Advanced Data Assimilation for Strongly Nonlinear Dynamics

Advanced data assimilation methods become extremely complicated and challenging when used with strongly nonlinear models. Several previous works have reported various problems when applying existing popular data assimilation techniques with strongly nonlinear dynamics. Common for these techniques is that they can all be considered as extensions to methods that have proved to work well with linear dynamics. This paper examines the properties of three advanced data assimilation methods when used with the highly nonlinear Lorenz equations. The ensemble Kalman filter is used for sequential data assimilation and the recently proposed ensemble smoother method and a gradient descent method are used to minimize two different weak constraint formulations. The problems associated with the use of an approximate tangent linear model when solving the Euler‐Lagrange equations, or when the extended Kalman filter is used, are eliminated when using these methods. All three methods give reasonable consistent results with the data coverage and quality of measurements that are used here and overcome the traditional problems reported in many of the previous papers involving data assimilation with highly nonlinear dynamics.

[1]  P. Brasseur,et al.  Data Assimilation: Tools for Modelling the Ocean in a Global Change Perspective , 1994 .

[2]  G. Evensen,et al.  Assimilation of Geosat altimeter data for the Agulhas current using the ensemble Kalman filter with , 1996 .

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

[4]  Robert N. Miller,et al.  Data assimilation into nonlinear stochastic models , 1999 .

[5]  Pierre Gauthier,et al.  Chaos and quadri-dimensional data assimilation: a study based on the Lorenz model , 1992 .

[6]  Boon S. Chua,et al.  Open-ocean modeling as an inverse problem: the primitive equations , 1994 .

[7]  F. Bouttier.  A Dynamical Estimation of Forecast Error Covariances in an Assimilation System , 1994 .

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

[9]  A. Bennett.  Inverse Methods in Physical Oceanography , 1992 .

[10]  A. Bennett,et al.  The generalized inverse of a nonlinear quasigeostrophic ocean circulation model , 1992 .

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

[12]  G. Evensen.  Using the Extended Kalman Filter with a Multilayer Quasi-Geostrophic Ocean Model , 1992 .

[13]  Lance M. Leslie,et al.  Tropical Cyclone Prediction Using a Barotropic Model Initialized by a Generalized Inverse Method , 1993 .

[14]  Michael Ghil,et al.  Advanced data assimilation in strongly nonlinear dynamical systems , 1994 .

[15]  P. Courtier,et al.  Assimilation of Simulated Wind Lidar Data with a Kalman Filter , 1993 .

[16]  G. Evensen,et al.  Data assimilation and inverse methods in terms of a probabilistic formulation , 1996 .

[17]  Robert N. Miller.  Perspectives on Advanced Data Assimilation in Strongly Nonlinear Systems , 1994 .

[18]  G. Evensen.  Inverse methods and data assimilation in nonlinear ocean models , 1994 .