A Non-Gaussian Ensemble Filter Update for Data Assimilation

Abstract A deterministic square root ensemble Kalman filter and a stochastic perturbed observation ensemble Kalman filter are used for data assimilation in both linear and nonlinear single variable dynamical systems. For the linear system, the deterministic filter is simply a method for computing the Kalman filter and is optimal while the stochastic filter has suboptimal performance due to sampling error. For the nonlinear system, the deterministic filter has increasing error as ensemble size increases because all ensemble members but one become tightly clustered. In this case, the stochastic filter performs better for sufficiently large ensembles. A new method for computing ensemble increments in observation space is proposed that does not suffer from the pathological behavior of the deterministic filter while avoiding much of the sampling error of the stochastic filter. This filter uses the order statistics of the prior observation space ensemble to create an approximate continuous prior probability dis...

[1]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[2]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[3]  M. Suárez,et al.  A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models , 1994 .

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

[5]  Jeffrey L. Anderson.  A Method for Producing and Evaluating Probabilistic Forecasts from Ensemble Model Integrations , 1996 .

[6]  G. Evensen,et al.  Analysis Scheme in the Ensemble Kalman Filter , 1998 .

[7]  K. Emanuel,et al.  Optimal Sites for Supplementary Weather Observations: Simulation with a Small Model , 1998 .

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

[9]  Jeffrey L. Anderson,et al.  A Monte Carlo Implementation of the Nonlinear Filtering Problem to Produce Ensemble Assimilations and Forecasts , 1999 .

[10]  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 .

[11]  T. Hamill.  Interpretation of Rank Histograms for Verifying Ensemble Forecasts , 2001 .

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

[13]  D. Pham.  Stochastic Methods for Sequential Data Assimilation in Strongly Nonlinear Systems , 2001 .

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

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

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

[17]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

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

[19]  D. McLaughlin,et al.  Hydrologic Data Assimilation with the Ensemble Kalman Filter , 2002 .

[20]  P. J. van Leeuwen,et al.  A variance-minimizing filter for large-scale applications , 2003 .

[21]  Jeffrey L. Anderson.  A Local Least Squares Framework for Ensemble Filtering , 2003 .

[22]  J. Whitaker,et al.  Ensemble Square Root Filters , 2003, Statistical Methods for Climate Scientists.

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

[24]  J. Hansen,et al.  Implications of Stochastic and Deterministic Filters as Ensemble-Based Data Assimilation Methods in Varying Regimes of Error Growth , 2004 .

[25]  P. L. Houtekamer,et al.  Ensemble Kalman filtering , 2005 .

[26]  Olwijn Leeuwenburgh,et al.  The impact of ensemble filter definition on the assimilation of temperature profiles in the tropical Pacific , 2005 .

[27]  Timothy J. Hoar,et al.  Assimilation of Surface Pressure Observations Using an Ensemble Filter in an Idealized Global Atmospheric Prediction System , 2005 .

[28]  W. Collins,et al.  The Formulation and Atmospheric Simulation of the Community Atmosphere Model Version 3 (CAM3) , 2006 .

[29]  P. Bickel,et al.  Obstacles to High-Dimensional Particle Filtering , 2008 .

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

[31]  P. Oke,et al.  Implications of the Form of the Ensemble Transformation in the Ensemble Square Root Filters , 2008 .

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

[33]  Peter R. Oke,et al.  A deterministic formulation of the ensemble Kalman filter : an alternative to ensemble square root filters , 2008 .

[34]  Jeffrey L. Anderson,et al.  The Data Assimilation Research Testbed: A Community Facility , 2009 .

[35]  Stephen J. Thomas,et al.  A robust formulation of the ensemble Kalman filter , 2009 .

[36]  J.L. Anderson,et al.  Ensemble Kalman filters for large geophysical applications , 2009, IEEE Control Systems.

[37]  Jeffrey L. Anderson.  Spatially and temporally varying adaptive covariance inflation for ensemble filters , 2009 .

[38]  Alexander Y. Sun,et al.  Comparison of deterministic ensemble Kalman filters for assimilating hydrogeological data , 2009 .

[39]  G. Evensen.  The ensemble Kalman filter for combined state and parameter estimation , 2009, IEEE Control Systems.

[40]  P. L. Houtekamer,et al.  Ensemble Kalman Filter Configurations and Their Performance with the Logistic Map , 2009 .