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The future state of a dynamical model depends on control parameters such as initial conditions, model errors, empirical parameters of the model, and boundary conditions. Insufficient knowledge of these parameters leads to uncertainty of the prediction, which implies a probabilistic nature of the problem. The chaotic nature of nonlinear dynamical systems in weather and climate, and in geosciences in general, confirms the fundamentally probabilistic character of dynamical systems. Information about the dynamical state and its uncertainty is collected from observations. Blending the information from observations with information from dynamical models requires a coordinated effort in several areas of Physics and Mathematics: Probability Theory, Estimation Theory, Control Theory, Nonlinear Dynamics and Chaos/Information Theory. Since we are primarily interested in geosciences applications to high-dimensional dynamical systems, the computational component of the problem is also of great importance to our research.
Our research is encompassing all mentioned disciplines with the goal of developing a general methodology for uncertainty estimation of dynamical systems. At present, our focus is the development of the Maximum Likelihood Ensemble Filter (MLEF) with applications to weather, climate, and carbon cycle.
The weather research and forecasting (WRF) model and the maximum likelihood ensemble filter (MLEF) data assimilation approach are used to examine the potential impact of observations from the future Geostationary Operational Environmental Satellite, generation R (GOES-R) on improving our knowledge about clouds. Synthetic radiances are assimilated from the 10.35 μm channel of the GOES-R advanced baseline imager (ABI) employing a ‘non-identical twins’ experimental setup. The experimental results are examined for an extratropical cyclone named Kyrill that produced unusually strong winds, widespread damage and fatalities in Western Europe in January 2007. The data assimilation problem is especially challenging for this case, as there is a large error in the model-simulated radiances resulting from incorrect cloud location. Although this problem is difficult to eliminate, data assimilation results indicate the potential of GOES-R data to significantly reduce these errors. 