Estimation of Data Assimilation Error: A Shallow-Water Model Study

Four-dimensional variational data assimilation (4D-Var) produces unavoidable inaccuracies in the models initial state vector. In this paper the authors investigate a novel variational error estimation method to calculate these inaccuracies. The impacts of model, background, and observational errors on the state estimate produced by 4D-Var are analyzed by applying the variational error estimation method. The structure of the method is similar to the conventional 4D-Var, with the differences in that (i) instead of observations it assimilates observational errors, and (ii) the original model equations (used in 4D-Var as constraints) are first linearized with respect to a small perturbation in the initial state vector and then used as the constraints. The authors then carry out a proof-of-concept study and validate the reliability of this method through multiple twin experiments on the basis of a 2D shallow-water model. All required differentiated models were generated by means of algorithmic differentiation directly from the nonlinear model source code. The experiments reveal that the suggested method works well in a wide range of assimilation windows and types of observational and model errors and can be recommended for error estimation and prediction in data assimilation.