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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.
A parameter estimation problem in context of ensemble data assimilation is addressed. In an example using a one-point soil temperature model, the parameters corresponding to the emissivity and to the effective depth between the surface and the lowest atmospheric model level are estimated together with the initial conditions for temperature. The nonlinear synthetic observations representing various fluxes are assimilated using the Maximum Likelihood Ensemble Filter (MLEF). The results indicate that typical data assimilation that adjusts only initial conditions may not be appropriate if the model has incorrectly specified key parameters. As indicated by our experiments, this may lead to a large error of the prediction model. A simultaneous estimation of the initial conditions and model parameters seem to be a preferred choice. We also show that the estimated uncertainties are in general agreement with actual uncertainties.