Making Forecasts for Chaotic Processes in the Presence of Model Error

Numerical weather forecast errors are generated by model deficiencies and by errors in the initial conditions which interact and grow nonlinearly. With recent progress in data assimilation, the accuracy in the initial conditions has been substantially improved so that accounting for systematic errors associated with model deficiencies has become even more important to ensemble prediction and data assimilation applications. This dissertation describes two new methods for reducing the effect of model error in forecasts.The first method is inspired by Leith (1978) who proposed a statistical method to account for model bias and systematic errors linearly dependent on the flow anomalies. DelSole and Hou (1999) showed this method to be successful when applied to a very low order quasi-geostrophic model simulation with artificial "model errors." However, Leith's method is computationally prohibitive for high-resolution operational models. The purpose of the present study is to explore the feasibility of estimating and correcting systematic model errors using a simple and efficient procedure that could be applied operationally, and to compare the impact of correcting the model integration with statistical corrections performed a posteriori. The second method is inspired by the dynamical systems theory of shadowing. Making a prediction for a chaotic physical process involves specifying the probability associated with each possible outcome. Ensembles of solutions are frequently used to estimate this probability distribution. However, for a typical chaotic physical system H and model L of that system, no solution of L remains close to H for all time. We propose an alternative and show how to "inflate" or systematically perturb the ensemble of solutions of L so that some ensemble member remains close to H for orders of magnitude longer than unperturbed solutions of L. This is true even when the perturbations are significantly smaller than the model error.