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Investigating the universality of the estimation models in multiple regions is important for improving the performance of the neural network structures and parameters. P and Rdc were calculated in the path analysis for all selected capital stations in the south (Tables 4 and 5, respectively). The hours of sunshine, N, which had the largest P, reaching 0.60–0.85, was selected as the core variable, and the relative humidity, RH, which was the only negative parameter and had the second largest absolute value among all parameters, was selected as the limited variable. Rdc, however, fluctuated between 0.53 and 0.81 when the single parameter N was selected as the input variable, so the error oscillation may be larger when applying the models on a larger scale. Rdc increased and maintained a range of 0.8–0.9 when RH was used as the second input variable, indicating that the double-parameter model was stable and highly credible when applied in the entire selected stations.

Table 4

Path coefficients between each meteorological parameter and ET0 at the capital stations in southern China

PTmeanTmaxTminRHU2N
Guangzhou 0.0088 0.0553 0.0660 − 0.1504 0.0867 0.8216 
Nanning 0.0360 0.0686 0.0496 − 0.0929 0.0972 0.8302 
Kunming 0.0387 0.0536 0.0610 − 0.1715 0.0929 0.7940 
Haikou − 0.0111 0.1400 0.0507 − 0.1435 0.0856 0.7986 
Guiyang 0.0032 0.0659 0.1038 − 0.1827 0.1310 0.7423 
Chongqing 0.0547 0.0043 0.0831 − 0.1620 0.1294 0.7435 
Fuzhou − 0.0376 0.1019 0.1047 − 0.2326 0.1127 0.6880 
Changsha 0.0551 0.0282 0.0894 − 0.2017 0.1070 0.6825 
Hangzhou 0.0355 0.0668 0.0983 − 0.2310 0.0779 0.6673 
Shanghai − 0.0969 0.1715 0.1558 − 0.2787 0.1077 0.6463 
Nanchang 0.0668 0.0649 0.0707 − 0.1659 0.1060 0.6975 
Wuhan 0.1020 0.0231 0.0840 − 0.1439 0.1282 0.7360 
PTmeanTmaxTminRHU2N
Guangzhou 0.0088 0.0553 0.0660 − 0.1504 0.0867 0.8216 
Nanning 0.0360 0.0686 0.0496 − 0.0929 0.0972 0.8302 
Kunming 0.0387 0.0536 0.0610 − 0.1715 0.0929 0.7940 
Haikou − 0.0111 0.1400 0.0507 − 0.1435 0.0856 0.7986 
Guiyang 0.0032 0.0659 0.1038 − 0.1827 0.1310 0.7423 
Chongqing 0.0547 0.0043 0.0831 − 0.1620 0.1294 0.7435 
Fuzhou − 0.0376 0.1019 0.1047 − 0.2326 0.1127 0.6880 
Changsha 0.0551 0.0282 0.0894 − 0.2017 0.1070 0.6825 
Hangzhou 0.0355 0.0668 0.0983 − 0.2310 0.0779 0.6673 
Shanghai − 0.0969 0.1715 0.1558 − 0.2787 0.1077 0.6463 
Nanchang 0.0668 0.0649 0.0707 − 0.1659 0.1060 0.6975 
Wuhan 0.1020 0.0231 0.0840 − 0.1439 0.1282 0.7360 
Table 5

Decision contribution rates (Rdc) between each meteorological parameter and ET0 at the capital stations in southern China

RdcTmeanTmaxTminRHU2NN+RH
Guangzhou 0.0068 0.0437 0.0312 0.1058 0.0015 0.7985 0.9044 
Nanning 0.0275 0.0567 0.0154 0.0683 0.0080 0.8136 0.8820 
Kunming 0.0262 0.0420 0.0082 0.1186 0.0303 0.7599 0.8785 
Haikou − 0.0082 0.1037 0.0194 0.1010 0.0044 0.7703 0.8713 
Guiyang 0.0024 0.0529 0.0367 0.1456 0.0373 0.7112 0.8567 
Chongqing 0.0449 0.0037 0.0486 0.1381 0.0387 0.7109 0.8490 
Fuzhou − 0.0296 0.0839 0.0587 0.1867 0.0302 0.6515 0.8382 
Changsha 0.0463 0.0238 0.0596 0.1763 0.0276 0.6530 0.8293 
Hangzhou 0.0273 0.0547 0.0520 0.1919 0.0193 0.6339 0.8258 
Shanghai − 0.0646 0.1232 0.0818 0.2148 0.0265 0.5978 0.8125 
Nanchang 0.0543 0.0540 0.0454 0.1398 0.0201 0.6707 0.8105 
Wuhan 0.0773 0.0188 0.0453 0.1071 0.0313 0.7023 0.8094 
RdcTmeanTmaxTminRHU2NN+RH
Guangzhou 0.0068 0.0437 0.0312 0.1058 0.0015 0.7985 0.9044 
Nanning 0.0275 0.0567 0.0154 0.0683 0.0080 0.8136 0.8820 
Kunming 0.0262 0.0420 0.0082 0.1186 0.0303 0.7599 0.8785 
Haikou − 0.0082 0.1037 0.0194 0.1010 0.0044 0.7703 0.8713 
Guiyang 0.0024 0.0529 0.0367 0.1456 0.0373 0.7112 0.8567 
Chongqing 0.0449 0.0037 0.0486 0.1381 0.0387 0.7109 0.8490 
Fuzhou − 0.0296 0.0839 0.0587 0.1867 0.0302 0.6515 0.8382 
Changsha 0.0463 0.0238 0.0596 0.1763 0.0276 0.6530 0.8293 
Hangzhou 0.0273 0.0547 0.0520 0.1919 0.0193 0.6339 0.8258 
Shanghai − 0.0646 0.1232 0.0818 0.2148 0.0265 0.5978 0.8125 
Nanchang 0.0543 0.0540 0.0454 0.1398 0.0201 0.6707 0.8105 
Wuhan 0.0773 0.0188 0.0453 0.1071 0.0313 0.7023 0.8094 

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