Research Article

Comparative Study of M5 Model Tree and Artificial Neural Network in Estimating Reference Evapotranspiration Using MODIS Products

Algorithm 1

Tree-structured regression model generated by M5 algorithm using training data.
LSTn <= 19.43:                                                                         LM num: 1
    LSTms <= 15.55: LM1                                                                    Pm = 0.0147 Tn + 0.1048 Tms − 0.0007 DOY + 0.8963
    LSTms > 15.55:                                                                     LM num: 2
          DOY <= 282.5:                                                                            Pm = 0.0349 Tn + 0.0312 Tms + 0.028 DOY + 1.3107
                  DOY <= 81.5: LM2                                             LM num: 3
                  DOY > 81.5:                                                                           Pm = 0.046 Tn + 0.081 Tms − 0.0134 DOY + 3.9221
                          DOY <= 106:                                                   LM num: 4
                                  LSTd <= 31.2: LM3                                           Pm = 0.0719 Tn + 0.0642 Tms − 0.0088 DOY + 3.8864
                                  LSTd > 31.2: LM4                                 LM num: 5
                          DOY > 106:                                                                   Pm = 0.0705 Tn + 0.0073 Td + 0.0301 Tms + 0.0003 DOY + 4.6615
                                  DOY <= 207:                                          LM num: 6
                                          LSTn <= 17.72:                                             Pm = 0.201 Tn + 0.0147 Td + 0.0301 Tms + 0.0003 DOY + 2.5252
                                                  DOY <= 129: LM5              LM num: 7
                                                  DOY > 129: LM6                              Pm = 0.118 Tn + 0.0301 Tms + 0.0026 DOY + 4.7479
                                          LSTn > 17.72: LM7                      LM num: 8
                                  DOY > 207:                                                          Pm = 0.0529 Tn + 0.0301 Tms − 0.0087 DOY + 6.254
                                          DOY <= 272.5: LM8                 LM num: 9
                                          DOY > 272.5: LM9                                 Pm = 0.0529 Tn − 0.0348 Tms − 0.0116 DOY + 8.4773
          DOY > 282.5:                                                                 LM num: 10
                  DOY <= 311.5: LM10                                                     Pm = 0.0328 Tn + 0.0201 Tms − 0.0012 DOY + 3.367
                  DOY > 311.5: LM11                                             LM num: 11
LSTn > 19.43:                                                                                         Pm = 0.1437 Tn + 0.0201 Tms − 0.0012 DOY + 1.7414
    DOY <= 227.5:                                                                     LM num: 12
          DOY <= 159.5:                                                                           Pm = −0.1076 Tn + 0.0018 Tms − 0.0393 DOY + 15.9787
                  DOY <= 147.5: LM12                                         LM num: 13
                  DOY > 147.5: LM13                                                        Pm = 0.0297 Tn + 0.0018 Tms + 0.0032 DOY + 8.0036
          DOY > 159.5:                                                                  LM num: 14
                  DOY <= 198.5:                                                                  Pm = 0.3445 Tn + 0.0769 Td + 0.0018 Tms − 0.1664 DOY + 26.3097
                          DOY <= 167.5: LM14                                LM num: 15
                          DOY > 167.5: LM15                                               Pm = 0.0316 Tn + 0.0018 Tms − 0.006 DOY + 10.5743
                  DOY > 198.5:                                                          LM num: 16
                          DOY <= 216.5:                                                          Pm = −0.0175 Tn + 0.0018 Tms + 0.0225 DOY + 4.5799
                                  DOY <= 206.5: LM16                      LM num: 17
                                  DOY > 206.5: LM17                                     Pm = −0.206 Tn + 0.0018 Tms + 0.0185 DOY + 11.1645
                          DOY > 216.5: LM18                                   LM num: 18
    DOY > 227.5: LM19                                                                    Pm = 0.0015 Tn + 0.0018 Tms − 0.0046 DOY + 9.6864
                                                                                                             LM num: 19
                                                                                                                        Pm = 0.022 Tn + 0.0018 Tms − 0.0387 DOY + 16.0569