Title: Comparison of Polynomial Chaos and Gaussian Process surrogates for uncertainty quantification and correlation estimation of spatially distributed open-channel steady flows,
Abstract: Data assimilation is widely used to improve flood forecasting capability,
especially through parameter inference requiring statistical information on the
uncertain input parameters (upstream discharge, friction coefficient) as well
as on the variability of the water level and its sensitivity with respect to
the inputs. For particle filter or ensemble Kalman filter, stochastically
estimating probability density function and covariance matrices from a Monte
Carlo random sampling requires a large ensemble of model evaluations, limiting
their use in real-time application. To tackle this issue, fast surrogate models
based on Polynomial Chaos and Gaussian Process can be used to represent the
spatially distributed water level in place of solving the shallow water
equations. This study investigates the use of these surrogates to estimate
probability density functions and covariance matrices at a reduced
computational cost and without the loss of accuracy, in the perspective of
ensemble-based data assimilation. This study focuses on 1-D steady state flow
simulated with MASCARET over the Garonne River (South-West France). Results
show that both surrogates feature similar performance to the Monte-Carlo random
sampling, but for a much smaller computational budget; a few MASCARET
simulations (on the order of 10-100) are sufficient to accurately retrieve
covariance matrices and probability density functions all along the river, even
where the flow dynamic is more complex due to heterogeneous bathymetry. This
paves the way for the design of surrogate strategies suitable for representing
unsteady open-channel flows in data assimilation.