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Theory and measurement of oceanic wind vector using a dual-frequency microwave airborne radiometer

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THEORY AND MEASUREMENT OF OCEANIC WIND VECTOR USING
A DUAL-FREQUENCY MICROWAVE AIRBORNE RADIOMETER
by
Mark Duane Jacobson
B.S., Electrical Engineering, Montana State University, 1980
M.S., Electrical Engineering, University of Colorado, 1985
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirement for the degree of
Doctor o f Philosophy
Department of Electrical and Computer Engineering
1996
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UMI Number: 9628563
Copyright 1996 by
Jacobson, Mark Duane
All rights reserved.
UMI Microform 9628563
Copyright 1996, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized
copying under Title 17, United States Code.
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Ann Arbor, MI 48103
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This thesis for the Doctor o f Philosophy degree by
Mark Duane Jacobson
has been approved for the
Department of Electrical and Computer Engineering
by
William J. Emery
Edgeworth R. Westwater
Date A O C .
CV
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ABSTRACT
The near-surface wind speed and direction create a rough ocean surface
consisting of a variety of waves and foam. Consequently, the microwave
emissivity o f the ocean surface is not only a function of the sea skin temperature
and salinity but also of the surface roughness and foam distribution. A sensitive
microwave radiometer can measure the surface emissivity (brightness temperature)
variations and the data can be used to infer the near-surface wind speed and
direction. This paper examines the inferred wind vector measurements from data
taken by an airborne dual-frequency microwave radiometer using real ocean and
atmospheric measurements. Furthermore, the inferred wind vector is computed
using both ocean surface and atmospheric models specific to the parameters o f this
radiometer. The experimental and theoretical results are compared.
An expression for the total brightness temperature observed by an airborne
radiometer viewing the ocean is derived. The effects of the cosmic background
radiation, the atmosphere, the rough ocean surface, and the radiometer’s antenna
power patterns are included. Atmospheric emission is calculated by a unique
radiative transfer equation (RTE) algorithm. The rough ocean surface is modeled
as a two-scale surface. Unlike many two-scale formulations, this one allows for
the small-scale roughness to be similar to the incident electromagnetic wavelength
which is necessary to model the capillary-ultragravity wave region more
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realistically. In addition, a realistic surface slope profile is incorporated into the
large-scale features. New developments for the complex dielectric properties of
sea water at microwave frequencies and the sea skin temperature measurements are
incorporated into this model.
A suite o f atmospheric and oceanographic measurements were taken during
a 1993 remote sensing experiment o f the ocean surface. The in situ wind vector
measurements are compared with the experimental and theoretical brightness
temperature results. This comparison shows that this microwave radiometer can
measure the wind vector for certain atmospheric and oceanic conditions.
Furthermore, both theory and measurements produce an upwind/downwind
asymmetry in the brightness temperatures results. This feature has recently been
measured by passive microwave radiometers. The comparison may provide some
insight into the small-scale features.
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DEDICATION
To my Father and Mother, whose support, encouragement, and prayers made this
work possible
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ACKNOWLEDGMENTS
I would like to thank my thesis advisor, Professor William "Bill" Emery o f
the Colorado Center for Astrodynamics Research (CCAR) at the University of
Colorado at Boulder, for his consistent supervision, encouragement, and
resourceful suggestions. I would also like to thank my thesis committee member,
Dr. Ed Westwater, o f the Ocean Remote Sensing Division o f the Cooperative
Institute for Research in Environmental Science (CIRES) at NOAA’s
Environmental Technology Laboratory (ETL), for his support throughout this
project, especially in his help in implementing the RTE software and his in-depth
suggestions and comments on the thesis. Furthermore, I also thank the rest o f my
thesis committee, Professors Ernie Smith, Carl Johnk, and Zoya Popovic, all o f the
Electrical and Computer Engineering Department at the University of Colorado at
Boulder, for their valuable comments and suggestions.
I especially thank Jack Snider o f CIRES at ETL for his for invaluable
guidance and help throughout this work. The airborne microwave and infrared
radiometers were installed and made operational by Duane Hazen, Bill Madsen,
and Anthony Francavilla, all of NOAA at ETL. They deserve special recognition
for their contributions. I also thank Dr. Yong Han o f CIRES at ETL, Janelle
Reynolds, Michael Falls, and Rich Beeler, all of NOAA at ETL, and Donna
McKeown and Rebecca Beck, both o f STC at ETL, for their help and suggestions
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on the computer implementation o f the atmosphere and rough ocean surface
model. I am very thankful to Dr. David Hogg, now retired from NOAA’s ETL, for
designing the antenna reflector system and housing. His leadership enabled ETL
to produce a quality antenna system for this airborne radiometer. Paul G. Schmidt
of NOAA at ETL did the initial construction o f the antenna reflector system and
housing. The pressure compensating feature on the corrugated feed horn was
designed by Dr. A1 Bedard of NOAA at ETL. Randy Nishiyama of CIRES at ETL
provided assistance in the corrugated feed hom measurements. Len Fedor of
CIRES at ETL coordinated the aircraft operations out o f San Diego, California
during the experiment. I thank Dr. Chris Fairall o f NOAA at ETL for providing
the in situ data from the experiment and the Fortran program for calculating the sea
skin temperature. I also thank Dr. Rich Lataitis o f NOAA at ETL for his help and
ideas on the thesis outline and format. Several enlightening discussions and useful
suggestions regarding this work occurred with Dr. Vladimir Irisov, Dr. Yuri
Trokhimovski, Dr. Alex Voronovich, Dr. Mike Jones, Professor Konstantin
Naugolnvkh, Professor Lev Ostrovsky, all o f CIRES at ETL, and Joe Shaw of
NOAA at ETL. Dr. Jim Chumside, Division Chief of the Ocean Remote Sensing
Division o f NOAA at ETL, provided assistance and pertinent ideas to this work.
Bob Zamora of NOAA at ETL provided the radiosonde data for the atmospheric
portion o f the emission model. I also thank Dr. Steve Clifford, Director of NOAA
at ETL, for his support throughout this research.
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I am grateful for Mike Nunnelee’s, o f NOAA’s National Weather Service,
assistance in the aircraft operations during the experiment and in calibrating the
infrared radiometers.
I gratefully acknowledge Brad Patten o f NOAA’s AOC for his dedicated
work on the design, construction, and operation o f the different fairings. I thank
Tom Gates and Lieutenant Randy TeBeest, both o f NOAA’s AOC for their
excellent aircraft navigation during the experiment.
I would like to thank the United States Customs staff at North Island Naval
Base in San Diego, California, for their help in providing invaluable support for
the aircraft and personnel.
I thank NIST’s personnel Mike Francis, Doug Kremer (now with Orbit
Technology, Inc.), Nino Canales, and Teresa Rusyn for their assistance in
processing the overall planar near-field measurements.
Dr. Hans Liebe of the National Telecommunications and Information
Administration (NTIA) provided very useful guidance on the calculation o f the
complex permittivity o f sea water.
I also thank Sharon Kirby-Cole and Merri Richeson, both of NOAA at
ETL, and Pam Wheeler of the Electrical and Computer Engineering Department at
the University o f Colorado at Boulder for their help on providing the proper paper
work and forms necessary for this thesis.
I also thank Dick Harriss, Dave Wirth, and Gerald D’Spain, all of the
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Scripps Institution of Oceanography at the University of California in San Diego,
California, for obtaining the sea water’s salinity at the SCOPE location and the
FLIP log book.
Finally, I would like to thank A1 Romero o f NOAA’s MASC for the
excellent quality o f the drafted and optically scanned figures.
The Department of Defense partially funded this project under NIPR
N93051, ajointNOAA/DoD-Advanced Sensor Applications Program.
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TABLE OF CONTENTS
1.
INTRODUCTION............................................................................................ 1
2.
THEORETICAL BRIGHTNESS TEMPERATURE
FORMULATION.......................................................................................... 10
3.
2.1
Background........................................................................................ 10
2.2
Focus o f Present W ork.......................................................................14
2.3
Theory.................................................................................................15
2.4
Algorithm Implementation................................................................ 22
2.5
Summary............................................................................................ 28
THEORETICAL OCEAN SURFACE EMISSION
FORMULATION.......................................................................................... 30
3.1
Background........................................................................................ 31
3.2
Focus o f Present W ork.......................................................................34
3.3
Theory................................................................................................ 35
3.3.1
T wo-scale m odel................................................................. 36
3.3.2
Steepest descent evaluation...............................................46
3.3.3
Large-scale tilt translation................................................... 56
3.3.4
Polarization transformation................................................. 64
3.3.5
Extended boundary condition.............................................. 68
3.3.6
Sinusoidal corrugated surface............................................. 77
3.3.7
Complex permittivity o f sea w ater......................................78
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3.4
4.
Summary............................................................................................ 79
SCOPE MEASUREMENTS.........................................................................82
4.1
Background........................................................................................ 82
4.2
Focus o f Present W ork.......................................................................83
4.3
Instrumentation..................................................................................88
4.3.1
Microwave radiometer......................................................... 88
4.3.1.1 Antenna configuration..............................................89
4.3.1.2 Antenna pattern measurements and
implementation........................................................ 100
4.3.1.3 Electronics package................................................ 106
4.3.1.4 Calibration...............................................................110
4.3.1.5 Data smoothing and filtering................................. 115
4.3.1.6 Incidence angle correction..................................... 117
4.3.1.7 Corrected brightness temperature
measurements...........................................................120
4.3.2
Airborne infrared radiometers............................................ 120
4.3.3
Radiosondes........................................................................ 123
4.3.4
Sonic anemometer onTitan and F L IP ................................ 125
4.3.5
Other instruments on Titan and F L IP ................................ 126
4.4
Wind Speed Algorithm.....................................................................128
4.5
Skin Temperature of Sea W ater....................................................... 130
4.6
Summary............................................................................................131
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5.
6.
7.
A COMPARISON OF EXPERIMENTAL AND
THEORETICAL RESULTS.......................................:.............................. 134
5.1
Background......................................................................................135
5.2
Focus o f Present W ork.....................................................................135
5.3
Brightness Temperature Comparison
on a High Wind D ay.......................................................................139
5.4
Summary.......................................................................................... 159
CONCLUSIONS...........................................................................................162
6.1
Specific Contributions......................................................................165
6.2
Suggestions for Future W ork.......................................................... 167
REFERENCES..............................................................................................169
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TABLES
Table 2.1. Planck’s law constants...........................................................................11
Table 4.1. Aircraft way points parameters at Titan and F L IP ...............................86
Table 4.2. Aircraft way points parameters at Titan and FLIP
during clear sky conditions.....................................................................87
Table 4.3. Half-power beamwidths for the corrugated pressure-compensating
feed h orn.................................................................................................. 93
Table 4.4. Half-power beamwidths for the overall antenna................................ 102
Table 4.5. Radiometer characteristics during SCOPE........................................ 107
Table 4.6. Various instruments on Titan and F L IP ............................................. 127
Table 5.1. Calculated upward and downward atmospheric brightness
temperatures, and upward transmissivity............................................ 138
Table 5.2. Corrugation heights as a function of wavelength............................... 142
Table 5.3. Empirical and true near-surface wind speeds at a
Titan location........................................................................................ 156
Table 5.4. Brightness temperature variations at a Titan location........................159
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FIGURES
Figure 2.1. Total brightness temperature incident upon a
downward-viewing antenna.................................................................13
Figure 2.2. An airborne radiometer observing the ocean surface......................... 16
Figure 2.3. Spectra of the normalized radiometric sensitivity for
various geophysical parameters..........................
21
Figure 2.4. Levels and layers for discretizing the downward
brightness temperature integral............................................................. 25
Figure 3.1. The tilt angle connecting the two sets of coordinates........................ 40
Figure 3.2. A plot o f the P(ZJ slope and normal distributions............................ 44
Figure 3.3. Constant-phase (steepest) contours o f exp(-x tan20„)
in the complex plane............................................................................. 52
Figure 3.4. An electromagnetic wave incident upon a tilted sinusoidal surface.. 58
Figure 3.5. Three-dimensional geometry o f Fig. 3 .4 ............................................. 59
Figure 3.6. An electromagnetic wave vector in two coordinates sets.................. 61
Figure 3.7. The aircraft pitch angle relative to the radiometer’s
polarization vectors............................................................................... 66
Figure 3.8. Electric field strength at each frequency for a given pitch angle
67
Figure 3.9. The complex permittivity of sea water versus temperature at
23.87 and 31.65 G H z......................................................................... 80
Figure 4.1. Geographical location o f SCOPE........................................................ 85
Figure 4.2. Side view o f offset parabolic reflector's geometry with the
feed h o m ..................................................................................................91
Figure 4.3. Pressure-compensating corrugated feed h o m ..................................... 92
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Figure 4.4. The measured amplitude radiation patterns of a corrugated
feed hom at 23.87 and 31.65 G H z.......................................................94
Figure 4.5. The antenna, reflector system, and housing for the
airborne microwave radiometer........................................................... 95
Figure 4.6. Composite-material fairing....................................................................98
Figure 4.7. The fairing on the NOAA King Air C-90 aircraft...............................99
Figure 4.8. Basic components of a planar near-field measurement system
101
Figure 4.9. Principal far-field patterns at 23.87 and 31.65 GHz
o f overall antenna................................................................................. 103
Figure 4.10. Three-dimensional far-field patterns of Fig. 4 .9 .............................. 105
Figure 4.11. Electrical layout of the ETL microwave radiometer.....................108
Figure 4.12. Tipping curve structure.................................................................... 112
Figure 4.13. Triangular weighting function with a half width of 15 s .................116
Figure 4.14. Brightness temperature measurements versus incidence angle
119
Figure 4.15. Brightness temperature measurements versus azimuth angle......... 121
Figure 4.16. Partial printout o fa radiosonde launch from San Nicolas Island.. 124
Figure 4.17. Sonic anemometer wind speed measurements versus the
23.87 and 31.65 GHz brightness temperature variations..................129
J
Figure 5.1. NOAA’s aircraft flight track around T itan ........................................ 137
Figure 5.2. Measured and computed (specural and antenna pattern directions)
brightness temperatures at 23.87 and 31.65 GHz versus azimuth
angle...................................................................................................... 141
Figure 5.3. Measured and computed brightness temperatures at
23.87 and 31.65 GHz versus azimuth angle....................................... 144
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Figure 5.4. Same as Fig. 5.3except the sinusoidal wavelength is 0.5 c m .......... 145
Figure 5.5. Same as Fig. 5.3except the sinusoidal wavelength is 0.75 c m .........146
Figure 5.6. Same as Fig. 5.3
except the sinusoidal wavelength is 1.0 c m .... 147
Figure 5.7. Same as Fig. 5.3
except the sinusoidal wavelength is 1.25 cm
Figure 5.8. Same as Fig. 5.3
except the sinusoidal wavelength is 15 c m .... 149
Figure 5.9. Same as Fig. 5.3
except the sinusoidal wavelength is 2.0 c m .... 150
Figure 5.10. Same as Fig. 5.3 except the sinusoidal wavelength is 5.0 cm
148
151
Figure 5.11. Same as Fig. 5.3 except the sinusoidal wavelength and
height are 0.5 cm and 0.5 mm, respectively.................................... 154
Figure 5.12. Same as Fig. 5.3 except only the brightness temperature
measurements are shown....................................................................155
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1. INTRODUCTION
The near ocean surface wind vector is an important measurement for local
and global climatic and oceanographic studies. A direct result o f this wind is that
it creates a rough ocean surface consisting of a variety o f waves and foam.
Recently, passive ocean-viewing microwave radiometers are producing promising
results for measuring the near-surface wind vector by measuring the thermal
emission from the combined rough surface and atmosphere. In particular, the
microwave emissivity o f the ocean surface is a function o f surface roughness, seaskin temperature, foam, and salinity. On the other hand, the microwave emissivity
o f a non-precipitating atmosphere is a function of atmospheric temperature,
integrated atmospheric water vapor, integrated liquid water, cosmic background
radiation, and discrete sources such as the moon or sun. When the atmosphere is
unchanging and unpolarized at microwave frequencies, then the primary
microwave emissivity (brightness temperature) variations are caused solely by the
rough ocean surface. These brightness temperature variations o f the rough ocean
surface provide the necessary information for determining the near ocean surface
wind speed and direction.
Microwave radiometers have been measuring ocean wind speeds for many
years [Hollinger, 1971a, 1971b; Blume et al., 1977; Webster et al., 1976; Wilheit
and Chang, 1980; Hofer and Njoku, 1981; Bespalova et al., 1982; Ginsberg et al.,
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1982; Wentz et al., 1982; Lipes, 1982; Miller et al., 1982; Cardone et al., 1983;
Wilheit et al., 1984; Wentz et al., 1986; Schluessel and Luthardt, 1991; Wentz
1992] based on the ocean surface brightness temperature variations. In contrast,
the ocean wind direction measurements have only recently been obtained by
microwave radiometers [Etkin et al., 1991; Irisov et al., 1991; Wentz, 1992; Dzura
et al., 1992; Yueh et al., 1995; Trokhimovski and Irisov, 1995]. These recent wind
direction measurements showed that ocean brightness temperature variations with
respect to azimuth angle (wind direction) were a few kelvin. All these radiometers
measured the azimuthal dependence o f vertically- and horizontally-polarized (Tv
and Th) ocean brightness temperatures. However, Dzura etal. [1992] and Yueh et
al. [1995] showed that brightness temperature measurements at other polarization
states are also sensitive to near surface ocean wind direction. Now the full
polarization states are characterized by four Stokes parameters I, Q, U, and V,
which are related to the horizontal and vertical polarization components of the
radiated electric fields [Yueh et al., 1995] as
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Tk +
Q
L ~ h
(EhE i ) + ( E E ; )
CE X > - < v * >
—tC
-
u
TP ~ T m
V
r, - Tr
2 Re (EvE ’)
21m ( £ X )
where Tr is the vertically-polarized brightness temperature, Th is the horizontally-
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polarized brightness temperature, Tp is the +45°-polarized brightness temperature,
Tmis the -45°-polarized brightness temperature, T, is the left-hand circularlypolarized brightness temperature, Tr is the right-hand circularly-polarized
brightness temperature, Ev is the vertically-polarized electric field, E ’ is the
vertically-polarized complex-conjugate electric field, Eh is the horizontallypolarized electric field, Eh' is the horizontally-polarized complex-conjugate
electric field in, C = k/X2 with k denoting Boltzmann’s constant (see Table 2.1) and
X the wavelength in m, and () is the symbol for ensemble average. The above
brightness temperatures and electric fields are given in K and V/m, respectively.
Yueh et al. [1995] found that Q and U data were less sensitive to clouds,
breaking waves, and whitecaps, than Tv and Th data. Since these are strong thermal
radiation sources, 0 and U are potentially better indicators for wind direction
measurements. Nevertheless, this paper focuses on a nonpolarimetric aircraftbased dual-frequency dual-polarized microwave radiometer that was developed at
the Environmental Technology Laboratory (ETL) of the National Oceanic and
Atmospheric Administration (NOAA) [Fedor et al., 1988; Jacobson et al., 1994].
The lower frequency at 23.87 GHz is horizontally-polarized with respect to the
aircraft’s flight direction and the 31.65 GHz frequency is vertically-polarized to
that direction. This radiometer was one of several instruments deployed in ETL’s
first Advanced Sensor Applications Program (ASAP) experiment. This
experiment was named the San Clemente Ocean Probing Experiment (SCOPE)
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[Fedor and Irisov, 1994; Kropfli and Clifford, 1994]. The main puipose of the
airborne microwave radiometer was to determine if it could measure azimuthaldependent brightness temperature variations from a rough ocean surface, and thus
infer the near-surface wind vector.
Recent theoretical studies have suggested remote sensing of geophysical
media by passive polarimetry [Tsang, 1991; Veysoglu et al., 1991; Nghiem et al.,
1991; Johnson et al., 1993; Yueh et al., 1993; Johnson et al., 1994; Yueh et al.,
1994a; Yueh et al., 1994b]. For instance, the theory byYueh et al. [1994b]
calculates the Stokes parameters 0 and U using a two-scale sea surface model with
the small-scale surface scattering modeled by Bragg scattering. These theoretical
results are in reasonable agreement with aircraft radiometer measurements over the
open ocean for nadir viewing at a frequency of 14 GHz [Dzura et al., 1992]. Their
measured and calculated azimuth modulation signature comparison is one o f the
few found in the open literature. To gain a better understanding on the potential o f
the NOAA dual-frequency radiometer for near-surface wind vector determination,
the SCOPE radiometer measurements are compared with a new combined
atmospheric and two-scale ocean surface model. This model calculates the total
brightness temperature for a downward-viewing geometry. A unique RTE method
developed at ETL [Schroeder and Westwater, 1991] models the atmospheric
portion o f the received brightness temperature, whereas the two-scale model
simulates the surface portion of the brightness temperature.
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Section 2 contains a development of the apparent brightness (brightness
temperature) observed by an airborne radiometer viewing the ocean at some angle
relative to the nadir direction. To accomplish this, this section begins by
introducing some fundamental definitions of brightness, brightness temperature,
emissivity, apparent brightness (temperature), and antenna brightness
(temperature). The relationships between these quantities are shown. The two
primary radiation sources received at the downward-viewing radiometer are the
atmosphere and the rough ocean surface. The downward propagating atmospheric
source is formulated by the ETL RTE method. Similarly, the upward propagating
atmospheric source is calculated by modifying the downward propagating RTE
algorithm.
A derivation of the brightness temperature (emission) from a two-scale
ocean surface model is presented in section 3. This rough surface produces
polarization-dependent brightness temperature variations in azimuth angle. The
two-scale surface method models the ocean surface as two independent structures
with the small-scale features riding on top of the large-scale features, where the
small- and large-scale features are referenced to the incident electromagnetic
wavelength. For purposes of this research, the small-scale surface is restricted to
be in the capillary-ultragravity region, i.e., wavelengths up to a few tens of
centimeters [Kinsman, 1984], and is modeled as a long crested wave, i.e., a
sinusoidal corrugated surface. Although a long crested wave is very simplistic
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compared with real sea surfaces, valuable physical insights are gained into the
mechanisms responsible for the azimuthal-dependent brightness temperature
variations. On the other hand, the large-scale surface (wavelengths on the order of
meters) is determined by the Cox and Munk [1954a,b] slick-surface data.
The two-scale surface emission model is applied to the NOAA radiometer
parameters during SCOPE. With this application, the main emission occurs when
the small-scale roughness is averaged over the distribution o f the surface normals
of the large-scale features [Wu and Fung, 1972]. The averaging process is
described by an integral involving the bistatic scattering coefficient of the smallscale roughness, the Cox and Munk [1954a,b] slick-surface slope distribution for
the large-scale roughness, and the large-scale surface slopes. To gain some
physical insight into this integral, as well as for simplification purposes, an
asymptotic approximation o f the integral is done by the method of steepest
descent. The main result is that the small-scale features are tilted by the large-scale
roughness at angles o f ± tan'1(m), where m is the rms slope from the Cox and
Munk [1954a,b] slick-surface measurements.
The small-scale features are chosen to have a sinusoidal corrugated profile.
In contrast, a one-dimensional Gram-Charlier slick-surface slope profile [Cox and
Munk, 1954a,b] is used for the large-scale roughness. The extended boundary
condition (EBC) method [Chuang and Kong, 1982; Johnson et al., 1993] is used to
calculate the brightness temperature from a tilted periodic surface for an arbitrarily
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linearly-polarized electric field. An attractive feature o f the EBC method is that it
allows for the small-scale features to be similar to the incident electromagnetic
wavelength. This feature is necessary when describing the capillary-ultragravity
wave region. Although this is a simple rough ocean surface model, it does provide
for two important ocean surface features: first, it includes a realistic surface slope
profile for the large-scale features; and second, it allows for large slopes in the
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small-scale roughness. In addition, the Liebe et al. [1991] pure water model with
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an additional standard salt term is used to calculate the complex permittivity of sea
water in place o f the Klein and Swift [1977] model. This model does not include
foam coverage because the wind speeds encountered in this research are less than
12 m/s.
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The location, aircraft flight strategy, and instruments used in SCOPE for
j
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measuring and calculating the downward-viewing radiometric brightness
temperatures are discussed in section 4. The ocean region between San Clemente
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and Santa Catalina Islands provides realistic ocean conditions with good logistical
support for SCOPE. In this region, the NOAA microwave radiometers flew
several 360° banked turns at a roll angle o f about 32° to measure the azimuthaldependent brightness temperature variations. In addition, two ocean vessels, the
moored Scripps research vessel the FLoating Instrument Platform (FLIP) and the
NOAA R/V Titan ship, recorded both meteorological and oceanographic data to
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provide ocean-surface truth data.
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In section 4, the NOAA airborne dual-frequency radiometer is also
discussed in detail. Careful radiometric system calibrations, data smoothing, data
filtering, and incidence angle corrections are performed to produce accurate and
sensitive brightness temperature data for these azimuthal flights. Furthermore, the
techniques for measuring the radiometer’s three-dimensional antenna patterns are
addressed. The other instruments, located on the NOAA aircraft and the two ocean
vessels, provided the necessary measurement inputs to model accurately the
received brightness temperatures at the airborne radiometers. Several results are
obtained by comparing this suite of instruments with the airborne radiometer data.
For example, an empirical wind speed algorithm is obtained by comparing the
horizontally-polarized 23.87 GHz brightness temperature variations with the
measured wind speed from the sonic anemometers located on FLIP and Titan.
Also, an airborne downward-viewing infrared (IR) radiometer is calibrated to
measure accurately the sea skin temperature by comparing the IR temperature with
a new in situ sea-skin temperature algorithm developed at ETL.
The measured and theoretical azimuthal brightness temperatures observed
from the downward-viewing NOAA microwave radiometer over the ocean are
presented in section 5. The three-dimensional antenna patterns are used to
calculate the antenna temperatures. Unfortunately, only one set o f measured
azimuthal flights are used for this comparison due to low wind speeds and
excessive internal radiometer noise. As expected, the highest wind day (about 8
8
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m/s) produced the largest azimuthal brightness temperature variations. In order to
provide ocean-surface truth for the airborne radiometer measurements, the flights
were coordinated around Titan on this day.
Brightness temperature comparisons between theory and measurement
show that the 23.87 and 31.65 GHz brightness temperatures agree best when the
small-scale height and wavelength are about 0.5 mm and 0.5 cm, respectively (i.e.,
the capillary wave region with a large slope). The wind speed comparison during
this time shows that the inferred speed from the measured brightness temperatures
is slightly lower than the true wind speed. In contrast, the inferred speed from the
calculated temperatures is higher than the true measurement. Encouraging wind
direction results are also obtained from this comparison. In particular, azimuthal
brightness temperature variations are located reasonably close to the upwind,
downwind, and crosswind directions for the 23.87 GHz channel. In contrast, the
azimuthal temperature variations at 31.65 GHz do not agree as well as those
obtained at 23.87 GHz. However, asymmetrical brightness temperature
differences between the upwind and downwind directions are detected at both
frequencies for the measured and calculated results.
Section 6 highlights the main topic and significant conclusions of this
paper. An emphasis is placed on original contributions. Suggestions for future
work are also presented.
9
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2. THEORETICAL BRIGHTNESS TEMPERATURE FORMULATION
Fundamental to the successful radiometric detection o f the geophysical
parameters of the atmosphere and the ocean surface is an understanding o f their
composition, absorption, extent, structure, and polarization properties and of the
radiometer’s antenna power pattern. The radiometer is assumed to be properly
calibrated for absolute brightness temperature measurements. In this section, the
geophysical parameters that are most important in describing the received radiation
for a downward-viewing passive radiometer are identified and incorporated into a
single equation.
2.1 Background
A blackbody is an idealized body which, when in thermodynamic
equilibrium at a temperature T, radiates at least as much energy as any other body
at the same temperature T [Ulaby et al., 1981]. Also a blackbody is a perfect
absorber and a perfect radiator. A blackbody absorbs all the radiation falling upon
it at all wavelengths, and the noise-like radiation emitted by it is a function of only
the temperature and wavelength.
The brightness of the radiation from a blackbody is given by Planck’s
radiation law. This law states that the spectral brightness Bhb o f a blackbody
10
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radiator is expressed by [Kraus 1982]
2hf
B„b =
(2 . 1)
hL
kT
where Bbh is in watts-m'2-Hz'I-rad'2, h is the Planck constant in J -s,/is the
frequency in Hz, c is the speed o f light in m-s'1, k is the Boltzmann constant in J-K"
', and T is the thermodynamic temperature in K. Table 2.1 gives the definitions,
values, and units o f the physical constants used in this equation.
Table 2.1. Constants used in Planck’s law.
Symbol
Definition
Value
Units
c
Speed of light in a
vacuum
2.99792458x10s
m-s'1
h
Planck constant
6.6260755x1 O'34
J-s
k
Boltzmann
constant
1.380658xl0-23
J-K'1
Real materials, usually referred to as greybodies, emit less energy than a
blackbody does and do not necessarily absorb all the energy incident upon them.
Furthermore, the observed brightness of greybodies depends on their material
composition and associated absorption properties, and on their spatial extent. If its
brightness is 5(0, <j>), i. e., direction-dependent, and its physical temperature is T, a
11
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blackbody equivalent radiometric temperature may be defined so that 5 ( 0 ,4>) can
assume a form similar to (2.1). Such a temperature usually is called the brightness
temperature, Tb(Q, (j)), and accordingly 5 (0, (J)) is defined as
2h f
5(0, $) = 5(r.(0,<j)» =
\
-
/
f
Ve
1
hf
*rA(0. <|>)
)
(2 .2)
1J
The brightness B(Tb(Q, $)) of the material relative to that of a blackbody at the
same temperature is defined as the emissivity e(0, cj))
e(0, (j>) =
5 ( r fe(0,c})))
Bbb(T)
(2.3)
Since 5 (0 , <j>) s Bbb and Os e(0, <j>) s 1, the brightness temperature Tb(Q, <})) o f a
material always is smaller than or equal to its physical temperature T.
Now consider the antenna shown in Fig. 2.1. The radiation incident upon
the normalized antenna pattern, F„(0, (J)), from any specific direction may contain
components originating from several different sources. The apparent radiometric
temperature distribution Tap(Q, cj)) is a blackbody-equivalent temperature
distribution representing the brightness distribution 5 /0 , cj)) of the energy incident
upon the antenna. It is defined in the same manner used earlier to define the
brightness temperature Th(Q, cj>) of a material
12
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B(Ta)
Antenna Pattern
f«( e,<t>)
Apparent Brightness
Distribution B(Tap) (9, <j>)
Atmosphere
B(Tsky)
W w B {T bs)
Ocean Surface
Observation Area
Figure 2.1. A schematic representation o f the total brightness incident upon the
antenna. The apparent brightness B(Tap) consists of the downward sky brightness
B{Txky), the reflected atmospheric brightness B(Tj), the ocean surface brightness
B{TbX and the atmospheric upward brightness B(Tup). The antenna pattern and the
antenna brightness are given by F„ and B(Ta), respectively.
13
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5.(0, <j» = B(Tap(d, <j>))
(2.4)
In this paper, we use the term brightness temperature to refer to the self­
emitted radiation from a surface or volume, and the term apparent temperature to
refer to the energy incident upon the antenna.
On the other hand, the antenna brightness, B(Ta), where Ta is the antenna
temperature, is the true power spectral density measured by the radiometer. It is
equal to the apparent brightness distribution B(Tap(Q, (J))) integrated over 4n
steradians according to the antenna weighting function Fn(0,<J>) and normalized by
the integral o f the weighting function (which is the pattern solid angle) [Ulaby et
al., 1981]. So B(Ta) assumes the form
I
»,T
B{T“)
S ( T ( 6 , $)) Fn(0, ({)) sin0 d O d < p
|
_ J<t>=o Je=o
n r n
I
I
•
F„(0, 4>)
J(()=0v0=0
^
Bd d(f)
2.2 Focus of Present Work
The brightness sources considered in this paper are from the cosmic
background radiation, the atmosphere, and the rough ocean surface. The cosmic
radiation is essentially a fixed constant [Smoot et al., 1992], the atmospheric
14
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brightness temperature is calculated by the theory and software developed at ETL
[Schroeder and Westwater, 1991; Janssen, 1993; and Reynolds and Schroeder,
1993], and the rough ocean surface brightness temperature is developed in section
3. An equation is developed here to interconnect these sources for a downwardviewing airborne radiometer. The RTE provides the basic framework for this
equation.
2.3 Theory
The apparent brightness, i.e., apparent temperature, observed by an
airborne radiometer viewing the ocean at an angle 0 relative to the nadir direction
(see Fig. 2.2) is given by [Ulaby et al., 1986]
B ( T ap(f,Q, <j>,p)) = B ( T up(f,Q,lj>)) + ? up( 0 , s ( h a) ) { B ( T bs( f , Q , h p ) )
(2.6)
+ B (T r/ f , 0, <j),p))]
where
(2.7)
ha is the vertical line-of-sight aircraft height above the ocean surface, s(ha) is the
refracted ray path length from the ocean surface to the aircraft height ha, 0 is the
angle relative to the nadir direction, (J) is the azimuth angle,/is the frequency, x is
15
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s = s{ha) (Aircraft)
B(Tap) = B(Tltp) + Tup (B(Tbs) + B(Trf))
Upward
Atmospheric
Self-emmission
Transmissivity T!(
Downward
s = 0 (Surface)
Ocean Surface
Figure 2.2. An airborne radiometer observing the ocean surface at an angle 0
relative to the nadir direction, where ha is the vertical line-of-sight aircraft height
above the ocean surface, s{ha) is the refracted ray path length from the ocean
surface to the aircraft height ha. The received apparent brightness B(Tap) is a
function of the brightness from the universe (B(TJis) and B(TaJ ), the atmospheric
downward brightness B(TJn), the reflected atmospheric brightness B (T ^, the ocean
surface brightness B(Tbs), the atmospheric upward brightness B(Tup), and the
upward transmissivity (T up).
16
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the total atmospheric optical thickness as defined in (2.9), p is the polarization,
5(7^) is the upward atmospheric brightness, B(Tbs) is the ocean surface brightness,
and B(Tj) is the ocean surface-reflected brightness. The above brightness
temperatures are defined in the same manner as (2.4). The ray paths in these
equations are modeled by assuming a spherically stratified atmosphere [Schroeder
and Westwater, 1991]. The antenna brightness B(Ta) is calculated using a threedimensional antenna pattern as given in (2.5).
The first term on the right side of (2.6) represents the upward brightness
emitted by the atmosphere
B (T up( f , Q M = I
B (T (s))c c(s)e
(2 .8)
where s is the atmospheric ray path coordinate, ha and s(ha) are defined in (2.6),
T(s) is the temperature of the layer between s and ds, a(s) is the absorption o f the
layer between s and ds, and
(2.9)
The factor e'T(a,b) in each term represents the exponential decay o f the source
radiation as it is attenuated by the layer o f atmospheric between path coordinates a
and b. Equation (2.8) represents the sum o f the radiation contributions from an
infinite number o f atmospheric layers. Each layer’s contribution is attenuated by
the layers between it and the antenna.
17
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A key assumption underlying the validity o f (2.8) is that the atmosphere is
nonscattering, or, equivalently, that the scattering coefficient is much smaller than
the absorption coefficient. For clouds and nonprecipitating conditions, the
scattering coefficient is negligible compared with the absorption coefficient
(Rayleigh approximation) with particle radii less than about 100 pm for
frequencies less than 100 GHz.
The second term in (2.6), Y(0, s(ha)) B(Tbs) , represents the brightness
emitted by the ocean’s surface, B(Tbs) , as attenuated by the intervening
atmosphere. The ocean surface brightness is related to its physical temperature by
B ( T bs(f, 6, < M ) = e(f, 0, < M B ( T slan)
(2.10)
where e(v, 0, ({),/?) is the emissivity of the sea water and Tskmis the thermodynamic
(physical) temperature of the ocean surface (skin layer). The emissivity is
polarization-dependent and is a function of both the roughness, the dielectric
properties o f the sea surface, and the sea skin temperature.
The last term in (2.6), Y(0, s(ha)) B(T^ ) , is called the surface-reflected
brightness and represents that portion of the downward-emitted brightness that is
reflected off the ocean surface and then attenuated by the intervening atmosphere.
So B(T^) is given by
B ( T rf(f, 0, <j>,p)) = r{f, 0, 4\ p ) B { T sky(f, 0, (}>))
(2.11)
18
II
I
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where
r 0 I 0 ,< M
= 1 - e(f,B ,h p)
(2.12)
and
B ( T dn( f , Q M
+ T(0, ~)[B(rcJ + B { T dis(f, 6, (J)))] .
(2.13)
The relationship in (2.12) is Kirchoffs law which relates the emissivity to
the reflectivity o f a surface [Tsang et al., 1985]. The sky brightness, B(Tsky), in
(2.13)
consists o f three terms. The first term, B(Tdn), represents the downward
atmospheric brightness. This term is given by
B { T dn{ f M
= r £ ( T ( s ) ) C t ( s ) e - z(0-s)ds
(2.14)
Jo
where the above terms are defined in (2.8) and (2.9).
The second term, Y(0, ~) B(Tcat) , is the cosmic background brightness (Tcox
= 2.75 K) as attenuated by the entire atmosphere, see (2.7) with s(ha) replaced with
°°. The last term, Y(0, °°) B(Tdis) , includes discrete sources, such as the sun, moon,
or aircraft as attenuated by the entire atmosphere. Since these sources are assumed
to be outside the antenna field of view for this research, we set B(Tdjs) = 0.
Therefore (2 .1 3 ) becomes
B ( T, ky(f, 0, 4>)) = B ( T dn(f, 0, <}>)) + T (0 , ~ ) B ( T CJ
.
(2.15)
19
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The apparent brightness, B(Tap), contains two links to the ocean surface
emissivity, see (2.6). The first is the ocean surface brightness, B(Tbs), which is a
direct link, see (2.10). The second is the surface-reflected brightness, B(Tj), which
is an indirect link because the source of emission is the atmosphere, see (2.11)(2.13). The sea water emissivity in (2.10) and (2.12) is governed by several
geophysical parameters, including temperature, salinity, surface roughness, and the
presence or absence o f contaminants on the surface such as patches of foam or oil.
Therefore, the apparent brightness, B(Tap), in (2.6) is a function o f both
oceanic and atmospheric parameters. In terms o f the influence on 5(7^), the most
important geophysical parameters are the sea surface temperature Tski„, the surface
wind speed W (this produces the rough surface), the salinity S, the precipitable
water vapor V o f the atmosphere, and the integrated liquid water I o f
nonprecipitating clouds. So B(Tap) takes on the following functional form
B ( T ap) = B (Tap(f,Q,<$>,p; Tskin, W , S , V , L ) )
(2.16)
where the sensor variables (f, 0. (J),p) are defined in (2.6) and the geophysical
parameters (Tskin, W, S, V, L) are defined above. Wilheit and Chang [1980]
illustrate in Fig. 2.3 that there are optimal microwave frequencies for observing
these five geophysical parameters. This figure shows a spectral plot of the
sensitivity dB(Tap)/dg, for each of the five parameters, denoted by g,. These
normalized spectral sensitivity curves depict the incremental change in B(Tap) at
20
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Salinity
rWind Speed
/
/
■
4->
• pH
>
A
CO
C
0
Liquid
Clouds
/
cn
u
Water Vapor
0
t
T3
40
(S
\
T3
\
0
»N
IS
5=
5-1
O
2
Frequency (GHz)
A
Sea Surface
Temperature
\
\
\
\
\
Figure 2.3. Spectra of the normalized radiometric sensitivity Ox/(Os,)max where
Qgi=dTap Idg,, for various geophysical parameters g,. The arrows indicate the ETL
airborne microwave radiometer frequencies. The signs have been chosen to be
positive in the frequency range of primary importance to the given parameter [after
Wilheit and Chang, 1980].
21
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the frequency/ caused by an incremental change in the given parameter g (. The
arrows indicate the ETL’s airborne radiometer frequencies, which are centered at
23.87 and 31.65 GHz. The curve depicting sensitivity to salinity indicates that the
effect of salinity on B(Tap) is small at frequencies above 4 GHz. The sensitivity
dB{Ta^ /d T s exhibits a peak at about 5 GHz. This figure indicates that the ETL
airborne radiometer is most sensitive to wind speed, integrated precipitable water
vapor, and integrated liquid water.
2.4 Algorithm Implementation
When we substitute the Planck function defined in (2.2) back into that it
appears in (2.6), the ratio 2 h f c 2 falls out of the equation. Therefore, a modified
B (T), B \ T ) , is used to simplify the software as
B \T ) =
1
v
e kT - 1
(2.17)
where h , f and T were defined in (2.1). To extract the temperature from a known
B’(T), we solve (2.17) for T as
r--
*
fcln 1 +
1
(2.18)
B \D
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The total brightness defined in (2.6) is evaluated in the same way as
outlined by Schroeder and Westwater [1991]. The transmissivity, Y ^, and the
ocean-surface brightness, B(Tbs), are computed by (2.7), (2.9), and (2.10). The sea
surface emissivity is calculated in section 3. The sky brightness, B(Tsty), contained
in the ocean-surface reflected brightness, 5(7^), and the upward atmospheric
brightness, 5(1^), are the only unknown quantities in (2.6). These brightnesses are
calculated by the method given by Schoeder and Westwater [1991]. These
calculations require a model of the atmospheric physics and knowledge o f the
atmosphere state along the radiometer ray path. The atmospheric physics are
provided by radiosonde profiles and cloud models. The radiosonde provides
profiles of height, pressure, temperature, and humidity (see section 4.3.3). Cloud
models were not used since this research focused solely on clear sky conditions.
The downward atmospheric brightness integral, B(TJn), portion o f the sky
brightness in (2.15) is computed first. This integral, see (2.14), is evaluated by
defining a mean radiating temperature (T ^) over the layer defined by the limits of
the integral. Therefore we equate
j *B(T(s)) a(s) e ' r(0’s)ds = B ( T mr) f *a(s) e ’ r(0’s)ds .
Ja
(2.19)
Ja
The necessary substitutions are made to integrate (2.19) as eudu. This process
yields
23
i
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~ B ( T mr) e ' z^ | *
~ e ' ^ ' h)) .
(2.20)
' T(0’fl)[l - e ' I(a’4)] .
(2.21)
= B { T ur) ( e - ^
Therefore, for path coordinate a < b , we have
f bB (T (s ))a (s )e -x{0-s)ds =
Ja
Solving (2.21) for B(TJ) defines
for the layer of atmosphere between levels
a a n d b as
I bB ( T ( s ) ) a ( s ) e ' x{0-')ds
B (T J =
(2.22)
Ja
e -t(O.a)^ _ g-T(a,*)j
where Tm follows directly from (2.18). Substituting 0 for a and ~ for 6 in (2.22)
defines Tm for the entire atmosphere as
B ( T ( s ) ) a ( s ) e ~ ' {0’s)ds
Jo
•
S ( T mmr)
r ' = —-----------------------------------/n
v
^2 ‘23^
1 - e ' z(0- ]
For a profile containing nl levels, the integral in (2.14) is expressed as the
sum o f the integrals over each of the nl -1 layers as
zi°-s)ds = ^)
J ^ B ((T
T ((ss))))aa ((s ) e ' z(0-s)ds
j* ' B (T (s)) a(s) e ' z(0’j)ds
.
(2.24)
Figure 2.4 shows the relationship between the levels and the layers for
24
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Layer
Level
nl
- nl -1
nl -1
nl -2
nl -2
3
2
2
1
1
/ / / / / / / / / / / /
(Surface)
Figure 2.4. Relationship between the levels and layers for discretizing the
downward brightness integral for a profile containing nl levels.
25
I
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solving the above integral. Equation (2.21) is substituted into (2.24) to express the
layer integrals equivalently as
[ IlB ( T ( s ) ) a ( s ) e ' T(0'j)ds = B ( T mr)e
[l -
.
(2.2 5)
i s ,- \
For a given frequency, B(TJ) for the atmospheric layer between profile
levels i and z -1 is approximated as
BOFTLAY =
BOFT (i - 1) + BOFT (i) e ~,aulayi,)
K— ---- — ---- —-----------J + e -taulay(i)
(2.26)
where BOFT(i) = B \ T ) defined in (2.17) for profile level z, and taulayii) = x(5,_„
5,) defined in(2.9). BOFTLAY is a weighted average o f the B \ T ) from the two
profile levels that form the layer.
The exponential weight, e'lmIay(i>, represents the attenuation of B \ T ) over
the layer between profile levels / and i - 1. With this definition, the integral over a
single layer becomes
BATMLAY = BOFTLAY e ' TAU{i' l ) [\ -
(2.27)
where TAU {i-1) represents x(0,5,.,) from (2.9). Note that the attenuation factor
exp[-TAU (/-l)] goes to 1 for the first layer below the antenna. If the absorption is
large enough to cause exponential underflow in the above equations, we assume
26
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that the intensity contribution from the layer was completely attenuated
(.BATMLAY= 0).
The integrated intensity from the antenna to level j is
BOFTATMU) = ^ BAT ML A Y
(2.28)
1=2
so that B(Tdn) = BOFTAM(nl) represents the desired downward atmospheric term
in (2.15) for a profile with nl levels. Similarly, T A U (nl) represents t(0,«).
Therefore, the total downward intensity defined in (2.15), including the cosmic
background, becomes
BOFTOTL = BOFTBG e ~TAU(n,) + BOFTATM(nl)
(2.29)
where BOFTBG represents the cosmic background intensity, B'(TC0S). Then the
mean radiative intensity, B*(T^°), defined in (2.23) is
BOFTATM(nl)
BOFTMR = ---------------- — - .
I
_e -TAU(ni)
(O 301
Writing (2.29) out gives
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\BOFT(i - 1) + BOFT (i) e ~,aulay01
Lj
1 + e ~‘aulay(Q
(2.31)
i =2
where nl is the number of radiosonde profile levels, BOFT(i) = B \T ) defined in
(2.17) for profile level i, and taulay{i) =
s,) defined in(2.9).
The integral defining the upward atmospheric brightness, B(T^), in (2.8), is
computed in a similar way as the sky brightness. The result is
til
V
.
\
1 1
nl
.
B( T) =
up'
b
O F T (i + \ )
+ B O F T ( i ) e ' taulaAi*l)
] +
g -taulay(i*l)
(2.32)
1= 1
_
^-taulay(i +l)j
where nlh is the number of radiosonde profile levels between the aircraft and the
ocean surface, ha and s(ha) are defined in (2.6), and the other symbols are defined
in (2.31).
2.5 Summary
28
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Fundamental definitions of brightness, brightness temperature, emissivity,
apparent brightness (temperature), and antenna brightness (temperature) were
introduced first. Then the apparent brightness observed by an airborne radiometer
viewing the ocean surface was formulated. This equation included the cosmic
background radiation constant, the atmospheric radiation, and the rough sea
surface radiation. The atmospheric radiation was calculated by ETL’s RTE
algorithms. The apparent brightness calculation required the standard ETL
downward propagating atmospheric radiation algorithm and a newly developed
upward propagating algorithm. The rough sea surface emission model is
developed in section 3.
29
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3. THEORETICAL OCEAN SURFACE EMISSION FORMULATION
The problem o f electromagnetic wave scattering (emission) from randomly
rough surfaces has been studied by numerous approximate techniques. Although
the rough sea actually has a continuous distribution of surface roughness [Pierson
and Moskowitz, 1964; Fung and Lee, 1982], the two-scale model has been
practical. The two-scale emission model [Wu and Fung, 1972; Wentz, 1975;
Ulaby et al., 1982] treats surfaces as having only two average sizes o f roughness
with one large and the other small compared to the incident electromagnetic
wavelength. The long waves are usually taken into account by the Kirchhoff
(tangent plane) approximation while the short ones are typically calculated using
the small perturbation technique. These two approximate techniques work well
under certain statistical-surface restrictions [Ulaby et al., 1982; Tsang et al., 1985;
Fung, 1994]. However, in order to observe significant U (third Stokes parameter)
values (a few kelvin) from a sinusoidal surface, Veysoglu et al. [1991] found that a
large height-to-wavelength ratio was necessary. Since the above approximations
can not be used on large surface slopes, the extended boundary condition (EBC)
method is incorporated into a two-scale model. In particular, this section
formulates a unique two-scale surface model which consists of sinusoidal smallscale features averaged with respect to the Cox and Munk [1954a,b] slick-surface
slope distribution. Furthermore, the actual microwave radiometer parameters are
30
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incorporated into this model.
3.1 Background
The emission from an ocean surface is governed by several ocean surface
geophysical parameters, including temperature, salinity, surface roughness, and
presence or absence of contaminants on the surface such as patches o f foam or oil.
Surface roughness and foam patches are related to near-surface wind speed and
direction. A calm sea surface is characterized by a highly polarized emission.
When the sea becomes rough, the emission increases and becomes less polarized,
except at incidence angles above about 60° for which the vertically polarized
emission decreases [Ulaby et al., 1986]. There are four basic mechanisms that are
responsible for this variation in the emissivity. First, surface waves having
wavelengths long compared to the radiation wavelength mix the horizontal and
vertical polarization states by changing the local incidence angle. This mechanism
has been modeled as a collection of tilted facets, each acting as an independent
specular surface [Stogryn, 1967]. The second roughness effect is the diffraction of
microwaves by surface waves that are small compared to the radiation wavelength.
Rice [1951] provided the basic formulation for computing scattering from a
slightly rough surface. Wu and Fung [1972] and Wentz [1975] applied this
scattering formulation to the problem of computing the emissivity of a wind-
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roughened sea surface. The third mechanism is sea foam. This mixture o f air and
water increases the emissivity for both polarizations. Sea foam models have been
developed by Stogryn [1972], Smith [1988], and Ross and Cardone [1974]. These
first three roughness effects can be parameterized in terms o f the rms slope of the
large-scale roughness, the rms height of the small-scale features, and the fractional
foam coverage.
The last roughness effect is the diffraction of microwaves by ocean surface
waves whose wavelengths are similar compared to the incident radiation
wavelength. This resonance-like phenomenon of microwave radiation o f the
capillary-ultragravity waves with a wavelength equal to the electromagnetic
wavelength is most important at near-nadir angles as recognized by Kravtsov et al.
[1978] and was shown theoretically by Irisov [1991]. Therefore, the microwave
emission at near-nadir angles is determined mainly by the ripples rather than by
large energy-carrying waves.
The above four roughness mechanisms depend on wind speed as well as
wind direction. The wind direction’s influence on the ocean surface is evident by
several features. For instance, the probability density function o f the sea-surface
slope is skewed in the alongwind axis and has a larger alongwind variance than
crosswind variance [Cox and Munk, 1954a,b]. Also, the rms height of capillary
waves is very anisotropic [Mitsuyasu and Honda, 1982], where the capillary waves
traveling in the alongwind direction have a greater amplitude than those traveling
32
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in the crosswind direction. Another type o f directional dependence occurs because
the foam and capillary waves are not uniformly distributed over the underlying
structure o f large-scale waves. Smith's [1988] aircraft radiometer measurements
show that the forward plunging side o f a breaking waves exhibits distinctly warmer
microwave emissions than does the back side. In addition, the capillary waves
tend to cluster on the downwind side o f the larger gravity waves [Cox, 1958;
Keller and Wright, 1975]. The dependence of foam and capillary waves on the
underlying structure produces an upwind/downwind asymmetry in the sea-surface
emissivity.
Recent theoretical works continue to suggest the potential of passive
polarimetry in the remote sensing o f geophysical media [Tsang, 1991; Veysoglu et
al., 1991; Nghiem et al., 1991; Johnson et al., 1993; Johnson et al., 1994; Yueh et
al., 1994a; Yueh et al., 1994b]. These results show that the brightness temperature
in the third Stokes parameter, U, may become large for azimuthally asymmetric
fields o f observation. The horizontally- and vertically-polarized brightness
temperatures also vary as functions o f the azimuth angles. Johnson et al. [1994]
and Yueh et al. [1994b] have provided more realistic ocean surface models by
implementing ocean surfaces randomly rough in one dimension using a Monte
Carlo technique and the small perturbation method (SPM), respectively. Their
results indicate that these techniques are more representative of the actual ocean
surface structure.
33
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3.2 Focus of Present Work
M ost theoretical analyses describing the effects o f the ocean surface do not
account for large-scale surface tilting effects on resonant and near-resonant surface
waves. As mentioned above, a resonant effect occurs when the capillaryultragravity wavelength equals the electromagnetic wavelength at near-nadir
angles. A theoretical model including this wavelength region may possibly
provide a better understanding about how microwave radiation interacts with the
ocean's capillary-ultragravity wave region. This wavelength regime is very
important because most radiometers used for measuring wind speed and direction
operate in this wavelength region [Trokhimovski and Irisov, 1995]. The derivation
of such a model is the focus of this section.
There are different two-scale ocean surface configurations. Most two-scale
theoretical models superimpose small irregularities (ripples) on large undulations
[Ulaby et al., 1982; Wu and Fung, 1972; Valenezuela, 1978; Wentz, 1975].
However, these two-scale models do not account for resonant or near-resonant
ocean surface waves (capillary-ultragravity waves) tilted in accordance with the
slope distribution of large-scale roughness o f the surface (i.e., gravity waves).
A two-scale model that includes resonant or near-resonant waves is
developed here. In particular, this model includes a one-dimensional sinusoidal
surface profile for the smaller waves and a one-dimensional Gram Charlier slick-
34
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surface slope distribution for the larger waves [Cox and Munk, 1954a,b]. These
one dimensional surfaces permit the evaluation of the composite surface provided
the large scale slopes are not too large. The simplistic ocean wave of a one­
dimensional sinusoidal surface is known as a long crested wave [Kinsman, 1965],
where the wind direction is assumed to be perpendicular to the wave crests. For
the present research, swell waves are not considered here. Although this is a very
simplistic model of the ocean surface, it does provide valuable physical insight into
the mechanisms responsible for the azimuth modulation signatures. This model is
valid for wind speeds less than 12 m/s, so the foam coverage is about 1%
[Monoham and O’Muircheartaigh, 1986] and its contribution to the brightness
temperature is negligible at all microwave wavelengths. Therefore, the foam
coverage is not included in this model.
3.3 Theory
The ocean surface's emissivity is the key parameter for passive remote
sensing o f the ocean. The emissivity relates the brightness temperature emitted by
an object to its actual physical temperature, where the object is at a constant
physical temperature, Tphy. The brightness temperature from the object is
Tba = ea(6,<i» Tphy
(3.1)
35
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where a refers to the brightness temperature polarization, 0 to the polar
observation angle, and <j>to the azimuthal observation angle.
Kirchoff s law relates this emissivity to the reflectivity ro(0, (})) of the
surface by [Tsang et al., 1985]
eo(0,<j>) = 1 - r a(0, <t>) .
(3.2)
The reflectivity ro(0, <{)) for the given incident polarization a is defined as
the fraction o f the power incident from direction (0, (j)) that is rescattered. This is
evaluated by integrating the bistatic scattering coefficients yio(0, <j); 0 ', 4)') over all
scattering angles in the upper hemisphere and summing the results o f both
orthogonal scattering polarizations [Johnson et al., 1993]
r fl(0,cf>)= —
4tt J=] Jo
d d ' sin 0 ' P ” d $ Yifl(0, <j>; 6',
Jo
)
(3-3)
where (0, cj>) and (0', (J)') represent the incident and the scattered directions,
respectively, and a and b represent the polarizations o f the incident and the
scattered waves, respectively.
3.3.1 Two-scale model
A two-scale model is used here to describe the ocean surface [Ulaby et al.,
36
i
|
!
with permission of the copyright owner. Further reproduction prohibited without permission.
1982]. The scattering from such a surface is dominated by the large-scale
roughness at near-normal incidence (approximately, 0 °s 0 s 25°) and by the
small-scale roughness, which is tilted in accordance with the slope distribution of
the large-scale roughness o f the surface at large incidence angles (approximately, 0
>25°).
The two scales are summed together for the general case as follows [Wu
and Fung, 1972]
Yia(0, <j>; 0 ', (j)') = yL ( 0. <i>; 0 '
) + <yL (0. 4>; 0', 4>'))
(3.4)
where y°ba(Q, <j>; 0 ', <j>') denotes the main contribution by the large-scale roughness
and {ylba(Q, <j>; 0 ', <$>')) denotes the bistatic scattering coefficient o f the small-scale
roughness averaged over the distribution of the surface normals o f the large-scale
roughness.
To obtain an upper bound estimate on the quantity y°ba(Q, 4>; 0 ', 4>')> its
maximum value in the backscattered direction ((j) = 0 , 0 ' = 0, and (J)' = ti) is
calculated. The bistatic scattering coefficient in this direction is given by Wu and
Fung [1972] as
Y°a( M
=O;0' =0,4>' =Tt) =
\(RbB(°})l
2
2 m cos 0
exp
- tan20
(3.5)
2m 2
where m is the rms slope, 0 is the incidence angle, and (Rba(0)) is the modified
37
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i
1
Fresnel reflection coefficient [Wu and Fung, 1972] evaluated at normal incidence
(0 = 0 °).
The parameters in (3.5) have the following values for this research:
|(i?Ao(0)) |2 < 1 ,0 = 32°, and m = 0.1. Therefore, y°Afl(0, <}>= 0; 0' = 0, <])' = u) = 0,
which implies that yV (0, <j); 0 ', <})') is negligible for this research. With this in
mind, (3.4) then becomes
yAa(0,<j>;0',<i>') = < y L ( M ; e \ 4 > , )> •
(3.6)
Wu and Fung's [1972] formulation is used to model the small roughness
tilted by the large undulation's slope distribution. This is accomplished by
averaging the small feature’s bistatic scattering coefficient y ' 4a( 0 ', (j)'; 0 '*, (j)'.T)
with respect to the large roughness slope distribution. The two-scale surface
model for this research requires the large and small features to be uniform in the y
direction. Furthermore, the positive x axis is defined to be the upwind direction.
This yields
y4a(0, <i>, 0, ,<!>,) * (yL (0.
0, >4>,)> =
(3.7)
j
ffz,) Ji * z] dzi
where 0 and (j) are the incident angles; 0 Vand (j)tare the scattering angles; 0 ' and
4)' are the local incident angles; 0 '5and <j)'t are the local scattering angles; Zx is the
38
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surface slope; and P(ZX) is the surface slope distribution o f the large-scale waves.
The above integral is evaluated by determining the relations between the
surface slope and local angles. This surface slope is related to the tilt angle 0„in
Fig. 3.1 as
Zx = tan0B .
(3.8)
f l + z j = sec 0n
(3.9)
From (3.8) it follows that
and
dZ
dZx = H e n dQn =sec20n d%n'
(3-10)
The limits o f integration in (3.7) are rewritten as
+oo = t a n 0 B -
0n = + —
(3 .H )
2
and
— = tan 0„ - 0„ = - j
.
(3.12)
A one-dimensional Gram Charlier distribution is used to model the slope
distribution o f the waves [Cox and Munk, 1954a,b]. The slope distribution then
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
z
>
X
Figure 3.1. The tilt angle 0„ connecting the two sets of coordinates (x,y, z) and (x \
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
becomes
1+E C
exp
P(ZJ
m \f2TZ
{Tl)
(3-13)
i.J =l
where the summation on the right represents the deviation from a normal
distribution, # ,an d Hj are Hermite polynomials, C(>are coefficients from Cox and
Munk’s [1954a,b] measurements, and the standardized slope components, E, and T),
are defined by
I
= o ,
= h.
Tl
(3.14)
m
where m is the rms slope. The component \ is zero because there is no wave
profile variation in the y direction.
Substituting (3.14) into (3.13) yields
exp
P ( Z x) *
m
(
1 +
111
\
'03
( 2 )
'40
'2 2
(3.15)
- 3
L\ m /
K
\
/
2
-
m
.
\ 4
£*
1
/
- 6
\ 2
fx
+ 3
24
Cox and Munk [1954a,b] showed that this expansion is adequate for slopes
41
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up to T) = 2.5. Gathering like powers in Zx/m , gives (3 .1 5 ) in the following form
(3 .1 6 )
where
A0 = 1 + C40 /8 + C22 /4 + CM/ 8,
A j = (C2] + C03 )/2,
A2= "(On Co4)/4,
j43 = -C03/ 6, and
^ 4=
/24;
the clean surface coefficients are given as:
C21 = 0.01 -0.0086 JF± 0.03,
C03 = 0.04-0.033 W ± 0.12,
C40 = 0.40 ±0.23,
C22 = 0.12 ± 0.06, and
= 0.23 ±0.41;
and the oil-slick surface coefficients are:
C 21 = 0.00 ± 0.02,
C03 = 0.02 ±0.05,
C40 = 0.36 ±0.24,
42
I
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
= 0.10 ± 0.05, and
Co4 = 0.26 ±0.31; and
W is the wind speed in m/s, measured at an altitude o f 12.5 m above the sea level.
The rms slope m for Cox and Munk's (1954a,b) clean-sea upwind (i.e., oilfree) measurements is
m = ^3.16* 10"3 W ± 0 .004 .
(3.17a)
On the other hand, the rms slope m for slick-surface (i.e., oil surface)
upwind measurements is
m = \ j 0.005 + 0.78x 10 ' 3 W ± 0.002 .
(3.17b)
In view of the requirements of the two-scale model, it is reasonable to
choose the above oil slick measurements, i.e., the above slick-surface coefficients
and the rms slope m in (3.17b), since the small irregularities are suppressed.
The differences between the above slope distribution, P(ZX), and a normal
distribution, for values representative of this research, are shown in Fig. 3.2. The
slick surface measurements at a wind speed o f 7.8 m/s (see section 5.2) are used in
this computation. As Fig. 3.2 shows, the Gram Charlier distribution produces a
slightly narrower distribution than the normal one.
We substitute (3.8) - (3.12) and (3.16) into (3.7) to obtain
43
I
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.0
Normalized Surface Slope Distribution
Normal
0.8
0.6
0.4
0.2
0.0
-0.3
-
0.2
-
0.1
0.0
0.1
0.2
0.3
Surface Slope
Fig. 3.2. A plot of the slope distributions, P(ZX) and normal, versus surface slope,
Z„ for values representative of this research. The slick-surface values in (3.16) and
(3.17), at a wind speed of 7.8 m/s, are used in these plots.
44
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tan2 0_
Y6fl “ I
2 y L ( m / l i e ) - 1exp
2m
— 5 tan20 ft + —3 tan30
m
m
‘
An
u + — tan0„n +
m
(3.18)
A,
+ — a tan40 >sec30 ft d d ft
m
n
«I
where y ba = y ba(Q, 4>, 0 „ <t>.T) and y \ a = y ' J 0 ', 4>', 0,',4>,' )•
Equation (3.18) can be expressed as
y ba *
* [ ? v'Yifl/(
L 0 „ ) e x p [x g (0 B)]rf0n
(3.19)
where
/ ( 0 n) = ( m y f H y 1 An + — tan 0 . + —-ta n 20_ +
m
m
(3.20)
—-ta n 30 n + —-ta
4 n 4 0 n sec 30 _
m
m3
x = ( 2 m K)-I
(3.21)
g ( 0 J = “ tan 20 .
(3.22)
Since nr is usually sufficiently small (w - 0.1) for the sea and y \ 0
45
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assumed to be insensitive to 0„ for small values o f 0„, we evaluate (3.19) by the
method o f steepest descent [Bender and Orszag, 1978; Erdelyi, 1956].
33.2 Steepest descent evaluation
The steepest descent method requires that the integral in (3.19) be
deformed into a constant-phase contour in the complex plane. The asymptotic
behavior o f the integral is determined by the behavior of the integrand near the
local maxima o f the real part of g(0„), i.e., Re[g(0„)], along the contour. The
imaginary part o f g(0„) is designated by Im[g(0J]. These local maxima of
Rek ( 6 n)] may occur at end points of constant-phase contours or at an interior point
of a constant-phase contour. IfRe[g(0n)] has an interior maximum then the
directional derivative along the constant-phase contour rf{Re[g(0n)]}/Js = |V
Re[g(0„)] | vanishes. The Cauchy-Riemann equations imply that V Re£g(0n)] =
lm [g(0„)] = 0, so g '(0„) = 0 at an interior maximum of Re[g(0„)] on a constantphase contour.
A point at which g '(0„) = 0 is called a saddle point. Saddle points are
special because it is only at such points that two distinct steepest curves can
intersect. When g '(0„) * 0, there is only one steepest curve passing through 0„ and
its tangent is parallel to V Re[g(0„)]. In the direction of V Re[g(0„)], | exp(xg(0„) |
is increasing so this portion of the curve is a steepest-ascent curve; in the direction
46
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o f -V Re[g(0n)], | exp(xg(0„)| is decreasing so this portion o f the curve is a
steepest-descent curve. On the other hand, when g'((3J = 0 there are two or more
steepest-ascent curves and two or more steepest-descent curves emerging from the
point 0 „.
The constant-phase contours of (3.22) are evaluated now. To accomplish
this the following variable change is introduced
0B = « + iv .
(3.23)
where i = V - 1 for the remainder of this research.
Substituting (3.23) into g(0„) in (3.22) gives
g(u + iv) =
[cos(2K )cosh(2v)]2 + [sin(2«)sinh(2v)]2 - 1
-f2 sin (2K )sin h (2v)
(3-24)
[cos(2 a )co sh (2 v ) + l ] 2 + [sin (2a)sin h (2v)]2
Therefore, the real and imaginary parts o f g(u + iv) are given by
Re{£(w + /v )} =
tco s(2u) cosh(2v)]2 + [sin(2a)sinh(2v)]2 - 1
[cos(2a)cosh(2v) + l ] 2 + [sin(2a)sinh(2v)]2
T , .
...
-/2 sin (2 u )sin h (2 v )
Im {g(u + /v )} = -----------------------------------------------[cos(2w)cosh(2v) + 1] + [sin(2u)sinh(2v)]
.
(3 .26)
The constant-phase contours are found by imposing the condition Im[g(w +
47
i
I
with permission of the copyright owner. Further reproduction prohibited without permission.
iv)] = 0. This condition gives
sin(2u)sinh(2 v) = 0 .
(3.27)
Solving for u and v in (3.27) yields
u = —— , n = 0, ±1, ±2, ±3, . . .
2
v =0 ,
(3.28)
The contours are defined by the real axis (v = 0), the imaginary axis, and
the ir/2 spaced vertical axes. However, the points (u = m ill, v = 0) produce an
indeterminate form o f 0/0 in (3.26). These possible trouble points are addressed
shortly.
The function g(0„), see (3.22), is differentiated with respect to 0„ to find the
saddle points on the above contours. This yields
^ g ( 6n)
^0
= - 2 tan 0 ft sec20 n .
(3.29)
Equation (3.29) is differentiated with respect to 0„ to obtain
d 2z ( Q )
= - 2 [sec40 n + 2 tan20 nsec 0 n ] .
(3 .3 (
d Ql
We find that dg(Qn)ldQ„ = 0 at 0„ = rm for n = 0, ±1, ±2, — ; and
cfg(Qn)/dQn2 * 0 at 0„ = rm for n = 0, ±1, ± 2 ,
Therefore, 0„ = niz for n = 0,
48
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± 1, ± 2 ,
are first order saddle points.
The steepest-ascent and steepest-descent contours are found by using (3.28)
in (3.25) and (3.26). For v = 0, (3.25) reduces to
_
,
,
.
Re{g(u + iv)} =
-
c o s 2( 2 h )
-1
.
(3.31)
[cos(2u) + l ] 2
Therefore, the exponential in (3.19) is given by
exp [xg(u + iv))
=
expj * [cos2(M ~ U 1
[cos(2 w) + I ]2 j
(3 32)
The value o f (3.32) decreases as u ranges from n% to tt(2n + 1)/2 for n = 0,
±1, ± 2 ,
Therefore these paths are steepest-descent contours. However, (3.31)
has an indeterminate form of 0/0 as u - ± n(2n + l )/2 at v = 0. This is given as
lim w. ± it(2n * i) {g(« + iv)} =
2
“
(3.33)
c o s 2( 2 k ) - 1
I
lim
“
Tt(2n
- 1)
( ---------------------------------- ---
I
2
l ]2 J
[cos(2a) +
0
\
f -
—
0
L'Hdpital's rule [Riddle, 1974] is applied to (3.31) to obtain
lim v ± n{2n ♦ i)
{g(u + iv)} =
2
(3.34)
..
f
lim
"
cos(2w)
, t:(2n - 1) ( ------------------------2
I cos(2a) + 1
1
f
I
-1
- oo
0
49
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Therefore, exp{xg(« + iv)} - 0 as u - ± tc(2n + l)/2 at v = 0. Consequently, these
endpoints do not contribute to the integral in (3.19).
For u = ±iznl2, rt = 0 ,1 ,2 ,..., (3.25) reduces to
t, . .
...
cosh2(2 v ) - l
Re{g(w + iv)} = -----[ - l w cosh(2v) + l ] 2
.
(3.35)
Therefore, the exponential in (3.19) is given by
exp[xg(u + iv)] = expj — * [ co sh (2 v) 1]
I
I [ - l |Bicosh(2 v) + l ]2 J
(3.36)
The value o f (3.36) increases as v - ±°°. Therefore, these paths are
steepest-ascent contours. However, (3.35) has an indeterminate form o f 0/0 as v 0 at u = ±%(2n + l)/2. This is given as
lim v_±0
lim
{
{g(w + iv)} =
cosh2(2v) - 1
]
{ [-c o s h ( 2v) + l ]2 J
0_
^3'37^
0
As before, L'HOpital's rule [Riddle, 1974] is applied to (3.31) to obtain
lim v- ±0 {^(« + *'v)} =
~c°sh(2v)
I -cosh( 2 v) + 1 I
0
(3'38)
50
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Therefore, exp{;cg(w + iv)} - 0 as v - 0 at w = %(2n + l)/2. Consequently, these
points do not have an effect on the integrand in (3.19).
Figure 3.3 shows the steepest-ascent contours with double-tip arrows, the
steepest-descent contours with single-tip arrows, the first-order saddle points with
large dots, and the singularities (- °°) with X’s. The arrow tips point in the
direction o f increasing values of the exponential function in (3.19). The method of
steepest-descent is applied directly to (3.19) since the integration limits are on a
steepest-descent path as defined by the real axis segment from 0 „= -tt/2 to 0 „=
+iz/2, and the endpoints do not contribute to the integral. From Laplace's method
[Bender and Orszag, 1978], the entire asymptotic expansion o f y ba as x - +°» is
determined by a small neighborhood about 0„ = 0. The leading behavior of yba is
approximated by the steepest-descent path, a straight line, 0 „ = s about 0 „ = 0 .
A Taylor series expansion about 0„ = 0 for y \ a, f (0„), and g(0„) is used in
(3.19). First set
dQn = ds .
(3-39)
Then we expand tan(s) by one term and sec(s) by two terms as s - 0 to
obtain
tan(s) ~ s ,
sec(s) ~ 1 + — .
2
(3.40)
51
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A
it
it
it
K
J i,
<«X » > ' « <
i»y
Vr
T
Yr
>r
-7E
z!L
2
0
71
Figure 3.3. Constant-phase (steepest) contours of exp(-x tan20„) in the complex (0„
= u + iv) plane. Steepest-descent contours are shown by single-tip arrows.
Steepest-ascent contours are shown by double-tip arrows. The arrow tips point in
the direction of increasing values of exp(-x tan 20„). Saddle points lying at 0„= 0
and 0„= ± 7t are shown by large dots. Singularity points (-») lying at 0„= ±7t /2 are
shown as X’s.
52
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We substitute (3.37) and (3.38) into (3.19) and retain terms up to second
order to get
Iba »
P£-CyL f ( s ) e x p [ - x s
] ds
(3.41)
where
( 3 A0 + A 2 )
Al
/(s ) = (m ^ /I i) - ' A.0 + — s +
m
52
I
2
(3.42)
" ’J
as e - 0 .
The above integral is broken into the following two parts
yba s I i + I 2
(3.43)
yL / ( s )
(3.44)
where
h = I
Jo
e x p [ - x s 2] d s
72 = I Yiaf(s ) e x p [ - x s ‘]d s .
(3.45)
/, is evaluated first. As we mentioned before, y \ a is assumed to be
insensitive to s for small values of s, i.e., 0„. This allows y \ a to be taken outside
53
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the above integrals, where y '4a is evaluated at a tilt angle o f 0„. The surface slope
Zx is equated to the rms slope m. Therefore, the tilt angle is found from (3.8) as
0n = + ta n " 1(m) .
(3.46)
The slope distribution, P(ZX), in (3.15) is permissible since T) = 1 < 2.5.
Therefore, y '4u is evaluated at the above angle 0„. Extending 7,'s upper
limit o f integration to infinity yields
h = Y L(+ e „) I
Jo
(3.47)
f(s) e x p [ - x s 2]d s
where y ' 4a(+ 0 „) implies that y'ba is evaluated at 0 „ = + tan'(m).
Now (3.41) is substituted into (3.47) to obtain
[ 3 ^o + AA \
Al
s2
A.0 + —- s +
m
m 2t
\ 2
The above integral is evaluated by a standard integral table [Beyer, 1978].
The result is
yL (
+ 6„)
m \]2Tt
Ao
It +
2 \ x
1 3 A0 + A2) 1
A\
+
2m x
{
2
m 2j
4x ^
TZ
X
/, is evaluated in the same manner as /, except that s = -s and ds = -ds. The
result is
54
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where y 'Aa(-0 J is evaluated at 0„ = - tan'’(/w). Again, the slope distribution, P(ZX),
in (3.15) is permissible since |r| | = 1 < 2.5.
Combining (3.49) and (3.50) and using (3.19) gives
/
yL
( + 0 „)
■ba
Ao 1 +
\
?,
3m 2
I
)
2
+ A2 +
Tt
(3.51)
(
yL
( - 0„)
A0 1 +
I
\
2
3m 2
2
J
+ A2 ~ A iy
It
The total power reflectivity is found by substituting (3.51) into (3.3). The
result is
r (0, q>) = A
+ A
-----
-----------
(3.52)
where
r * ( 0 , <t>) =
(3.53)
— t f T iV sme' f 2’ d$
47t
Jo
Jo
0 = ± tan (m)
55
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where A0- A 2 are given in (3.16) and the rms slope m is given in (3.17).
3.3 3 Large-scale tilt translation
The power reflectivities ro*(0,<j)) in (3.53) are translated into the tilted ±0„
reference frame, referred to hereafter as the local reference frame. The local frame
has its axes parallel and perpendicular to either the +0„ or the -0„ angles. For this
research, the large-scale features are assumed to be gravity waves since their
wavelengths (on the order of several meters) are much larger than the incident
electromagnetic wavelengths (0.95 and 1.26 cm). Furthermore, ocean waves larger
than these, such as swells, are not considered here because o f modeling difficulties.
Consequently, the tilt angles ±0„ are assumed to be generated solely by gravity
waves. On the other hand, the small-scale surface roughness is now allowed to be
similar to the incident electromagnetic wavelength. However, the small waves are
restricted to have sinusoidal-corrugated surface profiles. These profiles are used to
model capillary-ultragravity waves. Therefore the power reflectivities ra'(0,(j)),
i.e., ra(0,4>), can be computed by the EBC method which allows for the small-scale
roughness to be similar to the incident electromagnetic wavelength.
56
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The two-dimensional geometry for this translation is shown in Fig. 3.4 with
an electromagnetic plane wave incident on a periodic surface described by/J(x') =
f ( x '+ As), tilted at an angle +0„, where As is the wavelength o f the surface in x '
direction. The tilted coordinate system is designated by x', y ‘, and z', whereas the
untilted coordinate system is designated by x, y, and z. The incident wave vector,
is incident on the periodic surface at angle 0 with respect to the untilted
coordinate system. For computation purposes, the periodic surface is chosen to be
uniform in the y~(jT') direction. In this figure, region one is the free space region
above the periodic surface, with permittivity e 0 and permeability (i0, and region one
is the sea water, with permittivity e, and p, = p0. The three-dimensional geometry
for this situation is shown in Fig. 3.5.
The electric field of the incident wave is given by
Ef = 7iE0e ik°7‘ ~
r,
(3.55)
where a time (/) factor of exp[/(2 rc/)/] is suppressed, t in s;
F = 2ti l k0, rad/m;
XQ= c/f m '1;
c is given in Table 2.1;
/ is given in (2 . 1);
n i = x sin 0 cos<j> + y sin0 sin4> - z cos0 ;
F = k o«7;
57
with permission of the copyright owner. Further reproduction prohibited without permission.
Region zero
£o> Ho
Region one
Figure 3.4. Two-dimensional geometry of an electromagnetic wave with wave
vector J , incident upon a tilted sinusoidal surface with wavelength Xx and height
hx. The local reference frame is shown by the coordinate system
z') which
is tilted by angle 0„ with respect to the coordinate system (x,y, z). The periodic
surface separates region zero from region one. The permittivity (e,) and
permeability (p,) for the two regions (/ = 0 , 1) are shown.
58
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Region zero
£q» P -0
i
Figure 3.5. Three-dimensional geometry of a single-layer sinusoidal-corrugated
surface tilted at angle 0„, see Fig. 3.4.
59
i
i
1
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
F is the source point to observation point vector, m;
E0 is the incident electric field amplitude, V/m; and
T = - x sincj) + y~cos(j), the electric field polarization vector.
The incident electric field is rotated about the y ~axis into the local
reference frame (in the primed system) as shown in Fig. 3.6. The electric field
takes on the following form:
(3.56)
where
n / = x 'sin 0 'cos<j>'+ _y'sin0 'sin(j>' - z'cos©';
e' = x $ ,+ y ' B 2 + z 'B 2,
5 „ B2, B2 are coordinate transform factors; and
r 'is the new position vector.
The above factors 5 ,, B2, and B2are related to the original coordinate frame
(unprimed) by the usual rotation equations [Riddle, 1974]
x
- x cos0 R + zsin0_R
y' = y
z
= - x s i n 0 R + zcos0_R .
(3.57)
(3.58)
(3.59)
60
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z
Figure 3.6. Incident electromagnetic wave vector k, referenced to two sets of
coordinates (x, y, z) and (*', y', z ‘). The rotation angle 0„ is about the y (j/) axis.
61
I
i
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The position vectors in the unprimed and the primed systems are identical,
therefore
r = r',
r - r' .
Furthermore, the transformation for the unit vectors ( P ,
(3.60)
<}>') to (x \ y \ z ')
are
r' =
sin0' cos<}>'x + sin0' siiKj)'^' + co s0 'z'
(3.61)
0 ' =cos0'cos<j>'x' + cos0'sintj ) '^ 7 “ sin 0 'z '
(3.62)
<{>' = - sin<j)'r' + cos<j)'j,/ .
(3.63)
Now (3.57) - (3.59) are substituted into (3.61), and also use (3.60), to obtain
r - x (sin0 ; cos(j>' cos0 B - cos0 's in 0 n ) + y (sin0 ' sincj)') +
(3.64)
z (sin0' cos(j)' sin0n - c o s0 'c o s0 n ) .
The position vector can also be expressed as
r
- sin0cos(})x + sin0sin(j)y + c o s 0 z .
(3.65)
The unit vectors in (3.64) and (3.65) are equated to each other to obtain
sin0cos(j) = sin0'cos(J)'cos0n - c o s 0 's in 0 n
(3.66)
62
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sin 0 sin<}> = sin 0 'sin(j)'
(3.67)
cos0 = sin0 'cos(j)'sin 0n + cos 0 'c o s 0 n .
(3.68)
From Fig. 3.6 the following angle relationship holds
0'
=
0
0
-
R
(3.69)
.
Equations (3.66) - (3.68) are used to obtain
costj)' =
1 -
sin0 _sin(j) ] 2
^ sin 0 ' j
(3.70)
With (3.69) and (3.70) substituted into (3.56), we obtain
_
_ [sin0 cos(}) + cos(0 - 0 n) sin 0 B]
„> = x -
+
COSO
R
(3.71)
y ' [sin0 sin(|)] - z'[co s (0 - 0 „ )] .
Therefore, the local coordinate wavenumber vector is expressed as
v
+/ y
(3.72)
where
63
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[sin0 cos(f> + cos(0 - 0 n)sin 0 1
kxi ' = k0. -----------------------------------------q
costly
(3.73)
k ■ = fcosin0 sin<j)
(3.74)
K i ' = *ocos(0 ■ 0„) •
(3.75)
From the above equation, we also find that
k 2' = k 2
[sin0 cos(}> + cos(0 - 0 n)sin 0 n]2
cos20 n
(3.76)
+ fco2sin20 sin2(j> + ifco2cos2(0 - 0 n)
The transformations for the unit vectors x and z are found by (3.57) and
(3.59). The results are
x = x'cos 0 _ - z'sin 0 _
(3.77)
z = x'sin 0 r + z'co s 0 n .
(3.78)
The coordinate transform factors 5, - B3 in (3.56) are derived in the next
section.
3.3.4 Polarization transformation
64
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I
The polarization vector e / in (3.56) is a function o f the large-scale surface
tilt angle ( 0 „), discussed in the preceding section, and the pitch angle (Qp) o f the
aircraft. The pitch angle is positive when the aircraft nose is up (see Fig. 3.7).
When the aircraft is flying level (0p = 0°) with a nonzero roll (incidence) angle (0
* 0°) the 23.87 GHz channel is horizontally polarized and the 31.65 GHz channel
is vertically polarized with respect to a flat water surface (0„ = 0°). In general
however, the pitch angle is nonzero, therefore both channels consist of both
horizontal and vertical polarizations as shown in Fig. 3.8. The polarization unit
vectors for the 23.87 ( e^4) and 31.65 ( e]2) GHz channels are given by
e24 = <|>cos0^ - 0 sin0^
(3.79)
e32 = OcosO^ + <j)sin0^
(3.80)
where F and (p are given in an unprimed (3.62) and an unprimed (3.63),
respectively.
In order to include the large-scale tilt, we substitute (3.77) and (3.78) into
(3.79) and (3.80) to obtain the coordinate transform factors, B]- B3, for each
frequency as
65
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31.65 GHz Polarization
(out of the page)
23.87 GHz Polarization
Figure 3.7. The aircraft pitch angle (0^) relative to the radiometer’s polarization
vectors.
66
I
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Linearly 31.65 GHz
Polarized Receiving
Antenna
Linearly 23.87 GHz
Polarized Receiving
Antenna
0
Figure 3.8. Electric field strength that each radiometric channel receives for a
given pitch angle dp.
67
i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
e24' = x [ ( - c o s 0 ncos0cos(})sin0;7) - (cos0Bsin(j) cos0p)
+ (sin0 sin0 sin0 ) ] + y' [ (cos(|) cos0 )
(3.81)
- (cos0 sin(J) sin0p )] + z' [ (sin0n sin<}> cos0p )
+ (sin0n cos0 cos(j) sin0p ) + (cos0Bsin0 sin0p ) ]
e32' = x' [ (cos0Bcos0 costjjcos©^ ) - (sin0Bsin0 cosO^)
- (cos0Bsintj) sin0 ) ] + y' [ (cos(j) sin0p )
(3.82)
+ (cos0 sin(j) cos0p )] + z ' [ - (cos0n sin0 cosO^)
- (sin0Bcos0 cos(J) cos0p ) + (sin0Bsin0 cos©^)].
3.3.5 Extended boundary condition
The EBC method is a technique for calculating scattering from single-layer
periodic surfaces [Chuang and Kong, 1982; Kong, 1986] and two-layer periodic
surfaces [Johnson et al., 1993]. The important equations from these papers are
presented here for completeness. In this method, Huygens' principle is applied at
the surface so that the scattered field can be obtained once the surface fields are
known. The Huygens' integral equation is solved by expanding the unknown
surface fields into a Fourier series and forming a truncated impedance matrix
which is inverted to obtain the surface fields. This method is known as the
extended boundary condition method because the calculations enforce the
68
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requirement that the Huygens' integral which equals the field value within the
region of interest must be zero outside that region. Although the extended
boundary condition method is exact, the numerical formulation becomes ill
conditioned if the surface height-to-wavelength ratio becomes too large [Garcia et
al., 1978].
Recall that the local frame's electric field o f the incident wave is given by
(3.56) and that the periodic structure is uniform in the y~direction. This uniformity
requires all the field components in regions 0 and 1 to be phase matched to the
same exp(ikyjy) dependence. Therefore, we replace all the d/dy terms in Maxwell's
equations with ikyias is commonly done in waveguide theory. The remaining
equations will thus have the exp(ikviy) dependence removed.
Maxwell's equations are now simplified so that the x and z components o f
the electric and magnetic fields can be expressed as functions of the y components
of the fields as
J
i 2 - kyi
i2
kj
kyi '51s E.j y K( r )' + tou.V
x H.y
(r)
nj s
j'
(3.83)
" * ^ , * EjyCr)
(3.84)
Hi*Cr) = h2
kj ~ kh2
y,
where j = 0 and 1 signifies regions 0 and 1, respectively, Vvis the gradient operator
69
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that is transverse to the y direction
V7
d
d
V
= x- —
+ z- —
dx
dz
n 85')
K
J
and s = (x, z) indicates the transverse components o f the fields for region j. The y
components o f the electric and magnetic fields now satisfy the partial differential
equations
(V ,2 + k] ~ k * ) A Jy = 0
where Ajy =
(3.86)
,Hjy. Since Vvoperates only in a two-dimensional space, the y
components o f the electric and magnetic fields satisfy a two-dimensional wave
equation. A periodic Green's function for such an equation has been given by
Chuang and Kong [1982]. This Green's function is
ga
( p , > p ',) =
.
-r
-
.
,
E o - exP [*%«>,(* - *'> +
» =— Pj«
(3-87)
ikjAJz ~z 'l]
where
pf = xx + zz
(3.88)
- A/ -
(3.89)
70
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k
+ n—
a jn = --------------- ,
P,. -
n = 0, ±1, ±2, . . .
■
P,. =‘ K
7 * ■
(190)
< <1
<191>
< > 1■
(192)
The boundary conditions require the continuity of the y component
(tangential) of the electric and magnetic fields at the air-water interface. This
condition yields
E0y = E Xy
(3.93)
Hoy = H Xy ■
(3.94)
The other set o f boundary conditions are given by Chuang and Kong [1982] as
=
y ( n i ' VsH 0y) =
co”l*V,H\y*C2y(ni ' V, Ely'>
(3‘95)
- d0ni XV, E ly+ ^ y ^ l ’ ^ s 11^
(3‘96)
where
71
!
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Ir
co =
_
-
1
ky>
(3.97)
(i)€„
6C1 k O
2j
C2 =
lr
do =
_
(3.98)
eo k l
-
1
(3.99)
*i
d =
(3.100)
^0 k u2
<0 = 2rc/j e0 and e, are given in section 3.3.7, and n0= |i, =4tc * 10'7 (H/m), the
free space permeability.
The above four boundary conditions are used for solving the unknown
surface fields. These surface fields are expanded in the Huygens' integral
equations into a sum of unknown amplitude basis functions using the EBC
method. The results [Johnson et al., 1993] lead to the following coupled matrix
equation
72
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t
■ij
Bn
[0]
co C0
a
aoi
P
aoi
Y
0
8
0
0j
-dK
d ku
[0]
2T
K 0s
■
.
.* >
[0]
[0]
(3.101)
[°]
[0]
*r
where
aj
-1 a,.a„
*
exp
2%
■i(m - n ) — x - i*; j (±P, „)/,(* ) dx
(3.102)
\JPjmJx, (S)
-i
(3.103)
exp -i(m - n ) ^ - x - ikJs(±$Jm) f x(x) dx
K fc .
»
= a. B
J"
(3.104)
where (S) indicates that the integration is over the surface, f { x ) is the surface
profile, A, is the wavelength of the surface, m and n are integers (m is not the rms
slope for the remainder of this chapter), the surface field unknowns are given by a ,
73
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]J, y, and^, and
(3.105)
a,0 1 R
and
_ E0 _
_ _
ko — ( * / x e , ' y )
(3.106)
CO fX
where 8n0 =1 for n = 0, and <5n0 = 0 for«*0.
The above cTm elements are determined by the y ~component o f the incident
electric and magnetic fields. Truncating the Fourier series of the surface field
unknowns results in a finite matrix which can be inverted to obtain the surface
field unknowns. Fifteen basis functions (m, n = -7, -6, - 5 , . . . 0 . . . 5,6, 7) are
used. This number o f basis functions provided accurate results for the height-toperiod ratios encountered in this research [Chuang and Kong, 1982].
All the equations in this section are in the local reference frame, i.e., the
primed frame. Therefore, we substitute (3.81), (3.82), and (3.72) into (3.105) and
(3.106) to obtain
(3.107)
(3.108)
74
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ki
* ,
X e24 '
X
*32
~
y
* ?
*
X e24' * / = " ( * , / Z24 + fcr / A24)
k i'
V
X
*32 '
* /
=
- (
V
Z 32
+
(3-109)
( 3 - 1 1 0 )
where
X24 = - cos0 cos(j) cos0BsinSp - sin(j) cos0HcosS^ + sin0 sin0Bsin(J)p (3.111)
Y24 = cos<j)cos0D - cos0 sin(J) sin0o
(3.112)
Z24 = sin(j) sin0Bcos0^ + cos0 cos(}) sin0Bsin0p + sin0 cos0Bsin©^ (3.113)
X22 - cos0cos(j>cos0ncos0p - sin0sin0Bcos0p - sin<j)cos0Bsintj^ (3.114)
Y32 = cos<J)sin0 - cos0 sintf) cos0
Z32 = sin0 sin0n cos0 - cos0 cos(f) sin0Bsin0
(3.115)
- sin0 cos0Bcos0^. (3.116)
The upward field amplitudes are then calculated to be
^01
~ co
P-
c;
a
(3.117)
Os
15
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The above coefficients are the amplitudes of the y ~components o f the
scattered electric and magnetic fields. The x and z components can be calculated
from (3.83) and (3.84). The scattered plane waves in region zero propagate along
the directions determined by F0n+. Once the amplitudes o f the scattered modes are
calculated, the emissivity of the surface can be obtained by integrating the total
power reflected over the upper hemisphere and then applying Kirchhoff s law to
obtain the emissivity corresponding to the polarization o f the incident field. For
the
propagating scattered Floquet mode, the power reflectivity is given by the
power transmitted in the ^direction divided by the incident power and is found to
be
rn
(3.119)
where q 0 = (|i0/e0) ,/2,and a 0!0 and a(h)0]0 are defined in (3.105) and (3.106),
respectively. The polarized brightness temperature of the ocean surface, Tba, is
then given by
(3.120)
76
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where the sum n is over the propagating modes reflected, r„, for an incident wave
polarized in the a direction for a physical ocean skin temperature o f Tskin.
3.3.6 Sinusoidal corrugated surface
For a sinusoidal corrugated surface/i (x) = - hscos (2tvc/As), the A ±, B~, and
C * matrices described in the previous section can be obtained by carrying out the
integrations in (3.102) - (3.104). The results from Chuang and Kong [1982] are
•1 + a
=pJ m
b;
VJ m
-i
-a
ajn
(±0'— 1
( ±z) |m' B|
j”
( i i ) 1" - ’ 1
(3.121)
(.kj s hs $jm)
(3.122)
(3.123)
where J\ m. nj(kj shs$Jm) is the Bessel function of integer order \ m - n \ and argument
k j* h sPjm -
11
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3.3.7 Complex Permittivity of Sea Water
The complex permittivity o f sea water (e,) is calculated by using the Liebe
et al. [1991] pure water model with a salt term added to the complex part of the
permittivity. This model was recommended by Dr. Alison [1994] o f King’s
College London, an expert in the complex permittivity measurement of sea water
at microwave frequencies and also by Guillou et al. [1996]. The Liebe et al.
[1991] model represents one o f the most current experimental permittivity data of
pure liquid water. This single Debye model eDo f experimental data below 100
GHz for pure liquid is given by
M /) ‘
* e-
<3' 124>
where
e0( T ) = 77.66 - 103.3 -6,;
0, = 1 -300/(273.15 + 7);
T is the water temperature, °C;
e„ = 0.066-eo ;
Vi) = 20.27 + 146.5-0; + 314-0;2, GHz; and
/ is the frequency, GHz.
The salt term is given by Stogryn [1971] as
78
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CTe
es
1
2 7i e 0f
(3.125)
where
e0 = 8.854x1 O'12, F/m;
o = S J 0 .1 8 2 5 2 - 1.4619 x 10’X
+ 2.093 x 10'5S2iW- 1.282 x l O ^ J ;
Ssw is the salinity in parts per thousand, °/00;
<j>, = 4[2.033 x lO'2 + 1.266 x 104 J + 2.464x lO-6^ 2- S*, (1.849 x 1O'52.551 x 10'7A + 2.551 x 10’8 A 2) ] ; and
4 = 2 5 -1 .
The permittivity of sea water (e,) is given by the sum o f (3.124) and
(3.125)
e, = 6d + es .
(3.126)
A comparison between the Leibe et al. [1991] and the Klein and Swift
[1977] complex permittivity models for a 33.5 °/QQsaline water solution versus
temperature at 23.87 and 31.65 GHz is shown in Fig. 3.8. The curves in Fig. 3.9
shows that the Leibe et al. [1991] values are greater than the Klein and Swift
[1977] values by about 10%.
3.4 Summary
79
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40
Uebe 23.87 GHz
31.65 GHz
Wen 23.87 GHz
Wein 31.65 GHz
1
3 0 -
5
©
CO
o
27
(0
j
IL
* •-
>
©
CL
0
20
10
30
Temperature (deg C)
40
35
CQ
©
CO
30
Uebe 23.87 GHz
Uebe 31.65 GHz
25
KJen 31.65 GHz
20 1
10
20
30
Temperature (deg C)
Figure 3.9. (a) Real and (b) imaginary parts of the complex permittivity of sea
water versus temperature for 23.87 and 31.65 GHz. Salinity o f sea water is 33.5
°/' 0 0 -
80
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A two-scale emission model of the ocean surface was formulated. The
NOAA microwave radiometer parameters, as pertinent to the SCOPE operations,
were incorporated into this model. This revealed that the main emission
contribution from such a surface occurs when the small roughness was averaged
over the distribution of the surface normals of the large-scale features. An
asymptotic evaluation o f the integral describing this averaging process showed that
the small waves were tilted by the large roughness at prescribed angles related to
the wind speed. This model is valid for wind speeds less than 12 m/s, so the foam
contribution to the brightness temperature is negligible at all microwave
wavelengths. Therefore, the foam coverage is not included in this model.
A one-dimensional Gram Charlier slick-surface slope profile was used for
the large-scale waves. On the other hand, the small-scale features were chosen to
have a sinusoidal corrugated profile. The EBC method was used to calculate the
brightness temperature produced by a tilted periodic surface for an arbitrarily
linearly-polarized electric field. This method permitted the small-scale roughness
to be similar to the incident electromagnetic wavelength.
Also incorporated into this model was the Liebe et al. [1991] pure water
model with an added salt term. This provided an up-to-date model o f the sea
water’s complex permittivity.
81
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4. SCOPE MEASUREMENTS
Although ground-based microwave radiometer measurements o f water
surfaces with artificially constructed directional features [Johnson et al., 1993;
Yueh et al., 1994a] have provided physical understanding into the mechanisms of
the azimuthal brightness temperature variations, such sinusoidal profiles are too
simplistic to represent actual ocean surfaces. Therefore, open-ocean measurements
are needed to compare the applicability of coupled atmospheric and oceanic
emission models. A recent ocean experiment, SCOPE, was performed in
September and October 1993 by ETL to provide a better understanding of
microwave scattering and emission from the ocean surface. This section focuses
on the SCOPE instruments used for measuring and calculating the emissivity of
the combined atmosphere and rough ocean surface.
4.1 Background
SCOPE was a measurement program that utilized San Clemente Island as
an instrument platform for microwave remote sensing of the real ocean surface
under a variety o f oceanographic and meteorological conditions near an underwater
sea mount, other bathymetric features, and targets of opportunity. This experiment
was carried out from the middle of September through early October 1993 to
82
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provide a better understanding o f microwave scattering and emission from the
ocean surface.
Several instruments were deployed at various locations during this
experiment to meet the SCOPE objectives. In particular, an aircraft, two ocean
research vessels, and San Nicolas Island served as platforms for the remote sensing
and in situ instruments pertinent to this research. Specifically, the aircraft-based
microwave radiometers are used to measure remotely the emission from the rough
ocean surface and thereby infer the near-surface wind vector. In contrast, the
ocean vessel- and island-based instruments are used to measure the wind vector
and to compute the total emission at the aircraft. These measurements are used in
part to determine the feasibility o f application to the detection o f near-surface wind
speed and direction by passive microwave radiometers. Although microwave
radiometers can measure ocean wind speeds based on the sensitivity o f thermal
emission on surface roughness, the wind direction measurement from them has
only recently been observed. A few experimental observations [Etkin et al., 1991;
Irisov et al., 1991; Wentz, 1992; Dzura et al., 1992] before SCOPE indicated that
passive microwave radiometer measurements are sensitive to wind direction.
These observations showed that ocean thermal radiation could vary over azimuthal
angles relative to the wind by a few kelvin.
4.2 Focus of Present W ork
83
with permission of the copyright owner. Further reproduction prohibited without permission.
From 15 September through 4 October 1993, the NOAA King Air C-90
aircraft participated in SCOPE off the Southern California coast. In situ
measurements o f several sea surface, subsurface, and atmospheric quantities (see
section 4.3) were made from the moored Scripps research vessel the FLoating
Instrument Platform (FLIP), the NOAA R/V Titan, and San Nicolas Island. FLIP
was moored at 33.10 N and 118.7° W and Titan sailed to various locations
between the two islands. San Nicolas Island was the land-based radiosonde launch
site for SCOPE. The location of this experiment was between San Clemente and
Santa Catalina Islands as shown in Fig. 4.1.
Flight tracks for the NOAA aircraft were done at specified way points with
the radiometer’s antenna system fixed in the downward-viewing mode. The way
points were automatically selected by inertial navigation system equipment aboard
the aircraft. At each of the way points, the aircraft performed 360° banked turns at
a roll angle o f approximately 32°. A roll angle of 32° was chosen to minimize the
time per revolution and thereby maximizing the number of locations where the
turns would be made.
The aircraft flew 203 different way points during this time period. Sixteen
of the 203 way points were accomplished around Titan and FLIP. These sixteen
way points provided the necessary instrument measurements to compare measured
and calculated brightness temperatures. Table 4.1 shows the vessel, Julian date,
start time, stop time, number of 360° turns, aircraft altitude, and cloud conditions
84
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Santa
Rosa Island
Santa Cric
Island
\ Los
j
Angeles ;
Channel
Islands
Santo Barbara
Island
I
^
\
Santa
J Catalina
Titan • , ,
Islana
Radiosonde
Site
FLIP
33°
Aircraft
Operations
San C km entc
Isiand
-
120°
10
-119°
0
LLhHH
10
0
20
40
-11SC
60
1------- 1— 1-------------h
50
100
80
100 Miles
1--------1— 1
150 Kiiometere
Figure 4.1. Geographical location o f SCOPE. The airborne radiometers are flown
between San Clemente and Santa Catalina Islands. The radiosondes are launched
from San Nicolas Island. The moored position o f FLIP is shown. The Titan
position is shown on 17 September 1993 at approximately 2000 Universal Time
Coordinated (UTC).
85
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4.1. Some parameters associated with the aircraft’s way points at Titan and
FLIP. The Julian days are for the year 1993 and the UTC time is in
hours:minutes:seconds.
Aircraft
Altitude
Clouds
Present
(m)
(Y/N)
2
100
Y
17:18:00
4
100
Y
19:11:25
19:17:00
3
100
Y
260
18:17:15
18:23:00
4
100
N
Titan
260
19:50:00
19:58:00
4
100
N
Titan
262
17:46:15
17:48:45
1
200
Y
Titan
262
19:01:30
19:04:25
2
200
N
Titan
262
20:13:15
20:15:45
2
100
N
FLIP
262
20:27:55
20:31:00
2
100
Y
Titan
265
22:25:20
22:27:50
2
100
Y
FLIP
265
22:29:15
22:32:25
2
100
Y
Titan
265
23:50:50
23:53:00
2
100
Y
Titan
266
00:19:15
00:21:30
2
100
Y
FLIP
266
00:27:40
00:30:50
2
100
Y
FLIP
267
22:15:55
22:19:05
2
100
Y
FLIP2
270
23:08:00
23:14:00
2
100
N
Vessel
Day
Start
Time
Stop
Time
(Julian)
(UTC)
(UTC)
FLIP1
258
17:15:30
17:19:30
Titan
258
17:51:35
FLIP1
258
FLIP
360°
Turns
1The instruments on FLIP were not operational.
2 The aircraft radiometer was not operational.
86
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for these 16 cases. Experimental and theoretical results are only compared when
there were clear skies because the RTE software is accurate only for these
conditions. Modeling clouds in the RTE software is very difficult and usually
inaccurate because the vertical profile o f cloud liquid is not measured by
radiosondes. With this constraint, there are only four cases in Table 4.1 that are of
interest for this comparison. These four cases, including the measured in situ wind
speed and direction at 10 m elevation, are listed in Table 4.2. The wind direction
is relative to true north (0°). The required RTE inputs are obtained by radiosondes
measurements launched from San Nicolas Island. These radiosondes were
operated by the United States (US) Department o f Defense (DoD).
Table 4.2. Some parameters associated with the aircraft’s way points at Titan and
FLIP during clear sky conditions. The Julian days are for the year 1993.
Day
Start
Time
Stop
Time
Aircraft
Altitude
Wind
Speed
Wind
Direction
(Julian)
(UTC)
(UTC)
(m)
(m/s)
(deg)
FLIP
260
18:17:15
18:23:00
100
6.5
291.0
Titan
260
19:50:00
19:58:00
100
7.8
275.8
Titan
262
19:01:30
19:04:25
200
3.7
243.8
Titan
262
20:13:15
20:15:45
100
3.7
241.9
Vessel
These four way points are screened further in section 5 to determine which
circle flights are applicable for comparing the measured and theoretical brightness
87
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
temperature results.
4.3 Instrumentation
Several instruments were required to measure and to model the downwardviewing radiometric brightness temperatures. The brightness temperatures were
measured by two microwave radiometers on the NOAA aircraft. In contrast,
several different instruments provided data that were needed to compute the
microwave brightness temperatures. Other instruments provided ocean-surface
truth measurements for near-surface ocean wind speed and direction. Each
instrument is described below.
4.3.1 Microwave radiometer
The technology involved with the development o f this airborne radiometer
system is soundly based on years of experience within ETL in ground-based
zenith-viewing radiometry [Hogg et al., 1983]. The nadir-viewing requirement
came later as ETL needs changed [Fedor et al., 1988]. This modification required
a change in the lower operating frequency and a new fairing for the antenna
structure; otherwise, the impact on the rest o f the antenna structure was minimal.
The lower frequency was changed from 20.60 GHz to 23.87 GHz to provide
88
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protection from actively transmitting sources, i.e., the frequency band around 23.87
GHz is in the protected passive frequency band.
4.3.1.1 Antenna configuration
There are several key design parameters associated with this antenna. One
o f the most difficult facets in the design o f this radiometric system is to prevent
liquid from forming on the antenna surfaces when it is in the zenith position. The
antenna is designed without a radome because exposed reflectors provide better
performance than do radomes in wet conditions [Blevis, 1965; Jacobson et al.,
1986].
Other important parameters are that a single antenna must accommodate
both radiometric channels, that the two beams of the antenna must be coaxial, and
have approximately the same width [Hogg et al., 1979]. Equality o f the
beamwidths and coaxial alignment are necessary to ensure that clouds enter and
exit the beams o f the two systems simultaneously. Furthermore, this will ensure
that both beams are viewing the same ocean surface area. The two frequencies
differ by 30%, so the horn must have at least a 30% bandwidth. To meet this
constraint and the equal beamwidth criterion, a corrugated feed horn was used.
This type o f hom has already had successful application in ground-based dual­
channel systems [Hogg et al., 1983] and, therefore is also used in this aircraft
89
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design. The beamwidth o f a corrugated hom decreases approximately inversely
with frequency. Overall equality of beamwidths is achieved by use o f an offset
paraboloidal reflector with the corrugated feed hom. In addition, the operating
frequencies employ orthogonal linear polarizations for separating the two channels.
The most severe physical constraint on the antenna is the physical size that
can be accommodated by an available window in the NOAA King Air C-90
aircraft. The diameter that one of these windows can accommodate, allowing for
mounting and dismounting from inside the aircraft, is about 40 cm.
The basic antenna design is that of a prime-focus-fed partial paraboloid
offset at an angle o f 90°. This geometry is shown in Fig. 4.2. The focal length is
15.24 cm. The perimeter o f the reflector is elliptical (see insets), and the
subtended aperture of the system is about 25.4 cm in diameter. The pressurecompensating corrugated feed hom is shown in Fig. 4.3 at the focal point F of the
paraboloid. The aperture of this hom is located 2.54 cm "in front" of F to obtain
good phase center performances at each frequency. The unique pressurecompensating feature is addressed below. In the implementation for the NOAA
aircraft, the paraboloid is made rotatable about the axis shown dashed in Fig. 4.2,
for viewing up or down.
This offset antenna has no blockage in the aperture; therefore there is no
scattering that would degrade the radiation patterns. This is especially beneficial
for the noise performance o f the antenna. Measured far-field radiation patterns for
90
i
I
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OFFSET PARABOLOID FOR AIRBORNE RADIOMETER
(Central Cross Section)
View A-A’
Ellipse
b = 12.70 a n
X‘ = 24V
Angle
Softeners
22 °
Axis of Rotation
>
Partial
Paraboloid
Feed Hom
V (Vertex)
X (cm)
Figure 4.2. Side view of offset parabolic reflector's geometry with the feed horn
[after Jacobson et al., 1994].
91
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CORRUGATED HORN
Circumferential
Microoorous Tube
Plastic Tube'
Sealed
Pressure
Sealed
Pressure
Fitting
1.016
13.5'
0.102
0330
1331
1.006
1.407
0.051
0.635
Low-Loss Foam
y
48 Corrugations
0.102
—2210
0.635
1219
Stainless Steel
Taper Section
■7366
Dimensions in Centimeters
Figure 4.3. Detailed side view drawing of the pressure-compensating corrugated
feed hom [after Jacobson et al., 1994],
92
I
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the feed hom are shown in Fig. 4.4 for 23.87 and 31.65 GHz. The horn's half­
power beamwidths are shown in Table 4.3. The overall antenna radiation patterns
are discussed in section 4.3.1.2.
Table 4.3. Half-power beamwidths for the corrugated pressure-compensating feed
hom.
Frequency
E-Plane
Half-Power
Beamwidth
H-Plane
Half-Power
Beamwidth
(GHz)
(deg)
(deg)
23.87
16.5
19.0
31.65
14.0
15.4
The offset paraboloidal section is firmly mounted on the inner o f two
concentric cylinders that are about 38 cm in diameter and 51 cm long (Fig. 4.5).
The inner cylinder can be rotated on the two bearings mounted on the outer
cylinder. In this way the beam can be rotated in elevation. Appropriate top and
bottom holes in the outer cylinder and fairing allow for the beam to be rotated to
either zenith or nadir. The outer cylinder is welded to an external aircraft skin that
fits around the window, which in turn bolts into the aircraft's fuselage. The fairing
fits over this outer cylinder. The inner cylinder can be rotated from inside the
aircraft by hand or a motorized chain drive.
93
with permission o f the copyright owner. Further reproduction prohibited without permission.
'3.87GHz
2 3 .8 7 ffl
-10
— -15
a. -20
-25
E-Plane
H-Plane
-30
-35
-30 -20 -10 0 10 20
Angle (deg)
■20 -10 0 10 20 30
Angle (deg)
j1.65GHz
-10
a.
-20
-25
H -P lan e
E -P la n e
-30
-35
-30 -20 -10 0 10 20
Angle (deg)
■20 -10 0 10 20 30
Angle (deg)
Figure 4.4. The measured amplitude radiation patterns o f a 5.1 cm aperture
hybrid-mode corrugated feed hom in the two principal planes (a) and (b) for the
23.87 GHz channel received in horizontal polarization; (c) and (d) the 31.65 GHz
channel received in vertical polarization [after Jacobson et al., 1994].
94
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
AIRBORNE MICROWAVE RADIOMETER
45.72 cm
Blank for
W indow
R ad iatio n from
C loud Liquid
a n d V apor
Fixed
C ylinder
R o ta tab le
C ylinder
E lectro n ics
Box
B earing
M icroporous Tube
O u ter Microwave
Axis of
Rotation
.Window..........
F eed Horn
O ffset
Paraboloid*
R adiation from
th e O cean and
th e A tm o sp h ere
Figure 4.5. Schematic side view of the antenna and reflector system and housing
for the airborne microwave radiometer [after Jacobson et al., 1994].
95
j
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Another critical factor in the design o f this antenna is the feed horn's
microwave window. As indicated in Fig. 4.5, the aperture of the feed hom must be
covered by a microwave window to prevent foreign objects from entering the
radiometer waveguides. When the aircraft is in flight there is a difference between
the inside waveguide cavity pressure and the outside atmospheric pressure. This
differential pressure bends the window which is typically made of a low-loss
polymer only a few millimeters thick to prevent excessive microwave loss and
reflection. The bending of the thin window could produce undesirable fluctuations
in microwave reflection in the radiometer [Jacobson et al., 1988]. Therefore, a
pressure-compensating circuit, as indicated in Fig. 4.3, is used to minimize the
bending o f the window. This circuit provides a safe pressure differential across the
foam window by equalizing the radiometer waveguide pressure and the outside
atmospheric pressure. The outer micro porous tube is placed around the perimeter
of the foam window. This feature minimizes the pressure difference across the
window and also provides a clean environment for the feed hom and associated
waveguides. A short plastic tube connects the micro porous tube to the feed horn's
pressure fitting; this m inim izes the circuit's response time to less than one second.
The waveguide pressure is isolated from the aircraft cabin pressure by using an 0 ring gasket at each waveguide flange. The window is made of a 0.635 cm thick
low-loss closed-cell foam. This window produces hom power return loss o f -33.5
dB at 23.87 GHz and -29.0 dB at 31.65 GHz. The pressure circuit has performed
96
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very well on all flights, even flights up to altitudes o f 6 km above sea level.
The antenna's performance in flight also depends on the fairing. The
present fairing, shown in Fig. 4.6, minimizes both the airflow obstruction on the
aircraft and the liquid buildup on the upward viewing paraboloid. Figure 4.7 is a
photograph o f the antenna fairing mounted on the NOAA King Air C-90 aircraft.
The fairing is shown by the bird emblem on the fairing’s end cap. Its zenith and
nadir viewing holes above the aircraft’s identification letter F. The downwardviewing aperture does not normally encounter this liquid problem. Both aperture
diameters are about 28 cm. The design of the fairing's body is based on a National
Advisory Committee for Aeronautics (NACA-0024) profile [Abbott and Doenhoff,
1959] with a modified airfoil ratio o f 3:1, which ratio is determined by the fairing's
length (113 cm) to its height (38 cm). This nonmetallic composite-material fairing
is stronger and lighter than similar aluminum fairings. The fairing was designed
and constructed under the direction of the NOAA Aircraft Operations Center
(AOC) [Patten, 1994]. It was approved by the Federal Aviation Agency (FAA)
after several FAA flight tests. In preparation for these flight tests, several 15 cm
long tufts were distributed around the fairing about every 8 cm. During each
flight, the tufts' patterns were photographed from a nearby aircraft. The tests were
performed at different aircraft speeds with and without the fairing. Accelerometers
were positioned on the aircraft's tail to measure the frequencies induced by the
fairing. The flight results showed the fairing to be acceptable for operation on the
97
!
with permission o f the copyright owner. Further reproduction prohibited without permission.
Figure 4.6. Composite-material fairing for aerodynamic stability and deflection of
potential water flow. The fairing's end plate and antenna housing have been
removed [after Jacobson et al., 1994],
98
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 4.7. Side view of the antenna's fairing on the NOAA King Air C-90
aircraft. The fairing is recognized by NOAA's bird emblem on the fairing's end
cap. Furthermore, the fairing's zenith and nadir viewing holes are located above
the aircraft's identification letter F [after Jacobson et al., 1994].
99
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
NOAA aircraft.
4.3.1.2 Antenna pattern measurements and implementation
To verify that the dual-frequency radiometer met the design criteria, the
pattern o f the upward-viewing port was measured on the National Institute of
Standards and Technology (NIST) 2.4 m x 2.4 m planar near-field (PNF) range.
The basic components of a planar near-field measurement system are shown in Fig.
4.8. Because of time constraints, only the upward-viewing port was measured.
This technique uses near-field amplitude and phase measurements and a fast
Fourier transform (FFT) to determine the far field of the antenna under test (AUT).
Nominally, data are acquired at equally-spaced points on a plane. To satisfy the
sampling criterion, a sample spacing of one-half wavelength or less was used. The
AUT’s far-field is determined from [Newell and Crawford, 1974]
t (K)-s (K) = — ------ [ jB 0'(x,y)e '*lZe >k,ydxdy
(4.1)
where K = kxe ’x + kyTy is the transverse component o f the propagation vector, ex
and e^are unit vectors in the x andy directions, tI0 is the vector far-field spectrum
of the AUT, s02 is the vector far-field spectrum o f the probe used in the
measurement, y is the z-component o f the propagation vector, d is the distance
between the AUT’s aperture plane and the probe’s aperture plane (scan plane), F
100
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Scan Plane
Isolator
Probe Isolator ( Mixer
Generator
Load
Test Antenna
RVA
Mixer
Receiver
Synthesizer
Coupler
Sig. Ref.
[Out
Figure 4.8. Basic components of a planar near-field measurement system. The
rotatary vain attenuator (RVA) provides adjustable power to the transmitting
antenna.
101
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is the impedance mismatch factor, A ' is the normalization due to the insertion loss,
B 'o is the normalized near-field voltage amplitude and phase, and x and y are the
position coordinates within the plane. A detailed description of the PNF theory
can be found in [Kems, 1981] while the measurements are described in detail in
[Newell and Crawford, 1974].
A K-band standard gain hom was used to measure the antenna near-field
amplitude and phase at 23.87 GHz, while a K^-band standard gain hom was used
to measure the radiometer at 31.65 GHz. The main-component pattern o f a
standard gain hom can be calculated from theory [Chu and Semplak, 1965]. This
calculation allows probe correction to be performed on the main-component
principal-plane patterns. Figure 4.9 shows the resulting far-field E- and H-plane
patterns for 23.87 (dashed line) and 31.65 GHz (solid line). Table 4.4 contains the
results for the half-power beamwidths.
Table 4.4. Half-power beamwidths for the overall antenna.
Frequency
E-Plane
Half-Power
Beamwidth
H-Plane
Half-Power
Beamwidth
(GHz)
(deg)
(deg)
23.87
3.7
3.5
31.65
3.6
3.1
102
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E-Plane
31.65 GHz
23.87 GHz
-10
-20
2 -30
"a.
|
-40
-50
-60
-30
-25
-20
-15
-10
0
10
15
20
25
30
25
30
Elevation (deg)
H-Plane
31.65 GHz
23.87 GHz
-10
-20
3
-30 -
"a.
< -40
-50
-60
-30
-25
-20
-15
-10
0
5
10
15
20
A zim uth (deg)
Figure 4.9. Principal far-field (a) E-plane and (b) H-plane patterns at 23.87
(dashed line) and 31.65 (solid line) GHz, of overall antenna, calculated from full
two-dimensional planar scans, including probe correction [after Jacobson et al.,
1994],
103
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The main-beam patterns and the half-power beamwidths are nearly the
same at both frequencies for both principal planes to within about 10%. This is
especially true for the principal E-plane patterns, which have main beams that
nearly coincide down to about -15 dB. However, the principal H-plane pattern at
23.87 GHz is slightly broader in the main beam than the principal H-plane pattern
at 31.65 GHz. The three-dimensional far-field patterns for 23.87 and 31.65 GHz
are shown in Fig. 4.10. The half-power spot diameter of this radiation pattern at
100 m for a 32° incidence angle (typical aircraft radiometer parameters at the way
points during SCOPE) is about 8.5 m.
Calculation of the observed antenna brightness, B(Ta), requires knowledge
of the three-dimensional antenna pattern as given in (2.5). Equation (2.5) is
repeated here again
[
|
B (T (Q, $)) F„(0,4>) sine dQ rf4>
*<r .> = *‘° 7 „
f , --------------------------------- •
(2-5)
I
I F n(0, (j)) sin0 dQ <i(j)
J(j) =0 J q=o
This expression assumes that the brightness (emission) from different
directions is uncorrelated, since the brightness (powers) are summed directly. For
our antenna, each antenna brightness is calculated by averaging noncoherently over
841 points in each o f the above three-dimensional extrapolated antenna patterns.
In other words, the total solid angle is replaced by the 841 antenna pattern points
104
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 4.10. Three-dimensional far-field patterns at (a) 23.87 and (b) 31.65 GHz
of overall antenna.
105
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
distributed over the main lobe region (~ ±11 °).
Therefore, the observed antenna brightness, B(Ta), is rewritten as
841
£
B
i T
BVtJK
-----------
^
(4 2 )
£
n =1
where the subscript n refers to a unique observation angle ( 0 ,4>) in the antenna's
main-lobe pattern, F„, for incident brightness B(Tin). Hence, the observed antenna
temperature, Ta, can be extracted from B(Ta) by (2.17) and (2.18).
4.3.1.3 Electronics package
The radiometers are o f the Dicke switching type with automatic gain
control [Hazen et al., 1995]. Table 4.5 lists the basic characteristics o f the
radiometers. The accuracy and sensitivity values are for a one second integration
time. Absolute accuracy values were estimated by including the previous ETL
radiometric values [Fedor et al., 1986], the sensitivity values of this radiometric
system, and the tipping curve structure noise (see section 4.3.1.4). The large
sensitivity values clearly indicate excessive noise in the radiometric system.
Unfortunately, this additional noise reduces the radiometer’s capability to measure
the desired small brightness temperature variations from the ocean surface.
106
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Table 4.5. Radiometer characteristics during SCOPE.
Radiometer 1
Radiometer 2
Center frequency
23.87 GHz
31.65 GHz
Bandwidth
1 GHz
1 GHz
Receiver noise temp.
539 K
528 K
Accuracy1
~3K
- 3K
Sensitivity1
0.36 K
0.39 K
Polarization2
horizontal
vertical
1For a one second integration time.
2 With respect to the aircraft’s flight direction.
The radiometer design can best be understood by following the block
diagram. Fig. 4.11. Emission signals are focused into a wideband feed by an offset
25 cm x 25 cm paraboloidal surface (not shown in the block diagram). Following
the antenna feed, the two frequencies are split by an orthogonal mode transducer
and passed to the two radiometers. The through port o f the splitter is stepped
down in size to the 31.65 GHz waveguide, and the 23.87 GHz signal is taken from
the sidewall port. The switch is a three-junction, five-port, ferrite device: it
requires slightly over one microsecond to settle after being switched and can be
toggled at a 2 kHz rate. The design of the radiometers extends the normal Dicke
design by adding a second calibration source to the switching sequence [Guiraud et
al., 1979]. The source we refer to as the reference load is a temperature controlled,
waveguide termination; the temperature is controlled at 318 K, a level higher than
107
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31.65 GHz Radiometer
'Reference Load
Attenuator
Local
Oscillator
Horn
Mixer
IF Amplifier
Video Detector
Frequency
. Splitter
Voltage /
Frequency
Converter
Signal
Output
to Computer
Circulator
Driver
Computer
Control
Video
Amplifier
‘Hot Load* A
Temperature
Control
Temperature
Monitors
Analog
Temperatures
23.87 GKz Radiometer
Figure 4.11. Electrical layout of the ETL microwave radiometer; temperature is
monitored at points marked by asterisks.
108
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the expected ambient will reach. The second source, the "hot load", is also a
temperature controlled waveguide termination at 418 K. Junctions A and B are
used to connect in sequence the antenna, the hot load and the reference loads to the
mixer through junction C.
The microwave mixers are o f balanced design, using selected low noise
Schottky-barrier diodes. Incorporated in the mixer package is a series of thin-film
wideband amplifiers with a video detector at the output. A 50 MHz high-pass
filter is added in the intermediate frequency (IF) section to reduce shot noise; to
maximize sensitivity no other filtering is added. The high side of the band pass o f
the amplifiers exceeds 1.5 GHz. The signal is then directed into the video
amplifier for three processes. First, the 0 Hz offset o f the IF amplifier is removed.
Next, the signal is filtered by a 2 kHz low-pass filter to eliminate noise and
aliasing. And last, the signal is amplified to produce between a 0 and 10 volt
signal at the input to the voltage-to-frequency converter. The voltage-to-frequency
converter, as the name implies, converts the voltage signal to a frequency signal.
This signal is stored in the computer and recorded as counts.
The dotted lines surrounding areas in the block diagram (see Fig. 4.11), are
areas under temperature control; thermistors are used as the temperature-sensing
elements. The hot load and reference load are temperature controlled, and we also
include the ferrite switch block with the reference load. In addition, the feed horn,
frequency splitter, and associated waveguides are temperature controlled. These
109
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temperature controlled elements ensures that the associated waveguide losses do
not modify our reference noise level. A 0.1 °C temperature control for the
:
reference load and hot load is maintained for weeks on end. The whole electronic
package is temperature stabilized near 37°C. These temperatures values are
measured by the computer.
4.3.1.4 Calibration
Two procedures are used to calibrate the ETL microwave radiometers
[Decker and Schroeder, 1991]. One technique uses collocated radiosonde data
during clear sky conditions with an atmospheric absorption model to calculate the
absolute value o f atmospheric radiation that should be observed. The other
technique uses the known dependence of radiation on elevation angle to calibrate
the radiometer directly during clear sky conditions, without radiosonde
information. The first method requires a set of radiosonde data corresponding in
time and place to the radiometer measurements. Since clear sky brightness
temperature variations near zenith are fairly small at the radiometer’s operating
frequencies of 23.87 and 31.65 GHz, the upward-viewing aircraft radiometer could
be flown in an ascending or descending spiral pattern to obtain sufficient
brightness temperature variations. Unfortunately, the radiosonde launch site was
located about 100 km northwest of the SCOPE aircraft operations (see Fig. 4.1).
110
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i
with permission of the copyright owner. Further reproduction prohibited without permission.
Therefore, the second method was used in calibrating the microwave radiometers.
The radiometers were calibrated when the aircraft was on the ground by the
tipping curve method as outlined by [Hogg et al., 1983]. These calibrations were
made on cloudless days when the emission from the atmosphere was stable.
Scanning the antenna in elevation allowed absorption measurements to be plotted
against the number o f air masses (linear versus secant of the zenith angle). A
separate structure was placed on top of the fairing during calibrations to provide
this scanning capability (see Fig. 4.12). It consists of two 43 cm * 30 cm elliptical
aluminum flats inclined at 45°; hereafter called the tipping curve structure. Flat 1
is fixed and flat 2 is rotated in elevation to the desired angles. This calibration
accounts for losses and emissions between flat 2 and the radiometer detector
output. These calibrations were performed after every aircraft flight.
Unfortunately, the tipping curve structure introduced an increase in
brightness temperature to the radiometers. A controlled test during clear sky
conditions showed that this structure increase the zenith brightness temperatures
by about 5.7 and 2.0 K for the 23.87 and 31.65 GHz channels, respectively. This
occurs primarily because the two reflector’s apertures were not large enough to
properly reflect the near-field energy pattern produced by the overall antenna at
both frequencies. Therefore, these two reflectors produced radiation spillover at
both frequencies, which increased both brightness temperature values due to the
hot temperatures from surrounding objects. The 23.87 GHz channel produced a
111
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
■RATI
cm
RATI
45°/
45°,
36 cm
Fairing—'
23.87,31.65 GHz
Radiometers
Offset Parabloid
Figure 4.12. Side view of the tipping curve structure on top o f the NOAA aircraft
radiometer antenna structure; a central ray from the zenith is shown as dashed lines
with arrows. Flat 1 is fixed in position and flat 2 can be rotated in elevation. Each
flat consists o f a 43 cm * 30 cm elliptical aluminum plate located at 45° with
respect to the horizontal. Dimensions are in centimeters.
112
i
!
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
larger brightness temperature change than the 31.65 GHz channel because the
23.87 GHz channel produced a larger near-field beamwidth than the 31.65 GHz
channel near-field beamwidth. Consequently, there was more radiation spillover
(increase in brightness temperature) at 23.87 GHz than at 31.65 GHz.
These offset brightness temperature measurements, 5.7 and 2.0 K, were
subtracted from their respective measured brightness temperatures during
calibrations to account, to first order, for the tipping curve structure. These new
brightness temperatures are called the corrected brightness temperatures, Tbc. The
corrected brightness temperatures are then used in the following equation [Hogg et
al., 1983] to find the corrected absorption (attenuation)
= l n t( ^
- 2 -7W * r - ^ ) ]
(4.3)
where xc is the corrected absorption (attenuation) in nepers, Tm is the mean
radiating temperature for the atmosphere, Tbc is the corrected brightness
temperature at the antenna input, and 2.75 is a constant accounting for the cosmic
background brightness temperature, all in K.
The t c values computed from the radiometer Tbc measurements are plotted
against air mass and fitted with a straight line. Then the entire line is offset to a
parallel position where it passes through the origin. The resulting value of t c at 1
air mass is taken as the true zenith absorption, x„. A true value of zenith brightness
temperature, Tb„, may then be computed from (4.3) as
113
with permission o f the copyright owner. Further reproduction prohibited without permission.
T,b n
=
T n ,r
~
P mr
^ g ) e x p ( - t n) .
-
(4.4)
This brightness temperature, Thn, is used in the Decker and Schroeder
[1991] radiometer equation to calculate the radiometer calibration constant Cf.
This equation is
/
T
= C
Vm ~ Vr
f
— _____- ( T
V - V
*
rj
h
- T ) + T
r
r
(4.5)
where Vmis the radiometer voltage when observing the antenna, Vh is the
radiometer voltage when observing the hot load, Vr is the radiometer voltage when
observing the reference load, Th is the temperature o f the hot load, and Tr is the
temperature o f the reference load; the voltages are in V and the temperatures are in
K.
A total o f twelve tipping curve calibrations were performed from 13
September to 23 September 1993. The average C j s for these calibrations were
0.97835 and 0.83202 for 23.87 and 31.65 GHz, respectively. Therefore, the
calibrated brightness temperatures were found from (4.4) by using these (Rvalues.
The radiometric system was expected to measure brightness temperatures with an
absolute accuracy o f about 3 K for a one second integration time at both
frequencies with the present sensitivities and calibration method.
114
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4.3.1.5 Data smoothing and filtering
The 1-s average radiometer data are smoothed and filtered to reduce the
excess radiometric noise. The smoothing is obtained using a triangular weighting
function with a half width of 15 s (see Fig. 4.13) on the reference and hot load
voltages. The algorithm for implementing this smoothing for the zth voltage (V ) is
given by
(4.6)
The filtering is obtained using a technique described by Press et al. [1986].
It removes any linear trend, and then uses a FFT to low-pass filter the data. Then it
does an inverse fast Fourier transform and reinserts the linear trend at the end. One
user-specified constant enters the amount o f smoothing, specified as the number o f
points over which the data should be smoothed (not necessarily an integer). Zero
gives no smoothing at all, while any value larger than about half the number o f
data points will render the data virtually featureless. This constant is set
equal to the total number of points for a specified time period divided by 10. This
value gives a reasonable smooth curve through the scattered points.
115
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-I—I I 1 I I I I I 1 I I
1 1
4 - 1 -I
-15
I
1 • >
15
Time (s)
Figure 4.13. Triangular weighting function with a half width of 15 s.
116
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Typically, the second level of data smoothing for azimuthal brightness
temperature measurements are fitted to a second-order harmonic expansion as
follows
Tb = Tbo +
+
cos(2<j))
(4.7)
where Tb is the observed brightness temperature in K, (j) is the angle between the
wind direction and observation plane, Tm is the average o f Tb over (j) in K, 5, and
B2 are coefficients found from least-squares fits.
The FFT data smoothing method is chosen instead o f the second-order
harmonic method because it allows the fine structure o f the data to be brought out.
In contrast, the other method averages the data into a second harmonic curve
shape. The FFT method did a fit to the data without prior knowledge of an
expected curve shape.
4.3.1.6 Incidence angle correction
The aircraft attitude variation (pitch and roll) has an effect on the
polarization basis alignment and on the incidence angle drift. The actual incidence
angle is affected most significantly by the aircraft roll (incidence) angle variation
during the circle flights. Figure 4.14 illustrates the measured brightness
temperature data as a function of incidence angle (0), with an average pitch angle
117
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(0^) of 5.30 at an aircraft altitude (ha) of 100 m, and the corresponding third-order
polynomial fits for the circle flights on 17 September 1993 from 194900-195800
UTC. The surface winds at 10 m elevation were 7.8 m/s with clear sky conditions
at this time. Notice that the nadir (0 = 0°) brightness temperatures at 23.87 and
31.65 GHz are different because the sea water’s complex permittivities are
different at these frequencies (see section 3.3.7). These fits are given by
Tb24 = 136.35 - 0.1601 0 - 0.0041 0 2 - O.OOOO2703
(4.8)
Th32 = 141.85 - 0.35550 + O.O33702 - O.OOO2603
where T„u is the 23.87 GHz brightness temperature in K, Ti32 is the 31.65 GHz
brightness temperature in K, and 0 is the incidence (roll) angle in degrees.
The incidence angle effect correction is the same as used by Yueh et al.
[1995]. The average incidence angle is first calculated over a full set o f circles.
Then we calculate the difference between the instantaneous incidence angle and
the average angle. The difference is converted into an expected brightness
temperatures variation using the third-order polynomials, which is used to translate
the measured 23.87 and 31.65 GHz data into those that would be measured as if
the incidence angle had remained constant at the average incidence angle. As
Yueh et al. [1995] stated, this is only a first-order correction, since brightness
temperatures are expected to be functions o f other environmental variables like
water vapor and may not be correctly modeled by polynomials with fixed
118
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194900 -195800 UTC, Septem ber 1 7 ,1 9 9 3
Tb24 = 136.35 - 0.1601 IA - 0.0041 IA*IA - 0 .0000271A’1A*IA
160
I— Tb32 = 141.85 - 0.3555 IA + 0.0337 !A*IA - 0.00026 IA*IA*IA
0
5
10
15
20
25
30
35
40
Incidence Angle (deg)
Figure 4.14. Brightness temperature measurements (Tb24 and Tb32) as a function
o f Incidence Angle (IA, i.e., 0); 17 September 1993 at about 2000 UTC. The
aircraft had an average pitch angle (0^) of 5.3° at an aircraft altitude (ha) of 100 m.
The surface winds were 7.8 m/s with clear sky conditions. Third-order polynomial
curve fits are shown.
119
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coefficients.
43.1.7 Corrected brightness temperature measurements
Figure 4.15 shows a plot o f the smoothed (solid circles and open squares)
and filtered (solid lines) brightness temperatures, with incidence angle correction,
for the four circular flights around Titan on 17 September 1993 from 194900195800 UTC. The azimuth angle (j) is the angle between the wind direction (4>M
)
and the radiometer azimuth look angle (<j)r), i.e., (j>= ( ^ - 4>r. With this definition,
<j) = 0 (180) degrees corresponds to the upwind (downwind) direction. The near­
surface wind speed ( W) and direction (<j)J for this time period were about 7.8 m/s
and 275.8°, respectively.
43.2 Airborne infrared radiometers
Two narrow-band IR radiometers are used to measure the skin temperature
o f the ocean surface and to measure the atmospheric temperature. One IR
radiometer was mounted in the NOAA aircraft’s belly to measure the ocean skin
temperature. While the other IR radiometer was mounted in the ceiling o f the
aircraft to measure the atmospheric temperature. The upward viewing IR
radiometer is used only as a cloud detector since most clouds radiate close to
120
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________ 194900 -195800 UTC, Septem ber 17,1993
L
120 I
1 I
1 I
1 i
i
■ :
i
:
-180 -150 -120
:
-90
1 !
1 I
•-------- :
-60
1 I
1 I
'
'
!
^
-30
!
0
:
30
!
1 !
1 !
’
:--------- — — --------;
60
90
120
150
180
Azimuth Angle (deg)
Figure 4.15. Brightness temperature measurements, including incidence angle
correction, as a function of azimuth angle; 17 September 1993 at about 2000 UTC.
The aircraft had an average pitch angle (0^) o f 5.3 ° and an incidence angle (0) o f
32.3 ° at an aircraft altitude (ha) o f 100 m. The surface winds were 7.8 m/s with
clear sky conditions. The upwind, downwind, and crosswind directions correspond
to 0°, ±180°, and ±90°, respectively. The smoothed data are shown by the solid
circles and open squares. The filtered data are shown by solid lines.
121
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blackbodies in the IR wavelength region. These model 4000 AL IR radiometers
are manufactured by Everest Interscience, Inc. They have a 4° field o f view,
where the field o f view encompasses 90% o f the energy, a half-power transmission
bandwidth (produced by a filter) between 9.98 to 11.41 pm, and an unpolarized
detector. The clear atmospheric emission is minimized by the narrow-band filter.
These radiometers are calibrated at ETL as outlined by Shaw and Fedor
[1993]. Consequently, the IR radiometer accuracies are no better than 1°C. This
requires that the radiometer’s case temperature is the same during calibration and
operation times. This requirement was satisfied since the aircraft’s skin was about
20 °C during the flights; the same abient temperature was used in the calibration
process. Furthermore, the external lens is required to be clean. This requirement
was met by cleaning the external optical lens with a nonresidue-achohol moistened
soft cotton tip after each flight. The upward-viewing radiometer is calibrated for a
temperature range between -70 °C to +20 °C, and the downward-viewing
radiometer is calibrated for a temperature range between -30°C to +20°C. The
voltage-to-temperature calibration equation for these radiometers is
Tt = C U * C 2 i V
(4.9)
for i = 1,2, where / = 1 is for the upward-viewing radiometer, i = 2 is for the
downward-viewing radiometer, Tt is the calculated infrared temperature in °C, V is
the measured IR radiometer voltage in V, C ,, = -61.94, C2] = -105.44, CI2= -
122
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0.8107, and Ca = -9.120.
4.3.3 Radiosondes
Radiosondes provide profiles of height, pressure, temperature, and
humidity. Recent articles by Elliot and Gaffen [1991], Schwartz and Doswell
[1991], Garand et al. [1992]. and Wade [1994] have discussed the quality o f North
American radiosonde data as well as factors that limit the accuracy and utility of
these data, particularly with respect to the measurement of atmospheric relative
humidity (RH). The radiosonde measurements that are used in the RTE software
are launched from San Nicolas Island by the US DoD, at 33.17° N and 119.310 W.
This is approximately 100 km northwest of the circular flights o f the NOAA
aircraft (see Fig. 14.1). These DoD radiosondes are used because of four criteria.
First, they are close to the experimental flight patterns. Second, they provide
launches in the ocean environment. Third, they provide profiles to a minimum of
300 mb. And last, they produce accurate results because the RH was relatively
high. A portion of the radiosonde profile printout for 17 September 1993 at 1920
UTC is shown in Fig. 14.16. Notice that the first row o f data points are at the
launch height.
Since the radiosonde’s first level data are at the launch height, which is 14
m above sea level, the data are extrapolated to sea level. Since the RH is assumed
123
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Sounding program Rev. 7.52 using Loran-C
Station: 72291 San Nicolas Island California
Location: 33.17°N 119.31° W 14m
Sounding: 287
RS-number: 048533847
Pressure (mbar):
Temperature (°C):
Humidity (%):
1015.7
19.5
61
1015.2 0.5
19.5 0.0
61
0
Started at: 17 September 1993 1920 UTC
Time AR
(s) (m/s)
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
0.0
5.49
5.24
5.18
5.24
5.21
5.09
4.94
4.82
4.79
4.60
4.54
4.63
4.51
4.45
4.42
4.36
(%)
DP
Dir
(°C) (deg)
Vel
(m/s)
61
57
59
60
62
64
66
67
67
68
68
68
69
68
69
69
70
11.8
10.4
10.6
10.4
10.5
10.6
10.8
10.8
10.5
10.4
10.1
9.8
10.0
9.7
9.9
9.8
9.9
7.2
9.1
9.4
9.7
10.0
10.2
10.5
10.8
11.0
11.2
11.5
11.7
11.9
12.1
12.3
12.5
12.6
z
(m)
P
(mbar)
T
RH
CO
14.0
25.0
35.1
45.1
56.1
66.1
75.0
82.9
91.1
100.0
106.1
114.0
125.0
131.1
139.0
146.9
156.1
1015.7
1014.5
1013.2
1012.0
1010.8
1009.5
1008.5
1007.6
1006.6
1005.6
1004.9
1003.9
1002.6
1001.9
1000.9
1000.0
999.0
19.5
19.1
18.7
18.3
17.9
17.5
17.2
16.9
16.6
16.3
16.0
15.7
15.7
15.6
15.5
15.4
15.3
300
297
295
293
292
290
289
288
287
287
287
287
288
289
289
290
291
Figure 4.16. Partial printout o f a radiosonde launch from San Nicolas Island,
California, on 17 September 1993, launched at 1920 UTC. The radiosonde time
from launch (Time), ascent rate (AR), height above mean sea level (z),
atmospheric pressure (P ), atmospheric temperature (T ), RH, dew point (DP),
direction (Dir), and velocity (Vel) are given.
124
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to change little between the two levels, the sea level RH is set equal to the launch
level RH. On the other hand, the temperature and pressure are extrapolated by the
following relations [Ulaby et al., 1981]
(4.10)
where T0 is the sea level temperature in K, Tx is the launch level temperature in K,
a = 6.5 K k m '1, and z, is the launch height = 0.014 km; and
(4.11)
where P0 is the sea level pressure in mbar, P, is the launch level pressure in mbar,
H x = 7.7 km, and z, is given above.
4.3.4 Sonic anemometers on Titan and FLIP
A sonic anemometer measures the wind speed by using reciprocal
transmission of acoustic signals across an air gap o f known length. The difference
in travel times in the two opposite directions yields the wind speed along the
acoustic path. It also measures the wind direction by the mechanical movement of
this structure. This anemometer is a Gill Solent type and is manufactured by
Bristol Industrial and Research Associates Ltd. in England. They have been
125
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specifically designed to stand up to the marine environment and produce highquality data despite nominal contamination with water and salt. These units were
deployed on both Titan and FLIP at 10 m elevation during SCOPE. The wind
speed accuracy of this device is ±3% for a 10 second averaging time. On the other
hand, the wind direction accuracy o f this unit is ± 3 0 for a 10 second averaging
time.
4.3.5 Other instruments on Titan and FLIP
The other important sensors used aboard Titan and FLIP are shown in
Table 4.6. Like the sonic anemometer, the infrared fast hygrometer has been
specifically designed to stand up to the marine environment and produce highquality data despite nominal contamination with water and salt. The remainder o f
the meteorological instruments are essentially the finest available standard units.
The Titan-motion-measuring system was used to provide data to correct the sonic
anemometer wind data to eliminate the motion contamination that invalidates most
seagoing eddy covariance stress measurements (the scalar fluxes are much less
affected). The system consists of a gyro-stabilized triaxial accelerometer set
mounted near the Titan’s center of motion and a strap down triaxial accelerometer
set and triaxial angular rate unit mounted on the mast as an integral part o f the
sonic anemometer base.
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Table 4.6. Various instruments aboard Titan and FLIP.
Instrument
barometer
(AIR)
thermistor
(Y SI46040)
Variable
Units
I Hour Accuracy
pressure
mbar
±0.1
sea surface
temperature
°C
±0.1
°C
±0.1
thermometer
(VaisalaHMP-35)
air temperature
hygrometer
(Vaisala HMP-35)
sea surface
specific humidity
g/kg
±3
same as above
air specific
humidity at 15 m
g/kg
±3
IR hygrometer
(Ophir IR2000)
bulk sensible heat
flux
W/m2
±1
same as above
bulk latent heat
flux
W/m2
±3
pyranometer
(Eppley PSP)
solar irradiance
W/m2
±4
pyrgeometer
(Eppley PIR)
longwave
irradiance
W/m2
±2.5
precipitation
mm/h
15%
GPS/gyrocompass
(Robertson)
ship’s heading,
course, and speed
deg-min-sec-dsec
m/s
± 15 m
± 0.1 m/s
inertial navigation
(Systron Donner
Motionpak CM
ODEC)
ship motions
degrees
±0.2
optical raingage
(STIORG-700)
.
127
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4.4 Wind Speed Algorithm
The predominately horizontally-polarized 23.87 GHz channel was used to
obtain an empirical wind speed algorithm. This was accomplished by measuring
the corrected 23.87 GHz brightness temperature variations (peak-to-valley) from
thirteen circle flights around Titan and FLIP. These measurements are regressed
against the Titan and FLIP sonic anemometer wind-speed measurements at 10 m
elevation (see Fig. 4.17a). These measurements correspond to negative stability
(air-sea difference approximately -2°C). The wind speed algorithm is given by
w =
(4.12)
where W is the wind speed in m/s, ms = 1.8, ATb24 is the 23.87 GHz brightness
temperature variation (peak-to-valley) in K, and b = - 0.15.
The standard deviation of 1.8 m/s from Fig. 4.17a is similar to that obtained
by Schluessel and Luthardt [1991] for satellite-derived surface wind speeds with
respect to in situ wind data. The standard deviation values from the Schluessel and
Luthardt [1991] data lie between about 2 to 4 m/s. More in situ SCOPE data
points would o f been helpful to formulate a better wind speed algorithm at this
frequency. For comparison purposes, the predominately vertically-polarized 31.65
GHz brightness temperature variation versus the sonic anemometer wind speed is
shown in Fig. 4.17b. Notice the poor agreement between the wind speed and the
128
with permission o f the copyright owner. Further reproduction prohibited without permission.
6 I<0
£
*©D
©
o.
€0
T3
C
I
0
1
2
4
3
23.87 GHz Brightness T em perature Variation (K)
8
;
:------------------------
W~047Tb32*2.9
7
~
0
$ t d * 2.2
1
2
3
4
5
6
7
8
31.65 GHz Brightness T em perature Variation (K)
Figure 4.17. Sonic anemometer wind speed (W) measurements versus the (a)
23.87 and (b) 31.65 GHz brightness temperature variations (peak-to-valley) during
13 sets o f circular flights around FLIP and Titan. The least squares linear fit
curves along with the standard deviations (std) are shown.
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31.65 GHz brightness temperature variation (ATb32) measurements, i.e., when
ATm = 0, the sonic anemometer wind speed ~ 3 m/s.
4.5 Skin Temperature of Sea Water
The sea water’s skin temperature, not the bulk water temperature, is
required to calculate the emissivity of the ocean surface at the NOAA microwave
radiometer frequencies. The physical rational is because electromagnetic waves at
these frequencies only penetrate about the upper millimeter o f the ocean. In
contrast to the microwave wavelengths, infrared waves at about 10 pm penetrate
only about the upper micrometer o f the ocean. We now assume that the sea water
temperature at these two depths are approximately the same. Therefore, the
calibrated downward-viewing IR radiometer was used to measure the skin
temperature o f the ocean at the NOAA radiometer operating frequencies.
However, in order to obtain an accuracy better than 1°C, the IR radiometer
measurements are compared with a new technique that also measures the ocean
skin temperature [Fairall et al., 1995]. As Fairall points out, to obtain the correct
ocean skin temperature, the bulk temperatures must be corrected for the warm
layer and the cool skin. The warm layer is a region in the upper few meters of the
ocean where the solar radiation has caused significant wanning relative to the
deeper mixed-layer temperature. The warm layer occurs during the day when
130
I
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temperature stratification caused by absorption of the solar flux is sufficiently
strong to suppress shear-induced mixing. The cool skin is a layer in the upper few
millimeters o f the ocean caused by the combined cooling effects of the net
longwave radiation, the sensible heat flux, the evaporation, and the latent heat flux.
A Fortran computer program written by Fairall calculates the ocean skin
temperature using the measurements obtained by the in situ sensors listed in
sections 4.3.4 and 4.3.5. The required instruments for determining the cool skin
temperature were deployed on both Titan and FLIP during SCOPE. Unfortunately,
the Titan’s thermistor for measuring the bulk ocean water did not operate properly
during the experiment. Therefore, only FLIP had the necessary sensors for
calculating the skin temperature of the sea surface.
Because o f this limitation, only four ocean skin temperature comparisons
were obtained between the downward-viewing IR radiometer measurements and
Fairall’s new method. This comparison showed that the IR radiometer sea skin
temperature measurements were about 0.7 K colder than Fairall’s method.
Therefore, 0.7 K was added to the airborne IR radiometer measurements. The
standard deviation o f this comparison was 0.2 K.
4.6 Summary
The location, aircraft flight strategy, and instruments used in SCOPE for
131
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measuring and calculating the downward-viewing radiometric brightness
temperatures were discussed. The airborne NOAA dual-frequency radiometer was
the first instrument described in this section. This description included the
radiometer hardware and the post processed data techniques. A unique antenna
and the electronic layout was discussed in detail. The post processed data
techniques included calibrating the radiometer data using the tipping curve
method, smoothing the data using a triangular weighting function, and filtering the
data using and a FFT low-pass filter function. The smoothed and filtered data
reduced the large noise in the radiometric data, thereby providing more accurate
and sensitive brightness temperature data. Clearly, the noise from the radiometer
instrument must be reduced to better measure the small azimuthal brightness
temperature variations from the sea surface and to measure the total received
emission at the radiometer more accurately. This noise reduction in the radiometer
hardware was accomplished at ETL after SCOPE by optically isolating the
hardware signals from the computer signals, reducing the ground loops, decreasing
the hysteresis of the temperature control circuity, and various filtering techniques.
These improvements produced sensitivities o f about 0.064 K at both frequencies, a
factor o f about six in noise improvement.
Several other instrument measurements provided the necessary inputs for
the brightness temperature model. Specifically, the total brightness temperature
calculation required radiosonde measurements for the atmospheric brightness
132
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temperature portion and downward-viewing airborne IR radiometer measurements
for the sea skin temperature. The remainder o f the instruments, located on Titan
and FLIP, were used to calibrate the downward-viewing IR radiometer and to
provide ocean-surface truth for near-surface wind speed and direction.
A result o f these instrument comparisons is that an empirical wind speed
algorithm was obtained by fitting the horizontally-polarized 23.87 GHz brightness
temperature variations with the measured in situ wind speed measurements at 10 m
elevation. The standard deviation of this wind speed algorithm of 2 m/s is similar
to that obtained by Schluessel and Luthardt [1991] for satellite-derived surface
wind speeds. Wind vector comparisons are analyzed in section 5.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5. A COMPARISON OF EXPERIMENTAL AND THEORETICAL
RESULTS
Emission models o f both the atmosphere and the rough ocean surface must
be compared with the downward-viewing radiometric emission measurements
above the real ocean surface. These types of comparisons provide insight into the
strengths and weaknesses of both theoretical and experimental results. They may
also provide a better understanding of the mechanisms responsible for the
azimuthal brightness temperature modulation signatures. These azimuth
signatures are particularly important because they provide the necessary
information for determining the near-surface ocean wind speed and direction. In
addition to these modulation signatures, the total emission from the atmosphere
and the rough ocean surface may provide additional insight into the sea surface
structure. In this section, a new emission model o f both the atmosphere and the
rough ocean surface (see sections 2 and 3) is compared with NOAA’s downwardviewing microwave radiometer emission measurements o f the real ocean surface.
In particular, the experimental and theoretical brightness temperature azimuthal
modulations are compared. The near-surface wind vector is inferred from the
azimuthal emission variations. In addition, the total emission values may help to
determine which small-scale ocean waves produce the majority of the emission at
the two microwave frequencies.
134
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5.1 Background
Very little work has been done on comparing measured and theoretical
azimuthal-dependent brightness temperatures observed from a downward-viewing
microwave radiometer over the ocean. These azimuthal emission signatures
contain the required information for determining the near-surface ocean wind
vector. Recently, Yueh et al. [1994] applied the SPM to small-scale sea surfaces
described by an empirical sea surface spectrum. Yueh et al. [1994] found that
theoretical azimuthal variations of Stokes parameters were in good agreement with
aircraft K^-band radiometer data [Dzura et al., 1992]. However, this work only
compared the brightness temperature variations and not the total brightness
temperature received at the aircraft platform. These variations are key parameters
in current polarimetric radiometer studies, whereas the total brightness
temperatures are only secondary. However, the total downward-viewing
radiometric emissivity values from theory and measurement may provide
additional insight into the small ocean wave structure.
5.2 Focus of Present Work
During the course of the experiment, Titan observed the highest winds on
17 September 1993, i.e., the Julian day is 260. As Table 4.3 shows, between
135
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194900-195800 UTC the surface winds at 10 m elevation were 7.8 m/s at 275.8°
with clear sky conditions. This way point is chosen to compare with the
theoretical model because o f the high winds, the cloudless sky conditions, and the
four circle flights. The four circle flights provided additional data for averaging
the brightness temperatures, thereby reducing the radiometric data noise.
Furthermore, this set o f circle flights produced the largest azimuthal brightness
temperature variations as compared to the other three circle flight sets in Table 4.3.
The lower surface wind speeds, the small number o f circle flights at the way
points, and the excess radiometric noise, masked the expected azimuthal brightness
temperature variations at the other way points. A view of the flight track as the
aircraft radiometer circles Titan is shown in Fig. 5.1 [Fedor and Irisov, 1994]. The
shift of the track in direction and magnitude was consistent with the winds
observed by Titan. The aircraft’s average roll (incidence, 0) and pitch (dp) angles,
the large-scale tilt angle (0„), and altitude (ha) for this set of flights were 32.3°,
5.3 °, 6.0°, and 100 m, respectively. Furthermore, the average sea skin temperature
(T,kin) was about 293.2 K (~ 20°C) and the average near-surface air temperature
( T ^ ) was about 291.6 K (~ 18.4°C). Therefore, the boundary temperature
difference, i.e., Tmir - Tsim, was -1.6 °C. The upward atmospheric brightness
temperature (Tup), downward atmospheric brightness temperature (Td„), and upward
transmissivity (T up) calculated values at both frequencies for the above parameters
are given in Table 5.1. In addition, the salinity o f the sea water for this location
136
permission of the copyright owner. Further reproduction prohibited without permission.
33.29
Wind
33.28
bO
a>
3
■§ 33.27
3
End
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33.26
Begin
33.25 ----------------- 1----------------- 1—
-118.33
-118.32
-118.31
-118.30
-118.29
-118.28
Longitude (deg)
Figure 5.1. The NOAA aircraft’s flight track around Titan on 17 September 1993
at 194900-195800 UTC. The arrows indicate the aircraft’s direction; the aircraft’s
roll (incidence, 0) angle was approximately 32° and the aircraft’s altitude (ha) was
about 100 m. The near-surface winds were about 7.8 m/s at 275.8°.
137
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Table 5.1. Calculated upward and downward atmospheric brightness temperatures
(Tupand Tdn), and upward transmissivity (T^) at 23.87 and 31.65 GHz for an
aircraft height (ha) o f 100 m above the ocean surface at an incidence (0) angle of
32.30 during clear sky conditions. The radiosonde was launched from San Nicolas
Island, California on 17 September 1993 at 1920 UTC.
•T‘in' _
Td„
T
(GHz)
(K)
(K)
(Np)
23.87
2.4
25.0
6.3 x lO'3
31.65
1.6
18.2
3.4 x lO'3
Frequency
was about 33.5 °/00. The sea water’s salinity was measured by the Scipps
Institution o f Oceanography at the University o f California in San Diego,
California. These brightness temperature values show that most o f the received
radiation at the downward-viewing radiometers (see Fig. 4.15) was from the ocean
surface.
The Fortran software development for the emission model the data
processing was done on a Silicon Graphics, Inc. (SGI) UNIX based workstation
using single precision. The SGI workstations provide many mathematical and
scientific libraries. These routines were very helpful in developing Fortran
software code for the combined atmospheric and oceanic surface brightness
temperature computations and for smoothing and filtering the radiometric data.
The RTE software [Reynolds and Schroeder, 1993], developed at ETL, was
modified to perform brightness temperature calculations for a downward-viewing
airborne radiometer. Since this program incorporates the radiometer’s three138
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
dimensional antenna patterns, the final output is the antenna brightness
temperatures, as given in (4.2). The time required for this workstation to calculate
a single brightness temperature point is about 4 minutes! In order to save time, the
brightness temperatures were sampled only every 15° in azimuth. This software is
available upon request.
5.3 Brightness Temperature Comparison on a High Wind Day
The 23.87 and 31.65 GHz brightness temperature measurements from the
microwave radiometer, for the time period in this section, are compared with the
model in sections 2 and 3. The two adjustable parameters in the model (see
section 3.3.6) are the height (hs) and the wavelength (At). These parameters are
varied for different height-wavelength pairs. The 23.87 and 31.65 GHz brightness
temperatures are calculated for each height-wavelength combination as a function
of azimuthal angle for the aircraft’s average incidence (0 = 32.3°) and pitch (0^ =
5.3 °) angles, the large-scale tilt angle (0„ = 6.0°), and the average sea skin
temperature (Tskin = 293.2 K) during the four circle flights. Theoretical points were
calculated every 15° in azimuth angle, so the interpolating lines shown should not
be taken to be exact.
In order to enhance the comparison between experimental and theoretical
results, the following process is used. First, the mean theoretical brightness
139
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temperatures for each 360° circle are computed. Then, these brightness
temperatures are subtracted from their respective mean measured brightness
temperatures. This is given as
^bm d
“
(5.1)
^bm m ~ ^ b m t
where T b m d is the mean brightness temperature difference,
T hm m
is the mean
measured brightness temperature in, and Tbml is the mean theoretical brightness
temperature in; the above temperatures are in K.
Before an in depth comparison of the experimental and theoretical results is
done, the effect of the radiometer’s antenna patterns (see section 4.3.1.2) on the
brightness temperature computations is addressed. In other words, the computed
brightness temperatures, including the three-dimensional antenna patterns, are
compared with those in the specular direction. Figure 5.2 is a plot of the measured
and theoretical brightness temperatures, at 23.87 and 31.65 GHz, for a sinusoidal
wavelength of 0.5 cm at a wave height of 0.5 mm; the brightness temperature
variation (peak-to-valley) and Tkmd are given as the first and second entries,
respectively, in the parenthesis. The antenna curves in Fig. 5.2 incorporate the
three-dimensional antenna patterns, whereas the specular curves include only the
specural direction. Notice that the antenna values are in better agreement with the
radiometer measurements than the specular values, i.e., the antenna curve | T b m d \
values are smaller than the specular curve | T b m d \ values, and the measured curve
140
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Height 0.5 mm
Wavelength 0.5 cm
!' I' ' '
u
I
•160 -150 -120 -90
-60
-30
0
30
60
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120 150 180
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Height 0.5 mm_________Wavelength 0.5 cm
A rt« v w ( 2 ? 9 K .2 7 K )
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1 3 0
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:
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i
1
0
■
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30
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I
90
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■
—
120 150 180
Azimuth Angle (deg)
Fig. 5.2. The measured and computed brightness temperatures at (a) 23.87 and (b)
31.65 GHz versus azimuth angle. The theoretical curves include the specular and
three-dimensional antenna directions. The sinusoidal height and wavelength are
0.5 mm and 0.5 cm, respectively. The brightness temperature variations (peak-tovalley) and the mean brightness temperatures differences (Thnul) are given by the
first and second entries in the parenthesis, respectively; na indicates not applicable.
The upwind, downwind, and crosswind directions correspond to 0°, ±180°, and
±90°, respectively. The aircraft’s average incidence (0 = 32.3°) and pitch (Qp =
5.3°) angles, the large-scale tilt angle (0„ = 6.0°), and the average sea skin
temperature (T%kin= 293.2 K) are used in these calculations.
141
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
brightness temperature variations agree better with the antenna brightness
temperature variations than the specular curve brightness temperature variations.
In general, the theoretical antenna pattern model produces values that agree better
with the radiometer measurements than the specular model values. Since this is
true, the three-dimensional antenna patterns must be taken into account in order to
model accurately the radiometer measurements. Therefore, the radiometer’s
antenna patterns are included in the model for the remainder of this comparison.
Furthermore, in this comparison the wavelengths range from 0.25 to 5 cm, and the
heights range from 0.1 to 1 mm. The above wavelengths are chosen to bracket the
radiometer’s free-space wavelengths of 1.26 cm (23.87 GHz) and 0.95 cm (31.65
GHz), whereas the heights are chosen to represent capillary waves [Kinsman
1984]. The corrugation heights in wavelengths are given in Table 5.2.
Table 5.2. Corrugation heights, h„ as a function o f electromagnetic wavelength, A.
K
X = 1.26 cm
A = 0.95 cm
(mm)
hJX
hJX
0.25
0.02
0.03
0.50
0.04
0.05
0.75
0.06
0.08
1.00
0.08
0.11
For the remainder of this section, the Tbmdvalues are subtracted from the
142
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with permission of the copyright owner. Further reproduction prohibited without permission.
I
theoretical brightness temperatures (Tbm). These adjusted brightness temperatures
are then overlayed with the measured brightness temperatures.
Figure 5.3 is a plot of the measured and theoretical brightness temperatures
at 23.87 and 31.65 GHz for a sinusoidal wavelength o f 0.25 cm at various small
wave heights, where the height and Tbmd are given as the first and second entries,
respectively, in the parenthesis. Figures 5.4 - 5.10 are similar to Fig. 5.3 with the
exception o f the wavelengths and some heights.
These figures show that for a given wavelength, an increase in height
generally produces a larger brightness temperature variation (peak-to-valley), i.e.,
brightness temperature difference between upwind and crosswind. In particular,
the calculated 23.87 GHz brightness temperature curves exhibit large changes as
the surface wavelength is changed with a fixed height (Figs. 5.3 - 5.10). These
curves have a sinusoidal like shape for surface wavelengths up to about 0.5 cm.
For surface wavelengths between approximately 0.75 and 2.0 cm, these curves
exhibit large shape changes. The characteristic "jumps" in brightness temperature
for this region are due to the transition of a Floquet mode from propagating to
nonpropagating and visa versa. The curves have similar shapes for surface
wavelengths greater than about 5.0 cm. For this region, the characteristic ‘jumps"
in brightness temperature becomes less pronounced as the surface wavelength is
increased. This is due to the fact that a greater number of Floquet modes are
obtained for the longer wavelength surfaces, which results in a smaller shift in total
143
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Sinusoidal Wavelength 0.2S cm
- • ThM«y{0Smm.>12310
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Figure 5.3. The measured and computed brightness temperatures at (a) 23.87 and
(b) 31.65 GHz versus azimuth angle. The measured values were taken on 17
September 1993 at 194900-195800 UTC. The sinusoidal wavelength is 0.25 cm;
the small-scale wave heights and the mean brightness temperatures differences
(Tbml) are given by the first and second entries in the parenthesis, respectively. The
upwind, downwind, and crosswind directions correspond to 0°, ±180°, and ±90°,
respectively. The aircraft’s average incidence (0 = 32.3°) and pitch (0^ = 5.3°)
angles, the large-scale tilt angle (0„ = 6.0°), and the average sea skin temperature
{TsUn = 293.2 K) are used in these calculations.
144
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151
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
power as one mode makes the transition from propagating to non-propagating. In
fact, these curves have a sinusoidal like shape that agrees well with the measured
curve. However, the theory underestimates the mean measured brightness
temperature by approximately 10.4 K
In a similar fashion, the calculated 31.65 GHz brightness temperature
curves exhibit large changes as the surface wavelength is changed with a fixed
height (Figs. 5.3-5.10). The curves have narrow peaks at 0 and ± 180° for surface
wavelengths up to about 0.5 cm. Two additional brightness temperature peaks are
formed at approximately ± 90° for surface wavelengths between 0.5 and 1.0 cm.
The curve shapes remain about the same for surface wavelengths greater than
about 1.0 cm with heights less than 0.5 mm. In contrast, the curve shapes continue
to change for surface wavelengths between 1.0 and 2.0 cm with heights £ 0.5 mm.
Like the 23.87 GHz case, the curves have similar shapes for surface wavelengths
greater than about 2.0 cm. In this case, the curve variations do not agree with the
measured curve variations. Furthermore, the theory' underestimates the mean
measured brightness temperature by approximately 14.9 K.
The four criteria, in descending importance, for determining which surface
height-wavelength pair produces brightness temperatures that compare closest to
the measured brightness temperature data are chosen when (a) | Tbmi| is minimized,
see (5.1), (b) the azimuth angle locations of the measured and computed brightness
temperature peaks are minimized, (c) the azimuth angle locations of the measured
152
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and computed brightness temperature valleys are m inim ized, and (d) the difference
between the measured brightness temperature variation ( peak-to-valley) and the
computed brightness temperature variation is minimized. The absolute accuracy o f
the microwave radiometer (- 3 K) permits using the first (a) criterion, whereas the
marginally sensitive radiometer (~ 0.4 K) permits using the other three (b) - (d).
The 23.87 GHz brightness temperature comparison is analyzed first.
The height-wavelength pair that satisfies the above criteria for the 23.87
GHz (1.26 cm) channel is when hs = 0.5 mm and As = 0.5 cm, i.e., the capillary
wave region. Notice, this Xs is not the Bragg resonance condition. The Bragg
resonance condition [Ulaby et al., 1982] occurs at Xs ~ 1.26 cm since the incidence
angle - 30°. This gives a corrugation height o f 0.047., a corrugation wavelength o f
0.47., which produces a maximum slope angle at its sides -3 2° . This theoretical
curve and the measured curve are shown in Fig. 5.11a. The measured curve is
shown by itself in Fig. 5.12a to show the measured brightness temperature
variations more clearly.
In a similar way, the height-wavelength pair that satisfies the above criteria
for the 31.65 GHz (0.95 cm) channel also occurs when hs = 0.5 mm and Xs = 0.5
cm, the same wave shape as the 23.87 GHz case. Again, this As is not the Bragg
resonance condition. The Bragg condition for this wavelength occurs when Xs ~
0.95 cm. This gives a corrugation height o f 0.057., and a corrugation wavelength
of 0.57., which produces a maximum slope angle at its sides - 32°. This
153
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Sinusoidal Wavelength 0.5 cm
130
129
127
126
m
125 I—
124 t
M sw n d
123 -
Theory (0.5 mm. 1 8 K)
1 2 2 ------------------------------------------------------------------------------------------180 -150 -120 -90 -60 -X
0
30 60
90 120 150 180
Azimuth Angle (degrees)
Sinusoidal Wavelength 0.5 cm
175 -
M aan n d
Theory (0.5 mm. 2.7 K)
170 ■
(b)
Q.
E
160 t
155 r
150 *
145
-180 -150 -120 -90
-60
-30
0
30
60
90
120
150
180
Azimuth Angle (degrees)
Figure 5.11. Same as Fig. 5.3 except the sinusoidal wavelength and height are 0.5
cm and 0.5 mm, respectively.
154
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Measured
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127
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124 L
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-60
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60
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120
150
180
90
120
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60
Azimuth Angle (degrees)
Figure 5.12. Same as Fig. 5.3 except only the brightness temperature
measurements are shown.
155
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theoretical curve and the measured curve are shown in Fig. 5.1 lb. As above, the
measured curve is shown alone in Fig. 5.12b to show the measured brightness
temperature variations more clearly.
The emission curves in Fig. 5.11 provide the necessary information for
comparing theoretical and experimental near-surface wind vector results. The
near-surface wind speed is compared first. The measured and calculated wind
speeds are compared by the empirical wind speed algorithm in (4.12). The
calculated 23.87 GHz brightness temperature variation of about 6.8 K results in a
wind speed o f 12.2 m/s. On the other hand, the measured 23.87 GHz variation of
3.5 K results in a wind speed of 6.2 m/s. The true measured near-surface wind
speed at this time was 7.8 m/s is inbetween these two values. The 31.65 GHz
frequency is not used in this comparison because of the poor agreement between
the in situ wind speed and the 31.65 GHz brightness temperature variations, see
Fig. 4.17b. Table 5.3 shows the near-surface wind speed results.
Table 5.3. Empirical and true near-surface wind speeds on 17 September 1993 at
approximately 2000 UTC at the Titan location. The empirical wind speeds are
calculated from (4.12); the true speed is measured by a sonic anemometer at 10 m
elevation.
Speed
True Wind Speed
Theory
Measure
Measure
(m/s)
(m/s)
(m/s)
12.2
6.2
7.8
Empirical
Wind
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The near-surface wind direction comparison is now addressed. The wind
direction is determined by the azimuth angle position o f the emission peaks and
valleys. The horizontally-polarized 23.87 GHz channel is addressed first. Figure
5.1 la shows the computed and the measured 23.87 GHz brightness temperature
peaks at the crosswind (azimuth angle = ± 90°) direction. The measured
brightness temperature values at the peaks are approximately the same. Likewise,
the computed peak emission values are the same. The calculated and measured
emission valleys occur at the upwind (azimuth angle = 0°) and downwind
(azimuth angle = ± 180°) directions, with the exception that the upwind measured
valley is displaced by +30°. Notice that the measured and calculated upwind
brightness temperatures are less than the downwind temperatures by approximately
1.5 and 0.8 K, respectively. In contrast, Yueh et al. [1995] measured a slightly
warmer upwind temperature than the downward one o f about 0.2 K for a
horizontally-polarized 19.35 GHz radiometer for a near-surface wind speed o f 12
m/s at 20 m elevation. This discrepancy between Yueh et al. [1995] and NOAA’s
data may be due to the particular property of the frequency band, aircraft altitude,
incidence angle, near-surface wind speed, wind measurement height, excessive
radiometric noise, data smoothing and filtering techniques, and other instrument
differences.
Even though the 31.65 GHz brightness temperature curves in Fig. 5.11b
show a lack of shape agreement, there are several important features. First, the
157
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calculated and measured peaks occur close to the upwind (azimuth angle = 0°) and
downwind (azimuth angle = ± 180°) directions. However, the measured emission
peak is fairly broad and has an azimuth angle range from 0 to 90°. Second, the
calculated and measured brightness temperatures are higher in the upwind
direction than in the downward direction. Specifically, the calculated upwind
brightness temperature is approximately 5 K higher than the downwind brightness
temperature. Similarly, the measured upwind temperature is approximately 2.5 K
higher than the downwind brightness temperature. This asymmetrical trend agrees
with that made by the Yueh et al. [1995] vertically-polarized radiometer, i.e., the
upwind brightness temperature is greater than the downwind temperature.
The 31.65 GHz curves exhibit three noticeable differences. First, both
curves are not entirely out-of-phase with the 23.87 GHz curves. This characteristic
trend is expected because o f recently reported data by Yueh et al. [1995] and
Trokhimovski and Irisov [1995]. Second, the calculated curve has several more
peaks and valleys than the measured one. In particular, the measured emission
curve has only one major valley (azimuth angle = -120°), whereas the calculated
emission curve has two major valleys (azimuth angles = -150 and -45°). Third, the
computed brightness temperature variation (25 K) is approximately 8 times greater
than the measured brightness temperature variation (3.3 K). Table 5.4 shows the
azimuth angles (relative to the upwind direction, i.e., 0°) o f the brightness
temperature peaks and valleys at both frequencies.
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Table 5.4. Measured and computed brightness temperature variations (Tb) on 17
September 1993 at approximately 2000 UTC at the Titan location. The azimuth
angles are relative to the measured upwind direction (0°).
Frequency
Azimuth
Angle
Th Peak
T„ Valley
Measure
Theory
Measure
Theory
(GHz)
(deg)
(deg)
(deg)
(deg)
23.87
±90
±90
+30, ±180
0, ±180
31.65
0 - 9 0 , ±180
0, ±180
-120
-150,+45
5.4 Summary
The experimental and theoretical 23.87 and 31.65 GHz brightness
temperature results agreed best, using the given criteria in section 5.3, when the
small-scale wave height and wavelength were approximately 0.5 mm and 0.5 cm,
respectively, i.e., the capillary wave region. These criteria were based upon the
brightness temperature modulations as well as the total brightness temperatures.
This result agreed with other findings [Kravtsov et al., 1978; Irisov, 1991;
Trokhimovski and Irisov, 1995] that the capillary waves are primarily responsible
for creating the anisotropic brightness temperature variations at microwave
frequencies. The measured three-dimensional antenna patterns were incorporated
into the above computations in order to model the actual received emission at the
radiometer.
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The near-surface wind speed was inferred from the horizontally-polarized
23.87 GHz brightness temperature variations, see section 4.4. The inferred nearsurface wind speed from the radiometric modulation measurements was about 1.6
m/s lower than the true wind speed at 10 m elevation. In contrast, the inferred
wind speed from the model was about 4.4 m/s higher than the true near-surface
wind speed.
In addition to near-surface wind speed measurements, the measured and
computed brightness temperatures from the dual-frequency microwave radiometer
were useful in determining the near-surface wind direction. In particular, the
measured and computed peaks of the horizontally-polarized 23.87 GHz brightness
temperatures were located at the crosswind directions, whereas the valleys were
close to the upwind/downwind directions. Unfortunately, the vertically-polarized
31.65 GHz measured and computed brightness temperature curves did not agree as
well as the 23.87 GHz channel. For example, the peaks of the 31.65 GHz
brightness temperature were located at the upwind/downwind directions.
However, the computed brightness temperature peaks were fairly narrow in
azimuth angle and the measured brightness temperature upwind peak was fairly
broad. Moreover, the computed and measured temperature valleys were not at the
crosswind directions. In fact they differed by as much as 60°.
The effect of the tilted small-scale sea surfaces was borne out in the
upwind/downwind brightness temperature differences. Specifically, the measured
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and calculated 23.87 GHz downwind brightness temperatures were wanner than
the upwind temperatures by about 1.5 and 0.8 K, respectively. Conversely, the
measured and computed 31.65 GHz upwind brightness temperatures were warmer
than the downwind temperatures by approximately 2.5 and 5.0 K, respectively.
Finally, the differences between the experimental and theoretical brightness
temperature results were most probably due to the simplistic two-scale model o f
the ocean surface, excessive radiometric noise, and too few data samples in the
circular flights. Secondary causes of disagreement may have come from not
knowing the precise complex permittivity values of sea water, modeling only
monochromatic frequencies, data smoothing and filtering techniques, possible
cross polarization problems, not including the foam coverage, and not correcting
properly for the incident (roll) angle.
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6. CONCLUSIONS
The passive microwave radiometer is rapidly gaining acceptance as a
valuable tool for measuring the near-surface ocean wind vector. The azimuthallypolarized microwave emission from the ocean surface has been observed to be
correlated with the wind speed and direction by several independent
experimenters. Recent American and Russian experimental results substantiate the
potential o f using passive microwave radiometer for the wind vector recovery.
The near-surface wind speed measurement by passive microwave
radiometers is not new. Many researches have described the experimental and
theoretical aspects o f this technique. These empirically derived measurements are
obtained by fitting radiometer brightness temperature measurements with in situ
wind speed measurements from buoys and/or ships. Recently, experimental
observations show potential for the near-surface wind direction measurement by
passive microwave radiometers. Because this is a new development in wind
direction sensing, only limited amounts o f radiometric data are available to
demonstrate the ocean brightness temperature variation over azimuthal angles
relative to the wind. Furthermore, new theoretical models of the ocean surface are
presently being developed to describe this process.
The goals o f this research have been to develop a new atmosphere and
ocean surface model for the NOAA microwave radiometers and to compare its
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results to actual radiometer measurements taken over the ocean. The theoretical
development o f the ocean surface focused on a traditional two-scale model with
the exception that the small-scale features are allowed to be similar to the incident
electromagnetic wavelength. On the other hand, the atmospheric portion o f the
theory used the ETL RTE algorithms to calculate the downward and upward
propagating atmospheric radiation. In addition, the measured three-dimensional
antenna patterns were incorporated into the model to simulate the actual received
emission at the radiometer more realistically. The differences between
measurement and theory were assumed to be due mainly to a simplistic ocean
surface model, excessive radiometric noise, and too few data samples in the
circular flights.
An experimental and theoretical comparison between the radiometric
emission results obtained at SCOPE provided further evidence that passive
microwave radiometers are capable of measuring the near-surface ocean wind
vector. Specifically, the standard deviation o f the inferred wind speed from the
horizontally-polarized 23.87 GHz brightness temperature measurements was
approximately 2 m/s. Consequently, we expect a standard deviation of the inferred
wind speed from the model to be about 4 m/s.
In addition to the wind speed measurements, the measured and computed
brightness temperatures from the dual-frequency microwave radiometer were
useful in determining the wind direction. In particular, the measured and
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computed peaks o f the horizontally-polarized 23.87 GHz brightness temperatures
were located at the crosswind directions, whereas the valleys were located at the
upwind/downwind directions. In contrast, the peaks o f the measured and
calculated vertically-polarized 31.65 GHz brightness temperatures were located at
the upwind/downwind directions. However, the computed brightness temperature
peaks were fairly narrow in azimuth angle and the measured brightness
temperature upwind peak was fairly broad in azimuth angle. Moreover, the
computed and measured temperature valleys were offset from the crosswind
directions by a maximum of 60°.
The effect o f the tilted small-scale sea surface was borne out in the
upwind/downwind brightness temperature differences. Specifically, the measured
and calculated 23.87 GHz downwind brightness temperatures were warmer than
the upwind temperatures by about 1.5 and 0.8 K, respectively. Conversely, the
measured and computed 31.65 GHz upwind brightness temperatures were warmer
than the downwind temperatures by approximately 2.5 and 5.0 K, respectively.
For wind speeds less than 12 m/s with clear sky conditions, we expect that
the inferred wind vector from the NOAA microwave radiometer can give wind
speed to an accuracy of about 2 m/s (~ 4 m/s for the model) and wind direction to
within 15° accuracy. Furthermore, the upwind and downwind directions can be
distinguished from each other.
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6.1 Specific Contributions
Section 2 contained a derivation o f the total received brightness (brightness
temperature) received at a downward viewing radiometer. The development
represents the first time the NOAA/ETL RTE software had been used for such an
application. The combined effects of the cosmic background radiation, the
atmosphere, and the rough ocean surface were incorporated into a single equation.
The emission (brightness temperature) from a rough two-scale ocean
surface was developed in section 3. This surface was comprised of small waves
tilted by the large-scale features at an angle determined by the wind speed. Unlike
previous two-scale formulations, the small-scale roughness was permitted to be
similar to the incident electromagnetic wavelength. Also, the dielectric properties
o f sea water were obtained by the Leibe et al. [1991] pure water model and a
standard salt conductivity model. This model did not include foam coverage since
it is valid for wind speeds less than 12 m/s.
Section 4 describes the pertinent instruments used in SCOPE to measure
and to compute the wind vector. The NOAA/ETL microwave antenna system was
unique and had never been operated in the downward-viewing position over the
ocean. The radiometer’s three-dimensional antenna patterns were measured at the
NIST near-field antenna range. Downward-viewing IR radiometer measurements
were compared with a new in situ technique that measured the ocean skin
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temperature, another first. This provided a way to absolutely calibrate the IR
radiometer measurements for sea skin temperatures. An empirical wind speed
algorithm was developed for the 23.87 GHz channel for the first time with
reasonable agreement. A few potential sources for the observed discrepancies
were suggested.
Finally, experimental and theoretical brightness temperature results were
discussed in section 5. The three-dimensional antenna patterns were incorporated
into computing the antenna brightnesses (temperatures). The absolute brightness
temperature measurements provided possible insight into the small-scale wave
features. Also, for the first time, upwind/downwind asymmetries in brightness
temperature were produced by a new atmosphere and two-scale ocean surface
model. The asymmetries were also measured in the data taken by the microwave
radiometer at SCOPE. Specifically, the 23.87 GHz downwind brightness
temperatures were warmer than the upwind temperatures. Conversely, the 31.65
GHz upwind brightness temperatures were warmer than the downwind
temperatures. Furthermore, the experimental and theoretical emission comparison
showed that the 23.87 GHz brightness temperature results agreed reasonably well
when the model’s small-scale height and wavelength were 0.5 mm and 0.5 cm,
respectively. However, the 31.65 GHz results did not agree as well as the 23.87
GHz comparison for the same sinusoidal parameters. The differences between
measurement and theory were assumed to be due mainly to a simplistic ocean
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surface model, excessive radiometric noise, and too few data samples in the
circular flights.
6.2 Suggestions for Future Work
The corrugated sinusoidal surface profiles used in the small-scale region
are too simplistic compared with actual ocean surfaces. An improvement over this
simple surface would be to use a surface randomly rough in one dimension using a
Monte Carlo technique [Johnson et al., 1994; Yueh et al., 1994]. This surface
formulation will hopefully model the capillary-ultragravity wave region in a more
realistic way. In addition, ocean waves larger than gravity waves, such as swells,
will hopefully be included in the model. A way to include foam in the model will
also be investigated. New techniques to model the ocean surface in two
dimensions will also be explored. A comparison between the Monte Carlo
technique and the small perturbation method would also be very useful. This
would hopefully provide further physical insight in the small-scale features of the
ocean surface. A way to include the stability factor (air-sea temperature
difference) will also be explored [Pospelov, 1996; Shaw and Chumside, 1996].
The NOAA/ETL internal radiometer noise was reduced by about six times
after SCOPE by D. A. Hazen of NOAA’s ETL. This noise reduction in the
radiometer will greatly enhance its ability to measure the ocean’s anisotropic
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surface in future experiments such as the Coastal Ocean Probe Experiment
(COPE). COPE is ETL’s second ocean probing experiment. It was conducted
from about the middle of September to the first of October 1995 off the Northwest
coast o f Oregon. The NOAA/ETL microwave radiometer, with improved noise
characteristics, and a new Russian K^-band polarimetric radiometer were operated
in COPE on a helium blimp over the ocean. The radiometer measurements will be
compared with the present atmosphere and ocean surface emission model and the
proposed Monte Carlo model. These new comparisons may clarify some of the
observed discrepancies in this paper. Undoubtably, new ideas on passive
radiometric wind vector sensing and on a better understanding of the ocean surface
will be found from this comparison.
168
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