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).