Possible bias in the assessment of karst hydrological model performance. Example of alpha and beta parameters compensation when using the KGE as performance criterion.

Performance criteria such as the mean squared error (MSE), the Nash-Sutcliffe efficiency (NSE) and the Kling-Glupta efficiency (KGE) are extensively used to calibrate hydrological models. In recent years, numerous authors have stressed the inherent limitations of squared-error based criteria such as MSE and NSE. As a result, KGE criterion is gaining in popularity and is being widely used for calibration and for assessment. KGE has been initially proposed to address the poor consideration of discharge variability by NSE, but it also helps to lower the impact of squared errors in highly variable time series. KGE is a combination of (i) the Pearson correlation coefficient (r), (ii) the ratio between simulated and observed means (β), and (iii) the ratio between simulated and observed variances (α). In this study, we used KGE to compare the performance of two karst hydrological models (ANN and LP) over different flow regimes (dry, intermediate, wet) of two karst springs. The considered karst systems exhibit high contrasts in geometrical and hydrodynamic properties, inducing a high variability of the discharge at the springs. The discharge time series were divided into three sub-time series (dry, intermediate, and wet flows) according to fixed thresholds of discharge values. KGE values were higher for LP model for each sub-time series of both karst systems, thus indicating a better performance of LP over ANN at dry, intermediate and wet flows. However, KGE of the whole discharge time series were higher for ANN model, thus indicating a better overall performance of ANN over LP. The analysis of the decomposition of KGE (r, β, α) alongside a visual assessment of the simulated discharges of both models revealed that a compensation bias may be induced by β and α parameters. Simultaneous and equal overestimations and underestimations of multiple parts of the discharge time series seem to favour β and α values, leading to an overall better KGE coefficient without being associated to an increased model relevance.