Local sensitivity for uncertainty analysis in one-dimensional open channel flow modelling

Abstract

Uncertainty analysis may be of high importance in the field of water engineering. Sampling-based techniques, that resort to extensive exploration of the space of possible model inputs are a common approach. When inputs uncertainties can be described statistically by means of probability distribution functions, Monte Carlo simulation yields a statistical description of uncertain model outputs. However, the combination of commonly encountered input space dimensions and model CPU times often makes this approach hardly practicable. We propose to assess the potential of a local sensitivity analysis for uncertainty analysis in the modelling of open channel flows with the one-dimensional shallow water equations, which are generally viewed as being largely non linear. The first-order local sensitivity is simply assessed using the so-called empirical method requiring only two runs of the model (for a single uncertain parameter). The global sampling-based approach consists in running Monte Carlo simulations with the hydrodynamic model, given a statistical distribution of the model input parameters. Monte Carlo results can be analysed through classical statistical estimators, such as mean and standard deviation. It is shown that these characteristics can also be accurately estimated from the local sensitivity and the input distribution. Steady state and highly transient configurations (gate opening and closing) are explored, accounting for uncertainty of the main parameters (bottom slope, friction coefficient, boundary and initial conditions).