Sequential estimation of systematic error on near-surface mesoscale grids

An optimal filter for systematic error is impossible to achieve in practice because a priori estimates of systematic error and a propagation model for the error are unavailable. When a running-mean error is the system of interest, a suboptimal filter with reduced error is available. Such an algorithm is derived to estimate the 30-day running-mean error on mesoscale grids of 2-m temperature.

The algorithm is tested during a winter season of very short-range MM5 forecasts over New Mexico. Results using an isotropic Gaussian-shaped error covariance model with parameters derived from observed running-mean error, and error covariance estimates from a recent history of running-mean forecasts, are compared. Evaluation at observed location shows that using the Gaussian covariance can produce a gridded estimate that nearly perfectly agrees with observations. The estimated covariance results in less agreement with observations because the model does not support the necessary variability. Cross validation shows that estimates of systematic error at unobserved locations are better when using running-mean forecasts rather than an isotropic covariance model. The results suggest that when systematic error is significant, the total error can be reduced by using a filter based on running-means.