外文翻译.docx

外文翻译.docx

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外文翻译

外文资料与中文翻译

MetricsofscaleinremotesensingandGIS

MichaelFGoodchild

（NationalCenterforGeographicInformationandAnalysis,DepartmentofGeography,UniversityofCalifornia,SantaBarbara）

ABSTRACT:

Thetermscalehasmanymeanings,someofwhichsurvivethetransitionfromanalogtodigitalrepresentationsofinformationbetterthanothers.Specifically,theprimarymetricofscaleintraditionalcartography,therepresentativefraction,hasnowell-definedmeaningfordigitaldata.Spatialextentandspatialresolutionarebothmeaningfulfordigitaldata,andtheirratio,symbolizedasUS,isdimensionless.USappearsconfinedinpracticetoanarrowrange.TheimplicationsofthisobservationareexploredinthecontextofDigitalEarth,avisionforanintegratedgeographicinformationsystem.Itisshownthatdespitetheverylargedatavolumespotentiallyinvolved,DigitalEarthisneverthelesstechnicallyfeasiblewithtoday’stechnology.

KEYWORDS:

Scale,GeographicInformationSystem,RemoteSensing,SpatialResolution

INTRODUCTION:

ScaleisaheavilyoverloadedterminEnglish,withabundantdefinitionsattributabletomanydifferentandoftenindependentroots,suchthatmeaningisstronglydependentoncontext.Itsmeaningsin“thescalesofjustice”or“scalesoveroneseyes”havelittleconnectiontoeachother,ortoitsmeaninginadiscussionofremotesensingandGIS.Butmeaningisoftenambiguouseveninthatlattercontext.Forexample,scaletoacartographermostlikelyrelatestotherepresentativefraction,orthescalingratiobetweentherealworldandamaprepresentationonaflat,two-dimensionalsurfacesuchaspaper,whereasscaletoanenvironmentalscientistlikelyrelateseithertospatialresolution（therepresentation’slevelofspatialdetail）ortospatialextent（therepresentation’sspatialcoverage）.Asaresult,asimplephraselike“largescale”cansendquitethewrongmessagewhencommunitiesanddisciplinesinteract-toacartographeritimpliesfinedetail,whereastoanenvironmentalscientistitimpliescoarsedetail.Acomputerscientistmightsaythatinthisrespectthetwodisciplineswerenotinteroperable.

InthispaperIexaminethecurrentmeaningsofscale,withparticularreferencetothedigitalworld,andthemetricsassociatedwitheachmeaning.Theconcernthroughoutiswithspatialmeanings,althoughtemporalandspectralmeaningsarealsoimportant.Isuggestthatcertainmetricssurvivethetransitiontodigitaltechnologybetterthanothers.

Themainpurposeofthispaperistoproposeadimensionlessratiooftwosuchmetricsthatappearstohaveinterestingandusefulproperties.IshowhowthisratioisrelevanttoaspecificvisionforthefutureofgeographicinformationtechnologiestermedDigitalEarth.Finally,Idiscusshowscalemightbedefinedinwaysthatareaccessibletoamuchwiderrangeofusersthancartographersandenvironmentalscientists.

FOURMEANINGSOFSCALELEVELOFSPATIALDETAIL

REPRESENTATIVEFRACTION

Apapermapisananalogrepresentationofgeographicvariation,ratherthanadigitalrepresentation.AllfeaturesontheEarth’ssurfacearescaledusinganapproximatelyuniformratioknownastherepresentativefraction（itisimpossibletouseaperfectlyuniformratiobecauseofthecurvatureoftheEarth’ssurface）.Thepoweroftherepresentativefractionstemsfromthemanydifferentpropertiesthatarerelatedtoitinmappingpractice.First,papermapsimposeaneffectivelimitonthepositionalaccuracyoffeatures,becauseofinstabilityinthematerialusedtomakemaps,limitedabilitytocontrolthelocationofthepenasthemapisdrawn,andmanyotherpracticalconsiderations.Becausepositionalaccuracyonthemapislimited,effectivepositionalaccuracyonthegroundisdeterminedbytherepresentativefraction.Atypical（andcomparativelygenerous）mapaccuracystandardis0.5mm,andthuspositionalaccuracyis0.5mmdividedbytherepresentativefraction（eg,12.5mforamapat1:

25,000）.Second,practicallimitsonthewidthsoflinesandthesizesofsymbolscreateasimilarlinkbetweenspatialresolutionandrepresentativefraction:

itisdifficulttoshowfeaturesmuchlessthan0.5mmacrosswithadequateclarity.Finally,representativefractionservesasasurrogateforthefeaturesdepictedonmaps,inpartbecauseofthislimittospatialresolution,andinpartbecauseoftheformalspecificationsadoptedbymappingagencies,thatareinturnrelatedtospatialresolution.Insummary,representativefractioncharacterizesmanyimportantpropertiesofpapermaps.

Inthedigitalworldthesemultipleassociationsarenotnecessarilylinked.Featurescanberepresentedaspointsorlines,sothephysicallimitationstotheminimumsizesofsymbolsthatarecharacteristicofpapermapsnolongerapply.Forexample,adatabasemaycontainsomefeaturesassociatedwith1:

25,000mapspecifications,butnotall;andmayincluderepresentationsoffeaturessmallerthan12.5montheground.Positionalaccuracyisalsonolongernecessarilytiedtorepresentativefraction,sincepointscanbelocatedtoanyprecision,uptothelimitsimposedbyinternalrepresentationsofnumbers（eg,singleprecisionislimitedtoroughly7significantdigits,doubleprecisionto15）.Thusthethreepropertiesthatwereconvenientlysummarizedbyrepresentativefraction-positionalaccuracy,spatialresolution,andfeaturecontent-arenowpotentiallyindependent.

Unfortunatelythishasledtoacomplexsystemofconventionsinanefforttopreserverepresentativefractionasauniversaldefiningcharacteristicofdigitaldatabases.Whensuchdatabasesarecreateddirectlyfrompapermaps,bydigitizingorscanning,itispossibleforallthreepropertiestoremaincorrelated.Butinothercasestherepresentativefractioncitedforadigitaldatabaseistheoneimpliedbyitspositionalaccuracy（eg,adatabasehasrepresentativefraction1:

12,000becauseitspositionalaccuracyis6m）;andinothercasesitisthefeaturecontentorspatialresolutionthatdefinestheconventionalrepresentativefraction（eg,adatabasehasrepresentativefraction1:

12,000becausefeaturesatleast6macrossareincluded）.Moreover,theseconventionsaretypicallynotunderstoodbynoviceusers-thegeneralpublic,orchildren-whomayconsequentlybeveryconfusedbytheuseofafractiontocharacterizespatialdata,despiteitsfamiliaritytospecialists.

SPATIALEXTENT

Thetermscaleisoftenusedtorefertotheextentorscopeofastudyorproject,andspatialextentisanobviousmetric.Itcanbedefinedinareameasure,butforthepurposesofthisdiscussionalengthmeasureispreferred,andthesymbolLwillbeused.Forasquareprojectareaitcanbesettothewidthofthearea,butforrectangularoroddlyshapedprojectareasthesquarerootofareaprovidesaconvenientmetric.Spatialextentdefinesthetotalamountofinformationrelevanttoaproject,whichriseswiththesquareofalengthmeasure.

PROCESSSCALE

Thetermprocessrefersheretoacomputationalmodelorrepresentationofalandscape-modifyingprocess,suchaserosionorrunoff.Fromacomputationalperspective,aprocessisatransformationthattakesalandscapefromitsexistingstatetosomenewstate,andinthissenseprocessesareasubsetoftheentirerangeoftransformationsthatcanbeappliedtospatialdata.

Defineaprocessasamappingb（x,

）=

（a（x,

））whereaisavectorofinputfields,bisavectorofoutputfields,

isafunction,tistime,

islaterintimethan

andxdenoteslocation.Processesvaryaccordingtohowtheymodifythespatialcharacteristicsoftheirinputs,andthesearebestexpressedintermsofcontributionstothespatialspectrum.Forexample,someprocessesdetermineb（x,,

）basedonlyontheinputsatthesamelocationa（x,

）,andthushaveminimaleffectonspatialspectra.Otherprocessesproduceoutputsthataresmootherthantheirinputs,throughprocessesofaveragingorconvolution,andthusactaslow-passfilters.Lesscommonly,processesproduceoutputsthataremoreruggedthantheirinputs,bysharpeningratherthansmoothinggradients,andthusactashigh-passfilters.

Thescaleofaprocesscanbedefinedbyexaminingtheeffectsofspectralcomponentsonoutputs.Ifsomewavelengthsexistssuchthatcomponentswithwavelengthsshorterthanshavenegligibleinfluenceonoutputs,thentheprocessissaidtohaveascaleofs.ItfollowsthatifsislessthanthespatialresolutionSoftheinputdata,theprocesswillnotbeaccuratelymodeled.

Whiletheseconclusionshavebeenexpressedintermsofspectra,itisalsopossibletointerpretthemintermsofvariogramsandcorrelograms.Alow-passfilterreducesvarianceovershortdistances,relativetovarianceoverlongdistances.Thustheshort-distancepartofthevariogramislowered,andtheshort-distancepartofthecorrelogramisincreased.Similarlyahigh-passfilterincreasesvarianceovershortdistancesrelativetovarianceoverlongdistances.

L/SRATIO

Whilescalingratiosmakesenseforanalogrepresentations,therepresentativefractionisclearlyproblematicfordigitalrepresentations.Butspatialresolutionandspatialextentbothappeartobemeaningfulinbothanaloganddigitalcontexts,despitetheproblemswithspatialresolutionforvectordata.BothSandLhavedimensionsoflength,sotheirratioisdimensionless.Dimensionlessratiosoftenplayafundamentalroleinscience（eg,theReynoldsnumberinhydrodynamics）,soitispossiblethatL/Smightplayafundamentalroleingeographicinformationscience.InthissectionIexaminesomeinstancesoftheL/Sratio,andpossibleinterpretationsthatprovidesupportforthisspeculatio