Development of a Two-Step EOF Statistical Postprocessing Algorithm to Identify Patterns of Systematic Error and Variance within GEFSv12 Reforecasts

Abstract Analysis of seasonally varying signals of model error biases, as well as the diagnosis of space–time patterns of synoptic error, here is accomplished through the development of a statistical postprocessing algorithm based on time-extended empirical orthogonal functions (EEOFs) built on patterns of variance. This work analyzes GEFSv12 200-hPa geopotential height (Z200) model error against ERA5 reanalysis data. The mean-square error variance between GEFSv12 reforecast and ERA5 grows rapidly after day 7 of a forecast and continues to increase through the end of the 16-day forecast period. At lead time 16, the largest variance occurs in mid- to high-latitude oceanic storm tracks. Variance is highest during hemispheric winter when baroclinic energy is abundant. The seasonal cycle of error shows largest anomalies in the high latitudes during hemispheric winter. After running the titular two-step, space–time EEOF algorithm, a standardized spatial eigenspectrum shows that eigenvalues increase at longer lead times after decreasing in the medium range, demonstrating that the algorithm extracts large-scale signals of systematic error in the long range. Leading wintertime space–time eigenmode pairs include high-latitude blocking structures and Rossby wave trains. Results suggest that the large-scale systematic errors in GEFSv12 Z200 initiate in part from inaccurate representations of phase speeds of atmospheric waves in the polar jet.