Heuristic Algorithm Optimization of CNN–BiLSTM–Attention for Reference Crop Evapotranspiration Forecasting Under Limited Meteorological Data Availability

Accurate prediction of reference evapotranspiration (ET0) using integrated deep learning approaches with limited meteorological data is highly significant for efficient water resource utilization and management in arid regions. Nevertheless, parameter optimization is frequently overlooked in current research, leading to unsatisfactory estimation accuracy that cannot meet practical application requirements. To overcome this limitation, a CNN–BiLSTM–attention hybrid model is constructed by combining the powerful feature-extraction capability of CNN and excellent sequence-processing performance of BiLSTM, followed by the integration of an attention mechanism. Five metaheuristic algorithms, namely the osprey optimization algorithm (OOA), grey wolf optimization (GWO), whale optimization algorithm (WOA), particle swarm optimization (PSO), and northern goshawk optimization (NGO), are adopted to optimize the key parameters of the proposed model. The developed hybrid models are then applied to ET0 estimation in Linze County, China. The results demonstrate that the error indices of these models vary within the ranges of MAPE [14.28%, 14.48%], MAE [0.4270, 0.4482], RMSE [0.5596, 0.5844], and NMSE [0.0490, 0.0577]. Overall, the OOA–CNN–BiLSTM–attention model exhibited the most robust and consistent estimation performance across multiple evaluation metrics among the investigated models.