A comparison of the hybrid and EnSRF analysis schemes in the presence of model errors due to unresolved scales

A hybrid analysis scheme is compared with an ensemble square root filter (EnSRF) analysis scheme in the presence of model errors as a follow-up to a previous perfect-model comparison. In the hybrid scheme, the ensemble perturbations are updated by the ensemble transform Kalman filter (ETKF) and the ensemble mean is updated with a hybrid ensemble and static background-error covariance. The experiments were conducted with a two-layer primitive equation model. The true state was a T127 simulation. Data assimilation experiments were conducted at T31 resolution (3168 complex spectral coefficients), assimilating imperfect observations drawn from the T127 nature run. By design, the magnitude of the truncation error was large, which provided a test on the ability of both schemes to deal with model error. Additive noise was used to parameterize model errors in the background ensemble for both schemes. In the first set of experiments, additive noise was drawn from a large inventory of historical forecast errors; in the second set of experiments, additive noise was drawn from a large inventory of differences between forecasts and analyses. The static covariance was computed correspondingly from the two inventories. The hybrid analysis was statistically significantly more accurate than the EnSRF analysis. The improvement of the hybrid over the EnSRF was smaller when differences of forecasts and analyses were used to form the random noise and the static covariance. The EnSRF analysis was more sensitive to the size of the ensemble than the hybrid. A series of tests was conducted to understand why the EnSRF performed worse than the hybrid. It was shown that the inferior performance of the EnSRF was likely due to the sampling error in the estimation of the model-error covariance in the mean update and the less-balanced EnSRF initial conditions resulting from the extra localizations used in the EnSRF.

[1]  Ryan D. Torn,et al.  A Data Assimilation Case Study Using a Limited-Area Ensemble Kalman Filter , 2007 .

[2]  S. Cohn,et al.  Assessing the Effects of Data Selection with the DAO Physical-Space Statistical Analysis System* , 1998 .

[3]  M. Zupanski.  Maximum Likelihood Ensemble Filter: Theoretical Aspects , 2005 .

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

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

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

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

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

[9]  Renate Hagedorn,et al.  Representing model uncertainty in weather and climate prediction , 2005 .

[10]  P. Courtier,et al.  The ECMWF implementation of three‐dimensional variational assimilation (3D‐Var). I: Formulation , 1998 .

[11]  D. Zupanski.  A General Weak Constraint Applicable to Operational 4DVAR Data Assimilation Systems , 1997 .

[12]  Istvan Szunyogh,et al.  A local ensemble transform Kalman filter data assimilation system for the NCEP global model , 2008 .

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

[14]  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 .

[15]  J. Whitaker,et al.  Ensemble Data Assimilation without Perturbed Observations , 2002 .

[16]  Takemasa Miyoshi,et al.  Localizing the Error Covariance by Physical Distances within a Local Ensemble Transform Kalman Filter (LETKF) , 2007 .

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

[18]  W. Briggs.  Statistical Methods in the Atmospheric Sciences , 2007 .

[19]  Istvan Szunyogh,et al.  Assessing a local ensemble Kalman filter: Perfect model experiments with the NCEP global model , 2004 .

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

[21]  A. O'Neill.  Atmospheric Data Assimilation , 2000 .

[22]  S. Julier,et al.  Which Is Better, an Ensemble of Positive–Negative Pairs or a Centered Spherical Simplex Ensemble? , 2004 .

[23]  P. Houtekamer,et al.  Data Assimilation Using an Ensemble Kalman Filter Technique , 1998 .

[24]  松山 洋.  「Statistical Methods in the Atmospheric Sciences(2nd edition), International Geophysics Series 91」, Daniel S. Wilks著, Academic Press, 2005年11月, 648頁, $94.95, ISBN978-0-12-751966-1(本だな) , 2010 .

[25]  Jeffrey P. Walker,et al.  Extended versus Ensemble Kalman Filtering for Land Data Assimilation , 2002 .

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

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

[28]  J. Whitaker,et al.  An Adjoint Sensitivity Study of Blocking in a Two-Layer Isentropic Model , 1993 .

[29]  Thomas Schlatter,et al.  Some Experiments with a Multivariate Statistical Objective Analysis Scheme , 1975 .

[30]  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 .

[31]  M. Rienecker,et al.  Initial testing of a massively parallel ensemble Kalman filter with the Poseidon isopycnal ocean general circulation model , 2002 .

[32]  Chris Snyder,et al.  Evaluation of a Nonlocal Quasi-Phase Observation Operator in Assimilation of CHAMP Radio Occultation Refractivity with WRF , 2008 .

[33]  P. Houtekamer,et al.  A Sequential Ensemble Kalman Filter for Atmospheric Data Assimilation , 2001 .

[34]  Craig H. Bishop,et al.  A Comparison of Hybrid Ensemble Transform Kalman Filter- OI and Ensemble Square-Root Filter Analysis Schemes , 2006 .

[35]  Eugenia Kalnay,et al.  Weight interpolation for efficient data assimilation with the Local Ensemble Transform Kalman Filter , 2009 .

[36]  Thomas M. Hamill,et al.  Predictability of Weather and Climate: Ensemble-based atmospheric data assimilation , 2006 .

[37]  J. Whitaker,et al.  Accounting for the Error due to Unresolved Scales in Ensemble Data Assimilation: A Comparison of Different Approaches , 2005 .

[38]  Carolyn A. Reynolds,et al.  Stochastic Nature of Physical Parameterizations in Ensemble Prediction: A Stochastic Convection Approach , 2008 .

[39]  Martin Ehrendorfer,et al.  A review of issues in ensemble-based Kalman filtering , 2007 .

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

[41]  Arlindo da Silva,et al.  Data assimilation in the presence of forecast bias , 1998 .

[42]  R. Daley.  Atmospheric Data Analysis , 1991 .

[43]  J. Whitaker,et al.  Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter , 2001 .

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

[45]  C. Bishop,et al.  Resilience of Hybrid Ensemble/3DVAR Analysis Schemes to Model Error and Ensemble Covariance Error , 2004 .

[46]  Lars Nerger,et al.  Ensemble Data Assimilation , 2009 .

[47]  Xue Wei,et al.  Reanalysis without Radiosondes Using Ensemble Data Assimilation , 2004 .

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

[49]  Stéphane Laroche,et al.  Implementation of a 3D variational data assimilation system at the Canadian Meteorological Centre. Part I: The global analysis , 1999 .

[50]  Xuguang Wang,et al.  A Comparison of Breeding and Ensemble Transform Kalman Filter Ensemble Forecast Schemes , 2003 .

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

[52]  M. Buehner,et al.  Atmospheric Data Assimilation with an Ensemble Kalman Filter: Results with Real Observations , 2005 .

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

[54]  Geir Evensen,et al.  The Ensemble Kalman Filter: theoretical formulation and practical implementation , 2003 .

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

[56]  T. Palmer,et al.  Stochastic representation of model uncertainties in the ECMWF ensemble prediction system , 2007 .

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

[58]  Craig H. Bishop,et al.  A Comparison of Hybrid Ensemble Transform Kalman Filter–Optimum Interpolation and Ensemble Square Root Filter Analysis Schemes , 2007 .

[59]  Istvan Szunyogh,et al.  Assessing a local ensemble Kalman filter: perfect model experiments with the National Centers for Environmental Prediction global model , 2005 .

[60]  Jeffrey L. Anderson.  An Ensemble Adjustment Kalman Filter for Data Assimilation , 2001 .