Dynamical Predictability in a Simple General Circulation Model: Average Error Growth

Abstract

Average predictability and error growth are studied in a realistic two-level general circulation model of the atmosphere via a series of Monte Carlo experiments for fixed external forcing (perpetual winter in the Northern Hemisphere). For realistic initial errors, the dependence of the limit of dynamic predictability on total wave number is similar to that found for the ECMWF model for 1980/81 winter conditions, with the lowest wavenumbers showing significant skill for forecast ranges of more than 1 month. For very small amplitude error (1.2 m rms height at 500 mb) distributed according to the climate spectrum, the total error growth is superexponential, reaching a maximum growth rate (2-day doubling time) in about 1 week. A simple empirical model of error variance involving two broad wavenumber bands (large scales: n < 10 and small scales: 10 ≤ n ≤ 15), provides an excellent fit of the GCM's error growth behavior. The interpretation of the empirical model, based on an analogy with the stochastic dynamic equations developed by Epstein, suggests that the initial rapid increase in the growth rate of errors in the large scales is primarily due to interactions with the small-scale error. These interactions have preferred geographical locations associated with the position of the climate mean jet streams. However, the error growth of the small scales is large unaffected by the presence of the large-scale error. The initial strong growth rate (2-day doubling time) of the small scales is attributed to the model's high level of eddy activity.