Optimal observations-based retrieval of topography in 2D shallow water equations using PC-EnKF

Parameter estimation is an important problem because in many instance uncertain parameters cannot be measured accurately, especially in real-time applications. Information about them is commonly inferred via parameter estimation techniques from available measurements of different aspects of the system response. In this work, we consider the reduction of the uncertain topography parameters of 2D shallow water equations to be inconsistency with the physical observations. This is often quite challenging due to its ill-posed nature of the inverse problem, particularly for the present nonlinear case in high-dimensional random space. We have explored an efficient computational strategy for the solution of the problem in the framework of the polynomial chaos (PC)-based ensemble Kalman filter (PC-EnKF for short). The main idea pursued in this methodology is to introduce a determination of the potential optimal observation location followed by the update of the input topography parameters to be retrieved through the PC-EnKF, wherein the identification of the optimal observation locations is accomplished sequentially via the predictive uncertainty controlled by standard deviation, and then places the corresponding measurement for data assimilation purpose. This is not only to provide more informative measurements but also to improve the topography parameters estimation. The numerical experiments indicate that the optimal observations-based PC-EnKF algorithm is effective in dealing with the current retrieval of topography parameters. It is worth mentioning that an iterative PC-basis rotation technique is particularly useful when attempting to enhance the sparsity and the resulting accuracy. The solution strategy is well suited in the current high-dimensional nonlinear inverse modeling and has shown its appealing potential in the real-world application of complex systems. (C) 2019 Elsevier Inc. All rights reserved.