Statistical criterion

Equations

Values

Classification of Performance

References

NSE

$1-\frac{{{\displaystyle \sum }}^{\text{}}{\left(Q_{obs}-Q_{sim}\right)}^2}{{{\displaystyle \sum }}^{\text{}}{\left(Q_{obs}-{\overline{Q}}_{obs}\right)}^2}$

0.75 < NSE ≤ 1.00

0.65 < NSE ≤ 0.75

0.50 < NSE ≤ 0.65

0.4 < NSE ≤ 0.50

NSE ≤ 0.4

0.4 ≤ NSE ≤ 0.70

Very good

Good

Satisfactory

Acceptable

Unsatisfactory

Acceptable

[53]

R²

$\frac{{{\displaystyle \sum }}^{\text{}}{\left(\left(Q_{obs}-{\overline{Q}}_{obs}\right)\left(Q_{sim}-{\overline{Q}}_{sim}\right)\right)}^2}{{{\displaystyle \sum }}^{\text{}}{\left(Q_{obs}-{\overline{Q}}_{obs}\right)}^2\ast {{\displaystyle \sum }}^{\text{}}{\left(Q_{sim}-{\overline{Q}}_{sim}\right)}^2}$

R²>0.5

R² values > 0.5 are regarded as acceptable for model simulation

[54]

PBIAS

$\frac{{{\displaystyle \sum }}^{\text{}}\left(Q_{obs}-Q_{sim}\right)\ast 100}{{{\displaystyle \sum }}^{\text{}}\left(Q_{obs}\right)}$

PBIAS < ±10

±10 ≤ PBIAS < ±15

±15 ≤ PBIAS < ±25

PBIAS ≥ ±25

Very good

Good

Satisfactory

Unsatisfactory

[55]

RMSE

$\sqrt{\frac{{{\displaystyle \sum }}^{\text{}}\left(Q_{obs}-Q_{sim}\right)}{n}}$

Value below half the

standard deviation

Satisfactory

[56]

RSR

$\sqrt{\frac{{{\displaystyle \sum }}^{\text{}}{\left(Q_{obs}-Q_{sim}\right)}^2}{{{\displaystyle \sum }}^{\text{}}{\left(Q_{obs}-{\overline{Q}}_{obs}\right)}^2}}$

0.00 ≤ RSR ≤ 0.50

0.50 < RSR ≤ 0.60

0.60 < RSR ≤ 0.70

RSR > 0.70

Very good

Good

Satisfactory

Unsatisfactory

[57]