Quantification of Forecast Uncertainty Using Polynomial Chaos Expansion

Uncertainty in the forecast based on a dynamical model can arise from the randomness in (1) the initial conditions and/or (2) the forcing term (including both the external forcing and the boundary conditions), and/or (3) the parameters of the model. In each of these cases, the solution of the model is a stochastic process. Methods for quantifying uncertainty in forecast may be classified into two groups: sampling based and non-sampling methods. The classical Monte Carlo methods, the method of unscented transformation, particle filters, to name a few, belong to the sampling based methods. Wiener's Polynomial Chaos (PC) expansion and generalized polynomial chaos expansion are examples of the non-sampling based approach. In this paper, using a model that consists of a system of five coupled ordinary differentiate equations (ODE) which describes the return flow event over the Gulf of Mexico that often occurs during cool season, we study the effectiveness of the PC expansion approach in quantifying the forecast uncertainty by using Hermite polynomials and Legendre polynomials. The PC expansion approach is compared to classical Monte Carlo method.