Consideration of radiation for improving the Hargreaves-Trajkovic model to calculate reference crop evapotranspiration in Huaibei Plain

Accurately estimating reference crop evapotranspiration (ET₀) is critical for irrigation planning and water resource management. While the Penman-Monteith (P-M) model is the FAO-recommended standard, its data-intensive requirements limit its application in regions with sparse meteorological stations. The Hargreaves–Trajkovic (H–T) model, requiring only temperature data, offers a practical alternative but exhibits significant errors in humid and sub-humid climates due to its simplified representation of solar radiation dynamics. This study aims to enhance the calculation accuracy of the H–T model for such regions by integrating physical principles with data-driven calibration.We propose an improved methodology centered on a hierarchical Bayesian seasonal parameter model. This model innovatively refines the H–T formula by incorporating prior physical knowledge of solar radiation patterns. It dynamically calibrates key model parameters to capture their intrinsic annual cyclical variations, thereby achieving a more physically consistent and locally adapted estimation of the radiation term. The method was developed and validated using comprehensive daily meteorological data (1980-2023) from 20 weather stations across the Huaibei Plain in Anhui Province, a representative humid-subhumid area. Model performance was rigorously evaluated against the P-M model as the benchmark, employing multiple statistical metrics including the Root Mean Square Error (RMSE), coefficient of determination (R²), and Mean Absolute Error (MAE) at daily, monthly, and seasonal scales.The results demonstrate a substantial improvement in ET₀ estimation. First, the improved H–T model successfully replicates the long-term trend of ET₀ calculated by the P-M model, with performance significantly surpassing that of existing radiation-based simplified models. Second, at the regional level, the improved model reduces the mean RMSE by 0.31 mm/d and increases the R² from 0.834 to 0.924 compared to the original H–T model, all while maintaining a simple and practical computational structure. Third, a detailed spatial and temporal analysis reveals consistent gains. For daily ET₀ in three subregions, the MAE decreased from 0.32, 0.39, and 0.36 mm/d to 0.16, 0.15, and 0.14 mm/d, respectively, while the daily R² increased correspondingly. For monthly ET₀, accuracy gains were even more pronounced, with MAE reductions to approximately 0.07 mm/d across subregions and monthly R² values exceeding 0.97. Spatially, the accuracy improvement was high across most of the region, with nearly 80% of the area achieving an improvement rate exceeding 50% and a maximum annual improvement of 86.1%. Seasonally, the most significant enhancement was observed in winter, with a maximum accuracy improvement of up to 93.7%.In conclusion, the improved H–T model, driven by the hierarchical Bayesian seasonal parameter framework, effectively balances computational simplicity with high accuracy. It provides a reliable, data-efficient tool for ET₀ estimation in the Huaibei Plain and offers a transferable methodological framework for improving temperature-based ET₀ models in other humid and sub-humid regions where full meteorological datasets are unavailable.