Abstract
Abstract. The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find unknown parameters of the model. The observation data, and hence the optimal solution, may contain uncertainties. A response function is considered as a functional of the optimal solution after assimilation. Based on the second-order adjoint techniques, the sensitivity of the response function to the observation data is studied. The gradient of the response function is related to the solution of a nonstandard problem involving the coupled system of direct and adjoint equations. The nonstandard problem is studied, based on the Hessian of the original cost function. An algorithm to compute the gradient of the response function with respect to observations is presented. A numerical example is given for the variational data assimilation problem related to sea surface temperature for the Baltic Sea thermodynamics model.
Highlights
The methods of data assimilation have become an important tool for analysis of complex physical phenomena in various fields of science and technology
The problems of variational data assimilation can be formulated as optimal control problems (e.g., Lions, 1968; Le Dimet and Talagrand, 1986) to find unknown model parameters, such as initial and/or boundary conditions, right-hand sides in the model equations, and distributed coefficients, based on minimization of the cost function related to observations
The first studies of sensitivity of the response functions after assimilation with the use of second-order adjoint were done by Le Dimet et al (1997) for variational data assimilation problems aimed at restoration of initial condition, where sensitivity with respect to model parameters was considered
Summary
The methods of data assimilation have become an important tool for analysis of complex physical phenomena in various fields of science and technology. The first studies of sensitivity of the response functions after assimilation with the use of second-order adjoint were done by Le Dimet et al (1997) for variational data assimilation problems aimed at restoration of initial condition, where sensitivity with respect to model parameters was considered. This paper is based on the results of Shutyaev et al (2017) and presents the sensitivity analysis with respect to observations in variational data assimilation aimed at restoration of unknown parameters of a dynamic model. We consider a dynamic formulation of the variational data assimilation problem for parameter estimation in a continuous form, but the presented sensitivity analysis formulas with respect to observations do not follow from our previous results for the initial condition problem (Shutyaev et al, 2017) and constitute a novelty of this paper.
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