Application of the Gaussian anamorphosis to assimilation in a 3-D coupled physical-ecosystem model of the North Atlantic with the EnKF: a twin experiment

Abstract. We consider the application of the Ensemble Kalman Filter (EnKF) to a coupled ocean ecosystem model (HYCOM-NORWECOM). Such models, especially the ecosystem models, are characterized by strongly non-linear interactions active in ocean blooms and present important difficulties for the use of data assimilation methods based on linear statistical analysis. Besides the non-linearity of the model, one is confronted with the model constraints, the analysis state having to be consistent with the model, especially with respect to the constraints that some of the variables have to be positive. Furthermore the non-Gaussian distributions of the biogeochemical variables break an important assumption of the linear analysis, leading to a loss of optimality of the filter. We present an extension of the EnKF dealing with these difficulties by introducing a non-linear change of variables (anamorphosis function) in order to execute the analysis step in a Gaussian space, namely a space where the distributions of the transformed variables are Gaussian. We present also the initial results of the application of this non-Gaussian extension of the EnKF to the assimilation of simulated chlorophyll surface concentration data in a North Atlantic configuration of the HYCOM-NORWECOM coupled model.

[1]  Janet W. Campbell,et al.  The lognormal distribution as a model for bio‐optical variability in the sea , 1995 .

[2]  Lars Nerger,et al.  Assimilation of SeaWiFS data into a global ocean-biogeochemical model using a local SEIK filter , 2007 .

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

[4]  G. Evensen,et al.  Assimilation of ocean colour data into a biochemical model of the North Atlantic: Part 1. Data assimilation experiments , 2003 .

[5]  William Carlisle Thacker,et al.  Data assimilation with inequality constraints , 2007 .

[6]  F. L. Dimet,et al.  Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects , 1986 .

[7]  Laurent Bertino,et al.  The TOPAZ monitoring and prediction system for the Atlantic and Arctic Oceans , 2008 .

[8]  G. Evensen,et al.  Sequential Data Assimilation Techniques in Oceanography , 2003 .

[9]  Geir Evensen,et al.  A singular evolutive extended Kalman filter to assimilate ocean color data in a coupled physical–biochemical model of the North Atlantic ocean , 2001 .

[10]  P. Friederichs,et al.  Multivariate non-normally distributed random variables in climate research - introduction to the copula approach , 2008 .

[11]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[12]  Watson W. Gregg,et al.  Skill Assessment in Ocean Biological Data Assimilation , 2009 .

[13]  Y. Sasaki,et al.  A Fundamental Study of the Numerical Prediction Based on the Variational Principle , 1955 .

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

[15]  J. Chilès,et al.  Geostatistics: Modeling Spatial Uncertainty , 1999 .

[16]  Jean-Michel Brankart,et al.  A truncated Gaussian filter for data assimilation with inequality constraints: Application to the hydrostatic stability condition in ocean models , 2008 .

[17]  Ricardo Torres,et al.  Sequential data assimilation in an upwelling influenced estuary , 2006 .

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

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

[20]  Ibrahim Hoteit,et al.  A singular evolutive interpolated Kalman filter for efficient data assimilation in a 3-D complex physical biogeochemical model of the Cretan Sea , 2003 .

[21]  P. Courtier,et al.  A strategy for operational implementation of 4D‐Var, using an incremental approach , 1994 .

[22]  Jens Schröter,et al.  Sequential weak constraint parameter estimation in an ecosystem model , 2003 .

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

[24]  G. Evensen,et al.  An Ensemble Kalman Filter with a complex marine ecosystem model: hindcasting phytoplankton in the Cretan Sea , 2003 .

[25]  Rainer Bleck,et al.  An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates , 2002 .

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

[27]  W. Gregg,et al.  Global and regional evaluation of the SeaWiFS chlorophyll data set , 2004 .

[28]  J. Siddorn,et al.  How well can we forecast high biomass algal bloom events in a eutrophic coastal sea , 2008 .

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

[30]  E. Hunke,et al.  An Elastic–Viscous–Plastic Model for Sea Ice Dynamics , 1996 .

[31]  A. Samuelsen,et al.  Influence of horizontal model grid resolution on the simulated primary production in an embedded primary production model in the Norwegian Sea , 2009 .

[32]  M. Skogen,et al.  A user's guide to NORVECOM V2.0. the norwegian ecological model system , 1998 .

[33]  Dag L. Aksnes,et al.  Ecological modelling in coastal waters: Towards predictive physical-chemical-biological simulation models , 1995 .

[34]  Jacques Verron,et al.  A singular evolutive extended Kalman filter for data assimilation in oceanography , 1998 .