Model Error and Predictability over Different Timescales in the Lorenz '96 Systems

Abstract

Prediction problems have been described by Lorenz as falling into two categories. Problems that depend on the initial condition, such as short- to medium-range weather forecasting, are described as ?predictions of the first kind,? while problems that depend on boundary rather than initial conditions, such as, in many cases, the longer-term climatology, are referred to as predictions of the second kind. Both kinds of prediction will be affected by error in the model equations used to approximate the true system. In this paper, predictability over different timescales for the medium-dimensional Lorenz '96 systems is examined. Models are constructed for the purposes of optimizing both short-range prediction and climatological behavior, and studied over a range of forcings for which they show periodic, quasi-periodic, or chaotic behavior. It is shown that, for the models discussed here, there is a link between short- and long-range predictability, which is held independent of the effects of chaos. The role of stochastic terms is considered, and the possible implications for atmospheric or oceanographic modeling are discussed.