In Situ Estimation of Erosion Model Parameters Using an Advection-Diffusion Model and Bayesian Inversion

We describe a framework for the simultaneous estimation of model parameters in a partial differential equation using sparse observations. Markov Chain Monte Carlo sampling is used in a Bayesian framework to estimate posterior probability distributions for each parameter. We describe the necessary components of this approach and its broad potential for application in models of unsteady processes. The framework is applied to three case studies, of increasing complexity, from the field of cohesive sediment transport. We demonstrate that the framework can be used to recover posterior distributions for all parameters of interest and the results agree well with independent estimates (where available). We also demonstrate how the framework can be used to compare different model parameterizations and provide information on the covariance between model parameters.

Automated summary

We present a framework for simultaneous parameter estimation in partial differential equations using sparse observations. Markov Chain Monte Carlo sampling is employed in a Bayesian framework to estimate posterior distributions for each parameter. We discuss the essential components of this approach and its wide applicability in modeling unsteady processes. The framework is applied to three case studies in cohesive sediment transport, demonstrating its ability to recover posterior distributions for all desired parameters and its agreement with independent estimates. Furthermore, we show how the framework enables comparison of different parameterizations and offers insights into parameter covariances.