Equation	Range	Ideal value	References
$MAE=\frac{1}{N}\sum _{i=1}^N\left|Q_i^{Obs}-Q_i^{Cal}\right|$	0 to ∞	0	Tikhamarine et al. [117]	(12)
$MBE=\frac{1}{N}\sum _{i=1}^N\left(Q_i^{Obs}-Q_i^{Cal}\right)$	−∞ to +∞	0	Valipour [118]	(13)
$RE=\frac{\frac{1}{N}\sum _{i=1}^N\left(Q_i^{Cal}-Q_i^{Obs}\right)}{\frac{1}{N}\sum _{i=1}^N\left(Q_i^{Obs}\right)}$	0 to ∞	0	Walther [119]	(14)
$RMSE=\sqrt{\frac{1}{N}\sum _{i=1}^N{\left(Q_i^{Obs}-Q_i^{Cal}\right)}^2}$	0 to ∞	0	Pandey et al. [120]	(15)
$R^2=1-\frac{\sum _{i=1}^N{\left(Q_i^{Obs}-Q_i^{Cal}\right)}^2}{\sum _{i=1}^N{\left(Q_i^{Obs}-\overline{Q_i^{Cal}}\right)}^2}$	0 to 1	1	Nagelkerke [121]	(16)
$PCC=\sqrt{1-\frac{\sum _{i=1}^N{\left(Q_i^{Obs}-Q_i^{Cal}\right)}^2}{\sum _{i=1}^N{\left(Q_i^{Obs}-\overline{Q_i^{Cal}}\right)}^2}}$	−1 to +1	1	Ozer [122]	(17)
$NSE=1-\frac{\sum _{i=1}^N{\left(Q_i^{Obs}-Q_i^{Cal}\right)}^2}{{\left(Q_i^{Obs}-\overline{Q_i^{Obs}}\right)}^2}$	−∞ to 1	1	Nash and Sutcliffe [123,124]	(18)
$d=1-\frac{\sum _{i=1}^N{\left(Q_i^{Obs}-Q_i^{Cal}\right)}^2}{\sum _{i=1}^N{\left(\left|Q_i^{Cal}-\overline{Q_i^{Obs}}\right|+\left|Q_i^{Obs}-\overline{Q_i^{Obs}}\right|\right)}^2}$	0 to 1	1	Willmott [125,126]	(19)
$KGE=\sqrt{{\left(PCC\right)}^2+{\left(\frac{CD}{RD}\right)}^2+{\left(\frac{CM}{RM}-1\right)}^2}$	−∞ to 1	1	Gupta et al. [127]	(20)

Note: ${\mathrm{Q}}_{\mathrm{i}}^{\mathrm{C}\mathrm{a}\mathrm{l}}$ = ith forecasted discharge data; ${\mathrm{Q}}_{\mathrm{i}}^{\mathrm{O}\mathrm{b}\mathrm{s}}$ = observed discharge data; N = number of observations; $\overline{{\mathrm{Q}}_{\mathrm{i}}^{\mathrm{C}\mathrm{a}\mathrm{l}}}$ = mean value of observed discharge; $\overline{{\mathrm{Q}}_{\mathrm{i}}^{\mathrm{C}\mathrm{a}\mathrm{l}}}$ = mean value of forecasted discharge; CC is the Pearson correlation coefficient value; RM is the average of observed values; CM is the average of forecast values; RD is the standard deviation of observation values; and CD is the standard deviation of forecast values. Following the maximum values of NSE, d, KGE, PCC(r), and R²; the minimum values of RMSE, MBE; MAE, and RE were near zero among the all-developed models, the most accurate models were chosen [77,78,128,129].