Automatic Differentiation: A Tool for Variational Data Assimilation and Adjoint Sensitivity Analysis for Flood Modeling

Abstract

This paper illustrates the potential of automatic differentiation (AD) for very challenging problems related to the modeling of complex environmental systems prone to floods. Numerical models are driven by inputs (initial conditions, boundary conditions and parameters) which cannot be directly inferred from measurements. For that reason, robust and eficient methods are required to assess the effects of inputs variations on computed results and estimate the key inputs to fit available observations. We thus consider variational data assimilation to solve the parameter estimation problem for a river hydraulics model, and adjoint sensitivity analysis for a rainfall-runo. model, two essential components involved in the generation and propagation of floods. Both applications require the computation of the gradient of a functional, which can be simply derived from the solution of an adjoint model. The adjoint method, which was successfully applied in meteorology and oceanography, is described from its mathematical formulation to its practical implementation using the automatic differentiation tool Tapenade.