First-order uncertainty analysis using Algorithmic Differentiation of morphodynamic models

Abstract : We present here an efficient first-order second moment method using Algorithmic Differentiation (FOSM/AD) which can be applied to quantify uncertainty/sensitivities in morphodynamic models. Changes with respect to variable flow and sediment input parameters are estimated with machine accuracy using the technique of Algorithmic Differentiation (AD). This method is particularly attractive for process-based morphodynamic models like the Telemac-2D/Sisyphe model considering the large number of input parameters and CPU time associated to each simulation. The FOSM/AD method is applied to identify the relevant processes in a trench migration experiment (van Rijn, 1987). A Tangent Linear Model (TLM) of the Telemac-2D/Sisyphe morphodynamic model (release 6.2) was generated using the AD-enabled NAG Fortran compiler. One single run of the TLM is required per variable input parameter and results are then combined to calculate the total uncertainty. The limits of the FOSM/AD method have been assessed by comparison with Monte Carlo (MC) simulations. Similar results were obtained assuming small standard deviation of the variable input parameters. Both settling velocity and grain size have been identified as the most sensitive input parameters and the uncertainty as measured by the standard deviation of the calculated bed evolution increases with time.