Automatic differentiation strategy for the local sensitivity analysis of a one-dimensional hydraulic model

In this paper, automatic differentiation (AD) techniques are introduced and applied in the local sensitivity analysis of the state function handled by the one-dimensional hydraulic model, Mage. We have proposed the different steps to easily compute automatic derivatives of a given numerical model. More specifically, Tapenade software, in the tangent linear mode (TLM), has been used to calculate derivatives of the model outputs (discharge and water level) with respect to the bottom friction expressed in terms of Strickler relation. We have shown the independent contribution of the main stream and floodplain Strickler coefficients on discharges and water levels. Furthermore, numerical comparison has shown that derivatives computed using the AD tool are more accurate than those using the forward divided differences scheme. Copyright (C) 2010 John Wiley & Sons, Ltd.