# Evapotranspiration Prediction Method Based on K-Means Clustering and QPSO-MKELM Model
## 4 Discussion  
This study first estimated the importance of meteorological features for predicting ET\({}_{0}\) based on the correlation between each meteorological feature and ET\({}_{0}\) and the correlation among the meteorological features themselves. The normalized variance values of the features were used to assess their significance, and important features were selected while redundant ones were excluded. The study identified temperature and sunshine duration as the two most important features for estimating evapotranspiration. All models achieved over 95% prediction accuracy in experiments when only temperature and sunshine duration were used as inputs. This is consistent with the findings of [PERSON] et al. (2023), who predicted evapotranspiration for 14 sites in southern China [48]. This indicates that estimating ET\({}_{0}\) using only temperature and sunshine duration in southern China with limited meteorological conditions is reasonable. This finding provides valuable guidance for sensor selection and data collection in practical applications that require ET\({}_{0}\) prediction.  
Considering that evapotranspiration varies uniformly and exhibits significant periodicity in the study region, the sine and cosine values of the date were added as inputs, resulting in a noticeable improvement in prediction accuracy across all models. Similarly, [PERSON] et al. (2024) incorporated extraterrestrial radiation (Ra), a parameter that can be calculated from the date and latitude, into their model, and observed a significant improvement in prediction performance [49]. Building upon the widely recommended PSO-ELM model for ET\({}_{0}\) prediction, this study proposes the Kmeans-QPSO-MKELM algorithm, which addresses the shortcomings of the original model. The new model improves prediction accuracy and achieves a shorter training time. At the research site, the new model outperformed the WOA-SVR model proposed by [PERSON] et al. (2020) for ET\({}_{0}\) prediction [24], achieving higher prediction accuracy and shorter training time. The prediction accuracy of the new model was also higher than that of the traditional ANFIS and RF models.  
At the same time, this study has several limitations and areas for improvement:  
1. In this study, the Kmeans-QPSO-MKELM model used a linear kernel function, a polynomial kernel function, and an RBF kernel. Future research could compare the impact of different kernel functions on the model's ability to capture meteorological features and predict ET\({}_{0}\). Given that ET0 exhibits periodicity, periodic kernel functions could be included.
2. This study was conducted only in one location within a single climatic zone. Future studies should expand to different climatic zones to assess the model's performance in varied conditions.
3. This study used the FAO-56 model to calculate the target values of ET\({}_{0}\), which is a common practice. However, the conclusions drawn may not be robust enough, and therefore, future research should use experimental ET0 data as the target value for more reliable experiments.
4. The models compared in this study were limited. Future work could include comparisons with other models, such as deep learning models, to assess their performance.