Making forecasts for chaotic processes in the presence of model error

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. An elementary data assimilation scheme (Newtonian relaxation) is used to compare two simple but realistic global models, one quasi-geostrophic and one based on the primitive equations, to the NCEP reanalysis (approximating the real atmosphere). Forecasts corrected during model integration with a seasonally-dependent estimate of the bias remain useful longer than forecasts corrected a posteriori. The diurnal correction (based on the leading EOFs of the analysis increments) is also successful. Although the global impact of this computationally efficient method is small, it succeeds in reducing state-dependent model systematic errors in regions where they are large. The method requires only a time series of analysis increments to estimate the error covariance and uses negligible additional computation during a forecast. As a result, it should be suitable for operational use at virtually no computational expense.; 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. (Abstract shortened by UMI.)...