Research papersA hierarchical Bayesian approach to the modified Bartlett-Lewis rectangular pulse model for a joint estimation of model parameters across stations

- A hierarchical Bayesian model is proposed to jointly estimate parameters.
- Parameter uncertainty is formally taken into account through a Bayesian framework.
- Parameters with better reproduction of rainfall statistics are reliably estimated.
- Seasonal patterns of the estimated parameters are correctly identified.
- Spatial variability of the parameters is substantially reduced.

Poisson cluster stochastic rainfall generators (e.g., modified Bartlett-Lewis rectangular pulse, MBLRP) have been widely applied to generate synthetic sub-daily rainfall sequences. The MBLRP model reproduces the underlying distribution of the rainfall generating process. The existing optimization techniques are typically based on individual parameter estimates that treat each parameter as independent. However, parameter estimates sometimes compensate for the estimates of other parameters, which can cause high variability in the results if the covariance structure is not formally considered. Moreover, uncertainty associated with model parameters in the MBLRP rainfall generator is not usually addressed properly. Here, we develop a hierarchical Bayesian model (HBM)-based MBLRP model to jointly estimate parameters across weather stations and explicitly consider the covariance and uncertainty through a Bayesian framework. The model is tested using weather stations in South Korea. The HBM-based MBLRP model improves the identification of parameters with better reproduction of rainfall statistics at various temporal scales. Additionally, the spatial variability of the parameters across weather stations is substantially reduced compared to that of other methods.