Fast Bayesian Regression Kriging Method for Real‐Time Merging of Radar, Rain Gauge, and Crowdsourced Rainfall Data

Crowdsourcing of rainfall measurements incorporating common citizens as a rich source of data is an emerging concept with huge potential to provide valuable high spatiotemporal resolution rainfall observations. Here we investigate the merging of crowdsourced rainfall data with traditional radar and rain gauge data to maximize their utility. For this purpose, we develop a tailored fast Bayesian regression kriging (FBRK) method combining regression kriging and Laplace approximation in a Bayesian framework. A strength of the FBRK method lies in its ability to capture the differences between rain gauge and crowdsourced measurement errors. Another lies in its fast yet reasonably accurate approximation of the Bayesian posterior, making it suitable to use in real time. We conduct synthetic computer simulations to evaluate the FBRK method alongside three other merging methods. In the simulations, we compare the accuracies of their resulting rainfall estimates, as well as the skill of those estimates as input to a storm water flow forecasting model. In both aspects, we observe the FBRK method to lead to more accurate results and truer representations of the associated uncertainties. However, we also observe the performance of the FBRK method to be sensitive to the choice of the Bayesian prior under certain conditions. Finally, from the synthetic simulations, we find merging crowdsourced data with traditional data to lead to more accurate estimation of the ground truth rainfall field and, subsequently, more accurate flow forecasts (though only when an adequate merging method, e.g., the FBRK method, is used), and the results to be fairly robust to bias in the input crowdsourced data.