hydroeval.kgenp

hydroeval.kgenp(simulations, evaluation)

Non-Parametric Kling-Gupta Efficiency (KGE_NP) and its three components (r_S, α_NP, β) as per Pool et al., 2018.

Note, all four values KGE_NP, r_S, α_NP, β are returned, in this order.

Calculation Details

\[E_{\text{KGE}_\text{NP}} = 1 - \sqrt{[r_{\text{S}} - 1]^2 + [\alpha_{\text{NP}} - 1]^2 + [\beta - 1]^2}\]

\[r_{\text{S}} = \frac{\sum_{i=1}^{N} [E_i-\mu(E)] [S_i-\mu(S)]} {\sqrt{ \big[ \sum_{i=1}^{N}[E_i-\mu(E)]^2 \big] \big[ \sum_{i=1}^{N} [S_i-\mu(S)]^2 \big]}}\]

\[\alpha_{\text{NP}} = 1 - \frac{1}{2} \sum_{k=1}^{N} \Bigl| \frac{s_{I(k)}}{N \cdot \mu(s)} - \frac{e_{J(k)}}{N \cdot \mu(e)} \Bigr|\]

\[\beta = \frac{\mu(s)}{\mu(e)}\]

where N is the length of the simulations and evaluation periods, e is the evaluation series, s is (one of) the simulations series, E and S are the series of ranks for the e and s series of streamflow, respectively, I and J are the functions giving the indices of the k^th largest flood in s and e series, respectively, and μ is the arithmetic mean.