# Evapotranspiration Prediction Method Based on K-Means Clustering and QPSO-MKELM Model
## 3 Results and Analysis
### Ablation Experiment  
In the ablation experiment, six models were selected for comparison: Kmeans-QPSO-MKELM-30, QPSO-MKELM, PSO-MKELM, QPSO-ELM, and MKELM. These models were evaluated on the prediction accuracy and modeling time using the eight feature inputs proposed earlier. The results are shown in Table 6.  
Figure 4: Comparison of program runtime for each model under different inputs. From the analysis of Table 6:  
1. Comparison between Kmeans-QPSO-MKELM-30 and QPSO-MKELM models: To observe the effect of adding the K-means clustering algorithm, it can be seen that the prediction accuracy of the two models is very similar. In inputs 2, 3, and 6, the Kmeans-QPSO-MKELM-30 model has slightly better accuracy than the QPSO-MKELM model. However, in inputs 5, 7, and 8, the QPSO-MKELM model outperforms the Kmeans-QPSO-MKELM-30 model. For inputs 1 and 4, the prediction accuracy of both models is nearly the same. Regarding training time, Kmeans-QPSO-MKELM-30 shows an average improvement of 41.84 times over QPSO-MKELM. 2. Comparison between QPSO-MKELM, PSO-MKELM, and MKELM models: To observe the impact of optimization methods on model performance, it was found that except for input 6, where QPSO-MKELM and PSO-MKELM show similar prediction accuracy, the QPSO-MKELM model performs better than the PSO-MKELM model for the other inputs. Both models significantly outperform the MKELM model. Similarly,  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Input/Model** & **R2** & **MAE (mm)** & **RMSE (mm)** & **TIME (s)** \\ \hline
1. T, rh, u,  
comparing QPSO-ELM and PSO-ELM models, it was found that, except for input 2, where the PSO-ELM model is superior, the QPSO-ELM model outperforms PSO-ELM for the other seven inputs. For input 5, the MAE and RMSE decreased by 50.8% and 48.7%, respectively. This suggests that the QPSO, which improves upon traditional PSO with segmental attraction points and segmental mutation, enhances the global search ability of the optimization algorithm and reduces the likelihood of falling into local optima, increasing the probability of finding the optimal or a better solution. Regarding runtime: The runtime for QPSO-MKELM is between 18,364 s and 20,932 s. The runtime for PSO-MKELM is between 18,538 s and 20,674 s. The runtime for QPSO-ELM is between 598 s and 735 s. The runtime for PSO-ELM is between 500 s and 613 s. The runtime for MKELM is between 12 s and 15 s. Overall, the change in the optimization algorithm has a relatively small effect on the runtime, with PSO being slightly faster than QPSO. However, when adding multiple kernel functions, the computation of large kernel matrices becomes very time-consuming. 3. Comparing the QPSO-MKELM model with the QPSO-ELM model, as well as the PSO-MKELM model with the PSO-ELM model, to observe the impact of adding multiple kernel functions on the performance of the ELM: It was found that adding multiple kernel functions significantly improved the performance of the models, particularly in inputs 5 and 7, which include wind speed features. Specifically: Input 5: QPSO-MKELM and QPSO-ELM had R\({}^{2}\), MAE, and RMSE values of 0.99999 and 0.9983, and 0.00187 mm and 0.04328 mm, 0.00390 mm, and 0.06404 mm, respectively. PSO-MKELM and PSO-ELM had R\({}^{2}\), MAE, and RMSE values of 0.99999 and 0.99352, 0.00216 mm and 0.08800 mm, 0.00473 mm and 0.12488 mm, respectively. Input 7: QPSO-MKELM and QPSO-ELM had R\({}^{2}\), MAE, and RMSE values of 0.97744 and 0.97061, 0.15908 mm and 0.19089 mm, 0.2331 mm and 0.26602 mm, respectively. PSO-MKELM and PSO-ELM had R\({}^{2}\), MAE, and RMSE values of 0.97736 and 0.96739, 0.15934 mm and 0.19304 mm, 0.23362 mm and 0.28023 mm, respectively. However, the performance improvement was minor in inputs 2 and 6, where wind speed features were not included. This is likely because the relationship between wind speed and ET\({}_{0}\) is more complex and nonlinear compared to humidity.