Statistical criterion

Equation

Correlation coefficient (R)

$R=\frac{{\displaystyle {\sum }_{i=1}^n\left(v_i-\overline{v}\right)\left(e_i-\overline{e}\right)}}{n{\sigma }_i{\sigma }_e}$

Bias (B)

$B=\overline{e}-\overline{v}$

RMSE (Root Mean Square Error)

$RMSE=\sqrt{\frac{1}{n}}{\displaystyle \sum _{i=1}^n{\left(e_i-v_i\right)}^2}$

Nash index (I)

$I=1-\frac{RMS{E}^2}{{\sigma }_v^2}$