Table 1. The mathematical definitions of relevant measures used in this study [8,15,18,30].

Error/accuracy Measure	Definition*
Mean absolute error (MAE)	${\displaystyle \sum _1^n\left|y_i-\widehat{y_i}\right|/n}$
Mean square error (MSE)	${\displaystyle \sum _1^n{\left(y_i-\widehat{y_i}\right)}^2/n}$
Relative MAE (RMAE)	$\left(\frac{MAE}{\overline{y}}\right)100 \left(\%\right)$
Root MSE (RMSE)	MSE1/2
Relative RMSE (RRMSE)	$\left(\frac{RMSE}{\overline{y}}\right)100 \left(\%\right)$
Standardised RMSE (SRMSE)	RMSE/s
Mean square reduced error (MSRE)	MSE/s2
Variance explained (VEcv)	$\left(1-\frac{{{\displaystyle \sum }}_1^n{\left(y_i-\widehat{y_i}\right)}^2}{{{\displaystyle \sum }}_1^n{\left(y_i-\overline{y}\right)}^2}\right)100 \left(\%\right)$
Legates and McCabe’s (E1)	$\left(1-\frac{{{\displaystyle \sum }}_1^n|y_i-\widehat{y_i}|}{{{\displaystyle \sum }}_1^n\left|y_i-\overline{y}\right|}\right)100 \left(\%\right)$
Willmott et al.’s refined index of agreement (dr)	E1, if E1 > = 0; $\left(\frac{{{\displaystyle \sum }}_1^n|y_i-\overline{y} |}{{{\displaystyle \sum }}_1^n\left|y_i-\widehat{y_i}\right|}-1\right)100 \left(\%\right)$, if E1 < 0
Pearson product-moment correlation coefficient (r)	$\frac{{{\displaystyle \sum }}_1^n\left(y_i-\overline{y}\right)\left(\widehat{y_i}-\overline{{\widehat{y}}_i}\right)}{{\left({{\displaystyle \sum }}_1^n{\left(y_i-\overline{y}\right)}^2{\left(\widehat{y_i}-\overline{{\widehat{y}}_i}\right)}^2\right)}^{1/2}}$

* n: the number of observations in a validation dataset; y_i: the observed value in the validation data; $\widehat{y_i}$: the predicted value; $\overline{y}$: mean of the observed values; s: standard deviation of the observed values; and $\overline{{\widehat{y}}_i}$: mean of the predicted value.