Correlation-Cutoff Method for Covariance Localization in Strongly Coupled Data Assimilation

Strongly coupled data assimilation (SCDA), where observations of one component of a coupled model are allowed to directly impact the analysis of other components, sometimes fails to improve the analysis accuracy with an ensemble Kalman filter (EnKF) as compared with weakly coupled data assimilation (WCDA). It is well known that an observation’s area of influence should be localized in EnKFs since the assimilation of distant observations often degrades the analysis because of spurious correlations. This study derives a method to estimate the reduction of the analysis error variance by using estimates of the cross covariances between the background errors of the state variables in an idealized situation. It is shown that the reduction of analysis error variance is proportional to the squared background error correlation between the analyzed and observed variables. From this, the authors propose an offline method to systematically select which observations should be assimilated into which model state variable by cutting off the assimilation of observations when the squared background error correlation between the observed and analyzed variables is small. The proposed method is tested with the local ensemble transform Kalman filter (LETKF) and a nine-variable coupled model, in which three Lorenz models with different time scales are coupled with each other. The covariance localization with the correlation-cutoff method achieves an analysis more accurate than either the full SCDA or the WCDA methods, especially with smaller ensemble sizes.

[1]  Kristian Mogensen,et al.  A coupled data assimilation system for climate reanalysis , 2016 .

[2]  Takuma Yoshida,et al.  Covariance Localization in Strongly Coupled Data Assimilation , 2019 .

[3]  E. Kalnay,et al.  Lyapunov, singular and bred vectors in a multi-scale system: an empirical exploration of vectors related to instabilities , 2013 .

[4]  E. Kalnay,et al.  Separating fast and slow modes in coupled chaotic systems , 2004 .

[5]  Wei Li,et al.  Error Covariance Estimation for Coupled Data Assimilation Using a Lorenz Atmosphere and a Simple Pycnocline Ocean Model , 2013 .

[6]  Stephen G. Penny,et al.  Assimilating atmospheric observations into the ocean using strongly coupled ensemble data assimilation , 2016 .

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

[8]  Geoffrey K. Vallis,et al.  Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation , 2017 .

[9]  A. Rosati,et al.  System Design and Evaluation of Coupled Ensemble Data Assimilation for Global Oceanic Climate Studies , 2007 .

[10]  Robert Jacob,et al.  Strongly Coupled Data Assimilation Using Leading Averaged Coupled Covariance (LACC). Part II: CGCM Experiments* , 2015 .

[11]  Stephen G. Penny,et al.  Coupled Data Assimilation for Integrated Earth System Analysis and Prediction: Goals, Challenges, and Recommendations , 2017 .

[12]  E. Kalnay,et al.  Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter , 2009 .

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

[14]  Dake Chen,et al.  An Improved Procedure for EI Ni�o Forecasting: Implications for Predictability , 1995, Science.

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

[16]  A. Rosati,et al.  The Adequacy of Observing Systems in Monitoring the Atlantic Meridional Overturning Circulation and North Atlantic Climate , 2010 .

[17]  Lars Nerger,et al.  On Serial Observation Processing in Localized Ensemble Kalman Filters , 2015 .

[18]  Antonio J. Busalacchi,et al.  The Tropical Ocean‐Global Atmosphere observing system: A decade of progress , 1998 .

[19]  Gregory J. Hakim,et al.  Coupled atmosphere–ocean data assimilation experiments with a low-order climate model , 2014, Climate Dynamics.

[20]  E. Kalnay,et al.  Finding the driver of local ocean–atmosphere coupling in reanalyses and CMIP5 climate models , 2017, Climate Dynamics.

[21]  Uang,et al.  The NCEP Climate Forecast System Reanalysis , 2010 .

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

[23]  R. Jacob.  Low frequency variability in a simulated atmosphere-ocean system , 1997 .

[24]  Mariana Vertenstein,et al.  A global coupled ensemble data assimilation system using the Community Earth System Model and the Data Assimilation Research Testbed , 2018, Quarterly Journal of the Royal Meteorological Society.

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

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

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

[28]  Dara Entekhabi,et al.  The role of model dynamics in ensemble Kalman filter performance for chaotic systems , 2011 .

[29]  Nancy Nichols,et al.  Estimating Forecast Error Covariances for Strongly Coupled Atmosphere–Ocean 4D-Var Data Assimilation , 2017 .

[30]  Shunji Kotsuki,et al.  Can We Optimize the Assimilation Order in the Serial Ensemble Kalman Filter? A Study with the Lorenz-96 Model , 2017 .

[31]  Kayo Ide,et al.  “Variable localization” in an ensemble Kalman filter: Application to the carbon cycle data assimilation , 2011 .

[32]  Lawrence L. Takacs,et al.  Data Assimilation Using Incremental Analysis Updates , 1996 .

[33]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[34]  Mark Buehner,et al.  Coupled Data Assimilation for Integrated Earth System Analysis and Prediction: Goals, Challenges, and Recommendations , 2017 .

[35]  Hong Li,et al.  Data Assimilation as Synchronization of Truth and Model: Experiments with the Three-Variable Lorenz System* , 2006 .

[36]  James Cummings,et al.  Facilitating Strongly Coupled Ocean-Atmosphere Data Assimilation with an Interface Solver , 2016 .

[37]  Christopher K. Wikle,et al.  Atmospheric Modeling, Data Assimilation, and Predictability , 2005, Technometrics.

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

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

[40]  Istvan Szunyogh,et al.  A Local Ensemble Kalman Filter for Atmospheric Data Assimilation , 2002 .

[41]  Feiyu Lu,et al.  Strongly Coupled Data Assimilation Using Leading Averaged Coupled Covariance (LACC). Part I: Simple Model Study* , 2015 .

[42]  Luigi Palatella,et al.  Nonlinear Processes in Geophysics On the Kalman Filter error covariance collapse into the unstable subspace , 2011 .

[43]  Istvan Szunyogh,et al.  Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter , 2005, physics/0511236.

[44]  Keith Haines,et al.  Origin and impact of initialisation shocks in coupled atmosphere-ocean forecasts , 2015 .

[45]  E. Kalnay,et al.  Balance and Ensemble Kalman Filter Localization Techniques , 2011 .