The Predictability Problem: Effects of Stochastic Perturbations in Multiequilibrium Systems

Abstract

This chapter discusses the predictability problem and the effects of stochastic perturbations in multiequilibrium systems. Most theoretical studies of atmospheric predictability focus on the initial uncertainty and its propagation forward in time through the integration of an otherwise deterministic flow model. The chapter states the predictability problem and discusses the prototype convection model and associated nomenclature, along with the introduction of stochastic forcing. It also analyzes a specific mechanism that arises from the effects of stochastic perturbations on a deterministic flow that possesses more than one possible asymptotic solution regime. The perturbations are introduced to represent the effects, on the model variables, of particular realizations of those scales of motion and physical processes not modeled deterministically, but which occur in the atmosphere. The focus is on the fundamental mechanism of transition between different configurations, using a highly idealized convection model as a prototype. Parameter values and a random forcing process are chosen that facilitate clarity of demonstration, rather than quantitative comparison with atmospheric data. A description of computational procedures is presented, followed by the numerical results. Implications of the results for modeling and predicting atmospheric behavior are also discussed.