plan till a

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AN IMPROVED MODEL FOR THE MICROWAVE

BRIGHTNESS TEMPERATURE SEEN FROM SPACE

OVER CALM OCEAN

by

Your name here

A thesis submitted in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCEin

ELECTRICAL ENGINEERING

UNIVERSITY OF PUERTO RICOMAYAGEZ CAMPUS

2005Approved by:

________________________________Sandra L. Cruz-Pol, PhDMember, Graduate Committee

__________________Date

________________________________

Sandra L. Cruz-Pol, PhDMember, Graduate Committee

__________________

Date

________________________________Sandra L. Cruz-Pol, PhDPresident, Graduate Committee

__________________Date

________________________________Sandra L. Cruz-Pol, PhDRepresentative of Graduate Studies

__________________Date

________________________________

Sandra L. Cruz-Pol, PhDChairperson of the Department

__________________

Date


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This thesis was auto-formatted by Dr. Sandra Cruz-Pol, please use to ease your life.

ABSTRACT

This thesis was formatted so that you only type on top of it your material and it should redo theTable of contents automatically by the command on the Menu: Insert>Reference>Index andTables. IMPORTANT: when pasting material to this file be sure to use Edit>Paste_Special>Unformatted_Text, so that the format given by this file is not changed. When pasting figures,be sure to use Paste_special>Picture(JPEG) to make the size of your thesis file as much as 10times smaller than using just Paste, which usually utilized the BMP format for figure, makingyour file huge and not portable. The figures should be inserted usingInsert>References>Caption>(Figure ), and typing the caption of the figure. In some versionsof Word you can skip the Reference part. The tables should be inserted using

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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.

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RESUMEN

Este trabajo presenta un modelo que predice la razn de extincin para seales de 33 y 95 GHz

debido a los gases atmosfricos en funcin del ngulo de elevacin. Se computo la mnima

reflectividad detectable por el radar (dBZemin) para ambas frecuencias usando medidas de

radiosonda y radimetro de microondas. En general la sensitividad decrece con el ngulo de

elevacin debido principalmente a que el vapor de agua y su correspondiente alta extincin

suceden en la porcin baja de la atmsfera.

.

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To my family . . .

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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 Cruz-Pol

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. Jos 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.

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Table ofContents

ABSTRACT .................................................................................................................................................................II

RESUMEN ................................................................................................................................................................III

ACKNOWLEDGEMENTS .......................................................................................................................................V

TABLE OF CONTENTS ............................................................................................................................... ..........VI

TABLE LIST ............................................................................................................................................................VII

FIGURE LIST ........................................................................................................................................................VIII

1 INTRODUCTION .....................................................................................................................................................2

0.1 MOTIVATION..................................................................................................................................................... 20.2 LITERATURE REVIEW.........................................................................................................................................30.3 SUMMARYOF FOLLOWING CHAPTERS...................................................................................................................5

1 THEORETICAL BACKGROUND .........................................................................................................................6

1.1 RADIATIVE TRANSFEREQUATIONS .....................................................................................................................61.2 SCAN EQUATIONS............................................................................................................................................ 121.3 RADARSYSTEM CHARACTERISTIC AND MCTEX EXPERIMENT LAYOUT.................................................................17

2 MICROWAVE ATMOSPHERIC ABSORPTION MODEL ........................................................... ..... ..... ......19

2.1 ATMOSPHERIC ABSORPTION............................................................................................................................... 192.2 NEW MODEL RETRIEVED PARAMETERS..............................................................................................................212.3 BACKSCATTERINGWITH DDSCAT ...................................................................................................................23

3 CONCLUSIONS AND FUTURE WORK ...................................................................................................... ..... .26

4 APPENDIX A. IDL CODES FOR DBZEMIN .................................................................................................. .29

APPENDIX B PROGRAMS FOR BULLET AND DWR ..................................................................... ..... ..... ....32

APPENDIX B1 IDL PROGRAM FORREFRACTION INDEX...........................................................................................32......................................................................................................................................................................... 32

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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

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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 2.4 MINIMUM DETECTABLE SIGNAL FOR A SINGLE ZENITH PULSE AT DIFFERENT

MODES OF RADAR PULSE WIDTH.(A) MODE 1: = 200NS, (B) MODE 2: = 500NS, (C) MODE 3: = 1,000NS.....................................................................................................................................................................11

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 2.7 MINIMUM DETECTABLE DBZE IN MODE IN MODE 2 (= 500 NS), (A) 33 GHZ, (B) 95GHZ..............................................................................................................................................................................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..........................................................................................................................................................................15

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)...............16

FIGURE 3.10 BULLET AND BULLET ROSETTES WITH DIFFERENT ANGLES OF JUNCTION.......20

FIGURE 3.11 WIND SPEED MODEL RELATING 0 TO WIND SPEED FOR THE MCWALGORITHM AS CALIBRATED FOR TOPEX ALTIMETER.................................................................... ...22

FIGURE 3.12 METHODOLOGY USED TO CREATE A BULLET FORMED BY AN ARRAY OF N

DIPOLES SEPARATED BY, (A) GENERAL PROCESS, (B) BULLET 3D-VIEW, AND (C) BULLET

ROSETTE WITH 3 BULLETS.............................................................................................................................. ..23

FIGURE 3.13 BACKSCATTERING (10 LOGB) OF DIFFERENT INDEXES OF REFRACTION, (A)BACKSCATTERING IN DB TO 33GHZ WITH 652 DIPOLES ARRAY, (B) BACKSCATTERING IN DB

TO 95GHZ ..................................................................................................................................................................24

FIGURE 3.14 VARIATION OF THE NUMBER OF RAOB PROFILES USED DEPENDING ON THE

LIMITS IN SPACE AND TIME SEPARATION IMPOSED ON THE DATA............................................... ..25

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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 oceans surface

emission. Microwave radiometers on satellites can completely cover the earths 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.

0.1 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 water. This type of calibration reduces the cost

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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.

0.2 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].

, cloud water content, and ocean surface wind speeds [Hollinger et al., 1990].

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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 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 [Gnther 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].

Sekelsky et al. [1998, 1999] used simulations from the ice crystals backscattering at various

millimeter wavelengths using the DDA models on the version 5 of DDSCAT, using a more

realistic density model where ice density is not constant, as in previous studies, but decreases

with the particles diameter. They calculated the dual-wavelength ratio (DWR). Their findings

also agree with previous studies where the shape and orientation are the principal causes of

error on the DWR estimates and other products.

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

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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 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.

0.3 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.

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1 THEORETICAL BACKGROUND

1.1 Radiative Transfer Equations

1.1.1 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 objects

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

=

1

12)(

/2

3

kThff ec

hfTB 2.1

Using the Rosenkranzs model for gaseous attenuation due to oxygen, KO2(I), and a modified

Liebes model for gaseous attenuation due to water vapor,Kwv(l), for every layer (see Fig. 2.1)

and for each radar frequency, 33 GHz and 95 GHz [Cruz-Pol, 1998;Keihm, et al. 2002] total

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gaseous attenuation were calculated. The equation forKwv(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..

( )( ) = 1143.25.30109.0 ePCT wvLL 2.2

( ) ( )

+++

=

222

11

fffffT

zzzS 2.3

( 5.102738 1057.31013.1 wvdrywvCC PPPCT += 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 are the parameters

for scaling the line strength, the line width and the continuum, respectively. Herefis the radar

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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:

t

300= 2.5

7223.0

shPwv = 2.6

wvdry PPP = 2.7

wheresh is the specific humidity, tis the air temperature in Kelvin. The width parameter,, is

defined as:

1.16.08.4002784.0 wvdryW PPC += 2.8

The oxygen absorption model is defined as:

( ) ( )=

=

33

1

23

2

oddn

nn

dryO fL

f

fTS

cPK

2.9

where c=0.5034 x 1012, S(T) is the line strength [Rosenkranz, 1993]

( ) ( ) ( ) ( )110068952.020

'+= nneTSTS 2.10

1.1.2 Water vapor profile and zenith attenuation statistics at 33 and 95 GHz

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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).

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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 satellite-based

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

W

band

Ka band

Frequency (GHz) 95 33Peak power (kW) 1.5 120

Average power (W) 15 120Pulse width (ns) 500 200

Gain 105.8 104.83Range gate spacing (m) 75 30

Pulse repetition freq. (kHz) 10 5Noise figure (dB) 13 11Bandwidth (MHz) 2 5Beam width (deg) 0.18 0.50

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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

(a) (b) (c)

Figure 2.4 Minimum detectable signal for a single zenith pulse at different modes of

radar pulse width.(a) Mode 1: = 200ns, (b) Mode 2: = 500ns, (c) Mode 3: = 1,000ns.

TABLE 2.2CPRS Operational Models

M M M

Pulse width (ns) 200 500 1,000WBand. Pulse Repetition

Frequency (kHz)10,000 10,000 10,000

Ka Band. Pulse RepetitionFrequency (kHz)

2,500 1,000 500

Bandwidth (MHz) 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

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1.2Scan 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.

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:

sec),0(sec),0(sec),0( ))(1( HCDNsH

ssUPa eeTTeTTT +++= 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.

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Figure 2.5 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.

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(a) (b)

Figure 2.6 Mnimum detectable dBZe in mode 1 ( = 200 ns), (a) 33 GHz, (b) 95 GHz

(a) (b)

Figure 2.7 Minimum detectable dBZe in mode in mode 2 (= 500 ns), (a) 33 GHz, (b) 95GHz

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(a)

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.

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.

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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).

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

R

e

g

i

o

n

1

R R

e

g

i

o

n

3

Mean dBZemin33GHz (dB) -27.9162 -28.8563 -29.1437Mean Reflectivity at 33GHz (dB) 3.718391 7.22807 -2.63717

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Mean dBZemin95GHz (dB) -12.9728 -17.7505 -23.7513Mean Reflectivity at 95GHz (dB) -8.31193 -7.19231 -3.61205

1.3 Radar System Characteristic and MCTEXExperiment Layout

1.3.1 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 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.

1.3.2 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).

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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].

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2 Microwave Atmospheric AbsorptionModel

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 climatological properties San Diego, CA and

West Palm Beach, FL were used as ground truth for comparison with in situ radiosonde

derived brightness temperatures. The retrieval of the new models 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.

2.1Atmospheric Absorption

Various shapes of the bullet rosettes are observed (see Fig. 3.1). The angles among the bullets

within the rosette are random between 70 and 90. Each bullet has a longitude relation

[Heymsfield, 1972],L (mm), versus wide, w (mm), (twice times the apothem) for temperatures

between 18 and 20 C given by

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J

T

C

T

C

T

C

T

C

T

C

T

C

T

C

T

CT

C

T

C

T

C

T

C

T

C

T

C

T

C

T

C

B

L

B

W

B

C

B

X

B

L

B

W

B

C

B

X

B

L

B

W

B

C

B

X

Bn

L

Bn

W

Bn

C

Bn

X

=

1 1 1 1

2 2 2 2

3 3 3 3

3.12

and the Gross Line shape is given by [Gross, 1955]

+=

=)conditions0(unstable'/for)'/181(

)conditions0(stable'/for'/71

)conditions(neutral0'/for1

)'/(25.3 LzLz

LzLz

Lz

Lz

u

u

3.13

Although DDA can describe any geometry, it is limited by a minimum distance dthat 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 3.10 Bullet and Bullet Rosettes with different angles of junction

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In this way the equations were determined for the bulk density, , 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 Wieners 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

.

( ) ( )

LY f f

f f

Y f f

f f

nn n n

n n

n n n

n n

=+

+

+

+

( ) ( )2 2 2 2

Equation 3.14

The pressure-broadened line half-width is,

[ ] n dry H Ow P P= +0 001 118 2. ..

Equation 3.15

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.

2.2 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. Each

graph has a plot corresponding to the L87R93 and new models. Also shown are the radiometer

measured brightnesses. 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

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figures we have included the L93 model which, as explained above, is similar to L87R93

except that it has a higher water vapor line

Although DDA can describe any geometry, it is limited by a minimum distance dthat 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 3.11 Wind speed model relating 0 to wind speed for the MCW algorithm ascalibrated for Topex altimeter.

2.2.1 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.

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(a)

(b) (c)

Figure 3.12 Methodology used to create a bullet formed by an array of N dipoles separated by,(a) General process, (b) bullet 3D-view, and (c) Bullet rosette with 3 bullets.

2.3Backscattering with DDSCAT

Once the bullet toolbox was created in DDSCAT, we proceeded to use it to simulate the

crystals backscattering at 33 and 95 GHz. Figure 3.4 shows the backscattering for 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

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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 3.13 Backscattering (10 log b) of different indexes of refraction, (a) Backscattering in dB to33GHz 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 compute the backscattering

and again this value is saved in IDL to obtain the DWR. TheDWR is defined as [Sekelsky, et

al. 1999]

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( ) ( ) ( )( )

( ) ( ) ( )( )

=

+

+

+

+

0

67.3224

0

67.3224

0

0

,,

,,

log10

dDeDDK

dDeDDK

DWR

D

D

hblIh

D

D

lbhIl

3.16

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 3.14 Variation of the number of raob profiles used depending on the limits in space and timeseparation imposed on the data

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3 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.

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REFERENCES

Altshuler, E. E. and R. A. Marr, A comparison of experimental and theoretical values ofatmospheric absorption at the longer millimeter wavelengths, IEEE Trans. AntennasPropagat., vol. 36, no. 10, pp. 1471-1480, Oct. 1988.

Aydin, K. and C. Tang, Millimeter wave radar scattering from model ice crystaldistributions,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 AbsorptionModel,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 transfermodeling 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 PropulsionLaboratory, Internal Report, October 6, 1997.

Klein, L. A., and C. T. Swift, An Improved Model for the Dielectric constant of Sea Water atMicrowave Frequencies, IEEE Trans. on Antennas Propagation, Vol. AP-25, No. 1, 1977.

Hogan, R. J. and A. J. Illingworth, The potential of spaceborne dual-wavelength radar tomake 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 andCalibration of the 20-32 GHz Tropospheric Water Vapor Absorption Model, IEEE Trans.Geosci. Remote Sensing. 2002, 40, No. 6, pp. 1199-1210

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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 AtmosphericAttenuation Using Combined Ground-based and Airborne 95 GHz Cloud RadarMeasurements,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: AtmosphericRemote 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 Oceans Surface at37 GHz, J. Geophys. Res., Vol. 84, No. C8, pp. 244-249, 1979.

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4 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 dataget_mwr_cdfdata, mwrfilename, VAPcm, LIQcm, DEWflag, t_begin$, $

date$,unix_time,sec_into_UTCday

;**Function to read radiosonde dataget_sonde_cdfdata, sondefilename, tdry, sh, rh, dp, h, pres, $

wspd, deg, t_begin$, date$,unix_time,sec_into_UTCday

;**Function to read Radar dataRadar,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_especificaaltura = altura*1000.;altitude [m]

presion = presion*0.1 ;pressure [ mbars]tdry = temperatura ;temperature [deg C]sh = humedad_especifica ;specific humidity [gm^-3]

pres = presionh = altura

;omit radiosonde data above 35 km to speed up processingalt=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

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num_elem=500del=alt/num_elemh_prof = findgen(num_elem) * del ; 0-35km

tdry = INTERPOL(tdry, h, h_prof) ; regrid profilessh = INTERPOL(sh, h, h_prof) > 0.

pres = INTERPOL(pres, h, h_prof)h = h_prof

; compare radiosonde and mwr dataL=0FOR 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 profileL = 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 profilesindx = where(dewflag LT 1) ; filter out flagged datash = 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 kilometrosrangesamples = 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

ENDFORAH2O_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:altura+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)

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Position = [0.1, 0.9, 0.9, 0.95], Color=!P.Backgroundstop

END

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APPENDIX B PROGRAMS FOR BULLET AND DWR

APPENDIX B1 IDL PROGRAM FORREFRACTION 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

plan till a

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