Scale-dependent estimates of the growth of forecast uncertainties in a global prediction system

Abstract

We assess the scale-dependent growth of forecast errors based on a 50-member global forecast ensemble from the European Centre for Medium Range Weather Forecasts. Simulated forecast errors are decomposed into scales and a new parametric model for the representation of the error growth is applied independently to every zonal wavenumber. In contrast to the standard fitting method, the new fitting function involves no time derivatives and provides the asymptotic values of the forecast errors as a function of the fitting parameters. The range of useful prediction skill, estimated as a scale where forecast errors exceed 60% of their asymptotic values is around 7 days on large scales and 2–3 days at 1000 km scale. The new model is easily transformed to the widely used model of Dalcher and Kalnay (1987) to discuss the scale-dependent growth as a sum of two terms, the so-called $ \alpha $ and $ \beta $ terms. Their comparison shows that at planetary scales their contributions to the growth in the first two days are similar whereas at small scales the $ \beta $ term describes most of a rapid exponential growth of errors towards saturation.

Keywords

• forecast errors
• error growth
• parametric models
• prediction limits
• scale dependency