The Independent Set Perturbation Adjoint Method Applied To a Finite Element Shallow Water Equation Model

An adjoint model for a 2D finite element Galerkin shallow water model is developed using the Independent Set Perturbation Adjoint method (ISP-Adjoint, [33]). Its performance in a full 4-D VAR setup with a limited area is assessed by comparing with the adjoint model derived by the automatic differentiation approach, where it is used for optimising the initial conditions. It is shown that ISP-Adjoint is a very simple approach of forming the adjoint code/gradients/differentiation of discrete forward model (even complex governing equations, discretization methods and non-linear parameterizations) and is applied using a graph coloring approach combined with a perturbation method. Importantly, the adjoint is automatically updated as the forward code continues to be developed. In this work, it is shown the ISP-Adjoint model can achieve the accuracy of traditional adjoint models derived by the automatic differentiation Method (TAMC). Further comparison shows that the CPU time required for running the ISP-Adjoint model is much less than that for the automatic differentiation derived adjoint ∗ Corresponding author Email address: [email protected] (I.M. Navon). Preprint submitted to Elsevier Science 6 January 2011 model since the ISP-Adjoint CPU time scales linearly with the problem size.