## 4 Discussion
The investigation of the GWFB's R\({}^{2}\) showed that the SVR and Sc2 had the highest R\({}^{2}\) at 0.9846 followed by the XGB-SVR hybrid model and Sc2 with an R\({}^{2}\) value of 0.9809, while the lowest R\({}^{2}\) value was detected under XGB and Sc3 (remote sensing indices) at 0.2322. This is strongly consistent with the research findings, as the analysis showed that the single model followed by hybrid models obtained the highest R\({}^{2}\) values. In a research endeavour conducted by [PERSON] et al. [67], the amalgamation of the Extreme Learning Machine (ELM) framework with two innovative meta-heuristic methodologies, specifically the Whale Optimization Algorithm (WOA) and the Flower Pollination Algorithm (FPA), was investigated for the forecasting of monthly pan evaporation (Ep). Hybrid models incorporating WOA-ELM and FPA-ELM were formulated to estimate monthly Ep within the Poyang Lake Basin located in Southern China. These hybrid models were evaluated against the differential evolution algorithm-optimized ELM (DEELM), the enhanced M5 model tree (M5P), and artificial neural network (ANN) frameworks. The findings revealed that the FPA-ELM model exhibited the highest predictive accuracy across all four monitoring stations, with the WOA-ELM model following closely behind, both outperforming conventional models. The application of heuristic algorithms, particularly the FPA, was strongly advocated for the enhancement of the efficacy of independent machine learning frameworks. The outcomes corroborated the results concerning RMSE, a pivotal metric for evaluating model accuracy in forecasting the GWFP, as our investigation illustrated that the hybrid models produced minimal values, thereby endorsing the efficacy of hybridization in diminishing errors and augmenting result precision (Figure 11). [PERSON], [PERSON] [68] utilized artificial neural networks (ANNs), support vector machines (SVMs), random forests (RFs), and k-nearest neighbours (KNNs) in their investigation to forecast green water evapotranspiration (GWET) and blue water evapotranspiration (BWET). Among the employed models, the random forest (RF) model demonstrated superior efficacy in estimating BWET, achieving a coefficient of determination (R2) of 0.96, a mean inter-annual (MIA) of 0.91, a root mean square error (RMSE) of 10.77 mm month\({}^{-1}\), a Nash-Sutcliffe efficiency (NSE) of 0.92, and a mean absolute error (MAE) of 6.84 mm month\({}^{-1}\). Furthermore, the RF model, except for the Pre variable, exhibited satisfactory simulation outcomes (0.3 \(\leq\) NSE < 0.6), whereas all alternative machine learning algorithms displayed inadequate simulation results (NSE < 0.3). When evaluating the outcomes for predicted wheat BWFP, it was noted that the RF model in conjunction with Sc2 (climatic parameters) yielded the lowest NSE value of 0.05, which was regarded as inadequate. Incontrast, the highest NSE of 0.98 was recorded under Sc2 (climatic parameters), and the XGB-SVR hybrid model was categorized as perfect, while the lowest NSE of 0.09 was noted with SVR and Sc3, which was classified as inadequate. The NSE values for Sc1, Sc2, Sc4, and Sc5 were assessed as very good across all models, while the data for Sc3 from both single and hybrid models were categorized as satisfactory to unsatisfactory. Conversely, the results of the research are inconsistent with the investigation carried out by [PERSON], [PERSON] [69], who employed three distinct machine learning algorithms, specifically random forest (RF), extreme gradient boosting (XGB), and the hybrid random forest-extreme gradient boosting (XGB-RF), to predict the uniformity of water distribution from fixed set sprinklers. This analysis was predicated on several variables including operating pressure, sprinkler elevations, discharge rates, nozzle diameters, wind velocity, and humidity levels, along with maximum and minimum temperature readings. The findings revealed that the peak R2 coefficients were 0.796, 0.825, and 0.929 for RF, XGB, and XGB-RF, respectively, in the initial context for CU.