dart tutorial sec’on 9: more on dealing with error: inflaon · dart tutorial sec’on 9: slide...

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DARTTutorialSec'on9:MoreonDealingwithError:Infla'on

SomeErrorSourcesinEnsembleFilters

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1.ModelError

2.herrors;Representa'veness

3.‘Gross’Obs.Error 4.SamplingError;GaussianAssump'on

5.SamplingError;AssumingLinearSta's'calRela'on

tk

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tk+2h h h

DARTTutorialSec'on9:Slide2

DealingwithEnsembleFilterErrorsFix1,2,3independently,HARDbutongoing.O\en,ensemblefilters...1-4:Varianceinfla'on,Increaseprioruncertaintytogiveobsmoreimpact.5.‘Localiza'on’:onlyletobs.impactasetof‘nearby’statevariables.O\ensmoothlydecreaseimpactto0asfunc'onofdistance.

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1. Model Error

2. h errors; Representativeness

3. ‘Gross’ Obs. Error 4. Sampling Error; Gaussian Assumption

5. Sampling Error; Assuming Linear Statistical Relation

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DARTTutorialSec'on9:Slide3

Model/FilterError:FilterDivergenceandVarianceInfla'on

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"TRUE" Prior PDF

1.Historyofobserva'onsandphysicalsystem=>‘true’distribu'on.

DARTTutorialSec'on9:Slide4

Model/FilterError:FilterDivergenceandVarianceInfla'on

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"TRUE" Prior PDF

Variance Deficient PDF

1.Historyofobserva'onsandphysicalsystem=>‘true’distribu'on.2.Samplingerror,somemodelerrorsleadtoinsufficientpriorvariance.3.Canleadto‘filterdivergence’:prioristooconfident,obs.Ignored.

DARTTutorialSec'on9:Slide5

Model/FilterError:FilterDivergenceandVarianceInfla'on

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"TRUE" Prior PDF

Variance Deficient PDF

1.Historyofobserva'onsandphysicalsystem=>‘true’distribu'on.2.Samplingerror,somemodelerrorsleadtoinsufficientpriorvariance.3.Canleadto‘filterdivergence’:prioristooconfident,obs.Ignored.

Naïvesolu'onisvarianceinfla'on:justincreasespreadofprior.Forensemblememberi, inflate xi( ) = λ xi − x( )+ x

DARTTutorialSec'on9:Slide6

Model/FilterError:FilterDivergenceandVarianceInfla'on

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"TRUE" Prior PDF

1.Historyofobserva'onsandphysicalsystem=>‘true’distribu'on.

DARTTutorialSec'on9:Slide7

Model/FilterError:FilterDivergenceandVarianceInfla'on

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"TRUE" Prior PDF Error in Mean (from model)

1.Historyofobserva'onsandphysicalsystem=>‘true’distribu'on.2.Mostmodelerrorsalsoleadtoerroneousshi\inen'redistribu'on.3.Again,priorcanbeviewedasbeingTOOCERTAIN.

DARTTutorialSec'on9:Slide8

Model/FilterError:FilterDivergenceandVarianceInfla'on

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"TRUE" Prior PDF Error in Mean (from model)

Variance Inflated

Infla'ngcanamelioratethis.Obviously,ifweknewE(error),we’dcorrectforitdirectly.

1.Historyofobserva'onsandphysicalsystem=>‘true’distribu'on.2.Mostmodelerrorsalsoleadtoerroneousshi\inen'redistribu'on.3.Again,priorcanbeviewedasbeingTOOCERTAIN.

DARTTutorialSec'on9:Slide9

PhysicalSpaceVarianceInfla'on

Inflateallstatevariablesbysameamountbeforeassimila'on.Capabili'es:1.  Canbeeffec'veforavarietyofmodels.2.  Canmaintainlinearbalances.3.  Staysonlocalflatmanifolds.

4.  Simpleandcheap.

Liabili'es:1.  Statevariablesnotconstrainedbyobserva'onscan‘blowup’.

ForinstanceunobservedregionsnearthetopofAGCMs.2. Magnitudeofλnormallyselectedbytrialanderror.

DARTTutorialSec'on9:Slide10

PhysicalSpaceVarianceInfla'oninLorenz63

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Observa'onoutsideprior:dangeroffilterdivergence.

Observa'oninred.Priorensembleingreen.

DARTTutorialSec'on9:Slide11

PhysicalSpaceVarianceInfla'oninLorenz63

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A\erinfla'ng,observa'onisinpriorcloud:filterdivergenceavoided.

Observa'oninred.Priorensembleingreen.

Inflatedensembleinmagenta.

DARTTutorialSec'on9:Slide12

PhysicalSpaceVarianceInfla'oninLorenz63

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Priordistribu'onissignificantly‘curved’.

Observa'oninred.Priorensembleingreen.

DARTTutorialSec'on9:Slide13

PhysicalSpaceVarianceInfla'oninLorenz63

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Inflatedprioroutsidealractor.Posteriorwillalsobeoffalractor.

Observa'oninred.Priorensembleingreen.

Inflatedensembleinmagenta.

Canleadtotransientoff-alractorbehavioror…Model‘blow-up’.

DARTTutorialSec'on9:Slide14

Basiccontrolofinfla'oninDARTisin&filter_nml

inf_flavor =0, 0,inf_ini'al_from_restart =.false., .false.,inf_sd_ini'al_from_restart =.false., .false.,inf_determinis'c =.true., .true.,inf_ini'al =1.0, 1.0,inf_sd_ini'al =0.0, 0.0,inf_damping =1.0, 1.0,inf_lower_bound =1.0, 1.0,inf_upper_bound =1000000.0, 1000000.0,inf_sd_lower_bound =0.0, 0.0,

BeforeAssimila'on

A\erAssimila'on

Flavor: 0=>NONE 1=>deprecated 2,3=>physicalspace

Infla'onValue

Ini'ally,we’llchangeinf_flavorandinf_ini*alinfirstcolumn.DARTTutorialSec'on9:Slide15

priorinfla'oncolumn

posteriorinfla'oncolumn

&assim_tools_nml filter_kind = 1 cutoff = 1000000.0 spread_restoration = .false. sampling_error_correction = .false. …&filter_nml ens_size = 20 perturb_from_single_instance = .false. … inf_flavor = 3, 0 inf_initial_from_restart = .false., .false. inf_sd_initial_from_restart = .false., .false. inf_initial = 1.0, 1.0 inf_sd_initial = 0.0, 0.0 inf_damping = 1.0, 1.0 inf_lower_bound = 1.0, 1.0 inf_upper_bound = 1000000.0, 1000000.0 inf_sd_lower_bound = 0.0, 0.0

Physicalspacevarianceinfla'oninLorenz96

Setinf_flavorto3tousestatespaceinfla'on.Inthefirstcolumn,setinf_ini*altovalueslike1.05,1.08,1.10

DARTTutorialSec'on9:Slide16

models/lorenz_96/work/Trysomevaluesandseewhathappenstoassimila'onswithLorenz96.

Varianceinfla'oninobserva'onspace

1.Forobservedvariable,havees'mateofprior-observedinconsistency.

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S.D.

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S.D.

NotcurrentlysupportedinDARTManhalan.

DARTTutorialSec'on9:Slide17

Varianceinfla'oninobserva'onspace

1.Forobservedvariable,havees'mateofprior-observedinconsistency.2.Expected(prior_mean–observa'on)=

Assumesthatpriorandobserva'onaresupposedtobeunbiased.Isitmodelerrororrandomchance?

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S.D.

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S.D.Expected Separation

Actual 4.714 SDs

σprior2 +σobs

2

DARTTutorialSec'on9:Slide18

Varianceinfla'oninobserva'onspace

1.Forobservedvariable,havees'mateofprior-observedinconsistency.2.Expected(prior_mean–observa'on)=3.Infla'ngincreasesexpectedsepara'on.

Increases‘apparent’consistencybetweenpriorandobserva'on.

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Prior PDF Obs. Likelihood

S.D.Inflated S.D. Expected Separation

Actual 3.698 SDs

σprior2 +σobs

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DARTTutorialSec'on9:Slide19

Varianceinfla'oninobserva'onspace:Lorenz96

Varianceinfla'oninobserva'onspacenotcurrentlysupported.TrysomevaluesandseewhathappenstoLorenz96assimila'on.

Setinf_flavor=1,observa'onspaceinfla'oninfirstcolumn.TrysomevaluesandseewhathappenstoLorenz96assimila'on.

Setinf_ini*altovalueslike1.05,1.08,1.10infirstcolumn.Makesurethatcutoff=10000000andens_size=20.

(Thesewereserngsthatdivergedwithoutinfla'on)

DARTTutorialSec'on9:Slide20

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'on9:Slide21