# Evapotranspiration Prediction Method Based on K-Means Clustering and QPSO-MKELM Model
## 3 Results and Analysis
### Comparative Experiment
Effect of different feature inputs on model prediction accuracy: The combination of temperature, humidity, and sunlight duration (input 2, input 6) outperformed the combination of temperature, wind speed, and sunlight duration (input 3, input 7) regarding prediction accuracy. For input 5, the predicted R\({}^{2}\) values for all models ranged from 0.99135 to 0.99999, MAE from 0.00187 to 0.08962 mm, and RMSE from 0.00390 to 0.14437 mm. In the scatter plot (Figure 5e), the predictions were closely aligned with the 1:1 line, and in the Taylor diagram (Figure 6e), the points were very near the observed values. All models achieved remarkably high accuracy, making input 5 a recommended feature set when sufficient meteorological data are available. For input 8, the predicted R\({}^{2}\) values ranged from 0.95739 to 0.9639, MAE from 0.21065 to 0.24072 mm, and RMSE from 0.29486 to 0.32035 mm. The scatter plot (Figure 5h) showed an even distribution with only a few outliers, demonstrating that even with just temperature and sunlight duration as features, the prediction accuracy for ET\({}_{0}\) remained relatively high. This result can guide the selection of meteorological features when equipment and budget resources are limited. Adding the date feature to the input significantly improved the prediction accuracy for all models, with only a slight increase in runtime. Therefore, it is recommended that the date feature be included when building predictive models. 2. Comparing the prediction accuracy of different models with the same input features, it can be observed that the QPSO-MKELM and Kmeans-QPSO-MKELM-30 models outperform all other models across all input features. These two models are also closer to the observed points on the Taylor diagram (Figure 6). Additionally, by comparing the three error metrics and scatter plots (Table 7 and Figure 5), it is found that the inclusion of the date feature leads to a more significant improvement in prediction accuracy for these two models compared to other models. In the Taylor diagram (Figure 6), the distance between these two models and the target observation point is further reduced by including the date feature. This can be attributed to the fact that the  
Figure 6: Taylor diagrams of prediction results of each model under different inputs in the comparison experiment. MKELM model's weighted multi-kernel function is more capable of capturing various data structures and relationships, including the relationship between the date feature and ET\({}_{0}\). Particularly in input 5, which includes the most features, the QPSO-MKELM and Kmeans-QPSO-MKELM-30 models almost perfectly fit the 1:1 line in the scatter plot (Figure 5e), and they are the only models without any outliers. The PSO-ELM and WOA-SVR models have similar prediction accuracy, falling in the middle range. They each have strengths and weaknesses depending on the meteorological feature inputs: in inputs 4 and 8, which only include temperature and sunshine duration, the PSO-ELM model performs better, while in inputs 1 and 5, which include humidity and wind speed, the WOA-SVR model performs better. The ANFIS model has slightly lower overall accuracy compared to the two models mentioned earlier. The RF model performs relatively poorly in terms of prediction accuracy, consistently ranking among the bottom two in inputs 1 through 6. It is also farther from the observed values on the Taylor diagram (Figure 6). 3. Comparing the running times of different models, it can be observed that the QPSO-MKELM model (18,364-20,932 s) and the WOA-SVR model (3504-4236 s) have significantly longer running times compared to the other models. This is primarily due to the computation of a large kernel matrix. The RF model has the shortest running time, ranging from 96 s to 151 s. The running times of the Kmeans-QPSO-MKELM-30 model (399 s-544 s), PSO-ELM model (500-613 s), and ANFIS model (370-590 s) are within the same range, with the Kmeans-QPSO-MKELM-30 model being slightly faster.