3.1.3 Validation of the model with synthetic hydrographs
The sensitivity tests were performed on a dataset of 31 stations, using average observed water levels as reference. From now on, for the actual validation, the model was run on a reduced subset of 23 stations (the ones that also have available LiDAR data). Running the model using synthetic hydrographs produced three simulated water level increases for the three examined return periods (20, 100 and 350 years). A plot with the results can be found in Figure 2 of supplementary materials.
[Table 1]
[Table 2]
To evaluate the performance of the physical model and determine if it is worth implementing it in the workflow of flood modelling, the results were compared to using a median GEV distribution for all the 23 stations. Table 1 summarises the error that would derive from applying a median GEV distribution to all the 23 lakes in the subset, while Table 2 shows how the physical model would perform in terms of bias and RMSE (Root Mean Square Error). By comparing the RMSE values to the standard deviation associated with the GEV distribution, it is possible to deduce that, although the physical based approach produces smaller errors than just referring to the average values predicted by a statistical analysis across all the stations, the difference in precision of the two methodologies is not substantial. The error varies from 0.58 to 0.71 m when using a fixed GEV distribution and from 0.49 to 0.63 m when using the physical model. Figure 3 presents examples where the physical model greatly underestimates lake levels (Lake Simon, station 040408), one where it is close to the GEV (Lac Barrière, station 040407) and one that overestimates the lake level (lac du Poisson Blanc, station 040602), whereas graphical results for all the stations are presented in Figure 1 of supplementary material.
[Figure 3]
A study of the error associated with this type of model was performed to check the assumption of homoscedasticity and potentially identify any influence of some specific variables on the performance of the model. The model was analysed in relation to several variables: lake area, watershed area, peak discharge, peak discharge times lake area, degree of regulation and surface area variation index. The degree of regulation (DOR) is an index designed to quantify hydrological alterations induced by dams (Mailhotet al. 2018) and should show if dams have an identifiable effect on the water level fluctuations in lakes. The surface area variation index refers to the increase in the extension of the lake’s surface area with level increase and thus considers the impact of topography on the process. The tests revealed the errors to be homoscedastic, being homogeneously distributed when plotted against the possible predictors, and there was no clear relationship between the residuals of the model and any of the analysed variables (plot in Figure 2 of supplementary materials).