the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 10 Jun 2025
Improving Precipitation Interpolation Using Anisotropic Variograms Derived from Convection-Permitting Regional Climate Model Simulations
Abstract. The consideration of the spatial variability of daily precipitation, assessed through spatial covariance, is crucial for hydrological modeling. Estimating this covariance is particularly challenging in regions with sparse rain gauge networks or limited radar coverage. To address this issue, this study explores the potential of Convection-Permitting Regional Climate Model (CP-RCM) simulations to estimate anisotropic variograms. We compare five approaches: (1) SPAZM, an interpolator based on local precipitation-altitude regressions, Trans-Gaussian Random Fields, differing by their covariance structure and data source with (2) isotropic covariance from rain gauges, (3) anisotropic covariance from rain gauges, (4) isotropic covariance from CP-RCM simulations, and (5) anisotropic covariance from CP-RCM simulations. The models are evaluated with cross-validation and spatial metrics using radar-derived analyses. Results demonstrate that Trans-Gaussian Random Fields outperform SPAZM. Anisotropic covariance models derived from CP-RCM simulations capture orography-induced directional precipitation structures more effectively than the other models, leading to improved interpolation accuracy and better representation of spatial variability. The generated ensemble of conditional simulations successfully reproduces intense precipitation events at the catchment scale, providing valuable uncertainty quantification. For a 17 km2 catchment, mean catchment precipitation can range from 175 mm to 450 mm for a convective event, despite high rain gauge density. These findings highlight the benefits of using CP-RCM simulations to generate anisotropic variograms for probabilistic precipitation interpolation. This approach improves the spatial variability of precipitation, making it highly relevant for hydrological applications such as flood forecasting. Future work will explore the integration of these ensembles into probabilistic hydrological modeling.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2025-1779', Anonymous Referee #1, 08 Aug 2025
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AC1: 'Reply on RC1', Valentin Dura, 07 Jan 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-1779/egusphere-2025-1779-AC1-supplement.pdf
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AC1: 'Reply on RC1', Valentin Dura, 07 Jan 2026
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RC2: 'Comment on egusphere-2025-1779', Vincent Fortin, 16 Nov 2025
In this paper, the authors propose a geostatistical framework which relies on a high-resolution regional climate model (RCM) to provide information on the precipitation climatology as well as on the anisotropy of the departures of observations from that climatology. The focus of the paper is on documenting, in particular through two case studies, the added value of the RCM for estimating the anisotropy of the covariogram. A statistical analysis of the performance of the method for 786 events is also presented. The experiment is well designed, and allows the authors to assess separately the impact of using an anisotropic covariogram and the impact of estimating the anisotropy using the RCM. A comparison against a reference interpolation method (SPAZM) is also proposed.
The introduction reads well but fails to mention a relevant paper by Khedhaouiria et al. (2022) published in NPG which proposed a method based on an ensemble of NWP models to estimate the anisotropy of innovations for optimal interpolation of precipitation.
For the section on domain and data, I suggest including a subsection on the study period. The study period is mentioned in the section on COMEPHORE, but it would be simpler to add a section dedicated to the study period after the section on meteorological data, because the study period is constrained by the availability of COMEPHORE and AROME. A subsection on observed data should also be added. The rain gauge network is currently described in the study domain subsection.
In the sub-section describing the CP-RCM AROME, I would like the authors to provide more details on the model configuration, more specifically w.r.t. to the ability of the system to represent specific events and not only the climatology of precipitation over the domain. This is important since AROME is used later to inform the interpolation method on the anisotropy of the covariogram, but not on the amount of precipitation associated with the event. Figure 4.6 and 4.8 show that there are significant discrepancies between COMEPHORE and AROME precipitation fields. Is this happening because CP-RCM AROME is not sufficiently constrained by ERA-Interim or is it inherent to the predictibility of precipitation events in this region? Would we expect a similar degree of agreement for a short-term forecast of precipitation based on AROME? Is ERA-Interim only used as boundary conditions or is some form of spectral nudging used to prevent RCM model drift? How far is the study domain from the ALADIN and AROME boundaries? Given the model configuration, do we expect AROME to only be able to provide information on the precipitation climatology but yet be able to provide useful information on the anisotropy of the precipitation structures? Why would that be the case?
In the methods section, the authors choose to consider observed precipitation of less than 0.5 mm as zeros for the purpose of normalizing the precipitation field. How was this number chosen? Are results sensitive to this choice? The back-transformation introduces a bias, which the authors do not take into account (see Van Hyfte et al., 2023, Tellus A). Can the authors quantify the impact of ignoring this source of bias on their analysis?
The authors chose 786 precipitation events to evaluate the proposed method. It would be interesting to know more about the type of events that were selected. Please categorized them by weather regime and season. In particular, can you identify events for which orographic intensification is expected and events for which snow was observed at higher elevations? Do we expect the performance and ranking of the methods to vary depending on the type of event?
In the results section, the authors should present and discuss the covariograms that are obtained for each of the two case studies. The 2D covariograms derived from AROME are presented in Figure 4.8, but that does not tell us how well it fits the experimental covariogram. Furthermore, no information is provided on the fitted covariograms for the other three experiments (rgISO, rgANISO and arISO). This is important, in particular to show that the choice of an exponential covariogram is appropriate based on the data. Did the authors check that the exponential variogram provided a good fit for the 786 events considered in this study?
In the discussion, the authors address many limitations of the method, in particular the fact that it would be difficult to apply on a larger domain. This is an important limitation, because it would seem impractical to deploy such a complex interpolation method operationally if it cannot be applied on a large domain. I encourage the authors to propose a workflow that would allow the application of the method on a larger domain. Could it not be applied watershed by watershed? Would the cost of doing so be prohibitive? Are there other solutions?
Although evaluating the method on significant events (where more than 50mm/day was observed by at least 5 gauges), in practice one would likely want to apply the method for all days. Did the authors assess how well the method performs for less intense precipitation events?
The authors also mention in the discussion the possibility of applying the method using numerical weather forecasts rather than using a RCM. I think this is worth discussing in more details. In particular, I would expect the precipitation field of a short-term forecast to correlated better with observed precipitation, and thus it might be possible to infer more from the forecast than simply the anisotropy of the precipitation field. Furthermore, one might have access to an ensemble of weather forecasts.
Finally, one important aspect of precipitation interpolation that is not discussed in this paper is the issue of quality control. When interpolating precipitation observations, in particular in complex terrain, the issue of quality control is central because it can be very difficult to identify problematic observations based on neighboring stations, given the impact of orography on precipitation amounts over short distances. I understand that this issue might be out of scope for this paper, but I wonder if it was an issue for the authors when applying the method over 786 events. Was the observed data quality controlled? How? Could the presence of outliers impact the results of your analysis? Could your method be used to improve the quality control process through the use of cross-validation? This would likely be crucial to address before the method can be used for real-time applications.
Citation: https://doi.org/10.5194/egusphere-2025-1779-RC2 -
AC2: 'Reply on RC2', Valentin Dura, 07 Jan 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-1779/egusphere-2025-1779-AC2-supplement.pdf
-
AC2: 'Reply on RC2', Valentin Dura, 07 Jan 2026
- AC3: 'Comment on egusphere-2025-1779', Valentin Dura, 07 Jan 2026
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-1779', Anonymous Referee #1, 08 Aug 2025
This paper presents a method to interpolate daily (gauges) precipitation data using variograms derived from climate model simulations. The manuscript is well written, and results show potential in the proposed methodology to improve daily precipitation estimations, when gridded rainfall fields such radar-based rainfall estimations may not be available.
In addition of the methods of validation presented by the authors, I suggest adding a comprehensive comparison between the anisotropic variograms derived from CP-RCM (the target of this paper) with those from the radar-derived precipitation analyses. See more details below. This additional comparison targets directly the approach presented in the manuscript and may provide evidence of the advantages and limitations of the proposed technique.
Additional comments:
L134: Please describe what a Trans-Gaussian Random Field is, as I believe this is the first time the reader is introduced to this term.
L154: Please elaborate why only 25% of AROME grid cell were selected to calculate the variograms. Were the selected cells from AROME used as 'virtual' gauges to calculate the variograms? Velasco-Forero et al 2009 and other papers describe methods to estimate 2D variograms using all the grid points from radar images that could be applicable to estimate variograms from AROME and COMEPHORE datasets.
L195: Authors are using TWS to verify the spatial structure of the precipitation fields, however spatial multi-scale dependencies are key characteristics of any rainfall fields and authors should add comparisons to account these effects. Seppo Pulkkinen et al. 2019 presents some examples on how to evaluate different rainfall fields based on their multi-scale characteristics (for example figure 8) GMD - Pysteps: an open-source Python library for probabilistic precipitation nowcasting (v1.0)
L215: Please indicate where "the ensemble means, a sample of conditional simulations, …" are show (Figure, section???)
Figure 2: It is hard to discriminate the ME and MAE colours from the topographical background. Please try to use contours for the topography, so score colours become more visible. For the discussion of results of this figure (ME, MAE) please consider if a scatterplot between elevation and scores could help to support your conclusions. If elevation is not relevant here, then please consider removing the topography of the figure.
L235: It is not true that "rgANISO does not outperform rgISO in gauge gradient similarities" as rgANISO TWS score values are mostly lower that rgISO values for the 66 events with strong anisotropy as shown in Figure 3. Also Figure 3 shows that arANISO generally outperforms rgANISO and arISO also generally outperformes rgISO, which could highlight the advantages of using AROME fields to estimate the spatial variability of the rainfall fields.
L251: last sentence should indicate with dataset is used to estimate the anisotropic covariance. Is from AROME?
Figure 5: Please highlight the data points from the event (2014-09-18) in the scatter plots?
Figure 5: Please add to the boxes with the catchments name, the code ID and areas of the catchments as described in Table 1. Â Â
Figure 5: Consider adding best-fit lines fitted across the ensemble mean points on each scatter plot as they could help to illustrate biases in the simulations for each catchment.
Table 3: it would be valuable to add the same stats for COMEPHORE in this table. This allows a direct comparison of the anisotropy parameters derived from AROME and from COMEPHORE
Figure 6: please add AROME rainfall fields to this figure as the variogram for arISO and arANISO were derived from AROME. Â Please consider adding the TWS values for each field.
Figure 7 and discussion. Given that the relatively small size of the catchments with the whole domain, would be valuable to present the distribution of the rainfall values of few (all?) members for each catchment as complement to the precipitation fields?
L312: please elaborate when rgANISO improves rgISO and when does not and why?
L334: Please elaborate what it could be needed to extend this methodology to real-time and sub-daily applications as this study only has assessed daily time scales.
Citation: https://doi.org/10.5194/egusphere-2025-1779-RC1 -
AC1: 'Reply on RC1', Valentin Dura, 07 Jan 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-1779/egusphere-2025-1779-AC1-supplement.pdf
-
AC1: 'Reply on RC1', Valentin Dura, 07 Jan 2026
-
RC2: 'Comment on egusphere-2025-1779', Vincent Fortin, 16 Nov 2025
In this paper, the authors propose a geostatistical framework which relies on a high-resolution regional climate model (RCM) to provide information on the precipitation climatology as well as on the anisotropy of the departures of observations from that climatology. The focus of the paper is on documenting, in particular through two case studies, the added value of the RCM for estimating the anisotropy of the covariogram. A statistical analysis of the performance of the method for 786 events is also presented. The experiment is well designed, and allows the authors to assess separately the impact of using an anisotropic covariogram and the impact of estimating the anisotropy using the RCM. A comparison against a reference interpolation method (SPAZM) is also proposed.
The introduction reads well but fails to mention a relevant paper by Khedhaouiria et al. (2022) published in NPG which proposed a method based on an ensemble of NWP models to estimate the anisotropy of innovations for optimal interpolation of precipitation.
For the section on domain and data, I suggest including a subsection on the study period. The study period is mentioned in the section on COMEPHORE, but it would be simpler to add a section dedicated to the study period after the section on meteorological data, because the study period is constrained by the availability of COMEPHORE and AROME. A subsection on observed data should also be added. The rain gauge network is currently described in the study domain subsection.
In the sub-section describing the CP-RCM AROME, I would like the authors to provide more details on the model configuration, more specifically w.r.t. to the ability of the system to represent specific events and not only the climatology of precipitation over the domain. This is important since AROME is used later to inform the interpolation method on the anisotropy of the covariogram, but not on the amount of precipitation associated with the event. Figure 4.6 and 4.8 show that there are significant discrepancies between COMEPHORE and AROME precipitation fields. Is this happening because CP-RCM AROME is not sufficiently constrained by ERA-Interim or is it inherent to the predictibility of precipitation events in this region? Would we expect a similar degree of agreement for a short-term forecast of precipitation based on AROME? Is ERA-Interim only used as boundary conditions or is some form of spectral nudging used to prevent RCM model drift? How far is the study domain from the ALADIN and AROME boundaries? Given the model configuration, do we expect AROME to only be able to provide information on the precipitation climatology but yet be able to provide useful information on the anisotropy of the precipitation structures? Why would that be the case?
In the methods section, the authors choose to consider observed precipitation of less than 0.5 mm as zeros for the purpose of normalizing the precipitation field. How was this number chosen? Are results sensitive to this choice? The back-transformation introduces a bias, which the authors do not take into account (see Van Hyfte et al., 2023, Tellus A). Can the authors quantify the impact of ignoring this source of bias on their analysis?
The authors chose 786 precipitation events to evaluate the proposed method. It would be interesting to know more about the type of events that were selected. Please categorized them by weather regime and season. In particular, can you identify events for which orographic intensification is expected and events for which snow was observed at higher elevations? Do we expect the performance and ranking of the methods to vary depending on the type of event?
In the results section, the authors should present and discuss the covariograms that are obtained for each of the two case studies. The 2D covariograms derived from AROME are presented in Figure 4.8, but that does not tell us how well it fits the experimental covariogram. Furthermore, no information is provided on the fitted covariograms for the other three experiments (rgISO, rgANISO and arISO). This is important, in particular to show that the choice of an exponential covariogram is appropriate based on the data. Did the authors check that the exponential variogram provided a good fit for the 786 events considered in this study?
In the discussion, the authors address many limitations of the method, in particular the fact that it would be difficult to apply on a larger domain. This is an important limitation, because it would seem impractical to deploy such a complex interpolation method operationally if it cannot be applied on a large domain. I encourage the authors to propose a workflow that would allow the application of the method on a larger domain. Could it not be applied watershed by watershed? Would the cost of doing so be prohibitive? Are there other solutions?
Although evaluating the method on significant events (where more than 50mm/day was observed by at least 5 gauges), in practice one would likely want to apply the method for all days. Did the authors assess how well the method performs for less intense precipitation events?
The authors also mention in the discussion the possibility of applying the method using numerical weather forecasts rather than using a RCM. I think this is worth discussing in more details. In particular, I would expect the precipitation field of a short-term forecast to correlated better with observed precipitation, and thus it might be possible to infer more from the forecast than simply the anisotropy of the precipitation field. Furthermore, one might have access to an ensemble of weather forecasts.
Finally, one important aspect of precipitation interpolation that is not discussed in this paper is the issue of quality control. When interpolating precipitation observations, in particular in complex terrain, the issue of quality control is central because it can be very difficult to identify problematic observations based on neighboring stations, given the impact of orography on precipitation amounts over short distances. I understand that this issue might be out of scope for this paper, but I wonder if it was an issue for the authors when applying the method over 786 events. Was the observed data quality controlled? How? Could the presence of outliers impact the results of your analysis? Could your method be used to improve the quality control process through the use of cross-validation? This would likely be crucial to address before the method can be used for real-time applications.
Citation: https://doi.org/10.5194/egusphere-2025-1779-RC2 -
AC2: 'Reply on RC2', Valentin Dura, 07 Jan 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-1779/egusphere-2025-1779-AC2-supplement.pdf
-
AC2: 'Reply on RC2', Valentin Dura, 07 Jan 2026
- AC3: 'Comment on egusphere-2025-1779', Valentin Dura, 07 Jan 2026
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Guillaume Evin
Anne-Catherine Favre
David Penot
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(2861 KB) - Metadata XML
This paper presents a method to interpolate daily (gauges) precipitation data using variograms derived from climate model simulations. The manuscript is well written, and results show potential in the proposed methodology to improve daily precipitation estimations, when gridded rainfall fields such radar-based rainfall estimations may not be available.
In addition of the methods of validation presented by the authors, I suggest adding a comprehensive comparison between the anisotropic variograms derived from CP-RCM (the target of this paper) with those from the radar-derived precipitation analyses. See more details below. This additional comparison targets directly the approach presented in the manuscript and may provide evidence of the advantages and limitations of the proposed technique.
Additional comments:
L134: Please describe what a Trans-Gaussian Random Field is, as I believe this is the first time the reader is introduced to this term.
L154: Please elaborate why only 25% of AROME grid cell were selected to calculate the variograms. Were the selected cells from AROME used as 'virtual' gauges to calculate the variograms? Velasco-Forero et al 2009 and other papers describe methods to estimate 2D variograms using all the grid points from radar images that could be applicable to estimate variograms from AROME and COMEPHORE datasets.
L195: Authors are using TWS to verify the spatial structure of the precipitation fields, however spatial multi-scale dependencies are key characteristics of any rainfall fields and authors should add comparisons to account these effects. Seppo Pulkkinen et al. 2019 presents some examples on how to evaluate different rainfall fields based on their multi-scale characteristics (for example figure 8) GMD - Pysteps: an open-source Python library for probabilistic precipitation nowcasting (v1.0)
L215: Please indicate where "the ensemble means, a sample of conditional simulations, …" are show (Figure, section???)
Figure 2: It is hard to discriminate the ME and MAE colours from the topographical background. Please try to use contours for the topography, so score colours become more visible. For the discussion of results of this figure (ME, MAE) please consider if a scatterplot between elevation and scores could help to support your conclusions. If elevation is not relevant here, then please consider removing the topography of the figure.
L235: It is not true that "rgANISO does not outperform rgISO in gauge gradient similarities" as rgANISO TWS score values are mostly lower that rgISO values for the 66 events with strong anisotropy as shown in Figure 3. Also Figure 3 shows that arANISO generally outperforms rgANISO and arISO also generally outperformes rgISO, which could highlight the advantages of using AROME fields to estimate the spatial variability of the rainfall fields.
L251: last sentence should indicate with dataset is used to estimate the anisotropic covariance. Is from AROME?
Figure 5: Please highlight the data points from the event (2014-09-18) in the scatter plots?
Figure 5: Please add to the boxes with the catchments name, the code ID and areas of the catchments as described in Table 1. Â Â
Figure 5: Consider adding best-fit lines fitted across the ensemble mean points on each scatter plot as they could help to illustrate biases in the simulations for each catchment.
Table 3: it would be valuable to add the same stats for COMEPHORE in this table. This allows a direct comparison of the anisotropy parameters derived from AROME and from COMEPHORE
Figure 6: please add AROME rainfall fields to this figure as the variogram for arISO and arANISO were derived from AROME. Â Please consider adding the TWS values for each field.
Figure 7 and discussion. Given that the relatively small size of the catchments with the whole domain, would be valuable to present the distribution of the rainfall values of few (all?) members for each catchment as complement to the precipitation fields?
L312: please elaborate when rgANISO improves rgISO and when does not and why?
L334: Please elaborate what it could be needed to extend this methodology to real-time and sub-daily applications as this study only has assessed daily time scales.