Determination of Model Valid Prediction Period Using the Backward Fokker-Planck Equation
Abstract
How long is an ocean (or atmospheric) model valid once it has been integrated from its initial state? What is the model valid prediction period (VPP)? To answer these questions, uncertainty in ocean (or atmospheric) models should be investigated. It is widely recognized that this uncertainty can be traced back to three factors: measurement errors; model errors, such as discretization and uncertain model parameters; and chaotic dynamics. The measurement errors cause uncertainty in initial and/or boundary conditions. The discretization causes small-scale "subgrid" processes to be either discarded or parameterized. The chaotic dynamics may trigger a subsequent amplification of small errors through a complex response. In this study, the authors develop a theoretical framework of model predictability evaluation using VPP, and they illustrate the usefulness and special features of VPP. Section 2 describes the prediction error of deterministic and stochastic models. Section 3 presents an estimate of VPP. Section 4 discusses the determination of VPP for a one-dimensional stochastic dynamical system. Section 5 presents the conclusions. In conclusion, the model VPP depends not only on the instantaneous error growth, but also on the noise level, the tolerance level, and the initial error. A theoretical framework was developed in this study to determine the mean and variability of model VPP for a nonlinear stochastic dynamical system. The joint probability density function of the valid prediction period and initial error satisfies the backward Fokker-Planck equation when the VPP is assumed homogeneous. After solving the backward Fokker-Planck equation, it is easy to obtain the ensemble mean and variance of the model VPP.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2002
- Accession Number
- ADA483219
Entities
People
- C. W. Fan
- Leonid M. Ivanov
- Peter Cheng Chu
Organizations
- Naval Postgraduate School