Towards a data assimilation system for morphodynamic modeling: bathymetric data assimilation for wave property estimation

Data assimilation is mainly concerned with the proper management of uncertainties. The main objective of the present work is to implement and analyze a data assimilation technique capable of assimilating bathymetric data into a coupled flow, wave, and morphodynamic model. For the case presented here, wave significant height, wave direction of incidence, and wave peak period are being optimized based on bathymetric data taken from a twin experiment. An adjoint-free variational scheme is used. In this approach, a linear reduced order model (ROM) is constructed as an approximation of the full model. The ROM is an autoregressive model of order 1 (AR1) that preserves the parametrization. Since the ROM is linear, the construction of its adjoint is straightforward, making the implementation of 4D variational data assimilation effortless. The scheme is able to update the morphodynamic model satisfactorily despite the fact that the model shows nonlinear behavior even for very small perturbations of all three parameters. The size and direction of the perturbations necessary for constructing the ROM have a significant impact on the performance of the technique.