the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 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.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2025-4590', Anonymous Referee #1, 25 Jan 2026
- AC2: 'Reply on RC1', Li-Pen Wang, 02 Mar 2026
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CEC1: 'Comment on egusphere-2025-4590 - No compliance with the policy of the journal', Juan Antonio Añel, 07 Feb 2026
Dear authors,
Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".
https://www.geoscientific-model-development.net/policies/code_and_data_policy.html
You have archived your the nowcasting framework pySTEPS in readthedocs.io, and the CSGD error-modelling code in GitHub. Unfortunately, none of these sites are acceptable repositories. GitHub itself instructs authors to use other long-term archival and publishing alternatives, such as Zenodo. Therefore, the current situation with your manuscript is irregular. Please, publish your code in one of the appropriate repositories and reply to this comment with the relevant information (link and a permanent identifier for it (e.g. DOI)) as soon as possible, as we can not accept manuscripts in Discussions that do not comply with our policy. Also, please include the relevant primary input/output data.Also, the 'Code and Data Availability’ section must also be modified to cite the new repository locations, and corresponding references added to the bibliography.
I must note that if you do not fix this problem, we cannot continue with the peer-review process or accept your manuscript for publication in GMD.
Juan A. Añel
Geosci. Model Dev. Executive EditorCitation: https://doi.org/10.5194/egusphere-2025-4590-CEC1 -
AC1: 'Reply on CEC1', Li-Pen Wang, 11 Feb 2026
Dear Executive Editor,
Thank you very much for your careful assessment of our manuscript and for drawing our attention to the requirements of the Geoscientific Model Development Code and Data Policy. We sincerely apologise for not fully complying with the archival requirements in the initial submission. We agree that long-term repositories with persistent identifiers (e.g. DOIs) should have been used for code and data archiving.
We have now taken the following corrective actions:
- The version of pySTEPS used in this study has been archived on Zenodo and is available at: https://zenodo.org/records/15860833.
- The source code for the CSGD_error_model method that we adopted in our nowcasting application had been archived on Zenodo and is available at: https://zenodo.org/records/15485071
- The full source code and the derived CSGD parameters corresponding to all deterministic and ensemble nowcast outputs have been archived at: https://doi.org/10.5281/zenodo.17984774 (this has been provided in the Code and Data section).
Regarding input data:
- The NIMROD radar data are available via the Centre for Environmental Data Analysis (CEDA) for non-commercial research use upon registration and acceptance of the UK Met Office licence agreement. Due to licence restrictions, redistribution of the raw NIMROD data is not permitted. Users are therefore referred to CEDA to obtain the data directly.
- The rain gauge observations used in this study are from MIDAS Open v202407, available via CEDA at: https://catalogue.ceda.ac.uk/uuid/c50776e4903942cdb329589da70b83fe/, and its DOI: https://doi.org/10.5285/c50776e4903942cdb329589da70b83fe.
We have drafted a revised Code and Data Availability section as below and will add the corresponding references to the bibliography to ensure full compliance with the GMD Code and Data Policy.
Kind regards,
Li-Pen Wang
on behalf of all co-authors
A draft of the revised Code and Data Availability section:The computational framework used in this study consists of (i) the pySTEPS nowcasting library and (ii) the CSGD_error_model adopted in this work. The version of \textbf{pySTEPS} used in this study had been archived on Zenodo and is available at: https://zenodo.org/records/15860833, and the version of the CSGD_error_model had been archived on Zenodo and is available at:
https://zenodo.org/records/15485071. Both repositories provide permanent, versioned archives with persistent DOIs to ensure long-term accessibility and reproducibility.The input radar data used in this study are from the NIMROD radar composite archive, available via the Centre for Environmental Data Analysis (CEDA). The data are accessible for non-commercial research use upon registration with CEDA and acceptance of the UK Met Office licence agreement. Due to licensing restrictions, redistribution of the raw NIMROD data is not permitted. Users wishing to reproduce the results should obtain the data directly from CEDA under the applicable licence terms.
Rain gauge observations were obtained from MIDAS Open v202407, available via CEDA at: https://catalogue.ceda.ac.uk/uuid/c50776e4903942cdb329589da70b83fe/ (DOI: https://doi.org/10.5285/c50776e4903942cdb329589da70b83fe).
The source code of the proposed work and all derived CSGD parameters corresponding to the deterministic and ensemble nowcast outputs have been archived at: https://doi.org/10.5281/zenodo.17984774. Because the complete set of nowcast output fields is extremely large, these are not archived in their entirety. However, the archived CSGD parameters, together with the published source code and the original input data (obtainable via CEDA), allow full regeneration of all deterministic and ensemble output fields.
Citation: https://doi.org/10.5194/egusphere-2025-4590-AC1 -
CEC2: 'Reply on AC1', Juan Antonio Añel, 11 Feb 2026
Dear authors,
Many thanks for your reply. We can consider the current version of your manuscript in compliance with the Code and Data Policy of the journal.
Juan A. Añel
Geosci. Model Dev. Executive Editor
Citation: https://doi.org/10.5194/egusphere-2025-4590-CEC2
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AC1: 'Reply on CEC1', Li-Pen Wang, 11 Feb 2026
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RC2: 'Comment on egusphere-2025-4590', Anonymous Referee #2, 15 Aug 2026
General remarks
The authors address a pertinent question, namely how to improve radar rainfall nowcasting, by applying the Censored Shifted Gamma Distribution (CSGD) post-processing approach. They transfer the method that was previously applied to satellite-derived QPE to radar-based QPE, where the radar product replaces the satellite product in the methodology. The radar dataset used is the Nimrod radar-based QPE with rain gauge corrections. Rain gauge records used are the MIDAS hourly rain gauge data and 5-minute records from the Environmental Agency over the Severn Trent region. The pointwise CSGD calibration is interpolated to the entire grid and then applied to radar-based nowcasts. A thorough study of the interpolation methods was performed and shows results which are scientifically interesting and novel at these spatial scales. The data and code are made available on Zenodo with DOIs which is very good practice. However, the method seems to perform adequately at (very) long lead times, but performs worse at short (i.e. skillful) lead times, making it hard to justify why one would use this method for most nowcasting applications.
The clarity of the writing could be improved; for example, the introduction jumps back and forth between subjects and the goal of the manuscript is not immediately clear. The notions of error and uncertainty are used interchangably (see also my specific remarks below), for example Fig. 10 shows error variances (in (mm/h)^2) but then this is referred to as "uncertainty reduction of 20%". Some language is also imprecise, e.g. "Generally better" should be specified (in how many percent of cases, and is it significantly better?)
Methodologically, there are several aspects which should be improved, first of all the validation strategy. The temporal validation approach seems correct, with a clearly separate calibration and verification period. However, repeating the validation over different subset (k-fold cross-validation, taking into account temporal correlations) is necessary to get information about the variance/significance of the obtained results.
As for the spatial interpolation verification, the set of rain gauges that was used to estimate the errors in the spatial interpolation of the CSGD parameters was not picked randomly, but chosen to be centrally located, so the results might be too optimistic. Like for the temporal validation, the authors should apply k-fold cross-validation to get at least some information about the significance of these results.A major methodological flaw is that, in the nowcast validation, all gauges are used for the calibration. Therefore, the validation does not represent the error for any random pixel, only for gauged pixels. A proper validation of the whole process, that represents skill at any location (including where there's no gauges), should therefore use data that was both temporally and spatially withheld from the calibration procedure. This must be addressed in the revised manuscript.
Another, minor, methodological concern that I have, is that the authors might be applying a double correction: the Nimrod radar dataset already makes use of real-time rain gauge measurements to correct the QPE. Are these also in MIDAS? This should be clarified and the possible implications should be discussed. Moreover, it would be good to compare to a simple baseline (Mean field bias correction with MIDAS) to show that the proposed complex model really has added value.
As for improving the nowcasting, the manuscript makes some claims which are very selective and not well-supported. The authors report skill improvement for nowcasts at 6-hour lead times evaluated on MIDAS. My first concern is that these are very long lead times for purely extrapolation-based nowcasting, which typically loses most skill after 1-2 hours unless combined with NWP forecast data. Indeed correlations with gauges are very low for 6h lead times, cfr table 3. How does the method do for shorter lead times, where nowcasts are supposed to have more skill? It seems to degrade the nowcasts there, which a serious disadvantage. For the average user, this would make their model less useful than the original nowcast. For example, in Table 4 it is clear that after 1h, the CSGD methods will underestimates rainfall wrt the original, which is a major issue.
As mentioned before, the significance/variability of the reported reductions should be discussed more in depth since this is an evaluation on a limited number of events (20 events in the validation set). The vocabulary "approaching x% or y%" is also a bit strange, just state the percentage (ideally with an error bar) instead of rounding up.
The variance reduction might be due to bias increase, which is not ideal either.Another issue that I see, is that of the whole obtained CDF, only the median is used. From the description of the method, I expected that the whole distribution would be used, but only deterministic scores for the median are reported. Why is this distribution not used? Moreover, why are there no probabilistic scores CRPS, rank histograms, reliability diagrams etc. reported? And what about looking at the performance of the method (false positives/negatives, CSI etc) for different thesholds? These are standard evaluation methods for probabilistic nowcasts, and are readily available in python packages. I also wonder how the RMSE of an ensemble computed? Does it compare to the ensemble mean or add the errors of each member separately (not correct)?
The authors mention that they apply to sub-hourly resolutions, but the calibration only seems to be done with hourly data (5min data are also aggregated to 1h) so this claim should be weakened.
Specific remarks:
- Abstract, L9-10: . "In this process, predicted rainfall intensities are transformed into 10 cumulative distribution functions (CDFs), enabling probabilistic nowcasting." This sentence seems to suggest that the CSGD is needed to provide probabilistic forecasts, while in fact this can be also derived from STEPS ensemble nowcasts alone.
- p2 L27: what are "the inherent errors"?
- p2 L31-33: The authors write about the concepts of uncertainty and error: "These two concepts primarily originate from two sources: the difficulty in accounting for uncertainty in nowcasting models and the differences between radar rainfall (RR) estimates and gauge rainfall (GR) measurements (Dai et al., 2015, 2013)." This explanation seems circular, please fix this sentence. What is perhaps meant is that error comes from both extrapolation errors and measurement errors? In the following paragraphs, the words uncertainty and error still seem to be used interchangably.
- p2: In L41-47, the authors repeat themselves somewhat about DL/AI based nowcasting (already discussed in L22-26). Discuss whether this method could also be applied to DL/AI based nowcasting.
- p2 L54 and further: please quote the seminal works on dual pol radar e.g. Bringi, Chandrasekar, Rhyzhkov, Zrnić
- p4 L95: explain NLDAS-2. is it really radar reference data?
- p4 L102: the methodology can be a described more accurately, e.g. "treating RR data as the satellite dataset" I see what you mean, but this phrasing is a bit confusing.
- p4 L105: "Restricted to grids containing...." - do you mean grid points?
- P6 L150-152: can you explain the low fraction of stations with sufficiently high correlations with the Midas dataset? Are the other stations wrong or does it simply reflect the high spatial variability of rain?
- P16 L379: please specify what the RMSE is calculated over in Eq. (13).
- Some residual errors are clearly not spatially smooth (e.g. due to the bright band, as visible in Fig. 2b, or geographically fixed sources of non-meteorological echoes) and the parameters may not interpolate trivially to neighbouring pixels. Please discuss
- P29 L509-510 please compute scores such as CSICitation: https://doi.org/10.5194/egusphere-2025-4590-RC2
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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.