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Heat–Water Differential Indices: A Curve-Based Weather Representation in Agricultural Systems

Published by the American Society of Agricultural and Biological Engineers, St. Joseph, Michigan www.asabe.org

Citation:  2026 ASABE Annual International Meeting  2600968.(doi:10.13031/aim.202600968)
Authors:   Md. Samiul Basir, Yaguang Zhang, Dennis R. Buckmaster, Ignacio A. Ciampitti, James V. Krogmeier
Keywords:   Click here to enter keywords and key phrases, separated by commas, with a period at the end

Abstract. Crop phenology and yield at a given location and time are primarily controlled by weather conditions, particularly temperature and precipitation. Precipitation provides direct water input to crops, while temperature reflects solar energy intensity and regulates water demand through evapotranspiration. This interaction can be conceptualized as a supply–demand system using cumulative precipitation and potential evapotranspiration (PET), where PET was estimated using the Hargreaves model as a function of temperature and extraterrestrial solar radiation. In this study, shape-based features derived from the interaction between cumulative precipitation and PET curves were extracted and defined as heat–water differential indices (HWDIs). These include the area bounded between the two curves of cumulative rainfall and cumulative PET, the magnitude and timing of crossover points where these curves intersect, the temporal position and value of centroids of polygons formed between successive crossovers, and the total number of polygons generated during the corn cropping season (April–September for the U.S. Corn Belt). An analysis was conducted using county-level aggregated weather data from the European Center for Medium-Range Weather Forecasts ERA5 reanalysis dataset for 12 major U.S. Corn Belt states over the year 2000–2024. HWDIs, along with commonly used weather heuristics such as mean temperature, cumulative GDD, cumulative precipitation, rainfall event count, cumulative PET, mean precipitation intensity, and maximum dry spell length, were used as potential variables to estimate county-level corn yield reported by USDA. HWDIs were correlated with traditional heuristic variables due to their shared meteorological origin but provided complementary temporal information. For example, these HWDIs mathematically capture minor and major droughts along with their timing relative to growth stage (with GDD as a proxy), excessive rainfall in spring that would influence emergence, and excessive rain that interferes with harvest, etc. Depending on the structural complexity of rain-PET curves, county-year weather was classified into 8 weather regimes using an expert system, and those classes were used as categorical HWDI features. Because HWDI features showed weak linear relationships with yield, nonlinear machine-learning models were used to estimate yield. Across Random Forest, XGBoost, CatBoost, and Multilayer Perceptron (MLP) models, adding HWDI descriptors to conventional weather heuristics consistently improved prediction performance. XGBoost performed best, with HWDIs increasing R2 from 0.566 to 0.663. SHAP (SHapley Additive exPlanations) analysis showed that PET and temperature-based variables remained the dominant predictors, while HWDI descriptors such as total absolute area, polygon centroid timing/value, last-polygon timing, and signed area also ranked among the important features. This indicates that HWDIs provide complementary information by capturing seasonal timing, magnitude, and structure of water–energy imbalance beyond conventional weather summaries.

Keywords. Area, centroid, classification, crossover time, dominance, XGBoost, weather, weather structure.

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