Evaluation metrics

Evatueltion matrics with several methods.

Usage

eva_ME(num_Sim, num_Obs)

eva_MAE(num_Sim, num_Obs)

eva_MSE(num_Sim, num_Obs)

eva_RMSE(num_Sim, num_Obs)

eva_R2(num_Sim, num_Obs)

eva_NSE(num_Sim, num_Obs)

eva_KGE(num_Sim, num_Obs, num_Scal = c(1, 1, 1))

Arguments

num_Sim, num_Obs

A numeric vector of simulated (\(S_i\)) and observed (\(O_i\)) values. Both vectors must have the same length.

num_Scal

A numeric vector of length 3 with scaling factors for r, alpha, and beta in the eva_KGE calculation. Default is c(1, 1, 1).

Value

A numeric value representing the calculated error metric.

Details

Mean Error (BIAS / ME)

\[ \mathrm{ME} = \frac{1}{N} \sum_{i=1}^N \left( S_i - O_i \right) \]

Mean Absolute Error (MAE)

\[ \mathrm{MAE} = \frac{1}{N} \sum_{i=1}^N \left| S_i - O_i \right| \]

Mean Squared Error (MSE)

\[ \mathrm{MSE} = \frac{1}{N} \sum_{i=1}^N \left( S_i - O_i \right)^2 \]

Root Mean Square Error (RMSE)

\[ \mathrm{RMSE} = \sqrt{ \frac{1}{N} \sum_{i=1}^N \left( S_i - O_i \right)^2 } \]

Coefficient of Determination (R2)

\[ R^2 = \frac{\left( \sum_{i=1}^n (O_i - \bar{O})(S_i - \bar{S}) \right)^2}{\left( \sum_{i=1}^n (O_i - \bar{O})^2 \right) \cdot \left( \sum_{i=1}^n (S_i - \bar{S})^2 \right)} \]

Nash-Sutcliffe Efficiency (NSE)

from

\[ \mathrm{NSE} = 1 - \frac{ \sum_{i=1}^N \left( S_i - O_i \right)^2 }{ \sum_{i=1}^N \left( O_i - \bar{O} \right)^2 } \]

Kling-Gupta Efficiency (KGE)

from

\[ \mathrm{KGE} = 1 - \mathrm{ED} \]

\[ \mathrm{ED} = \sqrt{ \left( s[1](r-1) \right)^2 + \left( s[2](\alpha-1) \right)^2 + \left( s[3](\beta-1) \right)^2 } \]

where

\[ r = \frac{\text{cov}(S, O)}{\sigma_s \sigma_o} \]

\[ \alpha = \frac{\sigma_s}{\sigma_o} \]

\[ \beta = \frac{\mu_s}{\mu_o} \]

References

Adummy A (2024). “Not avalable.” Failed to insert reference with key = NSE_1970 from package = 'HydroRUB'. Possible cause — missing REFERENCES.bib in package 'HydroRUB' or 'HydroRUB' not installed. . Adummy A (2024). “Not avalable.” Failed to insert reference with key = KGE_2009 from package = 'HydroRUB'. Possible cause — missing REFERENCES.bib in package 'HydroRUB' or 'HydroRUB' not installed. . Adummy A (2024). “Not avalable.” Failed to insert reference with key = KGE_Kling_2012 from package = 'HydroRUB'. Possible cause — missing REFERENCES.bib in package 'HydroRUB' or 'HydroRUB' not installed. .

Examples

sim <- rnorm(100)
obs <- rnorm(100)
eva_ME(sim, obs)
#> [1] -0.0440676
eva_MAE(sim, obs)
#> [1] 1.189457
eva_MSE(sim, obs)
#> [1] 2.170289
eva_RMSE(sim, obs)
#> [1] 1.47319
eva_R2(sim, obs)
#> [1] 0.0007170596
eva_NSE(sim, obs)
#> [1] -1.130922
eva_KGE(sim, obs)
#> [1] -0.0967146