International Journal of Applied Earth Observation and Geoinformation国际应用地球观测和地理信息Word文档格式.docx
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International Journal of Applied Earth Observation and Geoinformation国际应用地球观测和地理信息Word文档格式.docx
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Abstract:
Downscalinghasanimportantroletoplayinremotesensing.Itallowspredictionatafinerspatialresolutionthanthatoftheinputimagery,basedoneither(i)assumptionsorpriorknowledgeaboutthecharacterofthetargetspatialvariationcoupledwithspatialoptimisation,(ii)spatialpredictionthroughinterpolationor(iii)directinformationontherelationbetweenspatialresolutionsintheformofaregressionmodel.Twoclassesofgoalcanbedistinguishedbasedonwhethercontinuaarepredicted(throughdownscalingorareatopointprediction)orcategoriesarepredicted(superresolutionmapping),inbothcasesfromcontinuousinputdata.Thispaperreviewsarangeoftechniquesforbothgoals,focusingonareatopointkriginganddownscalingcokrigingintheformercaseandspatialoptimisationtechniquesandmultiplepointgeostatisticsinthelattercase.Severalissuesarediscussedincludingtheinformationcontentoftrainingdata,includingtrainingimages,theneedformodelbaseduncertaintyinformationtoaccompanydownscalingpredictions,andthefundamentallimitsontherepresentativenessofdownscalingpredictions.Thepaperendswithalooktowardsthegrandchallengeofdownscalinginthecontextoftimeseriesimagestacks.Thechallengehereistousealltheavailableinformationtoproduceadownscaledseriesofimagesthatiscoherentbetweenimagesand,thus,whichhelpstodistinguishrealchanges(signal)fromnoise.
1.Introduction
Downscalingreferstoanincreaseinspatialresolution.Conversely,upscalingreferstoadecreaseorcoarseningofspatialresolution(AtkinsonandTate,2000).Bothgoalsarerequiredforcomparisonandintegrationofdisparatedatasetsandforcalibrationandvalidationofmodelsinarangeofapplications.Inthecontextofremotesensing,downscalingreferstoadecreaseinthepixelsizeofremotelysensedimages.Thistask,whichamountstoanimplicitassumptionthattheinformationcontentofthedownscaledimagerywillincrease,hasbeenattemptedthroughavarietyofdifferentapproachesandtechniques.Theseapproachesarereviewedinthispaper.Withintheoverarchinggoalofdownscaling,severalsubgoalscanbedefined.Theseincludeareatopointprediction,whichinvolvespredictingthesamecontinuousvariableasisinputtothedownscalingprocess,butwithafinerspatialresolutionthantheinput,andsuperresolutionmapping,atermcoinedtodescribetheprocessofdownscalingwhilstatthesametimetransformingtheinputvariabletoacategoricalvariable,usuallyrepresentinglandcoverclass.Bothofthesemainsubgoalsaredescribedinthispaper.Beforereviewingthetechniquesusedinthesetwobroadsubgoals,therationaleandjustificationfordownscalingareconsideredinthenextsection.
1.1.Whyscaling?
Scalingisimportantinarangeoffields.Inecologyandbiogeographyscalingiscentraltosomeofthecoretheoriessuchasislandbiogeography(MacArthurandWilson,1967).Moreover,coreconceptssuchaspatches,ecosystems,populationsandbiomesareallscaledependentdefinitions.Ecologistsareparticularlyinterestedtounderstandhowbiodiversityscalesbetweenanddiversity.Inclimatescience,downscalinghasbecomecommonplaceintheproductionofregionalscaleclimatecirculationmodelsfromglobalcirculationmodels(GCMs)(e.g.,Huth,2002).Thetechniquesusedforthisimportantendeavorarenotalwaysthemostsophisticated,withseriousimplicationsforthequalityoftheresults.Forexample,acommonapproachtoforecastingfuturefineresolutionscenariosistotakeapresentdayspatiallydistributedscenario(e.g.,rainfall),averageittoalargerGCMcell,andadjustthedistributedvaluesbyafactorequaltothedifferencebetweenthepresentdayaverageandsomeclimateforecastforthesameGCMcell.However,moresophisticatedapproachesarebeingdeveloped(Deidda,2000).
Scalinghasalonghistoryofimportanceingeomorphologyandhydrology.Forexample,Thorns(1973)examinedthescaledifferencesinrillsandgullies.Inbothgeomorphologyandhydrology,downscalingisoftenusedtopreparedataforinputtoprocessmodels.Goodchild(2011)providesareviewofscaleissuesinGISwithinthecontextofgeomorphology,focusingonbothmeasurementconceptsandprocessrepresentations.Downscalinghasalsofoundapplicationinpopulationmapping.Forexample,severalregressiontypemodelshavebeendevelopedtodownscalethepopulationfromcensusenumerationareastogridsfortheEuropeanUnion(GallegoandBamps,2008)andglobally(Hayetal.,
2005;
Balketal.,2006;
Tatemetal.,2011).Distributingpopulationongridsfacilitatesintegrationandcomparisonwithothergriddeddatasets,althoughuncertaintyinthepredictionsremainsaconcern(Martinetal.,2011).Populationdownscalingapproachesaredescribedfurtherbelowinrelationtothemodifiablearealunitproblem(MAUP).
Scalinghasalsogainedprominenceinthefieldofremotesensing.Manyexamplesnowexistinwhichdataareupscaled,forexample,grounddataareaveragedtoprovideamorecoherentmatchwithimagepixels(e.g.,Atkinsonetal.,2000).Similarly,examplesnowexistinwhichdataaredownscaled.Thebenefitsofdownscalingareexplainedbelowinrelationtoareatopointpredictionandsuperresolutionmapping.
1.2.Measurementconcepts
Itisusefultodistinguishbetweenprocessesandstates.Processesarerepresentedbyprocessmodels,whichinageographicalcontextareusuallyspatiallydistributedtosomeextent.Suchprocessmodelsarescaledependentintheirconstruction,thatis,theyaredefinedataparticularresolution.Moreover,akeyconcernintestingmodelsforapplicationtonewsitesistoensure“gridindependence”,thatis,thattheresultsofthemodelareindependentofresolutionwithinadefinedrange(AtkinsonandTate,2000).Ontheotherhand,statesmaybeinvestigateddirectlythroughmeasurementprocesses.Withinthismeasurementprocess,twoaspectsareimportant.Thefirstissamplingandthesecondismeasurementuncertainty.Thesamplingprocessisdefinedbythefollowingparameters:
thesupport(thespaceoverwhicheachobservationisdefined)andthespatialextent.Inturn,thespatialextentcanbedecomposedintothesamplingscheme(e.g.,random,stratified),thenumberofobservationsandthedensityofthesample(AtkinsonandTate,2000).Measurementerrorisincurredatthescaleoftheobservationasfollows:
公式1
where,Zˆu(x)istheobservation(theonlyinformationthatwecan
gainaboutreality),Z•(y)istheunderlyingprocessdefinedonapointsupport,thelefthandtermontherighthandsideoftheequationistheintegraloftheunderlyingprocessoverthespaceofobservationandεu(x)isameasurementerrorterm.
Thesupportistheparameterofinterestinrelationtodownscal
ing.Ingeostatistics,thesupporthasbeenoflongstandinginterest.Forexample,Clark(1977)andJournelandHuijbregts(1978)developedsomeoftheearliestmodelsforregularising(increasingthesupportof)thesemivariogram,afunctiondescribingthecharacterofspatialvariation(Atkinson,1999).Thisgeostatistical“operation”ofregularisation(alsoknownasconvolutioninthefrequencydomainliterature),allowsonetochangethesupport(ormeasurementscale)ofthesemivariogramfunctionwithoutrequiringnewdataonthenewsupport.Theimportanceofregularisationinthecontextofremotesensing,andinrelationtomeasurementerror,wasexploredbyAtkinson(1993,1997a)andAtkinsonetal.(1996).Issuesofscaleinremotesensinghavealsoledresearcherstoattempttodefineanoptimalpixelsize(WoodcockandStrahler,1987;
Atkinson,1997b;
AtkinsonandCurran,1995,1997;
CurranandAtkinson,1999),includingforharmonisationoftimeseriesimagery(Tarnavskyetal.,2008).
Thesupporthasalsobeenthesubjectofmuchresearchonthesocalledmodifiablearealunitproblem(MAUP)(Openshaw,1984)whichhasconfoundedresearchersusingcensusdataonirregularcensusunitssuchasWardsuntilrecently(Liuetal.,2008;
Yooetal.,
2010).TheMAUPcomprisestwo“problems”;
thezonationproblemandtheaggregationproblem,theformer(despitetheconfusingname)essentiallybeingachangeofsupportproblem.Recentdevelopmentsingeostatisticshaveprovidedaprincipledandefficientsolutiontothisproblem.Thesupportisalsogainingininterestinrelationtodatafusion.Imagesandotherdataarenowprovidedfrequentlyinmassivevolumes,atoftenlowcostfromheterogeneoussources.Forexample,remotelysensedimagesmaybeprovidedatdifferentviewangles,fromdifferentpositions,fromdifferentsensorswithdifferentspatialresolutionsetc.Datafusionapproachesthatinferanunderlyingmodelfromthesedifferentsourcesofdatadependonknowledgeofthemeasurementprocessandcriticallytheeffectofthesupport.
Inmanyways,itisnotsurprisingthatthesupporthasbecomethefocusofattentioninremotesensing.Satelliteandairborneremotesensingprovidedataintheformofanimage,usuallyinseveralwavebandsoftheelectromagneticspectrum.SuchimagesprovidecompletecoverageofanareaonthesurfaceoftheEarth,synoptically,ataparticularspatialresolution.Thus,giventhatthesupportisusuallyapproximatedbythepixelsize,thesamplingprocessisdefinedbythepixelsizeandthenumberofpixelsinxandyonly.Inshort,forremotelysensedimages,thesupporthasaspecialsignificanceindefiningtheentiresamplingstrategy(CurranandAtkinson,1999;
AtkinsonandTate,2000).
Th
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