1.Examplesofprofileretrievals

IntroductionThecurrentDPR-operationalalgorithmadoptsanoptimizationapproachthatisbasedonarelationshipbetweenrainrate(R)andmass-weighteddiameter(Dm),i.e.,R-Dmrelation.ConstraintoftheR-DmrelationleavesgammaDSDhavingonlyonefreeparameter,suchasDm,ifitsshapefactoriseitherfixedorexpressedasafunctionofDm.Thus,oneisabletorelatetheradarreflectivitytoDm.AnadjustmentfactorisusedtomodifyR-Dmrelationforeachverticalhydrometeorprofile.Asearchfortheadjustmentfactorisconductedbyminimizingdifferencesbetweensimulatedandmeasuredradarreflectivitiesaswellasthepath integral attenuation (PIA) in the case of a single wavelength and differential PIA(δPIA)fordual-wavelengths.Oncetheadjustmentfactor isfound,theDSDandRcanbeuniquelyderivedalongeachprofile.Anobviousadvantageofthisoptimalapproachistoavoid retrieval uncertainties arising from the double solutions such as those that occurfromtheuseof theDFR. Itsperformancedependsonanumberof factorsthatincludethemodel assumptions and the degree of uniformity of theDSD along the profiles. Anevaluation of the algorithm performance is important in assessing the strengths andweaknessesofthealgorithmandingaininginsightintothewaystoimproveit.Simultaneouscomparisonsofco-locatedPRandDPRestimateswiththesimilarquantitiesderivedfromthegroundmeasurementsprovidedirectchecksofthePR/DPRalgorithms.This is in fact a very important task for the validation of the DPR products. However,becauseofdifferentbeamwidths,scanninggeometriesandpossibletemporaloffsets,thespace-andground-radarscatteringvolumescannotbeperfectlymatched.Inaddition,theissue of non-uniform beam filling (NUBF) further complicates the algorithm evaluation.While direct comparisons between space- and ground-based sensors remain essential,theydonotfullymeettheneedforalgorithmtestingand improvement.Tovalidatethealgorithmprinciplesandtheirassumptions,aphysicalandrealisticframework/test-bedisemployedtoenableanaccurateassessmentoftheperformanceofthealgorithms.Toachievethis,measuredtime-seriesDSDdataareusedtoconstructverticalrainprofiles.With the known profile of particle size distribution, the true andmeasured reflectivityfactorsaswellaspathintegralattenuation(PIA)canbecomputedfromforwardscatteringmodels.TheKu-andKa-bandmeasuredreflectivityprofilescanthenbeusedasinputtothe retrieval algorithms. The degree to which the radar estimates agree with the truevalues,whicharederiveddirectlyfromtheassumedDSDprofiles,constitutesameasureoftheretrievalaccuracy.Thebasicapproachcanalsobeusedtoevaluatetheimpactofdifferentmodelassumptionsandvariousconstraintsadoptedintheretrievalalgorithms.

DPRAlgorithms

AlgorithmEvaluation

Fig.1 Comparisonsofradarreflectivities,DSDandrainfall rateprofilesbetweentheDPR-estimated(red)andtheirtruevalues(black).Theresultsfrom4casesthatcorrespondtolight(top-leftsetoftheplots),moderate(top-right),heavy(bottom-left)andhigh-degreenon-uniform(bottom-right)rainareprovided.ForreferencealsogivenarethebestsolutionswithrespecttoDmandR inthesolutionspace inwhichthesolutionsarearrangedasafunctionof log10(εk),k=1,2,…,K. Inperfectconditionsorunderstrongconditionstheestimatedsolutionscoincidewiththebestsolutions.Weakconstraintsleadtodeparturesoftheestimatedfromthebestsolutions.Thedifferencesbetweenthebestandtrutharelargelyduetoimperfectionofthemodelsassumed,suchasverticallyconstantR-DmrelationandDSDparameterizations.

DmcoulduniquelybesolvedfromEq.(4).OnceDmisdetermined,RandNwareobtainedfromEq.(1)and(3),respectively.FromderivedDSDparametersZ(λ)andk(λ)arethencomputed.εischosensothat

(1)

(2)

(3)

(4)

FromR-Dmrelationexpressedas

Then,wehave

Substituting(3)intoaboveequation,weobtain

FromLook-uptables

Andalso,

2.Statisticalcomparisons

Fig.2 ComparisonsofDm (leftpanel) andR (rightpanel)estimatedby theDPRdual-wavelength algorithm with their true values at the gates of rain top andsurface as the forward recursive approaches are applied to non-uniform DSDprofiles.ThePDFsobtainedfromthedatapointsofestimatedandtruevaluesareshownintheleftcolumnofeachpanelwhilethemeans(thickbluecurves)andthe 2-time standard deviations (thin blue vertical bars) derived from the samedatapointsaredisplayedintherightcolumn.One-to-onerelations(blackandredlines)arealsoplottedforreferences.

Fig.3 PDFs of Dm (left column) and R(right column) estimated by the DPRdual-wavelength algorithm with thetrue rain rates at the gatesof rain top(top row) and surface (bottom row) asthebackwardrecursiveapproachesareappliedtonon-uniformDSDprofiles.

AlgorithmEvaluation(Cont’d)3.Retrievalfromvariousdegreesofnon-uniformityofhydrometeorprofiles

Fig.4 ComparisonsofDm(leftpanel)andR(rightpanel)estimatedbytheDPRdual-wavelengthalgorithmwithtruthatthegatesofraintop (top row) and surface (bottom row) as the forward recursive approaches are applied to the fully-correlated (uniform), partially-correlated(non-uniform)andtotally-uncorrelated(extremelynon-uniform)verticalDSDprofiles.Themeans(thickbluecurves)andthe2-time square root of error variances (thin blue vertical bars) are computed from the data points of estimated and true valueswithinintervalsbetweenDm(R)andDm+ΔDm(R+ΔR).AnunbiasedstatisticalδPIAmodelwiththestandarddeviationof0.8dBisassumed.One-to-onerelations(redlines)arealsoplottedforreferences.

Fig.5ComparisonsofRestimatedbytheDPRdual-wavelengthalgorithm with DPR-default (left), Parsivel-DSD-derived(middle) and 2DVD-DSD-derived (right) R-Dm relations beingused with true R as the forward recursive approaches areappliedtothenon-uniformverticalDSDprofiles.

4.RetrievalfromdifferentR-Dmrelations 5.Rolesofp1,p2andp3toretrieval

Fig.6 PDFs of R estimated by the DPR dual-wavelengthalgorithm and true rain rates as the algorithms employ onlysingle individual constraints in selection of ε, such as p1 (leftcolumn),p2(centercolumn)andp3(rightcolumn).

6.Comparisonofsingle-anddual-wavelengthretrieval

Fig.7 ComparisonsoftheDPRdual-wavelengthandsingle-wavelengthperformances inestimatingDm(left)&R(right)astheDPR-likeforwardrecursiveapproachesareappliedtothenon-uniformverticalDSDprofiles.Themeans(thickbluecurves)andthe2-timesquarerootoferrorvariances(thinblueverticalbars)arecomputedfromthedatapoints.

StudiesonSingle-andDual-WavelengthDPRRetrievals:AlgorithmEvaluation Liang Liao

GESTAR/MSU, Greenbelt, MD Robert Meneghini

NASA/GSFC, Greenbelt, MD Ali Tokay

UMBC/JCET, Greenbelt, MD Hyokyung Kim

GESTAR/MSU, Greenbelt, MD

Reference:

Seto,S.,T.IguchiandT.Oki,2013:ThebasicperformanceofaprecipitationretrievalalgorithmfortheGlobalPrecipitationMeasurementmission’ssingle/dualfrequencyradarmeasurements.IEEETrans.Geosci.RemoteSens.,51,5239–5251.Seto,S.,andT.Iguchi,2015:IntercomparisonofattenuationcorrectionmethodsfortheGPMdual-frequencyprecipitationradar.J.Atmos.OceanicTechnol.,32,915-926.