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.
Monte Carlo Markov Chain (MCMC) 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.