Application of a hybrid EnKF-OI to ocean forecasting

Abstract. Data assimilation methods often use an ensemble to represent the background error covariance. Two approaches are commonly used; a simple one with a static ensemble, or a more advanced one with a dynamic ensemble. The latter is often non-practical due to its high computational requirements. Some recent studies suggested using a hybrid covariance, which is a linear combination of the covariances represented by a static and a dynamic ensemble. Here, the use of the hybrid covariance is first extensively tested with a quasi-geostrophic model and with different analysis schemes, namely the Ensemble Kalman Filter (EnKF) and the Ensemble Square Root Filter (ESRF). The hybrid covariance ESRF (ESRF-OI) is more accurate and more stable than the hybrid covariance EnKF (EnKF-OI), but the overall conclusions are similar regardless of the analysis scheme used. The benefits of using the hybrid covariance are large compared to both the static and the dynamic methods with a small dynamic ensemble. The benefits over the dynamic methods become negligible, but remain, for large dynamic ensembles. The optimal value of the hybrid blending coefficient appears to decrease exponentially with the size of the dynamic ensemble. Finally, we consider a realistic application with the assimilation of altimetry data in a hybrid coordinate ocean model (HYCOM) for the Gulf of Mexico, during the shedding of Eddy Yankee (2006). A 10-member EnKF-OI is compared to a 10-member EnKF and a static method called the Ensemble Optimal Interpolation (EnOI). While 10 members seem insufficient for running the EnKF, the 10-member EnKF-OI reduces the forecast error compared to the EnOI, and improves the positions of the fronts.

[1]  Geir Evensen,et al.  Assimilation of ocean colour data into a biochemical model of the North Atlantic: Part 2. Statistical analysis , 2003 .

[2]  Jiang Zhu,et al.  A “dressed” Ensemble Kalman Filter using the Hybrid Coordinate Ocean Model in the Pacific , 2009 .

[3]  P.Y. Le Traon,et al.  SSALTO/DUACS and operational altimetry , 2003, IGARSS 2003. 2003 IEEE International Geoscience and Remote Sensing Symposium. Proceedings (IEEE Cat. No.03CH37477).

[4]  F. Vukovich Loop Current boundary variations , 1988 .

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

[6]  Laurent Bertino,et al.  Ensemble Optimal Interpolation: multivariate properties in the Gulf of Mexico , 2009, Tellus A.

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

[8]  G. Evensen Data Assimilation: The Ensemble Kalman Filter , 2006 .

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

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

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

[12]  Robert R. Leben,et al.  Frequency of Ring Separations from the Loop Current in the Gulf of Mexico: A Revised Estimate , 2000 .

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

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

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

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

[17]  F. Hernandez,et al.  A mean dynamic topography computed over the world ocean from altimetry, in situ measurements, and a geoid model , 2004 .

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

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

[20]  Laurent Bertino,et al.  High-resolution ensemble forecasting for the Gulf of Mexico eddies and fronts , 2009 .

[21]  Geir Evensen,et al.  Coordinate Transformation on a Sphere Using Conformal Mapping , 1999 .

[22]  Geir Evensen,et al.  Efficiency of high order numerical schemes for momentum advection , 2007 .

[23]  W. Teague,et al.  A Comparison Between the Generalized Digital Environmental Model and Levitus climatologies , 1990 .

[24]  Eric P. Chassignet,et al.  Loop Current Ring Shedding: The Formation of Cyclones and the Effect of Topography , 2005 .

[25]  Lie-Yauw Oey,et al.  Bred-ensemble ocean forecast of loop current and rings , 2007 .

[26]  Peter R. Oke,et al.  Ensemble data assimilation for an eddy‐resolving ocean model of the Australian region , 2005 .

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

[28]  Stephen J. Lord,et al.  Observing System Simulation Experiments , 2010 .

[29]  Initialization of the shallow water equations with open boundaries by the bounded derivative method , 2010 .