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\begin{document}
\title{Large-scale flood models in watersheds with several lakes and reservoirs}
\author[1]{Gaia Olcese}%
\author[1]{Christopher Sampson}%
\author[2]{Guénolé Choné}%
\author[2]{Pascale Biron}%
\author[3]{Thomas Buffin-Bélanger}%
\affil[1]{Fathom}%
\affil[2]{Concordia University}%
\affil[3]{Université du Québec à Rimouski}%
\vspace{-1em}
\date{\today}
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\begin{abstract}
A series of recent flood events in Canada affecting areas around lakes
and reservoirs have highlighted the need to explicitly represent such
features in large scale flood models. Water level fluctuations in lakes
are traditionally modelled using detailed hydrological models designed
-- as far as possible -- to represent the actual physical processes that
take place. This approach, while appropriate for local-scale studies in
data-rich areas, is not applicable for large-scale flood modelling where
data availability for model calibration and validation is often severely
limited. This paper explores two methodologies, one statistical and one
physically based, designed to approximately predict the increase in the
water level of lakes in Quebec (Canada) using only limited morphological
information about the lakes and the estimated discharge entering the
water body during a flood event. Of the two methods, the statistical
approach proved to be the most applicable to a large-scale modelling
framework as it exhibited lower errors whilst being considerably easier
to implement in a semi-automated modelling chain.%
\end{abstract}%
\sloppy
\section*{Introduction}
{\label{introduction}}
Over recent years interest in large-scale flood modelling has grown due
to the increase in computational capacity and availability of
remotely-sensed terrain data sets (Alfieri et al., 2013; Dottori et al.,
2016; Sampson et al. 2015; Wing et al. 2017; Winsemius et al., 2013).
Historically, the vertical accuracy of large-scale terrain data sets has
proven to be one of the most significant obstacles to obtaining accurate
flood projections (Schumann 2014). Recent improvements to the wider
accessibility of high-quality terrain data sets at large scales, such as
the LiDAR-rich US National Elevation Dataset or the rapidly improving
LiDAR coverage in Quebec with 1-m Digital Elevation Models (DEMs) freely
available, have permitted the development of such models at national
scales (Wing et al., 2017; Chon\selectlanguage{ngerman}é et al., in review). When built with
high quality input data, national scale flood models have been shown to
demonstrate levels of skill approaching those of local scale models
(Wing et al., 2017), and even where input data are less detailed they
remain a useful starting point for the scoping of more detailed
strategic and local-scale flood risk assessments. Due to the lack of
accessible information on lakes and reservoirs and the complexity and
heterogeneity of the physical processes involved, these models do not
usually consider the effect of lakes during flood events and their skill
in such areas remains poorly understood (Sampson et al., 2015).
With nearly 900,000 lakes covering more than 10 hectares, Canada
accounts for 62\% of the world's lakes, a legacy of glaciers' scouring
action and their subsequent melting (Loïc et al. 2016). Recent flood
events, such as the spring floods of 2017 and 2019 caused not only
rivers but also lakes to overflow in the province of Quebec. In 2019,
these inundations caused major flood stage to be recorded at 6 locations
and middle flood stage at 12 locations, including the Lake of the Two
Mountains (Lac des Deux Montagnes) and Lake Louise, damaging 2,341 homes
and forcing around 1,200 residents to evacuate (Floodlist.com 2019). It
is therefore unsurprising that the need for a more thorough
understanding of lake water levels at large-scale has emerged in this
context.
The literature currently provides various approaches to tackle the
challenge of modelling water level stages in lakes. Previous studies
focused on modelling the hydrological water balance of water basins
including lakes (Setegn et al. 2008) or on identifying trends in the
water level variability in a specific lake (Jöhnk et al. 2004). Other
studies focused on the long-term prediction of changes in the water
level using artificial intelligence methods (Altunkaynak 2006;
Buyukyildiz et al. 2014; Khan \& Coulibaly 2006; Piaseck et al. 2018) or
on real time monitoring via satellite observations (Crétaux et al.
2011). Detailed hydrological models of lakes were developed in data-rich
areas, considering riverine inflow, precipitation on the lake surface,
evaporation and riverine outflow (Gibson et al. 2006). In other cases,
spatially distributed hydrologic models were used for flood event
simulation over basins with a complex system of reservoirs (Montaldo et
al. 2004) and flood routing methods were applied to evaluate the effect
of large artificial reservoirs (Gioia et al. 2016; Lee et al. 2001).
However, no studies focused on analysing the impact of extreme flows on
the increase of water level in both natural lakes and reservoirs and the
consequential flood that could occur on the lakeshore.
This study sought to address this knowledge gap and derive a methodology
that could approximately define the water level increase in lakes and
reservoirs due to an extreme event with a specific probability of
occurrence, and thus delineate the flood prone area in the surroundings.
Ideally this method should be applicable to different types of water
bodies, including natural lakes and artificial reservoirs. Since the
final purpose of such a methodology is to be applied in the framework of
large-scale flood simulations, the information required for each lake
cannot be extensive and has to be easily available in a semi-automated
way at national scales.
\section*{Methodology}
{\label{methodology}}
Two approaches were considered to assess this problem: a physically
based approach and a statistical approach.
\emph{Physical based model}
The initial premise of the physically based approach was to develop a
model that could simulate the fluctuations in the water level using an
inflow peak hydrograph and remotely-sensed morphological characteristics
of the lake as inputs. It is known from compensating reservoir modelling
that lakes and reservoirs usually have an attenuation effect on the
inflow hydrograph, causing a reduction of the peak discharge value and a
release of the water volume during a longer period (United States
National Resources Conservation Service, National Engineering Handbook.
Section 630, Hydrology. Chapter 17, Flood Routing April 2014). The scale
of the attenuation depends on the characteristics of the lake or
reservoir, such as its storage capacity and the geometry of the spillway
(Gioia 2016). To simulate this behaviour, it is possible to proceed with
what is called flood routing, using as inputs the inflow discharge, the
volume of water retained in the lake and a relationship between the
variation of the water level and the outflow discharge.
A water balance equation is used to link the increase in the surface
water elevation to the difference between the volume entering the lake
and the volume leaving it at each time step.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(\frac{S_{2}-S_{1}}{t}=\frac{Q_{in1}+Q_{in2}}{2}-\frac{Q_{out1}+Q_{out2}}{2}\) & (1)\tabularnewline
\bottomrule
\end{longtable}
Where \(S\) stands for storage volume, \(t\)
the timestep used for the calculations, \(Q_{\text{in}}\) is the inflow
discharge,\(Q_{\text{out}}\) is the outflow discharge and the subscripts
1 and 2 represent different times (\emph{t} ). The water level at each
time step is calculated using the following equation.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(H_{2}=H_{1}+\frac{{(Q}_{in1}-Q_{out1})\ t}{A}\) & (2)\tabularnewline
\bottomrule
\end{longtable}
Where \(H_{1}\) represents the water level increase at
\(t_{1}\),\(H_{2}\) the water level at
\(t_{2}\) and \(A\) is the lake area. This
equation assumes the lake area as constant: the lake is assumed to have
a cylinder-type shape, in which the area is not a function of the water
level.
There are various equations that can be used to compute the outflow
discharge. In this study the rectangular weir equation was used. This
choice was driven by the simplicity of the equation, which requires only
the weir width to be derived from remotely sensed data.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(Q_{out,i}=\mu\ L\ \sqrt{2gh_{i}}\ h_{i}\) & (3)\tabularnewline
\bottomrule
\end{longtable}
\(\mu\) is a shape coefficient, \(L\) represents
the weir width (assumed as the width of the downstream river channel),
\(g\) is the acceleration of gravity and \(h_{i}\)
the height over the weir (equal to the water level increase). The
subscript\selectlanguage{ngerman} i refers to the time step: the outflow
discharge is calculated at each time step as a function of the varying
height over the weir, derived at the previous time step using equation
(2). The shape coefficient was initially assumed as equal to 0.5; this
value was identified as the value producing the smallest errors by some
calibration tests. The parabolic weir equation was also tested: it
proved to be less effective whilst also requiring more detailed
information about the spillway.
The ideal test case to validate this model with observed data would be a
lake with three gauges providing time series (instant values) of the
water level and the upstream and downstream discharge. This way the
inflow hydrograph of an event can be used as input for the model and the
computed outputs can be compared with observed records. The lake should
be small enough to be influenced by the inflow hydrograph in terms of
fluctuations in the water level -- a very large lake's water elevation
won't vary during a short single event -- and without a dam or any
regulation device that could influence drastically the water level and
the discharge downstream. Unfortunately, we were unable to identify such
an ideal test case in either Canada or the United States, where most
medium size lakes are dammed and/or do not have a gauging station
upstream. Despite this, three test cases were used to compare the
physically-based model output with water level observations: lake
Maskinongé, lake Brulé in Quebec and Waterbury reservoir in Vermont. For
lake Maskinongé and Waterbury reservoir three gauging stations were
available, although both water bodies are dammed. There is no gauging
station downstream Lake Brulé and the main inflow is influenced by a dam
(barrage Ludger). Different peak hydrographs isolated from gauging
stations upstream the lakes were used as inputs for the model, after
being appropriately scaled to the watershed area at the lake's outflow.
This procedure allows to consider the inflow from ungauged tributaries.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(Q_{\text{in}}=Q_{in,recorded}*F\) & (4)\tabularnewline
\midrule
\endhead
\(F=\ \frac{\text{Downstream\ watershed\ area}}{\text{Upstream\ watershed\ area}}\) & (5)\tabularnewline
\bottomrule
\end{longtable}
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.
\emph{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.
\section*{Results}
{\label{results}}
\emph{3.1 Physical based model}
\emph{3.1.1 Validation of the model with recorded hydrographs}
The results obtained by running the model with recorded hydrographs show
that even though the water level variation doesn't always match the
pattern of the recorded fluctuations, the peak water level can be
reproduced with an accuracy varying between 0.05 and 0.25 m (Figure 1).
These results were positive, especially considering that all the test
cases were influenced to varying degrees by a dam downstream that
imposed a regulating effect on the lake outflow. These preliminary
results suggested that this approach, even if very simplistic, could
produce sensible outputs for specific events and thus led the research
toward testing it with synthetic hydrographs (for ungauged rivers) in
order to produce water level frequency curves.
{[}Figure 1{]}
\emph{3.1.2 Definition of an appropriate time to concentration}
During the initial model runs, times to concentration derived from
Fathom's global flood model (Sampson et al. 2015) were used. The model
uses the velocity method (United States National Resources Conservation
Service, National Engineering Handbook. Section 630, Hydrology. Chapter
15, Time of Concentration) to calculate the time to concentration as a
sum of the travel time in shallow concentrated flow and the travel time
in open channel flow. The travel time is derived using the longest flow
path from the point of interest and an average velocity derived using
Manning's coefficient. This produced a substantial underestimation of
the observed water levels. To understand the reason of this behaviour,
several experiments were undertaken to help understand model parameter
sensitivity. All the following tests were performed using the discharge
estimated for a return period of one hundred years.
Initially, the model was run for each lake keeping the same weir value
(best estimate from GIS and remotely sensed data) and varying the time
to concentration from 1 hour up to 600 hours (24 days), in order to
evaluate model sensitivity to this variable. In some cases, the time to
concentration had a big influence on the modelled water level, while in
others it seemed to be relatively insensitive. In all cases the time to
concentration showed an asymptotic trend. The asymptotic behaviour
indicates that it is essential not to underestimate time to
concentration, while overestimation will be less harshly penalised in
terms of model performance. This is intuitively correct as water levels
in lakes are naturally self-regulating, with outflow increasing as lake
level increases until an equilibrium level is reached. The weir equation
represents this, with discharge being proportional to\emph{h}
\textsuperscript{3/2}, where \emph{h} is water height above the weir
crest.
The other variable shown to have a strong influence on model behaviour
is the weir width. To evaluate model sensitivity to this variable, the
time to concentration value was held constant while weir width was
varied across a wide range of values. Again, some test cases proved to
be very sensitive to this variable while others exhibited minimal
sensitivity, with water level increases remaining almost constant
regardless of weir width.
Following the univariate analysis of time to concentration and weir
width, the next step was to try and delineate the behaviour of these
lakes and reservoirs using a bivariate analysis. A range of different
simulations were therefore run for each lake, varying both the weir
width and the time to concentration. Figure 2 represents an example of
the results obtained for the Lake Massawippi (Quebec) station,
representing the absolute error between the peak water level increase
produced by the model and the maximum recorded water level increase
(difference between annual maximum and annual mean).
{[}Figure 2{]}
From these results, it is possible to identify some general patterns
across a subset of 31 water level measuring gauging stations with time
records longer than 25 years, known lake area and synthetic discharge in
Quebec. Overestimation typically occurs when the weir is narrow or when
the time to concentration drastically increases, whilst it appears more
difficult to provoke underestimation from the model. In most cases it is
also possible to note that time to concentration maintains its
asymptotic trend: once the inflow hydrograph has a long enough duration,
the water level fluctuation stabilises and grows very slowly. Bigger
lakes generally appear to be more sensitive to the time to
concentration, and less to the weir width, while for smaller lakes the
best estimation of the water level seems to be very dependent on a good
estimate of the weir width whilst still requiring a long enough
hydrograph. Unfortunately, it doesn't seem possible to generalise
overall behaviour in water levels as even lakes that seem to be similar
in size and with a comparable inflow show different values of recorded
water lake fluctuation. Since these analyses highlighted how an
overestimation of the inflow duration shouldn't heavily penalize the
model performance, a fixed value of 200 hours was chosen for the time to
concentration to use hereafter.
\emph{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 Barri\selectlanguage{ngerman}ère, 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 (Mailhot\emph{et 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).
\emph{3.2 Statistical model}
\emph{3.2.1 Single variable regression analysis}
The relationships between the 350-year water level (estimated using a
GEV distributions fitted to gauged level data at 23 stations and a set
of individual predictor variables were initially tested using single
variable regressions. Note that these 23 stations are a subset of the 31
stations with at least 25 years of water level data, as for this
analysis we also needed LiDAR data as well as HYDROTEL discharge data to
be available. The first step consisted of identifying significant
correlations between water level and any single variable such as lake
area, upstream drainage area, peak discharge or outflow channel width.
The results showed no statistically significant relationship existed
between water levels and any single variable; performing standard
transformations to the variables, such as applying a logarithm or square
root, did not yield any improvements.
\emph{3.2.2 Multivariable regression analysis}
A multi-variable regression analysis was undertaken to identify any
significant relationship between the same 350-year water level variation
and a range of sets of variables. In order to find a plausible
regression model, different predictors were taken into consideration, as
well as their possible interaction terms. To conduct the analysis in a
systemic way and explore all the possible combinations of the
predictors, a maximum of ten input variables have been considered: lake
area, watershed area, outflow channel width, peak discharge (return
period of 350 years) and their six associated interaction terms (i.e.
lake area multiplied by watershed area, lake area multiplied by outflow
channel width, etc.). Most of the regression models showing p-values
lower than the threshold value of 0.05 are associated with high RMSE or
very low values of adjusted R squared. Moreover, none of the regression
models proved to be robust: by simply removing a few stations from the
sample and re-running the fitting we can obtain models that use
completely different variables as predictors.
\emph{3.2.3 Multivariable regression analysis applying variable
transformations}
Two transformations were then applied to the predictors (logarithmic and
square root), to identify any linear correlation between the water level
above the LiDAR level and the transformed variables. The predictors
considered by this analysis were lake area, upstream drainage area,
outflow channel width and peak discharge with return period of 350
years. In this context it was observed that squaring the discharge
values made a relevant difference in the predictive performance of the
model, while performing the same transformation on the area and
watershed areas was not as significant. The weir value was not
identified as a relevant variable. The simplest significant model used
as predictors the lake area and the square root of the peak discharge,
and shows a RMSE of 0.48 m with an adjusted R squared of 0.5495. The
p-values for both the predictors are in the order of
10\textsuperscript{-5}, showing a statistically significant correlation
(Table 3, Figure 4).
{[}Table 3{]}
{[}Figure 4{]}
The error characteristics of this approach show the assumption of
homoscedasticity to be valid in this model. Neither the error nor the
absolute value of the error are shown to be linked with an increase of
any of the predictors or other lake characteristics (plot in Figure 3 of
supplementary materials).
An identical multivariable regression procedure was applied using return
periods of 100 and 20 years. The results show that an equivalent model,
with slightly modified coefficients, provides a good performance for a
100 year flow (RMSE = 0.48 m, adjusted R squared of 0.4849). However,
the adjusted R squared dropped to 0.3574 for the 20-year events,
indicating that the model was not able to predict water levels
associated with more frequent events. We hypothesise that this is
because higher frequency events are more readily controlled by
engineered features leading to highly unpredictable water level
behaviour.
\section*{Conclusions}
{\label{conclusions}}
Even though the physically based approach shows some predictive skill in
estimating lake water level fluctuations, the small difference in
precision when compared to using an average distribution inevitably
leads to the question of whether it is worth implementing it in a
large-scale modelling framework. Including it in the automated process
of flood simulation and deriving all the data needed as input
(especially the outlet channel width, which needs to be measured
manually) would require a considerable amount of effort. Moreover, the
results suggest that the physical model is not suitable to simulate the
complexity of the processes that take place during flood routing of a
streamflow in lakes. Although it performs reasonably well when accurate
streamflow data is provided, it is not reliable enough when run with
synthetic hydrographs across all Quebec. It is likely that similar
findings would have been obtained in other geographical contexts.
The statistical approach on the contrary provides a lower RMSE than the
one obtained using the physical based model and eliminates the need for
measuring the outflow channel width for every lake, thus simplifying the
process. This procedure can be easily implemented in a more extensive
large-scale modelling framework to provide first-order approximations of
water levels associated with extreme floods. These levels could be used
as boundary conditions for two-dimensional hydraulic simulations of
river flow into the lake, a very common situation in Canada but also in
many other regions affected by the Laurentide or Scandinavian ice
sheets, as well as to define flood prone areas around lakes where
detailed hydrological models are not available.
\textbf{Acknowledgements}
This work was funded by the Ministry of Environment of Quebec (Ministère
de l'Environnement et de la Lutte contre les changements climatiques).
\textbf{References}
Alfieri L., Salamon P., Bianchi A., Neal J., Bates P., Feyen L. 2013.
Advances in pan-European flood hazard mapping. Hydrological Processes,
28(13), 4067--4077. doi:10.1002/hyp.9947
Altunkaynak A. 2007. Forecasting surface water level fluctuations of
lake van by artificial neural networks. Water Resour. Manage.
21:399-408. doi: 10.1007/s11269-006-9022-6.
Buyukyildiz, M., Tezel, G. \& Yilmaz, V. 2014. Water Resources
Management 28:4747. doi: 10.1007/s11269-014-0773-1.
Choné, G., Biron, P.M., Buffin-Bélanger, T., Mazgareanu, I., Neal, J.C.,
Sampson, C.C. In review. An assessment of large-scale non-calibrated
flood modelling based on LiDAR data. Hydrological Processes.
Crétaux, J.-F., Jelinski, W., Calmant, S., Kouraev, A., Vuglinski, V.,
Bergé-Nguyen, M., Gennero M.-C., Nino F., Abarca Del Rio R., Cazaneve A,
Maisongrande, P. 2011. SOLS: A lake database to monitor in the Near Real
Time water level and storage variations from remote sensing data.
Advances in Space Research 47(9), 1497--1507. doi:
10.1016/j.asr.2011.01.004.
Dottori, F., P. Salamon, A. Bianchi, L. Al\selectlanguage{english}fieri, F. A. Hirpa, and L.
Feyer (2016), Development and evaluation of a framework for global \selectlanguage{english}flood
hazard mapping, Adv. Water Resour., 94, 87--102. doi:
10.1016/j.advwatres.2016.05.002.
Floodlist.com. (2019). Canada -- Floods Damage Over 2,000 Homes in
Quebec. {[}online{]} Available at:
http://floodlist.com/america/canada-floods-quebec-april-2019 {[}Accessed
16 Dec. 2019{]}.
Fortin, J. P., R. Moussa, C. Bocquillon, J. P. Villeneuve. 1995.
Hydrotel, a Distributed Hydrological Model Compatible with Remote
Sensing and Geographical Information Systems. Revue Des Sciences de
l'Eau 8 (1): 97--124.
Fortin, J.P, R. Turcotte, S. Massicotte, R. Moussa, J. Fitzback, J.-P.
Villeneuve. 2001. Distributed Watershed Model Compatible with Remote
Sensing and GIS Data. I: Description of Model. Journal of Hydrologic
Engineering 6 (2): 91--99.
Gibson J. J., Prowse T. D., Peters D. L. 2006. Hydroclimatic controls on
water balance and water level variability in Great Slave Lake.
Hydrological Processes, 20(19), 4155--4172. doi: 10.1002/hyp.6424
Gioia, A., 2016. Reservoir routing on double-peak design flood. Water.
8. 553. doi: 10.3390/w8120553.
Khan M. S., Coulibaly P. 2006. Application of support vector machine in
lake water level prediction. Journal of Hydrologic Engineering 11(3)
199-205. doi: 10.1061/(ASCE)1084-0699(2006)11:3(199).
Lee K.T., Chang C.H., Yang M.S., Yu W.S. 2001. Reservoir attenuation of
floods from ungauged basins. Hydrological Sciences Journal Vol. 46, No.
3, pp. 349-362.
Mailhot A., Talbot G., Ricard S., Turcotte R., Guinard K. 2018.
Assessing the potential impacts of dam operation on daily flow at
ungauged river reaches. Journal of Hydrology: Regional Studies. doi:
10.1016/j.ejrh.2018.06.006.
Messager M., Lehner B., Grill G., Nedeva I., Schmitt O. 2016. Estimating
the volume and age of water stored in global lakes using a
geo-statistical approach. Nature Communications 7, 13603 (2016)
doi:10.1038/ncomms13603
Montaldo N., Mancini M., Rosso R. (2004). Flood hydrograph attenuation
induced by a reservoir system: analysis with a distributed
rainfall-runoff model. Hydrological Processes, 18(3), 545--563.
doi:10.1002/hyp.1337
Piasecki A., Jurasz J., Adamowski, J.F. 2018. Forecasting surface
water-level fluctuations of a small glacial lake in Poland using a
wavelet-based artificial intelligence method. Acta Geophysica (2018) 66:
1093. doi: 10.1007/s11600-018-0183-5.
Sampson, C. C., A. M. Smith, P. D. Bates, J. C. Neal, L. Al\selectlanguage{english}fieri, and J.
E. Freer (2015), A high-resolution global \selectlanguage{english}flood hazard model, Water
Resour. Res., 51, 7358--7381, doi:10.1002/ 2015WR016954.
Setegn S. G., Srinivasan R., Dargahi B. 2008. Hydrological Modelling in
the Lake Tana Basin, Ethiopia Using SWAT Model. The Open Hydrology
Journal. doi: 10.2174/1874378100802010049.
Schumann G. 2014. Fight floods on a global scale. Nature 507, 169 (2014)
doi:10.1038/507169e
United States. National Resources Conservation Service. National
Engineering Handbook. Section 630, Hydrology. Chapter 17, Flood Routing.
Washington, D.C.: U.S. Dept. of Agriculture, Natural Resources
Conservation Service, 2014.
United States. National Resources Conservation Service. National
Engineering Handbook. Section 630, Hydrology. Chapter 15, Time of
Concentration. Washington, D.C.: U.S. Dept. of Agriculture, Natural
Resources Conservation Service, 2014.Wing, O. E. J., P. D. Bates, C. C.
Sampson, A. M. Smith, K. A. Johnson, and T. A. Erickson (2017),
Validation of a 30 m resolution \selectlanguage{english}flood hazard model of the conterminous
United States, Water Resour. Res., 53, 7968--7986, doi:10.1002/
2017WR020917.
Winsemius, H. C., L. P. H. Van Beek, B. Jongman, P. J. Ward, and A.
Bouwman (2013), A framework for global river \selectlanguage{english}flood risk assessments,
Hydrol. Earth Syst. Sci., 17, 1871--1892, doi:10.5194/hess-17-1871-2013.
\textbf{Data availability statement}
The data that support the findings of this study are available from the
corresponding author upon reasonable request.\selectlanguage{english}
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