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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.
Assimilation of remote-sensed precipitation observations into numerical weather prediction models can improve precipitation forecasts and extend prediction capabilities in hydrological applications. This paper presents a new regional ensemble data assimilation system that assimilates precipitation-affected microwave radiances into the Weather Research and Forecasting (WRF) model. To meet the challenges in satellite data assimilation involving cloud and precipitation processes, hydrometeors produced by the cloud-resolving model are included as control variables and ensemble forecasts are used to estimate flow-dependent background error covariance. Two assimilation experiments have been conducted using precipitation-affected radiances from passive microwave sensors, one for a tropical storm after landfall and the other for a heavy rain event in southeastern US. The experiments examined the propagation of information in observed radiances via flow-dependent background error auto- and cross-covariance, as well as the error statistics of observational radiance. The results show that ensemble assimilation of precipitation-affected radiances improves the quality of precipitation analysis in terms of spatial distribution and intensity in accumulated surface rainfall, as verified by independent ground-based precipitation observations. 