Statistical Properties of Three-Hour Prediction “Errors” Derived from the Mesoscale Analysis and Prediction System

Abstract

Statistical properties of observed residuals from the Mesoscale Analysis and Prediction System (MAPS), a real-time data assimilation system, were investigated. Observed residuals are defined as differences between rawinsonde observations interpolated vertically to the model levels and the predicted values from MAPS interpolated horizontally to the radiosonde locations. One-point statistical moments up to order 4 (including skewness and flatness) were computed to investigate the normality of the probability distribution of observed residuals. The finding of near-zero skewness indicates symmetry in the distribution of observed residuals, but values of flatness significantly different from 3 indicate deviations from a normal (Gaussian) distribution. These results are supported by an effective statistical test. The spatial distributions of these statistical moments show strong local variability, which is ascribed to occasional gross errors in the rawinsonde data. The spatial correlation of observed residuals was computed for the Montgomery streamfunction and the components of the horizontal wind, following a model proposed by Roger Daley and used at the European Centre for Medium-Range Weather Forecasts. This model allows for divergence in the analyzed wind field. Complications arising from lateral boundary conditions were addressed. The spatial correlation was also computed from observed residuals of condensation pressure, which is the moisture variable in MAPS. All empirical correlations were approximated by truncated series of Bessel functions. The results are similar to those of other authors, with the exception that 3-h prediction errors in the MAPS model tend to be less geostrophic than 12-h prediction errors in global models, which have coarser resolution. The correlation range for condensation pressure was large, approaching 1000 km, reflecting the conservation of this quantity on isentropic surfaces in nonsaturated flow.