Local Adjustment of the Background Error Correlation for Surface Analyses over Complex Terrain

Abstract

The terrain between grid points is used to modify locally the background error correlation matrix in an objective analysis system. This modification helps to reduce the influence across mountain barriers of corrections to the background field that are derived from surface observations. This change to the background error correlation matrix is tested using an analytic case of surface temperature that encapsulates the significant features of nocturnal radiation inversions in mountain basins, which can be difficult to analyze because of locally sharp gradients in temperature. Bratseth successive corrections, optimal interpolation, and three-dimensional variational approaches are shown to yield exactly the same surface temperature analysis. Adding the intervening terrain term to the Bratseth approach led to solutions that match more closely the specified analytic solution. In addition, the convergence of the Bratseth solutions to the best linear unbiased estimation of the analytic solution is faster. The intervening terrain term was evaluated in objective analyses over the western United States derived from a modified version of the Advanced Regional Prediction System Data Assimilation System. Local adjustment of the background error correlation matrix led to improved surface temperature analyses by limiting the influence of observations in mountain valleys that may differ from the weather conditions present in adjacent valleys.