Backward Fokker‐Planck equation for determining model valid prediction period

Abstract

A new concept, valid prediction period (VPP), is presented here to evaluate ocean (or atmospheric) model predictability. VPP is defined as the time period when the prediction error first exceeds a predetermined criterion (i.e., the tolerance level). It depends not only on the instantaneous error growth but also on the noise level, the initial error, and the tolerance level. The model predictability skill is then represented by a single scalar, VPP. The longer the VPP, the higher the model predictability skill is. A theoretical framework on the basis of the backward Fokker‐Planck equation is developed to determine the mean and variance of VPP. A one‐dimensional stochastic dynamical system [ Nicolis , 1992 ] is taken as an example to illustrate the benefits of using VPP for model evaluation.