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

Abstract

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.

Reward‐Based Participant Management for Crowdsourcing Rainfall Monitoring: An Agent‐Based Model Simulation

“…While both statistics estimate the difference between the estimated rainfall field and the “ground truth,” REAA I concentrates on the relative difference of the areal average rainfall intensity and RMSE I on the root‐mean‐square difference of each grid cells (Yang & Ng, ). The error statistic REAA I does not provide information about the detailed spatial distribution of the estimated rainfall field but is selected because of its direct connection with the storm water modeling skill of a crowdsourced rainfall field when fed to a storm water model (Yang & Ng, , ).…”

“…We test the active management policies with 1‐hr rainfall data during the peak raining periods of five rainfall events, with their detailed statistics shown in Table (based on observed radar data retrieved from the Next Generation Weather Radar (NEXRAD) radar product at https://www.ncdc.noaa.gov/data-access/radar-data/nexrad). The peak raining hour is selected as the crowdsourcing rainfall monitoring approach is proved to be most suitable during heavy raining periods, especially when the crowdsourced data are used for storm water modeling purposes (Yang & Ng, , ). We stochastically downscale (Deutsch & Journel, ) the NEXRAD radar data into a synthetic ground truth rainfall field with 100 m × 100 m × 5 min resolution (thus resulting in a 5‐min time step) and assume no variability of rainfall at finer scales.…”

Evaluation of the Radar QPE and Rain Gauge Data Merging Methods in Northern China

“…(2) Fast Bayesian regression kriging (FBRK) In this category, we integrated both rainfall data with the purpose of obtaining the estimation at the minimum uncertainty. For this purpose, methods in a Bayesian framework are widely used, and we applied the fast Bayesian regression kriging (FBRK), method, as proposed by Yang and Ng [42], to merge different data types [42]. We explicitly considered the difference in the errors from the raw input data and aimed to estimate an accurate rainfall field and obtain better precipitation data.…”

Rainfall monitoring with opportunistic sensors

“…Several studies have explored the merging of gauges, links and/or radar (e.g. Bianchi et al, 2013;Scheidegger & Rieckermann, 2014;Liberman et al, 2014;Trömel et al, 2014;Haese et al, 2017;Fencl et al, 2017;Yang & Ng, 2019), but much work is yet to be done, especially concerning merging in an operational setting. Openly sharing data and tools will facilitate this process.…”

“…Estévez et al, 2011), or internal consistency between stations and/or in time (e.g. Zahumenskỳ, 2004;Chen et al, 2018). PWS rainfall data is arguably highly prone to errors as the typically low-cost devices are often installed without knowledge of or access to optimal set-up locations, and are not regularly maintained.…”