Inverse problem statement

Warning

Section in development

Hydrological optimization problems generally consist in fitting catchment model response to the available observations, that is potentially multi-source and multi-site heterogeneous data used to inform the model. The misfit between observations and model response is measured with a cost function \(J\) (see section Cost functions) that depends on hydrological parameters \(\theta\) through the forward hydrological model \(\mathcal{M}\) composed of hydrological operators that can include a pre-regionalization (see section Forward problem statement). The inverse problem consists in searching an optimal parameter set \(\hat{\boldsymbol{\theta}}\) such that:

(1)\[\hat{\boldsymbol{\theta}}=\arg\min_{\boldsymbol{\theta}}J\left(\boldsymbol{\theta}\right).\]