Using Functional Data Analysis to Calibrate and Evaluate Hydrological Model Performance

The performance of a hydrological model depends strongly on the calibration procedure, and in particular on the goodness-of-fit measure used. It is widely recognized that traditional goodness-of-fit measures such as the Nash-Sutcliffe efficiency (NSE) are biased toward securing a particular aspect of a hydrograph (high flows, in the case of the NSE). This paper proposes a new strategy for model calibration that evaluates the ability of the model to simulate the complete shape, timing, and variability of the observed hydrographs. The methodology is based on the comparison of the simulated and observed whole annual hydrograph as a single curve using the functional data analysis (FDA) framework. FDA is a recent statistical framework that considers observations as curves or functions. The hydrograph is a particular example of such functions. The proposed approach is applied to calibrate the CEQUEAU model on the Lac St-Jean drainage basin (Quebec, Canada) and is compared with a traditional approach using NSE. Both calibrations yield to similar results for high flows, with NSE of 0.89 during calibration and 0.94 during the validation period. The results show an improvement for winter low-flow bias by 10% over the traditional calibration using NSE. Moreover, the application of the functional Student’s test suggests that winter flows simulated by the model calibrated with NSE are significantly different, whereas flows simulated by the model calibrated with the proposed approach are accurate for almost all periods of the year.