The motivation comes from a well-known weakness of classical interpolation. Techniques such as inverse distance weighting, ordinary kriging, and kriging with external drift estimate values at unmeasured points by weighting observations from surrounding stations. These methods work reasonably well when gauges are dense, but their accuracy collapses as networks thin out, because the statistical relationships they exploit are inferred from the stations themselves. In sparsely instrumented regions, the reconstructed fields often lose realistic spatial variability, and those errors cascade directly into hydrological models used for flood forecasting, reservoir management, and climate impact assessment. Previous studies have shown that during extreme rainfall events, forecast quality depends strongly on how many gauges are available to capture the storm’s structure.

SPR takes a fundamentally different route. The key insight is that regional climate model simulations, even when biased in absolute terms, encode physically consistent patterns of how meteorological variables vary across space. Rather than using these simulations only as a mean climatology, as some existing methods do, SPR extracts their dominant modes of spatial variability through principal component analysis, computed via singular value decomposition. Each mode, known as a spatial pattern or empirical orthogonal function, is an eigenvector of the spatial covariance structure and captures a coherent way in which values across a region tend to rise and fall together, independently of their magnitude on any given day.

Once these patterns are extracted, the method works in two steps. First, during an auxiliary period, the full archive of daily model fields is decomposed into a fixed basis of spatial patterns ordered by the variance they explain. Second, for each day of the interpolation period, the observed values at the available stations are regressed onto the patterns restricted to the station locations. Ordinary least squares estimates a set of coefficients that describe how strongly each spatial pattern contributes on that particular day. The full gridded field is then rebuilt as a linear combination of the patterns, scaled by those daily coefficients and anchored to the model-derived mean field. In effect, the model supplies the shape of the weather, while the sparse observations set its amplitude.

This design has several practical advantages. The regression is performed independently for each day, so the method does not require a fixed station network over time; the pattern matrix simply adapts to however many stations report on a given day. Nor do the observations need to be temporally aligned with the period used to extract the patterns, which gives considerable flexibility when working with archives of different lengths. Because the patterns come from model simulations that can span both historical and future climates, SPR can, in principle, adapt to changing spatial structures in a warming world, something earlier reduced-space reconstruction methods built on observational archives cannot easily do.

To test the method rigorously, the researchers designed a battery of controlled synthetic experiments. They used high-resolution simulations from the ClimEx project, produced with the Canadian Regional Climate Model over a 280 by 280 cell grid at roughly 11 kilometer resolution covering North America. Virtual stations were created by sampling grid cells at densities ranging from 90 percent down to 10 percent, across nested regions of large, medium, and small extent in both a southern and a northern study area, yielding 30 distinct experiments per variable for daily precipitation, minimum temperature, and maximum temperature. Because the full model field serves as ground truth by design, every method could be evaluated with perfect knowledge of what it was trying to reconstruct.

The results were striking. Across the vast majority of the 90 synthetic experiments, SPR delivered the best combination of low root mean squared error and high structural similarity, the latter measured by the Structural Similarity Index, a metric borrowed from image quality assessment that captures how well spatial texture and contrast are preserved. At moderate to high station densities, SPR dominated regardless of region size or location. Kriging with external drift, the strongest baseline, edged out SPR in only six of the 90 experiments, mostly for precipitation in small regions, and even then SPR typically reproduced the spatial patterns better. Ordinary kriging and inverse distance weighting consistently trailed both.

The most dramatic test came from a stress experiment mimicking the harshest conditions of remote monitoring: a large northern Quebec region of 2,970 grid cells with only three virtual stations, roughly 0.1 percent density. Here SPR again produced lower average and median errors than kriging with external drift for all three variables, and higher structural similarity for both temperature variables. A revealing diagnostic showed that the kriging fields were almost perfectly correlated with the climatological background, a Spearman correlation of 0.9997, meaning the method essentially reproduced its auxiliary information. SPR’s fields were less tied to the background, yet far more faithful to the true spatial organization, with an average structural similarity of 0.4151 against 0.2504 for kriging.

Crucially, the method also held up against real-world data. Using quality-controlled observations from Environment and Climate Change Canada stations in southern Quebec, with 15 complete precipitation records and 44 temperature records over two-year windows, the researchers ran 100 independent random subsamplings at 10 and 30 percent station density, corresponding to as few as two to four training stations across a 70,000 square kilometer region. At the sparser level, SPR systematically achieved lower median errors and higher structural similarity than kriging with external drift, and its performance varied less from one station configuration to another, indicating genuine robustness rather than luck. At 30 percent density the advantage narrowed, confirming that the method’s main value lies in data-scarce settings.

The authors are candid about limitations. SPR inherits some of the smoothness of its 11 kilometer source model, and any systematic spatial bias in the simulation can propagate into the reconstructed fields, so pairing the method with convection-permitting models running at one to four kilometer resolution is a promising next step. The current implementation also ignores temporal dependence between days and uses a fixed number of patterns, both natural targets for future refinement. Still, the conceptual shift is significant: rather than treating auxiliary gridded data as a drift term that constrains absolute values, SPR uses it to define spatial organization itself. For hydrologists calibrating models against historical observations while projecting future change with climate simulations, that consistency between past and future spatial structures could prove quietly transformative, turning sparse gauges and model archives into weather maps that are finally good enough to trust.

Subject of Research: A new interpolation method combining climate model spatial patterns with sparse station observations to reconstruct daily meteorological fields

Article Title: Spatial pattern regression for meteorological fields interpolation

Article References: Houssou, V., & Carreau, J. (2026). Spatial pattern regression for meteorological fields interpolation. Hydrology and Earth System Sciences, 30(18), 5791-5807. https://doi.org/10.5194/hess-30-5791-2026

Image Credits: AI Generated

DOI: 10.5194/hess-30-5791-2026

Keywords: spatial interpolation, meteorological fields, regional climate model, principal component analysis, hydrology, kriging, precipitation, temperature, station networks, empirical orthogonal functions, climate data, Quebec