An adaptive variational method for data assimilation with imperfect models

Abstract

The solutions of the weak constraint data assimilation problems depend on a priori errorcovariance. If a priori error covariance have poor quality, a posteriori evaluation may havenegative impact and solutions are not optimal. A novel variational data assimilation methodis proposed, which does not assume the model is perfect, and can adaptively adjust model statewithout knowing explicitly the model error covariance matrix. Not by adjusting the initialcondition in 4D-VAR, but by adjusting a steady gain matrix in a class of filters in this approachto yield a filter solution that minimize the norm of analysis innovation vector in a given spanof time interval. The method enables very flexible ways to form some reduced order problems.A proper reduced-order problem not only reduces computational burden but leads to correctionsthat are more consistent with the model dynamics that trends to produce better forecast.It is shown that the optimal nudging can be reinterpreted as an example of the reduced orderproblems. The method is demonstrated using a simple nonlinear model (Burgers equationmodel) and simulated data. Full and several reduced order forms of the adaptive variationalmethod are performed and compared with a simplified strong constraint 4D-VAR and the spacevariable optimal nudging scheme in assimilation-forecast experiments.