advances in calculating electromagnetic field propagation near the earth… · ·...

462 JOHNSHOPKINSAPLTECHNICALDIGEST,VOLUME22,NUMBER4(2001)

M. H. NEWKIRK, J. Z. GEHMAN, and G. D. DOCKERY

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AdvancesinCalculatingElectromagneticFieldPropagationNeartheEarth’sSurface

Michael H. Newkirk, Jonathan Z. Gehman, and G. Daniel Dockery

hepropagationof electromagneticfields through the lower atmosphere is greatlyaffectedbytheenvironment,surfacecharacteristics,andsensorconfiguration.Thisispar-ticularlytrueforshipboardsensorsthataretaskedwithdefendingthemselvesandnearbyshipsagainst low-altitude threats.With theNavy’s focusnowdirectedatcoastalareas,thepropagationenvironmentsincludeterrainbackgroundsandcomplicationscausedbyland–seainteractions.Theselittoralsituationspresentnotonlyacomplicatedfieldpropa-gationproblemforthesesensorsbutalsoincreasedsurface,volume,anddiscretecluttersourcesthatincreaseradarsystemloadinganddegradecommunicationscapabilities.Wesummarizetherecentadvancesinpropagationmodelingaimedatimprovingtheabilitytomodelpropagationandcluttereffectsinlittoralregions.Whiletheimprovementsdis-cussedhereareparticulartotheTroposphericElectromagneticParabolicEquationRou-tine(TEMPER),apropagationmodeldevelopedatAPL, theyhavealsoadvanced thestateoftheartinpropagationmodeling.Wealsodiscussthefuturedirectionsofpropaga-tionmodeling,outliningseveralareasofcurrentresearchwithinAPLthataimtofurtherimprovethiscriticalcapability.

INTRODUCTION AND MOTIVATIONThe U.S. Navy has been aware of atmospheric

impactsonradarperformancesince thefirst introduc-tionof radar into theFleet50years ago, and impactson radio transmissions were observed much earlier.Attemptstounderstandandcharacterizetheseimpactsalso date back to the 1940s.1 The review article byHitney et al.2 provides an introduction to some ofthe relevant propagation effects and references forearly work in this field. The current “generation” ofAPL’sworkinunderstandingenvironmentalimpactsonsystems began in conjunction with the development

of the AN/SPY-1 radar for the Aegis weapon systemaround1980.

The performance of systems radiating energy innear-horizontal directions is significantly affected byseveral environmental phenomena, including atmo-spheric refraction,diffractionover the sphericalEarth(oversea)andaroundterrainfeatures,scatteringfromseaandland,andattenuationbygaseousabsorptionandscatteringfromprecipitation.Narrowingthediscussiontoradardetectionoflow-flyingtargetsforthemoment,refractioncancausedetectionrangestovarybyafactor

JOHNSHOPKINSAPLTECHNICALDIGEST,VOLUME22,NUMBER4(2001) 463

CALCULATING ELECTROMAGNETIC FIELD PROPAGATION

of3ormore(e.g.,Fig.8)andcanresultinstrongsur-facebackscattering(clutter)fromverylongranges(e.g.,Fig. 6), which may degrade radar performance in anumberofways.Furthermore,multipathfading,causedby interference between direct and reflected propaga-tionpaths,mayresultindroppedtracksonlow-to-mod-eratealtitudetargets.

Over the sea, low-flying targets, which are nor-mally hidden from the radar until they come abovetheEarth’shorizon,presentastressingthreattoship-boardweaponsystemsbecausetheyarequiteclosebythe time they are detected. Furthermore, the radar’sactualperformanceinthesesituationsisverysensitivetoatmosphericrefractivityconditions,andbefore1980methods to analyze and predict these effects did notexist.EarlierversionsoftheTroposphericElectromag-netic Parabolic Equation Routine (TEMPER) weredevelopedtoanswerthisneedfortheAegissystem3–6andwereused inconjunctionwith thenewlydevel-oped APL AN/SPY-1 FirmTrack simulation to ana-lyzeradarandmissileilluminatorperformance.Inaddi-tiontothedevelopmentofTEMPERandFirmTrack,atmosphericmeasurement instrumentationand tech-niques were developed to characterize the refractiveconditions.Thisworkisdescribedinacompanionarti-clebyRottieretal.inthisissue.Thatarticlealsoservesas a good introduction to the types of atmosphericrefractivity conditions that are typically encounteredovertheoceans.

The combination of propagation modeling, radarsimulation,andenvironmentalmeasurementandchar-acterization provided the first capability to quantita-tivelyreconstructradarperformanceduringNavytests.This capability served the important role of relatingobservedradarperformancetothesystemspecifications,whicharetypicallybasedon“standard”refractivecon-ditions.Thisanalysiscapabilityalsoprovided,againforthefirsttime,anunderstandingofthephenomenacaus-ingdegradationsinradarperformance.Thenextmajorchallengetoradarperformanceanalysisingeneral,andpropagation modeling in particular, appeared as newmissionsandtacticsbroughttheformerly“blue-water”Fleetincloseproximitytoland.Irregularterrainintro-ducesmanylarge,nonuniformeffectsinradarsystems,includingtarget shadowing,hugebackscatter(clutter)returns,andsensitivitytotheship’spositionrelativetoland.Developingacapabilitytomodelradarpropaga-tionandperformancenearandoverlandbecameapri-oritywhenactualradarperformancewasobservedtobehighly variable and often degraded in littoral regions.These effects spurred development of improvementsin existing systems, such as the AN/SPY-1D, whichis being upgraded to the AN/SPY-1D(V), and newdesigns for future radars, such as the Multi-FunctionRadar (MFR). A high-fidelity, terrain-capable propa-gation model was required to support the design and

evaluation of these systems. Recent upgrades toTEMPERweredesignedtoprovidethiscapability.

There have been several approaches to represent-ing radio-frequency propagation in the atmosphere,includinggeometricoptics(raytracing),normalmodetheory, and physical optics (spherical-Earth diffrac-tionandmultipathmodels).Eachoftheseapproacheshas well-documented limitations in accuracy and/orapplicabilityrelatingtoallowablefrequencies,diffrac-tioneffects,terrainmodeling,andcomplexityofatmo-spheric refractivity. These restrictions severely limitthe utility of such methods for high-fidelity applica-tions, such as predicting the radar detectability oflow-altitude targets in realistic environments. Thedevelopment of efficient numerical solutions of theparabolicwaveequation (PE)offeredamajorbreak-through inelectromagneticpropagationmodelingbyallowingaccuratecalculationsforrealisticallycompli-catedrefractiveenvironments.

The PE is a forward-scatter approximation to thefullHelmholtzwaveequationandinherently includeseffects caused by spherical-Earth diffraction, atmo-spheric refraction, and surface reflections (i.e., mul-tipath).7 As a direct numerical evaluation of the for-ward wave equation, PE-based models avoid most ofthe limitations associated with the other modelingapproachesmentionedbecauseofthelackofsimplify-ingassumptions.AdvancedversionsofPEmodelsalsoincludeimpedanceboundaries,roughsurfaces,compli-cated antenna patterns, irregular terrain, atmosphericabsorption, and/or other scattering phenomena. PEmethodshavebecomethepreferredpropagationmod-elingapproachformanyNavyapplicationscoveringawiderangeoffrequencyandpropagationgeometriesforradar,communications,weapon,andelectronicsupportmeasuressystems.

The PE method was first introduced in the 1940sbyFock.7At that time themethodcouldbeappliedonlytosimplegeometriesandrefractiveconditions.Intheearly1970saspectralmethod,calledtheFouriersplit-step(FSS)method,wasappliedtotheparabolicequation8topredictunderwateracousticpropagation.With this improvement, practical application of themodel to more complicated atmospheres and surfaceboundaries became possible. In the early 1980s, theFSS-basedPEmodelfirstbegantoseeapplicationtoradio-frequency propagation, resulting in the EMPEmodel.9Since then, several advanceshave increasedtheaccuracy,speed,andflexibility3–6ofthebasicPEmethodthatistheheartofTEMPER.Thisarticledis-cussestheadvancesmadeinthelastfewyearsthatcul-minatedinthereleaseofTEMPERVersion3.10tothepropagationcommunity.

AnumberofPE-basedandPE-hybridmodels existtoday. These include Radio Physical Optics (RPO),10TerrainParabolicEquationModel(TPEM),11Advanced



Propagation Model (APM), and Variable TerrainRadio Parabolic Equation (VTRPE),12 all created bytheSpaceandNavalWarfareSystemsCommandSys-tems Center in San Diego, and the PCPEM andTERPEMmodels,whichweredevelopedintheUnitedKingdom. The APL model of this class, TEMPER,is regarded as the benchmark PE model in the U.S.Navypropagationcommunity.Severalalgorithmsorig-inally developed for TEMPER have been integratedintoothermodelslikeAPMandTERPEM.Reference13 provides an excellent discussion of the historysurrounding the development of these PE models aswellastheinterchangeamongorganizationsthathasadvancedthestateofpropagationmodeling.

TEMPERhasfounduseinnumerousU.S.Navyandother DepartmentofDefenseprograms in addition totheAegisProgramforwhichitwasprimarilydevelopedandfromwhichtheprimaryfundingoriginated.SomeofthesebeneficiariesincludetheCooperativeEngage-mentCapability(CEC),DD21,MultifunctionRadar/VolumeSearchRadar(MFR/VSR),NATOSeaSpar-row, Ship Self-Defense System, and High FrequencySurfaceWaveRadarprograms.Asaresult,theTEMPERmodel is, or has been, used by more than 30 govern-mentagencies,commercialcontractors,anduniversitiesacrossthecountry.

Within the Aegis Program, TEMPER is an impor-tant part of the APL SPY-1 FirmTrack model, whichprovidesthehighest-fidelityrepresentationofthatradarsystem’sperformanceagainstawidevarietyofthreats.Also,TEMPERhas beenoptimized, alongwithFirm-Track, for near–real-time use in the Shipboard Envi-ronmental Assessment Weapons System Performance(SEAWASP) shipboard Tactical Decision Aid. SEA-WASP is currently a prototype system on USS Anzio(CG68)andUSSCape St. George(CG71).(SeeRef.14andthearticlebySylvesteretal.,thisissue.)

PE MODELING ADVANCESThis section provides some detailed information

about improvements made to the TEMPER programinthepast5years.While someof thesechangesarespecifictotheTEMPERinterface,othershavesignifi-cantly advanced the state of the art for propagationmodeling.

General ImprovementsSeveralgeneralimprovementshavebeenmadetothe

TEMPER model that warranted incrementing the ver-sionnumberfrom2to3.Anumberofthesechangesarecategorizedasrecoding,toallowforsuchcapabilitiesasdynamicarraysizesandmoreefficientcalculations.SomeoftheseimprovementsarediscussedinRef.15.

Another change to the model was the addition ofnewsource-fieldtypestoaugmentthesmalloriginalset.

Thesesourcetypesincludeabuilt-inplanewave,whichhasbeenparticularlyusefulwhencomparingTEMPERwith other models. Also, the generic asymmetricpattern typewasaddedtoprovide themostflexibilitywhenspecifyingageneric(i.e.,non-symmetric)antennapattern.

Another improvement relates to how the wide-angle propagator in the PE model affects the sourcefield. Kuttler16 found that this propagator distortedthe sourcefields as theywerepreviouslydefinedandthattheintroductionofa“correctionfactor”intothisinitialfieldwouldcounter thisdistortionas thefieldpropagates. The result of this work allows TEMPERto more accurately represent fields that propagate atsteeperangles.

Another improvement that relates to wide-anglepropagationistheuseoffiltersinbothrealandtrans-formspaces.TEMPERmitigatesagainstenergy reflec-tions from the upper numerical boundary by periodi-cally applying a filter in both the real and transformspaces.TEMPER2usedthesamefilterinbothdomains,and the filter coefficients were represented by single-precision values. TEMPER 3 now uses double-preci-sioncoefficients,whichsignificantly reducenumericalnoise levels. Inaddition, thetransform-domain’sfilter(termed the “p-space filter”) has been widened fromthepreviouslimitofaround49°(relativetothehori-zontaldirectionofpropagation)toapproximately60°.This increase in available “problem space” reinforcedtheLinearShiftMapterrainmethod(describedlater),as it allows themodel to includea greater amountofterrain-scatteredenergy.

OtherchangestotheTEMPERmodelcanbecat-egorized as improvements to the previous interfaces.Forexample,anumberofnewinputparametersaffordgreater control over the program, while a significantamountoflogichasbeencodedintoTEMPERtopre-vent incorrect parameter combinations. TEMPER 3canautomaticallychoosesomeparametersiftheuserhasnospecificrequirement.Also,themainoutputfilesfromTEMPERhavebeen significantlyupdated.ThePrintFilenow includesmuchmorediagnostic infor-mationthaninthepast.ThebinaryFieldFileincludesa great deal more information in its header recordthanbefore;italsoincludesgrazingangleandterrainheight informationwith thepropagation factordata.TEMPER now offers two compression schemes toreducethefilesizebyfactorsof2and4,althoughattheexpenseofsomefidelity.

In summary, many of the improvements to theTEMPERcodehaveresultedinaneasier-to-usemodelthat provides a more accurate field solution. As evi-dence of its utility, more than 100 people now useTEMPER3inapproximately30militaryinstallations,DoDcommercialcontractors,anduniversities,includ-ingmanyuserswithinAPL.



Grazing Angle EstimationThereisnoquestionthatthemostusedandimpor-

tant TEMPER product is the propagation factor data.Thisquantity is critical to the implementationof theradar range equation for low-elevation-angle propaga-tion.RecentattentionwithintheAirDefenseSystemsDepartment has been directed toward surface cluttermodeling, which requires not only propagation factordatanearthesurfacebutalsothelocalgrazingangle.17,18This is the angle at which the incident field energystrikesthesurface.Toaccountforrough-surfaceeffectsonpropagation,TEMPERalsorequiresthegrazingangleateachrangestep.TEMPERusesthisvaluetocalculatetheMiller-Brownrough-surfacereductionfactor.19Thisfactor reduces thevaluesof the smooth-surface reflec-tioncoefficientusedinthediscretemixedFouriertrans-form(DMFT)methodof accounting forfield interac-tionwiththelowerboundary.

Simple geometry provides a straightforward tech-niqueforcalculatinggrazingangles.TEMPERiscapableofbothflat-andspherical-Earthcalculations.Geomet-ricmethodsareonlyusefulforverysimpleatmosphereshavinglinearrefractivegradientsandcannotbeusedforcomplicatedterrainboundaries.

An alternate method is geometric optics (GO),whichcanbeused in complicated refractive environ-mentsandcanaccountforterrain.TEMPER2employeda separate, external program to compute this type ofangle.20Theproblemwiththisapproachwas twofold:(1) the potential for errors associated with how theexternalGOprogramandTEMPERhandledthenec-essaryrefractivity interpolationsand(2)ensuringthatboth programs used the same physical and electricalparameters.TEMPER3nowhasavariantofGOcodeincluded within the program, which eliminates theseconcerns.

AlthoughGOcodesarecertainlycapableofdeter-mining grazing angles for terrain surfaces, they canonlydosofordirectlyilluminatedareas.Thatis,apureGOmethodcannotaccountfordiffraction.Analter-nativethatperformsquitewellinthiscaseisspectralestimation(SE),morespecifically,anSEmethodthatusestheMultipleUnknownSignalIdentificationandClassification (MUSIC) algorithm.21 TEMPER canuse theSE/MUSICalgorithm in all cases, but ithasbeendemonstrated that thismethodperformspoorlyin evaporative ducting environments.22 This limita-tion iscausedbythestrongrefractivegradientsasso-ciatedwithevaporativeducts.Thesegradientsdrasti-cally refract thefieldwithin theMUSICalgorithm’ssamplingwindow,leadingtoerrorsinthespectralesti-mation. Finer resolution in altitude mitigates theseerrorsbuthastheundesirablesideeffectoflargetrans-formsizesandconsequently longcomputation times.As a result, it is impractical to use the SE/MUSICtechniqueforevaporativeducts.

TEMPER3nowmakesuseofallthreeofthesegraz-ingangleestimationmethods.Forverysteeppropaga-tionangles(i.e.,largerthanabout1.5°andclosetotheemitter), simple geometry is used. This is acceptablebecauserefractiveeffectsonpropagationarenegligibleabovethislimit.Forover-seaportionsofapropagationpath,theGOmethodisusedbecauseitperformsbetterthan the SE method in all refractive environments.Foranyterrainalongthepath,theSE/MUSICmethodis used. The SE/MUSIC evaporation duct limitationis not a concern because terrain tends to break upanyevaporativeductwithinashortdistancefromtheshoreline.Incaseswhereterrainshadowsaportionofanoceanpath,theSE/MUSICresultisuseduntiltheSEgrazingangles fallbelow thosevaluesdeterminedby the GO method. In this way, the grazing anglesfor terrain-diffracted fields are adequately captured.Figure1illustratestheapplicationofthisproceduretoamixedland–seapropagationpathinthepresenceofamoderateevaporationduct.Figure1bshowsthesur-faceheightprofile,whichisasimple“terrainwedge”witha3°slope;Fig.1aprovidestheresultsoftheSE,GO, and automatically combined grazing angle esti-mation.NotehowtheSEmethodsignificantlyunder-estimatesthegrazinganglesovermostoftheseapath;however,thismethoddoesanexcellentjobofdetect-ingthoseanglesontheilluminatedfaceofthewedge,quickly diminishes to small values on the shadowedface,thenaccuratelyprovidesthediffraction-inducedgrazinganglesoveranappreciableportionoftheshad-owedseasurface.Ontheotherhand,theGOmethoddoes well in the directly illuminated sea region butignorestheterrainaltogether.

Figure 1. Illustration showing how the automated grazing angle algorithm handles mixed terrain/refractivity conditions. (a) The resul-tant grazing angle profile is given by the blue line (Auto = auto-matically combined, GO = geometric optics method, SE = spectral estimation method); (b) the ocean/terrain boundary.

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TEMPERautomatesthiswholeprocesssothatauserneednotbeanexpertindecidingwhichofthesemeth-odsshouldbeusedtogether.Foragivencase,TEMPERfirst lookstoseeifthereisterrainintheproblemandwhetherastrong,negativerefractivegradient(indica-tiveofanevaporativeduct)ispresentintherefractiv-ityfile.Dependingonwhichoftheseconditionsexists(including whether grazing angles are either requiredby the rough-surface model or requested by the userfor later use), TEMPER will decide which algorithmsmustbeusedandthenwillautomaticallysplicetogethertheappropriate results for each region.A summaryofthemethodsthatwereusedinconstructingthegrazinganglearrayisprovidedinthePrintFile.

Asnotedintheprevioussection,thegrazinganglesare now included in the binary Field File along withthepropagationfactordata.Inaddition,TEMPERcancreateaseparateASCIIgrazinganglefileforotheruses.

Including Terrain EffectsAnother significant improvement inrecentyears is

the method by which TEMPER accounts for generalterrainsurfaces.TEMPER2hasasingle,simplemethodthat essentially zeros thefield from the terrainheightdowntomeansealevelbeforepropagatingthesolutiontothenextstep.Thismethodistermedthe“knife-edge”(KE)methodbecause it resemblespropagationover aseriesofperfectlyconductingknifeedges.Thismethodisextremelysimpletoimplementandactuallyprovidesaremarkablyreasonableresultfordiffractedfieldswhencompared to analytical solutions for propagation oversingleandmultipleknifeedges.

While theKEmethoddoesquitewellwith terraindiffraction,itcannotrepresenttheeffectsofscatteringby terrain surfaces. Donohue and Kuttler23,24 recentlyprovided an alternate method that maps the compli-cated terrain boundary onto a flat surface through acombinationofverticalshifts,phasesteering,andsur-faceimpedancemodifications.Thismethod,calledtheLinearShiftMap(LSM)method,expandsuponearlierwork by Beilis and Tappert.25 It provides reasonablyaccurate results for terrain slopes that do not exceedabout14°.Sincethatworkwaspublished,anadditionallimitonthechange in slopehasbeenobserved,andthislimitisdependentonthechosenproblemangle(trans-formspacebandwidth)foraparticularcase.

Figure2showsTEMPERcoveragediagramsfortheKE and LSM methods. Note how the LSM methodprovides forward-scattered fields that the KE methodcannotrepresent.

Improved Numerical StabilityOne of the most recent improvements to the

TEMPER model addresses a longstanding numericalinstability.ThisproblemcausederrorsintheTEMPER

solution that were manifested as unrealistically largepropagationfactorvaluesinsomeportionoftheoutput.Whileitisdifficulttoascertaintheparametercombina-tionsthatcausetheinstability,itgenerallyariseswhenrough-surface calculations are performed at high fre-quenciesand/orroughnessvalues.Tosomedegree,thesurfaceelectricalparametersalsoaffecttheinstability.

ThisproblemoccurredintheDMFTmethod,whichintroducesanauxiliaryfunctiontoeffectivelyhalvethenumberoftransformcalculations.Thisauxiliaryfunc-tioninvolvesasecond-orderdifferenceequation,whichuses a second-order, centereddiscretizationof bound-ary-conditionderivatives.Alternatenumerical formu-lationsoftheauxiliaryfunctionwereinvestigated,onethat uses a first-order forward difference and anotherthatusesafirst-orderbackwarddifference.Thesefirst-order equations turned out to be less susceptible tonumerical instabilities than their second-order coun-terpart.26 As an additional benefit, where one of thefirst-orderequations isunstable, theother isgenerallyfoundtobestable.Asaresult,onecanalmostalwaysfind a combination of these two first-order methodsthatworks.

A secondarybenefitofusing thefirst-orderdiffer-enceequationsisareductioninthenumberoffloat-ing-pointoperationsrequiredinthesealgorithms.The

Figure 2. L-band examples of (a) the knife-edge terrain method and (b) the Linear Shift Map terrain method.

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originalsecond-orderequationsrequiretwoback-solv-ing operations per range step to arrive at a solution,while the new first-order equations require only oneback-solvingoperation for the same range step.Asaresult,TEMPER’snewalgorithmisslightlyfasterthanitspredecessor.

Thecostofthisimprovementinstabilityandcompu-tationtimeisaninherentlylessaccuraterepresentationof the boundary condition, owing to the lower-orderapproximation.However,whentheTEMPERaltitudestepsizeiskeptreasonablysmall,thedifferencebetweenfirst-andsecond-ordersolutionmethodsisnegligibleformicrowavefrequencies.Forthehigh-frequencythroughultrahigh-frequencybands,thefirst-ordersolutionsgiveunacceptableerrorswhencomparedtothesecond-ordersolution.Theoriginalsecond-ordermethodisretainedfor these lower frequencies, where this method rarelyexhibitstheinstabilityproblem.

Thus,acarefullyselectedcombinationofbothfirst-and second-order difference equations is now appliedacrossTEMPER’svalid frequencyrangeof10MHzto20 GHz, providing generally faster calculation timesandbetternumericalrobustnessthanearlierversionsofTEMPER.

Application to SectorsRecentattentionhasbeenfocusedonmodelingprop-

agation conditions over wide areas (sectors) for ship-board sensor applications. These sectors may containterrainwithwidelyvaryingrelief.Ofparticularinterestisthelandandseacluttercrosssectionpresentedtosuchsystems. TEMPER is a two-dimensional (2-D) propa-gation model and thus cannot model effects such asterrain-influenced out-of-plane scattering, diffraction,and depolarization. With those limitations in mind,TEMPER can still provide useful “first-order” terraineffects for wide-area situations by combining the 2-Dresultsformultiplebearings.

Oneobservationisthattherefractiveenvironmentnear the ship is independent of azimuth. With thisassumption,TEMPERcalculationsclosetotheshipareredundantinazimuthouttoacertainrange.Arecentupdate to TEMPER includes the ability to initializea new TEMPER run using complex field informationcalculated from earlier TEMPER calculations. Withthis approach, a single sea-surface calculation coversall bearings up to the range where the environmentchanges.Then,atthatrange,thesea-surfacecasecanbeusedto“restart”anewTEMPERcalculationoneachparticularbearing.

Figure3illustratesthisconceptforashiplocatedsomedistanceoffshore.First,asingleterrain-freeTEMPERrunisperformedouttoamaximumrangeofinterest,Rf,andat certain intervals (Ri, with i = 1, 2,…, N) the com-pletecomplexfieldsolutionisstored.Theseintervalsare

somewhatarbitrary,butiftherearetoomanyintervals,thesizeoftheStorageFilemaybecomelargerthantheFieldFile,negatingthereasonforthismethod.Thenona particular bearing, TEMPER initializes a new run atthe location,Ri,where the “openocean,homogeneousenvironment” assumption is no longer valid. This newrunbeginsbyextractingthestored“base”fieldatrangeRi.TEMPERthenpropagatesthisfieldouttothemaxi-mum range Rf using the bearing-specific environment.The procedure is repeated for all bearings of interest,potentiallysavingagreatdealofcomputationtimeandstoragespace.Thismodelingprocedureisbeingusedinan effort to integrate the powerful capabilities of theTEMPERmodel into a program that calculates surfaceandvolumecluttercrosssections,includingpropagationeffects,forgenericradarsystems.ThisIntegratedClutterModel,arecentlylaunchedeffortwithintheAirDefenseSystems Department, seeks to combine the TEMPERpropagationmodelwithacceptedmodelsforseaandlandclutteraswellaswithnewlydevelopedmodelsforrain,dust,biological,anddiscretecluttersources.

Figures4through6provideanexampleoftheappli-cation of this restart technique. Figure 4 shows a ter-rainmapconstructedfromtheDigitalTerrainElevationDatabaseforanotionalshiplocatedinthemiddleoftheArabian Gulf, approximately 100 km north of Qatar.In this example there are terrain heights in excess of3kmtowardthenortheastandcomparativelymoderateterraintothesouthandwest.Figure5showsarefrac-tivityprofileconstructedfromballoon-sondemeasure-mentsmadeaboardUSSLake Erie(CG70)inOctober1999atthepositionshowninFig.4.Forthepurposeofdemonstratingtherestartmethod,thisprofileisassumed

Figure 3. Illustration showing the use of multiple two-dimensional solutions to represent three-dimensional regions. (Rf = maximum range of interest, Ri = range at interval i.)

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tobevalidfortheentireregion.Itisworthnotingthatthisassumption isgenerallynot true,especiallyas therange from the ship increases and as the propagationpathtransitionsfromseatoland.

TheTEMPERprogramwasappliedto360bearingsoriginatingfromthecenterofFig.4,butonlythosepor-tions of each bearing with terrain are actually calcu-lated.For the remainderof thosepaths,abasecase isused. Figure 6 shows the TEMPER calculation resultsfor a standardatmosphere (Fig.6a)and themeasuredrefractivity profile (Fig. 6b) in Fig. 5. The plots showtheone-waypropagationfactor,indecibels,atanalti-tude of 1.2 m above the sea or terrain surface for anS-bandemitter.Theeffectsofsurface-basedductingaredramaticinmostareasexceptinthenortheast,wherecoastalmountainshaveblockedtheductedenergy.Forthis example, the restart method saved about 45% in

computationtimeand55%indatastoragecomparedtocalculatingeachbearingentirely.

VERIFICATION, VALIDATION, AND ACCREDITATION

During the development of the model, TEMPERhasbeenengaged inseveralverificationandvalidation(V&V)efforts.V&Vmethodsincludedcomparisonwithothermodels intheirapplicableparameterspaces,datacollectionsatfield testsdevotedtopropagationexperi-ments,andradarsystemfield-testingagainstlivetargets.

ComparisonsofTEMPERwithothermodelsarewelldocumented.27Theseothermodelsincludewaveguide-mode calculations, spherical-Earth diffraction models,ray optics methods, and moment-method techniques.In addition, TEMPER has been compared with otherPE-basedandhybridpropagationmodelsthroughpartic-ipationinseveralorganizedpropagationmodelingwork-shops.28Inallcases,TEMPERcomparedveryfavorablywiththesemodelsintheirregionsofvalidity.

Figure 4. Arabian Gulf terrain map as an example of the “restart” method.

Figure 5. Measured refractivity profile from the Arabian Gulf in October 1999.

Figure 6. Comparison of propagation factor maps for (a) stan-dard atmosphere and (b) measured refractivity conditions.

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On several occasions, well-organized propagation-orientedfieldtestsinthemid-AtlanticandPuertoRicoareashaveprovidedvaluabledatawithwhichtomakecomparisons.Whensufficientmeteorologicaldatawerecollected to adequately characterize the environment,TEMPER-modeledresultscomparedveryfavorablywithreceived signal and/or surface clutter power measure-ments.27Figure7providesanexamplecomparisonfroma 1986 propagation test in the Wallops Island, VA,area.TheredcurveisaTEMPERresultfora4/3-Earth(standard atmosphere) environment, the green curveistheTEMPERresultusingthemeasuredenvironmen-tal data, and the blue curve is the measured receivedpower.

TEMPERhasalsoundergoneextensiveV&Vaspartof theFirmTrack radar systemperformancemodel. Inthis case, thecomparison tobemade is themeasuredversusmodeledfinalfirmtrackrangeforaradarsystemagainstaparticulartargetinagivenenvironment.Thefirmtrackrangeisdefinedastherangefromtheshipatwhichagiventargetwillbeintrackacertainpercentofthetime.Overthelasttwodecades,APL’sTheaterSystemsDevelopmentGrouphasdevelopedthisradarmodeltorepresentthefunctionsandprocessingmeth-ods of the AN/SPY-1 class of radars (i.e., the radarclass associated with the Aegis Weapons System). Akey part of the FirmTrack modeling process for low-altitude targets is the propagation factor result fromTEMPER.TheinterdependenceofTEMPERandFirm-Trackmeans thatV&Vresultsof thiskindassess thevalidityofTEMPER’spropagation factors,albeit indi-rectly.Onceagain,incaseswhereadequate,timelyenvi-ronmentaldatawerecollected,thecombinedTEMPER/FirmTrack-modeledfirmtrackrangecomparedverywellwithmeasureddata.FurtherdiscussiononthismodelingaspectandanexamplethatdemonstratestheagreementbetweenmodeledandmeasuredtrackingperformanceisprovidedinthearticlebySylvesteretal.inthisissue.

ThisextensiveV&Veffortspanningthelast15yearshasresultedintheaccreditationoftheTEMPERmodelby several U.S. Navy programs, including the MFR

Program (PMS-500), Cooperative Engagement Capa-bility(CEC)OperationalEvaluation(OPEVAL)analy-sis(PMS-400andPMS-465),andtheDDG51LiveFireTestandEvaluation(LFT&E)Program(PMS-400).

SHIPBOARD APPLICATIONTEMPER development began as an engineering

model and was not initially intended for use in oper-ational systems. It soon became apparent that such amodelingcapabilitywouldbevaluableonboardopera-tionalNavyshipsfornear–real-timeradarsystemperfor-manceassessmentandresourcemanagement.AnefforttoprovidethiscapabilitytotheNavyculminatedintheShipboardEnvironmentalAssessmentWeaponsSystemPerformance(SEAWASP)system,aprototypetailoredtotheAN/SPY-1radaronUSSAnzioandUSSCape St. George.14Inthiscase,theTEMPERmodelhasbeentai-loredtoacceptinputsfromtheEnvironmentalAssess-mentSubsystem,toefficientlyrepresenttheAN/SPY-1radarphysicalandelectricalparameters,andtoprovidestreamlinedoutputforsubsequentuseinanoptimizedversionofFirmTrack.

TheSEAWASPsystemhasgainedwideacceptanceby the ships’ crews and has demonstrated the impor-tance and need for accurate environmental assessmentfor all shipboard sensors. As a result of this system’sdeployment,effortsarecurrentlyunderwaytoprovideanupdatedenvironmentalassessmentsystemintheformoftheShipboardMeteorologicalOceanographicObserva-tionSystem(Replacement).Whiletherecurrentlyisnoprogram to transition theweapons systemperformancesubsystem into anoperational system, efforts areunderwaytoreconcilethisapproachwithothermethodsthatarebeingproposedintheNavalMeteorologyandOcean-ographyCenterandoperationalcommunities.

FUTURE MODELING DIRECTIONSAlthough the current TEMPER implementation is

mature, there are still areas to be explored. As thenewercapabilitiesareappliedto increasinglycomplexlittoral environments, it is certain that fine-tuning ofthegrazingangleandterrainmethodswillberequired.Inaddition,severalprojectsareunderwaywithinAPLthatseektoimproveourunderstandingofpropagationthroughrealenvironmentsandovercomplexterrain.

Aneffortrecentlybegancreatingafullypolarimet-ric,three-dimensional(3-D)modelforpropagationover2-Dterrain.Thecurrent2-DTEMPERprogramisonlycapableof representingtheeffectsofone-dimensionalsurfaces.The inherent limitationsof a2-Dmodel arethatitcannotaccountforout-of-planescatteringordif-fractioncausedbyrealterrainorout-of-planerefractioncausedbyazimuthallydependentenvironments.A2-Dmodel also cannot deal with depolarization caused bytheenvironmentorsurface.

Figure 7. Comparison of modeled and measured power levels from an October 1986 test in the Wallops Island, VA, area.

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Theimpetusfora3-Dmodelistoprovideabench-markagainstwhichthecurrent2-Dcodescanbecom-pared. Since the 3-D model can account for energythat may scatter and diffract around the terrain, it isthoughtthatthismightexplainobserveddiscrepanciesbetween measured clutter power levels and simulatedclutterpowerderivedfrom2-Dmodels.Studiesofthistypewillimprovethestateoflandcluttermodeling.

Another area where 3-D propagation modelingmay contribute is ship signature modeling. The prob-lem is centered on how well a low-flying anti-shipcruisemissilemayviewasurfaceshipinaclutterback-ground.This is a topicof great interest to efforts likeDD21,wheretheeffectivenessofreducingtheshipsig-naturemayinpartdependontheenvironmentinwhichitoperates.Depolarizationandout-of-plane scatteringmaylimittheeffectivenessofshipsignaturereductionmethodsastheresultingradarcrosssectionapproachesthatoftheclutterbackground.Two-dimensionalpropa-gationmodelscannotaccountfortheseeffectsontheirownandthereforecannotbeusedtoassessthesensitiv-ityofshipdesigntotheseeffects.

The3-DnatureoftheproblemprecludesuseoftheFouriermethodsthathaveworkedsoefficientlyfor2-Dpropagationmodels likeTEMPER.Themostefficientmethodavailableforthe3-Dproblemisimplicitfinitedifferences.Boththe2-DFouriermethodsandthe3-Dimplicit finite differences methods are marching solu-tions;beyondthat,themethodsarecompletelydiffer-ent.Earlyresultsarepromising;forexample,3-Dprop-agation results have already been achieved for simpleobjectslikebuildingsandsmoothGaussianhills.Even-tuallythemodelwillbeexpandedtohandlegeneralter-rainsurfaces.

Anothercurrenteffortintendstoimprovehowprop-agationmodelsaccountforroughoceansurfacereflec-tion. TEMPER’s current approach uses an empiricalmodelthatreducesthesmooth-surfacereflectioncoef-ficient,therebyreducingthecoherentlyreflectedfield.The limitation of this method is that the empiricalmodel’sassumptionsbreakdownathighseastatesandgrazingincidence.Theamountoferrorinthismethodiscurrentlyunknown,however,becauseitisextremelydifficult to collect data to support such a study. Anumericalstudyisunderwaythatwillattempttoquan-tify these errors. This effort will compute exact scat-tering results for realisticocean surface realizationsbyacceleratedmomentmethodtechniques,thenensembleaverageovermanyrealizationstodeterminetheaveragescatteredfieldasafunctionofgrazingangle,frequency,polarization,andsurfaceconditions.This isa tremen-douscomputationalchallenge,requiringsupercomput-ingresourcesforresultsfromasinglesurfacerealization.However, recent acceleration techniques are makingthisstudypossiblewithavailableDoDsupercomputingresources.Theendresultwillbeanimprovedmodelfor

representing rough-surface effects in 2-D propagationmodels.

An investigation that has just begun is the appli-cation of the propagation model to wideband (e.g.,pulsed) applications. TEMPER and other PE modelsprovideinherentlysingle-frequencyormonochromaticsolutions. This type of solution is adequate for nar-rowband (long pulsewidth) and continuous wave sys-tems,butwithnewradardesignsconsideringtheuseofshortpulsewidthsthenarrowbandassumptionmaynothold. A candidate approach uses Fourier synthesis ofseveralsingle-frequencysolutionstosimulatewidebandpropagation.

SUMMARYIn recent years many improvements have been

madetotheTEMPERpropagationmodel,anumberofwhicharegenerallyapplicabletoanyPE-basedmodel.Improved grazing angle estimation is important notonlytofieldpropagationbutalsotocluttermodelsthatapplytheTEMPERgrazinganglesdirectly.Themod-eling of terrain effects has also progressed markedly.Usingthesegrazingangleandterrainmodelingmeth-ods, TEMPER can provide an excellent representa-tionoffieldpropagationinlittoralenvironments.Theimprovement in numerical robustness afforded by aslight reformulation of TEMPER’s DMFT allows themodeltobeusedathigherfrequenciesandseastatesthaneverbeforepossible.Theserecentimprovementshave also helped in the effort to provide wide-area,propagation-modifiedsurfaceandvolumeclutterdataforsite-specificradarsystemmodelingapplications.

TEMPER has been recognized as the benchmarkpropagation model by the Navy community and hasreceivedaccreditationfromseveralprograms.TEMPERhasalsobeenincorporatedintotheshipboardprototypeSEAWASP,providingcriticalpropagationinformationtoAegisAN/SPY-1performancemodelsonUSSAnzioandUSSCape St. George.

Future efforts include 3-D model development formoreaccuraterepresentationofdepolarizationandout-of-plane scattering, diffraction, and refraction. Also,improvement of TEMPER’s rough-surface modelingprocedure is anticipated through the studyof rigorousmomentmethodcalculations.

REFERENCES 1Symposium on Tropospheric Wave Propagation,NavalElectronicsLabo-

ratory(nowSSC-SD),Report173(Jul1949). 2Hitney, H. V., Richter, J. H., Pappert, R. A., Anderson, K. D.,

andBaumgartner,G.B.Jr.,“TroposphericRadioPropagationAssess-ment,”Proc. IEEE73(2),265–283(1985).

3Dockery,G.D.,“ModelingElectromagneticWavePropagationintheTroposphere Using the Parabolic Equation,” IEEE Trans. Antennas Propag.36(10),1464–1470(1988).

4Kuttler, J. R., and Dockery, G. D., “Theoretical Description of theParabolicApproximation/FourierSplit-stepMethodofRepresenting



ElectromagneticPropagationintheTroposphere,”Radio Sci.26(2),381–393(1991).

5Dockery,G.D.,andKuttler,J.R.,“AnImprovedImpedance-Bound-aryAlgorithmforFourierSplit-stepSolutionsoftheParabolicWaveEquation,”IEEE Trans. Antennas Propag.44(12),1592–1599(1996).

6Dockery, G. D., and Konstanzer, G. C., “Recent Advances in Pre-dictionofTroposphericPropagationUsingtheParabolicEquation,”Johns Hopkins APL Tech. Dig.8(4),404–412(1987).

7Fock,V.A.,Electromagnetic Diffraction and Propagation Problems,Per-gamonPress,Oxford(1965).

8Hardin, R. H., and Tappert, F. D., “Applications of the Split-stepFourierMethodtotheNumericalSolutionofNonlinearandVariableCoefficientWaveEquations,”SIAM Rev.15,423(1973).

9Ko,H.W.,Sari,J.W.,andSkura,J.P.,“AnomalousMicrowaveProp-agationThroughAtmosphericDucts,”Johns Hopkins APL Tech. Dig.4(1),12–26(1983).

10Hitney,H.V.,“HybridRayOpticsandParabolicEquationMethodsfor Radar Propagation Modeling,” in Proc. IEE Int. Conf. Radar,Brighton,U.K.,p.58(Oct1992).

11Barrios,A.E.,“ATerrainParabolicEquationModelforPropagationin the Troposphere,” IEEE Trans. Antennas Propag. 42(1), 90–98(1994).

12Ryan,F.J.,“RoughSurfaceForwardScatterintheParabolicEquationModel,”inProc. ACES 2000 Conf.,Monterrey,CA(Mar2000).

13Dockery,G.D.,“DevelopmentandUseofElectromagneticParabolicEquation Models for U.S. Navy Applications,” Johns Hopkins APL Tech. Dig.19(3),283–292(1998).

14Konstanzer, G. C., Rowland, J. R., Dockery, G. D., Neves, M. R.,Sylvester,J.J.,Slujtner,F.J.,andDarling,J.P.,“SEAWASP:Real-timeAssessmentofAN/SPY-1PerformanceBasedonInSituShip-board Measurements,” in Proc. Electromagnetic/Electro-Optics Predic-tion Requirements & Products Symp.,Monterey,CA,pp.87–96(June1997).

15Newkirk,M.H.,“RecentAdvancesintheTroposphericElectromag-netic Parabolic Equation Routine (TEMPER) Propagation Model,”inProc. 1997 Battlespace Atmospherics Conf. 2–4 December 1997,SanDiego,CA,pp.529–538(1998).

16Kuttler,J.R.,“DifferencesBetweentheNarrow-angleandWide-anglePropagatorsintheSplit-stepFourierSolutionoftheParabolicWaveEquation,”IEEE Trans. Antennas Propag.47(7),1131–1140(1999).

17Dockery,G.D.,“MethodforModellingSeaClutterinComplicatedPropagationEnvironments,”IEE Proc.137-F(2),73–79(1990).

18Reilly,J.P.,andLin,C.C.,Radar Terrain Effects Modeling for Shipboard Radar Applications,FS-95-060,JHU/APL,Laurel,MD(1995).

19Miller,A.R.,Brown,R.M.,andVegh,E.,“NewDerivationfortheRough-surfaceReflectionCoefficientandfortheDistributionofSea-waveElevations,”IEE Proc.131-H(2),114–116(1984).

20Wasky,R.P.,A Geometric Optics Model for Calculating the Field Strength of Electromagnetic Waves in the Presence of a Tropospheric Duct,Univer-sityofDaytonmaster’sthesis,Dayton,OH(Dec1977).

21Schmidt, R. O., “Multiple Emitter Location and Signal ParameterEstimation,”IEEE Trans. Antennas Propag.34,276–280(1986).

22Newkirk,M.H.,Dockery,G.D.,Konstanzer,G.C.,Kuttler, J.R.,and Giare, V., “Propagation Modeling Considerations AssociatedwithRepresentingLow-angleSurfaceClutter,”inProc. NATO-RTO Symp. on Low Grazing Angle Clutter: Its Characterization, Measurement and Application, RTO-MP-60,pp.17-1–17-11(Oct2000).

23Donohue,D.J.,andKuttler,J.R.,“PropagationModelingOverTer-rain Using the Parabolic Wave Equation,” IEEE Trans. Antennas Propag.48(2),260–277(2000).

24Donohue,D.J.,andKuttler,J.R.,“ModelingRadarPropagationOverTerrain,”Johns Hopkins APL Tech. Dig.18(2),279–287(1997).

25Beilis,A.,andTappert,F.D.,“CoupledModeAnalysisofMultipleRough Surface Scattering,” J. Acoust. Soc. Am. 66(3), 811–826(1979).

26Kuttler, J. R., “The Forward, Backward, and Central DifferenceAlgorithmsforImplementingMixedFourierTransformstoImproveTEMPER,” enclosure to Technical Letter TL-00-272, JHU/APL,Laurel,MD(2000).

27Dockery,G.D.,Description and Validation of the Electromagnetic Par-abolic Equation Propagation Model (EMPE), FS-87-152, JHU/APL,Laurel,MD(1987).

28Paulus, R., Proceedings of the Electronmagnetic Propagation Workshop,NRaDTechnicalDocument2891(Dec1995).

ACKNOWLEDGMENTS: TEMPER model development has been supportedby the Aegis Shipbuilding Program Office, PMS-400B3D. J. R. Kuttlerprovidednumeroushelpfulcommentsandsuggestionsduringthepreparationofthisarticle.

THE AUTHORS

MICHAELH.NEWKIRKisamemberoftheAPLSeniorProfessionalStaff.HereceivedB.S.,M.S.,andPh.D.degrees,allinelectricalengineeringfromVirginiaTech,in1988,1990,and1994,respectively.Dr.Newkirkhelda1995–1996post-doctoral fellowship with the U.S. Army Research Laboratory in Adelphi, MD,where he performed basic research and design, fabrication, and data analysis formillimeter-waveradiometricsystems.HejoinedAPLin1996andhassincebeeninvolved inpropagationmodeling,environmentalcharacterization, radar systemsperformanceanalysis,andfieldtestplanningandexecution.Heisthetechnicalleadandco-developeroftheTEMPERpropagationmodel.Dr.NewkirkisamemberofIEEEandURSI.Hise-mailaddressismichael.newkirk@jhuapl.edu.



JONATHANZ.GEHMANgraduatedmagnacumlaudefromCornellUniversityin1999withaB.S.inappliedandengineeringphysics,andiscurrentlypursuinganM.S.inappliedphysicsatTheJohnsHopkinsUniversity.SincejoiningAPL’sTheaterSystemsDevelopmentGroupin1999,Mr.Gehmanhasfocusedonpropa-gationandcluttermodelingwithapplicationstoshipself-defense.HehasplayedamajorroleindevelopingthelatestversionoftheTEMPERpropagationmodel.Hise-mailaddressisjonathan.gehman@jhuapl.edu.

G.DANIELDOCKERYreceivedaB.S.inphysicsin1979andanM.S.inelectricalengineeringin1983,bothfromVirginiaPolytechnicInstituteandStateUniversity.HealsotookgraduatecoursesinphysicsandengineeringattheUniversityofMary-land.Mr.Dockery joinedAPL in1983andhasworked inphasedarrayantennadesign,analysisandmodelingofelectromagneticpropagationinthetroposphere,and the associated performance impacts on Navy radar and communication sys-tems.Heisaco-developerofadvancedparabolicwaveequationpropagationmodelsandhasperformedresearchinscattering,radarclutter,andatmosphericrefractiv-ityeffects, includingextensivefield testexperience.NavyprogramssupportedbyMr.DockeryincludeAegis,CEC,multifunctionradar,andNavyAreaandNavyTheaterWideTBMD.Mr.DockeryisamemberoftheAPLPrincipalProfessionalStaffandSupervisorofADSD’sTheaterSystemsDevelopmentGroup.Hise-mailaddressisdan.dockery@jhuapl.edu.

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