| 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.
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.