A Bayesian method for missing rainfall estimation using a conceptual rainfall–runoff model
Résumé
The estimation of missing rainfall data is an important problem for data analysis and modelling
studies in hydrology. This paper develops a Bayesian method to address missing rainfall estimation
from runoff measurements based on a pre-calibrated conceptual rainfall–runoff model. The
Bayesian method assigns posterior probability of rainfall estimates proportional to the likelihood
function of measured runoff flows and prior rainfall information, which is presented by uniform
distributions in the absence of rainfall data. The likelihood function of measured runoff can be
determined via the test of different residual error models in the calibration phase. The application
of this method to a French urban catchment indicates that the proposed Bayesian method is able
to assess missing rainfall and its uncertainty based only on runoff measurements, which provides
an alternative to the reverse model for missing rainfall estimates.