# Evapotranspiration Prediction Method Based on K-Means Clustering and QPSO-MKELM Model
## 3 Results and Analysis
### Comparative Experiment  
In the comparative experiment, the QPSO-MKELM model, Kmeans-QPSO-MKELM-30 model, ANFIS model, PSO-ELM model, WOA-SVR model (with RBF kernel), and RF model were selected to compare the impact of different input features on ET\({}_{0}\) prediction accuracy. The modeling results of these models under eight different input feature sets, including their ET\({}_{0}\) prediction accuracy and runtime, are shown in Table 7. Additionally, scatter plots of the models' predictions under the eight input sets are displayed in Figure 5, and the Taylor diagram is shown in Figure 6. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Input/Model** & **R2** & **MAE (mm)** & **RMSE (mm)** & **TIME (s)** & **G\({}_{\mathbf{p}}\)-Rank** \\ \hline
1. T, rh, u, n & & & & & \\ QPSO-MKELM & 0.99425 & 0.08062 & 0.11764 & 19.785 & 1 \\ Kmeans-QPSO-MKELM-30 & 0.99416 & 0.08081 & 0.11862 & 427 & 2 \\ ANFIS & 0.98919 & 0.12372 & 0.16138 & 781 & 6 \\ PSO-ELM & 0.99234 & 0.10183 & 0.13582 & 500 & 4 \\ WOA-SVR & 0.99368 & 0.08372 & 0.12340 & 4025 & 3 \\ RF & 0.98956 & 0.10902 & 0.15859 & 131 & 5 \\
2. T, rh, n & & & & & \\ QPSO-MKELM & 0.98303 & 0.14444 & 0.20217 & 19.235 & 2 \\ Kmeans-QPSO-MKELM-30 & 0.98411 & 0.14278 & 0.19560 & 418 & 1 \\ ANFIS & 0.98006 & 0.16750 & 0.21913 & 680 & 6 \\ PSO-ELM & 0.98303 & 0.15325 & 0.20214 & 586 & 4 \\ WOA-SVR & 0.98334 & 0.14657 & 0.20050 & 3954 & 3 \\ RF & 0.98018 & 0.15779 & 0.21846 & 120 & 5 \\
3. T, u, n & & & & & \\ QPSO-MKELM & 0.96726 & 0.19034 & 0.28079 & 18,957 & 2 \\ Kmeans-QPSO-MKELM-30 & 0.96775 & 0.18919 & 0.27870 & 413 & 1 \\ ANFIS & 0.96512 & 0.20250 & 0.28981 & 488 & 3 \\ PSO-ELM & 0.96368 & 0.20110 & 0.29575 & 3876 & 4 \\ WOA-SVR & 0.96365 & 0.21556 & 0.29588 & 108 & 5 \\ RF & 0.95993 & 0.21579 & 0.31065 & 112 & 6 \\
4. T, n & & & & & \\ QPSO-MKELM & 0.95354 & 0.23813 & 0.33448 & 18,364 & 1 \\ Kmeans-QPSO-MKELM-30 & 0.95351 & 0.23821 & 0.33459 & 399 & 2 \\ ANFIS & 0.95094 & 0.24797 & 0.34373 & 370 & 5 \\ PSO-ELM & 0.95251 & 0.23674 & 0.33818 & 549 & 3 \\ WOA-SVR & 0.95148 & 0.25316 & 0.34185 & 3504 & 4 \\ RF & 0.95046 & 0.24759 & 0.34540 & 96 & 6 \\
5. T, rh, u, n, day\_cos & & & & & \\ QPSO-MKELM & 0.99999 & 0.00187 & 0.00390 & 20.933 & 1 \\ Kmeans-QPSO-MKELM-30 & 0.99998 & 0.00274 & 0.00664 & 544 & 2 \\ ANFIS & 0.99541 & 0.07593 & 0.10514 & 553 & 4 \\ PSO-ELM & 0.99352 & 0.08800 & 0.12488 & 605 & 5 \\ WOA-SVR & 0.99975 & 0.01177 & 0.02483 & 4236 & 3 \\ RF & 0.99135 & 0.08962 & 0.144437 & 151 & 6 \\
6. T, rh, n, day\_sin, day\_cos & & & & & \\ QPSO-MKELM & 0.98911 & 0.10102 & 0.16194 & 20,467 & 2 \\ Kmeans-QPSO-MKELM-30 & 0.99033 & 0.10107 & 0.15263 & 528 & 1 \\ ANFIS & 0.98752 & 0.12311 & 0.17338 & 588 & 5 \\ PSO-ELM & 0.98866 & 0.11702 & 0.16526 & 561 & 4 \\ WOA-SVR & 0.98876 & 0.11645 & 0.16252 & 4036 & 3 \\ RF & 0.98537 & 0.12201 & 0.18768 & 141 & 6 \\
7. T, u, n, day\_sin, day\_cos & & & & & \\ QPSO-MKELM & 0.97744 & 0.15908 & 0.23310 & 20,674 & 1 \\ Kmeans-QPSO-MKELM-30 & 0.97687 & 0.16354 & 0.23601 & 498 & 2 \\ ANFIS & 0.96938 & 0.18848 & 0.27153 & 590 & 3 \\ PSO-ELM & 0.96739 & 0.19304 & 0.28023 & 573 & 6 \\ WOA-SVR & 0.96889 & 0.19362 & 0.27372 & 3967 & 5 \\ RF & 0.96899 & 0.18729 & 0.27329 & 136 & 4 \\
8. T, n day\_sin, day\_cos & & & & & \\ QPSO-MKELM & 0.96390 & 0.21065 & 0.29486 & 19,978 & 1 \\ Kmeans-QPSO-MKELM-30 & 0.96311 & 0.21284 & 0.29805 & 480 & 2 \\ ANFIS & 0.95853 & 0.22874 & 0.31601 & 536 & 5 \\ PSO-ELM & 0.96076 & 0.21592 & 0.30740 & 613 & 3 \\ WOA-SVR & 0.95739 & 0.24072 & 0.32035 & 3854 & 6 \\ RF & 0.95820 & 0.22506 & 0.31729 & 126 & 4 \\ \hline \end{tabular}
\end{table} 
Table 7: Error metrics and runtime statistics of each model in the comparative experiment. Figure 5: Scatter plots of prediction results of each model under different inputs in the comparison experiment. Figure 6: _Cont._  
Analysis based on the table (Table 7), scatter plot, and Taylor diagram (Figures 5 and 6):  
1.