Time-frequency Localization and Long- and Short-term Memories In The GFS Precipitation Forecasts

Abstract

Precipitation possesses its own temporal variability, such as seasonal and diurnal cycles. It is important for numerical weather prediction (NWP) models to correctly capture these natural variabilities. Meanwhile, due to uncertainty in the forecast model, there are day-to-day random forecast errors. Hence, a given time series of precipitation forecast errors will most likely consist of variability on several different scales. Distinguishing these signals and variabilities from this complex dataset may provide us with crucial insight into the temporal characteristics of forecast errors. The first issue we investigate in this study is the frequency of our current precipitation forecast errors have, and the time at which these errors occur. In another words, we want to know what time scale the NOAA/NCEP’s Global Forecast System (GFS) precipitation forecast errors project to, (e.g., daily, weekly, or otherwise), and whether these errors occur on a certain day, or in a particular month, or season. The time scale of errors may provide us with the information about the type of precipitation systems that the GFS may have difficulty forecasting. The time information may help us pinpoint the possible physical reasons why the GFS generates these large forecast errors. Once we identify different time scales of forecast errors, we would like to know if these errors possess any time memory. Even errors that appear to be random may still have some built-in persistence or correlation. This is the basic concept of forecast error memory. The different length of these memories may indicate possible model intrinsic deficiencies in different precipitation parameterizations corresponding to different physical scales. In this study, we will use a continuous wavelet to conduct the time-frequency localization of precipitation forecast errors. We will then conduct an analysis for the multi-moment correlation function of the forecast errors. This is known as the Hurst parameter analysis (Lu and Koch 2007). From these analyses, we may gain a better understanding of temporal characteristics of precipitation forecast errors.