Properties of Advection Algorithms in the Context of Variational Data Assimilation

Abstract

The influence of numerical advection algorithm properties on variational data assimilation results are investigated. Nonlinear and linear advection algorithms are tested in a 2D idealized scalar advection framework in which the true solution was known. The accuracy of the optimal solutions after the data assimilation was positively correlated with the accuracy of numerical approximations used in both the forward and adjoint advection models. The accuracy of the optimal solutions was significantly smaller in the experiments in which linearized versions of the nonlinear advection algorithm were used. This property was the consequence of the optimization convergence to a local minimum in the cost function. The local minimum was avoided in the experiments in which the adjoint equation was solved by the original nonlinear advection algorithm. The results presented here suggest application of the exact same scalar advection algorithm in forward and adjoint computations in order to obtain, at lower cost, an optimal solution accuracy that is consistent with the forward model accuracy.