SSM/I Project Summary Report - apps.dtic.mil · SSM/I PROJECT SUMMARY REPORT I. INTRODUCTION The Microwave Environmental Sensor System, referred to as the Mission Sensor Microwave/Imager

NRL Memor-n dum Repyi 5055

SSM/I Project Summary Report

J. P. HOLLINGER AND R. C. Lo

Space Sensing Applications BranchAerospace Systems Division

April 20, 1983

7Orrc.4

NAV,'-,L RESEARCH LABORATORY JU -Washington, D.C.

Approwd for public release; distribtion unlimited.

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IS. SUPPLEMENTARY NOTES

19. KEY WORDS (Codnnue .,on res ide it necessary and Ideify by block number.)

Parameters Retrieval GeophysicalSSM/I Microwave Passive

Algorithm

20. A STRACT (Continue ort reverse oldi if nacooaev and Identify by block numaber)

-1 Th;e Special Sensor Microwave/Imager (SSM/I) is a passive microwave radiometricsystem designed to provide retrievals of tile environmental parameters sea surface wind,precipitation, atmospheric moisture content, soil moisture and sea ice conditions. It isa joint Navy/Air Force project developed by the Hughes Aircraft Company under thedirection of the Navy Space System Activity (NSSA) and the Air Force Space Divisionto be flown on the Defense Meteorological Satellite Program (DMSP). The Space Sensing

(Continues)

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20. AhSTIACT (Coetinuod)

"Applications Branch of the Naval Research Laboratory has served as a technicalconsultant to NSSA beginning in fiscal year 1982.

A summary description of the SSM/I instrument; and descriptions of thegeophysical models, the interaction model, the ,etrieval technique and climatologyused for the SSM/I environmental retrieval algorithm are presented. This infor-mation may serve as an introduction to the SSM/I for those individuals who havean interest in the SSM/I and its geophysical data products.

The studies, conducted at the request of the NSSA to evaluate and investigatespecific details of the instrument and algorithms are attached as AppendixA through E.

SECuRITY CLASSIFICATION OF THIS PAOI(Uhom Dine fffleroO

ii

CONTENTS

Acknowledgem ents ................................................... iv

Section I. Introduction ........................................... 1

Section II. Description of the SSM/I ...... .......................... 1

Section III. Environmental Retrieval Algorithm ......................... 12

III. A. Geophysical M odels ..................................... 12

III. B. Interaction M odel ....................................... 28

III. C. The Retrieval Technique and Climatology ..................... 31

R eferences ......................................................... 35

Appendix A - NRL Comments on the ERT SST Study for the SSM/I ........... 37

Appendix B - Selection of Optimal Combination of Frequencies for theSpecial Sensor Microwave Imager (SSM/I) EnvironmentalR etrievals ............................................... 50

Appendix C - A Simulation Study of the Sensitivity of EnvironmentalParameter Retrievals Based on the Special Sensor MicrowaveIm ager (SSM /I) ......................................... 67

Appendix D - A Comparison Study of the Sensitivity and RetrievalPerformance of 21.0 and 22.235 GHz Channels ................. 78

Appendix E - A Study of the Cross Polarization Effects on the SpecialSensor Microwave Imager (SSM/I) EnvironmentalParameter Retrievals ..................................... 94

iii1

@ "

Acknowledgements

The authors wish to thank Messrs. A. T. Edgerton and J. L. Pierce ofthe Hughes Aircraft Company for providing a set of photographs of the SSM/Iand for various detailed discussions concerning the instrument.Appreciation is also due Dr. Kenneth R. Hardy for providing informationconcerning the algorithms developed at the Environmental Research &Technology, Inc. for the SSM/I. This work would not have been possiblewithout the support of CMDRS F. Wooldridge and T. M. Piwowar of the NavySpace Systems Activity.

iv

SSM/I PROJECT SUMMARY REPORT

I. INTRODUCTION

The Microwave Environmental Sensor System, referred to as the MissionSensor Microwave/Imager (SSM/I), is a joint Navy/Air Force Project. It is apassive microwave radiometric system developed by the Hughes AircraftCompany under the direction of the Navy Space Systems Activity (NSSA) andthe Air Force Space Division to be flown on the Defense MeteorologicalSatellite Program (DMSP) operational spacecraft as an all weather oceano-graphic and meteorological sensor. The Space Sensing Applications Branch ofthe Naval Research Laboratory (NRL) has served as technical consultant tothe NSSA beginning in fiscal year 1982.

In this capacity NRL has performed a number of studies and analysesrequested by NSSA, prepared a draft SSM/I calibration/validation plan andconducted the SSM/I Calibration/Validation Workshop on 10 and 11 August1982. This report is intended to describe and document these efforts. Inaddition, a description of the instrument and the geophysical retrievalalgorithms is included so that this report might also serve as an intro-duction to the SSM/I for those individuals who have an interest in the SSM/Ior its geophysical data products.

A summary description of the SSM/I instrument is presented in SectionII. Section III contains a description of the environmental retrievalalgorithm designed by Environmental Research and Technology, Inc. (ERT)under subcontract to Hughes Aircraft Company. Five letter reports,describing studies which were conducted at the request of NSSA, are attachedas Appendix A through E.

II. DESCRIPTION OF THE SSM/I

The SSM/I is a seven channel, four frequency, linearly polarized,passive microwave radiometric system. The instrument measuresatmospheric/ocean surface brightness temperatures at 19.3, 22.2, 37.0, and85.5 GHz. These data will be processed by the Naval Oceanography Commandand the Air Force Air Weather Service to obtain near real time globalprecipitation maps, sea ice morphology, marine surface wind speed, columnarintegrated liquid water, and soil moisture percentage. In addition, Navyand Air Force DMSP tactical sites will be capable of receiving this samedata directly from the satellite to satisfy their unique customer missionrequirements.

The DMSP Block 5D-2 satellite and the SSM/I are depicted in Figure II.1.The instrument consists of an offset parabolic reflector of dimensions 24 x26 inches, fed by a corrugated, broad-band, seven-port horn antenna. The

Manuscript approved January 27, 1983.

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reflector and feed are mounted on a drum which contains the radiometers,digital data subsystem, mechanical scanning subsystem, and power subsystem.The reflector-feed-drum assembly is rotated about the axis of the drum by acoaxially mounted bearing and power transfer assembly (BAPTA). All data,commands, timing and telemetry signals, and power pass through the BAPTA onslip ring connectors to the rotating assembly.

A small mirror and a hot reference absorber are mounted on the BAPTA anddo not rotate with the drum assembly. They are positioned off axis suchthat they pass between the feed horn and the parabolic reflector, occultingthe feed once each scan. The mirror reflects cold sky radiation into the

feed thus serving, along with the hot reference absorber, as calibrationreferences for the SSM/I. This scheme provides an overall absolutecalibration which includes the feed horn. Corrections for spillover andantenna pattern effects fror the parabolic reflector are incorporated in thedata processing algorithms.

The prototype of the SSM/I is shown in the stowed position in Figure11.2 and deployed in Figure 11.3. The feed horn antenna may be seen inFigure 11.2 and the sky reference reflector in Figure 11.3. The hotabsorber reference is under the thermal blanket in both figures. Photo-graphs of the feed horn antenna, sky reference reflector, and hot absorberreference are given in Figures 11.4, 11.5, and 11.6, repectively.

The radiometers are total power, balanced mixer, superheterodyne typereceivers. The exact operating frequencies and radiometric performance

characteristics are given in Figure 11.7. The weight, size, power, and

orbit specifications are given in Figure 11.8.

Details of the scan geometry are shown in Figure 11.9. The SSM/Irotates at a uniform rate making one revolution in 1.90 seconds during which

time the satellite advances 12.5 km. The antenna beams are at an angle of45°0 to the BAPTA rotational axis, which is normal to the earth's surface.Thus as the antenna rotates the beams define the surface of a cone and, fromthe orbital altitude of 833 km, make an angle of incidence of 53.1 at theearth's surface. The scene is viewed over a scan angle of 102.40 centeredon the ground track aft of the satellite resulting in a scene swath width of1394 km. The radiometer outputs are sampled differently on alternate scans.During the scene portion of the scans labeled scan A in Figure 11.9, thefive lower frequency channels are each sampled over 64 equal 1.60 intervalsand the two 85.5 GHz channels are each sampled over 128 equal 0.80 intervalsor approximately each 11 km along the scan. During the alternate type Bscans, only the two 85.5 GHz channels are sampled at 128 equal intervals.Sampling, to 12 bit precision, is accomplished by the integrate, hold anddump method with an integration period of 7.95 milliseconds for the fivelower frequency channels and 3.89 milliseconds for the two 85.5 GHzchannels. Alternate 0.80 intervals are centered on the midpoints of the

1.60 intervals so that samples of all seven channels are collocated withadditional 85.5 GHz samples equally spaced between them. Thus the fivelower channels are sampled on an approximate 25 km grid along the scan andalong the track. The two 85.5 GHz channels are sampled at one half thisspacing both cross and along track.

3

Figure 11.2 The prototype of the SSM/I in the stowed position

4

Figure 11.3 The prototype of the SSM/I in the deployed position

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Figure 11.5 The sky reference reflector of the SSM/I

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The hot absorber and cold sky reflector references are each sampled inthe same manner as the scene data but over total angles of 8.00, rather than102.h ° , as they occult the feed horn during the remaining portion of thescan. The scene, absorber and reflector samples along with the temperatureof the absorber, various instrument parameters and zero's required to matchinput and output data rates result in 3636 bit blocks of data each second.

The radiometer outputs are converted to absolute antenna temperatureusing the hot and cold sky reference measurements and then corrected forantenna pattern effects to obtain absolute brightness temperatures. Thebrightness temperatures are then used with a "D" matrix retrieval algorithmto estimate variuus environmental parameters. The measured environmentalparameters, the geometric resolution, and the range, quantization andabsolute accuracy of the measurements are given in Figure I.10.

III. ENVIRONMENTAL RETRIEVAL ALGORITHM

The SSM/I environmental retrieval algorithm includes several importantcomponents: climatology and radiosondes, an interactive (radiative transfer)model, a geophysical model and the parameteric extraction algorithm. FigureIII.1 shows the relationship among these elements. The geophysical modeland the interaction model are employed in the brightness temperature (T

B'simulations. The D-matrix approach is used for all parameter extractionexcept for sea ice morphology. In that case, a deterministic approach isused. The environmental retrieval algorithm was developed at EnvironmentalResearch and Technology, Inc. (ERT) under a sub-contract from HughesAircraft Company. Detailed documentation of the algorithm and models wasnot part of the contract and is not generally available. The followingsub-sections contain descriptions of the geophysical and interactive models,the environmental parameters, the climatology, and the parameter extractionalgorithm as compiled from several different sources (1,2,3,4). Thissection serves as a comprehensive digest of the SSM/I environmentalretrieval algorithm.

A. Geophysical Models

A.1 Ocean Surface Wind Speed

The calculation of the emissivity of a smooth water surface isrelatively straightforward. The dielectric properties of sea water, derivedfrom the measurements of Lane and Saxton (5) and expressed in analytic formby Chang and Wilheit (6), are used for the SSM/I algorithm. The Fresnelequations for a plane dielectric interface are used to calculate theemissivity of the smooth surface for a given view angle and polarization.

Wind driven waves and foam on the ocean surface both significantly alterthe microwave emissivity of the ocean surface. The wind speed is highlyvariable both horizontally and vertically. Marine wind speed measured froma ship is usually referenced to a standard height of 20 meters. However,the wind speed which directly relates to roughness and foam, and the oneused in the development of the physical relationships, is the frictionvelocity at the ocean-sea interface. The relationship developed by Cardone(7) is then used to translate it to the standard 20 meter height.

12

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The roughness effect is modeled using a study by Cox and Munk (8) andtreating the sea surface as a collection of plane facets large compared tothe observational wavelength. The variance in sea surface slope is definedas a function of wind speed and then used for calculation of emissivityassuming a Gaussian slope distribution for the facets and using the Fresnelr~lations. The derived wind speed dependence of the surface slope variance,, is given by

22(f) = (0.3 + 0.02 f) (0.003 + 0.48 W) for f < 35 GHz, and

(111.1)

= 0.003 + 0.48 w for f > 35 GHz;

where f is frequency in gigahertz (GHz) and W is the wind speed at 20 meterheight in m/sec.

In the ERT model, foam is treated as partially obscuring the surface ina manner independent of polarization but dependent upon frequency. The foamfraction, K, is defined as

K = a(l - e o) (W - 7) for W > 7 m/sec, and

(111.2)

= 0 for W < 7 m/sec;

where a = 0.006 sec/m and f is 7.5 GHz. This equation is based onNordberg's (9) observation ?hat the brightness temperature increaseslinearly with wind speed exceeding 7 m/sec, and that no foam forms belowthat wind speed.

Figure 111.2 demonstrates the response of ocean surface wind speed at 19V and H, 22 V, and 37 V and H, assuming a tropical clear atmosphere.

A.2 Precipitation Over Ocean and Land

Precipitation size droplets are the primary contributors to atmosphericattenuation at microwave wavelengths. The attenuation results from bothabsorption and scattering by the hydrometeors. The magnitude of theseprocesses depends upon wavelength, drop size distribution, and precipitationlayer thickness. This leads to the potential application of microwaveobservations for the detection of precipitation as well as the estimation ofrain rate at the surface.

At lower frequencies, such as 19.35 GHz, rain is highly absorptive andresults in an apparent warm brightness temperature over cold backgroundssuch as the oceans. At frequencies greater than about 80 GHz, scatteringeffects become predominent and result in an apparent cool brightnesstemperature relative to warm backgrounds such as land (10). These effectsincrease with increasing rain rates.

15

240-

W220

19VW210- 7

~200-

CL 190-

180 19

W~ 170-zZ160-

150-

140-

0 5 10 15 20 25 30

WIND SPEED (m/sec)Figure 111.2 Brightness temperatures function of frequency and wind speed

16

Some of the important physical properties of precipitation affectingmicrowave radiation are the drop size distribution, rain layer thickness,

and the possibility of ice crystal coverage above the rain layer.

The drop size distribution employed for the SSM/I rain algorithm isderived by fitting the Deirmendjian distribution to the empirically observedspectra of Laws and Parson (11). The Deirmendjian distribution is definedas

C1 Cn(r) = Ar exp (-Br , (111.3)

where n(r) is the drop size distribution in cm-m -I, r is the radius ofrain drops in pm, and A and B are scale parameters.Here, /Me2 I "B c + 4 ) / c 2 I

where M is the total liquid water content in gm/m,, and

M Pw 4 r3 YI(r)dr

C2 -C2

B ( r ° 2

and r is the mode radius in pm. The shape parameters are C and C 2 The

former of these, affects the distribution of the smaller radii while thelatter affects the larger radii.

The analytical results from fitting the Laws-Parson empirical spectrum

are M = 0.0636 (R 8 8 1 ) (gm/cm 3), where R is rain rate in mm/hr,

r = 225 +9.16 (R 881); (r o)max = 375 Pm,

C1 = h.o, (111.4)

C2 = .70 - .00458 (R 881); (C2 )min = .625.

This formulation relates the rain rate to mode radius and liquid water

density. It parameterizes the distribution as a function of rain rate onlyand thus simplifies the solution to the Deirmendjian distribution. On the

other hand, it still retains the sensitivity of scattering to drop size,which would be lost if the simpler Marshall-Palmer distribution is used.

Figure 111.3 shows the good agreement between the Deirmendjian model and theLaws and Parson distributions.

For weak storms with low rain rates, R<8 mm/hr, the ceiling for the rainlayer does not exceed the 0 C isotherm. For more intensive convective

storms, the ceiling is higher with a supercooled water layer on top. The

17

10 -- LAWS PARSONS10 ___ MODEL DISTRIBUTIONS

~ f ____25.4 mm/hr-'E 26.7

1* 10E

2.mm/hr

101.3 mm/hr-1 .

I 2 3

DROP RADIUS (mm)Figure 111.3 The matching of the Deirmendjian raindrop-size distributions

used in model computations to the observed Laws and Parsonsdistributions.

18

thickness of this layer depends on the intensity of convection. Climatologyusing categories of latitudes (tropics, mid-latitudes and Arctic regions)and surface types (land and ocean) is used to provide the estimation of thesupercooled water layer thickness as a function of rain rate. The thicknessof the supercooled layer, AZ, for rain rates in excess of 8 mm/hr, is givenas

AZ = (R - 8.0) Zinc,and (1II.5)

AZ < Z

where Zinc and Zmax are determined from climatology (1).

At lower frequencies the absorption effect of ice particles isinsignificant, but large ice or snow crystals, which may occur on the top ofa storm, can cause significant scattering effects at 85.5 GHz. From simu-lation studies, it is evident that layers of ice particles having a size of4OO pm would cause the loss of all sensitivity to rain rate. With 200 gm

particle size, the effect could also be significant depending on the layerthickness. For most rain conditions, the typical ice particle size is 100mm, which does not cause significant attenuation at 85.5 GHz. A 1 km thickcloud layer of 200 pm ice particles would be considered unusually severe(1).

Brightness temperature calculations are based on the radiative transfertheory and the atmoshpere and rain models. The brightness temperatureversus rain rates over mid-latitude ocean and over mid-latitude land arepresented in Figures III.h and 111.5. These calculations include thepresence of supercooled water layers for rain rates above 8mm/hr. The 19.35and 37.0 GHz frequencies are used for retrieval of rain over ocean, whilethe 37.0 and 85.5 GHz are used over land.

A.3 Cloud Water Over Ocean and Land

Cloud water is defined to consist of droplets smaller than 100 m indiameter. Droplets this size produce negligible scattering at the SSM/Ifrequencies and only absorption due to the mass of water present need beconsidered. The absorption coefficient, ) , in nepers/m for droplets withdiameter small compared to a wavelength is given by Staelin (12) as

1.0016 x lo4 m 100.0122(291-T) (11.6)

where m is liquid water content gm/m3; T is atmospheric temperature in K andX is wavelength in cm.

The water vapor in the cloud is taken as the saturation value. Theabsorption coefficient for water vapor is computed using the Van-Vleck and

19

260,19

H

~230-

WH0w Hw

200

w

I-

ra 170C',w=CD

Cr 140

0 10 20 30

RAIN RATE (mm/hr)Figure III.I Brightness temperature vs. rain rate over mid-latitude ocean

background at 19.35 and 37 GHz~ vertical and horizontalpolarizations (look angle =50 )

20

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280

19V

0w 2 7 00%-0 1.9 H

w

i 260-w

w

cn250-z

I-

(r)a'240 -

030

23 5 10 15 20 25 30

RAIN RATE (mm/hr)Figure 111.5 Brightness temperature vs. rain rate over mid-latitude land

at 85.5, 37 and 19.35 GHz. The look angle is assumed to be0

50

21

(.9-,>

Weisskopf (19) collision broadened line shape with an empirical correctionterm for the wings of the line (20). The absorption coefficient of oxygenis computed using line shape factors defined by Rosenkranz (21). These arecomputed for all parameters for each level and integrated using theradiative transfer equation to provide brightness temperatures. Theresponse due to cloud water at 19, 22, and 37 GHz over a mid-latitude oceanbackground is shown in Figure 111.6. The figure is an idealizeddemonstration assuming the existence of only one type of cloud.

In general, the retrieval of cloud water over the ocean can be achievedwith a high degree of accuracy due to the fact that the ocean surface is acold background in the microwave range, and is relatively homogeneous. Theretrieval of cloud water over land can be difficult because the land back-ground is much warmer than the ocean and results in less contrast betweencloud and background and because the variations in the land background aresignificant relative to the cloud contrast. As a result, cloud signaturesfrequently fall within the environmental noise range.

When rain occurs, the sensitivity of the algorithm to cloud water islost. Criteria including the 85.5 GHz vertical polarization brightnesstemperature, and the brightness temperature difference between thehorizontal and vertical polarizations at 85.5 GHz, have been set todetermine whether rain exists over land. Similar criteria using 37.0 GHzdata have been chosen for ocean cases. These are used to determine whethercloud water or rain rate is to be retrieved. The brightness temperaturecriteria are given for different latitude regions and seasons. Those formid-latitude land for spring and autumn and tropical ocean for summer areillustrated in Figures 111.7 and 111.8.

A.h Soil Moisture

The soil moisture model developed for SSM/I is based on the concept thatthermal microwave radiation in soils results from the random, microscopiccurrent loops within the soil volume (13). The intensity of radiation at agiven point depends on the local dielectric constant and the physicaltemperature of the soil. Moisture produces a marked increase in both thereal and the imaginary parts of the dielectric constant of soil, leading toa decrease in the soil emissivity. Experimental observations andtheoretical calculations indicate that the emissivity of soil at microwavefrequencies can range from > 0.9 for dry soils to < 0.6 for very moistsoils.

A generalized incoherent layered surface model (24) was used to simulateexpected SSM/I soil moisture signatures. In this model, layers of soil withdifferent moisture contents are modeled as multilayer media, with thereflection coefficients between layers and opacities within the layercalculated from the dielectric properties of the medium.

For a plane dielectric-air interface the Fresnel coefficients are

cos 0 - sin 20FH = (I1I.7)

cos 0 +Vc-sin 2

22

II-

240

37V

22V

3

.

0w

200 19 V

012

CLUCLER(mc =

w

(f)U)160-wz 1

cc

12

0 .05 .10 .15

CLOUD WATER (gm/cm')Figure 111.6 Brightness temperature vs. cloud water over mid-latitude

ocean

23

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U))

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S-.

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000

wwz

00OiXl

4-

V- z 25

F -C cose (111.8)

C Cos# sin 2

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RH = IFH 12 and RV = lFvI2 (111.9)

The soil moisture model uses existing measurements of the dielectricproperties of the soil. The layered surface is combined with the radiativetransfer equations of the atmosphere to obtain brightness temperatures forthe generation of the inversion algorithms.

Figure 111.9 gives the predicted emissivity at 1.43, 19 and 37 GHz as afunction of soil moisture. The SSM/I soil moisture retrieval uses only the19 GHz H and V channels.

Choudhary and Schumugge (14) developed a simple correction factor to thereflectivity to take into account the surface roughness effect. Thecorrected reflection coefficient is given by

2R'(8) = R(O) exp (-h cos 6),

where (III.10)

h =4 2 (21/A) 2

2.a is the variance of the surface roughness, A is the observationalwavelength and h at 19 GHz is assumed to vary between 0 and 0.6.

A.5 Sea Ice

A detailed geophysical model is not used for sea ice since the sea iceparameters are not obtained from the general "D" matrix retrieval algorithmemployed for the other geophysical parameters but rather are obtained fromdeterministic equations with empirically determined constants. Theupwelling brightness temperature sensed by the SSM/I radiometer from a scenecontaining various amounts and types of sea ice may be expressed as

TBp = e- 1C'F (Elp Tf + (1-Cfp) Tsk) + C'(I-F) (Cmp T m + (1-C rp) Tsky

+ (1-C) (+TT +(l£ )T s + at m

26

1.0I

0.9

0.8-

37 GHzo) 0.7'- 1.43 GHz

U)iLI.I

0.6-18s GHz

0.5-

0.4 15 10 15 20 25 30 35

PERCENT MOISTUREFigure 111.9 Predicted emissivities at 37, 18, and 1.43 GHz for various

soid moisture contents

27

where T is total atmospheric opacity; p indicates polarization (H or V), Cis the fraction of sea ice including all ice types; F and M are fractions offirst year ice and multiyear ice relative to the total ice present and

F+M=l. The emissivities are given byE , and T is the surface temperatures

in Celsius. Subscripts f, m, and w indicate first year ice, multiyear ice,and sea water. T , is the incident sky temperature at the surface, andTatm is atmospheric contribution to the upwelling radiation.

The difference between the vertical and horizontal emissivities at 37GHz (see Table III.1) exhibits significantly less dependence on ice age thanthe corresponding 19.35 GHz emissivity differences or the vertical andhorizontal components themselves at either frequency. This property isemployed to obtain the ice concentration using only the difference in thevertical and horizontal 37 GHz brightness temperatures through thedeterministic inversion method.

The algorithms used to extract sea ice concentration and ice temperatureare given by

C = a + 1 IT (37) - T BH(37)] (111.12)

=[(a 2 + a TBV(37)/C + a4 (111.13)

Ice type is determined by the derived temperature T in the following manner:

FY if T > To,

MY if T < T0

The coefficients a thru a4 , as well as T are different for each seasonof the year and are

a° a1 a2 a3 a4 T 0

winter 1.165 -0.0206 -217.70 1.1050 192.28 218.0spring 1.164 -0.0176 -217.70 1.1050 192.28 218.0summer 1.164 -0.0176 -219.06 1.1050 193.64 228.0autumn 1.163 -0.0276 -219.06 1.1050 193.64 228.0

The ice edge locations is determined using a two dimensionalinterpolation technique. If a pixel is determined to be ice by the abovealgorithm, the four cardinal adjacent pixels (two perpendicular and twoalong the scan) will also be tested. If any of these four pixels is foundto be water, the center pixel will be flagged as the ice edge.

B. Interaction Model

The geophysical models define the physical and electromagneticproperties of the surface and atmospheric constituents. The interactionmodel determines the radiative transfer properties of the totalsurface-atmospheric system. The liquid water present in the systemdominates the radiative transfer calculation. When only very small droplets

28

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>_____________ (r!_________________________________________ 0

O U)

I. - u

0 ccU.

29

in the form of clouds are present, the calculations are relatively simplebecause only absorption effects need be considered. However, whenscattering is present, e.g., in the case of precipitation, a much morecomplicated scheme must be employed. The Mie theory is employed to evaluatethe extinction coefficients and a variational, iterative approach (16, 17)is used to solve the radiative transfer equation.

The radiative transfer equation, using the Rayleigh-Jeans approximationfor a blackbody, can be written as

dT = TB (A,) - T, (111.14)

dr'

where T is the brightness temperature and T is the physical temperature inB

degrees K; r' is the total opacity of the atmosphere along the line of sight(in nepers); Z is the height and 0 is the look angle. When no scattering is

present, TB sensed by the satellite can be written as (18)

TB(Z , ) = TGB(Z, ) + I(-R) TG + R TB ] exp (-r') (111.15)

where T is the upward atmospheric emission; R is the effective surface

reflectivity; T is the surface temperature, and T is the downwardG B 2atmospheric emission plus the attenuated sky background emission.

Intergrating over the entire atmospheric yields.

HTBl = /T(z)7(z) exp I - J (z') sec dz'] sec~dz,

and (111.16)-T' H

T =T eT + f T(z)y(z) • exp '[ v(z')sec~dz']sece dzB2 sky fJ

H 0where r = f (z) sec dz. Here H is the height of the radiometer andV

o

is the total extinction coefficient at height z.

The Mie scattering theory is the formalism used to account for thecoupling of the absorption and multiple scattering effects when rain ispresent. It is based on the diffraction of a plane monochromatic wave by asphere with a homogeneous complex index of refraction. The absorption inthe sphere and the scattered wave are calculated to provide the extinctioncoefficient and single scatter albedo.

QE = QA + QS'.0 = Qs/QA '(11117)

where the Q's are efficiency factors defined as the ratio of actual to

geometric cross sections. A, S, and E indicate absorption, scattering and

30

extinction. w0 is the single scattering albedo. The extinction coefficientis derived by integrating the efficiency factor over the drop sizedistribution encountered in the geophysical model for rain.

IVE =JN(r) QE r2 dr (111.18)

Note that Q is a function of wavelength, temperature and drop size. Theradiative transfer equation is now

dTB ('0) = TB (z,) - Ts (z,O) (111.19)dr'

The difference between this and equation (III.lh) is that the sourcefunction is no longer the physical temperature. Equation (111.19) can bewritten as

dT (T)=r T B(r, ) - T S(r,j,) (111.20)

where s = cos 9 and 7 = r' ,'p.

TS [1- T o /p(,,') TB(r, ,) dm' (111.21)21where P is phase function. It is reduced to 1 in the isotropic scatteringcase. It can be shown that the integral equation for the source functionTS including the boundaries i

TT) [-rJ .Tke]7+ 0 O Tr(T) El( (T-ri )dr

(111.22)W (r)r( 1) i

+---E (*-) + R TS (T) exp --2 2 LlJG+ L SJ

0

where r* is total optical depth of the atmosphere and En is

En (x) =f1exp (-x/$)M n- 2 d

The variational-iterative approach (16,17) is then used to solve for theintegral for T . The method essentially finds the "extremum" of a function

in N-dimensional parameter space. It is a fast and accurate technique forhandling large ensembles of data.

C. The Retrieval Technique and Climatology.

The statistical inversion method is used for retrieving the geophysicalparameters with the exception of the ice parameters, from the brightnesstemperatures. The method determines the statistical correlations between anensamble of sets of brightness temperatures derived from the environmentalmodel and the associated environmental parameters. The resulting

31

correlation cofficients are contained in the so-called D-matrix. Thistechnique assumes a linear relationship between the T B's and the physicalparameters.

P* = D t, (111.23)

Where p* is the vector of estimates of the parameters, t is the vector of

brightness temperatures and D is the D-matrix.

C.1 Averaging technique for each parameter

Another feature used in the inversion process is to "tune" the D-matrJxto the average value of each parameter. Though the resulting inversion isstill linear in brightness temperature, D is now focussed on a correlateddeviation from the statistically averaged values of the parameters. TheD-matrix is determined from the least squares process based on the actualparameters and the corresponding simulated brightness temperatures.

C.2 Separate inversion scheme for each climatology.

In order to minimize non-linearities between the TB's and theenvironmental parameters to be derived, and hence to enhance the accuracy ofthe retrievals the earth is divided geographically into three major regionsover four seasons (see Table 111.2). Transition zones are also designed toavoid drastic transition between the neighboring regions. Stations,representative of each climate region, are selected for the collection of aatmospheric radiosondes and surface observations necessary for thecalculation of the brightness temperatures needed for the construction ofthe D-matrices. The stations selected are shown in Table 111.3.

C.3 Piece-wise Scheme for regression

Another type of non-linearity encountered in the retrieval of thegeophysical parameters involves the relationship between the parameter andbrightness temperature. The radiative signatures, particularly rain rate,are highly non-linear. The signatures for no rain, light rain, and heavyrain are very different. A piece-wise decision test for rain was designed.The algorithm for the estimation of rain over ocean is shown in Figure111.8. The criterion for no rain, light rain, and heavy rain are the 37.0GHz vertical polarization and the difference between the vertical andhorizontal polarization brightness temperatures at 37.0 GHz. The criteriafor rain over land are based on brightness temperatures from both the 37.0and the 85.5 GHz channels. (See Figure 111.9.) For each of the categories,seasons and locations, a separate D-matrix is available for retrievalpurposes.

32

zzD w

0 0 (

0z 0 o

w) w 0 w< 6 z zSz z < Zo -

'- W z.. U

ULLU 0

02 LU C

CD 0

Zw >'hJ L U Ii co > >

ci Zi < C) 0<a .12 LL I 0Ii - E-~ zcn - w a-u C

PU z~ F- C)L <cr. 0 -'F z0 <0 p rZL 00~ L

co 00 L00

* 000 0 0 LU0 LOl 00a d

E L W 0 0 0

C0

-J 0 0 LL >-0 a-0

- -) -

33

i I i> I

4I I 4I i I

S I I I I I-L X I i I I< IJ 0 I C I I

)I~ I I I IE 0 " - u

I I I I I

- I I I a t~I

u $4 = i~ I I 0 IC0 CO

4-) U3 0J • o Io o Io o io

o0 0 1 I 0 0 I 0 0 t ' I 0 I 01

0 N, ( IN 1V" 'C N I~f I., I IN -. I (

SI I V % I Iq -4 - I

1' I I I I I

) I I I €z I I•Z - - - - -I -

-t ,I I It-o .- 4 N I (n " m 4 - I 0

. 0 0 0 1 0 10 0 0 tO0 0 ICa 0 IC0

00 i U 0 I C N i(I N I:: 0. I'

- I I I * -4 I I

0I I I \ I I

a)I I I Cu I i

I I II c I

E) & ( I V I I)3 * ,4 o I I II

. 0 Z 3,-C. I r I r 4 I =0 0 -4 0 t J I c - I c ,-" c U I CO I4-J -4 - I V C I U, I )

4• , I * I - )-1 u LL. I I .1< cd I UIUL 0 i0 1 I0

Ij I co I "0 u. )X I -)0 41 S.,.4 *-4 0lV 0)11 W-I

be u I r- ILrL.>

4-4 I I I 4 I

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u I" . I r U, II-4 1 .1 -4

- I~ I0 1141 - 1I- 0 Iu I u

34

References

1. Burke, H. K., and K. C. Jones, "Models of Environmental Parameters forthe SSM/I Program," Environmental Research and Technology, Inc.,February 1980.

2. Burke, H. K., A. J. Bussey, K. C. Jones, N. K. Tripps and J. Ho,"Inversion Algorithm for Environmental Parameter Extraction of theSSM/I Program," Environmental Research and Technology, Inc., February1980.

3. "Proposal for Microwave Environmental Sensor System (SSM/I); Vol. I.Technical Proposal," Hughes Airicraft Companry, Hughes RFP No.FO4701-78-R-0094, January 1979.

4. "Special Sensor Microwave/Imager (SSM/I) Critical Design Review; Vol.II. Ground Segment," Hughes Aircraft Company, HS 256-0006-0150, March1980.

5. Lane, J. A. and J. A. Saxton, "Dielectric Dispersion in Pure Polar

Liquids at Very High Radio Frequencies, III. The Effect of Electrolytesin Solution," Proc. Roy. Soc., London A, 214, pp. 531-545, 1952.

6. Chang, A. T. C. and T. Wilheit, "Remote Sensing of Atmospheric WaterVapor, Liquid Water, and Wind Speed at the Ocean Surface by PassiveMicrowave Techniques from the NIMBUS-5 Satellite," Radio Science, 1979,p. 793.

7. Cardone, V. J., "Specification of the Wind Field Distribution in theMarine Boundary Layer for Wave Forecasting," Report TR 69-1, Geophys.Sci. Lab., New York University, 1969.

8. Cox, C. and W. Munk, "Measurement of the Roughness of the Sea Surfacefrom Photographs of the Sun's Glitter," J. Optical Society of America,Vol. 44, No. 11, 1954, p. 838.

9. Nordberg, W., et al., "Measurements of Microwave Emission from a FoamCovered Wind Driven Sea," J. Atmos. Sci., Vol. 28, p. 429, 1971.

10. Savage, Richard C., "The Transfer of Thermal Microwaves ThroughHydrometeors," Ph.D. Thesis, University of Wisconson-Madison, 1976.

11. Laws, J. 0., and D. A. Parson, "The Relation of Raindrop Size toIntensity", Trans. American Geophys. Union, Vol.24, p. 452, 1943.

12. Staelin, D. H., et al., "Remote Sensing of Atmospheric Water Vapor andLiquid Water with the NIMBUS-5 Microwave Spectrometer," J. Appl. Met.,Vol. 15, pP. 1204-1214, 1976.

13. Stogryn, A., "The Brightness Temperature of a Vertically StructuredMedium," Radio Science, Vol. 5, No. 12, pp 1397-1406, December 1970.

35

14. Choudhury, B. J., T. J. Schmugge, A. Cheng, and R. W. Newton, "Effectof Surface Roughness on the Microwave Emission From Soils," J. ofGeophy. Res., Vol. 84, No. C9, September 1979, p. 5699.

15. Gloersen, P., et al., "Time-Dependence of Sea-Ice Concentration andMultiyear Ice Fraction in the Arctic Basin," Boundary-Layer Met.,Vol. 13, 1978, p. 339.

16. Sze, N. D. "Variational Methods in Radiative Transfer Problems," J.Quant. Spectroe, Radiat. Transfer, Vol. 16, 1976, p. 763.

17. Burke, H.-H. K., and N. D. Sze, "A Comparison of Variational and DiscreteOrdinate Methods for Solving Radiative Transfer Problems," J. Quant.Spectrosc. Radiat. Transfer, Vol. 17, 1977, p. 783.

18. Gaut, N. T. and E. C. Reifenstein III, "Interaction Model of MicrowaveEnergy and Atmospheric Variables," Final Report, Environmental Researchand Technology, Inc., Corcord, Massachusetts, 1971.

19. Van Vleck, J. H. and V. F. Weisskopf, "On the Shape of Collision-Broadened Lines", Rev. Mod. Phys., Vol. 17, 1945, p. 227.

20. Gaut, N. E., "Studies of Atmospheric Water Vapor by Means of PassiveMicrowave Techniques", Research Laboratory for Electronics, Tech.Report 467, Massachusetts Institute of Technology, 1968.

21. Rosenkranz, P. W., "Shape of the 5 mm Oxygen Band in the Atmosphere,"IEEE Trans. Antenna and Propagation, Vol. AP-23, No. 4, 1975, p. 498.

36

Appendix A

NRL comments on the ERT SSTStudy for the SSM/I

December 1981

Robert C. Lo and James P. HollingerSpace Sensing Applications Branch

Naval Research LaboratoryWashington, D. C. 20375

37

NRL COMMENTS ON THE ERT SST STUDY FOR THE SSM/I

Robert C. Lo and. James P. HollingerSpace Sensing Applications Branch

Naval Research LaboratoryWashington, DC 20375

In anticipation of the presentation of the sea surface temperature(SST) studies by Environmental Research and Technology, Inc. (ERT), atEl Segundo, CA on November 24, 1981 NRL requested and received copies ofthe report. In the few days available before the presentation NRLexamined the report and conducted a number of comparison studies;particularly in the area of sensitivity of the SSM/I instrument tochanges in the SST. Results analogous to Figures 2-1 to 2-6 of the ERTreport (Ref. 1) are attached as Figures 1 to 6. These were simulatedusing an environmental model previously developed at NRL (Ref. 2). Theset of figures were presented to ERT's Dr. K. Hardy and Commander F.Wooldridge of NSSA at the conference. Note that the rain cases shown inthe ERT figures are not included in Figures 5 and 6 because the NRLmodel does not yet contain a rain algorithm. Comparing figures 1through 6 with the corresponding figures in the ERT report, shows thatthe two sets are in general agreement. The only sifnificant discrepancybetween them are the curves representing 15 m sec-i wind in Figures 3and 4. Dr. K. Hardy of ERT, who made the presentations at the November24th conference, stated that the ERT 15 m sec -I curves are in error.

The D-matrix algorithm previously developed at NRL is distinctlydifferent from that used by ERT. Trade off studies were done at NRL in1978 during the definition study phase of the SSM/I (Ref. 3). In-cluded in these studies is a sensitivity study of radiometric noise onSST estimations. The climatic data selected for this sensitivity studywere mid-latitude summer (see Ref. 3). The study used 5 frequencies with2 polarizations each (i.e. 14.5 H,V and 22.2 H in addition to the SSM/Ifrequencies). This early study indicates that in order to obtain a SSTretrieval error of 1.6 K from climatic data with an a priori uncertainityof 3.8 K, as in the ERT report, no radiometer noise can be present.Assuming a realistic radiometric noise of about 0.8 K, as specified inthe ERT report, the retrieval error would be approximately 3.2 K.Current but preliminary studies based on an updated D-matrix model forthe SSM/I developed at NRL confirm this result. On this basis it appearsthat the 1.6 AK accurracy indicated in the ERT study might be too optimistic.NRL suggested at the meeting that ERT should perform a sensitivity studyconcerning the effects of radiometric noise.

The following are some other observations made while examining theERT report.

1. The surface air temperature is used in place of SST for theclimatic SST data set since the actual SST data were not available.This artificially introduces a greater variance in the SST. Sinceregression models tend to be more sensitive to variables withgreater variance the accuracy obtained by the ERT model may be lessif actual SST data were used.

38

2. The climatic data are taken from two stations chosen torepresent warm mid-latitude and cool mid-latitude ocean conditions.From Figures 3-2 to 3-4 of the ERT report (Ref. 1), the dataappear to represent a bi-model sample. This may be inadequatefor the linear regression model which implies a normal distribution.The effect of the bi-model sample is usually an over-estimateof the a priori variance in the SST.

3. The ERT model uses half of the climatic data set to arriveat the D-matrix and the other half to verify the algorithm.It appears that a more independent set of climatic data shouldbe employed. For example, those taken from a third station inthe mid-latitude ocean.

4. The verification of the model through the climatology isof the nature of internal verification showing model self-consistency. External verification is also necessary toestablish that the model is not only self-consistent but alsorelates to reality. An independent benchmark set of, say,mid-latitude ocean SST and the corresponding TB's at the SSM/Ifrequencies ought to be collected. These should be testedwith the D-matrix produced from the ERT model. This benchmarkset should include cases of warm and cool mid-latitude ocean.Since the ERT model produces D-matrixes for other climatesbenchmark data sets for all of these climates should be collectedfor tests. Only then can an understanding of the ERT model'sreal performance be achieved.

Among those in the audience when Dr. Hardy presented the SST algorithmand an algorithm for the retrieval of land surface temperature (LST)(Ref. 4) and who made significant remarks concerning the SST algorithmwere Mr. F. Wentz of Wentz & Associates, Dr. E. Njoko of Jet PropulsionLaboratory and Mr. J. Cornelius of Fleet Numeric Oceanic Center. Dr.Robert C. Lo (Code 7911L) represented NRL at the meeting.

Dr. Hardy presented simulation results which indicate the sen-sitivity of 19.35 GHz TB to SST and wind speed. Changes in TB (ATB)corresponding to a change of 20 K in SST for three different wind speedswere presented. Similar simulationo of ATB for thin clouds, thickclouds and rain were also presented. The approach for the SST retrievaland the climatic data base employed, were then presented. The followingis a list of some of the relevant comments made during the meeting.

1. ERT cloud and rain models assume single scattering. Thisassumption is not adequate for thick cloud and rain cases. Multiplescattering should be included in the considerations. (Njoko)

2. From the sensitivity studies, the relationship between SST andT at the SSM/I frequencies is apparently non-linear, while the ERTmodel implies linearity. The estimated 1.6 K accuracy appears tobe too small under such a situation. (Wentz)

*For SST retrieval, rain cases were excluded using pre-determined criteria.

39

3. Analysis of data from SEASAT SMMR, which includes lower frequencychannels approximately 3 times more sensitive to SST While severaltimes less sensitive to the atmospheric effects than the SSM/Ihigher frequency channels, indicates an accuracy of 1.0 K for SSTestimates given an instrumental RMS error of 0.2 K. Based on theSEASAT results, the fact that instrumental error for SSM/I wasassumed to be about 1.0 K and assuming similiar algorithms, theretrieval accuracy should be about 4 K (Njoko, Wentz).

4. The SST used in the ERT algorithm was in fact air temperatureat the surface rather than the skin temperature of the sea surfacesince the SST was not available. This results in a much largervariance of SST than what would actually be expected from the twostations if the SST had been measured directly. Questions wereraised as to whether the artifically large variance led to a goodresult. (Wentz) Some discussion was also made concerning impliedsurface stability from decoupling SST from air temperature. (Wentz,Njoko) No definite conclusions were reached concerning thesepoints, due to the lack of data and comparison studies. Anotherquestion was raised about using surface air temperature, for it isusually closely related to water vapor burden in the lower troposphere.(Cornelius) However, the ASST (actually radiosonde measurements ofsurface air temperature minus predicted SST) was plotted againstthe integrated water vapor, which is another parameter estimated bythe D-matrix algorithm. No clear correlation is indicated in theplot. This appears to indicate that even using the air temperature,the algorithm is relatively independent of water vapor. By thesame means, estimated SST appears to be independent of wind speedand integrated cloud water.

Additional Comments are:

5. That a sensitivity study as to model certainty should be performed.The result from the model is highly dependent on the input climatology.It is important to understand how reliable the model parameterestimates are when certain error exist in the climatology. (Njoko)

6. A sensitivity study of the model to instrumental noise shouldbe done. (Lo)

7. Climatology data should be collected from more stations toconstitute a more representative data base for the mid-latitudeocean. (Wentz)

It is observed that besides NRL, none of the critics in the audiencehas done an in depth comparison of the ERT model with their own.The evaluation and comments, valuable as they were, were morequalitative than quantitative.

40

In summary it appears that in its present state the ERT model has thefollowing shortcomings.

1. Using air temperature rather than the SST for retrieval andevaluation.

2. Not enough sensitivity studies done concerning the model uncertainty,therefore, not enough understanding as to how well the model couldperform.

3. Not adequate cloud model for thick clouds and rain cases.

4. Not enougb understanding as to the effect of the linear assump-tion to the bdsically non-linear problem.

5. Not enough data for climatology.

6. Not adequately verified with independently collected data.

A possible explanation for the discrepancy in the sensitivity of the 'RTand the NRL models to radiometer noise is in the way the noise wasintroduced into each model. Further comparison of this aspect is needed.

NRL strongly recommends that the SST retrieval algorithm be incorporatedin the SSM/I retrieval since it is of relatively very low cost and willbe the only SST test bed in the known future. NRL concurs with othercritics that the environmental models are not yet fully understood, thatthe techniques for retrieval need further development and refinementsand that the climatological data base needs to be increased. It is forthese very reasons that the SST algorithm should be included in orderthat experience and data can be gained to improve our knowledge in thesevery areas. Only in this way can the NAVY develop the capability foraccurate spaceborne sensing of SST as required. The algorithm is constructedin such a way that improvements can be incorporated and tested fairlyeasily in the operational system. NRL also recommends that sets ofbenchmark TB observations with corresponding atmospheric and surfacetruth data at the SSM/I frequencies be collected which include allclimate conditions considered by the ERT model. The algorithm shouldbe tested against this data set. Finally, NRL recommends that modelvalidity be tested as well as sensitivity tests be done for radiometricnoise effects on SST retrieval errors.

41

List of Figures

Figure 1 The variation of the 19.35 GHz (vertical) brightnesstemperature with SST for several wind speeds.

2 The variation of the 19.35 GHz (horizontal) brightnesstemperature with SST for several wind speeds.

3 Change in brightness temperature (vertical polarization)

for a change in SST from 5 to 25C for three different windspeeds.

4 Change in brightness temperature (horizontal polarization)for a change in SST from 5 to 25C for three differentwind speeds.

5 Change in brightness temperature (vertical polarization)

for a change in SST from 5 to 25C for two different -1atmospheric conditions. The surface wind speed is 7 m sec

6 Change in brightness temperature (horizontal polarization)for a change in SST from 5 to 25C for two differentatmosyheric conditions. The surface wind speed is 7 msec

42

L

(W >wUU*~~ w~G q

0~ 030Oo

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w *

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w

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(A1 930) 3HnlVh3dVW31 SS3NIUHO18S

43

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CL

130- 9 msec'7C,)C,)

Z 12 7 msec-1

1I26-

3 msec-I124

0 5 10 15 20 25 30SEA SURFACE TEMPERATURE (DEG C)

Figure 2 The variation of the 19.35 GHz horizontal brightnesstemperature with sea surface temperature for several windspeeds.

44

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References

1. Hardy, K. R., et al. " A Study of Sea Surface Temperature EstimatesUsing the SSM/I", ERT Document No. P-BO88-F, October 29, 1981.

2. Wisler, M. M., and J. P. Hollinger. "Estimation of MarineEnvironmental Parameters Using Microwave Radiometric RemoteSensing Systems", NRL Memorandum Report 3661, November 1977.

3. Hollinger, J. P., et al. "Joint Services 5D-2 Microwave ScannerDefinition Study", NRL Memorandum Report 3807, August 1978.

4. Hardy, K. R., et. al. "A Study of Land Surface Temperature EstimatesUsing the SSM/I", ERT Document No. P-B144-F, November 16, 1981.

49

Appendix B

Selection of Optimal Combination of Frequencies for the

Special Sensor Microwave Imager (SSM/I) Environmental Retrievals

April 1982



50

SELECTION OF OPTIMAL COMBINATIONS OF FREQUENCIES FOR THE SPECIALSENSOR MICROWAVE IMAGER (SSM/I) ENVIRONMENTAL RETRIEVALS


Aerospace Systems DivisionNaval Research LaboratoryWashington, DC 20375

I. Introduction

The SSM/I brightness temperature observations are related to theenvironmental parameters as independent variables through the so-called 'D'matrices of regression coefficients. Some of the most important parametersfor ocean retrievals are wind speed, sea surface temperature, columnardensity of water vapor, and liquid water contained in clouds. The bestestimation of each parameter is expected when all seven SSM/I channels areused. However, limitations of the computing facility dedicated for theSSM/I project, dictated the use of at most four channels for eachenvironmental parameter (6).

The purpose of this study is to evaluate the retrieval performance ofall four-channel subsets from the seven SSM/I channels, and to determine theoptimum subset for each environmental parameter. The performance of acertain frequency combination depends on the instrumental noise (1), (2),the geophysical model and the climate statistics utilized for the derivationof the 'D' matrices. A model originally designed by Wisler and Hollinger(1) is used for this study. The climate statistics were compiled by Wentzfor the SSM/I definition study (3). They include all four seasons for threelocations representing high, middle, and low latitudes. Instrumental noiseis simulated. The environmental parameters examined in this study are thesea surface temperature, wind speed and the columnar densities of cloud

liquid water and water vapor.

II. Approach

All four-channel subsets are evaluated for the sake of completeness.The total number of possible combinations is 7C4 = 71/(41/31) = 35 and thechannels included in each of the combinations are listed in Table 1. Thecriteria chosen for the evaluations are the residual RMS errors of theparameter for a certain frequency combination, and a quantity called theconfidence factor which is defined as:

CF = 1 - 2 - ;r )/U * (If.1)

51

Table .

Listing of Frequency Combinations

Combination No. Channels

1 19.3 H 19.3 V 22.2 V 37.0 H2 19.3 H 19.3 ' 22.2 V 37.0 V3 19.3 H 19.3 V 22.2 V 85.5 H4 19.3 H 19.3 V 22.2 V 85.5 V

5 19.3 H 19.3 V 37.0 H 37.0 V6 19.3 H 19.3 V 37.0 H 85.5 H

7 19.3 H 19.3 V 37.0 H 85.5 V8 19.3 H 19.3 V 37.0 V 85.5 H9 19.3 H 19.3 V 37.0 V 85.5 V

10 19.3 H 19.3 V 85.5 H 85.5 V11 19.3 H 22.2 V 37.0 H 37.0 V12 19.3 H 22.2 V 37.0 H 85.5 H13 19.3 H 22.2 V 37.0 H 85.5 V14 19.3 H 22.2 V 37.0 V 85.5 H15 19.3 H 22.2 V 37.0 V 85.5 V16 19.3 H 22.2 V 85.5 H 85.5 V17 19.3 H 37.0 H 37.0 V 85.5 H18 19.3 H 37.0 H 37.0 V 85.5 V19 19.3 H 37.0 H 85.5 H 85.5 V20 19.3 H 37.0 V 85.5 H 85.5 V21 19.0 V 22.2 V 37.0 H 37.0 V22 19.0 V 22.2 V 37.0 H 85.5 H23 19.0 V 22.2 V 37.0 H 85.5 V24 19.0 V 22.2 V 37.0 V 85.5 H25 19.0 V 22.2 V 37.0 V 85.5 V26 19.0 V 22.2 V 85.5 H 85.5 V27 19.0 V 37.0 H 37.0 V 85.5 H28 19.0 V 37.0 H 37.0 V 85.5 V29 19.0 V 37.0 H 85.5 H 85.5 V30 19.0 V 37.0 V 85.5 H 85.5 V31 22.2 V 37.0 H 37.0 V 85.5 H32 22.2 V 37.0 H 37.0 V 85.5 V33 22.2 V 37.0 H 85.5 H 85.5 V34 22.2 V 37.0 V 85.5 H 85.5 V

35 37.0 H 37.0 V 85.5 H 85.5 V

The seven SSM/I channels are 19.0 H, 19.0 V, 22.2 V, 37.0 H,37.0 V, 85.5 H and 85.5 V.

52

Where 072 is the natural variance of a parameter given as a climate2

statistic, ar is the variance predicted by the retrieval model and is partrrof the modelrotu and, 2Y_ 2is the residual RNS error.Th

confidence factor is then a measure of the fraction of the error explained

by the retrieval model. If it is unity, the estimation is perfect, and if

it is zero, the scheme is completely unable to retrieve the environmentalparameters.

The RMS error and the confidence factor for each of the 35 frequencycombinations are examined with respect to different climate conditions

assuming the same instrumental noise. They are then examined with respectto changes in the instrumental noise for a given climate. The noise for the85.5 GHz channels is assumed to be one-half those of the other channelssince its linear resolution is one-half of the other frequencies. It isassumed that four samples will be averaged together for use with a singlesample of each of the other channels. The two frequency combinations which

exhibit the best overall performance are then recommended for eachparameter.

II.A. Sea Surface Temperature

The residual RMS and confidence factors for Azores Summer with

instrumental noise of 0.5 K are listed in Table 2. The RMS error is alsoplotted in Figure 1. Based on the RMS error and confidence factor values,the best frequency combination is determined to be number 26 which iscomposed of the 19 V, 22 V, 85 H and 85 V channels. Numbers 30 and 10which, substitute the 37 V and 19 H, respectively, for the 22 V channel, are

the next best choices. The same examination is performed for all 11remaining climates. The climate statistics used for the development of theSSM/I algorithm by the Environmental Research and Technology, Inc. (ERT) (4)

are included as an additional climatology. The natural variance of seasurface temperature introduced by use of the ERT climatology is much greaterthan for any of the Wentz climates. The ERT climatology implies that thesea surface temperature is equal to the measured air temperature. This is

an inappropriate assumption but it does afford an evaluation of theperformance of the retrieval scheme under large variance conditions. Thebest three frequency combinations for each of the cases are shown in Table 3together with the associated RMS error and confidence factor values. Theretrievals for Azores Summer climatology are also shown in Table 3 withsimulated instrumental noise of 0.1 and 1.0 K. In general, a larger naturalvariance leads to a better estimation in the sense that the confidencefactor tends to be greater. Retrievals are also sensitive to theinstrumental noise. For example, it is greatly improved as the instrumentalnoise decreases from 0.5 to 0.1 K.

Even a cursory examination of Table 3 will reveal the fact that none of

the frequency combinations is best for every climate condition. In order tochoose a combination which has the best over-all performance, the confidencefactor and the RMS error, averaged over all the climate conditions, are usedas the criteria of selection. The best frequency combination selected for

53

Table 2

RMS and CF of SST for Climate 7 and IN of 0.5

Combination No. Residual RMS CF

1 0.7377 0.03132 0.7394 0.02903 0.7385 0.03024 0.7455 0.02105 0.7469 0.01916 0.7474 o.o1867 0.7322 0.03858 0.7470 0.01909 0.7299 0.0415

10 0.7125 0.064411 0.7586 0.003812 0.7583 0.004213 0.7309 0.04Ol14 0.7598 0.002215 0.7449 0.021816 0.7219 0.052017 0.7580 0.004518 0.7277 o.o44419 0.7195 0.055120 0.7227 0.051021 0.7377 0.031322 0.7377 0.031323 0.7276 o.o44524 0.7406 0.027525 0.7319 0.038926 0.7073 0.071227 0.7528 .011428 0.7221 0.051829 0.7126 0.064230 0.7102 0.067331 0.7584 O.0O4l32 0.7367 0.032533 0.7261 0.046534 0.7258 0.046935 0.7434 0.0238

Natural standard deviation = 0.7615Residual RMS for all 7 channels = 0.7029

54

ALL 7 CHANNELS

rC I

2

3

4

6

7

8

9

10

11

12

13

14

16

17

18

19

20

21

22 124

25

26

27

28

29

30

31

32

33

34

35I I j A LWL

.70 .71 .72 .73 .74 .75 .76 .77

RESIDUAL R14S ERROR

Figure 1 Residual RMS Error of SST for Azores, Summner

55

(Y) I-'~ H.--Lr 1- 0%_t N 0n00 t-- 0OJrt

0

HC u\0 \0 _T ,D ( \C Lr c0 MC\J __r C-I _

C~Jt-Lr 0 m qt- -H k C~j ~0 C\j a\ __r --

NN

C) C\J 0 --r(Y) *00 0 0\ C'j \ m 00Dr. M ' -H(Y) ('j C'1-4.-r-I -4AC.J N(\ H-- 0.3.4

a) * L4c ~(Y) P\- C\j 0 t C t-.-H1-4 0 \0 -\U C\_z C)i o HQ\o \o 0HO r- 0 -4 E- t j

v 0 0 0 OHr-4o A0 q 00 00 --. --.t0

0 Cd C)

0

C~ 0\ 0) 0j.Jir 0 (Y)C\J 0\ CJ 00H O -- (\I --4' ~CU\\ODC\.J \0 _:r0 r-4q -HO \._:r 0 (\_-

Ca) t- - 0 0 \0 0\ (Y) 0.31 H - Lf\ 00 Ul\ O\ C\ _:(Y) C\JC- LC\0 (Y)C\j t- H CUjC'.30 Cj a\ fn t--

o 4 4iH .-4 . H.- 4 LC'\@+' (Y)Cl

H4 a) 0.30(Y \) C'j m 0 oc00 C'b Y) o 0 \0 \0~U0C) -4 H CV)-4 (Y fl1C (Y) C\j C.j C.j C\j C\ H- r- Oj

o m'

N4 HN (J'CM 1 0 ~ J CM Y)O\ -4C ~ Jt-H '.J H t--_:O'.C'JOCOD t-'. C t-H H

,0 \ oHO OHOH14 0 0- 0000 t __0

~ @3 0

4) 0 rC) H0O C _ L\C\ - \'O O HC~j _: H4 -S -0 O\ Lr\ t l0 0- _z HILr\ ao UN t-- 0\ --

Cj.0 U,\ 0 m 04j -H-~ .CJ o0. N~ C7\ mW3 H r-4 . . . . * *S.. Cd.4H~Z4 4.' N4

0) 000 0 c Y o0 o 0 C\O)t- - co 0 m

930 m m0 CY O UN0 t- oC'j \0 r\ Lr\q 1 r Moo Nt- o (Y) r4 \ (NJ ClCj t- 0 HH 1

tio o0E- m\1 ;ra \O0) co 4 \o c U\ 0 lZ\

0~ H- Hr H~ m mmNCj0 D tt

0~H

4$440 Cl. 4DS.OH14.' . 0 ' ' 8 @3

ltco )) 0 :w2)~ -ci2w E-4 0

56

sea surface temperature is number 10. The first runner-up is number 29.The RMS error and confidence factor of all the climate conditions for these

two combinations are listed in Table 4. From the RMS values, it appearsthat the estimation of sea surface temperature is reasonable. They are allunder 1.5 C except for the ERT case when the estimated RMS error is around2.0 C. But the confidence factors are often less than 0.1, indicating thatthe SSM/I is not well suited for the estimation of sea surface temperature.

The reasonable residual RMS error values are due to the fact that the

natural variance for each of the climate conditions is small and is within*the SSM/I specification value. The relatively higher confidence factors

values for the ERT case are due to the assumpti-i of an unrealisticallylarge initial RMS errors. The confidence factors are also relatively highfor the case when instrumental noise is equal to 0.1 K. But the actualnoise of the SSM/I is much closer to 0.5 than 0.1 K.

Note that both the 85.5 GHz polarizations are included in combinationnumber 10 as well as number 29. This may partly be due to the smallerinstrumental noise attributed to these channels. The selections made hereare appropriate only for the case when 85.5 GHz data are averaged to matchresolution with the other channels before retrieval.

II.B. Wind Speed

In the same fashion as for sea surface temperature, the best threefrequency combinations for all the climate and noise conditions are listedin Table 5 for wind speed retrieval. Again, no single combination is bestfor all cases. Based on the mean RMS error and confidence factor values,

the best over-all combination selected is number 2 (19 H, 19 V, 22 V, 37 V)with number 11, where 37 H is substituted for 19 V, as the second best. TheRMS errors and confidence factors for all the conditions associated withthese two combinations are listed in Table 6. The greatest RMS error foundamong all cases is less than 1.5 m/sec, which is quite acceptable. And theconfidence factors of about 0.6 indicate that the retrieval of wind speed is

much more reliable than that of sea surface temperature.

II.C. Columnar Density of Water Vapor and Liquid Water

The best two frequency combinations for water vapor and liquid waterdensities are selected in a fashion similar to the other parameters. Tables7 and 8 contain the results for water vapor density. Tables 9 and 10contain the results for cloud liquid water. As can be seen, the retrievalmodel is extremely sensitive to these two parameters. Especially in thecase of liquid water, every combination appears to yield good retrievalresults. The best combinations for water vapor are number 1 (19 H, 19 V, 22V, 37 H) and 13 where 85 V is substituted for the 19 V channel. The worstresidual MS error found in the results of these two combinations is around0.1 gm/cm which is much better than the SSM/I specification. The overallbest combinations for liquid water are numbers 3 (19 H, 19 V, 22 V, 85 H)and 14 where 37 V is substituted for 19 V. The2largest residual RMS errorfound for these two combinations is 0.004 gm/cm,; again much better than theSSM/I specification. The confidence factors are greater than 0.9 for boththese environmental parameters indicating that they may be very reliably andaccurately determined by the SSM/I.

57

Table 4

The Best Two Frequency Combinations for SST(C)

Instrumental Noise = .5 (19.35, 22.235, 37 GHz) and .25 (85.5 GHz)

FC 10 FC 29RMS(C) CF RMS(C) CF

Jan MayenWinter .2017 .0065 .2021 .0045Spring .7062 .0926 .7478 .0392Summer .5720 .0392 .5811 .0239Autumn 1.1674 .0786 1.1200 .0880

AzoresWinter .3365 .0113 .3370 .0097Spring 1.2319 .1749 1.2378 .1709Summer .7125 .0644 .7126 .0642Autumn 1.1722 .1537 1.1776 .1498

TrukWinter .2114 .0060 .2112 .0073Spring .2611 .0063 .2598 .0113Summer .0822 .0005 .0822 .0008Autumn .2555 .0083 .2548 .0107

ERT 1.9904 .4762 2.0711 .4550

Azores SummerIN = 0.1 .4141 .4562 .4032 .4775IN = 1.0 .7442 .0227 .7431 .0241

Average .6706 .1064 .6756 .1020

58

0 o ,\ 0 W\U,\ y) --

0 C)t

.4-4UP

L m ~H CL0L\C O\ c 7 T0(\\oO ~

0' c o 0 3ON~ LrH

LAt U-\ O\

0 a a 0 CP\ ~a ''C J.0 '-0 -tco u\ t j- ~ cC- L- .I .1 t . C7 4~ _: 4 a\ .~ _:

UN LU\O- YL AU C\i cmLAH~l_4-

U' rr.-4 v- -f -4 -

00

0 rl a\~ oa CO Cj o0 \ V t- N O N'. \COvJr

(Y (Y 'O~T-' C'\~~' LAr(a -- C\JH (i \-

I 14 0@

co O\O\Crv (Y LA-\ 0 LA Co cc) t-- \ ::T1 o" a O \ O C Q L A L A -I --.t C)Q H ~

4 )t o') O

o -4 a C \J~ ~C12 \0 \-4 L'\U\ --I \ Hq-r

:3 t- c co' - co (IN

co 4

4 N4-'W N' -4C~A if\4H HL CU LA\

4) 0 (\j-vH H, r-4 H Hr - H H

LA- t- t-.0' '. -C' - t-

r.4-4 .-

o4 .) \C) .4l .V .r \-O4 .

0 I

to o) 00 \- r 41- u N -

C) @3)00)'0 0 L Aco t. 0 coLM

C34

HH

.:cm Cq CU 0C~cmC'~j \ I HC~j0J- H CJC

4 4 4r4

\j .'oa0N oC c o0\ y -aHC 'J\,o4 U@3 0 0~~L (Y) (

t) co\0 H %D 0LA\ c (f0A 00 0 4

. ~ .4 4 . .4 . .4C

o~~ ~ b S I~~C C~~C4

4 OH

t,. 14 1

v59A

Table 6

The Best Two Frequency Combinations for WS (m/sec)

Instrumental noise = .5 (19.35, 22.235, 37 GHz) and .25 (85.5 GHz)

FC 2 FC 11RMS CF RMS CF

(m/sec) (m/sec)

Jan Mayen

Winter .9948 .7560 1.0307 .7472Spring .9326 .7968 .9502 .7929Summer .8764 .7155 .8996 .7079Autumn 1.0336 .7021 1.0624 .6938

AzoresWinter .8564 .7489 .8689 .7452Spring .8664 .5995 .8545 .6050Summer .8915 .5761 .8740 .5844Autumn .9387 .6928 .9406 .6922

TrukWinter .9427 .4555 .9417 .4578Spring 1.1848 .5074 1.2084 .4976Summer 1.3666 .6852 1.4164 .6737Autumn 1.1128 .4896 1.1066 .4924

ERT SST .9259 .8347 .9124 .8371

Azores SummerIN = 0.1 .2288 .8912 .2329 .8892IN = 1.0 1.4243 .3227 1.4098 .3296

Average .9720 .6516 .9806 .6498

60

U) C'j co CMJ m C\ - 0 00,-4 C\ t- t-H-

o- _:r \C - CO \ C\ t- t- O L\ 0\ 1.~4 Lr\ 0\ co __: -: _r'J -IC V I\ \ 0%C0 a\ tUl\ \0 ~ 4 \W0000 0000 0000 0 00

N

*U 1-4 .-q -I C\ 0.] C'.] 0M -A]4

C ~ LI'.

5--4

to N ~ 0o \C').] m\oC~ ~ 4 l 000 ao~ co1 N m\~~ LI'. t-I -o m 0 4 0 t-- t-H

o.0 c oO 00 coc 00m0\ C N00 00 0\00

..- 0

E4 V Lr\ '.

o- H ('C0 0.H- \O.** 0 \a

A ) 1- r- -*4L ' r- $L -1 11 ' ')tc - - 1 \ ~ H'

02 C) 0000 00 0 0 00 0 0

r. -40' +- Y o - \- - I C.c\-. :

CC 0 \ r4r4r4()Cj( : l ~ z

02 hN() 0 0 mHma - t-c4-U4 oO \00 mC\C N C C C 0 0 Nc

W ,4 ~ 5.

03tCI.% O34)i' 0 oco

C-) 061

Table 8

The Best Two Frequency Combinations For VAP (gm/cm2

Instrumental Noise = .5 (19.35, 22.235, 37 GHz) and 25 (85.5 GHz)

FC 1 FC 13RMS2 CF RMS 2 CF

(gm/cm) (gm/cm

Jan MayenWinter .0494 .8272 .0492 .8278Spring .0430 .8908 .0435 .8896Summer .0424 .9221 .0428 .9213Autumn .0544 .8329 .0535 .8355


TrukWinter .0633 .9342 .0684 .890jSpring .0834 .9077 .0897 .8913Summer .0956 .8112 .1085 .7857Autumn .0765 .8937 .0849 .8821

ERT SST .0869 .8354 .0697 .8681


Average .0607 .8832 .0613 .8794

62

~~--r~ 0\A r-H a \ VN

C\\\\ O\ON O \Oc\O\C\O\ O\ \ \

0 roc \, \_. C

-1(Y o 0 ) 3C :

QOH 0 000 0 0 H 0 C)HC

V~ : &0 0 0000 QO0 0

r~00 0000 000 00

0j r- C~ -z t0 0 --r co cc -- L\

\D N D -r t - co - c :

rCu CC 0.- HoO -C c -

)0 c

0 W 0 O\O\O\O\* .0 "D cc t. t- CO .Y -: \. *T *

u- toC A IH -

0 )oC) 00C: )0

o -N0 000 00

4-3~ 0

000t-CY 0 :r(Y N0 000 L\0 0 00

.4) 0 ) r-4 *q C\ *' .- . .* .

U) C C)oU - ,j O

r\ 0 O$\'4Y

4) ) ~ ~ ~ O a\ 0P C t C P\ .. * )\u a\t0 C~ '~

CI) .

0''. 0. c-lOi. 0 c P C ~ -

4 V' o ouC CuU'LI -m00 04 Q(

o. 0 000a0c 0ot~- t-0 0

r. 0 % 0~000 O\OO\O ~ \\\ ~ 00

a) ' .4 4 . . . . . . . .

0 -C -o 44

44L H CSz LP U \ L' % cp\ O' ('40\C) .(j -

0) O0M$t ,

4 0000 0000 0000 0 00

6 ) 1- 14 ..4 4 tI N t o

4) r.4 -

£4 41

H ~ ~ : HHH (D H u

CA CD c

.~~t z * Z

634

0q *N4)

Table 10

The Best Two Frequency Combinations for LIQ (gm/cm2

Instrumental Noise = .5 (19.35, 22.235, 37 GHz) and .25 (85.5 GHz)

FC 3 FC 14RMS CF RMS CF

2 2(gm/cm) (gm/cm

Jan MayenWinter .0005 .9905 .0015 .9737Spring .0007 .9801 .0005 .9846Summer .0006 .9882 .0017 .9675Autumn .0027 .9638 .0040 .9688


TrukWinter .0015 .9689 .0014 .9709Spring .0028 .9662 .0020 .9757Summer .0033 .9569 .0023 .9705Autumn .0017 .9531 .0014 .9617

ERT SST .0007 .9720 .0008 .9699


Average .0013 .9715 .0013 .9710

64

III. Conclusions and Discussions

In this study, a number of simulations were performed for the purposeof selecting four channel subsets from the seven SSM/I channels for theretrieval of sea surface temperature, wind speed, columnar water vapordensity and columnar cloud liquid water density The geophysical model andclimate statistics needed for the simulation were developed and assembled atNRL. The approach of applying the so-called 'D' matrix coefficients tosatellite observed brightness temperatures for environmental parameterretrievals is similar to that used to develop the algorithm for the SSM/I byHughes/ERT. The four channel subset recommended for the retrieval of eachparameter is listed in Table 11.

The expected RMS estimation error for each of the parameters is withinthe specifications for the SSM/I project, indicating that the use of fourchannel subsets for retrieval purposes is reasonable.

The small estimation error does not imply accuracy in the case of seasurface temperature, since the confidence factor for sea surface temperatureis extremely low. The small estimation error is mainly due to the fact thatthe natural variance of the sea surface temperature is small for properlydefined climate types as can be deduced from Table 3. The confidence factorfor wind speed estimation indicates it is much more reliably retrieved thanthe sea surface temperature. The SSM/I instrument is excellent forretrieving the distribution of moisture in the atmosphere, as indicated bythe large confidence factors and the small residual RMS errors for thecolumnar densities of water vapor and cloud liquid water content.

Even though the geophysical model employed in this study is basicallysimilar to the Hughes/ERT model, the performance of a channel subset stilldepends to an extent upon the model. NRL is presently acquiring theHughes/ERT model and plans to do a similar study for the selection ofoptimum channel subsets for the marine environmental parameters with thatmodel.

Table 11

The Recommended Frequency Subsets for theRetrievwl of Marine Environmental Parameters

Recommended Confidence EstimationParameter Frequency Subset Factor Error

SST(°C) 19.3 H 19.3 V 85.5 H 85.5 V .1064 .67o6

WS(m/sec) 19.3 H 19.3 V 22.2 V 37.0 V .6516 .9720

VAP(gm/cm ) 19.3 H 19.3 V 22.2 V 37.0 H .8832 .0607

LIQ(gm/cm 2 ) 19.3 H 19.3 V 22.2 V 85.5 H .9715 .0013

65

References

1. Wisler, M.M. and J.P. Hollinger, "Estimation of Marine EnvironmentalParameters Using Microwave Radiometric Remote Sensing Systems", NavalResearch Laboratory Memorandum Report 3661, November 1977.

2. Poe, G., "Retrieval Accuracy of Sea Surface Temperature (SST) fromSatellite Microwave Radiometer Data", Hughes 816318-61 A, December1981.

3. Hollinger, J.P., et al., "Joint Services 5D-2 Microwave ScannerDefinition Study", Naval Research Laboratory Memorandum Report 3807,August 1978.

h. Hardy, K.R., et al., "A Study of Sea Surface Temperature EstimatesUsing the SSM/I", Environmental Research and Technology, Inc., ERTDocument No. P-B088-F, October 1981.

5. "Special Sensor Microwave/Imager (SSM/I) Critical Design Review, Vol.II, Ground Segment", Contract No. F04701-79-C-0061, Hughes, p. 117,March 1980.

6. "Proposal for Microwave Environmental Sensor System (SSM/I), Volume 1.Technical Proposal", Hughes RFP No. F04701-78-R-O094, January 1979.

66

- l li l .. . . . .. I I I I I i i . . . ] n I I . . . . ..j . . l 1 I ' . . . . .. . . .

Appendix C

A Simulation Study of the Sensitivity ofEnvironmental Parameter Retrievals Based on the

Special Sensor Microwave Imager (SSM/I)

May 1982


Naval Research Laboratory

Washington, D. C. 20375

67

A SIMULATION STUDY OF THE SENSITIVITY OFENVIRONMENTAL PARAMETER RETRIEVALS BASED ON THE

SPECIAL SENSOR MICROWAVE IMAGER (SSM/I)

Prepared by


Aerospace Systems DivisionNaval Research LaboratoryWashington, D.C. 20375

Prepared for

Navy Space Systems ActivityLos Angeles, CA

May 1982

68

A Simulation Study of the Sensitivity ofEnvironmental Parameter Retrievals Based on the

Special Sensor Microwave Imager (SSM/I)

Robert C. Lo and James P. Hollinger

Space Sensing Applications BranchAerospace Systems DivisionNaval Research LaboratoryWashington, DC 20375

I. Introduction

During the qualification tests of the Special Sensor Microwave Imager(SSM/I) partial failure of the structure resulted in debris from the hotcalibration load lodging in the feed horn blocking the 85.5V port andrendering the channel inoperative. Since then the problem has been correct-ed but, as a consequence of the event, a number of questions were raised.How good would the retrieval of environmental parameters be if the 85.5Vchannel is lost? What if any one channel is lost? Which channel is theretrieval of each parameter most sensitive to? Would the loss of thatchannel cause significant loss of confidence in that retrieval?

The purpose of this study is to provide insight into these questionsthrough simulations using a geophysical model and retrieval scheme developedat the Naval Research Laboratory (NRL) (1), and a set of environmentalstatistics representing high, middle, and low latitude ocean conditions forall four seasons, produced by Wentz and Associates for the definition studythe of SSM/I performed at NRL (2).

II. Simulations and Discussions

The geophysical model employed in this study (1) is basically a set ofgeneral equations describing the physical relationship among a number ofenvironmental parameters and their microwave radiative characteristics. Aretrieval scheme based on the geophysical model, climate statistics and theinstrumental noise characteristics produces a matrix of linear regression

coefficients, or the so-called "D-matrix" for a given set of frequencies andpolarizations such as the SSM/I channels. The coefficients provide esti-mates of the environmental parameters when they are appropriately combinedwith brightness temperature observations. The geophysical model and retrie-val scheme are applicable to a subset of SSM/I channels or any combinationsof frequencies within the microwave and millimeter wave spectrum.

In addition to estimates of environmental parameters, the retrievalscheme produces certain other quantities which are indicative of theretrieval accuracy and the performance of a given channel combination. Twoof these quantities are the residual root-mean-square (RMS) error, which isthe total error associated with the retrieved parameter, and the confidencefactor (CF) associated with the retrieval. They are defined as follows:

69

RMS- ( 2 a2 (11.1)

2

where a is the original varince associated with a parameter as part ofthe climate statistics, and am is the amount of variance explanable by themodel and

CF-.- =- (11.2)

These two quantities are the main criteria for the evaluations made in thisstudy.

The climate statistics utilized in this study include twelve subsetsrepresenting the four season for three different locations: Jan Mayen,Azores and Truk. They are taken to represent high, middle, and low latitudeocean conditions (2).

The operational marine parameters to be retrieved by the SSM/I systeminclude ocean surface wind speed, ice concentration, age and edge location,rain rate, and the columnar densities of water vapor and cloud liquid water(3). The sea surface temperature was included later on an experiment basis.The NRL geophysical model presently does not contain a submodel for rainrate and the climatology for ice is not yet complete. The marine parametersexamined in this study are restricted to the columnar densities of watervapor and cloud liquid water, the surface wind speed, and the sea surfacetemperature.

The most accurate retrieval of the parameters is expected when allseven channels are used. However, limitations of the computational facili-ties at Air Force Global Weather Central dictated a maximum of four channelsfor the eetrieval of each parameter. The channels adopted for wind speedand the columnar densities of water vapor and cloud liquid water are 19.35H,22.235V, 37.OH and V (3). The combination of 19.35H, 22.235V, 85.5H and Vis assessed to be the best four channel subset for sea surface temperatureretrieval by the Environmental Research Technology, Inc. (ERT) (4) in astudy conducted under contract to Hughes Aircraft Company. The residual RMSerror in the sea surface temperature from the four channel retrieval is onlyminutely greater than the case when all seven channels are used according tothis study (4).

The instrumental noise temperatures measured at Hughes (5) during thefinal qualification test are used for the present simulations. They are0.48, 0.51, 0.64, 0.40, 0.39, 0.64 and 0.81K for 19.35H and V, 22.235V,37.OH and V, and 85.5H and V.

II.A. Sea Surface Temperatures

Simulations for the 12 climates were performed using the 19.35H,22.235V, 85.5H and V channel combination and all 3-channel subsets. Theresults are shown in Table 1. The same conclusion reached in a previousstudy (6) is apparent here; the SSM/I is not well-suited for the rqtrieval

70

of sea surface temperature. Even the highest confidence factor listed inTable 1 is less than 0.03. This is particularly true in the tropical cases,represented by Truk, where the combination of low surface emissivity andhigh atmospheric water content dimirsishes the little sensitivity the SSM/Ihas to sea surface temperature. The last two columns in Table 1 representsthe retrievals with the 85.5V channel missing. The confidence factors inthis case are significantly less than those for the other cases.

II.B. Wind Speed

Simulation of retrievals for wind speed and columnar densities of watervapor and cloud liquid water based on (19.35H, 22.235V, 37.OH and V) channelcombination and the three-channel subsets are listed in Tables 2 through 4.The SSM/I RMS error specification for surface wind speed retrieval is 2m/sec (3). Wind speed retrieval results for all the 12 climates in Table 2indicate that the results are good not only when all four channels are usedbut also for all the subsets of three channels. The only exception is thecase for tropical summer if the 37.OV channel is lost. The RMS error forthis case is approximately 2.1 m/sec. The confidence factor values indicatethat the most significant channels for wind speed retrievals are 19.35H and22.235V, especially for the polar and the mid-latitude climates. Fortropical ocean the most significant channel is 37V. The loss of it couldcause an increase in RMS error of o 0.8 m/sec.

II.C. Columnar Density of Water Vapor

The most significant channel for water vapor retrieval is the 22.235VGHz as is apparent from Table 3. However, for cases when the atmosphericwater content is very high as represented by spring, summer and autumn ofthe tropical ocean, 19.35H becomes the most significant channel. This isprobably due to the fact that the 22.235 GHz tends to approach saturationand becomes less sensitive when the water vapor content reaches a highlevel. It is observed, however, that even for these tropical cases, theretrieval performance for all channel combinations is significantly betterthan he SSM/I requirement which specifies the RMS error to be within +0.2gm/cM

III.D. Columnar Density of Liquid Water

Among the four marine parameters examined in this study, SSM/I has thegreatest sensitivity to cloud liquid water. The SSM/I specificationrequirement of liquid water retrieval RMS error is + 0.07 gm/cm (3). FromTable 4, the RMS error for the worst case is 0.0055-which is more than anorder of magnitude less than the requirement specification. This impliesthat the loss of any single channel will not significantly affect theaccuracy of liquid water content retrieval. The liquid water retrieval ismost sensitive to the 19.35H channel as indicated by the RMS error andconfidence factor values in Table 4.

71

III. Conclusion

A number of simulations were performed in this study to assess theeffect on SSM/I parameter retrieval accuracy when one of the channels usedin the retrieval was lost. Particular attention was given to the 85.5Vchannel which was rendered inoperative during a qualification vibrationtest. Results from this study indicate that the 85.5V channel is the mostsignificant one only for sea surface temperature retrieval. Although it'sloss could eliminate the ability of SSM/I to retrieve sea surface tempera-ture, it would have little impact since the simulations also indicate thatSSM/I has very little ability to assess the sea surface temperature evenwhen all channels are intact. This is not surprising since the sea surfacetemperature was not a required parameter, and its retrieval was not aconsideration during the design of the SSM/I.

The loss of 19.AH channel would deteriorate somewhat the wind speedretrieval for polar and moderate climates, and the water vapor densityretrieval for the tropics. However, the simulation results indicate thatthe deterioration is not significant enough to cause the retrieval resultsto be below specification. The 19.4H channel is also the most significantchannel for liquid water density retrieval. But the loss of this or anyother channel does not affect the excellent retrieval ability of SSM/I forliquid water. The loss of the 22.235V channel would result in a loss ofaccuracy in the wind speed and water vapor density retrievals for high andmiddle latitudes. However, the increased error would still be within theSSM/I specification.

The loss of 37.OV channel can cause the wind speed retrievalperformance to be below specification for tropical conditions.

The 19.35V channel is not used in the retrieval of the parametersexamined here, and the loss of either the 37.OH or 85.5H channel does notresult in deterioration in the retrieval of any of the four environmentalparameters.

72

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References

1. Wisler, M. M. and J. P. Hollinger, "Estimation of Marine EnvironmentalParameters Using Microwave Radiometric Remote Sensing Systems", NavalResearch Laboratory Memorandum Report 3661, November 1977.

2. Hollinger, J. P., et al., "Joint Services 5D-2 Microwave ScannerDefinition Study", Naval Research Laboratory Memorandum Report 3807,August 1978.

3. "Proposal for Microwave Environmental Sensor System (SSM/I) Volume I.Technical Proposal", Hughes RFP No. Fo4701-78-R-0094, January 1979.

4. Hardy, K. R., et. al., "A Study of Sea Surface Temperature Estimates

Using the SSM/I", ERT Document No. P-B088-F, October 1981.

5. "SSM/I Sensor Qualification Test Report", HS256-0006-0733; April, 1982.

6. Lo, R. C., and J. P. Hollinger, "Selection of Optimal Combinations ofFrequrncies for the Special Senscr Microwave Imager (SSM/I)Environmental Retrievals", NRL letter to NSSA and PME, 1982.

77

Appendix D

A Comparison Studyof the Sensitivity and Retrieval Performance

of 21.0 and 22.235 GHz Channels

September 1982


Naval Research Laboratory


78

NRL LETTER REPORT7910-152:JPH:ms

A COMPARISON STUDYOF THE SENSITIVITY AND RETRIEVAL PERFORMANCE

OF 21.0 AND 22.234 GHz CHANNELS

IIPrepared by


Aerospace Systems DivisionNaval Research LAboratoryWashington, D.C. 20375

For

Navy Space Systems ActivityLos Angeles, CA 90009

September 1982

79

A Comparison Study of the Sensitivity and RetrievalPerformance of 21.0 and 22.235 GHz Channels


Space Sensing Applications BranchAerospace Systems Division

Naval Research LaboratoryWashington, DC 20375

I. Introduction

The Special Sensor Microwave Imager (SSM/I) contains horizontally and

vertically polarized channels at 19.35, 37.0 and 85.5 GHz and a singlevertically polarized channel at 22.235 GHz. The 22.235 GHz channel iscentered on a water vapor absorption line and was selected primarily todetermine the columnar density of atmospheric water vapor and to providecorrections for its absorption and emission effects at the other channels.

Two arguments have been raised against the use of 22.235 GHz frequency forthese purposes. One is that the 22.235 GHz channel could saturate undertropical conditions. The other argument is that the absorption coefficient

per unit mass of water vapor at 22.235 GHz increases with height, whereas,at 21.0 GHz it varies only slightly with height and actually decreases above

about 7 km. Thus, moisture in the upper troposhere will be unduly weightedand cause a significant bias in the total water vapor content estimationbased on the 22.235 GHz frequency. An alternative frequency, 21.0 GHz on thewing of the absorption band, has been suggested in place of 22.235 0Hz. It

is speculated that at this frequency, there is enough sensitivity for accu-rate estimation of water vapor but not enough to cause saturation. Further,the absorption coefficient at 21.0 GHz is practically constant with heightover the lower atmospheric layers which contain most of the atmosphere water

vapor.

The purpose of this study is to assess the validity of the above two

arguments through the use of sensitivity studies and retrieval resultcomparisons.

II. Saturation Under Tropical Conditions

A. Comparison of Sensitivity

Wisler and Hollinger (2) designed a geophysical model and environ-

mental parameter retrieval scheme which provides a measure of the sensi-tivity of the -icrowave signal to the environmental parameter and theuncertainty in che retrieval for any given combination of microwave frequen-cies. This model was used for an SSM/I definition study (3) and other SSM/Irelated studies (4, 5, 6).

Climate statistics representing the most humid atmospheric conditions

generally encountered, i.e. tropical summer ocean (3), are used in the

80

geophysical model for the examination of the sensitivity of 21.0 and 22.235GHz channels to water vapor content in the atmosphere. First, all clouds

are removed from the climate statistics while the vertical temperaturestructure as well as surface statistics remain. A range from 0 to 7 gm/cm2

is assigned to the water vapor parameter, that is, the columnar density ofwater vapor. The upper end of this range is very high even for tropicalconditions (7, 8). Brightness temperatures at 21.0 and 22.235 GHz arecalculated and are presented in Figure 1. The slope of the curve repre-senting 22.235 GHz is §reater than that of 21.0 GHz for water vapor densityvalues up to 5.5 gm/cm . Then it becomes slightly less than at 21.0 GHz.The slope of both curves remains significantly high over the entire range.This implies that the 22.235 GHz channel is a better predictor of watervapor content than the 21.0 GHz channel in the absence of clouds for mostconditions found in the atmosphere. And even in the extremely humid case,the sensitivity of 22.235 GHz is still not significantly less than that of21.0 GHz.

A similar set of simulations is performed with clouds restored, toevaluate the effect of clouds on the sensitivity o the two channels. Theaverage cloud liquid water content is 0.0738 gm/cm corresponding to a cloudthickness of approximately2l.4 kms. The range used for water vapor densityis again from 0 to 7 gm/cm . The brightness temperature curves for the 21.0

and 22.235 GHz channels under these conditions are presented in Figure 2.The slopes of both curves are less than those in Figure 1. That is to say,the presence of the cloud deck decreases the sensitivity of both frequenciesto water vapor density. The slope of the 22.235 GHz curve is g eater thanthat of 21.0 GHz for water vapor density values up to 4.5 gm/cm . It thenbecomes slightly less than that of 21.0 GHz but not significantly so. From

this set of simulations, it appears that both frequencies would haveadequate sensitivity for the evaluation of water vapor density even with amoderately thick cloud. The 22.235 GHz has an advantage over the 21.0 GHzfor the majority of the cases. The opposite is true for the extremely humid

cases.

The third set of simulations is designed to compare the sensitivity ofthe two frequencies under various cloud conditions. The water vapor densityis held constant at 5.558 gm/cm representing a very umid atmosphere, whilecloud liquid water content varies from 0 to 0.2 gm/cm . Simulation resultsare presented in Figure 3. The curves in Figure 3 indicate that 21.0 GHz ismore sensitive to the variations in columnar density of cloud liquid waterthan 22.235 GHz. Both channels start to iose their sensitivity when theliquid water density approaches 0.2 gm/cm . The 22.235 GHz curve levels offfaster than the 21.0 GHz.

From the above sensitivity studies, it appears that 22.235 GHz is abetter frequency than the 21.0 GHz for the retrieval of water vapor densityover most of the atmospheric conditions. In the more humid conditions, ittends to lose some of the sensitivity but should still be adequate.

81

262

254-

246- 22.235 GHz

238-

230-

222- GHz

2141--

206

198-

190-

1820 1 2 3 4 5 6 7

COLUMNAR DENSITY OF WATER VAPOR (gm/cm2 )Figure 1 Sensitivity of the water vapor absorption bands under

cloudless conditions.

82

268

264-

260 22.235 GHz-

256-

2252-

t-!n248-~G~

244-

240--

236-

232-

228 -- I I I I20 1 2 3 4 5 6 7

COLUMNAR DENSITY OF WATER VAPOR (gm/cm2')Figure 2 Sensitivity of the vater vapor absorption bands under cloudy

conditions

83

270

22.235 GHz

266-

262-

_ 258

> ,21.0 GHzr254-

250-

246

242

0 .04 .08 .12 .16 .20COLUMNAR DENSITY OF WATER VAPOR (gm/cm 2 )

Figure 3 Sensitivity of the water vapor absorption bands as functionof cloud liquid water content

84

B. Comparison of Retrievals

The relative advantage of using the 21.0 GHz versus 22.235 GHzfrequency is further examined through simulated retrievals. The (19.35 H,22.235 V, 37.0 H and V) channels are the specified frequency combination forSSM/I retrieval of wind speed, columnar densities for water vapor and cloudliquid water (1). For comparison, another frequency combination, with 21.0V replacing the 22.235 V channel, is used for the retrievals. The twelvesets of climate statistics (3) describing the four seasons for arctic,moderate and tropical oceans are used in conjunction with the Wisler andHollinger (2) geophysical model and retrieval scheme. The residual root-mean-square (RMS) error and the confidence factor (CF) are included as partof the retrieval products. They are defined as follows:

2 2RMS a - ar

r

and

02

where 02 is the atural variance of the environmental parameter beingretrieved and 0 r is the variance of the parameter after retrieval. Theconfidence factor ranges between 0 and 1. A large confidence factor valueimplies a good retrieval ability.

The RMS errors and confidence factors of wind speed, columnar densityof water vapor and cloud liquid water retrievals for all 12 climates arelisted in Table 1. Results from both frequency combinations are included inthe table. The performance of the frequency combination with 22.235 Vchannel is consistently better in the retrievals of wind speed and watervapor density for 9 of the 12 climates. Only for the three warmest and mosthumid climates, i.e., the spring, summer and autumn seasons for the tropical

ocean does the 21.0 V channel combination result in lower retrieval errors.The difference in RMS error for wind speed retrieval of the tropical summercase, where this phenomenon is most pronounced, is approximatel 0.02 m/sec.And the difference for water vapor density is about .013 gm/cm • Both areextremely small. The SSM/I 5equirement specification is 2 m/sec RMS errorfor wind speed and 0.2 gm/cm for water vapor density (1). The performanceof both frequency combinations for all the 12 climates meets the SSM/Ispecifications. It is concluded, therefore, that the 22.235 GHz is prefer-red to 21.0 GHz for overall performance in the wind speed and water vapordensity retrievals.

Both of the frequency combinations yield excellent retrieval resultsfor the cloud liquid water density. he SSM/I specifications for the RMSerror of this parameter is 0.07 gm/cm (1), which is more than an order ofmagnitude greater than that from the retrieval results. The relativeperformance between the two frequency combinations does not follow thepattern for wind speed and water vapor density. Retrievals with 22.235 GHzare better in 8 out of the 12 climates, judging by the confidence factor

85

Table 1

Retrieval Result of Wind Speed and Moisture Termsfrom the Two Frequency Combinations

21.0 V19.35 H, or , 37.0 H, 37.0 V

22.235 V

Wind Speed Columnar Water Vypor Densit

(r/sec) (gm/cm

Residual Residual Residual ResidualOriginal RMS CF RIS CF Original RMS CF INS CF

RMS (21) (21) (22) (22) EMS (21) (21) (22) (22)

Jan MayenWinter 4.0773 1.0656 .7387 .9980 .7552 .2828 .0738 .7391 .0586 .7929Spring 4.5889 .96u6 .7907 .9021 .8034 .3873 .0660 .8295 .0520 .8658Summer 3.0801 .9163 .7025 .8637 .7196 .5477 .0648 .8816 .0518 .9055Autumn 3.4693 1.1234 .6762 I.O495 .6975 .3317 .0801 .7585 .0630 .8102

AzoresWinter 3.4100 .8867 .740 .8386 .7541 .4359 .0627 .8562 .0522 .8802Spring 2.1631 .8682 .5986 .8248 .6187 .5568 .0688 .8765 .0590 .8940Sumer 2.1029 .8702 .5862 .8411 .6000 .5292 .0685 .8706 .0613 .8841Autumn 3.0558 .9738 .6813 .9185 .6994 .5385 .0768 .8574 .o654 .8785

TrukWinter 1.7370 .9242 .4679 .9190 .4709 .9592 .0809 .9157 .0785 -182Spring 2.4052 1.1463 .5234 1.1831 .5081 .9055 .0996 .8900 .1050 .b4oSumner 4.3407 1.2746 .7064 1.3653 .6855 .5099 .1101 .784o .1233 .7582Autumn 2.1801 I.O463 .5201 1.0703 .5091 .7211 .0916 .8730 .0952 .8680

Columnar CI.. d Liquid Water Density (gm/cm2

Jan MayenWinter .0548 .0021 .9611 .0021 .9615Spring .0316 .o014 .9542 .0015 .9536Summer .0548 .0019 .9649 .0017 .9697Autumn .0707 .0025 .9649 .0028 .9599

AzoresWinter .0316 .0017 .9470 .0017 .9473Spring .0316 .o018 .9420 .0018 .9427Sumer .0316 .0019 .9396 .0019 .9403Autumn .0447 .0020 .9545 .0020 .9561

TrukWinter .0447 .0024 .9461 .0024 .9453Spring .0837 .0032 .9623 .0033 .9602Sumer .0775 .0034 .9565 .0029 .9624Autumn .0316 .0025 .92o8 .0025 .9211

86

Table 2

Retrieval Results of Sea Surface Temperaturefrom the Two Frequency Combinations

21.0 VSea Surface Temperature(K) 19.35 H, or 85.5 H, 85.5 V

22.235 V

Residual ResidualOriginal RMS CF RMS CF

IMS (21) (21) (22) (22)

Jan MayenWinter .2025 .2023 .0007 .2023 .0007Spring .7785 .7690 .0121 .7690 .0121Summer .5950 .5922 .0o47 .5921 .oo48Autumn 1.2669 1.2455 .0168 1.2437 .0183

AzoresWinter .3406 .3401 .0013 .3402 .0012Spring 1.4930 1.4501 .0287 1.4554 .0252Summer .7616 .7544 .0094 .7558 .0076Autumn 1.3849 1.3542 .0222 1.3583 .0193

TrukWinter .2121 .2119 .0010 .2120 .0007Spring .2627 .2623 .0015 .2623 .0013Summer .0837 .0837 .0001 .0837 .0001Autumn .2569 .2565 .0015 .2566 .0013

87

Li

values. The residual RMS error, however, shows no detectable difference inseveral of the cases. The conclusion is that the use of 21.0 GHz channel byno means improves the retrieval performance for the columnar density ofcloud liquid water.

The frequency combination suggested for the retrieval of sea surfacetemperature by a study performed at the Environmental Research and Technol-ogy, Inc. (9) is 19.35 H, 22.235 V, 85.5 H and V. Retrieval results for the12 climates using this frequency combination and the alternate combination(19.35 H, 21.0 V, 85.5 H and V) for sea surface temperature are listed inTable 2. The performance of the combination with 21.0 GHz is better in mostof the cases. An examination of the confidence factor values reveals, how-ever, that the ability to retrieve sea surface temperature is dismal forboth combinations. The minimal improvement in sea surface temperatureretrieval alone is not sufficient to justify the substitution of the 22.235GHz channel.

III. Upper Tropospheric Water Vapor

The vertical profiles of the absorption coefficient per unit mass ofwater vapor are calculated using the climatology of Azores, Summer (3) at22.235 GHz, 21.0 GHz and 23.470 GHz. The absorption coefficient integratedover the SSM/I passband of ± 10 to 250 MHz centered on the L.O. frequency of22.235 GHz (1) is also shown to display the effects of bandwidth smoothing.The equation used for the calculation is

2 20 2/T

( + 1 + 2.55 x 10 T-I. x 105 (111.1)((v-_O)+ AV 2 ( 0)2 AVT

where

A= 2.58 x 10- 3 + o.147 P 31--0. (111.2)

AH20 is the absorption of water vapor per unit mass; T is the temperature(K);

P is atmospheric pressure (mb); v is frequency (GHz); v0 is 22.235 GHz and o

is water vapor density (gm/m3). AH 20 has only a very weak dependence on p.

The four profiles are shown in Figure 4. AR20 increases steadily with height

at 22.235 GHz while only slightly at 21.0 GHz for the first few kilometerswhere most of the atmospheric moisture resides.

88

N Nf 0.iC00

00N~ CON.OOD

00

VCr4

(,wc)/wi/j.dqu 0dz)u

89N

Even though the profiles representing the two frequency regions aredistinctly different, the advantage of using one rather than the other in theSSM/I system must still be evaluated through retrieval simulations. A modi-fication is made to the climate statistics used for retrievals shown inTables 1 and 2, in order to keep the columnar water vapor density constantwhile allowing more moisture at the higher levels. An exponentially decreas-ing absolute humidity profile is assumed in the geophysical model (1). Theprofile is a function only of the surface absolute humidity and the watervapor scale height. By changing the scale height to 1.5 times the normalclimate mean while decreasing the surface absolute humidity so as to hold thetotal water vapor constant, some moisture is artificially moved from thelower to higher layers. A change of scale height by 50% is a very signifi-cant change for the real atmosphere as it represents quite an extremevariation in the vertical distribution of moisture. The retrieval resultsfor the new moisture profiles are shown in Tables 3 and 4. The comparisonbetween 21.0 and 22.235 GHz retrieval is very similar to those obtainedearlier and shown in Tables 1 and 2. The 22.235 GHz channel combination doesbetter for wind speed and water vapor in all except the tropical climates andthere is no difference for cloud water retrievals for any of the climates.Although the 22.235 GHz channel is to be slightly preferred the overallperformance, including all climates and parameters, is very similar for boththe 22.235 GHz and 21.0 GHz combinaticns. The RMS from the retrievals in allcases are within the SSM/I specifications (1).

IV. Summary and Conclusions

This comparison is performed to evaluate the speculation that 22.235GHz, included in the SSM/I, may become saturated and lose sensitivity forenvironmental parameter retrievals, particrlarly under tropical conditions,and that moisture present in higher leve Wy bias the estimation of totalwater vapor using 22.235 GH71.

The 21.0 and 22.235 GHz brightness temperatures as functions of thecolumnar density of water vapor with and without clouds, and as a function ofcolumnar density of cloud liquid water for the tropical summer ocean areexamined. The results indicate that the brightness temperature at 22.235 GHzis more sensitve to changes in water vapor content then that of 21.0 GHz inmost zases except when the humidity is very high. And even under suchcondition, the 22.235 GHz channel does not lose its sensitivitysignificantly.

Retrieval simulations with normal climate and with modified moistureprofiles are then performed comparing the performance of 22.235 GHz and 21.0GHz. The wind speed and water vapor density retrievals indicate that 22.235GHz is consistently better except for the more humid seasons in the tropics,for which case, 21.0 GHz offers a slight advantage. The retrieval resultswith either frequency are better than the SSM/I requirement specifications.The 21.0 GHz is somewhat better for the sea surface temperature retrieval.However, both frequency combinations yield extremely poor results for thisparameter. A channel of much lower frequency than both 21.0 and 22.235 GHzis needed before significant improvement in sea surface temperature retrievalcan be expected.

90

Table 3

Retrieval Results of Wind Speed and Moisture Termsfrom the Two Frequency Combinations

21.0 V19.35 H, or , 37.OH, 37.0 V

22.235 V

Wind Speed Columnar Water V4por Density(m/sec) (gm/cm

Residual Residual Residual ResidualOriginal RMS CF RMS CF Original RMS CF RMS CF

EMS (21) (21) (22) (22) RM'S (21) (21) (22) (22)

Jan MayenWinter 4.0773 1.0619 .7396 .9910 .7569 .2828 .0754 .7333 .0580 .7950Spring 4.5889 -9557 .7917 .8950 .8050 .3873 .0678 .8248 .0516 .8669Summer 3.0801 .9120 .7039 .8568 .7218 .5477 .0669 .8779 .0519 .9052Autumn 3.4693 1.1192 .6774 1.0419 .6997 .3317 .0823 .7518 .0624 .8118

AzoresWinter 3.4100 .8855 .7403 .8337 .7555 .4359 .0651 .8506 .0527 .8791Spring 2.1631 .8683 .5986 .8232 .6195 .5568 .0717 .8712 .0605 .8914Sumner 2.1029 .8732 .5848 .8465 .5975 .5292 .0722 .8636 .0648 .8774Autumn 3.0558 .9743 .6812 .9184 .6995 .5385 .0809 .8498 .0683 .8731

TrukWinter 1.7370 .9331 .4628 .9513 .4523 .9592 .0877 .9086 .0907 .9054Spring 2.4052 1.1709 .5132 1.3051 .4574 .9055 .1119 .8764 .1356 .8502Sumer 4.3407 1.3153 .6970 1.5833 .6352 .5099 .1261 .7527 .1684 .6698Autumn 2.1801 1.0643 .5118 1.1557 .4699 .7211 .1020 .8585 .1192 .8347

2Columnar Cloud Liquid Water Density (gm/cm

Jan MayenWinter .0548 .0021 .9616 .0021 .9610Spring .0316 .0015 .9527 .0014 .9546Sumer .0548 .0019 .9657 .0019 .9653Autumn .0707 .0026 .9638 .0026 .9628

AzoresWinter .0316 .0017 .9478 .0016 .9487Spring .0316 .0018 .9438 .0018 .9445Sumner .0316 .0019 .9408 .0018 .9418Autumn .0447 .0019 .9569 .0019 .9574


91

" ... .. *-- [llii I..... Il........... urn.....,,................. .. n,...... ..... , ...... 2nnd

Table 4

Retrieval Results of Sea Surface Temperaturefrom the Two Frequency Combinations

21.0 V

Sea Surface Temperature(K) 19.35 H, , 85. 5 H, 85.5 V22.235 V

Residual ResidualOriginal RMS CF RMS CF

RMS (21) (21) (22) (22)Jan MayenWinter .2025 .2023 .0007 .2023 .0007Spring .7785 .7690 .0122 .7690 .0122Summer .5950 .5922 .0047 .5921 .0049Autumn 1.2669 1.2475 .0153 1.2447 .0175

AzoresWinter .3406 .3401 ,0014 .3402 .0013Spring 1.4930 1.4474 .0305 1.4535 .0265Summer .7616 .7539 .0101 .7554 .0082Autumn 1.3849 1.3516 .0241 1.3563 .0206


92

It is concluded, therefore, that the arguments concerning these two

frequencies may be more academic and speculative than real. The minimal

advantage of using 21.0 GHz, for some of the tropical cases does not justify

the replacement of the 22.235 GHz.

References

1. "Proposal for Microwave Environmental Sensor System (SSM/I), Volume 1.Technical Proposal", Hughes RFP No. F04701-78R-0094, January 1979.

2. Wisler, M. M., and J. P. Hollinger, "Estimation of Marine EnvironmentalParameters Using Microwave Radiometric Remote Sensing Systems", NRLMemorandum Report 3661, November 1977.

3. Hollinger, J. P., R. M. Lerner, B. E. Troy and M. M. Wisler, "JointServices 5D-2 Microwave Scanner Definition Study", NRL Memorandum Report3807, August 1978.

4. Lo, R. C., and J. P. Hollinger, "NRL Comments on the ERT SST Study forthe SSM/I" NRL Letter Memo to NSSA and PME, December 1981.

5. Lo, R. C., and J. P. Hollinger, "Selection of Optimal Combinations ofFrequencies for the Special Sensor Microwave Imager (SSM/I)Environmental Retrievals" NRL, Letter Memo to NSSA and PME, April 1982.

6. Lo, R. C., and J. P. Hollinger, "A Simulation Study of the Sensitivityof Environmental Parameter Retrievals Based on the Special SensorMicrowave Imager (SSM/I)" NRL Letter Memo to NSSA and PME, May 1982.

7. Grody, N. C., A. Gruber and W. C. Shen, "Atmospheric Water Content Overthe Tropical Pacific Derived from the Nimbus-6 Scanning MicrowaveSpectrometer", Journal of Applied Meteorology, Vol. 19, No. 8, August1980, p. 986.

8. Prabhakara, C., G. Dalu, R. C. Lo and N. R. Nath, "Remote-Sensing ofSeasonal Distribution of Precipitable Water-Vapor Over the Oceans and theInference of Boundary-Layer Structure", Monthly Weather Review, Vol.

107, pp. 1388-1401, 1979.

9. Hardy, K. R., H. K. Burke, J. Ho and N. K. Tripp, "A Study of SeaSurface Temperature Estimates Using the SSM/I", ERT Document No.P-BO88-F, October 1981.

93

Appendix E

A Study of the Cross Polarization Effects on theSpecial Sensor Microwave Imager (SSM/I) Environmental

Parameter Retrievals

September 1982



94

NRL LETTER REPORT

7910-271:JPH:ms

A STUDY OF THE CROSS POLARIZATION EFFECTSON THE

SPECIAL SENSOR MICROWAVE IMAGER (SSM/T)ENVIRONMENTAL PARAMETER RETRIEVALS

Prepared by


Aerospace Systems DivisionNaval Research LaboratoryWashington, D.C. 20375

For

Navy Space Systems ActivityLos Angeles, CA 90009

September 1982

95

A Study of the Cross Polarization Effects on the

Special Sensor Microwave Imager (SSM/I) EnvironmentalParameter Retrievals


Aerospace Systems DivisionNaval Research Laboratory


I. Introduction

The origi.nal development specification required cross polarization

levels of less than one percent for all the seven SSM/I channels. This wasrelaxed later to two percent for the 19.35 GHz channels and the 22.235 GHzchannel and five percent for the four higher frequency channels (1). Therelaxation of the cross polarization specification could have a significantimpact on the environmental retrieval accuracies. Although larger crosspolarization will increase retrieval errors it is the uncertainty in the

cross polarization which can have the most serious consequences. Thisuncertainty will degrade the performance of the SSM/I and may result in

environmental parameter retrieval errors over specification.

The purpose of the present study is to examine the effects of cross

polarization and its uncertainty on the retrieval accuracy of the environ-mental parameters.

II. The Effect of Cross Polarization Errors

Let T and T be the true horizontal and vertical polarization bright-H V

ness temperatures and let T and TVM be the corresponding values measuredin the presence of cross polarization. Assume that the leakage of the twopolarizations are the same and denote it as 0 (0 < a < 1). The relationshipamong these variables can be written as follows.

T HM =(1-Q) T H + T TV (II.1)

TVM (l-a) TV + TH (1.2)

Solving for TH and TV

(1 ) T - TVMT = (11.3)H 12

96

(1 - l) T CL T

TV = VM HM (I.)

The error in Q, T and T would cause estimation errors in the truebrightness temperature T and'v, which are input to the retrieval schemes.Let a a and a be thu standXrd errors of T T and a. The relation-M4 sV a .VM.ship oetween these error terms and that of the #rue brightness temperatureis:

S2 (T 2 3 T 2

2 H orV 2 + H orV 2 + Hor V 02 (11.5)H or V a; ) \ aT VM VM \ B HM

For the sake of simplicity, assume that the instrumental error, n isthe same for both polarization, i.e., a = a a

(11.4), it follows: R V H. Applying equation

2 (1_o 2 a2

2 = (TVTHM) 2 + (.6)ayT )4 Cy(1-2 a) (1-2 .)2 R

where a is the standard deviation of the true brightness temperature,

either of the vertical or of the horizontal component.

The instrumental noise, a , is measured for each channel in the sensortests as a function of the radiometer only, and independent of the antenna.But the error that affects the retrieval result is aT. Equation (11.6)shows that both the cross polarization a and the uncertainty in crosspolarization, a, increase a and contribute to the degradation of the~Tretrieval accuracy. A number of cases are simulated to examine the effectof a and 0.

Figures 1 through 4 are constructed from equation (11.6) assumingT - T = 40, which is typical for ocean observation from the SSM/I. Thefiluresnepresent cases with cross polarization uncertainty, 0 , of 0, 0.5,1 and 2 percent, respectively. The instrument noise, a is allowed to varybetween 0 and 1 degree contigrade and the cross polarization, a, variesbetween 0 to 5 percent for each figure. The magnification of instrumentalerror is not very strong when 0 is zero, as indicated in Figure 1. Evenfor a five percent cross polarization, an instrument noise of 1.0 increasesto only 1.06. However, when Oa is no longer zero, the magnification ofinstrumental error becomes more significant as shown on Figures 2, 3 and 4.Even with a "perfect" radiometer, having no instrumental noise, i.e., =0, the cross polarization uncertainty would still introduce an error in the

97

CR,

00000

004-1

oo* 0

430

04-

'o1'V~ryk

tq C4

98 .-

.9-

00.05C.-a Z 0.04

- a . 0.03a = 0.02

b . = 0.01-a = 0.0

.5 -r

.2

0 .2 .4 .6 .8 1.0

'R (C)Figure 2 Retrieval Error as function of instrumental noise with 0.5%

cross-polarization uncertainty

99

j 0.00

0.9

-a a= 0.05a = 0.02a =0.01

.6- a = 0.02

.6

.5 a 0.01

.4

.3-

0 .2.4 .6 .8 1.0

Figure 3 Retrieval Error as function of instrumental noise with 1%cross-polarization uncertainty

100

I ! I I I

1.5-

1.3 -- !

o .2 -

bI. I -- 0.05

a= 0.04a 0.03a=0.02

1.0 -a= 0.01a=0.0

.9

o- = 0.02

.8

.7I i I I I I I I I i

0 .2 .4 .6 .8 1.0

o"R (C)

Figure 4 Retrieval Error as function of instrumental noise with 2%

cross-polarization uncertainty

101

brightness temperature measurement. The error, 0T' is 0.98 K when 0 is 5percent and 0a is 2 percent (see Figure 4), with no radiometric noise. Theerror is 0.8 K when * is zero. Two sets of cross polarization measurements(2, 3) made at the Hughes Aircraft Company facilities are listed in Table 1.

Table 1Cross Polarization Measurements

a x 100 (W)

Channels First Measurement Second Measurement

19.35 V .35 .10H .30 .10

22.235 V .65 .6337.0 V 1.80 .45

H 1.20 1.3085.5 V .60 1.4o

H 1.40 2.50

Note that the difference in * for 37.0 V and 85 H between the twomeasurements are 1.35 and 1.1 percent, respectively. This indicates thatthe a and 0. values used for Figure 1 through 4 are by no means unrealistic.

The effect of cross polarization error on geophysical parameter estima-tions must be examined through a retrieval model. The retrieval results, ofnecessity, are model dependent. In the present study, the model employed isthat originally designed by Wisler and Hollinger (5). Use of this modelprovided an understanding and useful evaluation in the application of theSSM/I system in several previous studies (6, 7, 8, 9, 10). The criterionchosen to examine the effect of cross polarization error is the percentageincrease in the retrieval RMS error.

RMS (a, ao,) - RM (0=0, cF,=O)P% = ) x 100% (11.7)

RlS (a=, OM=O)

Where P is the percentage increase, the parameters retrieved are the surfacewind speed, sea surface temperature, and the columnar densities of watervapor and cloud liquid water. The climate statistics (10) employed in themodel are those of Azores, Summer. The input data for the retrieval simu-lations are presented in Table 2 in the form of noise vectors. The value of( is taken from the most recent Hughes measurement (4) made on 2/16/82.

e cross polarization values are taken from the first measurement in Table1. The error vectors of = 0.0, .005, .010 and .020 are then derivedfrom Figures 1 through 4. ?Aesults of the retrieval simulations are shown inFigure 5.

102

100

columnar90- cloud liquid water

density

80-

surfaoce70- wind

speed

60-

50-columnarwatervapor

40- den ity

30-

20-

10-sea surfacetemperature

ax0 a a a aO0, %a,20 W .05 C .01 C~ .02

Figure 5 Percentage Increase in Retrieval Error as function ofcross-polarization uncertainty

103

Table 2

Instru- Cross aT (measurement error in TB)mentation Polariza- at cross polarization level of

tiona 0.0 .005 .010 .020

(measured) (measured) (inferred)

19.25 H .48 .0030 .481 .548 .630 .942V .51 .0035 .512 .552 .655 .960

22.235 V .64 .0065 .643 .687 .765 l.O42

37.0 H .40 .0120 .406 .459 .583 .933V .39 .0180 .398 .452 .585 .947

85.5 H .64 .0140 .650 .685 .775 1.068V .81 .0059 .816 .841 .912 1.151

From the results, it is apparent that the effects of cross polarizationerrors can be very significant. The curve for sea surface temperature inFigure 5 is misleading. It does not imply stability in sea surface temper-ature retrieval because of the low confidence of its estimation (7, 8).

Results shown in this section are derived under the assumptions ofidentical coupling between the two polarizations and the same instrumentalnoise. This assumption was made for simplicity. However, an exact formu-lation to take into account non symmetric leakage and instrumental error isstraightforward if precise measurements of these quantities become avail-able. Such a treatment is not likely to produce significantly differentresults than the present one. More important is the fact that the crosspolarization, though uncertain, is some fixed value and will remain constantover the life of the SSM/I. Thus the cross polarization uncertainty shouldnot merely be treated as a random error and simply squared and summed withthe radiometer noise to obtain the overall measurement error. Rather theuncertainty in cross polarization will result in an unknown bias in thederived brightness temperatures input into the environmental parameterretrieval algorithms. This can be assessed by comparing the values retriev-ed with and without cross polarization imposed biases as the biases arevaried over the expected range in uncertainty of the cross polarization inall possible channel combinations. A separate study has been planned toexamine the effects due to the biases.

III. Conclusions and Recommendations

The present study has demonstrated that the cross polarization and itsuncertainty can cause serious degradation of retrieved geophysical param-eters, even when the SSM/I cross polarization measurements are within therelaxed specification values.

104

Proper correction of the cross polarization effects, however, can bemade, as demonstrated in this study, if the cross polarization between portsat each frequency (i.e., H to V, and V to H) is accurately measured alongwith the VSWR of the feed horn for each channel. The uncertainty of thesemeasurements must also be accurately assessed, a it may be the mostimportant error source for the environmental retrievals.

The effect of cross polarization measurement uncertainty has beenevaluated as a factor which magnifies the noise in brightness temperaturemeasurements. Results of the study indicate that it can be very signifi-cant. However, the uncertainty, just like the true cross polarization valueis more likely a fixed value and should remain constant over the life of theSSM/I. Its greatest effect is probably in the form of bias rather thannoise in brightness temperatures. A separate study has been planned toexamine this aspect.

105

REFERENCES

1. "Specification Change Notice, Development Specification" (Part I, TypeB1), Code ID 82577, Spec. No. DS 32268-040, January 20, 1982.

2. "SSM/I Formal Qualification Review, Part I," Hughes, December 18, 1981.

3. "Acceptance Test Report, Option 1, SSM/I Antenna Subsystem," Hughes,CDRL Item No. 034A3.

4. "SSM/I Sensor Qualification Test Report," CDRL Item No. 054A2.

5. Wisler, M. M. and J. P. Hollinger, "Estimation of Marine EnvironmentalParameters Using Microwave Radiometric Remote Sensing Systems," NRLMemorandum Report 3661, Naval Research Laboratory, November 1977.

6. Lo, R. C. and J. P. Hollinger, "NRL Comments on the ERT SST Study forthe SSM/I," Letter Report to NSSA, Naval Research Laboratory, December1981.

7. Lo, R. C. and J. P. Hollinger, "Selection of Optimal Combinations ofFrequencies for the Special Sensor Microwave Imager (SSM/I) Environ-mental Retrievals," Letter Report to NSSA, Naval Research Laboratory,April 1981.

8. Lo, R. C. and J. P. Hollinger, "A Simulation Study of the Sensitivity ofEnvironmental Parameter Retrievals Based on the Special Sensor MicrowaveImager (SSM/I)," Letter Report to NSSA, Naval Research Laboratory, May1982.

9. Lo, R. C. and J. P. Hollinger, "A Comparison Study of the Sensitivityand Retrieval Performance at 21.0 and 22.235 Ghz Channels," LetterReport to NSSA, Naval Research Laboratory, August 1982.

10. Hollinger, J. P., R. M. Lerner, B. E. Troy, and M. M. Wisler, "JointServices 5D-2 Microwave Scanner Definition Study," NRL Memorandum Report3807, Naval Research laboratory, August 1978.

106 *U.S. GOVZRMZNT PRINTING oPTIC3: 1903-Ms,-314:0

Documents

SSM/I Project Summary Report - apps.dtic.mil · SSM/I PROJECT SUMMARY REPORT I. INTRODUCTION The Microwave Environmental Sensor System, referred to as the Mission Sensor Microwave/Imager