A Simulation Study Using a Local Ensemble Transform Kalman Filter for Data Assimilation in New York Harbor

Data assimilation approaches that use ensembles to approximate a Kalman filter have many potential advantages for oceanographic applications. To explore the extent to which this holds, the Estuarine and Coastal Ocean Model (ECOM) is coupled with a modern data assimilation method based on the local ensemble transform Kalman filter (LETKF), and a series of simulation experiments is conducted. In these experiments, a long ECOM “nature” run is taken to be the “truth.” Observations are generated at analysis times by perturbing the nature run at randomly chosen model grid points with errors of known statistics. A diverse collection of model states is used for the initial ensemble. All experiments use the same lateral boundary conditions and external forcing fields as in the nature run. In the data assimilation, the analysis step combines the observations and the ECOM forecasts using the Kalman filter equations. As a control, a free-running forecast (FRF) is made from the initial ensemble mean to check the relative importance of external forcing versus data assimilation on the analysis skill. Results of the assimilation cycle and the FRF are compared to truth to quantify the skill of each. The LETKF performs well for the cases studied here. After just a few assimilation cycles, the analysis errors are smaller than the observation errors and are much smaller than the errors in the FRF. The assimilation quickly eliminates the domain-averaged bias of the initial ensemble. The filter accurately tracks the truth at all data densities examined, from observations at 50% of the model grid points down to 2% of the model grid points. As the data density increases, the ensemble spread, bias, and error standard deviation decrease. As the ensemble size increases, the ensemble spread increases and the error standard deviation decreases. Increases in the size of the observation error lead to a larger ensemble spread but have a small impact on the analysis accuracy.

[1]  Ichiro Fukumori,et al.  A Partitioned Kalman Filter and Smoother , 2002 .

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

[3]  Carl Wunsch,et al.  Global ocean circulation during 1992-1997, estimated from ocean observations and a general circulation model , 2002 .

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

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

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

[7]  Istvan Szunyogh,et al.  Local ensemble Kalman filtering in the presence of model bias , 2006 .

[8]  Alan F. Blumberg,et al.  Evaluation of the Northern Gulf of Mexico Littoral Initiative Model Based On the Observed Temperature and Salinity In the Mississippi Bight , 2005 .

[9]  R. Signell,et al.  Modeling the seasonal circulation in Massachusetts Bay , 1994 .

[10]  N. A. Phillips,et al.  A COORDINATE SYSTEM HAVING SOME SPECIAL ADVANTAGES FOR NUMERICAL FORECASTING , 1957 .

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

[12]  Istvan Szunyogh,et al.  Assessing a local ensemble Kalman filter : perfect model experiments with the National Centers for Environmental Prediction global model , 2004 .

[13]  Carl Wunsch,et al.  Practical global oceanic state estimation , 2007 .

[14]  Andrew C. Lorenc,et al.  Development of an Operational Variational Assimilation Scheme (gtSpecial IssueltData Assimilation in Meteology and Oceanography: Theory and Practice) , 1997 .

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

[16]  Shian‐Jiann Lin,et al.  Multidimensional Flux-Form Semi-Lagrangian Transport Schemes , 1996 .

[17]  G. Mellor,et al.  Development of a turbulence closure model for geophysical fluid problems , 1982 .

[18]  A. Blumberg,et al.  Three-dimensional hydrodynamic model of New York Harbor region , 1999 .

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

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

[21]  P. Malanotte‐Rizzoli,et al.  An approximate Kaiman filter for ocean data assimilation: An example with an idealized Gulf Stream model , 1995 .

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

[23]  Alan F. Blumberg,et al.  Modeling of wind-induced destratification in Chesapeake Bay , 1990 .

[24]  G. Mellor,et al.  A time-dependent, three-dimensional model of the Delaware Bay and River system. Part 1: Description of the model and tidal analysis , 1990 .

[25]  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 .

[26]  L. Oey,et al.  Assimilation of drifter and satellite data in a model of the Northeastern Gulf of Mexico , 2004 .

[27]  Modeling hydrodynamics of the Mississippi Sound and adjoining rivers, bays and shelf waters , 2000, OCEANS 2000 MTS/IEEE Conference and Exhibition. Conference Proceedings (Cat. No.00CH37158).

[28]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[29]  George L. Mellor,et al.  A Gulf Stream model and an altimetry assimilation scheme , 1991 .

[30]  Istvan Szunyogh,et al.  Local ensemble Kalman filtering in the presence of model bias , 2006 .

[31]  Pierre F. J. Lermusiaux,et al.  Quantifying Uncertainties in Ocean Predictions , 2006 .

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

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

[34]  Alan F. Blumberg,et al.  Three-Dimensional Hydrothermal Model of Onondaga Lake, New York , 1999 .

[35]  P. A. Newberger,et al.  Downwelling Circulation on the Oregon Continental Shelf. Part I: Response to Idealized Forcing , 1995 .

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