How Reliable are Rainfall Observations? Assessing Credible Intervals with Bilinear Surface Smoothing

Rainfall regionalization refers to a broader spatial modeling process that transforms point measurements into reliable continuous fields, incorporating additional information.  Yet the fidelity of the resulting continuous surface is strongly influenced by the quality of the underlying data, as well as by the density and spatial configuration of the observational network. This contribution addresses the question of how reliable rainfall data are when evaluated against a regionalized rainfall surface, by extending the Bilinear Surface Smoothing with Explanatory variable (BSSE) framework to explicitly incorporate Bayesian credible intervals.

The proposed formulation exploits the linear smoother representation of BSSE to derive the posterior covariance of the fitted bilinear surface as a function of residual variance and effective degrees of freedom. Credible intervals are obtained analytically, allowing uncertainty in variance estimation to be accounted for without resampling. Beyond quantifying uncertainty in the spatial estimates, the credible intervals provide a diagnostic measure of data reliability relative to the regionalized signal.

The extended framework is demonstrated through the regionalization of average and extreme rainfall characteristics across Greece, using ground-based observations together with elevation as explanatory variable. Stations falling outside the 95% credible interval are identified and examined, revealing that such cases frequently occur in areas with sparse gauge coverage or complex rainfall regimes. These locations highlight regions where the observational network provides limited support to the regionalized surface, leading to increased uncertainty and reduced confidence in the available data.

The analysis further reveals a strong dependence of uncertainty on temporal aggregation scale, with markedly wider credible intervals at sub-daily extremes, where station density is lowest. The BSSE methodology is implemented in a fully reproducible workflow, facilitating straightforward application of the proposed uncertainty-aware regionalization framework to other hydro-climatic datasets.