外文翻译Word格式文档下载.docx
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(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