After validation of the model framework on these case studies (see
section 3.1.1), the next step was to test the model with synthetic
hydrographs (necessary as the inflows to most lakes are ungauged) in
order to produce water level frequency curves.
The model results from the synthetic hydrographs had to be validated
against observed water level fluctuations in the lakes (section
3.1.3).Observed values were derived from a subset of water level
measuring gauging stations with time records longer than 25 years in
Quebec (33 stations) and the physically-based model was then tested on
the gauges that also had synthetic discharge values available (31
stations). The maximum annual fluctuations were initially derived as a
difference between the recorded water levels and the mean at the
corresponding station. However, because water level gauges are not
available for most lakes, the final testing phase used water surface
elevation derived from LiDAR as the baseline elevation to which water
level increases were applied (on a subset of 23 stations at which all
the necessary information was available). For those lakes with gauges,
analysis shows that the average error between recorded mean water level
and LiDAR was approximately 0.50 m and the median error was about 0.25 m
(see Table 1 in supplementary information). A large portion of this
error is driven by a small number of reservoirs that are likely to be
affected by a strong seasonal regulation. Removing these stations from
the analysis would significantly reduce the average difference between
LiDAR and mean water level to a mean error of 0.25 m, but would also not
be representative of an error affecting a non-negligible portion of
lakes. Since the available LiDAR imagery is constantly increasing and
will represent the main source to derive water level data at larger
scale, the decision was to keep using the LiDAR elevation as a
reference. The values for each lake were fitted with an appropriate
distribution to extract values at different return periods (20, 100 and
350 years).
The inputs required to run the model for each lake are the inflow
discharge, the lake area and the outflow channel width. The discharge
was derived from the distributed hydrological model HYDROTEL (Fortin et
al. 1995; 2001) for three return periods of interest while the channel
widths were manually measured in QGIS for the different lakes in
question. The time to concentration of the inflow hydrographs was set to
a fixed value of 200 hours after performing a sensitivity analysis on
the model.
Statistical model
In contrast to a physically based methodology, a statistical approach
focuses on analysing the water level fluctuations at the available
gauging stations across the region in order to identify the driving
factors that determine the nature of water level increases. This is done
by analysing the recorded time series with a probabilistic distribution
and linking the results with observable characteristics of the lakes, in
order to identify a statistical model that can be used at ungauged
locations. The analysis focused on finding plausible linear regressions
that could link the water level increases to different variables, such
as lake area, upstream drainage area and peak discharge. To explore all
the different possibilities the analysis was assessed in three steps:
single variable regression analysis, multivariable regression analysis,
and multivariable regression analysis with variable transformation.
Several interaction terms were considered, in order to identify a
statistically significant relationship.