An adaptive mesh adjoint data assimilation method applied to free surface flows

In this paper, we describe the construction of a three‐dimensional adaptive mesh data assimilation method for oceanographic/coastal applications, including a free surface. This is the first attempt at introducing a moving computational domain into an adjoint model with mesh adaptivity. We also provide insight into the feasibility and reliability of the adaptive mesh adjoint model. The use of differing adapting meshes for forward and adjoint problems is considered here, where each mesh is optimized with respect to the individual properties of each solution. The free surface test case considered is that of flow in a two‐dimensional vertical fluid slice. In this test case the sea surface elevation boundary conditions is optimized by assimilating sea surface height observations. The feasibility of an assimilation approach on adapting moving domains is demonstrated by comparison with a fixed mesh result.