Correcting for Position Errors in Variational Data Assimilation
We present an implementation of a displacement scheme to correct phase errors based on the feature calibration and alignment procedure described in Grassotti et al. (1999). In its original formulation, a set of two-dimensional displacement vectors is applied to forecast fields to improve the alignment of features in the forecast and observations. These displacement vectors are obtained by a nonlinear minimization of a cost function that measures the misfit to observations, along with a number of additional constraints (e.g., smoothness and non-divergence of the displacement vectors) to prevent unphysical solutions. Results from this implementation will be compared with a more recent implementation within the WRF-Var algorithm, in which the nonlinear minimization is replaced by the (linear) conjugate gradient inner-loop minimization combined with outer loop nonlinear adjustments, and the ad-hoc penalty function constraints are replaced by an error-covariance representation of the displacement vectors (analogous to the regularization proposed by Nehrkorn et al. 2003). Approaches to deal with questions of model imbalance will be described for the example of the WRF model.