| Existing numerical models of water systems are based on assumptions and simplifications that can result in errors in a model's predictions; such errors can be reduced through the use of data assimilation, a technique that can significantly improve the success rate of predictions and operational forecasts. However, its implementation is difficult, particularly for physical ocean models, which are highly nonlinear and require a dense spatial discretization in order to correctly reproduce the dynamics. Kalman Filtering Techniques for Data Assimilation are the most widely used, and have been implemented in various applications, including the Ensemble Kalman Filter (EnKF). A Monte Carlo approach, this methodology has been extensively used in atmospheric and ocean prediction models to improve flow field forecasts; however, the computational effort and amount of memory required to implement it have proven an issue for operational use within a complicated, stratified system. Our General Curvilinear Environmental Modeling (GCEM) is the most complex system of its kind. Developed at the San Diego State University (SDSU) Computational Science Research Center (CSRC), it was specifically built for use on extremely high-resolution problems. The GCEM model solves the three-dimensional primitive Navier-Stokes' equation using the Boussinesq approximation in non-hydrostatic form under a fully three-dimensional, general curvilinear mesh. Data assimilation has not been utilized in this type of system to date. A major challenge to be addressed is the high computational cost, in addition to the physics, typically incurred by a high-resolution numerical model, with a three-dimensional data assimilation scheme. In this work we present a model that is capable of investigating very high resolution dynamics, as well as incorporating measured observations into the dynamical system in order to accurately forecast estimates of the variable states in a shorter amount of time. |
