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TheNa'onalCenterforAtmosphericResearchissponsoredbytheNa'onalScienceFounda'on.Anyopinions,findingsandconclusionsorrecommenda'onsexpressedinthispublica'onarethoseoftheauthor(s)anddonotnecessarilyreflecttheviewsoftheNa'onalScienceFounda'on.
©UCAR
DARTTutorialSec'on20:ModelParameterEs'ma'on
ModelParameterEs'ma'on
Supposeamodelisgovernedbya(stochas'c)DifferenceEqua'on:
(1)whereuandwarevectorsofparameters.Also,supposewereallydon’tknowtheparametervalues(verywell).Canweuseobserva-onswithassimila-ontohelpconstrainthesevalues?Rewrite(1)as:
(2)wheretheaugmentedstatevectorincludesxt, u, and w. The modelismodifiedsovaluesofuandwcanbechangedbyassimila'on.Themodelmightalsointroducesome'metendencyforuandw.
dxt = f xt ,t;u( ) +G xt ,t;w( )dβt , t ≥ 0
dxtA = f A xt
A ,t( ) +GA xtA ,t( )dβt , t ≥ 0
DARTTutorialSec'on20:Slide2
ModelParameterEs'ma'on
Fromtheensemblefilterperspec-ve:
Justaddanyparametersofinteresttothemodelstatevector;Proceedtoassimilateasbefore.Possibledifficul-es:
1. Whereareparameters‘located’forlocaliza'on?2. Parameterswon’thaveanyerrorgrowthin'me
(unlessweaddsome):couldleadtofilterdivergence.3. Parametersmaynotbestronglycorrelatedwithany
observa'ons.
DARTTutorialSec'on20:Slide3
Tes'ngParameterEs'ma'oninDART
DARTincludesamodels/forced_lorenz_96directory.
Eachstatevariablehasacorrespondingforcingvariable,Fi.
(3)Observa'onalerrorsforobs.insetiindependentofthoseinsetj.
(4)Canobserva'onsofsomefunc'onofstatevariablesconstrainF?
dXi / dt = Xi+1 − Xi−2( )Xi−1 − Xi + Fi
dFi / dt = N 0,σ noise( )
DARTTutorialSec'on20:Slide4
Addingnamelistcontrolaspectsrequiredforexperimenta'on:
1. reset_forcingif.true.,Fi=forcing(alsofromnamelist)foralli,t.
2. random_forcing_amplitude forFi'metendency,
notusedifreset_forcingis.true.
Usingthese,cancreateOSSEsetswithfixed,globalFvalue.
Assimilatethesewithfilter,es'matestateandforcing.
GetanensemblesampleofFiateach'me.
Randomnoisecanbeusefulforavoidingfilterdivergence.
σ noise
DARTTutorialSec'on20:Slide5
Sec'on5:6of15
Addingnamelistcontrolaspectsrequiredforexperimenta'on:
&model_nml num_state_vars = 40 forcing = 8.0 delta_t = 0.05 time_step_days = 0 time_step_seconds = 3600 reset_forcing = .false. random_forcing_amplitude = 0.10 /
Ifreset_forcing = .true.,Fi=forcing(alsofromnamelist)foralli,t.
forFi'metendency,notusedifreset_forcing = .true.
σ noise
models/forced_lorenz_96/work/
Usingthese,cancreateOSSEsetswithfixed,globalFvalue.
Assimilatethesewithfilter,es'matestateandforcing.
GetanensemblesampleofFiateach'me.
Randomnoisecanbeusefulforavoidingfilterdivergence.
Assimila'onintheforcedLorenz96model
cdmodels/forced_lorenz_96/workcshworkshop_setup.cshUseMatlab,etc.toexamineoutput.Same40randomly-locatedobserva'onsasinlorenz_96cases.Forcingwasfixedat8.0intheperfect_modelrun.ValuesofFiaremodifiedintheassimila'on.Therewassomenoise(amplitudeof0.1)addedtothe'metendency.AmazingFact:Bestassimila1onsofstatecomewhenFivaries,evenbe7erthanwhenFiissettoexactknownvalueof8.0!
DARTTutorialSec'on20:Slide7
Inmodels/forced_lorenz_96/workeditinput.nml
&filter_nml …
obs_sequence_in_name = "obs_seq.out”Ques-on:Whatwasthevalueoftheforcingintheperfect_modelrun?Youcantryanything(ethical)youwant.Feelfreetoaskforhelptotryexperimentsyoudon’tknowhowtodo.Remember:TheTruthisNOLONGERKNOWN!Consistentwiththethemeoftheworkshop…intheeventofa'e,arandomnumbergeneratorwillbeusedtodecidethewinner.Honor,fame,andfabulous(?)prizesgotothewinningteam!!!
Contest:Givenanobserva'onset,whatwasthevalueofF?
DARTTutorialSec'on20:Slide8
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'on20:Slide9
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