A practical approach to sequential estimation of systematic error on near-surface mesoscale grids

Statistical analysis arguments are used to construct an estimation algorithm for systematic error of near-surface temperatures on a mesoscale grid. The systematic error is defined as the observed running-mean error, and an averaging length of 7 days is shown to be acceptable. Those errors are spread over a numerical weather prediction model grid via the statistical analysis equation. Two covariance models are examined: 1) a stationary, isotropic function tuned with the observed running-mean errors and 2) dynamic estimates derived from a recent history of running-mean forecasts. Prediction of error is possible with a diurnal persistence model, where the error at one time of day can be estimated from data with lags of 24-h multiples. The approach is tested on 6 months of 6-h forecasts with the fifth-generation Pennsylvania State University-NCAR Mesoscale Model (MM5) over New Mexico. Results show that for a quantity such as 2-m temperature, the systematic component of error can be effectively predicted on the grid. The gridded estimates fit the observed running-mean errors well. Cross validation shows that predictions of systematic error result in a substantial error reduction where observations are not available. The error estimates show a diurnal evolution, and are not strictly functions of terrain elevation. Observation error covariances, localization operators, and covariance functions in the isotropic case must be tuned for a specific forecast system and observing network, but the process is straightforward. Taken together, the results suggest an effective method for systematic error estimation on near-surface mesoscale grids in the absence of a useful ensemble. Correction for those errors may provide benefits to forecast users.