Statistic

Formula

Range

Best value

Conditioning

Coefficient of determination

${\text{R}}^2={\left[\frac{{\displaystyle {\sum }_{i=1}^N\left(IN{S}_i-\overline{IN{S}_i}\right)\left(IN{S}_i-\overline{SA{T}_i}\right)}}{{\displaystyle {\sum }_{i=1}^N{\left(IN{S}_i-\overline{SA{T}_i}\right)}^2}{\displaystyle {\sum }_{i=1}^N{\left(SA{T}_i-\overline{SA{T}_i}\right)}^2}}\right]}^2$

0 to 1

1

Describes the proportion of variance in the in situ data that are accounted for by the satellite data the closer to 1 the better [30] .

RMSE-Observation standard deviation ratio

$\text{RSR}=\left[\frac{{\displaystyle {\sum }_{i=1}^N{\left(IN{S}_i-SA{T}_i\right)}^2}}{{\sigma }_{INS}}\right]$

0 to ∞

0

A low RSR is directly proportional to the Root Mean Square Error (RMSE). The closer it is to zero the better [31] .

Nash-Sutcliffe efficiency coefficient

$\text{NSE}=1-\left[\frac{{\displaystyle {\sum }_{i=1}^N{\left(IN{S}_i-SA{T}_i\right)}^2}}{{\sigma }_{INS}}\right]$

−∞ to 1

1

The normalized statistic determines the relative magnitude of the residual variance of the satellite observation in comparison to the in situ measured variance [31] . The closer the value is to 1 the better.

Bias percentage

$\text{PBias}=\frac{{\displaystyle {\sum }_{i=1}^{N}SA{T}_i}-{\displaystyle {\sum }_{i=1}^{N}IN{S}_i}}{{\displaystyle {\sum }_{i=1}^{N}IN{S}_i}}\ast 100$

−∞ to ∞

0

Measures the average tendency of satellite models to be smaller or larger than the in situ measurement [32] . Low values close to zero (0) indicate accurate simulation of the satellite data, positive values indicate underestimation while negative values indicate overestimation [31] .