Independent set perturbation method for efficient computation of sensitivities with applications to data assimilation and 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 (ISP, [46]) sensitivity analysis. 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 the ISP sensitivity anaylysis is a very simple approach of forming the adjoint code/gradients/differentiation of discrete forward models (even complex governing equations, discretization methods and non-linear parameterizations) and is realised using a graph colouring 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 adjoint model using the ISP sensitivity analysis 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 adjoint model using the ISP sensitivity analysis is much less ∗ Corresponding author Email address: [email protected] (I.M. Navon). Preprint submitted to Elsevier Science 26 January 2011 than that for the automatic differentiation derived adjoint model since the ISP derived adjoint CPU time scales linearly with the problem size.