| 17 Apr 2026
Spatial pattern regression for meteorological fields interpolation
Abstract. High-resolution gridded meteorological data are essential for hydrological impact studies, yet their reconstruction from sparse station networks remains challenging. We introduce Spatial Pattern Regression (SPR), a data-driven method that reconstructs gridded meteorological fields by combining spatial information extracted from high-resolution regional climate model (RCM) simulations with station observations. SPR operates in two steps: spatial patterns are first extracted from RCM data using principal component analysis, then daily fields are reconstructed through linear regression using available observations. The method is first evaluated using controlled synthetic experiments, where virtual stations selected as a subset of the RCM grid emulate observational networks with varying density, size, and location. SPR is then validated using real station observations. Daily precipitation, minimum temperature, and maximum temperature are considered. Results show that SPR performs better than inverse distance weighting, ordinary kriging, and kriging with external drift, particularly under sparse network conditions. Sensitivity analyses highlight the dominant role of station density and location on interpolation accuracy, supporting the robustness and applicability of SPR for hydrological studies.
The manuscript describes a spatial interpolation method applied over North America. The method is described in detail and is suitable for the described applications. The validation is carried out in a reasonable way and the results are correctly interpreted by the authors. However, there are a number of issues that need to be addressed before this manuscript can be considered for publication.
Comments:
1. The SPR method described in the manuscript is not original. It was introduced years ago and is called Reduced Space Optimal Interpolation (RSOI, Schiemann et al. 2010). Please adjust your manuscript to acknowledge the RSOI reference and eventually point out the elements of originality of your work with respect to RSOI.
Ref:
Schiemann, R., M. A. Liniger, and C. Frei (2010), Reduced space optimal interpolation of daily rain gauge precipitation in Switzerland, J. Geophys. Res., 115, D14109, doi:10.1029/2009JD013047.
2. The direct backtransformation proposed at the beginning of section 3.5 is prone to introducing systematic errors in the final reconstructed field. When the background is a deterministic model, applying inverse transformations directly to the analysis can lead to systematic underestimation of precipitation, as described by Fletcher and Zupanski (2006). This occurs because the analysis-error variance at grid points must be considered in the inverse transformation. A correction method can be implemented using a Taylor series decomposition of the inverse transformation, as outlined in Fortin et al. (2015) and van Hyfte et al. (2023) for Box-Cox transformations. Alternatively, a more computationally intensive approach proposed by Erdin et al. (2012) involves applying the inverse transformation to 399 quantiles, equidistant in probability.
Please make the readers aware of this consequence of applying a direct inverse transformation.
Ref:
Fletcher, S.J. & Zupanski, M. (2006) A data assimilation method for log-normally distributed observational errors. Quarterly Journal of the Royal Meteorological Society, 132, 2505–2519. Available from: https://doi.org/10.1256/qj.05.222
Fortin, V., Roy, G., Donaldson, N. & Mahidjiba, A. (2015) Assimilation of radar quantitative precipitation estimations in the canadian precipitation analysis (capa). Journal of Hydrology, 531, 296–307.
van Hyfte, S., Le Moigne, P., Bazile, E., Verrelle, A. & Boone, A. (2023) High-resolution reanalysis of daily precipitation using AROME model over France. Tellus A: Dynamic Meteorology and Oceanography, 75, 27–49. Available from: https://hal.science/hal-04271427
Erdin, R., Frei, C. & Künsch, H.R. (2012) Data transformation and uncertainty in geostatistical combination of radar and rain gauges. Journal of Hydrometeorology, 13, 1332–1346.
3. Lines 84-88. This part is not clear. Does your method require a fixed station network over time?
4. Lines 89-92. This part is not clear. It seems that you are not using station data in your interpolation. Please rephrase this part.
5. It is not clear what procedure was used to select the data for the computation of PCA for daily data. Do you extract the PCA considering all daily data over the whole period? Do you consider only the data belonging to that specific day of the year? Please elaborate more on this point.
6. Can you elaborate a bit more on which strategy you used to fit the linear regression model of Eqs. (2)-(3)?