0fr
i
! L
: i ; i
:li i i i I
I !
!
!
-«K
0
SO
100
ISO
200
250
300
350
Wind OracUan wsJL SIC OfrKton | * « m |
Figure 19 Direction differences vs. wind
direction
37
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
0-1
0
2 0 -8 0
1 0 -2 0
5
15
10
VMnd
20
25
Speed (ta e c s l
Figure 20 Speed differences vs. wind speed
0 -5 * .
f
f.
5 -1 0
O
D -5
9-
-,ol
10
15
VWnd Speed {towt*]
Figure 21 Direction Difference vs. wind
speed
38
R e p r o d u c e d with p e r m i s s io n o f th e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n proh ibited w ith o u t p e r m is s io n .
Figure 14 through Figure 21 show that SAEA retrievals are nearly identical to NSCAT
retrievals. There are no systematic algorithmic errors with incidence angle, wind
speed, or wind direction except for Figure 21. The large number of light and variable
wind speed comparisons contribute to the standard deviation in direction. SARA
retrievals may actually be more accurate than NSCAT in light and variable conditions
where the wind direction changes more often over a given area. The spatial gradient
in wind direction is higher in light and variable winds. SARA, using more frequent
sampling, may more readily measure this spatial gradient.
Another important comparison is to look at the number of aliases generated by each
retrieval. Figure 22 through Figure 27 show where the two, three, and four ambiguity
solutions occur for both SARA-25 and NSCAT for Rev 478. These figures
demonstrate that SARA-25 ambiguities closely match alias patterns generated by
NSCAT. Recall that the NSCAT wind retrieval algorithm generates several solutions
or ambiguities before assigning a unique solution for each location. The sets of
solutions generated by the MLE algorithm can have two, three, or four ambiguities
depending on the overall certainty o f the retrieval. It can be seen that corresponding
solution cases appear in similar locations in both types of retrievals. SARA-25
recovers the same percentage o f two, three, or four solution cases as does NSCAT.
However, in the SARA retrievals there are four sets of SARA-25 solutions for each
NSCAT solution due to the difference in sampling. Figure 22 and Figure 23 show the
“2 ambiguity solutions” for SARA and NSCAT respectively.
39
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
118
120
122
124
125
128
130
132
134
132
134
Longitude
Figure 22 SARA-25 Two Alias Solutions
30
28
25
24
22
20
18
118
120
122
124
125
128
130
Lonrjtude
Figure 23 NSCAT 2 Alias Solutions
40
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
30
2B
25
'24
22
20
18
118
120
122
124
125
128
130
132
134
U xgtide
Figure 24 SARA-25 Three Alias Solutions
30
28
25
24
22
20
18
118
120
122
124
125 128
Longtirfe
130
132
134
Figure 25 NSCAT Three Alias Solutions
41
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
30
28
26
|24
22
20
18
118
120 122
124
126
128
130
132
134
Longtude
Figure 26 SARA-25 Four Alias Solutions
30
28
26
»
v V.
22
i t l t
20
18
118
120 122
124
126
128
130
132
134
Longtude
Figure 27 NSCAT Four Alias Solutions
42
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r re p r o d u c tio n prohibited w ithout p e r m is s io n .
The three ambiguity cases are shown in Figure 24 and Figure 25. The four ambiguity
solutions are shown in Figure 26 and Figure 27. Close agreement in location of
solutions is evident in these figures. Thus NSCAT and SARA perform similarly in
generating aliases within the given TC wind field.
Finally, a comparison o f the number o f ambiguities generated in a global sample of
retrievals is presented in Table 7. These results confirm Figure 22 through Figure 27.
One can see that SARA retrievals virtually match NSCAT retrievals in terms of the
number of aliases produced. The data used in Table 7 does not include the TC Violet
wind fields used above. The data is from global samples of SARA fields and of
NSCAT fields.
Table 7 Percent o f Retrieval Locations with
2, 3, or 4 Ambiguities. Sample Size: SARA
193,000 Ambiguities, NSCAT 87,000
Ambiguities
Number of
Ambiguities at a
Retrieval Location
2
3
4
Total %
Percentage of Total Number o f Retrieval
Locations with Corresponding Number of
Ambiguities
NSCAT (%)
14.8
20.5
64.7
SARA (%)
13.5
100
100
22.2
64.3
43
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Difference
Difference (%)
1.3
-1.7
0.4
Having shown that NSCAT and SARA agree over a wide range of speeds and
directions, one might ask why generate SARA when NSCAT already provides nearly
identical information? The answer is that SARA-25 is an intermediate product that
provides the directions for the individual CT0 cell or SARA-max retrievals. These max
sampling retrievals provide the highest sampling NSCAT can use to generate a vector
wind field. This high sampling is needed to provide the best information in regions of
high speed gradients such as TC’s. Later, the higher information content with SARAmax retrievals will be shown using retrievals of super typhoon Violet. For now, a
discussion on NSCAT validation will be presented to illustrate how NSCAT, and
through syllogism SARA, performs as a wind retrieval.
Presented below are comparisons between NSCAT measurements and buoy
measurements [24]. This comparison to surface truth was made to calibrate and
validate the NSCAT instrument including the wind retrieval algorithm. Since SARA
matches NSCAT, this validation applies to SARA retrievals as well.
Figure 28 shows that the majority o f NSCAT - buoy direction differences are within
30 degrees of each other.
Figure 29 and Figure 30 show mean and standard deviation wind direction differences
vs. speed. Figure 29 corresponds to NSCAT retrievals at 25 km spatial resolution that
have been nudged. Nudged refers to using ocean surface wind analyses from
NOAA’s National Center for Environmental Prediction numerical weather models to
help dealias the wind field (resolves a 180° wind direction ambiguity). Figure 30
44
R e p r o d u c e d with p e r m i s s io n o f t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n proh ibited w ithout p e r m is s io n .
corresponds to the 50 km WVC nudged retrieval. From these graphs one can see
that mean direction differences are roughly ten degrees for speeds up to 18 m /s and
the standard deviations are less than 20 degrees (for wind speeds greater than 7 m/s).
N S C A T -1 (U N -N L tD G E D )
0.30
0.25
0.20
0 .T0
0.05
I
o.oo d
-100
•0
100
DIRECTION DIFF. ( n s c o t—Duoy, d eg .)
____________ 20 km distance cutoff
........................ 50 km distance cutoff
100 km distance cutoff
Figure 28 NDBC Buoy Wind Direction Comparison Histograms Mike Freilich, OSU
& Scott Dunbar, JPL
NSCAT-1 2 5 km (NUDGED)
TOO
SO
60
eo
o»
"O
40
V
20
-2 0
0
5
10
15
20
WIND SPEED ( m / s )
Figure 29 NDBC Buoy Wind Direction Comparisons Mike Freilich, OSU & Scott
Dunbar, JPL
45
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
NSCAT-1 5 0 km (NU0GE0)
100
— i ■ ■ ■ ■ i—■ 1 ■ ' i—1——■-
.
80
60
40
20
-2 0
10.
1J
20
WINO SPEED ( m / s )
Standard Deviation of Direction Differences
Mean Direction Difference
Figure 30 NDBC Buoy Wind Direction Comparisons Mike Freilich, OSU & Scott
Dunbar, JPL
SARA C ontrasted w ith N SC A T
From the above it is clear that SARA performs very closely to NSCAT for a wide
variety of conditions. The next goal for this chapter is to show where SARA improves
wind retrievals over those from NSCAT and thus offers important information for
understanding wind fields in high gradient situations. This contrast between SARA
and NSCAT is shown through retrievals of TC Violet.
The statistical analysis carried out for the globally sampled wind field above is
repeated for three NSCAT passes over TC Violet. The sample size drops from
25,000 NSCAT retrievals to 1,400 retrievals. To see the significance of SARA
retrievals, one needs to look at individual comparisons on a measurement by
measurement basis.
46
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure 31 and Figure 32 show histograms o f respectively the speeds and the directions
used in this sample, and Figure 33 and Figure 34 show histograms of speed
differences and direction differences respectively. In order to provide a detailed study
o f the differences, plots are generated for speed and direction differences vs.
incidence angle (Figure 35 & Figure 36), speed and direction differences vs. wind
direction with respect to S/C heading (Figure 37 & Figure 38), and speed and
direction differences vs. wind speed, (Figure 39 & Figure 40). All o f these figures
reflect the whole sample statistic that NSCAT and SARA generate similar wind fields
even when the sample contains a super typhoon.
Table 8 SARA-25 Retrievals Compared to
NSCAT Including a TC, 1400 NSCAT
Retrievals
Parameter
Speed Difference [knots]
Direction Difference [degrees]
M ean
Standard Deviation
0.11
2.07
14.90
0.23
47
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
R
tr
35
2.5
40
30
10
Sp««d(tov(sl
Figure 31 Histogram of SARA-25 speeds
14
50
100
150
200
250
350
OwcBfln (> a m i l
Figure 32 Histogram of SARA-25 directions
R e p r o d u c e d with p e r m i s s io n of t h e c o pyright o w n er. F u r th e r re p r o d u c tio n proh ibited w ithout p e r m is s io n .
Speed OrfTerence (tautsf
Figure 33 Histogram o f SARA-25 speed
differences, mean 0.11 knots, standard
deviation 2.07 knots
P
e
r
e
e
tan
9e
o
f
R
e
t
r
v
I■
*
10
•20
20
Figure 34 Histogram o f direction
differences, mean 0.23°, standard deviation
14.9°
49
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
inodwic* Angfe [degrees]
Figure 35 Speed differences versus
incidence angle
\
15
20
25
30
35
40
*5
50
55
60
h ad wice Angfe [<igrm l
Figure 36 Direction differences vs. incidence
angle.
50
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
I0
I
f
0 .
I
*0.5
Wind OiracttonwrL S/C Direction (dograosl
Figure 37 Speed differences vs. wind
direction
0 1
I
f
f.
0
='U
\7
0
• *1
8
•a
-a
0
SO
100
Wind Direction
150
200
250
300
350
S/C Direction (dogreosl
Figure 38 Direction differences vs. wind
direction
51
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
s
p
05
51*
to
d
0
I
f
f
i
n
kn
-05
tos
0
10
5
15
20
25
30
Wind SpMd (taotsl
Figure 39 Speed differences vs. wind speed
------- 1-------------- 1-------------- 1-------------- 1--------------
15
10
0
r
*
0
l
*
f.
00
0
«
9
0*
5
tt
10 20
5- 10
20 51'
-5
•10
•IS
(J
5
10
IS
20
25
31
Wind Speed pmois|
Figure 40 Direction differences vs. wind
speed
The above shows that SARA and NSCAT yield similar retrievals even when there is a
TC in the wind field. The systematic trend in speeds from Figure 39 is similar to the
52
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
global comparisons presented earlier. It can then be argued that the 25 km sampling
can be achieved by distributing the 50 km sampling vectors over the 25 km sampling
locations. However, the 25 km WVC offer differing wind direction information as
shown in the 14.9° standard deviation in direction. This information is passed on to
the SARA-max retrieval. SARA-25 is needed to provide direction information to the
SARA-max retrieval. It will be shown that the SARA-max retrieval does a better job
of profiling high speed gradients and providing more samples where there are high
speed gradients. These are the areas where SARA improves NSCAT retrievals.
The key to the importance of SARA is then in the SARA-max retrievals. When a TC
is analyzed on almost a point by point basis, the SARA-max retrievals offer much
higher information than does the 25 or 50 km sampling. The smoothing process of
using more than one measurement to generate a retrieval averages the fields generated
by the 25 and 50 km sampling. As shown below, the contrast between NSCAT and
SARA is in the SARA-max retrievals. These contrasts are more readily seen in radial
profiles of the storm, and in speed contour plots showing more detailed structure of
the storm rather than overall statistics as has been used so far.
In terms o f statistics the majority of points are for wind speeds less than 30 knots,
which in the mean, reduces the significance o f SARA retrievals. The three TC
-retrievals yield the following summary:
53
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Table 9 Differences between SARA-25 and
SARA-max Retrievals for Rev 478
Param eter
Speed Difference [knots]
Mean
Standard Deviation
0.31
3.09
Table 10 Differences between SARA-25 and
SARA-max Retrievals for Rev 485
Param eter
Speed Difference [knots]
Mean
Standard Deviation
0.73
3.61
Table 11 Differences between SARA-25 and
SARA-max Retrievals for Rev 492
Param eter
Speed Difference [knots]
Mean
Standard Deviation
0.46
3.54
Note that the SARA-max retrieval yields the highest speed standard deviation of 3.61
m /s in contrast from the SARA-25 wind speed standard deviation of 1.18 m/s. The
-differences between NSCAT and SARA solutions in a TC are due to several
interactions. These interactions include:
54
R e p r o d u c e d with p e r m i s s io n o f t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n proh ibited w ithout p e r m is s io n .
•
Spatial gradient: SARA-25 retrievals generate solutions at up to 4 locations
near every NSCAT retrieval location. In that SARA retrieves a larger
number of valid solutions than NSCAT for a given area, SARA retrievals are
better than NSCAT retrievals. The SARA-max retrieval offers up to 16
retrievals per NSCAT location. The SARA-max retrievals are more easily
affected by noise and rain since there is no averaging with SARA-max
retrievals. SARA-max generates more solutions that are more affected by
noise than are NSCAT solutions.
•
Sample Variance: SARA uses three to four backscatter measurements per 25
km WVC. NSCAT 50 km WVC retrievals use nominally sixteen backscatter
measurements.
•
Rain is thought to attenuate <J0 measurements. Identifying which cells are
affected by rain is needed to fully evaluate, use, and validate a SARA-max
retrieval.
Sam ple V ariance due to U sing Fewer M easurem ents
SARA uses fewer measurements than NSCAT to generate a statistical inference. This
section addresses how using fewer measurements can affect the retrieval. Assume
that the 16 measurements used in a 50 km WVC generate an unbiased estimate of the
wind speed or direction, with sample variance S 2.
Also assume that the SARA-25
55
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
measurements generate a biased estimate, with sample variance S 2 . Then we can
expect the SARA-25 sample variance to be larger than the unbiased estimate sample
variance by:
A
n
S ^ - ^ - S 2.
n —1
Using this guideline, one should expect SARA-25 retrievals to have 33% to 50%
higher sample variance when using four measurements or three measurements
respectively.
Assume or approximate that the NSCAT sample variance from Figure 30 is roughly
400 degrees squared. The SARA sample variance would then be 533 degrees squared
tor four measurements, and 600 degrees squared for three measurements. This
suggests that SARA retrievals have an approximate standard deviation in wind
direction from surface truth between 23.1° and 24.5° while NSCAT has a standard
deviation of 20°. Recall from Table 8 that the standard deviation between NSCAT
and SARA directions is 14.9°. Roughly half of this may be attributed to sampling
differences. This analysis does not account for any advantage SARA has by not
averaging the wind over all 16 measurements.
56
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
C ontrast B etw een SARA R etrievals, and NSCAT
Retrievals
In this section it is shown that SARA differs from NSCAT in regions of high speed
gradients such as in and near the eyewaUs of TC’s. Eyewails occupy a very small
region compared to the large regions used above for comparison. NSCAT is
designed for global winds, SARA is designed for TC’s. As a result, SARA differences
from NSCAT do not show up in the previous analyses involving large areas.
This section provides side by side comparisons of TC wind fields, radial plots, and
speed contours. These figures will show that the SARA-max retrieval does provide
more information about the TC’s structure than does NSCAT. This information is
vital for better understanding o f TC’s.
As an initial contrast, consider all three resolutions shown side by side to illustrate the
enhanced spatial resolution provided by SARA.
57
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
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59
fU ^ et
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cte
134
138
Figure 48 SARA-25 Retrieval o f Rev 492
61
Repra,^ m
h
Perr^ission
of,he^
lmowner
Funher^
uahn
Perr»ission.
126
12B
130
132
Lcngtijcte
134
136
Figure 49 SARA-max Retrieval of Rev 492
The wind field plots show dramatically how the higher resolution fields can aid
visualization of the storm. The higher sampled fields provide more insight into the
structure of the field than does the 50 km WVC field.
Radial plots provide a cell by cell contrast between the retrievals. In most cases, the
SARA-max retrieval will provide the highest wind speeds for the profiles. Retrievals
from individual cells are more easily affected by rain and noise. This can be seen by
the way the SARA-max retrievals fluctuate more than the other retrievals. However,
62
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
part of this fluctuation can be due to actual wind conditions. Learning more about
measurements affected by rain is the subject of chapter five.
Radial plots were generated for several radial profile angles for each retrieval below.
The radial profiles are generated by first interpolating the 50 km \W C to the SARAmax locations, and interpolating the SARA-25 retrievals to the SARA-max locations.
Then one defines a radial angle which is the angle from 0° = due East. Positive
angles are counter clockwise to due East. A plane is defined that is normal to the
tangent plane to the earth at the center of the storm and contains the radial line. The
closest points to this plane define the radial profile for the given radial angle. Three
profiles for each of rev’s 478, 485, and 492 are shown below.
63
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p ro d u c tio n prohibited w ith o u t p e r m is s io n .
fe r Nirfeer 47$ with
A ^e =90 Dagees
40-
-500 -400 -300 -200 -100
0
100
R xttD startB lforj
200
300
400
Figure 50 Rev 478 with radial angle = 90°
Rsv M rrter 478, wth Radal fir&e =30 DagBes
-600
-600
-400
-300
-200
-100
RacH D stancB(taj
0
100
Figure 51 Rev 478 with radial angle = 30°
64
R e p r o d u c e d with p e r m i s s io n of t h e c o pyright o w n e r. F u r th e r re p r o d u c tio n proh ibited w ithout p e r m is s io n .
fav M irber 478, v it\ facial Ar^e =-30 CBgiaes
-7TD
-eOD
-5D0
-40D -300 -200
Racial Dstanoe[!«T]
-100
0
100
Figure 52 Rev 478 with radial angle = -30°
f a / Mrrber. 486, wlh fad al A i^ e=90 CtegBes
j.
era
430
0
200
facial DstancePffiJ
Figure 53 Rev 485 with radial angle = 90°
-200
65
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Rw Nrrter. 485,wKhFfecHAn^e =30 Dagoes
2DI___i___ i___ i___ i___ i___ i___ i___ i___
-400-300-200
-100 0
100 200
Ffedal Clstanoe[|nj
300
400
SOO
Figure 54 Rev 485 with radial angle = 30°
Rev Njrber. 485, vulh Radal A%fe =-30 Cfegees
200
300
0
100
F&fai DsterDBDrrj
Figure 55 Rev 485 with radial angle = -30°
-300
-100
66
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
fav Nirber 492 w(h RacialPctfe =30 Cbgoes
-3D
-6G0 '4 00 -200
0
200 400
facial □sbarce On]
ODD 800
1000
Figure 56 Rev 492 with radial angle = 30°
fav Mirber. 492; wilhfacial fir&e=0 Dagees
-800-600-400
-200
0
200400800800
facial CSstance [Icr]
Figure 57 Rev 492 with radial angle = 0°
67
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Rsv Mrrber 432. Wlhfecial A g e =-30 DBgees
-1000
-600
0
500
1000
Racial D3ancB[l<rrJ
Figure 58 Rev 492 with radial angle = 30°
The radial plots were generated by interpolating each resolution to the locations
specified by the SARA-max field. This way, all fields could be compared at the same
location using numerical interpolation versus plotting all three samplings at their
corresponding locations and relying on graphical interpolation for comparison.
Interpolating each field to the SARA-max grid makes comparisons straightforward.
However, with interpolation, there are more measurements shown for the SARA-25
and 50 km WVC retrievals than there are in the original retrievals. Only the SARAmax retrievals provide all the points shown in the above radial profiles. An example
o f how a radial plot appears without interpolation is shown in Figure 59
68
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
55
♦ -+ 50 ton
0-0 25ten
*—* M k
-400 -300 -200 -100
0
100
2D0
300
400
500
te fa l □stance [tor]
Figure 59 30° Radial plot without
interpolation for Rev 485
It is shown in the radial plots that SARA-max provides in general the highest wind
speeds. These wind speeds of up to 45 knots do not compare with the JTWC
estimates of 80 to 90 knot wind speeds. The 80 to 90 knot wind speeds are mesoscale
and convective speeds, not synoptic wind speeds which NSCAT is designed to
measure even on the SARA-max level. The extent and persistence of the TC winds
do not match the synoptic wind patterns NSCAT is designed to measure. However,
-the increase in wind speeds in the SARA-max retrieval from NSCAT 50 km retrievals
is one of the predominant contrasts between the fields. Measuring higher wind
69
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
speeds in radial plots show that the SARA-max retrievals are performing better in
TC’s than does the NSCAT 50 km retrieval. More measurements means more
opportunities for the SARA-max measurements to measure winds at crucial points
such as the peak winds at the eyewall. This can be seen in the radial plots above.
In addition to radial profiles, speed contour plots can show the improvements in
wind field measurements provided by higher sampling. More detailed plots showing
higher wind speeds are provided by the SARA-max retrievals than by the other
retrievals. The contour plots below were generated by interpolating each field to a
grid with ten km spacing. The same interpolation is used for each retrieval. Plots are
shown below using 50 km WVC, SARA-25 and SARA-max retrievals for Rev’s 478,
485, and 492.
SCO
400
300
200
100
-100
-
20 0 -
-300
-400
-a n
-800
-400
-300
-200
-100
0
100
Saih
70
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Figure 60 Speed Contours for 50 km Sampling Rev 478
500
400
300
200
100
-100
-200
-300
-400
-700 -600 -500 -400 -300 -200 -100
Sxih
0
100
Figure 61 Speed Contours for SARA-25 Rev 478
500
300
200
100
-100
-300
-500
-700 -600 -500 -400 -300 -200 -100
0
100
Souh
Figure 62 Speed Contours for SARA-max Rev 478
71
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
400
300
200
100
-100
-200
-300
-500
-400 -300 -200 -100
0 100 200 300 400 500
Sxih
Figure 63 Speed Contours for 50 km Sampling Rev 485
300
200
100
-100
-200
-300
-600
-400 -300 -200 -100
0 100 200 300 400 500
Sxih
Figure 64 Speed Contours for SARA-25 Rev 485
72
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n er. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
300
200
100
-100
-200
-300
-BO
-SOO
-400 -300 -200 -100
0
100 200 300 400 500
SaUh
Figure 65 Speed Contours for SARA-max Rev 485
300
200
100
-100
-200
-300
-200
0
200
400
600
SoUh
Figure 66 Speed Contours for 50 km Sampling Rev 492
73
R e p r o d u c e d with p e r m i s s io n o f t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n proh ibited w ith o u t p e r m is s io n .
300
200
ioo!
1 100
-
|-
-200
-200
0
600
200
SaJh
Figure 67 Speed Contours for SARA-25 Rev 492
300
200
100
-100
-200
-300
-200
0
200
400
600
SaJh
Figure 68 Speed Contours for SARA-max Rev 492
74
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
The speed contour plots show increasing detail when going from low sampling to
high sampling retrievals. Each contour plot is generated using the same grid spacing
o f ten km for the interpolation needed to form the contours. The differences in the
plots are thus due to the difference in information content and not due to differences
in the plotting routines. The SARA-max contour plots show the most structure,
capturing the widest range of speeds and the highest speeds o f any of the plots. This
finer definition of the storm structure can aid researchers in better understanding TC
behavior.
75
R e p r o d u c e d with p e r m i s s io n o f t h e cop y rig h t o w n e r. F u r th e r re p ro d u c tio n p rohib ited w itho ut p e r m is s io n .
Chapter Five
Identifying <j0 Outliers
Ultimately, the validity o f individual CT0 measurements needs to be addressed. As
discussed, a 0 measurements can be affected by rain. One cannot compare CT„
measurements directly since each measurement uses different parameters to measure
cr0. For example, backscatter depends on incidence angle and electromagnetic
polarization which can vary with each measurement. In order to account for the
differences in measurement parameters one can use the SARA-max solution as a
means of comparing one measurement to neighboring measurements. The SARAmax solution is closely matched to the corresponding measurement through the
speed search routine error limit (0.0001 for this research). By using the retrieval for
one o 0 cell to generate residuals between neighboring cell measurements and model
function values, one can generate a figure of merit that indicates how well a
measurement in a SARA-25 WVC matches neighboring measurements in the same
WVC. The equation for this comparison is:
where
76
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
N = Number of <J0 cells within a 25 km WVC, nominally N=4
erf Q^ = normalized radar cross section for ith SARA-max cell computed from
model function using the speed and direction from the jth SARA-max cell.
a i0 = normalized radar cross section measurement from NSCAT for the ith cell
Compute r for every CT„ measurement cell.
At this point, it is only a hypothesis that as rf increases the likelihood that the cell is
affected by rain increases. There is no collocated rain data to validate this procedure
with TC Violet. This technique provides a heuristic means for finding cells affected
by rain. After calculating the residuals, one can select an r, cutoff value that, if
exceeded, causes the cell to fail the GOF test. The immediate benefit of this
technique is shown by comparing patterns generated by the GOF to typical patterns
for rain near TC’s (e.g. spiral rain bands).
77
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
The flow chart for the GOF test is shown in Figure 69.
J = Cell
number of
SARA-max
cells = 0
Increment j. Find
SARA-25 data for jth
cell. Set SARA-max
cell number i = 0.
<= Number o f \
SARA-max cells in
Sum residuals and
assign to jth cell
longitude and latitude
increment j.
No
s.SARA-25 groups
I
Yes
Choose ith cell speec
(spd) and direction (di^)
to use in GMF for all
cells in group
j > Number ofx
SARA-max cells'?.
No
Yes
Calculate residual foi
every cell in group
using spd, dir, and
ancillary data from
SARA-25 in GMF.
End
Figure 69 Flow Chart for GO F test
78
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
I
3
Lcnptufe
Figure 70 Rev 478 SARA-max Retrievals
failing 15% GOF test
I
■
‘
■
___■
125125127128129131131132133134
L cn£ufe
Figure 71 Rev 478 SARA-max Retrievals
Passing the 15 % GOF test
79
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
127 128
129 130 131 132 133 134 136
136 137
Lcrghxfe
Figure 72 Rev 485 SARA-max Retrievals
Failing 30% GOF test
L o rg h ife
Figure 73 Rev 485 SARA-max Retrievals
Passing 30% GOF test
80
R e p r o d u c e d with p e r m is s io n of t h e cop y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
W
325
Figure 74 Rev 492 SARA-max Retrievals
Failing 15% GOF test
Lcn^ufe
Figure 75 Rev 492 SARA-max Retrievals
Passing 15% GOF test
81
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Shown in Figure 70 through Figure 76 are the results of applying the GOF test to
Revs 478, 485, and 492. A fifteen percent cutoff is used for Revs 478 and 492 while a
30% cutoff is used for rev 485 to illustrate the effect o f choosing different cutoffs.
The test was applied to a region within a 300 km radius o f the storm where the
strongest rain activity is likely. Results show that the eyewall is selected as a rain
region in Rev’s 478 and 485. Rev 492 didn’t include an eyewall in the retrieval. In
addition, the patterns failing the GOF test outside the eyewall form patterns similar to
rain bands commonly seen in TC’s.
It can be seen in the radial plots for Revs 478 and 485 shown in chapter four that
some speed solutions are far lower than there neighboring solutions. This lowering of
the speed is probably due to attenuation of the backscatter due to rain. To illustrate
the effectiveness of the G O F test in identifying measurements affected by rain, radial
plots for rev 485 where measurements have been removed are compared to plots o f
the complete field to classify the types o f points that are removed by the GOF test.
It will be shown that the GOF test removes unusually low speed measurements, and
unusually high speed measurements, that are likely to have been affected by rain. For
this analysis, 15% of the points have failed the GOF test.
82
R e p r o d u c e d with p e r m i s s io n o f th e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n proh ibited w ith o u t p e r m is s io n .
+-+*
a —o QCFRsbmd
TP
-400
-300
-200
-100
0
tOO
200
300
<0
ftefalC istanoefln]
Figure 76 Rev 485 with Radial Angle = 20°
-300
-2 0 0 -1 0 0
o
ioo
aoo
300
«o
[fetfel □stancePaT j
Figure 77 Rev 485 with Radial Angle = 10°
83
R e p r o d u c e d with p e r m i s s io n o f t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
+-f-AI
e _0 QCFRaduced
-300
-200
-100
0 100
Ariai CUancelln]
200
300
400
Figure 78 Rev 485 with Radial Angle —0°
Q-fl GCFtoduoad
-300
-200
100
0
%&CUanoe[ln]
-100
200
300
Figure 79 Rev 485 with Radial Angle = -10°
84
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a - e GCFRaduoed
-300
-200
-100
0 1C0
f&bt Oaanspn]
200
300
40
Figure 80 Rev 485 with Radial Angle = -20°
■BP
-300
-200
-100
0
100
200
300
Rarfai Osbroepn]
Figure 81 Rev 485 with Radial Angle = -30°
Note the behavior at 300 km to the West o f the storm. The 10°, 0°, and -10° degree
radials show an extremely high speed, while the remaining radial plots show a very
85
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low speed. Both cases are rejected by the GOF test. The high speed can be due to
backscatter from rain which raises the signal received. The lower speeds are probably
due to attenuation from rain. The GOF test removes the extremes from the profiles,
showing that the GOF test can effectively identify outliers most likely caused by rain.
The contour plot for the field with the outliers removed is shown below. There is
little difference if any between
Figure 65, with oudiers, and Figure 82 without outliers.
430
300
200
100
1
-100
-200
-300
Saih
Figure 82 Speed contours for SARA-max
Rev 485 without outliers
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Chapter Six
Conclusion
This dissertation provides an extension to the NSCAT Wind Retrieval Algorithm that
provides improved measurements in high spatial gradient regions o f tropical cyclones.
In addition, SARA has developed a means for detecting outliers for wind retrievals
most likely caused by the effects of rain on the ocean backscatter.
After an introduction to the theory for wind retrievals and a functional description of
the SARA algorithm, it was shown that SARA retrieves tropical cyclone wind fields
when using simulated ideal measurements. Then, SARA-25 was shown to retrieve
wind vectors very close to the NSCAT algorithm through a wide range of speeds and
directions. SARA matches NSCAT so well that SARA-25 retrievals are essentially
reproductions of adjacent 50 km retrievals. Only when analyzed on a point by point
basis do the benefits of SARA retrievals become apparent.
SARA-25 wind vector retrievals provide the directions for the SARA-max wind speed
retrievals (at individual G0 measurement locations). These SARA-max wind speeds
were shown to provide an improved measurement of wind speed profiles near the
eyewall. The increased spatial sampling allowed more measurements of the peak
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winds than did the other retrievals. Further, the SARA-max retrievals provide the
most detailed speed contours on the structure of the TC.
The effects of rain on the retrieved winds were investigated using a goodness o f fit
test. This test is able to identify <JQmeasurement outliers that differ from their
neighbors (within about 10 km), and theoretical GMF sigma-O’s that are most likely
caused by heavy rain bands that surround the tropical cyclone eye. An examination
of “rejected” o0’s that fail the goodness o f fit test, demonstrated spatial correlation
that resemble the expected patterns o f rain (spiral bands). This suggests that the
scatterometer is able to make accurate measurements between these rain bands at the
individual CT„ locations.
It was shown that SARA can retrieve a simulated field with exactly the same speeds as
used in the simulation, when the measurements are noise free and the model function
is perfect. The model function is perfect in the simulation because the model
function was used to create the measurement values, so the SARA algorithm can
handle higher wind speed retrievals without error given a correct model function tor
TC winds, and relatively low noise measurements. Yet, using actual NSCAT <J0’s for
typhoon Violet, all o f the scatterometer inferred wind fields suffer from using a model
function (GMF) that does not properly handle high wind speeds. As a result the peak
wind speed retrievals are some 30 to 40 knots lower than measured or predicted by
the Joint Typhoon Warning Center. Nevertheless, SARA-max wind speeds are higher
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than NSCAT which is cause for optimism. One area for further research is to
develop a model function that provide realistic wind speeds for TC retrievals.
Another area of further research is using the outlier removal capability of SARA on all
types o f winds. Since rain affects retrievals regardless of the structure of the storm,
the SARA outlier procedure could be applied to global wind fields to screen out
measurements under other than TC conditions that are affected by rain.
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References
[1] R.K. Moore, and A.K. Fung, Radar determination o f winds at sea,
Proc. IEEE 67, pp 1504-1521 (1979)
[2] W. L. Jones, P. Black, V.E. Delmore, and C. T. Swift, “Airborne remote
sensing measurements o f hurricane alien,” Science, vol 24, no. 4518 pp. 274280, Oct. 1981.
[3] J. D. Black, R. Hawkins, C. Gentry, and W. L. Jones, “Remote measurements
of hurricane surface winds by seasat, ” Amen Geophys. Union, April 28, 1981
Baltimore, MD.
[4] WX Jones, V. J. Cardone, W. J. Pierson, L. P. Rice, A. Cox, and W. B.
Sylvester, NSCAT High Resolution Surface Winds Measurements in Typhoon
Violet, /. Geophys. Res. - Oceans, Feb. 1999.
[5] V. F. Dvorak, Tropical Cyclone Intensity Analysis and Forecasting from
Satellite Imagery, Mon. IVea. Rev. 103, 420-430, 1975.
[6] W. L. Jones, and J. Zee, Evaluation o f rain effects on NSCAT wind retrievals,
Oceans 96, Ft. Lauderdale, FL Sept. 23-26 1996.
[7] F. M. Naderi, F. K. Li, and D. G. Long, Spacebome radar measurements of
wind velocity over the ocean —an overview o f the NSCAT scatterometer
system, Proc. IEEE, 79, 6, 1991.
[8] W. L. Jones, F. J. Wentz, and L. C. Schroeder, Algorithm for inferring wind
stress from SeaSat -A, AEAA J Spacecraft and Rockets, Vol. 15, No. 6, 368-374,
Nov- Dec 1978.
[9] S. J. Shaffer, R. S. Dunbar, S. V. Hsiao and D. G. Long, “A Median-FilterBased Ambiguity Removal Algorithm for NSCAT,” IE EE Trans. On Geoscience
and Remote Sensing, vol. 29, no. 1 pp. 167-174, Jan. 1991.
[10]
W. J. Pierson, Probabilities and statistics for backscatter measurements
obtained by a scatterometer with application to new scatterometer design
data, NASA contractor’s report 4228, 123 p., 1989a
[11] W. J. Pierson, Probabilities and statistics for backscatter estimates obtained
by a scatterometer, J. Geephys. Res. 94, C7, 9743-9759, 1989b.
90
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[12] W. J. Pierson, Errata to above, in January 1990, J. Geophys. Res. 1990a.
[13] M.R. Spiegel, Probability and Statistics, New York: McGraw-Hill ch. 6, pp. 198.
[14] M. H. Frielich, D. G. Long, and R. M. Ruiz., N SC A T Wind RetrievalAlgorithm
[15] G. D. Gordon, and W. L. Morgan, Principles of Communications Satellites, New
York: John Wiley & Sons, ch. 3, pp. 67
[16] W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical
Recipes in FORTRAN The A rt of Scientific Computing, Cambridge: Cambridge
University Press, ch. 10, pp 396-398
[17] Jones, W. L., Rice L., Rudic N. P., and Uhlhom E. W., An improved algorithm
for NSCAT measurements of hurricanes, Oceans 96, Sept. 23-26,1996, Ft.
Lauderdale, FL
[18] W. L. Jones and L. P. Rice, The NASA scatterometer measurement of tropical
cyclone ocean surface winds, 4“ Intemat.. Corf. Rem. Sens. ForMarine and Coastal
Env. March 17-19, 1997, Orlando, FL
[19] W. L. Jones, L. P. Rice, J. Zee, V. J. Cardone, W. J. Pierson, and J. D.
Hawkins NSCAT Geophysical Algorithm for inferring hurricane ocean
surface winds, 22^ AM S Conference on Hurricanes and Tropical Meteorology, 19-23
May 1997, Fort Collins, CO
[20]
E. F. Thompson, V. J. Cardone, Practical modeling of hurricane surface
wind fields, Journal of Waterway, Port, Coastal and Ocean Engineering 122, 4, 195205, 1996.
[21] V. J. Cardone, W. L. Pierson, and E.G. Ward, Hindcasting the directional
spectra of hurricane generated waves, Journal of Petroleum Technology pp. 385394 April 1996.
[22] F. J. Wentz and D. Smith, A model function for ocean normalized radar
cross section at 14 GHz derived from NSCAT observations, J Geophys. Res. Oceans, Feb 1999.
[23] N. Ebuchi, Statistical distribution of wind speeds and directions observed by
NSCAT, N SC A T Calf Val Workshop Report, Jet Propulsion Lab, Jan 1997
[24] M. H. Freilich and R. S. Dunbar, The accuracy of the NSCAT1 vector winds:
Comparison with NDBC Buoys, J. Geophys. Res., Feb. 1999
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Appendix A
Introduction T o T ropical C yclone C haracteristics
Information from the 1998 Microsoft Encana Encyclopedia on hurricanes follows.
/Science Source/Photo
Researchers, Inc.
Figure 83 Hurricane Elena On September 2, 1985, Hurricane Elena was
photographed with a 70-millimeter lens from the space shuttle Discovery. Because the
hurricane is in the northern hemisphere, the air circles in a counterclockwise motion
toward the low pressure center, or eye.6
Hurricane, name applied to migratory tropical cyclones that originate over oceans in
certain regions near the equator, and particularly to those arising in the West Indian
region, including the Caribbean Sea and the Gulf o f Mexico. Hurricane-type cyclones
in the western Pacific are known as typhoons.
Most hurricanes originate within the doldrums, a narrow equatorial belt characterized
by intermittent calms, light variable breezes, and frequent squalls, and lying between
the northeast and southeast trade winds. As the doldrums of the Atlantic are situated
largely to the north o f the equator, hurricanes do not occur in the South Atlantic
Ocean. The Pacific doldrums extend north and south of the equator; thus hurricanes
occur in the South and North Pacific oceans.
Hurricanes consist o f high-velocity winds blowing circularly around a low-pressure
center, known as the eye o f the storm. The low-pressure center develops when the
warm, saturated air prevalent in the doldrums is underrun and forced upward by
6 NASA/Science Source/Photo Researchers. Inc.
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denser, cooler air. From the edge of the storm toward its center, the atmospheric
pressure drops sharply and the wind velocity rises. The winds attain maximum force
close to the point o f lowest pressure (about 724 torr, or about 28.5 in. of mercury).
The diameter of the area affected by winds of destructive force may exceed 240 km
(150 mi). Gale winds prevail over a larger area, averaging 480 km (300 mi) in diameter.
The strength of a hurricane is rated from 1 to 5. The mildest, Category 1, has winds
of at least 120 km /h (74 mph). The strongest (and rarest), Category 5, has winds that
exceed 250 km /h (155 mph). Within the eye of the storm, which averages 24 km (15
mi) in diameter, the winds stop and the clouds lift, but the seas remain very violent.
Hurricanes generally move in a path resembling the curve of a parabola. In the
northern hemisphere the storms usually travel first in a northwesterly direction and in
the higher latitudes turn toward the northeast. In the southern hemisphere the usual
path of the hurricane is initially to the southwest and subsequently to the southeast.
Hurricanes travel at varying rates. In the lower latitudes the rate ranges from 8 to 32
km/h (5 to 20 mph) and in the higher latitudes it may increase to as much as 80 km /h
(50 mph). Those areas in which the hurricane winds blow in the same direction as the
general movement o f the storm are subjected to the maximum destructive violence of
the hurricane.
Since 1943 U.S. military aircraft have been flying into hurricanes to measure wind
velocities and directions, the location and size of the eye, the pressures within the
storms, and their thermal structure. A coordinated system of tracking hurricanes was
developed in the mid-1950s, and periodic improvements have been made over the
years. Radar, sea-based recording devices, geosynchronous weather satellites (since
1966), and other devices now supply data to the National Hurricane Center in Florida,
which follows each storm virtually from the beginning. Improved systems of
prediction and communication have been able to help minimize loss of life in
hurricanes, but property damage is still heavy, especially in coastal regions. The
strongest hurricane to hit the western hemisphere in the 20th century, Gilbert,
devastated Jamaica and parts of Mexico in 1988 with winds that gusted up to 350
km/h (218 mph). Destructive hurricanes in recent U.S. history include Agnes (1972),
with $3 billion in damage and 134 deaths, Hugo (1989), with more than $4 billion in
damage and more than 50 deaths, and Andrew (1992), with an estimated $12 billion in
damage, more than 50 dead, and thousands left homeless.^
7"Hurricane," Microsoft® Encarta® 98 Encyclopedia. © 1993-1997
Microsoft Corporation. All rights reserved.
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Appendix B
P hysics for Scatterom eter M easurem ents
A scatterometer is fundamentally a special purpose radar sensor that measures the
absolute backscatter coefficient (normalized radar cross section, CT0) of the Earth’s
surface. The backscattered power from a surface is given by the radar equation as:
P -
A
where
Pt = transmit power
Pc = received power
G. = antenna gain at the cell
R = slant range (distance between the spacecraft and the cell)
A = integrated area of CFo cell
X = wavelength of the radar (Ku band, 13.995 GHz = ~2.3 cm)
a0 = radar backscatter coefficient
Making suitable approximations to the integral of the cross section over the area of
the cell, the radar equation can be inverted to yield the backscatter cross section CT0 as
a function of the transmitted and received radar powers and parameters.
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Ocean Backscatter
The remote sensing o f ocean surface wind vector is feasible because the radar
scattering properties o f the ocean respond to this geophysical parameter. For a
typical satellite scatterometer geometry, the antennas view the ocean’s surface at
incidence angles between about 20° and 65°. At this range of incidence angles, Bragg
resonant scattering from “small waves” on the ocean is the major contributor to the
backscattered power. Further, the amplitude of these waves depends on both the
surface wind speed and direction. “Small waves” are ocean waves with wavelengths,
(X^,), of a few centimeters that are rapidly formed in response to the surface wind
forcing. The restorative forces on these waves include surface tension, (where X^ <
1.74 cm), and gravity, (where X^. > 1.74 cm). These restoring forces classify the
waves as either capillary waves or gravity waves respectively. Bragg resonant
scattering evolves from an equivalent diffraction grating set up on the ocean surface
by capillar}' and short gravity waves.
Consider a simplified version ofwind-sea behavior where a series o f waves,
equally spaced by length X^, are formed from a wind at a single direction with a single
velocity, while ignoring any other ocean waves. If the wave crests are considered as
rods, the pattern formed is similar to a diffraction grating. Power received from this
grating, for a given incident power, increases when the reflections from each wave
crest or rod add coherently with all other reflections from the remaining rods. If 0 is
the incidence angle formed by the normal to the surface illuminated by a source, and
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the line o f sight traveled by the source radiation, then power reflection is maximized
for
K = (XJolttce/2)/sin(0)
The magnitude of the backscatter depends upon the amplitude of the Bragg scatterers
that grow monotonically with the surface wind speed. Further, these waves are
preferentially aligned with the wind direction that results in an anisotropy of the
reflection coefficient. These waves depend on the instantaneous wind speed and
wind direction at the surface; hence, they contain the information needed for
retrieving winds. Scatterometers thus provide an indirect measurement of wind
speed and direction by measuring the ocean absolute backscatter coefficient.
Scatterometer measurements near-nadir are avoided because the ocean scattering
coefficient in this region only responds weakly to wind speed and not direction.
Scatterometers need a significant azimuthal dependence for the remote sensor to
provide wind directions.
N A SA Scatterometer (NSCAT)
The NSCAT is a satellite scatterometer system that has been successfully launched in
August 1996 on the Japan Advanced Earth Observation Satellite (ADEOS). The onorbit configuration is illustrated in Fig. 1. The instrument measures the ocean
normalized radar cross section at multiple azimuths and polarizations. Each swath is
illuminated by four “fan beam” antennas (beams) at three azimuths. The middle
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azimuth has two antennas to measure dual polarized sigma-O’s and the other two
antennas are vertical polarized.
Figure 84 NSCAT antenna illumination
patterns on the ocean
A ntenna Beam-1
M easu rem en t S w ath
M easurem ent Sw ath
Doppler binning is used divide each antenna beam into 24 simultaneous received
power measurements. These are combined for the four azimuth looks to form a 25
km sigma-0 measurement cell. This cell division is shown below.
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Figure 85 NSCAT 25 km sigma-0 cell
geometry
Wind Vector Cells (WVC’s) are the regions that are averaged to retrieve wind vectors.
They are 50 km in size and are made up o f four sigma-0 cells. Filling in the four 25
km cells with corresponding integrated fields of view for each antenna beam is
illustrated in Figure 86.
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Figure 86 NSCAT 50 km sigma-0 cell
geometry
Wind Retrievals
NSCAT products for the scientific community include the backscatter data from the
measurements illustrated above, and wind fields where these measurements are
processed into wind fields. The wind retrieval process makes use of a Geophysical
Model Function, (GMF), which relates five inputs, (including wind speed and
direction), to a normalized radar cross section,
(g 0)
value.
The figure below uses the most recent GMF for NSCAT, SASS2, to generate wind speed versus dir
noise) degrade this picture when using the actual instrument. A statistical figure of
merit incorporating Go measurements and noise measurements is used to evaluate how
well the simultaneous solutions from 4 to 24 Go measurements agree. This figure of
merit function uses the maximum likelihood estimation technique, (MLE), for
comparing signals or information to each other and to a model, (see below). NSCAT
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wind retrievals thus converge to locate, in reality, what seems apparent in the figure
of ideal measurements below.
Figure 87 Wind Speed vs. Direction using
GMF
Wind Speed vs. direction from Four B eam s
1.20
tn
.=
15
’ Solution
100
150
200
250
300
350
Wind Direction [degrees]
Another crucial part of wind retrievals is the selection criteria used to converge to an optimal wind
unlimited combinations of speed and direction. NSCAT processing searches through
numerous directions and speeds, (using ancillary data such as incidence angle and
polarization for each measurement), where the agreement between all valid
measurements and the GMF are the “best.” Several possible solutions or ambiguities
are generated using all valid <S0 measurements in a WVC. Each solution has a
corresponding Maximum Likelihood Estimator, (MLE), value. An MLE value
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represents a probability that the corresponding ambiguity corresponds to the most
likely wind vector for a cell. The GMF and the MLE are further explained below.
GeophysicalModelFunction
The NSCAT wind retrievals utilize a geophysical model function (GMF) to provide
the relationship between the radar observable (sigma-0) and the surface •wind vector
(speed and direction). The GMF depends on measurement geometry. In all, the
GMF is a function of:
•
Wind Speed
•
Wind Direction
•
Cell Azimuth, (angle beam points relative to North)
•
Incidence Angle (angle between normal to cell surface and line of sight
between cell and satellite)
•
Beam Polarization - horizontal or vertical
Knowing four of the five inputs allows one to use root finding algorithms to
determine the remaining parameter. A plot o f the GMF for vertical polarization and
mid-range incidence angle is shown in Figure 88 Sample Fourier Series
Approximation to a GMF. To the first order, sigma-0 expressed in dB can be
represented as a three-term Fourier series:
<y° = A0 + A l c o s z + A2 c o s 2 x .
where:
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Ao is proportional to wind speed
A1 is approximately independent o f wind speed and is responsible for the
upwind/down wind asymmetry
A2 is approximately independent of wind speed and is responsible for the wind
direction anisotropy;
(A2 > A 1)
c is the antenna beam azimuth viewing direction relative to upwind; i.e., c = 0° is
upwind and
c = 90° is cross wind.
Figure 88 Sample Fourier Series
Approximation to a GMF
3 Term Fourier Series Approximation to Model Function
ID
-10
-11
ISO
200
250
100
Relative Azimuth Chi [deg.]
300
350
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Maximum Likelihood Estimator
The basis of the geophysical algorithm is the maximum-iikelihood estimation (MLE)
principle as applied to statistical parameter estimation. This method maximizes the
joint probability density of a set o f residuals (sigma-0 measurements minus GMF).
This is equivalent to finding the most likely set of the model parameters (wind speed
and direction) which produced the observed sigma-O’s. The gaussian probability
density P, for a given sigma-0 measurement T; compared to a corresponding GMF
value Fs is given by:
P, =(2rw(S,))~' exp{-(s, - F , f !2V ar{s$
where the variance (Var(Si)) o f the sigma-0 measurement is estimated from NSCAT
instrument parameters and the backscattered signal to noise ratio. The likelihood
function is the joint probability density, P, defined as the product of the Pi over the n
measurements in the wind vector cell (nominally 16 sigma-O’s for the 50 km WVQ.
Because of the harmonic nature o f the GMF, there are multiple wind solutions
produced. The number of solutions ranges from two to four depending upon the %
at which the measurements were made. These multiple solutions, called aliases or
ambiguities, are nearly equal in wind speed but vary in wind direction over the full
range o f 360°. For the case of two aliases, they generally differ by 180°. The
probability that a given solution is the correct wind can be estimated by the relative
value o f its likelihood function; therefore, the retrieved wind vectors are ranked
-according to this criterion.
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The last step in the geophysical algorithm is refinement in the retrieved wind
direction known as wind-direction alias-removal. The most common approach uses
the wind solution rankings and a median filter technique to select a single wind
direction. The accuracy of this procedure is estimated to be better than 90%.
Hurricane Wind Fields
Although NSCAT will produce some 190,000 wind measurements per day [7] there
remains additional geophysical algorithm development to be done. The NSCAT
algorithm has been designed to produce global wind vector measurements at spatial
resolution sufficient to sample the majority of synoptic weather patterns. Further,
because of its applications to numerical weather prediction, it is designed to be a
“pure scatterometer” product without using other independent information (e.g., no
surface truth). However, there are instances that would benefit from a geophysical
algorithm that has been tailored for the specific applications. O f particular interest is
the wind field associated with cyclonic storms (e.g., hurricanes and typhoons). For
these applications, conventional NSCAT processing is deficient. These deficiencies
are described below.
Below are three illustrations of the high wind gradient region including the eye of the
storm. Figure 89 NSCAT 50 km resolution wind field shows how NSCAT would
display the storm using conventional 50 km retrievals. Figure 90 High resolution
wind field, is a retrieval using a preliminary version o f an adaptive spatial resolution
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algorithm, (SARA for Spatially-Adaptive Retrieval Algorithm), that uses single 25 km
sigma-0 cells (to form new 25 km WVC’s) and individual <T0 cell data. Figure 91
Maximum resolution wind field —shows a wind retrieval corresponding to a wind
vector for every CT0 measurement taken in the region.
Figure 89 NSCAT 50 km resolution wind
field
NSCAT 50 km Cell Retrieval of Humcane Wind Field
27.8
27.6
272
26.8
26.6
262
-71
-70.5
-70
Longitude
-69.5
-69
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Figure 90 High resolution wind field
High Resolution Retrieval of Hurricane Wind Reid
28
278
276
27.4
272
*ao>
•I<5 27
- 1 26 8
26.6
>
v
^
/
/
26.4
26.2
26
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Longitude
Figure 91 Maximum resolution wind field
Finest Resolution Possible using Interpolations at Every Sigma-0 Cell Location
28
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106
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Retrieval Problems
Satellite scatterometer wind retrievals in tropical cyclones suffer from three major
shortcomings. First, the geophysical relationship (model function) between the
scatterometer measured normalized radar cross section and surface wind vector is not
well defined at speeds greater than 20 m/ s. The resulting wind retrievals generally
underestimate high wind speeds. Next, the relatively coarse spatial resolution of
scatterometer measurements produces wind field distortions, especially in high wind
gradient regions. Low spatial resolution causes inaccurate wind direction solutions,
and a smoothed field where winds are violent. Finally, contamination by heavy rain
alters the ocean backscatter and thereby produces errors in the resulting wind
retrievals
For clouds, the effect of liquid water droplets is negligible; however, the effects of
precipitation are not. Light to medium rain rates (0.5 —5 mm/hr) are absorptive and
have significant attenuation (up to about a dB). Heavy rains (>10 mm/hr) exhibit
both absorption and scattering for total changes of several dB’s. Further, rain
impacting upon the ocean surface alters the centimeter scale roughness elements that
are the Bragg scatterers for the Ku-band radar. Therefore, rain can significantly
modify the ocean backscatter characteristics that, in turn, will affect the scatterometer
wind retrievals.
107
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Appendix C
D istribution o f Sam ples u sed in Chapter Four
This appendix details the number and range (in wind speed, incidence angle, or wind
direction) of measurements used throughout the statistics in chapter four.
All SARA-25 Samples
Table 12 Sample size vs. Incidence Angle
Incidence angle (deg.)
17.5
22.5
27.5
32.5
37.5
42.5
47.5
52.5
57.5
Sample Size N'
3846
8193
10316
10516
12375
13575
14582
17690
6906
Table 13 Sample size vs. Direction with
respect to S/C heading
Direction with respect to
S/C heading
10
30
50
70
90
no
130
150
170
190
210
230
250
270
290
310
330
350
N
3258
2759
5033
4869
7223
7505
7926
5010
2857
2534
3389
3135
4100
5217
8004
10373
9360
5450
108
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Table 14 Sample Size vs. Mean Speed
Mean Speed
3.6413
7.9068
14.3571
24.2005
N
4119
19794
52156
11614
Violet Retrievals
Table 15 Sample size vs. Incidence Angle
Incidence Angle
17.5
22.5
27.5
3Z5
37.5
42.5
47.5
525
57.5
N
241
475
554
604
665
706
751
858
340
Table 16 Sample size vs. Wind Direction wrt
S/C Direction
S/C D ir
10
30
50
70
90
110
130
150
170
190
210
230
250
270
290
310
330
350
N
292
266
214
237
601
335
245
316
705
520
270
172
143
197
224
81
176
200
109
R e p r o d u c e d with p e r m i s s io n o f t h e co p y rig h t o w n e r. F u r th e r re p r o d u c tio n proh ibited w ithout p e r m is s io n .
Table 17 Sample size vs. mean speed
M
184
302
1231
3477
Mean Speed
3.3708
7.5265
16.4136
28.1795
To ensure adequate sampling for a wide range o f speeds and directions, the data was
binned according to wind speed, incidence angle, and wind direction with respect to
S/C direction. The binning is tabulated below where the rows correspond to an
incidence angle range and the columns correspond to a wind direction range. The
model function folds wind directions so that they lie within 0-180 degrees. The bins
are arranged to reflect this. The purpose o f these tables is to show that the sample
used to compare SARA to NSCAT is large and diverse, in addition to being random.
All speed and direction ranges have been adequately sampled.
Speed range 0-5 knots:
15-25
25-35
35-45
45-55
55-65
0-40;
180220
40-80;
220260
307
338
297
496
75
169
330
323
401
101
80120;
260300
31
88
148
272
70
120160;
300340
353
344
492
732
188
160180;
340360
74
155
210
211
43
110
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Speed range 5-10 knots:
15-25
25-35
35-45
45-55
55-65
0-40;
180220
40-80;
220260
1151
1052
815
944
274
287
1111
1489
2130
663
0-40;
180220
40-80;
220260
1544
1757
1982
2507
609
431
1565
2446
3217
716
0-40;
180220
40-80;
220260
707
1011
1225
1889
392
359
1260
2197
2771
463
80120;
260300
487
1291
1407
1840
449
120160;
300340
739
1226
1705
2047
360
160180;
340360
555
383
561
713
105
80120;
260300
919
1883
2097
2815
551
120160;
300340
833
1363
1677
2188
496
160180;
340360
532
611
525
518
112
80120;
260300
642
1152
1658
1689
330
120160;
300340
417
512
825
981
237
160180;
340360
157
255
242
555
115
Speed range 10-15 knots:
15-25
25-35
3d~4d
45-55
55-65
Speed range 15-20 knots:
15-25
25-35
35-45
45-55
55-65
R e p r o d u c e d with p e r m i s s io n of t h e co p y rig h t o w n e r. F u r th e r r e p r o d u c tio n prohibited w ith o u t p e r m is s io n .
Speed range 20-25 knots:
15-25
25-35
35-45
45-55
55-65
0-40;
180220
40-80;
220260
113
269
388
116
16
138
453
808
1121
180
0-40;
180220
40-80;
220260
56
12
5
14
7
50
212
381
286
54
80120;
260300
309
723
740
709
170
120160;
300340
156
299
376
574
138
160180;
340360
161
257
224
135
13
80120;
260300
137
276
134
123
34
120160;
300340
279
599
703
508
55
160180;
340360
7
180
84
95
14
Speed range 25-100 knots:
15-25
25-35
35-45
45-55
55-65
112
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IMAGE EVALUATION
TEST TARGET (Q A -3 )
1.0
|36
1
M
2.0
l.l
1.8
1.25
1.4
1.6
150mm
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