Reference Crop Evapotranspiration Prediction Based on Gated Recurrent Unit with Quantum Inspired Multi-head Self-attention Mechanism

Reference crop evapotranspiration (ET₀), as a critical element in climatology, hydrology and agricultural science, is essential for water hydrological cycle and irrigation scheduling. The FAO-56 Penman Monteith Equation (FAO-56 PM) is a standard method with complex formulation and strict meteorological factors for ET₀ calculation. To overcome the strict meteorological factor restriction, this paper proposes an ET₀ prediction model GRU-QIMSA, which is constructed based on gated recurrent unit (GRU) and quantum inspired multi-head self-attention mechanism (SA). The daily meteorological data from six weather stations in Yulin City from 1990 to 2019 are collected to calibrate the proposed model. By using cosine similarity and cross entropy, the saturation vapor pressure, actual water vapor pressure and solar radiation are selected as supplementary meteorological data to boost the prediction performance of the proposed model. The effectiveness and superiority of the proposed model are validated in comparison with GRU-SA, GRU and back propagation neural network (BPNN). The order of the prediction accuracy is GRU-QIMSA > GRU-SA > GRU > BPNN. The proposed model outperforms GRU-SA, GRU and BP neural network, which indicates that the quantum inspired multi-head self-attention mechanism can learn the time series data effectively. The prediction results of the proposed GRU-QIMSA show excellent performance on all the weather station datasets, which implies that the quantum inspired multi-head self-attention mechanism can obtain better generalization ability than other methods. In terms of 7 steps ahead prediction, the ET₀ prediction error is in the range of -1.5 to 1.5 (mm/day), which indicates that the proposed GRU-QIMSA model can obtain the high prediction accuracy and excellent generalization ability.