Improved Model for Microwave Brightness Temperature Seen From Space OVer Calm Ocean

8/3/2019 Improved Model for Microwave Brightness Temperature Seen From Space OVer Calm Ocean

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The Pennsylvania State University

The Graduate School

College of Engineering

AN IMPROVED MODEL FOR THE MICROWAVE

BRIGHTNESS TEMPERATURE SEEN FROM

SPACE OVER CALM OCEAN

A Thesis in

Electrical Engineering

by

Sandra L. Cruz Pol

1998 Sandra L.Cruz Pol

Submitted in Partial Fulfillmentof the Requirements

for the Degree of

Doctor of Philosophy

August 1998


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ABSTRACT

An improved model for the microwave brightness temperature seen from space over calm

ocean is presented. This model can be divided into two sub-models, the atmospheric absorption model

and the ocean surface emissivity model.

An improved model for the absorption of the atmosphere near the 22 GHz water vapor line is

presented in the first part of this work. 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 are used as ground truth for comparison with in situ radiosonde derived

brightness temperatures. Estimation of the new models four parameters, related to water vapor line

strength, line width and continuum absorption, and far-wing oxygen absorption, are performed using

the Newton-Raphson inversion method. Improvements to the water vapor line strength and line width

parameters are found to be statistically significant. The accuracy of brightness temperatures computed

using the improved model is 1.3-2% near 22 GHz. In addition, the Hill line shape asymmetry ratio

was evaluated on several currently used models to show the agreement of the data with the new model,

and rule out atmospheric vapor absorption models near 22 GHz given by Waters and Ulaby, Moore

and Fung which are based on the Gross line shape.

In the second part of this work, a modified ocean emissivity model is presented. The

brightness temperature measured above the sea surface depends, among other things, on the oceans

specular emissivity. We investigate the contribution to the brightness temperature from the specular

ocean emission. For this purpose, satellite-based radiometric measurements from the

TOPEX/Poseidon project are employed together with near-coincident radiosonde profiles from fifteen

(15) stations around the worlds oceans and TOPEX altimeter measurements for filtering of low wind

conditions. The radiosonde profiles are used to compute the upwelling and downwelling emission and

the opacity of the atmosphere. The radiative transfer equation is applied to the radiosonde profiles,


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using the atmospheric model developed in the first part of this work, in order to account for

atmospheric effects in the modeled brightness temperature. The dielectric properties of sea water are

found from the modified Debye equation using salinity and sea surface temperature data from NODC

ocean depth-profiles. The ocean complex permittivity model developed by Klein and Swift and, more

recently, by Ellison is tested and revised. The average error in the modified emissivity model, over the

range 18-40 GHz, is found to be 0.0037, which in terms of brightness temperatures, translates to a

model error of approximately 1K.


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TABLE OF CONTENTS

LIST OF FIGURES ....................... .............. .............. ............... .............. .............. .............. ..............

LIST OF TABLES ...................... ............... .............. .............. .............. .............. ............... .............. ...

ACKNOWLEDGEMENTS .................................................................................................................

INTRODUCTION ................................................................................................................................... 1

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

1-1RADIATIVE TRANSFEREQUATIONS.................................................................................................. 1

1-1.1 Ground-Based Radiometer ...................................................................................................... 3

1-1.2 Satellite-Based Radiometer ...................................................................................................... 5

2. MICROWAVE ATMOSPHERIC ABSORPTION MODEL ....................................................... 12

2-1ATMOSPHERIC ABSORPTION .......................................................................................................... 13

2-1.1 Line Shapes ............................................................................................................................ 15

2-2CURRENT MODELS AND THEIR LIMITATIONS ................................................................................. 152-2.1 Atmospheric Absorption Line Shapes .................................................................................... 17

2-3EXPERIMENT DESCRIPTION AND CALIBRATION ............................................................................. 22

2-3.1 Radiometer Data .................................................................................................................... 22

2-3.2 Radiosonde Data .................................................................................................................... 25

2-4ANALYSIS AND RESULTS ............................................................................................................... 28

2-4.1 Hills Ratio Test ..................................................................................................................... 28

2-4.2 Parameter Estimation: Newton-Raphson Iterative Method................................................... 30

2-4.3 New Model Retrieved Parameters ............. .............. .............. .............. ............... .............. ..... 31

2-4.4 Error Analysis ........................................................................................................................ 34

2-5CONCLUSIONS................................................................................................................................ 39

3. SEA SURFACE EMISSIVITY ........................................................................................................ 41

3-1CURRENT MODELS AND THEIR LIMITATIONS .................................................................................. 413-1.1 Specular sea surface emissivity model ................................................................................... 41

3-1.2 Wind-roughened emissivity Model ......................................................................................... 44

3-1.3 Air-Sea Stability ..................................................................................................................... 47

3-2DATA SETS ..................................................................................................................................... 49

3-2.1 TOPEX/Poseidon :Altimeter and Radiometer data ............. .............. .............. .............. ........ 49

3-2.2 Radiosonde Data .................................................................................................................... 52

3-2.3 NODC Ocean Temperature and Salinity Profiles.................................................................. 55

3-3ANALYSIS AND RESULTS ............................................................................................................... 59

3-3.1 Model for TB using raob, NODC, and altimeter data .............. .............. .............. .............. ... 593-3.2 Selection of the Maximum Time and Space Separation .............. .............. .............. .............. . 59

3-3.3 Evaluation of the Model Performance ................................................................................... 62

3-3.4 Modified Dielectric Model Parameter Estimation................................................................. 64

3-3.5 Error Analysis ........................................................................................................................ 68

3-4CONCLUSION.................................................................................................................................. 72

4. CONCLUSIONS .............. .............. .............. ............... .............. .............. .............. .............. .............. . 74

4.1CASE STUDY:RELEVANCE OF THIS WORK TO THE TOPEX/POSEIDON ALTIMETRY MISSION ......... 74

4.2CONCLUSIONS AND FUTURE WORK................................................................................................. 79

REFERENCES ...................................................................................................................................... 82

APPENDIX A OXYGEN MICROWAVE SPECTRUM PARAMETERS ............................... 88


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APPENDIX B GOFF-GRATCH FORMULATION FOR WATER VAPOR DENSITY AS AFUNCTION OF TEMPERATURE AND PRESSURE. .................................................................... 89

APPENDIX C TABLE OF MEAN, STANDARD DEVIATION AND COUNTS OF SEASURFACE TEMPERATURE AND SALINITY PER MONTH PER RAOB STATION FOR

THE PERIOD OF 1900 TO 1990. ........................................................................................................ 91

APPENDIX D FORTRAN PROGRAM FOR THE NEW ATMOSPHERIC MODEL .......... 93APPENDIX E FORTRAN PROGRAM FOR THE MODIFIED OCEAN SURFACEEMISSIVITY MODEL .............. .............. ............... .............. .............. .............. .............. .............. ........ 95


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LIST OF FIGURES

FIGURE 1.1THE POWER RECEIVED BY AN ANTENNA IS EQUIVALENT TO THE NOISE POWER DELIVERED BY

A MATCHED RESISTOR. IF THE BLACKBODY ENCLOSURE IS AT TEMPERATURE T, THE BRIGHTNESS

TEMPERATURE,TB, MEASURED BY THE ANTENNA IS DEFINED AS BEING EQUAL TO T.

[CHANDRASEKHAR,1960] ................................................................................................................... 2

FIGURE 1.2.PASSIVE REMOTE SENSING WITH(A) UPWARD-LOOKING RADIOMETER AND (B) DOWNWARD-LOOKING RADIOMETER. ...................................................................................................................... 3

FIGURE 1.3.DOWNWELLING BRIGHTNESS TEMPERATURE AS OBSERVED BY AN UPWARD LOOKING

RADIOMETER FORU.S.STANDARD AND DRY ATMOSPHERIC CONDITIONS AND FOR THE

HYPOTHETICAL CASE ABSOLUTELY NO WATER IN THE ATMOSPHERE. THE CONTRIBUTION AROUND

22.235GHZ ARE MAINLY DUE TO THE RESONANT WATER-VAPOR EMISSION. ...................... .............. 5

FIGURE 1.4.PASSIVE REMOTE SENSING WITH(A) UPWARD-LOOKING RADIOMETER AND (B) DOWNWARD-

LOOKING RADIOMETER. ...................................................................................................................... 6

FIGURE 1.5EFFECTS ON THE SEA SURFACE EMISSIVITY DUE TO (A) FREQUENCY,(B) SEA SURFACE

TEMPERATURE,(C) SALINITY AND (D) WIND SPEED. (UNLESS OTHERWISE NOTED, THE PLOTS ARE

GIVEN FORF=37GHZ,S=35 AND TS=280K.) .............................................................................. 9

FIGURE 2.1WATER VAPOR ABSORPTION VERSUS FREQUENCY FOR AT A PRESSURE OF 1013 MBARS, AIR

TEMPERATURE OF 290KFOR NO WATER VAPOR IN THE ATMOSPHERE AND FOR WHEN THERE IS

WATER VAPOR(2G/CM3). [ULABYET AL.,1980] .............................................................................. 14FIGURE 2.2WATER VAPOR ABSORPTION VERSUS FREQUENCY FOR SEVERAL MODELS AT A PRESSURE OF

1013 MBARS, AIR TEMPERATURE OF 290KAND RELATIVE HUMIDITY OF 50%. (L87=LIEBE 87,

L93=LIEBE 93,W76=WATERS 76 AND UMF81=ULABY,MOORE AND FUNG 81). .. .............. . 16

FIGURE 2.3(A)EFFECT OF LINE PARAMETER VARIATION BY 10% ON TOTAL ATMOSPHERIC ABSORPTION.

(B)DIFFERENTIAL EFFECT OF LINE PARAMETER VARIATION WITH RESPECT TO NOMINAL L87R93

MODEL. THE ARROWS AT THE BOTTOM OF THE FIGURE INDICATE THE FREQUENCIES MEASURED IN

THIS EXPERIMENT. (SAME ATMOSPHERIC CONDITIONS AS FIG.2.2). ............................................... 21

FIGURE 2.4ZENITH BRIGHTNESS TEMPERATURE INTERCOMPARISON BETWEEN RADIOMETER UNITS J1

AND J2 FOR ABSOLUTE CALIBRATION PURPOSES. MEASUREMENTS WERE CONDUCTED DURING

DECEMBER1991 AT SAN DIEGO,CA AT (A)20.7GHZ,(B)22.2GHZ AND (C)31.4GHZ. THE DATA

HAVE BEEN SMOOTHED BY A 30 MINUTES RUNNING AVERAGE......................................................... 24

FIGURE 2.5TOTAL ERROR IN CW LINE PARAMETER DUE TO A 0.5KUNCERTAINTY IN MEASURED TB AND

THE CORRECTION OF THE RAOB RELATIVE HUMIDITY READING, VERSUS NUMBER OF RAOB PROFILES

USED IN THE ESTIMATION (SEE SECTION 3.2 FOR A COMPLETE DISCUSSION). A TRADE OFF BETWEEN

THE AMOUNT OF DATA USED AND THE MINIMUM ERROR IN PARAMETER ESTIMATION YIELDS AN

OPTIMUM VALUE OF 21 RAOB PROFILES, PROVIDING A TOTAL OF 108 DATA POINTS. ............... ........ 27

FIGURE 2.6HILL 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).................................................................................... 29

FIGURE 2.7BRIGHTNESS TEMPERATURE SPECTRA COMPARISON BETWEEN RADIOMETER DATA (WVR)

AND RADIOSONDE-DERIVED DATA WITH NEW AND NOMINAL PARAMETERS FOR A VAPOR BURDEN OF

(A)2.9 G/CM2,(B)2.3 G/CM

2, AND (C)1.3 G/CM2. (NOTE THAT ONLY FIVE CHANNELS WERE IN

OPERATION DURING THE RAOB LAUNCHES FOR CONDITIONS (B) AND (C)). .............. .............. .......... 32

FIGURE 2.8PLOT OF THE DIFFERENCE TB-TBL87R93 FOR(A) HUMID (WEST PALM BEACH),(B)

MODERATE (SAN DIEGO) AND (C) DRY (SAN DIEGO) CONDITIONS.NOTE THAT TBLIEBE87IS

EQUIVALENT TO OUR NOMINAL MODEL (CL=CW=CX=1.0 AND CC=1.2). (ONLY FIVE CHANNELS

WERE IN OPERATION DURING THE RAOB LAUNCHES FOR CONDITIONS (B) AND (C))............... .......... 33FIGURE 2.9PERCENTAGE ERROR IN THE IMPROVED MODEL FOR ATMOSPHERIC ABSORPTION USING THE

1962U.S.STANDARD ATMOSPHERE AT SEA LEVEL WITHRH=50%. THE ERROR IN THE IMPROVED

MODEL MODEL ERRORS ARE DUE TO BIAS AND RANDOM MEASUREMENT UNCERTAINTIES IN

RADIOMETERTB, THE CORRECTION FOR RAOB RELATIVE HUMIDITY VALUES LESS THAN 20% OR

GREATER THAN 100%, AND THE UNCERTAINTY IN THE RADIOSONDE READINGS FOR PRESSURE,

TEMPERATURE AND RELATIVE HUMIDITY. ........................................................................................ 37

FIGURE 2.10PERCENTAGE ERROR IN THE IMPROVED DOWNWELLING TB FOR THE RADIOSONDE PROFILESUSED BY THE ESTIMATION ALGORITHM. MODEL ERRORS ARE DUE TO BIAS AND RANDOM


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MEASUREMENT UNCERTAINTIES IN RADIOMETERTB, THE CORRECTION FOR RAOB RELATIVE

HUMIDITY VALUES LESS THAN 20% OR GREATER THAN 100%, AND THE UNCERTAINTY IN THE

RADIOSONDE READINGS FOR PRESSURE, TEMPERATURE AND RELATIVE HUMIDITY. THE ERROR IN

THE PREDICTED BRIGHTNESS LIES BETWEEN 1.5% AND 2.0%. ERROR BARS IN THE GRAPH

REPRESENT THE STANDARD DEVIATION OF THE PERCENTAGE ERROR FOR ALL THE PROFILES USED IN

THE ANALYSIS. ................................................................................................................................. 38

FIGURE 3.1MECHANISMS RESPONSIBLE FOR THE MICROWAVE EMISSION OF A WIND-ROUGHENED SEA

SURFACE INCLUDE LARGE GRAVITY WAVES, SMALL CAPILLARY WAVES AND SEA FOAM. ................ 46

FIGURE 3.2WIND SPEED MODEL RELATING 0TO WIND SPEED FOR THE MCW ALGORITHM AS

CALIBRATED FORTOPEX ALTIMETER. .............................................................................................. 51

FIGURE 3.3LOCATION OF THE RADIOSONDE LAUNCH SITES. (SEE TABLE FOR COORDINATES). ............. 53

FIGURE 3.4HISTOGRAM OF THE RANGE OF PATH DELAY VALUES FOR THE DATA USED IN THIS WORK. .. 54

FIGURE 3.5AVERAGE SEA SURFACE TEMPERATURES VARIATION PER MONTH FOR STATION 9, LOCATED

IN THENORTH HEMISPHERE (BLUE), AND FOR STATION 29, LOCATED IN THE SOUTH HEMISPHERE

(PINK). THE ERROR BARS REPRESENT THE STANDARD DEVIATIONS FOR EACH MONTH. ................... 56

FIGURE 3.6AVERAGE SALINITY VARIATION PER MONTH FOR STATION 9, LOCATED IN THENORTH

HEMISPHERE (BLUE), AND FOR STATION 29, LOCATED IN THE SOUTH HEMISPHERE (PINK). THE

ERROR BARS REPRESENT THE STANDARD DEVIATIONS FOR EACH MONTH. ............. .............. ............ 57

FIGURE 3.7HISTOGRAMS OF THE RANGE OF (A) SALINITY AND (B) SEA SURFACE TEMPERATURE VALUES

FOR THE DATA USED IN THIS WORK. ................................................................................................. 58

FIGURE 3.8VARIATION OF THE NUMBER OF RAOB PROFILES USED DEPENDING ON THE LIMITS IN SPACE

AND TIME SEPARATION IMPOSED ON THE DATA. ............................................................................... 60

FIGURE 3.9VARIATION OF THE RMS DIFFERENCE BETWEEN DATA AND MODEL DEPENDING ON THE

LIMITS IN SPACE AND TIME SEPARATION IMPOSED ON THE DATA. .................................................... 61

FIGURE 3.10.PLOT OF THE MODEL ERROR(TBTMR-TBMODEL) VERSUS THE SEA SURFACE TEMPERATURE

FORE96. THE R2

VALUE OF THE LINEAR FIT IS SHOWN TO BE SMALL, DENOTING A SMALL

DEPENDENCE OF THE ERROR IN THIS MODEL ON THE SEA SURFACE TEMPERATURE.. ..................... ... 63

FIGURE 3.11THE MODIFIED AND NOMINAL OCEAN DIELECTRIC PERMITTIVITY MODELS,MODKS AND

KS77(IN PINK) AND MODE AND E96(IN BLUE). THE PLOTS SHOW THE VARIATION IN BOTH THE

REAL AND IMAGINARY PARTS OF THE PERMITTIVITY VERSUS FREQUENCY. THE ERROR BARS

DENOTE THE STANDARD DEVIATIONS IN THE MODIFIED MODELS. ALL PLOTS ARE FORTSEA=280K

AND S=35. ................................................................................................................................... 71

FIGURE 3.12ERROR IN THE MODIFIED OCEAN EMISSIVITY,MOD KS(IN PINK) AND MODE(IN BLUE)

VERSUS FREQUENCY. THE ERROR BARS DENOTE THE STANDARD DEVIATIONS AT EACH POINT. PLOTIS FORTSEA=280KAND S=35. ........................................................................................................ 72


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LIST OF TABLES

TABLE2.1NEW RETRIEVED ATMOSPHERIC ABSORPTION PARAMETERS ............................................... 31

TABLE2.2 STANDARD DEVIATIONS AND CORRELATION MATRIX FOR THE FOUR ESTIMATED

PARAMETERS TAKING INTO ACCOUNT ERRORS IN THE RAOB PROFILES ANDWVR

BRIGHTNESS

TEMPERATURE MEASUREMENTS. ...................................................................................................... 35

TABLE2.3 UNCERTAINTIES INTRODUCED TO THE CALCULATED BRIGHTNESS TEMPERATURES BY THE

L87R93(NOMINAL)[JOHANSSONET AL.,1987;ENGLAND ET AL.,1993] AND BY THE NEW

ATMOSPHERIC ATTENUATION MODEL. .............................................................................................. 38

TABLE3.1 COORDINATES OF THE RAOB STATIONS DEPICTED IN THE MAP ON FIGURE 3.3. .................. 53

TABLE3.2COMPARISON OF OVERALL PERFORMANCE OF SEVERAL OCEAN EMISSIVITY MODELS WITH

RESPECT TO TMRDATA. .................................................................................................................. 64

TABLE3.3COMPARISON OF THE OVERALL PERFORMANCE OF K77 AND E96 OCEAN EMISSIVITY

MODELS WITH TWO MODIFIED PARAMETER. ..................................................................................... 66

TABLE 3.4.COMPARISON AMONG OCEAN EMISSIVITY MODELS. ............................................................ 67

TABLE 4.1.ERRORBUDGET FOR THE PATH DELAY ALGORITHM ............................................................ 75

TABLE 4.2.TOTAL ERRORBUDGET FORTOPEXMICROWAVE RADIOMETER(TMR)WET TROPOSPHERE

RANGE CORRECTION.[KEIHMET AL,1995] ..................................................................................... 76

TABLE 4.3.RMSERRORS OF INDIVIDUAL SEA SURFACE TOPOGRAPHY ERROR(UNITS IN CENTIMETERS

[TSAOUSSIANDKOBLINSKY,1994;FUET AL.,1994] ......................................................................... 77

TABLEA-1. OXYGEN MICROWAVE SPECTRUM PARAMETERS [ROSENKRANZ,1993] ............................ 88


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ACKNOWLEDGEMENTS

First of all, I want to thank God, for without Him there would be nothing. And thanks to my

parents for raising me with love and for teaching me about Reincarnation and Allan Kardec. I admire

you Papi for being so humble and for always being ready with a joke. I admire you Mami for your

immense faith and noble example. The knowledge that our suffering and obstacles in life are a direct

consequence of our acts in this or past lives, strengthens my Christian faith. Without that knowledge,

so many questions about our purpose in life and what seems to be injustice sometimes would remain

unanswered. I know I had to go through many situations good and bad, but in each I learned

something. I know I had to be in this time and place, and thanks to that, I met a great human being, a

great friend, Justin Bobak.

Thanks JPB for answering all the hundred questions I always had, for being yourself, and for

your friendship, good humor and afternoon coffee. I would also like to thanks all my other lab partners

for making our working environment a fun place to come to every morning; to Hans Rosenberger for

coffee every morning and for his good nature; and to Jude Giampaolo for being so nice and for the

innumerable answers to my PC-networking, NT-registry, etc. questions. Thanks to Rafael Rodrguez

Sols, because approximately 77.14% of what I know about computers, I learned from him.

I would like to thank my advisor, Dr. Chris Ruf, for his valuable intellectual guidance through

these last three and a half years of research. Thanks also go to all the members of my committee; Dr.

Kultegin Aydin, Dr. Toby Carlson, Dr. Lynn Carpenter, Dr. Charles Croskey, Dr. Jenni Evans and Dr.

Charles Kilgus for their suggestions and revisions to the final document. Thanks are due to Prof.

Kwang Y. Lee for his well-meant advice and teaching, and to the sponsors behind the Fellowships

from GEE and GEM, and the University of Puerto Rico.

I will like to thank my daughters, Natal and Adriana, or as I like to call them my two most

challenging and rewarding projects, for giving me inspiration and bringing me joy as I watch them

bloom every day in front of me. I dont know who have learned more, you from me, or me from you.

To my dear and wise mother-in-law, Vilma, for coming from Puerto Rico for a month, so we could

work 12-15 hours a day, 6.3 days a week to finish this work in time, and for being a friend and

providing advice every time I asked for some.

And finally, I would like to thank my best friend, Jos Colom Ustriz, for being there all the

time for me, for sincerely enjoying and sharing every one of my accomplishments. You are a great

man, husband and father and I love you.


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The vanity of some men, who imagine that they know everything, and are bent on

explaining everything in their own way, will give rise to opposing opinions; but all who have

in view the grand principle of Jesus will be united in the same love of goodness, and in abond of brotherhood that will embrace the entire world. Putting aside all vain disputes about

words, they will devote their energies to matters of practical importance, in regard to which,

whatever their doctrinal belief, the convictions of all who receive the communications of thehigher spirits will be the same.

"Perseverance will render your labour fruitful. The pleasure you will feel in witnessing thespread of our doctrine and its right appreciation will be for you a rich reward, though perhaps

rather in the future than in the present. Be not troubled by the thorns and stones that the

incredulous and the evil-minded will place in your path; hold fast your confidence, for yourconfidence will ensure our help, and, through it, you will reach the goal.

"Remember that good spirits only give their aid to those who serve God with humility and

disinterestedness; they disown all who use heavenly things as a stepping-stone to earthly

advancement, and withdraw from the proud and the ambitious. Pride and ambition are abarrier between man and God; for they blind man to the splendours of celestial existence,

and God cannot employ the blind to make known the light."

"JOHN THE EVANGELIST, ST AUGUSTINE, ST VICENT DE PAUL, ST LOUIS, THE SPIRIT OFTRUTH, SOCRATES, PLATO, FENELON, FRANKLIN, SWEDENBORG, etc., etc."

from Spirits' Book by Allan Kardec,

1857 (translated from French),

[www.GEAE.org]

Mi patria es el mundo, sin fronteras, SLCP


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Ch. 1 Theoretical Background

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.

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].

The Defense Meteorological Satellite Program (DMSP) launched the first Special Sensor

Microwave Imager (SSM/I) in 1987 on a near polar orbiting, sun synchronous weather satellite. It was

the first of a series of several identical sensors launched to provide world-wide meteorological,

oceanographic and solar-terrestrial physics measurements on a twice-daily basis [ Petty and Katsaros,


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1992]. The SSM/I is a seven-channel, four frequency, linearly-polarized, passive microwave

radiometric system which operates at 19.35, 22.235, 37.0 and 85.5 GHz. It is used to measure ice

coverage, precipitation areas and intensities, cloud water content, and ocean surface wind speeds

[Hollingeret al., 1990].

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 [Gntheret al., 1993].

In 1992 the TOPEX/POSEIDON satellite was launched as a joint venture between NASA and

Centre National d'Etudes Spatiale (CNES) to provide high-accuracy global sea level measurements.

Data from TOPEX/Poseidon is used to map ocean circulation patterns, help understand how the oceans

interact with the atmosphere, and improve our ability to predict the global climate [Stewart, 1986]. It

includes a three channel nadir viewing microwave radiometer (TMR) at 18, 21 and 37 GHz designed

to measure the water vapor along the path viewed by the altimeter to correct the altimeter data for

pulse delay due to water vapor. It has a claimed accuracy of 1.2 cm [Keihm et al., 1995].

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 [Rufet al., 1996].

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 in hardware, complexity,


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3

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 [Rufet al., 1995].

Errors in the modeling of microwave brightness temperature, TB, seen from orbit over the sea

include errors in the models for vapor and oxygen absorption and sea surface emissivity. Conversely,

errors in the measurement of the microwave TB include errors in the antenna temperature calibration,

and beam pattern correction. Currently, the dominant error source when modeling the ocean

brightness temperature is the vapor absorption model. In the case of the TOPEX/POSEIDON

microwave radiometer, this uncertainty is approximately 35% higher than the radiometers TB

measurement error [Keihm et al., 1995]. Precise microwave radiometry equipment such as this

demands more accurate models for the retrieval of the oceans parameters. The accuracy of these

models must be consistent with the level of the errors introduced by the microwave sensor, otherwise

the model uncertainties dominate the error budget. The improvement and revision of two models

needed to achieve a higher accuracy in the ocean TB modeling are addressed in this work. The first

model accounts for atmospheric absorption. The second accounts for the sea surface emissivity.

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.

For the atmospheric absorption model, ground-based radiometric experiments were conducted

at two locations of contrasting humidity conditions; San Diego, CA and West Palm Beach, FL. In

addition, radiosonde profile data at each site were collected for comparison purposes in the retrieval of

the atmospheric model parameters. Advantages over previous such experiments include the use of

three independent radiometers for absolute calibration verification, sampling at eight distinct

frequencies across the 22 GHz absorption line, and filtering of the raob data to minimize the effects of

errors in the relative humidity readings.


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4

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.

For the ocean emission study, satellite-based radiometric measurements from the

TOPEX/Poseidon project are employed. In addition, altimeter (active remote sensor) data from the

same satellite is utilized for the purpose of wind speed estimation and specular emissivity

corroboration. We investigate the contribution from the specular ocean emission by employing the

altimeter to pinpoint the exact times when the wind is calm, in order to relax the dependence of the

correction to the specular model on the accuracy of the wind model.

The modified ocean dielectric models exhibit significant improvements in the estimate ofTB.

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.

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

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

(1.1)

where h is Plancks constant (6.63 x 10-34 J),fis frequency in Hz, kis Boltzmanns constant (1.38 x 10-

23 J/K), Tis absolute temperature in K, and c is the velocity of light (3 x 10 8 m/s) [Planck, 1914].

At the low-frequency limit, i.e. hf


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smaller than 300 GHz. For frequencies less than 117GHz and blackbody at 300 K, the Rayleigh-Jeans

approximation yields values less than 1% different from the Plancks expression. At microwave

frequencies, therefore, the power received by an antenna due to blackbody radiation is directly

proportional to the temperature of the object.

Radiometers are used to detect the electromagnetic radiation naturally emitted by the

atmosphere, oceans, terrain, celestial bodies, etc. These devices remotely sense the microwave noise

power in terms of the apparent temperature seen by the antenna. The apparent temperature is defined

as the equivalent blackbody temperature at which a matched resistor would have to be in order to

deliver the same amount of power at the antenna terminals (see Fig 1.1) [Chandrasekhar, 1960].

Figure 1.1 The power received by an antenna is equivalent to the noise power delivered by a matchedresistor. If the blackbody enclosure is at temperature T, the brightness temperature, TB, measured bythe antenna is defined as being equal to T. [Chandrasekhar, 1960]

The amount of radiation received by a radiometer depends on its viewing configuration. A

ground-based radiometer operates in an upward-looking position. Therefore, it measures the radiation

coming down from our atmosphere (see Fig. 1.2). A satellite-based radiometer, on the other hand,

looks down toward the surface of the Earth. It receives contributions from the upwelling atmospheric

radiation, the surface emission, and the radiation reflected at the air-surface interface (see Fig. 1.4).

Radiometer

Receiver

P

Antenna

Radiometer

Receiver

P

R

Blackbod enclosure

T

T


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Figure 1.2. Passive remote sensing withupward-looking radiometer .

1-1.1 Ground-Based Radiometer

Consider a non-scattering atmosphere in which the temperature and the absorption coefficient

are functions of altitude. The brightness temperature of the atmosphere, observed from the ground,

also known as downwelling temperature, is obtained by integrating the contributions of individual

layers of the atmosphere. The emission from each layer is attenuated by a factore-by the intervening

medium as it travels down towards the point of measurement. The downwelling temperature is the

sum of these contributions and it is given by [Ulaby et al., 1981]

(1.3)


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where is the incidence angle of the radiation which is measured with respect to the normal to the

surface, (f, z) is the atmospheric attenuation in Nepers/km at frequencyfand heightz, is the opacity

of the atmosphere between altitude 0 and z , and T(z) is the air temperature at height z. The opacity

measures the total amount of extinction suffered through the path and is given by

(1.4)

When the radiometer is looking directly up, the incidence angle is = 0o and sec reduces to unity.

This simplifies (1.3) to the form used in this work,

(1.5)

To compute the apparent temperature measured by the antenna, Ta, the contributions from the

cosmos and galaxy have to be added

(1.6)

In the above equation, TCis the cosmic background radiation incident on the atmosphere from the top.

As it travels down toward the antenna, it is reduced by a factor of e- due to absorption by the

intervening atmosphere. This factor is known as the transmissivity or transmittance function. The

cosmic radiation at microwave frequencies varies with frequency as

(1.7)

which has an average of 2.78 K for the 20-32 GHz range. The frequency dependence accounts for

departures from the Rayleigh-Jeans approximation [Janssen, 1993]. The physical behavior of equation

(1.3) depends on the atmospheric conditions. Examining (1.3) and (1.4), it is noted that Ta depends on

the vertical profiles of temperature and absorption. For a lossless atmosphere, (f, z)=0, and therefore

TDN = 0. At the other extreme, for a perfect blackbody, (f, z)=1, and the TDN is reduced to the


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physical temperature of the atmosphere. For a non-uniform temperature profile, Ta will never exceed

the physical temperature. Figure 1.3 shows plots ofTa for different atmospheric conditions.

Figure 1.3. Downwelling brightness temperature as observed by an upward looking radiometer forU.S. Standard and dry atmospheric conditions and for the hypothetical case absolutely no water inthe atmosphere. The contribution around 22.235 GHz are mainly due to the resonant water-vaporemission.

1-1.2 Satellite-Based Radiometer

Again consider a non-scattering atmosphere. The apparent temperature received by an

antenna from above the atmosphere has three components. The radiometer measures the radiation

coming up from the atmosphere, also known as the upwelling temperature, the radiation emitted by the

surface beneath and the radiation reflected at the air-surface interface (Fig. 1.4). This last component

consists of the downwelling atmospheric emission plus the cosmic background radiation. The total

apparent temperature is given by


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Figure 1.4. Passive remote sensing with downward-looking radiometer.

(1.8)

where Ts is the thermodynamic temperature of the surface in Kelvin, is the emissivity of the surface,

is the reflectivity of the surface,His the satellite height in km, TC is the cosmic radiation and

TDN is given by (1.3). The upwelling brightness temperature in the zenith direction is given by,

(1.9)

The absorption coefficient,(f, z), includes both the spectral (water vapor and oxygen) line absorption

and any other source of microwave opacity present in the atmosphere as clouds, fog and rain.


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Equation (1.8) contains all the quantities needed to compute the response of a satellite-based

microwave radiometer to changes in atmospheric and surface variables. The upwelling and

downwelling temperature terms depend on the atmospheric absorption weighted by the temperature

profile of the atmosphere. The background term, TC, is multiplied by the transmittance function, to

account for the attenuation along the vertical path between the satellite and the surface. It is then

added to TDN and reflected back toward the satellite. Hence, it is attenuated by the intervening

atmosphere, according to the transmittance function, and multiplied by the reflectivity parameter,

. The surface emission consists of the physical temperature of the surface multiplied by the

surface emissivity.

The emissivity is a function of the dielectric properties of the surface. In the case of the

ocean, it varies with frequency, temperature, wind speed and, to a lesser extent, on salinity. The

variation of emissivity with frequency, temperature, and salinity is shown in Figures 1.5(a)-(c) as

described by the most recent ocean emissivity model [Ellison et al., 1996]. Variation with wind speed

is shown in Figure 1.5(d) as described by Wilheit [1979b]. Note how the dependence on sea surface

temperature and frequency are much larger than that on salinity and wind speed. In general, the

emissivity increases with increasing frequency and decreasing temperature. The frequency, salinity

and temperature dependence will be examined further in Chapter 3.


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Figure 1.5 Effects on the sea surface emissivity due to (a) frequency, (b) sea surface temperature, (c)salinity and (d) wind speed. (Unless otherwise noted, the plots are given forf= 37 GHz, S= 35 and TS=280 K.)


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1-1.2.1 Radio path delay

Radio path delay is the path distortion that a radio signal undergoes when traversing the

atmosphere of the Earth. This refraction introduces uncertainties in the time of arrival of the signal due

to bending and retardation along the propagation path. The physical phenomena behind the delays are

the dispersion due to the free electrons of the ionosphere, the induced dipole moments of neutral

atmospheric molecules (principally nitrogen and oxygen), and the permanent dipole moments of water-

vapor and cloud liquid water molecules. The dry component of the delay due to the neutral

atmosphere contributes about 2.3 m in zenith direction at sea level. The wet component of the delay

caused by water vapor and cloud liquid water is smaller, but much more variable. It can range from

less than 1 cm to 40 cm or more in the zenith direction. When we mention path delay in the remainder

of this work, we refer to the variable wet component.

The wet delay can be inferred from microwave radiometer measurements. The electrical path

lengthL of a signal propagating along Sis defined as

(1.10)

where n is the refractive index of the atmosphere, and S is the path along which the signal propagates.

The signal will propagate along the path that gives the minimum value ofL. S is larger than the

geometrical straight line distance, defined as G. However, the electrical path length of the signal

propagating along G is longer than that for the signal propagating along S. The difference between the

electrical path length and the geometrical straight-line distance is called the excess propagation path

or path delay, defined as

(1.11)

In the case of a horizontally stratified atmosphere, the two paths Sand G are identical in the zenith

direction. In this case, the path delay is

(1.12)

The index of refraction, n, is conveniently expressed in terms of the refractivity,N, defined as


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(1.13)

The refractivity is expressed as the sum of a dry and wet (vapor and cloud induced) components. The

wet refractivity component due to vapor is given by [Bourdouris, 1963;Hills et al., 1982]

(1.14)

from which the vapor induced path delay component in centimeters can be found as

(1.15)

where v is the water vapor density in g/m3, Tis the atmosphere air temperature profile in K and zis

height in meters.


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2. 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 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. In addition, the Hill line shape asymmetry ratio was evaluated on several

currently used models to show the agreement of the data with the new model, and rule out

atmospheric vapor absorption models near 22 GHz given by Waters and Ulaby, Moore and

Fung which are based on the Gross line shape. Results show a 23% improvement in the

difference between modeled and measured brightness temperature from the atmosphere

compared to current models.

Absorption and emission by atmospheric gases can significantly attenuate and delay the

propagation of electromagnetic signals through the Earths atmosphere. Improved modeling of the

emission spectra for the dominant contributing gases, mainly water vapor and oxygen, is needed for

many applications in communications, remote sensing, and radioastronomy. More precise models of

atmospheric absorption can improve corrections for atmospheric effects on satellite observations ofland and ocean surfaces [McMillin, 1980], produce more accurate remote measurements of

atmospheric water vapor burden and temperature profiles [Grody, 1980], refine predictions of global

climate changes [NASA, 1993], enhance planetary radio science measurements [Pooley, 1976],

improve the accuracy of continental plate motion estimation [Shapiro et al., 1974], and expedite the

resolution of accumulated strain at fault zones [Shapiro, 1976].

Estimated uncertainties for current models of the 20-32 GHz water vapor absorption range

over 4-10% [Keihm et al., 1995]. For applications such as water vapor radiometer (WVR)

measurements of integrated vapor and cloud liquid used in meteorological and climate modeling, 10%

accuracies are often adequate. However, for many applications, especially those requiring calibration

of microwave signal delays in the troposphere (path delay), the vapor absorption model uncertainty

often dominates experimental error budgets. Examples include the measurement of the vapor-induced

path delay over the worlds oceans by the TOPEX Microwave Radiometer [Keihm etal., 1995] and

GEOSAT Follow-on Water Vapor Radiometer [Ruf et al., 1996], VLBI geodetic measurements


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Ch. 2 Microwave Atmospheric Water Vapor Absorption Model

13

[Linfield et al., 1996], and the tropospheric calibration effort planned for the Cassini Gravitational

Wave Experiment [Keihm and March, 1996].

Current models for atmospheric microwave absorption have been developed from both

laboratory and field experiments. Multimode cavity measurements by Becker and Autler[1946]

lacked diagnostics necessary to control systematic errors down to a desirable level; their estimated

error is between 5% and 10% [Walter, 1995]. The field measurements of water vapor absorption

calibration near the 22 GHz resonance feature generally involve comparisons between direct

measurements at two or three selected frequencies by a water vapor radiometer and theoretical

brightness temperatures calculated from radiosonde (raob) profiles of temperature, pressure and

humidity. raob comparison measurements [e.g. Westwater, 1978;Hogget al., 1980; Snider, 1995] are

well known to be subject to inaccurate humidity readings for extreme (very dry or very humid)

conditions [Wade, 1994; Nash et al., 1995]. Current oxygen model uncertainties range from 1.5% to

8% for the resonant oxygen lines cluster near 58 GHz [ Liebe et al. 1993], yet these fractional

uncertainties increase significantly for frequencies down in the 20-32 GHz range.

In this work, radiometric measurements of brightness temperature, TB, are used in conjunction

with in situ raob measurements to estimate parameters for a simplified model of the 20-32 GHz

atmospheric vapor and oxygen absorption. The experiment covered ~70 days of near-continuous

WVR measurements and twice per day raob launches at the San Diego and West Palm Beach National

Weather Service stations. Advantages over previous such experiments include the use of three

independent radiometers for absolute calibration verification, sampling at eight distinct frequencies

across the 22 GHz absorption line, and filtering of the raob data to minimize the effects of high and

low end errors in the relative humidity measurements. The spectrum of atmospheric absorption versus

frequency is shown for dry and typical conditions on Fig. 2.1

2-1 Atmospheric Absorption


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For a non-scattering atmosphere (rain-free conditions) the main contributors to atmospheric

radiation at microwave frequencies are the emission by water vapor and oxygen molecules. The

movement of molecules, through vibration, rotation and electronic spinning, determines the nature of

the radiation that they emit or absorb. Uncoupled electron charges or electron spins are responsible for

electric and magnetic dipoles, respectively, within the molecules.

Figure 2.1 Water vapor absorption versus frequency for at a pressure of 1013 mbars1, air temperatureof 290 K for no water vapor in the atmosphere and for when there is water vapor (2g/cm3). [Ulabyet al., 1980]

Water vapor and oxygen molecules both radiate due to molecular rotation. In the case of the

water vapor molecule, this rotation causes its permanent electric dipole to radiate. Oxygen has no

permanent electric dipole moment, but its magnetic dipole allows it to emit. The magnetic dipole

emission is much weaker than that of a molecular electric dipole, but the great abundance of oxygen in

the atmosphere compensates for the intrinsic weakness of its absorption.

1In this work pressure is expressed in mbars which is equal to 1 hPascal.


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2-1.1 Line Shapes

We are concerned with the absorption line spectra of the water vapor and oxygen molecules,

since they are the major contributors to atmospheric absorption. Their absorption spectra have been

most commonly described by the Van-Vleck Weisskopf (VVW) and the Gross line shapes. Both line

shapes are derived from a molecular oscillator analogy. In this analogy, the molecule is treated as a

classical oscillator with a fixed rotational frequency equal in value to the frequency of the resonant

line. Collisions between molecules cause reorientation and rotational phase shifts of the molecule,

which contribute to the broadening and shifting of the electromagnetic spectral lines. The basic

difference between the two line shape theories is that VVW assumes the oscillations are in phase with

the electric field after the collisions, whereas Gross assumes that the molecular oscillation phases stay

undisturbed and the post-collision momenta are randomized [Ben-Reuven, 1969]. The general form for

the Van-Vleck Weisskopt[1945] is given by

(2.1)

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

(2.2)

wherefis the measurement frequency, f0 is the center resonant frequency for the given molecule, Sis

the line strength and is the linewidth parameter. The line shape used in the atmospheric absorption

model employed in this work is the VVW and is discussed with further detail in section 2-2.1.

2-2 Current Models and their limitations

Currently used models for atmospheric absorption include those by Liebe and Layton [1987],

Liebe et al. [1993], Waters [1976] and Ulaby et al. [1981]. These will be referred to as L87, L93, W76


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and UMF81, respectively, in the remainder of this thesis. Figure 2.2 shows a plot of the water vapor

absorption spectrum for each of these models under typical mid-latitude surface conditions. Note that

significant differences are evident in both magnitude and shape of the spectra. Some of the reasons for

these differences are discussed below.

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

20

22

24

26

28

30

32

Frequency [GHz]

WaterVaporAbsorptionvapor[Np/km]

Figure 2.2 Water vapor absorption versus frequency for several models at a pressure of 1013 mbars,air temperature of 290 K and relative humidity of 50%. (L87 = Liebe 87, L93 = Liebe 93, W76 =Waters 76 and UMF81= Ulaby, Moore and Fung 81).

Each model includes an empirical continuum term to account for the discrepancy between

theoretical and experimental absorption spectra in the window region. The physical phenomena

behind the excess absorption in the continuum might be due to inaccuracies in the far wing line shape

of vapor resonances [Gebbie, 1980], the exclusion of the effects of water clusters [Bohlander, 1979]

and/or forbidden transitions between energy levels on these line functions [Rosenkranz, 1990].

UMF81

W76

L93

L87


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Although this excess has yet to be understood, empirical modifications are needed to obtain more

accurate agreement between measurements and theory.

Uncertainties in attenuation for the L87 water vapor model over tropospheric pressures are

estimated to be from 2.3 % to 21.2% [Liebe and Layton, 1987]. For the oxygen model used in L87R93

and L93, the uncertainties range from 1.5% to 8% at the nominal center frequency of 58 GHz, also for

tropospheric pressures [Liebe et al., 1993]. For frequencies farther from the center, the fractional

uncertainty increases significantly.

2-2.1 Atmospheric Absorption Line Shapes

The L87 and L93 models employ the Van Vleck-Weisskopf (VVW) line shape whereas the

W76 model uses the Gross line shape. The UMF81 uses the Gross line shape for the water vapor and

VVW for the oxygen absorption. Both line shapes are derived from a molecular oscillator analogy. In

this analogy, the molecule is treated as a classical oscillator with a fixed rotational frequency equal in

value to the frequency of the resonant line. Collisions between molecules cause reorientation and

rotational phase shifts of the molecule, which contribute to the broadening and shifting of the

electromagnetic spectral lines. The basic difference between the two line shape theories is that VVW

assumes the oscillations are in phase with the electric field after the collisions, whereas Gross [1955] -

assumes that the molecular oscillation phases stay undisturbed and the post-collision momenta are

randomized [Ben-Reuven, 1969].

2-2.1.1 The L87R93 Atmospheric Absorption Model

The baseline model which is refined in this work uses a simplified version of the L87 model

for water vapor absorption, in which we have combined the effects of other individual water vapor

absorption lines, above the 22.235 GHz line, into the continuum term for computational expediency.

We have incorporated the simplified L87 model for water vapor absorption together with the improved


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oxygen absorption model byRosenkranz[1993]. This model is referred to as L87R93. Refinements to

the water vapor absorption model are accomplished by the addition of three adjustable parameters, CL,

CW, and CC, which account for scaling of the line strength, line width, and continuum term,

respectively. The oxygen absorption model is refined with the addition of an adjustable scaling factor

CX.

Equations for the L87R93 atmospheric absorption model, including all refinement parameters,

are presented below. The water vapor absorption model is given by

(2.3)

where TL, TS, and TCrefer to the line strength, line shape and continuum terms and are given by

, (2.4)

, (2.5)

and,

(2.6)

wherefis frequency in GHz,fzis the water vapor resonant frequency = 22.235 GHz, = 300/T, Tis air

temperature in Kelvin,Pis air pressure,PH2O is water vapor partial pressure and Pdry = P -PH2O . The

first term in equation (2.6) is due to collisions of the water vapor molecule with foreign molecules like

oxygen or nitrogen, while the second term relates to the collision among water molecules. The width

parameter, , is defined as

. (2.7)

Equations (2.3)-(2.7) introduce the following parameters: water vapor line strength CL, line width CW,

and continuum CC.

The oxygen absorption model is given by


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(2.8)

where , S(T) is the line strength

(2.9)

and S(To) and fn are listed in Table A-1 on Appendix A, fn is the nth

oxygen resonant frequency andLn

is proportional to the shape of the lines

. (2.10)

The pressure-broadened line half-width is,

(2.11)

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, Yn, defined as

. (2.12)

where the coefficients y and v are listed in Table A-1. For the non-resonant spectrum (n=0), the

summation is given by

(2.13)

where

(2.14)


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and where w is also listed in Table A-1 on Appendix A for the n resonant lines. In equations (2.8)-

(2.14),fis frequency in GHz, = 300/T, Tis air temperature in Kelvin, w is water vapor density in g/

m3,Pis air pressure,PH2O is water vapor partial pressure given by e = T/217 andPdry = P-PH2O .

A selection ofCL =1.0, CW=1.0, CC =1.2 and CX=1.0 yields values within 0.5% of the exact

L87 water vapor absorption andRosenkranz[1993] oxygen absorption models over 20-32 GHz. (Note

that the value of the parameterCC has been increased from 1.0 to 1.2 to account for the wings of the

higher water vapor absorption lines.) We refer to these as the nominal values of the C parameters. We

note here that the L93 model in the range 20-32 GHz can be reproduced from L87R93 by using the

parameters CL =1.05, CW =1.0, CC=1.25 and CX=1.0. Liebes increase by 5% in the strength of the

water vapor absorption parameter, CL, from L87 to L93 was in large part due to earlier ground based

WVR inter-comparisons with radiosondes reported by Keihm [1991]. The line width parameter, CW,

was not adjusted in L93 because theKeihm [1991] data set did not include sufficient spectral resolution

of the line shape near 22 GHz. Our intent in this work is to reexamine the adjustment that was made to

L87 using an improved intercomparison database. It is for this reason that we begin with L87R93 as

our nominal model.

Figure 2.3a shows the change in absorption spectrum when each of the parameters is raised by

10% above the nominal L87R93 model. The line strength parameter, CL, increases the absorption

significantly, and this increase is accentuated for frequencies near resonance. The width parameter,

CW, increases the width of the curve but at the same time decreases the absorption near the center


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Figure 2.3 (a) Effect of line parameter variation by 10% on total atmospheric absorption. (b)Differential effect of line parameter variation with respect to nominal L87R93 model. The arrows atthe bottom of the figure indicate the frequencies measured in this experiment. (Same atmosphericconditions as Fig. 2.2).

CL 10%

CC 10%

CX 10%

L87R93

CW 10%

CL 10%

CC 10%

CX 10%

CW 10%


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(resonance) region. Both the continuum, CC, and the oxygen, CX, parameters, increase the absorption

through the 20-32 GHz frequency span, because of their dependence on the square of frequency.

These effects are also portrayed in Figure 2.3b, in which we have plotted the difference in absorption

with respect to the nominal L87R93 model.

2-3 Experiment Description and Calibration

2-3.1 Radiometer Data

The experiment consisted of the collection of data at two National Weather Service

radiosonde launch sites. These were chosen for their contrasting humidity conditions to provide

constraints on both the 22.235 GHz vapor emission line and the level of oxygen emission in the 20-32

GHz interval. The sites were at San Diego, CA from 11 December 1991 through 3 February 1992 and

West Palm Beach, FL from 8 through 21 March 1992. The overall range of humidity in terms of vapor

burden varied from 0.6 - 2.9 g/cm2. Only data obtained under cloud free conditions were used (90%

were from San Diego, CA and 10% from West Palm, FL).

The instruments used included three independently calibrated WVRs built by JPL, designated

J1, J2 and D2, which together provided measurements at 20.0, 20.3, 20.7, 21.5, 22.2, 22.8, 23.5, 24.0

and 31.4 GHz. The J1 unit operated in a continuous tip curve mode at preselected elevation angles

from 10o

to 165o

(where 90o

corresponds to the zenith direction) and at up to nine frequencies; 20.0,

20.3, 20.7, 21.5, 22.2, 22.8, 23.5, 24.0 and 31.4 GHz. The J2 WVR included 5 elevation angles and 3

frequencies at 20.7, 22.2, and 31.4 GHz. The D2 WVR operated at 20.7 and 31.4 GHz. The J2 and D2

units, which were located approximately 10 m from J1, were only used for the purpose of absolute-

calibration verification. The overall range of measured TB varied for each frequency as follows; from

16 to 30K at 20.0 GHz, from 12 to 33K at 20.3 GHz, from 19K to 38K at 20.7GHz, from 29K to 48K

at 21.5GHz, from 26 to 53K at 22.2GHz, from 20 to 35K at 22.8 GHz, from 18 to 50 K at 23.5 GHz,

from 23 to 46 K at 24GHz and from 16 to 26 at 31.4 GHz.


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A tip gain calibration [Elgered, 1993] was performed on all three WVR units. The zenith

brightness temperatures were obtained by combining the smoothed gains obtained from the tip curves

with antenna and reference counts from longer zenith integrations obtained between tip curves. Only

tip data for which the tip curve fit RMS residuals were less than 1.0 K were used for calibration.

Poorer quality tip results were deemed unreliable, in terms of absolute calibration, for the purposes of

this experiment and often indicated cloudy conditions. The processed high quality tip gains were

corrected for beam smearing effects using an opacity- and channel-dependent term derived using the J-

series beam pattern. Inter-comparison of TB data at frequencies common to J1 and J2 instruments

revealed absolute calibration accuracies of approximately 0.5 K or less as demonstrated in Figures

2.4(a)-(c). Only radiometer data from the J1 unit were actually used for comparison with raob-derived

TB s in the absorption model analysis.

The J1 radiometerTB data were averaged over one half hour for the times coinciding with the

radiosonde balloon launch. This was used as the ground truth for comparison purposes with the

radiosonde-derived TBs. The 22.8 GHz data was not used due to an unexplained bias in that channel.

The eight well-calibrated channels across the full line width of the 22.235 GHz feature constitute an

excellent radiometric data set for constraining the line shape model.


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Figure 2.4 Zenith Brightness temperature intercomparison between radiometer units J1 and J2 forabsolute calibration purposes. Measurements were conducted during December 1991 at San Diego,CA at (a) 20.7 GHz, (b) 22.2 GHz and (c) 31.4 GHz. The data have been smoothed by a 30 minutesrunning average.

20.7 GHz channel

31.4 GHz channel

22.2 GHz channel


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2-3.2 Radiosonde Data

Raob balloons at both sites were released approximately 15 m from the J1 WVR. Raob data

were obtained from the National Climatic Data Center (NCDC). These provide height profiles of

pressure, air temperature and dew point temperature. A reading was produced every few hundred

meters at irregular intervals of height up to approximately 16 km. Raob balloons were launched at

most twice a day. There were 130 profiles in our database. Of these, 23 corresponded to bad (invalid

frequency tuning) wvr data, and 31 did not coincide with the times wvr units were in operation. Of the

remaining 76 profiles, 36 had clouds present, leaving a total of 40 available raob profiles for this

analysis.

2-3.2.1 Radiosonde Processing

The measured air pressure and dew-temperature-derived-vapor profiles are exponentially

interpolated at regular intervals of height of 30 meters. The air temperature profile is linearly

interpolated for the same height intervals. The integration interval for the radiative transfer equation

was chosen to be every 30 meters of altitude for adequate precision in the resulting TB.

The relative humidity and water vapor content was derived from the temperature, dew point

and air pressure information using the Goff-Gratch formulation for saturation water vapor densityws

[Goff, 1949]. See Appendix B for a complete description of the formulation. Note that Goff-Gratch

includes a pressure dependence on saturation vapor density which has been largely neglected in the

past. The difference in TB when including the pressure dependence was found to be up to 1.4K for the

raob profiles considered here. This effect was largest for profiles with dry climate conditions.

2-3.2.2 Radiosonde Selection and Screening

Between 1973 and October 1993, the National Weather Service routinely truncated their

radiosonde humidity measurements at 20% RH, making the radiosonde hygristor appear to lose its

sensitivity below 20% RH [Wade, 1994]. Any humidity below 20% was recorded as 19%. The

relative humidities are still reported with a high bias. (See Wade [1994] for more details concerning


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NWS raob biases.). The data also suffered from the inability of the raob to properly report dew point

temperature for levels of relative humidity higher than 95%. To reduce these effects, a correction

factor was applied to relative humidity values outside the 20% - 95% range. The relative humidity was

set to 11% whenever it was less than 22% (this usually occurred at low altitudes) and to 20% (typical

high altitude value) whenever it was higher than 100%. The unphysical values ofRH greater than

100% generally arose at altitudes greater than 8 km, where the effects ofRHerrors are negligible for

the present analysis.

The selection of the radiosonde profiles to be used was based on the degree to which they

were affected by these RAOB humidity problems. Some profiles showed TB differences of up to

12.5K when the humidity correction factor was used. To study this effect, the four line parameters

were estimated with and without the correction. First, only one profile was use for the estimation, then

more profiles were added in order of less to greater change in TB due to the correction. In every case,

the change in each of the 4 parameters resulting from the correction was computed. This change was

then compared with the errors in the parameters due to 0.5K Gaussian noise on the WVR TBs. Both

effects are plotted in Fig. 2.5 versus the number of profiles used in the estimation, for the case of the

line width parameter, CW. The combined root sum square (RSS) error is also plotted. As seen in the

figure, the error due to the RHcorrection is of comparable magnitude to the error introduced by the

noise in the WVRTB when between 10 and 20 profiles are used. The highest number of profiles that

can be used without significantly increasing the RSS error in the estimated parameters is found to be

21 profiles. (Each profile is compared in the estimation with WVR data, with up to 8 frequency

channels, for a total of 108 data points). The error plots for the other three parameters look similar to

Fig. 2.5 except for the line strength parameter, CL. In the CL plot, the error starts increasing at 16

profiles, but at 21 profiles the RSS error is still only 0.04, so this number of profiles was chosen as a

compromise to accommodate the estimation of all 4 parameters simultaneously. This corresponded to

profiles with differences less than 4.5K between the TB calculated with the corrected and uncorrected

relative humidity values.


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0

0.01

0.02

0.03

0.04

0.05

4 6 8 10 12 14 16 18 20 22 24 26 28 30

No. of profiles used

NoiseinCWParameter

RH correction

0.5K TB noise

Total Noise

Figure 2.5 Total error in CW line parameter due to a 0.5 K uncertainty in measured TB and thecorrection of the raob relative humidity reading, versus number of raob profiles used in theestimation (see Section 3.2 for a complete discussion). A trade off between the amount of data usedand the minimum error in parameter estimation yields an optimum value of 21 raob profiles,providing a total of 108 data points.

Hoehne [1980] provides estimates of the functional precision for VIZ radiosonde packages as

0.7 hPa for barometric pressure and 0.84K for air temperature. England et al., [1993] suggest a

value of5% be used for relative humidity. Manufacturers specifications list 4% for the carbon

hygristor humidity sensors used by the VIZ radiosonde, but independent investigations have shown the

errors to be dependent on the particular manufactured lot. Therefore, asEnglandet al. [1993] note,

until more complete investigation of the uncertainties is undertaken, 5% is a reasonable estimate for

the humidity measurements. In any case, the dominant contribution to the error in brightness

temperatures inferred from the raobs comes from the 0.84K temperature uncertainty and not from the

5% humidity [Englandet al., 1993].


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2-4 Analysis and Results

2-4.1 Hills Ratio Test

Any of the absorption models described above could, in principle, be adjusted to fit our data

set. In order to select the appropriate absorption models and line shapes, we adopt an asymmetry ratio

test formulated by Hill [1986]. This test provides a clear-cut means for assessing the validity of the

VVW and Gross line shape models and is independent of line strength and insensitive to errors in line

width, continuum water vapor absorption and oxygen absorption. Two brightness temperatures

corresponding to frequencies approximately symmetric about the line center are used to compute the

ratio. In this work, 20.7 and 24.0 GHz are used. The ratio is defined as the difference of the two TBs

divided by their averages,

(2.15)

The Hill ratio was computed from the raob-based TB data for all models mentioned above including the

new model presented in this work, and for the water vapor radiometer data itself. Data obtained at

both sites are plotted as a time series in Figure 2.6. This test shows the superiority of VVW versus

Gross. The purpose of including this test here is to demonstrate that we are starting off with the more

reliable line shape model currently available which, as shown here, is the VVW line shape.


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Figure 2.6 Hill ratio comparison between various atmospheric models showing agreement of thechosen water vapor absorption line shape with the radiometer data. (See text for explanation ofmodels' acronyms).

Note that the Hill ratio for the W76 and UMF81 models, both of which use the Gross line

shape for the water vapor absorption, yields a much lower value than the corresponding ratio from the

WVR data. The W76 and UMF81 models have average ratios of 0.005 and 0.007, respectively,

whereas the WVR data has an average ratio of 0.045. In contrast, the new and L87R93 models, both

of which use the VVW line shape, yield average ratios of 0.044 and 0.043, respectively. 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 byHill[1986] when the ratio test was applied to the originalBecker

and Autler[1946] laboratory data.


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2-4.2 Parameter Estimation: Newton-Raphson Iterative Method

The modeled TBs were calculated using the radiative transfer integral and the parameterized

absorption model described in appendix A applied to the balloon profiles. The parameters CL, CW, CC

and CX were estimated using a Newton-Raphson iterative method [Kagiwada andKalaba, 1969]. The

Newton-Raphson method is a fast-converging iterative procedure for nonlinear models. The first

derivative of the nonlinear equation is taken with respect to each of the variables that will be estimated,

in this case CL, CW, CC and CX, which form a vector. The derivative is then evaluated using the initial

values for the four parameters to form the Jacobian matrix given by

(2.16)

The number of rows in the Jacobian is equal to the number of data points (i.e. the number of raob

profiles times the number of frequencies at each). The number of columns is equal to the number of

parameters being estimated. In our case, derivatives were calculated numerically due to the

complexity of the radiative transfer integral equation used to compute the TB. The initial values for the

four parameters were chosen to be the nominal values, i.e. CL =1.0, CW=1.0, CC =1.2 and CX =1.0.

Then the new C parameters are found as

c c cnew initial

= + (2.17)

where

c is the correction for the parameters and is computed from the minimum square error

inversion by

( )

c J J J T t t

B=

1

(2.18)


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and

TB

is the difference between the TB modeled with the initial value parameters and the true

(observed) TB. These new values for the Cs are used as initial values for the next iteration. The

process is repeated until changes in each of the parameters are less than 0.001. All four parameters

were estimated simultaneously. This is possible because of the number of frequency channels

employed and the range of humidity conditions (0.6 - 2.9 g/cm2 vapor burden) covered during the span

of our experiments.

2-4.3 New Model Retrieved Parameters

The final retrieved parameters, CL, CW, CCand 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. A better indication of this agreement

can be seen in Figures 2.8a-c, where we have plotted the difference in brightness temperature, taking

the L87R93 model as the reference (therefore, by definition the L87R93 model is a line at zero in

Figures 2.8a-c). In these figures we have included the L93 model which, as explained above, is similar

to L87R93 except that it has a higher water vapor line

TABLE 2.1 New retrieved atmospheric absorption parameters

Parameter Liebe87-Rosenkranz93 New Model

CL 1.0 1.064CW 1.0 1.066

CC 1.2 1.234

CX 1.0 1.074

RMS difference 1.36 K 1.05 K


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15

20

25

30

35

40

45

50

55

18 20 22 24 26 28 30 32

frequency [GHz]

(a)

BrightnessT

emperature[K]

10

15

20

25

30

35

40

45

50

18.0 20.0 22.0 24.0 26.0 28.0 30.0 32.0

frequency [GHz]

(b)

BrightnessTemperature[K]

14

16

18

20

22

24

26

28

30

18 20 22 24 26 28 30 32

frequency [GHz]

(c)

BrightnessTemperature[K]

L87R93

New

WVR

Figure 2.7 Brightness temperature spectra comparison between radiometer data (WVR) andradiosonde-derived data with new and nominal parameters for a vapor burden of (a) 2.9 g/cm2 , (b)2.3 g/cm

2, and (c) 1.3 g/cm

2. (Note that only five channels were in operation during the raob

launches for conditions (b) and (c) ).

Humid

Moderate

dry


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-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

18.0

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