| 04 Mar 2026
A deep learning framework for gridding daily climate variables from a sparse station network
Abstract. High-resolution gridded climate datasets are essential for Earth system modelling and impact assessments, yet generating them from sparse, irregularly distributed station networks remains a significant challenge, particularly in regions with complex topography. This study evaluates the Spatial Multi-Attention Conditional Neural Process (SMACNP), a probabilistic deep learning framework, for the daily spatial interpolation of air temperature and precipitation, marking the first application of its localized encoder variant to the challenge of gridding climate data from a sparse station network. We investigate two distinct encoder configurations—Global and Localized—to determine the optimal structural prior for capturing spatial dependencies in data-scarce regimes. The models were developed and evaluated using data from a sparse network of meteorological stations in Romania from 2020 to 2023. To ensure applicability for long-term historical reconstruction, the input features were restricted to static topographic predictors derived from a Digital Elevation Model (DEM). Performance was benchmarked against Regression Kriging (RK), a standard geostatistical baseline that incorporates these same topographic covariates. Results demonstrate that the SMACNP architectures substantially outperform the RK baseline for both variables. The SMACNP (Localized) configuration, which utilizes an attention mechanism, emerged as the most robust model, achieving the lowest Mean Absolute Error (MAE) and the highest correlation across the majority of seasons. The performance gains were particularly pronounced for precipitation, where the deep learning models effectively captured fine-scale spatial heterogeneity and non-linearities that traditional methods tended to over-smooth. Furthermore, the SMACNP framework demonstrated superior uncertainty quantification; while RK exhibited significant overconfidence in precipitation estimates, the SMACNP (Localized) model produced well-calibrated probabilistic predictions with near-ideal empirical coverage. These findings indicate that localized neural process-based models offer a powerful, scalable, and physically plausible alternative to geostatistical methods for generating high-quality gridded climate datasets in complex, data-sparse environments.
This interesting paper compares deep learning methods for gridding climate variables based on observations with a traditional residual kriging approach. The results of the deep learning approach show better performance than residual kriging, demonstrating the potential use of such methods for observation gridding.
In general the paper is well written, and the overall structure is good. There are, however, a few shortcomings that need attention before the paper should be accepted for publication.
In general, the author should consider that this is a novel approach which is not necessarily familiar to a wider community and therefore needs more explanation than for more established methods. In its present state it is full of details that maybe are not essential for documenting the outcome of this interesting and valuable study.
Data
Does the input data (context) distribution fit the distribution of the target points? How valid are the model outside the training data “window”? The distribution of the geographic parameters for both context and target points as well as for the grid cells should be presented and discussed.
Methods
The RK description is too limited. A description of the deterministic trend and the semi-variogram parameters should be presented and discussed.
The description of the SMACNP is very detailed, and these details overshadow the main message. Consider using the flow chart in figure 3 (or even a simplified version of it) as a guide to the presentations of the method. Move details that are not necessary for further reading, or not discussed further, to appendix. Be also sure to define all abbreviations, terms and symbols the first time they appear.
Figures.
Resolution and clarity of figures need to be improved. Figure 6 and 7 are very blurry. Figure 7 intends to include a lot of information that cannot be separated. Choose colors etc. that clearly distinct the models. (This also applies to the supplementary material).
Minor comments
L.60 Long sentence. Consider to split it to make the meaning easier to follow and understand
L.144: Give an explanation of pathway and encoder in this context. For overview, maybe figure 3 should be emphasized more as an introduction (guide) to the SMACP method?
L.146: Define MLP
L.147: Define Lp
L.150: Describe the functional role of query(Q), key(K) and value (V).
L.166-169: Consider to simplify and rephrase. Define terms! Are all details necessary?
L.205-206: Explain binary cross-entropy.
L.434-436. Could you elaborate on this a bit more? Is it so that there might be dependencies between precipitation and temperature that is captured by the deep learning method? Would e.g. co-kriging of precipitation using temperature as co-variate captured some of the same? And finally, for curiosity and further understanding. Would it be possible to run the deep learning as univariate approaches for temperature and precipitation respectively?
The study covers a relatively short time period. How sensitive will the method be to the training data period, and how applicable is the method for periods outside the training period? Please discuss with respect to potential use, e.g. for utilizing functions derived from observation dense period to extend data in periods with sparser data cover.