A hybrid data assimilation scheme for model parameter estimation: Application to morphodynamic modelling

We present a novel algorithm for joint state-parameter estimation using sequential three dimensional variational data assimilation (3D Var) and demonstrate its application in the context of morphodynamic modelling using an idealised two parameter 1D sediment transport model. The new scheme combines a static representation of the state background error covariances with a flow dependent approximation of the state-parameter cross-covariances. For the case presented here, this involves calculating a local finite difference approximation of the gradient of the model with respect to the parameters. The new method is easy to implement and computationally inexpensive to run. Experimental results are positive with the scheme able to recover the model parameters to a high level of accuracy. We expect that there is potential for successful application of this new methodology to larger, more realistic models with more complex parameterisations.

[1]  Clive D Rodgers,et al.  Inverse Methods for Atmospheric Sounding: Theory and Practice , 2000 .

[2]  James A. Hansen,et al.  On stochastic parameter estimation using data assimilation , 2007 .

[3]  Ionel Michael Navon,et al.  Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography , 1998 .

[4]  Nancy Nichols,et al.  Variational data assimilation for parameter estimation: application to a simple morphodynamic model , 2009 .

[5]  Nancy Nichols,et al.  Assimilation of data into an ocean model with systematic errors near the equator , 2004 .

[6]  Tania Ruth Scott,et al.  Data assimilation for a coastal area morphodynamic model: Morecambe Bay , 2007 .

[7]  Nancy Nichols,et al.  Treatment of systematic errors in sequential data assimilation , 1999 .

[8]  Michael Ghil,et al.  Data Assimilation for a Coupled Ocean–Atmosphere Model. Part II: Parameter Estimation , 2008 .

[9]  R. Soulsby.  Dynamics of marine sands , 1997 .

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

[11]  Nancy Nichols,et al.  Data assimilation for morphodynamic model parameter estimation: a hybrid approach , 2009 .

[12]  Eric P. Chassignet,et al.  Ocean modeling and parameterization , 1998 .

[13]  Nancy Nichols,et al.  Mathematical Concepts of Data Assimilation , 2010 .

[14]  Ian G. Enting,et al.  Using the Kalman filter for parameter estimation in biogeochemical models , 2008 .

[15]  Jens Schröter,et al.  Parameter Estimation in Dynamical Models , 1998 .

[16]  Philip E. Gill,et al.  Practical optimization , 1981 .

[17]  P. Courtier,et al.  The ECMWF implementation of three‐dimensional variational assimilation (3D‐Var). I: Formulation , 1998 .

[18]  Michael C. Quick,et al.  Sediment transport by waves and currents , 1983 .

[19]  B. Khattatov,et al.  Data assimilation : making sense of observations , 2010 .

[20]  Richard F. Katz,et al.  A semi‐Lagrangian Crank‐Nicolson algorithm for the numerical solution of advection‐diffusion problems , 2006 .

[21]  J. F. A. Sleath,et al.  Sediment transport by waves and currents , 1995 .

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

[23]  Ap van Dongeren,et al.  Beach Wizard: Nearshore bathymetry estimation through assimilation of model computations and remote observations , 2008 .

[24]  Nancy Nichols,et al.  Adjoint Methods in Data Assimilation for Estimating Model Error , 2000 .