Table 2 Formulae of accuracy assessment metrics.

From: The magnitude and frequency of detected precipitation determine the accuracy performance of precipitation data sets in the high mountains of Asia

Statistical indicators

Formulas

Unbiased estimates

No

Correlation Coefficient (CC)

\(CC=\frac{\sum_{i=1}^{N}\left({y}_{obs,i}-{\overline{y} }_{obs}\right)\left({y}_{i}-\overline{y }\right)}{\sqrt{\sum_{i=1}^{N}{\left({y}_{i}-\overline{y }\right)}^{2}\sum_{i=1}^{N}{\left({y}_{obs,i}-{\overline{y} }_{obs}\right)}^{2}}}\)

1

(1)

Bias (BIAS)

\(BIAS=\frac{\sum_{i=1}^{N}\left({y}_{sim,i}-{y}_{obs,i}\right)}{\sum_{i=1}^{N}{y}_{obs,i}}\)

0

(2)

Root Mean Square Error (RMSE)

\(RMSE={\left[\frac{\sum_{i=1}^{N}{\left({y}_{obs,i}-{y}_{sim,i}\right)}^{2}}{N}\right]}^\frac{1}{2}\)

0

(3)

Kling-Gupta Efficiency (KGE)

\(KGE=1-\sqrt{{\left(1-r\right)}^{2}+{\left(1-\alpha \right)}^{2}+{\left(1-\beta \right)}^{2}},\alpha =\frac{{\sigma }_{s}}{{\sigma }_{0}},\beta =\frac{{\mu }_{s}}{{\mu }_{0}}\)

1

(4)

  1. \({y}_{sim,i}\) and \({y}_{obs,i}\) are the estimated and observed values, respectively; \(N\) is the sample size; \(y\) and \({y}_{obs}\) are the remotely sensed precipitation estimates and ground observations, respectively; \(r\) is the correlation coefficient between the observed and modeled values; \({\mu }_{s}\) and \({\sigma }_{s}\) are the mean and standard deviation of the remotely sensed precipitation estimates, respectively; and \({\mu }_{o}\) and \({\sigma }_{o}\) are the mean and standard deviation of ground observations, respectively.
Back to article page