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.