E4DVar: Coupling an Ensemble Kalman Filter with Four-Dimensional Variational Data Assimilation in a Limited-Area Weather Prediction Model

AbstractA hybrid data assimilation approach that couples the ensemble Kalman filter (EnKF) and four-dimensional variational (4DVar) methods is implemented for the first time in a limited-area weather prediction model. In this coupled system, denoted E4DVar, the EnKF and 4DVar systems run in parallel while feeding into each other. The multivariate, flow-dependent background error covariance estimated from the EnKF ensemble is used in the 4DVar minimization and the ensemble mean in the EnKF analysis is replaced by the 4DVar analysis, while updating the analysis perturbations for the next cycle of ensemble forecasts with the EnKF. Therefore, the E4DVar can obtain flow-dependent information from both the explicit covariance matrix derived from ensemble forecasts, as well as implicitly from the 4DVar trajectory. The performance of an E4DVar system is compared with the uncoupled 4DVar and EnKF for a limited-area model by assimilating various conventional observations over the contiguous United States for June 2...

[1]  Craig H. Bishop,et al.  Adaptive sampling with the ensemble transform Kalman filter , 2001 .

[2]  Philippe Courtier,et al.  Dual formulation of four‐dimensional variational assimilation , 1997 .

[3]  Rosemary Munro,et al.  Diagnosis of background errors for radiances and other observable quantities in a variational data assimilation scheme, and the explanation of a case of poor convergence , 2000 .

[4]  Juanzhen Sun,et al.  Dynamical and Microphysical Retrieval from Doppler Radar Observations Using a Cloud Model and Its Adjoint. Part I: Model Development and Simulated Data Experiments. , 1997 .

[5]  M. Buehner.  Ensemble‐derived stationary and flow‐dependent background‐error covariances: Evaluation in a quasi‐operational NWP setting , 2005 .

[6]  G. Grell,et al.  A generalized approach to parameterizing convection combining ensemble and data assimilation techniques , 2002 .

[7]  T. Vukicevic,et al.  CIRA/CSU Four-Dimensional Variational Data Assimilation System , 2005 .

[8]  T. Hamill,et al.  A Hybrid Ensemble Kalman Filter-3D Variational Analysis Scheme , 2000 .

[9]  Jidong Gao,et al.  An Efficient Dual-resolution Approach for Ensemble Data Assimilation and Tests with Simulated Doppler Radar Data , 2022 .

[10]  Fuqing Zhang,et al.  Tests of an Ensemble Kalman Filter for Mesoscale and Regional-Scale Data Assimilation. Part I: Perfect Model Experiments , 2006 .

[11]  Philippe Courtier,et al.  Dynamical structure functions in a four‐dimensional variational assimilation: A case study , 1996 .

[12]  Chungu Lu,et al.  Four-Dimensional Variational Data Assimilation for Limited-Area Models: Lateral Boundary Conditions, Solution Uniqueness, and Numerical Convergence , 2000 .

[13]  Monique Tanguay,et al.  Extension of 3DVAR to 4DVAR: Implementation of 4DVAR at the Meteorological Service of Canada , 2007 .

[14]  R. James Purser,et al.  Recursive Filter Objective Analysis of Meteorological Fields: Applications to NESDIS Operational Processing , 1995 .

[15]  Ryan D. Torn,et al.  Boundary Conditions for Limited-Area Ensemble Kalman Filters , 2006 .

[16]  Fuqing Zhang,et al.  Tests of an Ensemble Kalman Filter for Mesoscale and Regional-Scale Data Assimilation. Part IV: Comparison with 3DVAR in a Month-Long Experiment , 2007 .

[17]  X. Deng,et al.  Model Error Representation in an Operational Ensemble Kalman Filter , 2009 .

[18]  Mingjing Tong,et al.  Ensemble kalman filter assimilation of doppler radar data with a compressible nonhydrostatic model : OSS experiments , 2005 .

[19]  Dacian N. Daescu,et al.  The Impact of Background Error on Incomplete Observations for 4D-Var Data Assimilation with the FSU GSM , 2005, International Conference on Computational Science.

[20]  M. Buehner,et al.  Intercomparison of Variational Data Assimilation and the Ensemble Kalman Filter for Global Deterministic NWP. Part II: One-Month Experiments with Real Observations , 2010 .

[21]  J. Dudhia,et al.  Four-Dimensional Variational Data Assimilation of Heterogeneous Mesoscale Observations for a Strong Convective Case , 2000 .

[22]  S. Cohn,et al.  Ooce Note Series on Global Modeling and Data Assimilation Construction of Correlation Functions in Two and Three Dimensions and Convolution Covariance Functions , 2022 .

[23]  Juanzhen Sun,et al.  Impacts of Initial Estimate and Observation Availability on Convective-Scale Data Assimilation with an Ensemble Kalman Filter , 2004 .

[24]  M. Buehner,et al.  Intercomparison of Variational Data Assimilation and the Ensemble Kalman Filter for Global Deterministic NWP. Part I: Description and Single-Observation Experiments , 2010 .

[25]  L. Berre.  Estimation of Synoptic and Mesoscale Forecast Error Covariances in a Limited-Area Model , 2000 .

[26]  P. Courtier,et al.  A strategy for operational implementation of 4D‐Var, using an incremental approach , 1994 .

[27]  Fuqing Zhang,et al.  Tests of an Ensemble Kalman Filter for Mesoscale and Regional-Scale Data Assimilation. Part III: Comparison with 3DVAR in a Real-Data Case Study , 2008 .

[28]  Andrew C. Lorenc,et al.  The potential of the ensemble Kalman filter for NWP—a comparison with 4D‐Var , 2003 .

[29]  Jean-Noël Thépaut,et al.  Impact of the Digital Filter as a Weak Constraint in the Preoperational 4DVAR Assimilation System of Météo-France , 2001 .

[30]  T. Hamill,et al.  On the Theoretical Equivalence of Differently Proposed Ensemble 3DVAR Hybrid Analysis Schemes , 2007 .

[31]  Jimy Dudhia,et al.  Four-Dimensional Variational Data Assimilation for WRF : Formulation and Preliminary Results , 2009 .

[32]  Dusanka Zupanski,et al.  Four-Dimensional Variational Data Assimilation for the Blizzard of 2000 , 2002 .

[33]  J. Dudhia,et al.  A Revised Approach to Ice Microphysical Processes for the Bulk Parameterization of Clouds and Precipitation , 2004 .

[34]  N. B. Ingleby,et al.  The Met. Office global three‐dimensional variational data assimilation scheme , 2000 .

[35]  Song‐You Hong,et al.  Improvement of the K-profile Model for the Planetary Boundary Layer based on Large Eddy Simulation Data , 2003 .

[36]  Takemasa Miyoshi,et al.  Ensemble Kalman Filter and 4D-Var Intercomparison with the Japanese Operational Global Analysis and Prediction System , 2010 .

[37]  Fuqing Zhang,et al.  Intercomparison of an Ensemble Kalman Filter with Three- and Four-Dimensional Variational Data Assimilation Methods in a Limited-Area Model over the Month of June 2003 , 2011 .

[38]  Craig H. Bishop,et al.  A comparison of the hybrid and EnSRF analysis schemes in the presence of model errors due to unresolved scales , 2009 .

[39]  Chris Snyder,et al.  A Hybrid ETKF-3DVAR Data Assimilation Scheme for the WRF Model. Part I: Observing System Simulation Experiment , 2008 .

[40]  Jordan G. Powers,et al.  A Description of the Advanced Research WRF Version 2 , 2005 .

[41]  Louis J. Wicker,et al.  Wind and Temperature Retrievals in the 17 May 1981 Arcadia, Oklahoma, Supercell: Ensemble Kalman Filter Experiments , 2004 .

[42]  Liang Xu,et al.  Development of NAVDAS-AR: formulation and initial tests of the linear problem , 2005 .

[43]  Wei Huang,et al.  A Three-Dimensional Variational Data Assimilation System for MM5: Implementation and Initial Results , 2004 .

[44]  X. Zou,et al.  Rainfall Assimilation through an Optimal Control of Initial and Boundary Conditions in a Limited-Area Mesoscale Model , 1996 .

[45]  Q. Xiao,et al.  An Ensemble-Based Four-Dimensional Variational Data Assimilation Scheme. Part II: Observing System Simulation Experiments with Advanced Research WRF (ARW) , 2009 .

[46]  Y. Honda,et al.  A pre‐operational variational data assimilation system for a non‐hydrostatic model at the Japan Meteorological Agency: formulation and preliminary results , 2005 .

[47]  G. Evensen.  Sequential data assimilation with a nonlinear quasi‐geostrophic model using Monte Carlo methods to forecast error statistics , 1994 .

[48]  P. Courtier,et al.  Extended assimilation and forecast experiments with a four‐dimensional variational assimilation system , 1998 .

[49]  X. Zou.  Tangent linear and adjoint of''''on-off''''processes and their feasibility for use in 4-dimensional , 1997 .

[50]  Q. Xiao,et al.  An Ensemble-Based Four-Dimensional Variational Data Assimilation Scheme. Part I: Technical Formulation and Preliminary Test , 2008 .

[51]  David J. Stensrud,et al.  Surface Data Assimilation Using an Ensemble Kalman Filter Approach with Initial Condition and Model Physics Uncertainties , 2005 .

[52]  Fuqing Zhang,et al.  Coupling ensemble Kalman filter with four-dimensional variational data assimilation , 2009 .

[53]  C. Snyder,et al.  Assimilation of Simulated Doppler Radar Observations with an Ensemble Kalman Filter , 2003 .

[54]  Thomas M. Hamill,et al.  Ensemble Data Assimilation with the NCEP Global Forecast System , 2008 .

[55]  Chris Snyder,et al.  A Hybrid ETKF–3DVAR Data Assimilation Scheme for the WRF Model. Part II: Real Observation Experiments , 2008 .

[56]  A. Simmons,et al.  The ECMWF operational implementation of four‐dimensional variational assimilation. I: Experimental results with simplified physics , 2007 .

[57]  Chris Snyder,et al.  Mesoscale Predictability of the “Surprise” Snowstorm of 24–25 January 2000 , 2002 .

[58]  Andrew C. Lorenc,et al.  Modelling of error covariances by 4D‐Var data assimilation , 2003 .

[59]  John Derber,et al.  The National Meteorological Center's spectral-statistical interpolation analysis system , 1992 .