SUBSTITUTE THIS TITLE FOR YOUR THESIS
TITLE… THE MICROWAVE BRIGHTNESS
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A thesis submitted in partial fulfillment of the requirements for the degree of
MASTER OF ARTS, SCIENCES, ETC.
in
YOUR GRADUATE PROGRAM
UNIVERSITY OF PUERTO RICO
MAYAGÜEZ CAMPUS
2005
Approved by:
________________________________
Sandra L. Cruz-Pol, PhD
Member, Graduate Committee
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Date
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Sandra L. Cruz-Pol, PhD
Member, Graduate Committee
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________________________________
Sandra L. Cruz-Pol, PhD
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Sandra L. Cruz-Pol, PhD
Representative of Graduate Studies
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Sandra L. Cruz-Pol, PhD
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José Mari Mutt, PhD (ONLY FOR PHD THESES)
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ABSTRACT
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This work presents models that predict extinction rates due to atmospheric gases for
35 GHz and 95 GHz radars as a function of elevation angle. The minimum detectable
radar reflectivity (dBZemin) is computed for both wavelengths using radiosonde and
microwave radiometer measurements. In general, sensitivity decreases with elevation
angle mostly because water vapor and their corresponding highest extinction rates
propagate through the lower portion of the atmosphere.
ii
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RESUMEN
Este trabajo presenta un modelo que predice la razón de extinción para señales de 33
y 95 GHz debido a los gases atmosféricos en función del ángulo de elevación. Se
computo la mínima reflectividad detectable por el radar (dBZemin) para ambas frecuencias
usando medidas de radiosonda y radiómetro de microondas. En general la sensitividad
decrece con el ángulo de elevación debido principalmente a que el vapor de agua y su
correspondiente alta extinción suceden en la porción baja de la atmósfera.
.
iii
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To my family . . .
iv
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ACKNOWLEDGEMENTS
During the development of my graduate studies in the University of Puerto Rico
several persons and institutions collaborated directly and indirectly with my research.
Without their support it would be impossible for me to finish my work. That is why I
wish to dedicate this section to recognize their support.
I want to start expressing a sincere acknowledgement to my advisor, Dr. Sandra CruzPol because she gave me the opportunity to research under her guidance and supervision.
I received motivation; encouragement and support form her during all my studies. With
her, I have learned writing papers for conferences and sharing my ideas to the public. I
also want to thank the example, motivation, inspiration and support I received from Dr.
José Colom. From these two persons, I am completely grateful. Special thanks I owe Dr.
Stephen M. Sekelsky for the opportunity of researching under his supervision, his support,
guidance, and transmitted knowledge for the completion of my work.
The Grant from NSF EIA 99-77071 provided the funding and the resources for the
development of this research. At last, but the most important I would like to thank my
family, for their unconditional support, inspiration and love.
v
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Table of Contents
ABSTRACT .................................................................................................................................................II
RESUMEN ................................................................................................................................................. III
ACKNOWLEDGEMENTS........................................................................................................................ V
TABLE OF CONTENTS ........................................................................................................................... VI
TABLE LIST ............................................................................................................................................. VII
FIGURE LIST ......................................................................................................................................... VIII
1
INTRODUCTION .............................................................................................................................2
1.1
1.2
1.3
2
MOTIVATION .................................................................................................................................2
LITERATURE REVIEW ....................................................................................................................3
SUMMARY OF FOLLOWING CHAPTERS ..........................................................................................5
THEORETICAL BACKGROUND ..................................................................................................6
2.1
RADIATIVE TRANSFER EQUATIONS ...............................................................................................6
2.1.1
Equations relating humidity profiles and microwave radiometer data to attenuation ............6
2.1.2
Water vapor profile and zenith attenuation statistics at 33 and 95 GHz .................................9
2.2
SCAN EQUATIONS ...................................................................................................................... 11
2.3
RADAR SYSTEM CHARACTERISTIC AND MCTEX EXPERIMENT LAYOUT................................. 16
2.3.1
Maritime Continent Thunderstorm Experiment (MCTEX) .................................................... 16
2.3.2
Radar Hardware of Cloud Profiling Radar System (CPRS) ................................................. 17
3
MICROWAVE ATMOSPHERIC ABSORPTION MODEL ..................................................... 18
3.1
ATMOSPHERIC ABSORPTION ..................................................................................................... 18
3.2
NEW MODEL RETRIEVED PARAMETERS ...................................................................................... 20
3.2.1
Bullet and Bullet Rosettes Toolbox for DDSCAT Program ................................................... 21
3.3
BACKSCATTERING WITH DDSCAT ........................................................................................... 21
4
CONCLUSIONS AND FUTURE WORK .................................................................................... 24
APPENDIX A.
IDL CODES FOR DBZEMIN .................................................................................... 27
APPENDIX B
PROGRAMS FOR BULLET AND DWR ............................................................. 29
APPENDIX B1 IDL PROGRAM FOR REFRACTION INDEX ........................................................................... 29
vi
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Table List
Tables
Page
TABLE 2.1CPRS Parameters ........................................................................................... 10
TABLE 2.2CPRS Operational Models ............................................................................. 11
TABLE 2.3 Mean values of the regions for CPRS data collected and dBZemin simulated 16
vii
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Figure List
Figures
Page
Figure 2.1 Passive remote sensing with upward-looking radiometer ................................. 7
Figure 2.2 Mean specific humidity profile ......................................................................... 9
Figure 2.3 Profile of extinction rates (--33 GHz and —95 GHz)Profile of extinction rates
(--33 GHz and —95 GHz) ........................................................................................ 10
Figure 2.5 Flowchart for the IDL routine used for calculating the dBZemin ................... 13
Figure 2.6 Mnimum detectable dBZe in mode 1 (= 200 ns), (a) 33 GHz, (b) 95 GHz . 14
Figure 2.8 The plot on (a) depicts the radar reflectivity measured at 95GHz with CPRS
and plot on data at same time than CPRS data was collected at 95GHz. ................. 14
Figure 2.9 Hill ratio comparison between various atmospheric models showing
agreement of the chosen water vapor absorption line shape with the radiometer data.
(See text for explanation of models' acronyms). ....................................................... 15
Figure 3.1 Bullet and Bullet Rosettes with different angles of junction ........................... 19
Figure 3.2 Wind speed model relating 0 to wind speed for the MCW algorithm as
calibrated for Topex altimeter. .................................................................................. 21
Figure 3.3 Backscattering (10 logb) of different indexes of refraction, (a) Backscattering
in dB to 33GHz with 652 dipoles array, (b) Backscattering in dB to 95GHz . ........ 22
Figure 3.4 Variation of the number of raob profiles used depending on the limits in space
and time separation imposed on the data .................................................................. 23
viii
1 INTRODUCTION
Knowledge of the state of the ocean plays a vital role in weather and ocean wave
forecasting models [Wilheit, 1979a] as well as in ocean-circulation models [Dobson et al.,
1987]. One approach to measuring the state of the ocean is by remote sensing of the
ocean’s surface emission. Microwave radiometers on satellites can completely cover the
earth’s oceans. Satellite radiometry offers numerous advantages over ship and buoy data.
Some of these advantages include the vast coverage of global seas, including locations
where radiosonde or buoys cannot be afforded, relatively low power consumption, no
maintenance and continuous operation under a wide range of weather conditions.
Measurements of the microwave brightness seen from the sea are used in the retrieval of
physical parameters such as wind speed, cloud liquid water and path delay. A suitable
model for these measurements includes contributions from atmospheric emission, mainly
water vapor and oxygen, and from ocean emission.
1.1 Motivation
The need to improve the calibration of existing models for atmospheric and ocean
emission is motivated by several current and upcoming satellite remote sensing missions.
In the case of TMR, an improved atmospheric model would enhance the inversion
algorithm used to retrieve path delay information. Another case is the JASON satellite, a
joint NASA/CNES radiometer and altimeter scheduled to be launched in 2000 [JPL,
1998]. For JASON, absolute calibration is performed by occasionally looking at calm
2
water. This type of calibration reduces the cost in hardware, complexity, size and power.
However, the quality of the calibration depends strongly on the accuracy of a model for
the calm water emission. In contrast, for the TMR an absolute calibration is performed
using hot and cold references carried by the satellite [Ruf et al., 1995].
In this document, a section is devoted to each of these models.
In Part I, the
development of an improved microwave atmospheric absorption model is presented. Part
II is dedicated to ocean microwave emission. In both cases, a model is developed and
iteratively adjusted to fit a carefully calibrated set of measurements.
1.2 Literature Review
Seasat was the first satellite designed for remote sensing of the Earth's oceans. It was
launched in 1978 by the National Aeronautic and Space Administration (NASA). The
mission was designed to demonstrate the feasibility of global satellite monitoring of
oceanographic phenomena and to help determine the requirements for an operational
ocean remote sensing satellite system. It included the Scanning Multichannel Microwave
Radiometer (SMMR) which measured vertical and horizontal linearly polarized
brightness temperatures at 6.6, 10.7, 18, 21 and 37 GHz. The SMMR was used to
retrieve surface wind speed, ocean surface temperature, atmospheric water vapor content,
rain rate, and ice coverage. Unfortunately, the mission only lasted approximately 100
days due to a failure of the vehicle's electric power system [Njoku et al.,1980].
In 1991 the European Space Agency launched The ERS-1 satellite. The primary
mission of ERS-1 was to perform remote sensing of the Earth's oceans, ice caps, and
3
coastal regions by providing global measurements of wind speed and direction, wave
height, surface temperatures, surface altitude, cloud cover, and atmospheric water vapor
levels. The mission included a nadir viewing radiometer operating at 23.8 and 36.5 GHz
and co-aligned with the altimeter to provide range corrections with 2 cm accuracy
[Günther et al., 1993].
In 1998 the US Navy launched the GEOSAT Follow On (GFO), designed to provide
real-time ocean topography data.
It includes a radar altimeter with 3.5 cm height
measurement precision. In addition, a dual frequency (22 and 37 GHz) water vapor
radiometer is included to provide path delay correction with an accuracy of 1.9 cm [Ruf
et al., 1996].
Uncertainties in the improved model for atmospheric emission are significantly
improved over previous published models. The line-strength and width parameters'
uncertainties are reduced to 1% and 1.6%, respectively. The overall uncertainty in the
new absorption model is conservatively estimated to be 3% in the vicinity of 22GHz and
approaching 8% at 32 GHz.
The RMS difference between modeled and measured
thermal emission by the atmosphere, in terms of the brightness temperature, is reduced by
23%, from 1.36 K to 1.05 K, compared to one of the most currently used atmospheric
models.
The modified ocean dielectric models exhibit significant improvements in the
estimate of TB. Of the two, the modified Ellison et al.[1977] model exhibits superior
overall performance, including the lowest bias at both frequencies, which is a very
important attribute indicative of the accuracy of the model. Its frequency dependence
4
was decreased to 0.30K, which will allow for more reliable extrapolation to higher
frequencies. In addition, this modified model has the lowest dependence on sea surface
temperature and the lowest RMS difference for both 18GHz and 37GHz. Consequently,
this is the model that we recommend for future remote sensing applications involving
microwave emissions from the ocean emissivity of the ocean. The average error in the
modified emissivity model, over the range 18-40 GHz, is found to be 0.37%, which in
terms of brightness temperatures, translates into a model error of approximately 1K.
1.3 Summary of Following Chapters
We first develop the necessary background theory in Chapter 1. Chapter 2 deals with
the model theory, experiments and data analysis related to the atmospheric absorption
model. The third chapter presents the model theory, data, statement of the problem, and
analysis for the ocean emission model. Conclusions are presented in Chapter 4.
5
2 THEORETICAL BACKGROUND
2.1 Radiative Transfer Equations
2.1.1 Equations relating humidity profiles and microwave radiometer data
to attenuation
The atmosphere receives most of its energy by means of solar electromagnetic
radiation. Some of this energy is absorbed by the atmosphere and some reaches the
surface of the Earth where it can also be absorbed or it can be reflected. Energy
absorption implies a rise in thermal energy and, therefore, temperature of the object. Any
object with a temperature above absolute zero emits electromagnetic radiation.
Electromagnetic emission implies a decrease in the object’s temperature.
These
processes, i.e. absorption and emission, altogether help create a balance between the
energy absorbed by the Earth and its atmosphere and the energy emitted by them. The
study of these energy transformation processes is called radiative transfer.
The Planck function for spectral brightness describes the radiation spectrum of a
blackbody at thermal equilibrium. It is given by
B f (T ) 
2hf 3 
1


2  hf / kT
c e
1
2.1
Using the Rosenkranz’s model for gaseous attenuation due to oxygen, KO2(I), and a
modified Liebe’s model for gaseous attenuation due to water vapor, Kwv(l), for every
6
layer (see Fig. 2.1) and for each radar frequency, 33 GHz and 95 GHz [Cruz-Pol, 1998;
Keihm, et al. 2002] total gaseous attenuation were calculated. The equation for Kwv(l) is
[Cruz-Pol, 1998]. It is given by shape and continuum terms.
Figure 2.1 Passive remote sensing with upward-looking radiometer
In this equations we delete the word Equation automatically inserted by Word® and we
formatted the text to the Right. You can leave the word Equation if you like. All the
body text is formatted as “justified” so that the margins are even..
TL  0.0109 C L Pwv 3.5e 2.1431 
TS 


1
1



f z   f z  f 2  f z  f 2   2 
2.2
 
TC  CC 1.1310 8 Pwv Pdry 3  3.57 10 7 Pwv 2 10.5
2.3

2.4
The absorption model for the water vapor resonance line is accomplished by the
addition of three parameters, given by CL = 1.064, CW = 1.066, and CC = 1.234. These
7
are the parameters for scaling the line strength, the line width and the continuum,
respectively.
Here f is the radar frequency in GHz, fz is the water vapor resonant
frequency, 22.235 GHz,  is the inverse temperature, Pwv is the water vapor partial
pressure, and Pdry is the difference between total pressure, P, and the water vapor
pressure, Pwv. Their respective equations are:

Pwv 
300
t
2.5
sh
0.7223
2.6
Pdry  P  Pwv
2.7
where sh is the specific humidity, t is the air temperature in Kelvin.
The width
parameter,, is defined as:

  CW 0.002784 Pdry 0.6  4.8Pwv 1.1

2.8
The oxygen absorption model is defined as:
K O2 
Pdry c 3

2
33
 f 
S T   Ln  f 
 fn 
n odd 1

2.9
where c=0.5034 x 1012, S(T) is the line strength [Rosenkranz, 1993]
S T   S ' T0  2 e 0.0068952nn1 1
8
2.10
2.1.2 Water vapor profile and zenith attenuation statistics at 33 and 95 GHz
Maritime Continent Island Thunderstorm Experiment was held during the Australian
summer monsoon. Thunderstorms develop in an environment with low shear and high
moisture. The data obtained by the radiosonde were corroborated with radiometer data.
Collecting the radiosonde measurements every day during the experiment, gaseous
attenuation, specific humidity and cumulative attenuation profiles were calculated for the
complete experiment. The average profile is shown in Figure 2.2.
Figure 2.2 Mean specific humidity profile
Gaseous attenuation mean for 33 GHz is 0.11 dB/Km and 0.74 dB/Km for 95 GHz (see
Fig. 2.3).
9
Figure 2.3 Profile of extinction rates (--33 GHz and —95 GHz)Profile of
extinction rates (--33 GHz and —95 GHz)
Equation (2.10) contains all the quantities needed to compute the response of a satellitebased microwave radiometer to changes in atmospheric and surface variables.
The 33 GHz signal has more peak power than the 95 GHz signal (see Table 2.1) to
compensate for its smaller gain (wide bandwidth).
TABLE 2.1CPRS Parameters
Frequency (GHz)
Peak power (kW)
Average power (W)
Pulse width (ns)
Gain
Range gate spacing (m)
Pulse repetition freq. (kHz)
Noise figure (dB)
Bandwidth (MHz)
Beam width (deg)
10
W
band
95
1.5
15
500
105.8
75
10
13
2
0.18
Ka band
33
120
120
200
104.83
30
5
11
5
0.50
Thus, the 95 GHz signal has a comparable performance and has similar values of
minimum detectable signal to the 33 GHz signal, obtaining similar resolution and noise
immunity for both signals for a single pulse in zenith angle. This is shown in Figure 2.5.
The other modes’ parameters are shown in the Table 2.2
TABLE 2.2CPRS Operational Models
Pulse width (ns)
W Band. Pulse Repetition
Frequency (kHz)
Ka Band. Pulse Repetition
Frequency (kHz)
Bandwidth (MHz)
Mode 1
Mode 2
Mode 3
200
10,000
500
10,000
1,000
10,000
2,500
1,000
500
5
2
1
But when the radar scans and many pulses are sent, the radar performance does not
behave in the same way as when as sending a single pulse in zenith angle. So we need to
analyze the performance of scanning radar
2.2 Scan Equations
The one-way path loss, Ag, depends on the frequency being used. For frequencies
where the path loss degrades the signal strongly, higher power was used to minimize this
effect.
11
After obtaining the atmospheric attenuation for every layer (see Fig. 2.1), we found
the cumulative gaseous attenuation. This one is calculated for a fixed angle and for every
range gate in which the radar operates. A matrix of radius times angles was used to save
the projected attenuation. Then the cumulative attenuation for specific angle and radius
was computed as:
Ta  TUP  s Ts e  ( 0,H ) sec  (1 s )(TDN  TC e  ( 0, ) sec )e  ( 0,H ) sec
2.11
Finally with the cumulative attenuation for every radius at a specific angle, the total
path loss, l, can be calculated. To implement all this procedure we used IDL program.
IDL is a language capable to process great amount of data, and a flow diagram in Figure
2.6 shows the algorithm implemented in this work.
12
Figure 2.4 Flowchart for the IDL routine used for calculating the dBZemin
Graphs from calculations of the dBZemin when the radar operates in modes 1, 2, and 3,
for every radio and each angle at 33 and 95 GHz are plotted in Figures 2.7, 2.8, and 2.9.
The delta between two lines of the contour is 2 dB. The lightest bar colors represent
larger minimum reflectivity values that can be detected by the radar, i.e. less signal can
be detected in those areas.
13
(a)
(b)
Figure 2.5 Mnimum detectable dBZe in mode 1 (= 200 ns), (a) 33 GHz, (b)
95 GHz
(a)
Figure 2.6 The plot on (a) depicts the radar reflectivity measured at 95GHz
with CPRS and plot on data at same time than CPRS data was collected at
95GHz.
14
The radar begins to detect the cloud from a radius of 13 km and from an angle
between 8 and 76 degrees. To the W band, the cloud looks much smaller than the one
shown by the Ka band. These data validate the simulation and confirm the effect of the
attenuation of the W band in angles smaller than 50 degrees (see Fig. 2.11a). Figures
2.10 and 2.11 show three regions, these are the dBZemin that represent the CPRS data. We
can see here that the radar received a greater reflectivity than the minimum estimated
reflectivity. We can see that this is also true for the 95 GHz signal.
These results strongly suggest that VVW is the preferred choice for vapor absorption
line shape at 22 GHz. Note that the same finding was obtained by Hill [1986] when the
ratio test was applied to the original Becker and Autler [1946] laboratory data.
Figure 2.7 Hill ratio comparison between various atmospheric models
showing agreement of the chosen water vapor absorption line shape with the
radiometer data. (See text for explanation of models' acronyms).
15
The other regions behave in the same way. All the reflectivity mean values are within
the limits of the mean dBZemin simulated for both, the 33 GHz as for the 95 GHz. The
other mean values are listed in Table 2.3.
TABLE 2.3 Mean values of the regions for CPRS data collected and dBZemin
simulated
Region 1
Region 2
Region 3
Mean dBZemin33GHz (dB)
Mean Reflectivity at 33GHz (dB)
-27.9162
3.718391
-28.8563
7.22807
-29.1437
-2.63717
Mean dBZemin95GHz (dB)
Mean Reflectivity at 95GHz (dB)
-12.9728
-8.31193
-17.7505
-7.19231
-23.7513
-3.61205
2.3 Radar System Characteristic and MCTEX Experiment
Layout
2.3.1 Maritime Continent Thunderstorm Experiment (MCTEX)
The MCTEX experiment was performed in the North Coast of Australia, and in the
Bathurst and Melville Islands. The principal objective of this experiment was to better
understand the physical processes, such as humidity balance over tropical islands on a
maritime continent. For this reason, the experiment was held between November 13th
and December 10th, 1995; season on which the transition phases occurs between the dry
and wet seasons. The data of this experiment were collected with different sensors. One
set was collected by means of the Cloud Profiling Radar System (CPRS). This one
16
collected data on the Ka frequency band (33.12 GHz) and W frequency band (94.92
GHz). Data from the W frequency band, 95 GHz, also was collected by the Airborne
Cloud Radar. The NOAA radar collected data on the S frequency band, at 2.8 GHz.
2.3.2 Radar Hardware of Cloud Profiling Radar System (CPRS)
The CPRS is a dual-frequency polarimetric Doppler radar system that works with two
sub-systems at 33 and 95 GHz.
This was fully developed by the University of
Massachusetts’ Microwave Remote Sensing Laboratory (MIRSL).
Table 2.1 shows the CPRS parameter. The CPRS has a programmable structure that
allows working in different modes of scanning. It has a high-speed VXI-bus-based data
acquisition and digital signal processing (DSP) system. A radome protects the system
from atmospheric effects. Both the 33 and 95 GHz sub-systems simultaneously transmit
and receive by means of a single aperture and not producing pointing errors between both
frequencies. Table 2.1 shows other typical characteristics of the CPRS operation. The
CPRS works in three different operational modes, changing the pulse width and by
consequence the pulse repetition frequency and the bandwidth change. These values are
shown in 2. 2. The CPRS measures can obtain the reflectivity (Ze), mean fall velocity (u)
linear depolarization ratio (LDR), velocity spectral width (v), and the full Doppler
spectrum (S(v)) [Firda, 1997; Lohmeire, et al. 1997].
17
3 Microwave Atmospheric Absorption Model
An improved model for the absorption of the atmosphere near the 22 GHz water
vapor line is presented. The Van-Vleck-Weisskopf line shape is used with a simple
parameterized version of the model from Liebe for the water vapor absorption spectra
and a scaling of the model from Rosenkranz for the 20-32 GHz oxygen absorption.
Radiometric brightness temperature measurements from two sites of contrasting
ground truth for comparison with in situ radiosonde derived brightness temperatures.
The retrieval of the new model’s four parameters, related to water vapor line strength,
line width and continuum absorption, and far-wing oxygen absorption, was performed
using the Newton-Raphson inversion method.
3.1 Atmospheric Absorption
Various shapes of the bullet rosettes are observed (see Fig. 3.1). The angles among the
bullets within the rosette are random between 70º and 90º. Each bullet has a longitude
relation [Heymsfield, 1972], L (mm), versus wide, w (mm), (twice times the apothem) for
temperatures between –18º and –20 ºC given by
18
 TB1
 C
 L
 TB 2
 C L
J   TB 3

 C L
 
 T
 Bn
 C L
TB1
CW
TB 2
CW
TB 3
CW

TBn
CW
TB1
CC
TB 2
CC
TB 3
CC
TBn
CC
TB1 
C X 

TB 2 
C X 
TB 3 

C X 
 
TBn 

C X 
3.1
and the Gross Line shape is given by [Gross, 1955]
 1

u ( z / L' )   1  7 z / L'
(1  18z / L'  3 ).25
u

for z / L'  0 (neutral conditions )
for z / L'  0(stable conditions )
for z / L'  0(unstable conditions )
3.2
Although DDA can describe any geometry, it is limited by a minimum distance d that
should exist between dipoles. This distance should be inversely proportional to any
structural longitude on the target and to the wavelength. Previous studies [Draine and
Flatau, 1994] sum up the two criteria in equation 3.6.
Figure 3.1 Bullet and Bullet Rosettes with different angles of junction
19
In this way the equations were determined for the bulk density, ρ, of the bullet,
considering the solid ice density as 0.9 g cm-3 and using the volume of ice in individual
crystals [Heymsfield, 1972]
As the Wiener’s theorem states [Oguchi, 1983], the complex index of refraction, m,
depends of the bulk density when dealing with dry ice particles:
Ln is proportional to the shape of the lines
.
 Y ( f  f )  Y ( f  f )
n
n
n
n 
Ln   n
 n
 n2   f  fn 2  n2   f  fn 2 


Equation 3.3
The pressure-broadened line half-width is,


 n  0.001w Pdry  .8  11
. PH2 O 
Equation 3.4
The O2 resonant lines are very close to each other and troposphere pressures are high
enough ( > 100 mbars) to cause the lines to broaden and overlap.
This is called
collisional broadening and is taken into account through the interference parameter.
3.2 New Model Retrieved Parameters
The final retrieved parameters, CL, CW, CC and CX, are shown in Table 2.1. As the
table indicates, the nominal parameters used in the L87R93 model are 3 to 7 percent
lower. Figures 2.7a-c depict plots of the brightness temperature for three climatological
conditions. The new estimated parameters show better agreement with the WVR data.
L87R93 model as the reference (therefore, by definition the L87R93 model is . In these
figures we have included the L93 model which, as explained above, is similar to L87R93
20
except that it has a higher water vapor line
Figure 3.2 Wind speed model relating 0 to wind speed for the MCW
algorithm as calibrated for Topex altimeter.
3.2.1 Bullet and Bullet Rosettes Toolbox for DDSCAT Program
We developed two toolboxes for DDSCAT where we implemented the most common
shapes of the cirrus ice crystals, i.e. the bullet and bullet rosettes.
Using a single
DDSCAT environment by means of the ddscat.par file [Draine and Flatau, 2000], we
specified which one of the geometries we wanted to use and parameters such as size,
dielectric constant of the material, and in general all the parameters related to the target to
be analyzed.
3.3 Backscattering with DDSCAT
Once the bullet toolbox was created in DDSCAT, we proceeded to use it to simulate
the crystal’s backscattering at 33 and 95 GHz. Figure 3.3 shows the backscattering for
21
one bullet crystal of different sizes using several models for index of refraction and
crystal density. The figure shows the sensitivity of the backscattering to the index of
refraction, showing the necessity of considering the index of refraction for each size and
density of the ice crystal, and not assuming a constant density for all the bullets sizes.
(a)
(b)
Figure 3.3 Backscattering (10 logb) of different indexes of refraction, (a) Backscattering
in dB to 33GHz with 652 dipoles array, (b) Backscattering in dB to 95GHz .
It can also be seen that the backscattering obtained when varying the index of
refraction according to the particle size is not significantly different to the results
obtained when using constant indexes of refraction for different particle sizes.
Given that one of the objectives is to analyze the DWR, we designed an interface
between DDSCAT and IDL program. We developed a routine that iteratively collects
data from IDL such as the index of refraction, m, which is computed according to the
particles size and the index of refraction of the solid ice, ni, and saving m in DDSCAT to
22
compute the backscattering and again this value is saved in IDL to obtain the DWR. The
DWR is defined as [Sekelsky, et al. 1999]

D





  3.67   
2
D
0 
 l 4 K I h   b D, l ,  D 2   e 
dD 


0

DWR  10 log
3.5

D



  3.67   
D0 
  4 K   2  D,  ,  D 2   e 
dD 
I l
b
h
 h

0


where l and h are the values of the smaller wavelength and greater respectively, KI is an


dimensionless quantity that depends on the index of refraction and on the density. For ice
we used 0.176 for both frequencies [Sekeslky, et al. 1999].
Figure 3.4 Variation of the number of raob profiles used depending on the limits in space
and time separation imposed on the data
23
4 CONCLUSIONS AND FUTURE WORK
Recent work to determine the sea water dielectric coefficient was based on laboratory
measurements of sea water samples from different parts of the ocean. Although these
measurements should render good understanding of the emission from a calm ocean
surface, their accuracy in providing values of the ocean still needed to be examined. Our
present investigation of the specular sea emission seen from space provides field
verification of the sea water specular emissivity over broader regions of the oceans. In
this work, we investigate and adjust two ocean dielectric models using well calibrated
radiometer data from the TOPEX/Poseidon satellite mission, paying particular attention
to reducing the overall bias of the estimated brightness. In addition, we evaluate the
performance of several models for their dependence on salinity and sea temperature.
The modified models exhibit significant improvements in the estimate of TB. Of the two
modified models, ModE exhibits superior overall performance. It has the lowest bias at
both frequencies (0.16 and 0.14K, respectively), which is indicative of the accuracy of
the model. Its frequency dependence was decreased from -2.3 to 0.30K. In addition,
ModE has the lowest dependence on sea surface temperature and the lowest RMS
difference of 2.58K and 3.52K for 18GHz and 37GHz, respectively. For these reasons,
we recommend this model for future remote sensing applications involving microwave
emissions from the ocean.
24
REFERENCES
Altshuler, E. E. and R. A. Marr, “A comparison of experimental and theoretical values of
atmospheric absorption at the longer millimeter wavelengths,” IEEE Trans. Antennas
Propagat., vol. 36, no. 10, pp. 1471-1480, Oct. 1988.
Aydin, K. and C. Tang, “Millimeter wave radar scattering from model ice crystal
distributions,” IEEE Trans. Geosci. Remote Sens., vol. 35, pp. 140-146, 1997 a.
Cruz-Pol, S. L., C. S. Ruf and S. J. Keihm, “Improved 20-32 GHz Atmospheric
Absorption Model,” Radio Sci., vol. 33, no. 5, pp. 1319-1333, 1998.
Draine, B. T. and P. J. Flatau, “Discrete-dipole approximation for scattering
calculations,” J. Opt. Soc. Am. A, vol. 11, pp. 1491-1499, 1994.
Doviak, R. J.and D. S. Zrnic, Doppler Radar and Weather Observations, Second edition,
Academic Press, San Diego, 1993.
Evans, K. F. and J. Vivekanandan, “Multiparameter radar and microwave radiative
transfer modeling of nonspherical atmospheric ice particles,” IEEE Trans. Geosci.
Remote Sensing., vol. 28, pp. 423-437, July 1990
Keihm, S. J., C. Ruf, V. Zlotnicki and B. Haines, “TMR Drift Analysis,” Jet Propulsion
Laboratory, Internal Report, October 6, 1997.
Klein, L. A., and C. T. Swift, “An Improved Model for the Dielectric constant of Sea
Water at Microwave Frequencies,” IEEE Trans. on Antennas Propagation, Vol. AP25, No. 1, 1977.
Hogan, R. J. and A. J. Illingworth, “The potential of spaceborne dual-wavelength radar to
make global measurements of cirrus clouds,” J. Atmos. Oceanic Technol., vol. 16,
518-531. 1999
Keihm, S. J., Y. Bar-Server, and J. C. Liljegren, “WVR-GPS Comparison Measurement
and Calibration of the 20-32 GHz Tropospheric Water Vapor Absorption Model”,
25
IEEE Trans. Geosci. Remote Sensing. 2002, 40, No. 6, pp. 1199-1210
Lhermitte, R., “A 95 GHz Doppler radar of cloud observations,” J. Atmos. Ocean.
Technol., vol. 4, pp. 36-48, 1987.
Li, L., S.M. Sekelsky, S.C. Reising, C.T. Swift, S.L. Durden, G.A. Sadowy, S.J. Dinardo,
F.K. Li A. Huffman, G.L. Stephens D.M. Babb, and H.W. Rosenberger, “Retrieval of
Atmospheric Attenuation Using Combined Ground-based and Airborne 95 GHz
Cloud Radar Measurements,” J. Atmos. Oceanic Technol., vol. 18, 1345-1353. 2001
Matrosov, S. Y. “Radar reflectivity in snowfall,” IEEE. Trans. Geosci. Remote. Sens., vol.
30, pp. 454-461, 1992.
Oguchi, T. “Electromagnetic wave propagation and scattering in rain and other
hydrometeors,” Proc. IEEE, vol. 71, pp. 1029-1078, 1983
Ray, P. S., “Broadband complex refractive indices of ice and water,” Appl. Opt., vol. 11,
pp. 1836-1844, 1972
Rosenkranz, P. W., “Absorption of Microwaves by Atmospheric Gases”, In: Atmospheric
Remote Sensing by Microwave Radiometry, Chapter 2, Ed. By Jansen, Wiley, New
York, 1993.
Sekelsky, S. M., “Multi-frequency radar Doppler Spectrum Measurements of Cirrus
Clouds,” Geoscience and Remote Sensing Symposium. IGARSS '01., vol. 2, 697 –699
2001.
Ulbrich, C. W., “Natural variations in the analytical form of the raindrop size
distribution,” J. Climate Appl. Meteor., vol. 22, pp. 1764-1775, 1983.
Wilheit, T.T., “The Effect of Wind on the Microwave Emission From the Ocean’s
Surface at 37 GHz,” J. Geophys. Res., Vol. 84, No. C8, pp. 244-249, 1979.
26
APPENDIX A.
IDL CODES FOR DBZEMIN
;********dBZemin Program********
;********MAIN PROGRAM*********
LoadCT, 5
sondefilename='c:/jorgemvg/prog-idl/DataAustralia/Radiosonde/sonde.951127.025800.cdf'
mwrfilename='c:/jorgemvg/prog-idl/DataAustralia/Radiometer/mwr.951127.000020.cdf'
;**Function to read microwave-radiometer data
get_mwr_cdfdata, mwrfilename, VAPcm, LIQcm, DEWflag, t_begin$, $
date$,unix_time,sec_into_UTCday
;**Function to read radiosonde data
get_sonde_cdfdata, sondefilename, tdry, sh, rh, dp, h, pres, $
wspd, deg, t_begin$, date$,unix_time,sec_into_UTCday
;**Function to read Radar data
Radar,z_mask_range_33,z_mask_range_95
;;********************************************************************************
h = h/1000. ;altitude [Km]
pres = pres/0.1 ;pressure [Kpascales]
; a extrapol le debe entrar h en (Km) y pres en (KPascales)
extrapol_general,z_mask_range_33,h,tdry,pres,sh,altura,temperatura,presion,humedad_especifica
altura = altura*1000.;altitude [m]
presion = presion*0.1 ;pressure
[ mbars]
tdry = temperatura ;temperature [deg C]
sh = humedad_especifica ;specific humidity [gm^-3]
pres = presion
h = altura
;omit radiosonde data above 35 km to speed up processing
alt=30000.
hlimit=max(where(h LT alt))
tdry=tdry(0:hlimit) & sh=sh(0:hlimit)
h=h(0:hlimit) & pres=pres(0:hlimit)
;setup regular height grid for profiles
num_elem=500
del=alt/num_elem
h_prof = findgen(num_elem) * del ; 0-35km
tdry = INTERPOL(tdry, h, h_prof) ; regrid profiles
sh = INTERPOL(sh, h, h_prof) > 0.
27
pres = INTERPOL(pres, h, h_prof)
h = h_prof
; compare radiosonde and mwr data
L=0
FOR i=0,n_elements(h)-2 DO L=L+sh(i)*(h(i+1)-h(i))
L=0.001*L ; mm of water vapor in column from radiosonde profile
L = L*0.1 ; cm of vapor ... compare to Vapcm from microwave radiometer
; probably will not be exactly the same since different meas. locations
; if mwr data valid then use to correct radiosonde humidity profiles
indx = where(dewflag LT 1) ; filter out flagged data
sh = sh*mean((vapcm(indx)))/L ; scale radiosonde profile by mwr total
prSH=fltarr(2,n_elements(sh)/2)
FOR par=0,(n_elements(sh)/2)-1 DO BEGIN
prSH(0,par)=sh(par*2)
prSH(1,par)=h(par*2)/1000.
ENDFOR
for the gases atten. SLCP June 2001
PRO atten_humidity_liebe, sh,tdry,pres,fi, h, AGASEOUS,Agas_liebe, KGASEOUS
_ground(n,rg) = extinction rate at ground level [dBkm^-1]
height=h/1000. ; h esta en metros , height esta en kilometros
rangesamples = size(height)
rangesamples = rangesamples(1)
AH2O_liebe(i, j) = TOTAL(KH2O_liebe(i, 0:j)*ABS((height(1:j+1)-(height(0:j))) > 0.))
ENDFOR
ENDFOR
AH2O_liebe(*,rangesamples -1 ) = AH2O_liebe(*,rangesamples -2 )
PRO scanning_new2, sh,tdry,pres,fi, h, AGASEOUS,Agas_liebe, KGASEOUS,LF1,LF0,ATKF1,ATKF0
ATKF1(zeta,altura)=TOTAL(KGASEOUS_EQUIf1(zeta,0:altura)*ABS(((proyeccion_radio(zeta,
1:altura+1)-proyeccion_radio(zeta,0:altura))/sin(angles(zeta) * !pi/180)) > 0.))
ATKF0(zeta,altura)=total(KGASEOUS_EQUIf0(zeta,0:altura)*abs(((proyeccion_radio(zeta,1:altu
ra+1)-proyeccion_radio(zeta,0:altura))/sin(angles(zeta) * !pi/180)) > 0.))
dbz0=imgpolrec(dbz0, 0., 91., 0., 40., 0., 25., .03, 0., 25., .03)
ocu95=intarr(n_elements(ymax),20)
Position = [0.1, 0.9, 0.9, 0.95], Color=!P.Background
stop
END
28
APPENDIX B PROGRAMS FOR BULLET AND DWR
APPENDIX B1 IDL PROGRAM FOR REFRACTION INDEX
;****IDL PROGRAM***
;*** Refraction Index
n=200 ;
index=complexarr(2,n)
D=fltarr(n)
aeff=fltarr(n)
p=fltarr(n)
fi=fltarr(n)
for i=0, n-1 DO BEGIN
D(i)=(i+1)*1E-2
;D[mm]
p(i)=0.78*D(i)^(-0.0038) ;Heymsfield density relationship bullet
pi=0.916 ; pi[g*cm^-3]
fi(i)=p(i)/pi
ni=[complex(1.785, 0.000235),complex(1.784, 0.00010)] ; 33GHz , 95GHz paper Ray 1972
f=fi(i)
for k=0, n_elements(ni)-1 DO BEGIN
n=ni(k)
index(k,i)=(2.+(n^2)+2.*f*(n^2-1))/(2.+(n^2)+f*(1-n^2))
end
aeff(i)=1e+3*D(i)/2 ;[um]
END
END
29