Time-frequency localization and long- and short-term memories in the GFS precipitation forecast errors

A time series of GFS daily precipitation forecast errors are computed for 2005-2006 by verifying the GFS 1-7 day precipitation forecasts against UC-Irvine's PERSIANN satellite observations. These errors are then averaged over different geographic areas. The classification of different geographic areas is based on considerations of continents vs. adjacent oceans (e.g., CONUS vs. Pacific/Atlantic Oceans), northern and southern hemispheric counterparts of continents and oceans (e.g., North America vs. South America; North Pacific vs. South Pacific), and Tropics vs. extra-Tropics (e.g., equatorial vs. mid-latitude regions).

Continuous wavelet (CW) analyses of these error time series are conducted. These analyses project the GFS precipitation forecast errors onto both time and frequency subspaces. In this way, one can identify on what time-scale (frequency) of forecast errors occur at what time of the year (season, month, and day). In addition, Hurst parameters are computed for these time series. This latter analysis provides information on whether the GFS precipitation forecasts possess memories in days, weeks, or months, which can give us an insight on how the precipitation forecast errors from GFS are correlated, and what data-assimilation cycles can refresh different time-memories of these forecast errors.