The Na’onal Center for Atmospheric Research is sponsored by the Na’onal Science Founda’on. Any opinions, findings and conclusions or recommenda’ons expressed in this publica’on are those of the author(s) and do not necessarily reflect the views of the Na’onal Science Founda’on. ©UCAR 2014 DART Tutorial Sec’on 8: Dealing with Sampling Error
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
![Page 1: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/1.jpg)
TheNa'onalCenterforAtmosphericResearchissponsoredbytheNa'onalScienceFounda'on.Anyopinions,findingsandconclusionsorrecommenda'onsexpressedinthispublica'onarethoseoftheauthor(s)anddonotnecessarilyreflecttheviewsoftheNa'onalScienceFounda'on.
©UCAR2014
DARTTutorialSec'on8:DealingwithSamplingError
![Page 2: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/2.jpg)
Upda'ngAddi'onalPriorStateVariables
Twoprimaryerrorsources:1.Samplingerrorduetonoise.Canoccurevenifthereisalinearrela'onbetweenvariables.Sampleregressioncoefficientimprecisewithfiniteensembles.2.Linearapproxima'onisinvalid.Ifthereissubstan'alnonlinearityin‘true’rela'onbetweenvariablesoverrangeofpriorensemble.(seesec'on10).Mayneedtoaddressbothissuesforgoodperformance.
DARTTutorialSec'on8:Slide2
![Page 3: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/3.jpg)
RegressionSamplingError&FilterDivergence
Supposeunobservedstatevariableisknowntobeunrelatedtosetofobservedvariables.Unobservedvariableshouldremainunchanged.
DARTTutorialSec'on8:Slide3
![Page 4: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/4.jpg)
RegressionSamplingError&FilterDivergence
Supposeunobservedstatevariableisknowntobeunrelatedtosetofobservedvariables.Finitesamplesfromjointdistribu'onwillhavenon-zerocorrela'on.Expected|correl|=0.19for20samples.Aaeroneobserva'on,unobservedvariablemean,standarddevia'onchange.
DARTTutorialSec'on8:Slide4
![Page 5: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/5.jpg)
RegressionSamplingError&FilterDivergence
Supposeunobservedstatevariableisknowntobeunrelatedtosetofobservedvariables.Unobservedvariableshouldremainunchanged.Unobservedmeanfollowsarandomwalkasmoreobserva'onsareused.
DARTTutorialSec'on8:Slide5
![Page 6: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/6.jpg)
RegressionSamplingError&FilterDivergence
Supposeunobservedstatevariableisknowntobeunrelatedtosetofobservedvariables.Unobservedvariableshouldremainunchanged.UnobservedS.Dsystema'callydecreases.Expectedchangein|SD|isnega'veforanynon-zerosamplecorrela'on.
DARTTutorialSec'on8:Slide6
![Page 7: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/7.jpg)
RegressionSamplingError&FilterDivergence
Supposeunobservedstatevariableisknowntobeunrelatedtosetofobservedvariables.Unobservedvariableshouldremainunchanged.UnobservedS.Dsystema'callydecreases.Expectedchangein|SD|isnega'veforanynon-zerosamplecorrela'on.
DARTTutorialSec'on8:Slide7
![Page 8: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/8.jpg)
RegressionSamplingError&FilterDivergence
Supposeunobservedstatevariableisknowntobeunrelatedtosetofobservedvariables.Unobservedvariableshouldremainunchanged.UnobservedS.Dsystema'callydecreases.Expectedchangein|SD|isnega'veforanynon-zerosamplecorrela'on.
DARTTutorialSec'on8:Slide8
![Page 9: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/9.jpg)
RegressionSamplingError&FilterDivergence
Supposeunobservedstatevariableisknowntobeunrelatedtosetofobservedvariables.Es'matesofunobservedbecometooconfident.Giveprogressivelylessweighttomeaningfulobs.Eventually,meaningfulobsareessen'allyignored.
DARTTutorialSec'on8:Slide9
![Page 10: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/10.jpg)
FilterDivergence
Ignoringmeaningfulobserva'onsduetooverconfidenceisatypeofFILTERDIVERGENCE.
Thiswasseeninini'alLorenz96(40-variable)experiment.Thespreadbecamesmall=>thefilterthoughtithadagoodes'mate.Theerrorstayedlargebecausegoodobserva'onswereignored.
DARTTutorialSec'on8:Slide10
![Page 11: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/11.jpg)
RegressionSamplingError&FilterDivergence
Plotshowsexpectedabsolutevalueofsamplecorrela'onversustruecorrela'on.Errordecreaseswithsamplesizeandforlarger|realcorrela'ons|.
DARTTutorialSec'on8:Slide11
![Page 12: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/12.jpg)
RegressionSamplingError&FilterDivergence
Plotshowsexpectedabsolutevalueofsamplecorrela'onversustruecorrela'on.Forsmalltruecorrela'ons,errorsares'llundesirablylargeevenfor80memberensembles.
DARTTutorialSec'on8:Slide12
![Page 13: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/13.jpg)
DealingwithRegressionSamplingError
1.Ignoreit:ifnumberofunrelatedobserva'onsissmallandthereissomewayofmaintainingvarianceinpriors.Wedidthisinthe3and9variablemodels.
2.Uselargerensemblestolimitsamplingerror(testinlorenz_96).
Thiscangetexpensiveforbigproblems.Trymodifyingens_sizein&filter_nml (try40,80,160).Note:Forensemblesizesgreaterthan80,set&filter_nml: perturb_from_single_instance = .true.ThistellsDARTtogenerateini'alensemblemembersusingarandomnumbergenerator,ratherthanreadingthemfromaninputfile(whichonlycontains80membersinthisdirectory).
DARTTutorialSec'on8:Slide13
![Page 14: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/14.jpg)
DealingwithRegressionSamplingError
1.Ignoreit:ifnumberofunrelatedobserva'onsissmallandthereissomewayofmaintainingvarianceinpriors.Wedidthisinthe3and9variablemodels.
2.Uselargerensemblestolimitsamplingerror(testinlorenz_96).
Thiscangetexpensiveforbigproblems.Trymodifyingens_sizein&filter_nml (try40,80,160).
3.Useaddi'onalaprioriinforma'onaboutrela'onbetween
observa'onsandstatevariables.Don’tletanobserva'onimpactstateiftheyareknowntobeunrelated.
4.Trytodeterminetheamountofsamplingerrorandcorrectforit.
Therearemanywaystodothis;somesimple,somecomplex. DARTTutorialSec'on8:Slide14
![Page 15: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/15.jpg)
DealingwithRegressionSamplingError
3.Useaddi'onalaprioriinforma'onaboutrela'onbetweenobserva'onsandstatevariables.
Foratmosphericassimila'onproblems:Weightregressionasfunc'onofhorizontaldistancefromobserva'on.Gaspari-Cohn:5thordercompactlysupportedpolynomial.
DARTTutorialSec'on8:Slide15
![Page 16: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/16.jpg)
DealingwithRegressionSamplingError
3.Useaddi'onalaprioriinforma'onaboutrela'onbetweenobserva'onsandstatevariables.
Canuseotherfunc'onstoweightregression.Unclearwhatdistancemeansforsomeobs./statevariablepairs.ReferredtoasLOCALIZATION.
Halfwidth
DARTTutorialSec'on8:Slide16
![Page 17: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/17.jpg)
DARTprovidesseverallocaliza'onop'ons
1.Differentshapesforthelocaliza'onfunc'onareavailable.Controlledbyselect_localiza-onin&cov_cutoff_nml.
2.Halfwidthoflocaliza'onfunc'onsetbycutoffin&assim_tools_nml
1=>Gaspari-Cohn
2=>Boxcar
3=>RampedBoxcar
DARTTutorialSec'on8:Slide17
![Page 18: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/18.jpg)
Experimen'ngwithLorenz96
Thelorenz_96domainismappedtoa[0,1]periodicrange.
TryavarietyofhalfwidthsforaGaspariCohnlocaliza'onbyWealreadyknowthataverylargelocaliza'onhalf-widthdiverges.
Whathappensforaverysmallvalue?
Whathappenswithintermediatevalues(saybetween0.1and0.5)?
Canalsotrychangingtheshape,(bestwith40memberensemble):Tryop'on2or3forselect_localiza-onin&cov_cutoff_nml.
DARTTutorialSec'on8:Slide18
&assim_tools_nml filter_kind = 1 cutoff = 1000000.0 …&filter_nml ens_size = 20 perturb_from_single_instance = .false. …
![Page 19: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/19.jpg)
DealingwithRegressionSamplingError
4.Trytodeterminetheamountofsamplingerrorandcorrectforit.
Manywaystodothis.DARTimplementsonenaiveway:1.Takesetofincrementsfromagivenobserva'on,2.Supposethisobserva'onandastatevariablearenotcorrelated,3.Computetheexpecteddecreaseinspreadgivennotcorrelated,4.Addthisamountofspreadbackintothestatevariable.
Theexpecteddecreaseinspreadiscomputedbyoff-lineMonteCarlo.Resultsofoff-linesimula'onaretabulatedandapplied.(Thiscanbeaveryusefultechniquewhenyou’reanaly'callyclueless).
Trythisalgorithm:set&assim_tools_nml: spread_restoration = .true.
Howdoesitworkwith20ensemblemembers,nolocaliza'on?
DARTTutorialSec'on8:Slide19
![Page 20: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/20.jpg)
DealingwithRegressionSamplingError
4.Trytodeterminetheamountofsamplingerrorandcorrectforit.Manywaystodothis.DARTalsoimplementsasamplingerrorcorrec'onalgorithmthatcanreducebutnoteliminateproblems.ThisalgorithmALMOSTALWAYSIMPROVESlargemodelresults.Trythisalgorithm:set&assim_tools_nml: sampling_error_correction = .true.
Howdoesitworkwith20ensemblemembers,nolocaliza'on?
DARTTutorialSec'on8:Slide20
![Page 21: DART Tutorial Sec’on 8: Dealing with Sampling ErrorDART Tutorial Sec’on 8: Slide 17 Experimen’ng with Lorenz 96 The lorenz_96 domain is mapped to a [0, 1] periodic range. Try](https://reader034.cupdf.com/reader034/viewer/2022050220/5f66095012f388209625cd75/html5/thumbnails/21.jpg)
1. FilteringForaOneVariableSystem2. TheDARTDirectoryTree3. DARTRun>meControlandDocumenta>on4. Howshouldobserva>onsofastatevariableimpactanunobservedstatevariable?
Mul>variateassimila>on.5. ComprehensiveFilteringTheory:Non-Iden>tyObserva>onsandtheJointPhaseSpace6. OtherUpdatesforAnObservedVariable7. SomeAddi>onalLow-OrderModels8. DealingwithSamplingError9. MoreonDealingwithError;Infla>on10. RegressionandNonlinearEffects11. Crea>ngDARTExecutables12. Adap>veInfla>on13. HierarchicalGroupFiltersandLocaliza>on14. QualityControl15. DARTExperiments:ControlandDesign16. Diagnos>cOutput17. Crea>ngObserva>onSequences18. LostinPhaseSpace:TheChallengeofNotKnowingtheTruth19. DART-CompliantModelsandMakingModelsCompliant20. ModelParameterEs>ma>on21. Observa>onTypesandObservingSystemDesign22. ParallelAlgorithmImplementa>on23. Loca'onmoduledesign(notavailable)24. Fixedlagsmoother(notavailable)25. Asimple1Dadvec>onmodel:TracerDataAssimila>on
DARTTutorialIndextoSec'ons
DARTTutorialSec'on8:Slide21
Related Documents
