Randomly Supported Variations of Deterministic Models and Their Application to One-Dimensional Shallow Water Flows

This paper deals with the prediction of flows in open channels. For this purpose, models based on partial differential equations are used. Such models require the estimation of constitutive parameters based on available data. After this estimation, the solution of the equations produces predictions of flux evolution. In this work, we consider that most natural channels may not be well represented by deterministic models for many reasons. Therefore, we propose to estimate parameters using stochastic variations of the original models. There are two types of parameters to be estimated: constitutive parameters (such as roughness coefficients) and the parameters that define the stochastic variations. Both types of estimates will be computed using the maximum likelihood principle, which determines the objective function to be used. After obtaining the parameter estimates, due to the random nature of the stochastic models, we are able to make probabilistic predictions of the flow at times or places where no observations are available.