EasyKrig30的说明文档kriging插值.docx

EasyKrig30的说明文档kriging插值.docx

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EasyKrig30的说明文档kriging插值

TheGLOBECKrigingSoftwarePackage–EasyKrig3.0July15,2004

Copyright（c）1998,2001,2004propertyofDezhangChuandWoodsHoleOceanographicInstitution.AllRightsReserved.

ThekrigingsoftwaredescribedinthisdocumentwasdevelopedbyDezhangChuwithfundingfromtheNationalScienceFoundationthroughtheU.S.GLOBECGeorgesBankProject'sProgramServiceandDataManagementOffice.ItwasoriginallyinspiredbyaMATLABtoolboxdevelopedbyYvesGrattonandCarolineLafleur（INRS-Océanologie,Rimouski,Qc,Canada）,andJeffRunge（InstitutMaurice-Lamontagne,nowwithUniversityofNewHampshire）.Thissoftwaremaybereproducedfornoncommercialpurposesonly.

Thisprogramisdistributedinthehopethatitwillbeuseful,butWITHOUTANYWARRANTY.ContactDr.Chuatdchuwhoi.eduwithenhancementsorsuggestionsforchanges.

TableofContents:

1.Introduction

1.1GeneralInformation

1.1.1Aboutkriging

1.1.2Briefdescriptionsofeasy_krig3.0

1.2Gettingstarted

1.2.1Operatingsystems

1.2.2Down-loadtheprogram

1.2.3Quickstart

2.DataProcessingStages

2.1DataPreparation

2.2Semi-variogram

2.3Kriging

2.4Visualization

2.5SavingKrigingResults

3.Examples

3.1Example1:

AnAerialImageofZooplanktonAbundanceData

3.2Example2:

AVerticalSectionofSalinityData–AnAnisotropicDataset

3.3Example3:

BatchProcessofPressure（dbar）atDifferentPotentialDensityLayers

3.4Example4:

3-DimensionalTemperatureData

4.References

1.Introduction

1.1GeneralInformation

1.1.1Aboutkriging

Thissectionprovidesabrieftheoreticalbackgroundforkriging.Iftheuser（s）isnotinterestedinthetheoreticalbackground,he/shecanskipthissectionandgotosection1.1.2directly.

KrigingisatechniquethatprovidestheBestLinearUnbiasedEstimatoroftheunknownfields（JournelandHuijbregts,1978;Kitanidis,1997）.ItisalocalestimatorthatcanprovidetheinterpolationandextrapolationoftheoriginallysparselysampleddatathatareassumedtobereasonablycharacterizedbytheIntrinsicStatisticalModel（ISM）.AnISMdoesnotrequirethequantityofinteresttobestationary,i.e.itsmeanandstandarddeviationareindependentofposition,butratherthatitscovariancefunctiondependsontheseparationoftwodatapointsonly,i.e.

E[（z（x）–m）（z（x’）–m）]=C（h）,

（1）

wheremisthemeanofz（x）andC（h）isthecovariancefunctionwithlagh,withhbeingthedistancebetweentwosamplesxandx’:

h=||x–x’||=

（2）

AnotherwaytocharacterizeanISMistouseasemi-variogram,

=0.5*E[（z（x）–z（x’））2].（3）

Therelationbetweenthecovariancefunctionandthesemi-variogramis

=C（0）–C（h）.（4）

Thekrigingmethodistofindalocalestimateofthequantityataspecifiedlocation,

.ThisestimateisaweightedaverageoftheNadjacentobservations:

（5）

Theweightingcoefficients

canbedeterminedbasedontheminimumestimationvariancecriterion:

（6）

subjecttothenormalizationcondition

.（7）

Notethatwedon’tknowtheexactvalueat

butwearetryingtofindapredictedvaluethatprovidestheminimumestimationvariance.Theresultantkrigingequationcanbeexpressedas

（8）

whereistheLagrangiancoefficient.Inaddition,wehavereplacedthecovariancefunctionwiththenormalizedcovariancefunction[normalizedbyC（0）].Equivalently,byusingEq.（4）,thekrigingequationcanalsobeexpressedintermsofthesemi-variogramas

（9）

wherewehaveusednormalizedsemi-variogram,i.e.,semi-variogramnormalizedbyC（0）aswedidinderivingEq.（8）.

Havingobtainedtheweightingcoefficients（

）andtheLagrangiancoefficient（

）bysolvingeitherEq.（8）OREq.（9）,thekrigingvariance,Eq.（6）,canbeexpressedas:

.（10）

TheaboveequationsarethebasisoftheEasykrigsoftwarepackage.

1.1.2BriefdescriptionofEasyKrig3.0

TheEasyKrigprogrampackageusesaGraphicalUserInterface（GUI）.ItrequiresMATLAB5.3orhigherwithorwithoutoptimizationtoolbox（seesection2.2）andconsistsoffivecomponents,orprocessingstages:

（1）datapreparation,

（2）variogramcomputation,（3）kriging,（4）visualizationand（5）savingresults.Itallowstheusertoprocessanisotropicdata,selectanappropriatemodelfromalistofvariogrammodels,andachoiceofkrigingmethods,aswellasassociatedkrigingparameters,whicharealsocommonfeaturesoftheotherexistingsoftwarepackages.Oneofthemajoradvantagesofthisprogrampackageisthattheprogramminimizestheusers'requirementsto"guess"theinitialparametersandautomaticallygeneratestherequireddefaultparameters.Inaddition,becauseitusesaGUI,themodificationsfromtheinitialparametersettingscanbeeasilyperformed.Anotherfeatureofthisprogrampackageisthatithasabuilt-inon-linehelplibrarythatallowstheusertoobtainthedescriptionsoftheuseofparametersandoperationoptionseasily.

ThecurrentEasyKrig3.0istheupgradedversionofthepreviousversion（EasyKrig2.1）.Inadditiontohavingcorrectedsomeprogrammingerrorsinthepreviousversion（mostlyGUIrelatederrors）,therearemanynewfeaturesincludedinthecurrentversion:

∙MatlabVersion6.xand7.0（testedunderWindows）compatible

∙Capableofhandling3-Ddata

∙Enhancedbatchfileprocessingcapability

∙Moreflexibleinloadinginputdataandsavingoutputdata

∙Capableofhandlingthecustomizedgridfile

∙Moreexampleswithdetailedstepbystepinstructionsareprovidedtoallowuser（s）tomasterthefunctionalityofthesoftwarepackagemorequicklyandeasily.

AlthoughthissoftwarepackagelackssomeabilitiessuchasCo-kriging,itdoesprovideaconvenienttoolforgeostatisticalapplicationsandshouldalsohelpscientistsfromotherfields.

ForpeoplewhodonotwanttouseGUIbutonlyinterestedinfunction-basedm-filescangotoadifferentwebsitethatprovidesafunction-basedm-fileKrigingpackage（globec.whoi.edu/software/kriging/V3/intro_v3.html）developedbyCarolineLafleurandYvesGratton,INRS-Océanologie,UniversitduQubecRimouski.

1.2GettingStarted

1.2.1Operatingsystems

ThesoftwarewasoriginallydevelopedunderMATLAB6.5onaPC（windows2000）andintendedtobecomputerand/oroperatingsystemindependent.Theprogramhasbeentestedonvariousmachines（PC,Macintosh,andSunWorkstation）andoperatingsystems（windows2000/Xp,Linux）andperformsfine.

1.2.2Down-loadtheprogram

TheuserneedstodownloadthecompressedfilefromGLOBECwebsitefirst,theURLis

ftp:

//globec.whoi.edu/pub/software/kriging/easy_krig/V3.0.1/

andthecompressedfileis

Windows95/98/NT/2000/XP,

MacintoshandLinux:

easy_krig30.zip

Unix:

easy_krig30.tar.gz

Afterhavingdownloadedthefile,theuserneedstouncompressthefile.Adirectoryofeasy_krig3.0willbecreatedandyouarereadytoruntheprogram.

1.2.3Quickstart

StartMATLABandgotothedesignatedeasy_krig3.0homedirectory.Justtype“startkrig”intheMATLABcommandwindow,awindowwillpopup.Thiswindowisthebasewindow,calledtheNavigatorwindow.TheMenubarinthiswindowcontainsmanyoptionsyoucanchoose.Nowyouarereadytomoveon.

Note:

YoucanaddthekriginghomedirectorytotheMatlabsearchpathandruntheprogramfromotherdirectories.However,youhavetomakesurethattherearenofunctionsofyourownhavingthesamenamesasthoseusedforeasy_krig3.0.Sincetheprogramwillallowyoutoloadandsavefilesusingafilebrowser,itisrecommendedthatyouruntheprogramundertheeasy_krig3.0homedirectory.

Theprogramprovidesafullon-linehelpfunctionthatprovidesthedescriptionstheuseofalmostalloftheselectablefunctions,options,andparameters.Itisquiteself-explanatoryandeasytouse.

2.DataProcessingStages

Thereareseveraldataprocessingstages（tasks）thatareselectablefromtheMenubaronthetopoftheNavigatorwindow,aswellasothertaskwindows.Byselectingorclickingonanyofthetasks,awindowcorrespondingtotheselectedtaskwillpopup.OneachtaskwindowincludingtheNavigatorwindow,thedescriptionsandexplanationsofeveryoptionandselectionineachtaskwindowcanbefoundbyclickonthe“Help”optionontheMenubar.Onanyofthetaskwindows,clickingonthe“Navigator”button,orselecting“Navigator”fromtheMenubarwillbringbacktheNavigatorwindow.

2.1DataPreparation

Selecting“LoadData”from“Task”ontheMenubarofanywindowleadstotheDataPreparationwindow.Clickonthe“'Load”buttonorselect“Load”fromtheMenubartoloadtherawdatafile.Theformatofthedatafileshouldbea3-columnASCIIfilefor2Ddataand4-columnASCIIfilefor3Ddata.Commentsatthebeginningofthedatafilewillnotaffectthedataaslongaseachcommentlinebeginswithapercentagesymbol“%”.

User（s）canprovidetheirownm-filetoloadthedatabyusing“ExternalProgram”optionintheDataPreparationwindow.ThisfunctionallowstheusertogeneratetheinputdatadirectlyfromtherawdatainsteadofgeneratinganASCIIfilethatisrequiredbytheEasykrig3.0.Therequiredformatfortheinputandoutputparametersbyusinganexternalprogramcanbefoundbyclickingonthe“Help”fromtheMenubarandselecting“ExternalProgram”.

Onecansettheotherparameterssuchasreductionfactor（orjustacceptdefaultsettings）beforeloadingthefile.Afterthefileisloaded,iftheuserwantstochangetheother（default）settings,suchasdatafilter,he/shecandosoandthenclickon“Apply”pushbuttonaftertheparametershavebeenset.Thedifferencebetween“Load'”and“Apply”isthatthelatteroperationisfastersinceitw