Parameter Estimation in EnKF: Surface Fluxes of Carbon, Heat, Moisture and Momentum *Ji-Sun Kang, *Eugenia Kalnay, *Takemasa Miyoshi, + Junjie Liu, # Inez Fung, *Kayo Ide *University of Maryland, College Park, MD + NASA/JPL, # University of California, Berkeley, CA PSU-UMD Data Assimilation Workshop, Dec. 13, 2012
Outline Parameter estimation in EnKF Carbon cycle data assimilation: LETKF-C Estimation of surface heat and moisture fluxes Sensible and latent heat fluxes (SHF, LHF) Estimation of wind stress in addition to SHF and LHF Summary
Parameter estimation in EnKF State vector augmentation X b Append CF (surface CO 2 fluxes) X CF : model state vector (U, V, T, q, Ps, C) : surface CO 2 flux Update CF as a part of the data assimilation process, minimizing the analysis errors caused by surface CO 2 forcing and atmospheric CO 2 transport < Schematic plot of LETKF-C framework > Observations U, V, T, q, Ps, C Forecast U, V, T, q, Ps, C During the ensemble forecast, C is forced by CF that is updated only by the analysis step. Ensemble forecast provides multivariate background (forecast) error covariance among U, V, T, q, Ps, C, and CF LETKF (analysis) U, V, T, q, Ps, C, CF During the LETKF analysis step, Kalman gain (or weight between forecast and observation) is determined by minimizing a combination of background and observation errors
UMD-UCB LETKF-C Simultaneous analysis of meteorological and carbon variables (Kang et al. 2011, 2012) Multivariate data assimilation with localization of variables We zero out the error covariance between some variables, because CO 2 does not have a strong physical relation with every variables in the state vector, so that sampling errors are reduced Analysis includes error covariance between atmospheric CO 2 and wind fields to take account for transport errors of CO 2 Advanced inflation methods Adaptive multiplicative inflation (Miyoshi, 2011) Additive inflation for parameters Vertical localization of column mixing CO 2 observations Short (6-hour) assimilation window Schematic plot of background error covariance matrix w/ localization of variables (Kang et al. 2011, JGR)
Results LETKF-C succeeded in estimating timeevolving surface CO 2 fluxes at model grid scale in a simulation experiment. Kang et al. 2012, JGR
Surface Heat and Moisture Fluxes Can we estimate surface moisture/heat fluxes by assimilating atmospheric moisture/temperature observations? We can use the same methodology! Observing System Simulation Experiments (OSSEs) Nature: SPEEDY (perfect model) Forecast model: SPEEDY with persistence forecast of Sensible/Latent heat fluxes (SHF/LHF) Observations: conventional observations of (U, V, T, q, Ps) and AIRS retrievals of (T, q) Analysis: U, V, T, q, Ps + SHF & LHF Fully multivariate data assimilation Adaptive multiplicative inflation + additive inflation Initial conditions: random (no a-priori information)
Results: SHF & LHF [perfect model of WSTR] True SHF @ end of JAN SHF analysis @ end of JAN W/m 2 True LHF @ end of JAN LHF analysis @ end of JAN W/m 2
Time series of SHF [perfect model of WSTR] 1 1 2 3 W/m 2 2 3
Summary of SHF & LHF DA [perfect WSTR] AIRS retrieval data of T and q provide very accurate and abundant information for constraining surface heat and moisture fluxes Observation error: 1K for T and 1.0g/kg for q Global coverage at every 12 hours After a short spin-up period (~a week), estimation of SHF and LHF converges very well Results shown here are given under the assumption of perfect wind stress model.
Can we also estimate wind stress? OSSEs Nature: SPEEDY Forecast model: SPEEDY with persistence forecast of Sensible/Latent heat fluxes (SHF/LHF) and wind stress (USTR, VSTR) [ALL_FLUXES] Observations: conventional observations of (U, V, T, q, Ps), AIRS retrievals of (T, q), and ASCAT ocean surface wind observations Observation error of ASCAT: 3.5m/s (not as good as AIRS data or rawinsonde data) ASCAT covers the global ocean every 12 hours, but little overlapped with AIRS data distribution Analysis: U, V, T, q, Ps + SHF, LHF, USTR, VSTR Fully multivariate data assimilation Initial conditions: random (no a-priori information)
Result: USTR from [ALL_FLUXES] Initial condition includes no a-priori information of USTR After one month of DA, USTR estimation converges to the true USTR
Results: SHF from [ALL_FLUXES] SHF analysis with WSTR DA True SHF SHF analysis with perfect WSTR Although the estimated wind stress does look okay, the imperfection of the wind stress contaminates the estimation of SHF and LHF significantly Analysis diverged
Filtering analysis increments & increasing an ensemble size Due to the limited observational contents, we may not be able to expect analysis increment with a full resolution Filtering out analysis increments at high wavenumbers for 2d parameters (SHF, LHF, USTR, VSTR) using the Shapiro filter (Kalnay, 2003) 1.2 1 0.8 Damping factor 0.6 0.4 0.2 0 U 8 8 j [1 sin ( x / L)] U j 1 6 11 16 21 26 T30 (SPEEDY) Wave number We introduce too many unknowns into the analysis system, and thus increasing ensemble size may help. We increase the ensemble size from 40 to 80
Results U Spatial correlation (left) and RMSE (right) Blue: 80 ensembles w/ filtering analysis increments (analinc) Red: 40 ensembles w/ filtering analinc Green: 40 ensembles w/o filtering analinc Orange: perfect WSTR with 40 ensembles T Doubling ensemble size & filtering out analysis increments over high wavenumber improve the results, but it seems not enough to produce stable estimation of parameters throughout the analysis period USTR SHF USTR SHF
USTR Results from the experiments with 80 ensemble members and filtering out analinc over high frequencies Estimated USTR looks reasonable overall Observation-poor area
SHF There are significant underestimation, especially over the ocean Estimation over the land (area 4 and 6) has relatively good performance Better observations over land Observation-poor area
LHF There are significant overestimation, especially over the ocean improper partitioning (e.g.vinukollu et al. 2012) Estimation over the land (area 5 and 7) has relatively good performance Area 6 is also over the land, but there are few rawinsonde observations Results depends on the observational contents since our methods does not use any a-priori states Observation-poor area
Global maps of USTR 00Z01FEB after a month of DA Estimation of USTR agrees well with the true USTR
Summary of WSTR DA and future work We attempt to estimate wind stress (WSTR) within LETKF (without computing it from a physical parameterization of the perfect model) in addition to SHF/LHF estimation Addition of ASCAT data gives fairly good estimation of WSTR The analysis system still needs further improvement to avoid a negative feedback among WSTR, SHF, LHF, and other prognostic variables due to the imperfect WSTR. Filtering analysis increment & increasing ensemble size help. Future work Localization of the variables may help. We can try to ignore error covariance between (SHF, LHF) and (USTR, VSTR) in the multivariate data assimilation For updating SHF/LHF, it would be better to assimilation AIRS T and q, but not ASCAT winds U V T q Ps SHF LHF UST U V T q Ps SHF LHF UST VST 0 0 0 0 0 0 VST 0 0