Kling–Gupta Efficiency¶
A hydrological model-performance score combining correlation, relative variability and mean bias against observed flow.
Core Idea¶
Kling–Gupta efficiency (KGE) scores a simulated hydrological flow series against same-time observations. Its original unweighted rule combines correlation, simulated-to-observed spread and mean, then subtracts their distance from the ideal triple from one. A score of one is perfect on those components; a lower score alone neither identifies the error nor certifies model adequacy.[ref-f05840f0ce26][ref-ea02abf86a28]
Scope of Application¶
This original rule applies to aligned discharge series with defined component ratios or an explicit exceptional convention:
- Synthetic offset: Knoben's observed-plus-0.45 mm/day construction tests benchmark interpretation, not predictive skill.[^ref-f05840f0ce26]
- Fitted rainfall–runoff model: Mathevet's Hérault GRX case evaluates split-sample flow and period-specific components.[^ref-ea02abf86a28]
Clarity¶
Unlike Nash–Sutcliffe efficiency, KGE's zero has no automatic mean-flow benchmark meaning; it marks a distance from the ideal triple. A constant simulated series makes ordinary Pearson correlation undefined; Knoben's approximate −0.41 mean-flow score requires explicitly assigning correlation zero. Ask which formula, period, convention and benchmark produced the score.[^ref-f05840f0ce26]
Manages Complexity¶
The scalar compresses co-movement, relative variability and mean into one framed ordering. Different component triples can share a score, and a favorable full-period value can hide yearly departures. Read the components beside KGE when diagnosing errors, and keep the evaluation period visible when comparing constructed and fitted series.[ref-f05840f0ce26][ref-ea02abf86a28]
Abstract Reasoning¶
Align observed and simulated time steps, then calculate r, α = σsim/σobs and β = μsim/μobs; the score is 1 − √[(r−1)² + (α−1)² + (β−1)²]. Vary one component to expose what the scalar conceals, and test thresholds against explicit benchmarks rather than NSE's zero. Where correlation or a ratio is undefined, state the domain limit or chosen convention.[ref-f05840f0ce26][ref-ea02abf86a28]
Knowledge Transfer¶
The rule applies literally to Knoben's constructed offset and Mathevet's fitted GRX output: both supply aligned observed/simulated flow pairs. KGE is a hydrology-specific Similarity Measure, inheriting Function Mapping and a shared-frame Comparison prerequisite. This relation transfers neither the synthetic example's illustrative threshold nor predictive skill. The general pair-to-degree pattern may travel farther; this exact formula and its evidence claims need separate support.[ref-f05840f0ce26][ref-ea02abf86a28]
Relationships to Other Abstractions¶
Current abstraction Kling–Gupta Efficiency Domain-specific
Parents (1) — more general patterns this builds on
-
Kling–Gupta Efficiency is a kind of Similarity Measure Prime
Original unweighted KGE is a hydrology-specific Similarity Measure mapping aligned observed and simulated flow series to a comparable degree of match through a fixed three-component rule.
Hierarchy paths (2) — routes to 2 parentless roots
- Kling–Gupta Efficiency → Similarity Measure → Function (Mapping)
- Kling–Gupta Efficiency → Similarity Measure → Comparison
Neighborhood in Abstraction Space¶
Kling–Gupta Efficiency sits in a sparse region of the domain-specific corpus (76th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (2721 abstractions)
Nearest neighbors
- Lag windowing — 0.85
- Least-Squares Adjustment — 0.83
- Kushner–Stratonovich Equation — 0.82
- Degree Day — 0.82
- Residual Sum of Squares — 0.82
Computed from structural-signature embeddings · 2026-10-17
References¶
[^ref-f05840f0ce26]: Wouter J. M. Knoben, Jim E. Freer, and Ross A. Woods (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. Original open publisher article, §1 Equations (2)–(3), §2 Equations (4)–(6), §3.1 Figure 1 caption and accompanying text. Equations and text/caption were inspected; figure pixels were not independently evaluated. [^ref-ea02abf86a28]: Thibault Mathevet, Nicolas Le Moine, Vazken Andréassian, Hoshin Gupta, and Ludovic Oudin (2023 volume), “Multi-objective assessment of hydrological model performances using Nash–Sutcliffe and Kling–Gupta efficiencies on a worldwide large sample of watersheds,” Comptes Rendus Géoscience 355(S1):117–141, DOI 10.5802/crgeos.189. Original open publisher article, §3.3 Equation (24), §§3.1–3.4 model and split-sample procedure, §4.2 Hérault Y2102010 discussion and Figure 8 caption. The publisher lists online first 2023 and published online 2024; 2023 denotes the cited volume. Original HTML and version-of-record text were inspected; no exact figure-pixel values are claimed.