| 06 Jan 2026
Exploring the applicability of Censored Shifted Gamma Distribution (CSGD) error model to radar based rainfall nowcasts: A UK case study
Abstract. Radar based rainfall nowcasting plays a critical role in hydrological operations such as stormwater management and flood early warning. Compared with Numerical Weather Prediction (NWP), it offers higher short-term accuracy and lower computational costs. However, operational uptake remains constrained by two key challenges: (i) uncertainties in nowcasting algorithms and (ii) discrepancies between radar rainfall estimates and ground based measurements. Focusing on the latter, this study explores the potential of the Censored Shifted Gamma Distribution (CSGD) error model to adjust high-resolution radar nowcasts using gauge observations, thus improving their hydrological applicability. The proposed framework involves calibrating both climatological and conditional CSGD models at gauge locations and interpolating parameters across the study area. Deterministic and ensemble nowcasts generated by the Short-Term Ensemble Prediction System (STEPS) are subsequently adjusted using linear and non-linear CSGD models. In this process, predicted rainfall intensities are transformed into cumulative distribution functions (CDFs), enabling probabilistic nowcasting. The median of the CSGD-derived distributions is then applied as the adjusted rainfall intensity, improving alignment with ground observations. Results suggest that combining STEPS ensemble nowcasting with the non-linear CSGD model generally yields the best performance, with error reductions approaching 6 % at the 6 h lead time (hourly scale) and at the 3 h lead time (5 min scale) and uncertainty reductions approaching 20 % across selected events. These findings demonstrate the potential of extending the CSGD method – originally developed for daily satellite precipitation estimation – to hourly and sub-hourly timescales. This advancement enhances the reliability of radar based predictions and their value for hydrological decision-making.
The authors developed a framework to combine a radar-based rainfall error model with rainfall nowcasting. The authors demonstrate that applying the non-linear CSGD model to rainfall ensemble nowcasting generally yields the best performance. This research enhances the reliability of radar-based rainfall nowcasting. I would recommend a major revision given the comments below:
1. CSGD has been applied to sub-daily or hourly time scale rainfall error modeling, such as
Peng, K., D.B. Wright, Y. Derin, S.H. Hartke, Z. Li, J. Tan, A Novel Near-Realtime Quasi-global Satellite-Only Ensemble Precipitation Dataset, Water Resources Research, 2025.
Li, Z., D.B. Wright, S.H. Hartke, D.B. Kirschbaum, S. Khan, V. Maggioni, Pierre-Emmanuel Kirstetter, Toward A Globally-Applicable Uncertainty Quantification Framework for Satellite Multisensor Precipitation Products based on GPM DPR, IEEE Transactions on Geoscience Remote Sensing, 2023.
I would not recognize the " potential of extending the CSGD method–originally developed for daily satellite precipitation estimation– to hourly and sub-hourly timescales" as a major finding in this research.
2. Scheuerer et al. (2015) developed CSGD to be used in precipitation forecasting. Could the authors clarify the rationale for applying an error model calibrated using historical radar observation time series to rainfall nowcasts, rather than calibrating the CSGD model directly on the nowcasted rainfall fields? The latter approach appears more direct for addressing precipitation errors that originate from both radar measurements and the nowcasting model itself. Under the current framework, the capacity to mitigate errors specifically associated with rainfall nowcasting seems limited.
3. Since CRPS is the objective function of CSGD and is also one of the widely used metrics to evaluate the accuracy of ensemble prediction, I would recommend the authors to report the CRPS value as well for the comparison between linear & non-linear CSGD. It can also be used to evaluate ensemble nowcasting accuracy.
4. Can the authors explain why, in Figs 8 & 9, the RMSE of CSGD is higher at a lead time of 1-3 hours? I would recommend the authors to report the evaluation for CSGD at the initial time step (i.e., lead time=0min, no nowcasting applied), so that we can investigate whether the error was propagated from the initial.
5 I would recommend that the author provide more clarification in the CSGD and the nowcasting model's performance in Tables A1-A6. As for different nowcasting methods, different CSGD models, and different metrics, the performance varies. This may imply some shortcomings in the current model that can be further improved in further study.
6. The authors selected the median as the adjusted rainfall intensity for comparison. The median is likely to smooth out the extreme values. I would recommand use ensemble-based metrics to evaluate the ensemble accuracy. Both CSGD and ensemble nowcasting are good tools for ensemble-based decision making. Only focusing on median accuracy may not be a comprehensive evaluation.
Minor revision:
1. I recommend that the authors revise figure3 into three boxes to be consistent with 3.2-3.4 subtitles, so that the authors would better clarify how the three parts are connected.
2. L442, the notation for RMSEI90 needs to be corrected.