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

Accurately estimating reference crop evapotranspiration (ET₀) is critical for irrigation planning and water resource. While the conventional Penman-Monteith (P-M) model has limited to the data-intensive requirements in the sparse meteorological stations, due to the FAO-recommended standard. Alternatively, the Hargreaves-Trajkovic (H-T) model is often required only temperature data. However, there are the significant errors in humid and sub-humid climates, due to the simplified representation of solar radiation dynamics. In this study, the accuracy of the H-T model was enhanced to integrate the physical principles with the data-driven calibration. An improved model was proposed using a hierarchical Bayesian seasonal parameter model. The H-T formula was then refined to incorporate the prior physical knowledge of solar radiation patterns. Key model parameters were dynamically calibrated to capture their annual cyclical fluctuations, thereby achieving a more physically consistent and locally adapted estimation of the radiation term. Daily meteorological data (1980-2023) was collected from 20 weather stations in the representative humid-subhumid area, such as the Huaibei Plain of Anhui Province. The performance was evaluated to take the P-M model as the benchmark. Multiple statistical metrics were employed, including the root mean square error (RMSE), coefficient of determination (R²), and mean absolute error (MAE) at daily, monthly, and seasonal scales. The results show that the substantial performance achieved in the ET₀ estimation. Firstly, the H-T model successfully replicated the long-term trend of the ET₀ from the P-M model, where the performance significantly surpassed that of the existing simplified ones. Secondly, the mean RMSE was reduced by 0.31 mm/d, whereas, the R² increased from 0.834 to 0.924 at the regional level, compared with the original H-T model, all while maintaining a simple and practical computational structure. Thirdly, spatial and temporal analysis revealed the consistent gains. In 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. In monthly ET₀, the high accuracy was obtained with the MAE reductions to approximately 0.07 mm/d in the subregions and monthly R² values exceeding 0.97. Spatially, the high accuracy was also distributed with nearly 80% of the area, with an improvement rate exceeding 50% and the maximum annual improvement of 86.1%. Seasonally, there was the most significant enhancement with the maximum accuracy improvement of up to 93.7% in winter. In conclusion, the H-T model with the hierarchical Bayesian seasonal parameter framework was effectively balanced the computational simplicity with high accuracy. A dependable and data-efficient tool can provide for the ET₀ estimation in the Huaibei Plain. The finding can offer a transferable framework to improve the temperature ET₀ models in the humid and sub-humid regions with the unavailable meteorological datasets.