Modified Kling-Gupta Efficiency (KGE')

Calculate the modified Kling-Gupta Efficiency (Kling et al., 2012), aka $KGE'$. Dimensionless (from $-\infty$ to 1). kge2012() assesses the accuracy of simulated data by considering correlation, bias, and variability relative to observed data.

Usage

kge2012(data, ...)

# S3 method for class 'data.frame'
kge2012(data, truth, estimate, na_rm = TRUE, ...)

kge2012_vec(truth, estimate, na_rm = TRUE, ...)

Arguments

data: A data.frame containing the columns specified by the truth and estimate arguments.
...: Not currently used.
truth: The column identifier for the true results (that is numeric). This should be an unquoted column name although this argument is passed by expression and supports quasiquotation (you can unquote column names). For _vec() functions, a numeric vector.
estimate: The column identifier for the predicted results (that is also numeric). As with truth this can be specified different ways but the primary method is to use an unquoted variable name. For _vec() functions, a numeric vector.
na_rm: A logical value indicating whether NA values should be stripped before the computation proceeds.

Value

A tibble with columns .metric, .estimator, and .estimate and 1 row of values.

For grouped data frames, the number of rows returned will be the same as the number of groups.

For kge2012_vec(), a single numeric value (or NA).

Details

The Modified Kling-Gupta Efficiency is a composite metric that decomposes model performance into three components: correlation ($r$), bias ratio ($\beta$), and variability ratio ($\gamma$). It improves upon the Kling-Gupta Efficiency (see kge) by replacing standard deviation with Coefficient of Variation. This ensures that the bias and variability ratios are not cross-correlated, which otherwise may occur when e.g. the precipitation inputs are biased.

The Modified Kling-Gupta Efficiency ($KGE'$) is estimated as follows: $$ KGE' = 1 - \sqrt{(r - 1)^2 + (\beta - 1)^2 + (\gamma - 1)^2} $$ where:

$r$ is the linear Pearson correlation coefficient between observed and simulated values
$\beta = \mu_{sim} / \mu_{obs}$ is the ratio of the means (bias ratio)
$ \gamma = \frac{\sigma_{sim} / \mu_{sim}}{\sigma_{sim} / \mu_{sim}} $ is the ratio of the Coefficients of Variation (variability ratio)

Note

Unlike the Nash–Sutcliffe Efficiency (nse), the KGE does not have an inherent benchmark such as "mean flow", and $KGE' = 0$ does not correspond to a baseline performance. Therefore, $KGE'$ values should not be interpreted as "good" or "bad" based solely on their sign or magnitude. Instead, users are encouraged to examine the individual components ($r$, $\beta$, $\gamma$) to understand the nature of model performance and consider defining explicit benchmarks based on the study context.

For further discussion, see Knoben et al. (2019), who caution against directly translating NSE-based interpretation thresholds to KGE.

References

Kling, H., Fuchs, M., & Paulin, M. (2012). Runoff conditions in the upper Danube basin under an ensemble of climate change scenarios. Journal of Hydrology, 424–425, 264–277. doi:10.1016/j.jhydrol.2012.01.011

Knoben, W. J. M., Freer, J. E., & Woods, R. A. (2019). Technical note: Inherent benchmark or not? Comparing Nash–Sutcliffe and Kling–Gupta efficiency scores. Hydrology and Earth System Sciences, 23, 4323–4331. doi:10.5194/hess-23-4323-2019

Examples

library(tidyhydro)
data(avacha)

# Supply truth and predictions as bare column names
kge2012(avacha, obs, sim)
#> # A tibble: 1 × 3
#>   .metric .estimator .estimate
#>   <chr>   <chr>          <dbl>
#> 1 kge2012 standard       0.947

# Or as numeric vectors
kge2012_vec(avacha$obs, avacha$sim)
#> [1] 0.9472891