Coupling Mage with Melissa to Compute Ubiquitous Sobol Indices for River Hydraulics

In global sensitivity analysis, ubiquitous Sobol indices are used to quantify the effect of the variation of some input parameters of a model on the variance of the model outputs at each time-step and at each spatial point of the model. This paper introduces the coupling of the 1D numerical solver for transient open-channel flows Mage with Melissa, a framework for large scale in-transit sensitivity analysis. This framework is fault tolerant and can manage the specific cases in which some sets of parameters can lead to a divergence in the numerical solver that causes an early stop of the simulation. In addition, as the Sobol index estimators are computed iteratively and in-transit, the analysis is run in parallel to the simulations and results are available as soon as the last simulation ends. Moreover, as the simulation results are not stored on the file-system, it allows to run large scale sensitivity analysis without extra cost on disk usage and read/write overhead. The Lower Seine River, a tide river, is being used to demonstrate the quantification of the influence of a set of Strickler coefficients on the water elevation and the flow rate over a tidal cycle. The Lower Seine River model is segmented into 14 zones, each with independent constant Strickler coefficients. Tidal transient models are challenging to calibrate because the Strickler coefficients of a single zone influences the water elevation and the flow rate in different cross-sections at different time-steps of the model. In our study, the Strickler coefficient values are sampled from a uniform distribution using a Monte Carlo sampling method, the corresponding simulations are run on a desktop computer and the results are aggregated iteratively and in-transit by the Melissa server to generate ubiquitous Sobol index maps. Melissa provides first order and total order Sobol indices, as well as their 95% confidence interval. The Sobol indices are useful to identify the most influential Strickler coefficients for each zone at each time-step, leading to a better understanding of the model. The modeler can then adjust the model by either defining more relevant zones for the Strickler coefficients, or fine-tuning the most influential coefficients to fit the model results to field data, with setting the other ones once and for all. This approach can be applied to any other uncertain input parameter.