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The results of the best fit of the different ETHSc versions are provided in Table 3. It shows the RMSE, the MAE, the coefficient of efficiency (Ceff) and the BIC value and the best estimates of k1, k2, k3 for different Köppen climate zones and each ETHSc.

Table 3

Performance measures (RMSE, mm day−1, MAE, mm day−1, Ceff and BIC) of ETHSc as compared to FAO-56 ET as well as the respective coefficients k1, k2, k3 of the different corrections

ClassModelRMSEMAECeffBICk1k2k3
Af HS1 0.575 0.451 −2,768 0.002 0.5  
Af HS2 0.537 0.419 0.129 −3,113 0.0023 0.43222  
Af HS3 0.425 0.335 0.453 −4,273 0.0051 0.07193  
Af HS4 0.491 0.391 0.271 −3,551 0.0010 0.5 1.8778 
Af HS5 0.425 0.335 0.454 −4,268 0.0049 0.07415 0.1289 
Af HS 0.804 0.663 −0.955 −1,093 0.0023 0.5  
As HS1 0.709 0.523 0.104 −1,106 0.00204 0.5  
As HS2 0.679 0.496 0.179 −1,247 0.0023 0.44523  
As HS3 0.595 0.446 0.369 −1,666 0.00458 0.15343  
As HS4 0.649 0.487 0.25 −1,386 0.00116 0.5 1.7492 
As HS5 0.594 0.444 0.371 −1,665 0.00511 0.14317 − 0.3678 
As HS 0.872 0.728 −0.355 −443 0.0023 0.5  
Aw HS1 0.74 0.551 0.393 −5,120 0.00208 0.5  
Aw HS2 0.726 0.537 0.416 −5,444 0.0023 0.45534  
Aw HS3 0.706 0.523 0.448 −5,914 0.00321 0.31546  
Aw HS4 0.719 0.54 0.426 −5,584 0.00163 0.5 0.9053 
Aw HS5 0.704 0.523 0.451 −5,954 0.00283 0.33314 0.3466 
Aw HS 0.859 0.702 0.181 −2,578 0.0023 0.5  
BS HS1 0.893 0.664 0.764 −2,693 0.00231 0.5  
BS HS2 0.893 0.663 0.764 −2,690 0.0023 0.49988  
BS HS3 0.883 0.657 0.769 −2,946 0.00296 0.40288  
BS HS4 0.886 0.657 0.768 −2,876 0.00217 0.5 0.2921 
BS HS5 0.881 0.654 0.77 −2,997 0.00272 0.42152 0.1783 
BS HS 0.893 0.663 0.764 −2,700 0.0023 0.5  
BW HS1 1.22 0.92 0.749 2,312 0.00262 0.5  
BW HS2 1.231 0.924 0.744 2,414 0.0023 0.54699  
BW HS3 1.211 0.919 0.753 2,235 0.00338 0.4038  
BW HS4 1.22 0.92 0.749 2,318 0.00259 0.5 0.0719 
BW HS5 1.211 0.918 0.753 2,237 0.00354 0.39352 − 0.1157 
BW HS 1.394 0.993 0.672 3,842 0.0023 0.5   
Cf HS1 0.539 0.403 0.853 −12,499 0.00212 0.5   
Cf HS2 0.531 0.396 0.858 −12,805 0.0023 0.46412   
Cf HS3 0.516 0.384 0.866 −13,386 0.00323 0.32259   
Cf HS4 0.517 0.387 0.865 −13,358 0.00192 0.5 0.3199 
Cf HS5 0.505 0.377 0.871 −13,813 0.00277 0.35817 0.2345 
Cf HS 0.594 0.45 0.822 −10,543 0.0023 0.5  
Cs HS1 0.557 0.423 0.863 −1,974 0.00214 0.5  
Cs HS2 0.545 0.412 0.868 −2,049 0.0023 0.46837   
Cs HS3 0.497 0.376 0.89 −2,350 0.00413 0.23782   
Cs HS4 0.543 0.42 0.869 −2,051 0.00198 0.5 0.2663 
Cs HS5 0.497 0.375 0.89 −2,343 0.00419 0.2342 − 0.0208 
Cs HS 0.608 0.471 0.836 −1,683 0.0023 0.5   
Cw HS1 0.645 0.476 0.709 −3,740 0.00210 0.5   
Cw HS2 0.645 0.476 0.709 −3,736 0.0023 0.46359  
Cw HS3 0.645 0.475 0.71 −3,734 0.00218 0.48548  
Cw HS4 0.64 0.471 0.714 −3,801 0.00195 0.5 0.2863 
Cw HS5 0.64 0.471 0.714 −3,794 0.00191 0.50728 0.2939 
Cw HS 0.737 0.598 0.62 −2,604 0.0023 0.5  
Df HS1 0.474 0.33 0.903 −6,287 0.00203 0.5  
Df HS2 0.475 0.33 0.902 −6,256 0.0023 0.45044  
Df HS3 0.473 0.331 0.903 −6,292 0.00174 0.56201  
Df HS4 0.467 0.322 0.906 −6,407 0.00195 0.5 0.1309 
Df HS5 0.463 0.323 0.907 −6,468 0.00130 0.65944 0.1695 
Df HS 0.559 0.39 0.865 −4,907 0.0023 0.5  
Ds HS1 0.331 0.224 0.963 −393 0.00210 0.5  
Ds HS2 0.33 0.222 0.963 −394 0.0023 0.46617  
Ds HS3 0.329 0.221 0.963 −389 0.00240 0.44976   
Ds HS4 0.327 0.216 0.964 −392 0.00205 0.5 0.0854 
Ds HS5 0.327 0.216 0.964 −386 0.00211 0.48956 0.08 
Ds HS 0.419 0.275 0.941 −313 0.0023 0.5   
Dw HS1 0.534 0.409 0.873 −1,362 0.00199 0.5   
Dw HS2 0.527 0.405 0.876 −1,391 0.0023 0.44041   
Dw HS3 0.518 0.403 0.881 −1,424 0.00358 0.26577   
Dw HS4 0.48 0.345 0.898 −1,589 0.00171 0.5 0.4566 
Dw HS5 0.464 0.335 0.904 −1,654 0.00317 0.25526 0.4441 
Dw HS 0.667 0.478 0.802 −884 0.0023 0.5   
HS1 0.44 0.346 0.843 −762 0.00228 0.5   
HS2 0.44 0.346 0.843 −763 0.0023 0.49626   
HS3 0.438 0.346 0.844 −760 0.00256 0.45471   
HS4 0.38 0.292 0.883 −894 0.00188 0.5 0.4621 
HS5 0.378 0.29 0.884 −892 0.00146 0.59181 0.5134 
HS 0.44 0.347 0.843 −768 0.0023 0.5   
All HS1 0.846 0.599 0.785 −1,7548 0.00223 0.5   
All HS2 0.845 0.599 0.785 −1,7588 0.0023 0.48657   
All HS3 0.845 0.599 0.785 −1,7583 0.00234 0.47934   
All HS4 0.844 0.595 0.786 −1,7743 0.00216 0.5 0.1272 
All HS5 0.844 0.595 0.786 −1,7734 0.00219 0.49465 0.1214 
All HS 0.855 0.625 0.78 −16,366 0.0023 0.5  
ClassModelRMSEMAECeffBICk1k2k3
Af HS1 0.575 0.451 −2,768 0.002 0.5  
Af HS2 0.537 0.419 0.129 −3,113 0.0023 0.43222  
Af HS3 0.425 0.335 0.453 −4,273 0.0051 0.07193  
Af HS4 0.491 0.391 0.271 −3,551 0.0010 0.5 1.8778 
Af HS5 0.425 0.335 0.454 −4,268 0.0049 0.07415 0.1289 
Af HS 0.804 0.663 −0.955 −1,093 0.0023 0.5  
As HS1 0.709 0.523 0.104 −1,106 0.00204 0.5  
As HS2 0.679 0.496 0.179 −1,247 0.0023 0.44523  
As HS3 0.595 0.446 0.369 −1,666 0.00458 0.15343  
As HS4 0.649 0.487 0.25 −1,386 0.00116 0.5 1.7492 
As HS5 0.594 0.444 0.371 −1,665 0.00511 0.14317 − 0.3678 
As HS 0.872 0.728 −0.355 −443 0.0023 0.5  
Aw HS1 0.74 0.551 0.393 −5,120 0.00208 0.5  
Aw HS2 0.726 0.537 0.416 −5,444 0.0023 0.45534  
Aw HS3 0.706 0.523 0.448 −5,914 0.00321 0.31546  
Aw HS4 0.719 0.54 0.426 −5,584 0.00163 0.5 0.9053 
Aw HS5 0.704 0.523 0.451 −5,954 0.00283 0.33314 0.3466 
Aw HS 0.859 0.702 0.181 −2,578 0.0023 0.5  
BS HS1 0.893 0.664 0.764 −2,693 0.00231 0.5  
BS HS2 0.893 0.663 0.764 −2,690 0.0023 0.49988  
BS HS3 0.883 0.657 0.769 −2,946 0.00296 0.40288  
BS HS4 0.886 0.657 0.768 −2,876 0.00217 0.5 0.2921 
BS HS5 0.881 0.654 0.77 −2,997 0.00272 0.42152 0.1783 
BS HS 0.893 0.663 0.764 −2,700 0.0023 0.5  
BW HS1 1.22 0.92 0.749 2,312 0.00262 0.5  
BW HS2 1.231 0.924 0.744 2,414 0.0023 0.54699  
BW HS3 1.211 0.919 0.753 2,235 0.00338 0.4038  
BW HS4 1.22 0.92 0.749 2,318 0.00259 0.5 0.0719 
BW HS5 1.211 0.918 0.753 2,237 0.00354 0.39352 − 0.1157 
BW HS 1.394 0.993 0.672 3,842 0.0023 0.5   
Cf HS1 0.539 0.403 0.853 −12,499 0.00212 0.5   
Cf HS2 0.531 0.396 0.858 −12,805 0.0023 0.46412   
Cf HS3 0.516 0.384 0.866 −13,386 0.00323 0.32259   
Cf HS4 0.517 0.387 0.865 −13,358 0.00192 0.5 0.3199 
Cf HS5 0.505 0.377 0.871 −13,813 0.00277 0.35817 0.2345 
Cf HS 0.594 0.45 0.822 −10,543 0.0023 0.5  
Cs HS1 0.557 0.423 0.863 −1,974 0.00214 0.5  
Cs HS2 0.545 0.412 0.868 −2,049 0.0023 0.46837   
Cs HS3 0.497 0.376 0.89 −2,350 0.00413 0.23782   
Cs HS4 0.543 0.42 0.869 −2,051 0.00198 0.5 0.2663 
Cs HS5 0.497 0.375 0.89 −2,343 0.00419 0.2342 − 0.0208 
Cs HS 0.608 0.471 0.836 −1,683 0.0023 0.5   
Cw HS1 0.645 0.476 0.709 −3,740 0.00210 0.5   
Cw HS2 0.645 0.476 0.709 −3,736 0.0023 0.46359  
Cw HS3 0.645 0.475 0.71 −3,734 0.00218 0.48548  
Cw HS4 0.64 0.471 0.714 −3,801 0.00195 0.5 0.2863 
Cw HS5 0.64 0.471 0.714 −3,794 0.00191 0.50728 0.2939 
Cw HS 0.737 0.598 0.62 −2,604 0.0023 0.5  
Df HS1 0.474 0.33 0.903 −6,287 0.00203 0.5  
Df HS2 0.475 0.33 0.902 −6,256 0.0023 0.45044  
Df HS3 0.473 0.331 0.903 −6,292 0.00174 0.56201  
Df HS4 0.467 0.322 0.906 −6,407 0.00195 0.5 0.1309 
Df HS5 0.463 0.323 0.907 −6,468 0.00130 0.65944 0.1695 
Df HS 0.559 0.39 0.865 −4,907 0.0023 0.5  
Ds HS1 0.331 0.224 0.963 −393 0.00210 0.5  
Ds HS2 0.33 0.222 0.963 −394 0.0023 0.46617  
Ds HS3 0.329 0.221 0.963 −389 0.00240 0.44976   
Ds HS4 0.327 0.216 0.964 −392 0.00205 0.5 0.0854 
Ds HS5 0.327 0.216 0.964 −386 0.00211 0.48956 0.08 
Ds HS 0.419 0.275 0.941 −313 0.0023 0.5   
Dw HS1 0.534 0.409 0.873 −1,362 0.00199 0.5   
Dw HS2 0.527 0.405 0.876 −1,391 0.0023 0.44041   
Dw HS3 0.518 0.403 0.881 −1,424 0.00358 0.26577   
Dw HS4 0.48 0.345 0.898 −1,589 0.00171 0.5 0.4566 
Dw HS5 0.464 0.335 0.904 −1,654 0.00317 0.25526 0.4441 
Dw HS 0.667 0.478 0.802 −884 0.0023 0.5   
HS1 0.44 0.346 0.843 −762 0.00228 0.5   
HS2 0.44 0.346 0.843 −763 0.0023 0.49626   
HS3 0.438 0.346 0.844 −760 0.00256 0.45471   
HS4 0.38 0.292 0.883 −894 0.00188 0.5 0.4621 
HS5 0.378 0.29 0.884 −892 0.00146 0.59181 0.5134 
HS 0.44 0.347 0.843 −768 0.0023 0.5   
All HS1 0.846 0.599 0.785 −1,7548 0.00223 0.5   
All HS2 0.845 0.599 0.785 −1,7588 0.0023 0.48657   
All HS3 0.845 0.599 0.785 −1,7583 0.00234 0.47934   
All HS4 0.844 0.595 0.786 −1,7743 0.00216 0.5 0.1272 
All HS5 0.844 0.595 0.786 −1,7734 0.00219 0.49465 0.1214 
All HS 0.855 0.625 0.78 −16,366 0.0023 0.5  

Best fit coefficients are in bold font while default values are in italics.

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