Influential point detection diagnostics in the context of hydrological model calibration

- Evaluating influence of individual data points is rare in hydrological modelling.
- Highly influential points can change mean/max predictions by 13/25%.
- Comparing numerical/analytical approaches identified similar influential points.
- Analytical approaches are faster, numerical approaches are more general.

SummaryInfluential data are those that have a disproportionate impact on model performance, parameters and/or predictions. This paper evaluates two classes of diagnostics that identify influential data for hydrological model calibration: (1) numerical “case-deletion” diagnostics, which directly measure the influence of each data point on the calibrated model; and (2) analytical diagnostics based on Cook's distance, which combine information on the model residuals with a measure of the distance of each input point from the centre of the range of the input data (i.e., the leverage). Case-deletion methods rank influence by changes in the model parameters (measured through the Mahalanobis distance), performance (using objective function displacement) and predictions (e.g. mean and maximum streamflow). For the analytical methods, both linear and nonlinear estimates of leverage are used to calculate Cook's distance, which is used to rank influential data. We apply these diagnostics to three case studies and show that a single point could change mean/maximum streamflow predictions by 7%/9% for a rating curve model, and 13%/25%, for a hydrological model (GR4J) in an ephemeral catchment. In contrast, the influence was far less for GR4J in a humid catchment (0.2%/2.3%). Assuming the data are of high quality this indicates deficiencies in the ability of the GR4J model structure to reproduce the flow regime in the ephemeral catchment. The linear Cook's distance-based metric produced reasonably similar rankings to the case-deletion metrics at a fraction of the computational cost (300-1000 times faster), but with less flexibility to rank influence using specific aspects of model behaviour. The nonlinear distance produced rankings that were virtually the same as the case-deletion metrics for all case studies - this highlights the importance of its use for nonlinear hydrological models. Visual assessment was not a reliable method of influence analysis as there was no direct relationship between the most influential data and the highest observed streamflows. The findings establish the feasibility and importance of including influence detection diagnostics as a standard tool in hydrological model calibration.