The Optimal Control Problem Of Numerical Weather Prediction Model Error

Initial error and model error are key factors restricting the accuracy of numerical weather prediction (NWP).The purpose of the present study is to estimate the time-varying and spatial-varying model errors both in the historical and forecast periods by using recent observations and analogue phenomenon of atmosphere. Considering the continuous evolution of atmosphere, the observed data (ignoring the measurement er-ror) can actually be viewed as a series of solutions of accurate model governing the actual atmosphere, and the model errors can be objectively supposed as an unknown functional term (a missing forcing term) of the numerical model, thus the NWP can be considered as an inverse problem to uncover the unknown model error term by us-ing the long periods of observed data. This study consists of two parts. In the first part, we construct an inverse problem model with its optimization problem, which con-strained by the numerical model, to estimate the time-varying and spatial-varying mod-el errors in historical period by using the historical observations. Then we construct another inverse problem with its optimization problem to extrapolate the time-varying and spatial-varying model errors in the forecast period according to the historical model error dataset and the analogue phenomenon of atmosphere.In order to make it easier to get the useful model error information for the opera-tional NWP model, we present the derivative-free optimization (DFO) methods, such as coordinate searching algorithm and adaptive differential evolution algorithm, to find the minimum solution of the optimization problem by running the numerical model with an external forcing term in the second part. The DFO method doesn’t need to compute the gradient of the objective functional and the tangent linear model or adjoint model of the original numerical model. The precedures described in this study open the possibility of utilizing the past observation data to extract useful information about model errors and enhance the prediction efficiency in the operational models.