📄 earth_science

Spatial interpolation alters heat-wave detection despite small temperature errors in data-sparse regions

This study demonstrates that while spatial interpolation methods like Inverse Distance Weighting may achieve acceptable predictive accuracy in data-sparse regions, they systematically reduce temperature variability and significantly alter the detection and duration of heat-wave events, suggesting that conventional error metrics are insufficient for evaluating their suitability in climate-risk assessments.

Original authors: Fabiano Fernandes Bargos, Maurício Lamano Ferreira, Danúbia Caporusso Bargos

Published 2026-08-19

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CC BY 4.0

Original authors: Fabiano Fernandes Bargos, Maurício Lamano Ferreira, Danúbia Caporusso Bargos

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Climate science relies heavily on maps that show how temperature changes across a landscape, filling in the blanks between weather stations to create a continuous picture of the atmosphere. These maps are essential for understanding risks like heat waves, which are periods of dangerously hot weather that threaten human health, strain power grids, and disrupt daily life. To build these maps, scientists use mathematical techniques to estimate the temperature at places where no thermometer exists, based on the readings from nearby stations. For decades, researchers have assumed that if a method produces a small average error in its temperature estimates, it is reliable enough for all purposes, including tracking extreme events. However, this assumption overlooks a critical detail: the way a method smooths out data can hide the very extremes it is meant to reveal.

A new study conducted in the state of São Paulo, Brazil, challenges this long-held view by showing that the choice of mathematical method can fundamentally alter the detection of heat waves, even when the temperature numbers look nearly correct. The researchers focused on a region with complex terrain, ranging from sea level to high mountain ranges, where weather stations are unevenly distributed. They took hourly temperature records from 2021 to 2025 and tested two common ways of filling in the gaps: a simple method that just picks the nearest station's reading, and a more sophisticated method that averages nearby stations, giving more weight to the closest ones. While the sophisticated method produced slightly more accurate average temperatures, it systematically smoothed out the data, reducing the sharpness of temperature swings.

The consequences of this smoothing became starkly clear when the team looked for heat waves, defined in this study as days when the maximum temperature exceeds 35°C for several days in a row. The sophisticated method, which is often preferred for its overall accuracy, consistently identified fewer heat waves and shorter durations than the simpler method. In some municipalities, the difference in the total number of heat wave days over the five-year period reached as high as 199 days. This happened because the sophisticated method slightly lowered the peak temperatures on the hottest days, just enough to break the chain of consecutive days required to classify an event as a heat wave. The study demonstrates that a method can be mathematically "better" at predicting the average temperature while simultaneously failing to capture the extreme events that matter most for public safety and climate planning.

The researchers found that this effect was not random but followed specific patterns linked to the landscape and the density of weather stations. In areas with complex topography or sparse data, the smoothing effect was stronger, particularly for minimum temperatures, where the method tended to erase the coldest extremes. This suggests that relying solely on standard error metrics, which measure how close an estimate is to an observation on average, is insufficient for climate risk assessment. A method that looks good on paper might still distort the reality of extreme weather, leading to an underestimation of the duration and frequency of dangerous heat events.

Ultimately, the study concludes that spatial interpolation is not a neutral step in preparing climate data but an active transformation that reshapes the signal. The findings imply that scientists and policymakers must be cautious when using interpolated data to assess risks, as the choice of method can change the story the data tells. For applications involving heat waves and other extremes, the goal should not just be to minimize average errors but to preserve the variability and persistence of temperature spikes. The research highlights that in a warming world, where the stakes of extreme weather are rising, the tools used to map the climate must be chosen with an eye toward preserving the very extremes they are designed to measure.

Technical Summary: Spatial Interpolation Alters Heat-Wave Detection Despite Small Temperature Errors in Data-Sparse Regions

Problem Statement
Climate assessments increasingly rely on spatially interpolated temperature fields to estimate exposure at administrative scales (e.g., municipalities) where observational networks are sparse or irregular. While interpolation methods are routinely evaluated using global accuracy metrics such as Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), their influence on the statistical structure of temperature fields and derived climate indicators remains insufficiently understood. Specifically, it is unclear whether methods that perform well on average error metrics preserve the variability, distributional tails, and temporal persistence required to accurately detect extreme events like heat waves. This study addresses the gap in understanding how distance-based interpolation methods alter the representation of temperature extremes and heat-wave detection in data-sparse, environmentally heterogeneous regions.

Methodology
The study focuses on the State of São Paulo, Brazil, a region characterized by complex topography (coastal plains, escarpments, plateaus) and uneven meteorological station coverage. The research utilized hourly air temperature observations from 2021 to 2025 obtained from the Brazilian National Institute of Meteorology (INMET). The dataset included 160 stations (42 within the state), with significant temporal gaps in data availability.

The methodological framework followed a four-step data-driven pipeline:

Preprocessing and Feature Construction: Hourly data were quality-controlled. A 250 km buffer around the state was included to incorporate neighboring stations and reduce edge effects.
Model Evaluation (LOOCV): A leave-one-out cross-validation (LOOCV) framework was employed to assess interpolation performance. The Nearest Neighbor (NN) method served as a baseline, compared against multiple configurations of Inverse Distance Weighting (IDW) with search radii of 150, 200, and 250 km and distance-decay exponents ( $\alpha$ ) of 2 and 3. Performance was quantified using RMSE, MAE, Bias, and $R^2$ .
Unsupervised Learning: Principal Component Analysis (PCA) and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) were applied to the performance metrics and geographic attributes (latitude, longitude, altitude) to identify spatial patterns of model skill and group stations with similar error regimes.
Spatial Prediction and Indicator Derivation: The best-performing IDW configuration ( $R=250$ km, $\alpha=2$ ) and the NN method were used to interpolate hourly temperatures to the centroids of 645 municipalities. These series were aggregated into daily statistics (mean, minimum, maximum). Heat waves were defined as sequences of consecutive days where daily maximum temperature exceeded $35^\circ$ C.

Key Results

Interpolation Accuracy: The IDW configuration with a 250 km search radius and $\alpha=2$ achieved the best performance among tested methods, yielding an RMSE of $1.97^\circ$ C and an $R^2$ of 0.877, outperforming the NN baseline (RMSE $2.65^\circ$ C, $R^2$ 0.778).
Spatial Structure of Errors: Clustering analysis revealed that interpolation errors are not randomly distributed but are spatially structured. Poorly performing stations (Cluster -1) were associated with heterogeneous environmental conditions and complex topography, while better performance was observed in regions with higher station density and more homogeneous terrain.
Impact on Temperature Distributions: While IDW adequately preserved the central tendency of maximum and mean temperatures, it systematically reduced temperature variability. This smoothing effect was most pronounced for minimum temperatures, where cold extremes were attenuated, and the lower tails of the distribution were distorted.
Heat-Wave Detection Discrepancies: The reduction in variability and temporal persistence led to significant differences in heat-wave detection. Compared to the NN method, IDW consistently identified fewer and shorter heat-wave events. In some municipalities, the cumulative heat-wave duration differed by up to 199 days over the study period. For example, in Pereira Barreto and Ilha Solteira, the NN method detected approximately 325 heat-wave days, whereas IDW detected only 126.
Nonlinear Amplification: The study found that even small temperature errors (relative to the overall RMSE) could trigger a nonlinear amplification mechanism. Because heat-wave detection relies on fixed thresholds and consecutive-day criteria, minor underestimations in interpolated temperatures could break sequences of threshold exceedances, leading to substantial underestimation of event frequency and duration.

Significance and Claims
The paper argues that spatial interpolation is not a neutral preprocessing step but an active transformation of the climate signal that can alter the representation of climate extremes. The authors claim that:

Conventional metrics are insufficient: Evaluating interpolation methods solely based on average error metrics (RMSE, MAE) may be inadequate for applications involving climate-risk assessment and extreme-event analysis, as these metrics fail to capture distortions in distributional tails and temporal persistence.
Methodological choices impact risk assessment: The choice of interpolation method directly influences the characterization of heat waves. Methods that introduce spatial smoothing (like IDW) may lead to the underdetection of heat-wave frequency and duration, potentially biasing assessments of exposure, vulnerability, and adaptation needs.
Context-dependent performance: The "best" interpolation method depends on the specific application. While IDW may minimize average prediction error, it may be suboptimal for preserving local extremes and consecutive threshold exceedances.
Implications for decision-making: In data-sparse regions where interpolated products serve as the primary basis for local climate assessment, these methodological sensitivities can affect resource allocation and the identification of municipalities most exposed to extreme heat.

The study concludes that future climate-impact assessments should explicitly account for interpolation uncertainty, particularly for threshold-based indicators, and suggests that evaluation frameworks must move beyond pointwise errors to include distributional diagnostics and the preservation of event characteristics.

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