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DATA ASSIMILATION WITH IMPERFECT MODELS Zoltan Toth and Malaquias Pena Mendez 1 Environmental Modeling Center NOAA/NWS/NCEP USA 1 SAIC at Environmental Modeling Center, NCEP/NWS Acknowledgements: Dusanka Zupanski, Guocheng Yuan http://wwwt.emc.ncep.noaa.gov/gmb/ens/index.html OUTLINE

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Information ASSIMILATION WITH IMPERFECT MODELS Zoltan Toth and Malaquias Pena Mendez 1 Environmental Modeling Center NOAA/NWS/NCEP USA 1 SAIC at Environmental Modeling Center, NCEP/NWS Acknowledgments: Dusanka Zupanski, Guocheng Yuan http://wwwt.emc.ncep.noaa.gov/gmb/ens/index.html

OUTLINE ANALYSIS ERRORS Observational mistakes Background blunders Chaotic slips Model-related lapses Stochastic blunders Systematic mistakes Tendency blunders State mistakes FORECAST DRIFT

OUTLINE/SUMMARY ANALYSIS ERRORS Observational blunders Background blunders Chaotic slips Model-related lapses Stochastic mistakes Systematic mistakes Tendency lapses State blunders FORECAST DRIFT HOW TO REDUCE DRIFT-INDUCED FORECAST ERRORS? Mapping beginning state on model attractor Estimating asymptotic slips Reducing model-related lapses Reducing aggregate gauge mistakes IMPROVED ANALYSES

DATA ASSIMILATION BASICS GOAL Represent nature as honestly as could be allowed USE OBSERVATIONAL DATA Incomplete scope in Space Time Variables Noisy Assume for this study that perceptions are impartial Otherwise, de-predisposition as in Derber & Wu NEED OTHER (BACKGROUND) INFORMATION TO Complete scope Filter out commotion Choices Climatology â Independent of current circumstance Persistence â Dynamics of circumstance overlooked Use dynamical short-range figure - Best decision with admonitions âChaoticâ conjecture blunders identified with starting vulnerability Errors identified with utilization of blemished model

DATA ASSIMILATION BASICS - 2 COMBINE OBSERVATIONS & BACKGROUND Statistical methodology Undesirable impacts from elements perspective Observational clamor Reduced however not wiped out Weights on perceptions & foundation Is truth in the middle? Minimize discretion by Relying more on powerfully reliable data Eg, outfit based foundation covariance Other methodologies? Essential ROLE OF BACKGROUND How to produce? How to utilize? Essentials ABOUT FORECASTING Well known realities Some presumptions basic Will return to a couple

NWP FORECASTING BASICS SOURCES OF FORECAST ERRORS Initial conditions Arise because of introductory mistake (flawed examination) and temperamental progress Reasonably surely knew Model Imperfect representation of nature Caused, for instance, by utilization of Limited space Limited worldly/spatial/physical determination (truncation) Structural lapses Parametric slips HOW TO REDUCE FORECAST ERRORS? Decrease beginning slips Make demonstrate more like nature USE OF FORECASTS General applications In DA cycles

HOW TO TREAT FORECAST ERRORS IN DA CHAOTIC ERRORS Statistical methodology âNMCâ system (contrasts between past short-range conjectures confirming at same time) Ensemble technique (contrasts between past outfit figures checking at same time) Dynamical methodology 4DVAR â Norm subordinate conformities Ensemble-based DA (expansive troupe of current gauges) â Norm-free modification MODEL-RELATED ERRORS 3 methodologies used to adapt to model blunders in DA: Assume model-related lapses donât vary from riotous mistakes (Ignore issue) Inflation of foundation blunders (ie, draw investigation nearer to perceptions ) Multiply foundation lapse covariance framework in 3/4DVAR Increase introductory annoyance size in gathering based DA Assume model-related slips are stochastic with attributes not quite the same as disorderly mistakes (D. Zupanski et al) Introduce extra (model) slip covariance term (permit investigation to draw nearer to obs.) How measurements decided? Expect blunders are deliberate (Dee et al) Estimate orderly distinction in the middle of investigation and foundation Before their utilization, move foundation by efficient contrast closer to examination Move foundation toward nature Move foundation toward nature IS THIS THE RIGHT MOVE? Treat starting and model blunder the same way?

MODEL-RELATED BACKGROUND ERRORS TWO COMPONENTS Systematic Time mean distinction Stochastic Whatâs left over Ignore for the present SYSTEMATIC ERROR Estimate as Climate mean contrast Regime subordinate contrast Based on latest information TRADITIONAL PARADIGM FOR ANALYSIS/FORECAST SYSTEM Estimate the condition of nature as honestly as would be prudent (examination); Run numerical model gauge from the investigation field; Statistically evaluate the deliberate lapse in the numerical conjecture; Remove the assessed orderly slip from the figure. Suspicion Removing efficient slip will enhance nature of examination/figure framework WILL IT???

SYSTEMATIC MODEL-RELATED FORECAST ERRORS Attractors of nature & model are distinctive Nature Forecast ORIGIN OF SYSTEMATIC ERROR IN FORECAST Systematic contrast in the middle of nature and our model â Model world is not the same as reality Tendencies are diverse Phenomena develop contrastingly in time Ignore for the time being States (ie, feasible, regular states) are diverse Phenomena not (precisely) the same Eg, atmosphere mean for nature and model are distinctive START MODEL FROM STATE OF NATURE State of nature not good with model Initial condition close nature is off of model attractor Forecast floats toward model attractor Drift-impelled slips presented REDUCE SYSTEMATIC MODEL-RELATED ERRORS? Inclinations will be blemished Accept that, yet Can we diminish float related blunders?

SEARCH FOR BEST INITIAL CONDITIONS FOR IMPERFECT MODELS How would we be able to lessen float prompted mistakes? What is the best introductory condition for a flawed model? A state as near nature as could reasonably be expected (âperfectâ beginning condition)? - Traditional, âfidelityâ worldview On/close attractor of nature Off attractor of model Forecast floats structure attractor of nature to that of model Lead-time subordinate methodical lapses A state on/close model attractor? â New worldview? No gauge float âImperfectâ starting conditions? How to discover state on model attractor comparing to state in nature? Is there a model direction that would âshadowâ nature? Locate a beginning state on/almost a model direction that compares with watched state Estimate vector mapping focuses in nature to focuses on model attractor Does such mapping exist? Until further notice, accept it does

HOW TO USE MAPPING IN DA/NWP FORECASTING? Testing step Estimate the mapping in the middle of nature and the model attractors Map the watched condition of nature into the model's space attractor Move obs. with mapping vector Analyze information Run the model from the mapped introductory condition âRemapâ the examination and figure back to the stage space of nature New step Standard methodology New step

COMPARING THE FIDELITY AND MAPPING PARADIGMS TRADITIONAL PARADIGM Estimate the condition of nature as honestly as could be expected under the circumstances (customary DA) Run numerical model gauges from the investigation field Statistically survey the deliberate slip in the numerical conjectures Correct the numerical estimates for orderly mistakes MAPPING PARADIGM Estimate the mapping in the middle of nature and the model attractors Map the watched condition of nature into the model's space attractor Move obs. with mapping vector Analyze information Run the model from the mapped starting condition âRemapâ the examination and conjecture back to the stage space of nature Analysis cycle Analysis cycle Move investigation toward nature Move examination to model attractor

Does mapping exist? Presumption: Forecasting would not be conceivable with defective models if mapping did not exist Not certain, need to attempt and see Mapping exists and very much assessed if conjecture mistakes with mapping versus loyalty worldview lessened If it exists, how to gauge it? Donât need immaculate assessment of mapping Initial state must be closer to model attractor than with constancy worldview Remapping mitigates potential issues with poor mapping vector appraise The greater the contrast in the middle of nature and model, the more outlandish we can discover mapping vector MAPPING QUESTIONS

MAPPING VECTOR Definition Vector that gives best remapped gauge execution Estimation Difference between long haul time method for figure direction & nature In rehearse, nature is not referred to Use customary investigations as intermediary: 2. Adaptive strategy If methodical lapses are administration ward, or atmosphere means are not accessible Details later

MODEL & DA DETAILS Lorenz (1963) 3-variable model: âNATUREâ ï³ =10 b =8/3 r =28 âMODELâ ï³ =9 z=z+2.5 Runge-Kutta numerical plan with a period venture of 0.01 Three instatement plans Perfect introductory conditions Replacement All 3 variables watched Observational slip = 2 (~5% regular variability) 3-DVAR: 15 time step cycle length (~7 hrs in environment) Diagonal R, R=2 B taking into account autonomous conjecture blunders, experimentally tuned fluctuation

RESULTS â CLIMATE MEAN MAPPING Except for short lead time, mapped conjecture beats conventional estimate with or without inclination remedy Remapped estimate beats customary gauge at all leads PERFECT INITIAL CONDITIONS 67% mistake lessening Drift-impelled slips tremendously diminished Shadowing period expanded 3-fold

RESULTS â CLIMATE MEAN MAPPING REPLACEMENT 3-DVAR Remapped examination beats customary examination In the vicinity of beginning mistakes, blunder decrease is littler (~20%)

ADAPTIVE MAPPING VECTOR ESTIMATION Needed when Systematic lapses are administration ward or Climate means are not accessible Iterative procedure: Based on generally little measure of information Length of emphasis period ~15 days 10 emphasess (~half year) Allow first figure fields to float with every cycle: M = M earlier + M Incr closer to model attractor ALGORITHM 1. M earlier = M = 0 2. Use M in mapping calculation during next emphasis period 3. 4. Upgrade M by M = M former + M Incr Mapping vector assessme