PhD Dissertation Prospectus Applied Mathematics and Scientific Computation Exploring satellite data assimilation with a local ensemble

Weather models forecast the future state of the atmosphere from an estimate of the current state of the atmosphere. However, the atmosphere is a chaotic physical system. That is, small differences illithe current state of the atmosphere lead to dramatic differences in weather events later on. Even if weather mgdels were perfect, small errors in the estimate for the current state of the atmosphere will yield large errors in the-resulting forecasts. In order to minimize these errors, "data assimilation " seeks an accurate estimate for the current state of the atmosphere using both current and past observations. Data assimilation schemes start with an estimate for the current state of the atmosphere provided by a prior forecast. They seek an analysis state that combines information from current observations and the forecast state (or "background"), relative to their error covariances, which quantify the uncertainty of each type of information. Many operational techniques, such as 3D-VAR and 4D-VAR, assume that the background error covariances are constant in time, spatially homogeneous, and isotropic. Ensemble schemes use the sample covariance from an ensemble of forecasts to estimate a flow dependent the background error covariance. In this way, ensemble schemes can better account for the "errors of the day " '[11] than many operational data assimilation schemes [15]. Satellites provide dense observation coverage over the entire globe. However, these observations ar