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\begin{document}

\title{Characteristic Time Scales of Reservoir Evaporation in a Subarctic
Climate}



\author[1]{Adrien Pierre}%
\author[1]{Daniel  Nadeau}%
\author[1]{Antoine Thiboult}%
\author[2]{Alain N. Rousseau}%
\author[3]{Alain Tremblay}%
\author[1]{Pierre-Erik Isabelle}%
\author[1]{François Anctil}%
\affil[1]{Universite Laval Departement de Genie Civil et de Genie des Eaux}%
\affil[2]{INRS Eau Terre Environnement}%
\affil[3]{Hydro-Quebec}%


\vspace{-1em}



  
  \date{June 18, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Water bodies such as lakes and reservoirs affect the regional climate by
acting as heat sinks and sources through the evaporation of substantial
quantities of water over several months of the year. Unfortunately,
energy exchange observations between inland water bodies and the
atmosphere remain rare in northeastern North America, which has one of
the highest densities of lakes in the world. This study helps to fill
this gap by analyzing field observations collected from a subarctic
hydropower reservoir (50.69\selectlanguage{ngerman}°N, 63.24°W) characterized by a mean depth of
44 m and a surface area of 85 km \textsuperscript{2}. Two eddy
covariance (EC) systems, one on a raft and one onshore, were deployed
from 27 June 2018 to 12 June 2022. The thermal regime of the reservoir
was monitored using vertical chains of thermistors. Results indicate a
mean annual evaporation rate of 590 ± 66 mm (\textasciitilde{}70\% of
the annual precipitation), with 84\% of the evaporation occurring at a
high rate from August to freeze-up in late December through episodic
pulses. It was difficult to close the energy balance because of the
magnitude and the large time lag of the heat storage term. In order to
circumvent this problem, we opted to perform calculations for a year
that started from the first of March, as the heat storage in the water
column was at its lowest at that point and could thus be ignored. From
June to December, monthly Bowen ratios increased from near-zero negative
values to about 1.5. After September, due to smaller vapor pressure
deficits, latent heat fluxes steadily declined until an ice cover sealed
up the reservoir. Two opposite diurnal cycles of sensible and latent
heat fluxes were revealed during the open water period, with sensible
heat fluxes peaking at night and latent heat fluxes peaking in the
afternoon.%
\end{abstract}\selectlanguage{ngerman}%



\sloppy


\textbf{1. INTRODUCTION}

Reservoirs are subject to substantial water level fluctuations caused by
water release operations and, as such, to shorter water residence times
than lakes. Evaporation (latent heat flux, \emph{LE} ) is a major
component of the mass and energy budgets of reservoirs, which can
compromise some typical key functions such as freshwater supply,
irrigation, hydropower, navigation, and other related economic
activities (Friedrich et al., 2018). In some arid regions of the world,
structural measures are put in place to limit evaporation, such as
floating balls or lattices (Assouline \& Narkis, 2021). Evaporation is
intangible and therefore a difficult hydrological flux to measure,
making it difficult to fully understand its magnitude and controlling
mechanisms.

Studies that have quantified reservoir evaporation are rare. Tanny et
al. (2008) reported an average evaporation rate of 5.5 mm
day\textsuperscript{--1} from July to September in the Eshkol reservoir
in Israel (33\selectlanguage{ngerman}°N), which has a hot and arid climate. Further north, in
the Eastmain-1 reservoir in Canada (52°N), Strachan et al. (2016) found
the evaporation rate to be 3.1 mm day\textsuperscript{--1} between
August and October. For the Great Slave Lake in Canada (61°N), Rouse et
al. (2003) reported 2 mm day\selectlanguage{english}\textsuperscript{-1} in summer and 5 mm
day\selectlanguage{english}\textsuperscript{-1} in December. These studies indicate that even in
cold regions, reservoir evaporation can be substantial.

In cold climates, reservoirs undergo two turnovers per year (dimictic).
Their thermal regime typically evolves into three successive phases
(Cole \& Weihe, 2016). During the ice cover phase, ice acts as a lid
over the water body, preventing direct interactions between the
atmosphere and the water column. The water column then becomes
stratified, with cold water (\textless{} 4degC) sitting on top of warmer
water. Latent heat fluxes tend to remain low during this period (Wang et
al., 2016). From ice breakup in spring to the middle or end of summer,
the heat storage phase unfolds. Energy is first stored in the top
several meters of the water column closer to the surface and eventually
reaches deeper layers due to wind-induced mixing and internal
hydrodynamics (Spence et al., 2003; Vincent, 2018). The result is a
surface mixing layer (epilimnion) that is separated from the homogeneous
deep layer (hypolimnion) by a zone with a steep temperature gradient
(metalimnion). Latent heat fluxes remain low during this phase, with
frequent and stable atmospheric stratification. The third and final
phase corresponds to the heat release period. This is characterized by a
decline in water temperature due to a substantial release of energy into
the atmosphere through turbulent heat fluxes that are high and sustained
day and night (Blanken et al., 2011). The epilimnion then slowly deepens
until the fall turnover, during which the temperature of the entire
water column becomes homogenous.

While evaporation varies seasonally in response to the three thermal
phases, it also fluctuates on smaller time scales in response to
meteorological forcing. For instance, incoming shortwave radiation
causes latent heat fluxes to peak during the day, thereby increasing the
rate of evaporation during peak times (Lensky et al., 2018). The
atmospheric demand for water vapour, driven by wind speed and vapour
pressure deficit, is also known to modulate evaporation in water bodies
(Perez et al., 2020). Evaporative demand can vary within a single day.
For instance, changing wind direction can lead to a reduced or enhanced
sheltering effect, increasing or decreasing evaporation rates (Markfort
et al., 2010; Venalainen et al., 1998). Evaporation can also vary over
the course of a few days, due to passing synoptic systems that can
generate sustained evaporation (Laird \& Kristovich, 2002; Spence et
al., 2013). Blanken et al. (2000) found that 50\% of annual evaporation
over the Great Slave Lake occurred over only 25\% of the year through
episodic evaporation water losses. Moreover, thermocline depth and
intensity, which depends in part on the reservoir morphometry (Gorham,
1964), influence turbulent heat fluxes by limiting or enhancing the
energy available in the upper water layers. Indeed, Piccolroaz et al.
(2015) identified positive feedback between the lake surface temperature
and the stratification dynamics of Lake Superior, Canada. Therefore, the
timing of evaporation occurs at different scales and remains poorly
documented or correlated to physical drivers (Beck et al., 2018).

Northeastern America is one of the densest regions of lakes and
reservoirs around the world (Downing et al., 2006). These lakes and
reservoirs are considered to be climate sentinels (Adrian et al., 2009;
Williamson, Saros, \& Schindler, 2009) as well as integrators and
regulators of climate change (Williamson, Saros, Vincent, et al., 2009).
Wang et al. (2018) showed that modifications in surface energy
allocation under warmer climate conditions will accelerate global lake
evaporation. In-situ evaporation observations are needed to develop and
improve lake models (McJannet et al., 2017) for future climate
estimates, particularly in remote areas.

There is a lack of direct in-situ measurements of turbulent heat fluxes
over reservoirs in remote northern regions. The overarching goal of this
study is to identify the characteristic time scales of evaporation from
a deep subarctic hydropower reservoir. Using four years of
eddy-covariance (EC) measurements, the specific objectives are to
quantify turbulent heat fluxes at daily, monthly and annual time scales,
and to identify the key processes and surface energy budget terms that
govern \emph{LE} at each time scale. The paper is organized as follows.
We first introduce the study site and measurement methods. Then, we
describe the meteorological conditions over the whole study period and
the driving factors for each time scale. Finally, uncertainties in the
flux data are discussed, given the energy budget of several water layers
in the reservoir.

\textbf{2. MATERIALS AND METHODS}

\textbf{2.1} \textbf{Study Site}

The study site is located at the southern tip of the Romaine-2
hydropower reservoir, 80 km north of the city of Havre-Saint-Pierre, on
the north shore of the Gulf of St. Lawrence, Quebec, Canada (50.68degN,
63.25degW; Fig. 1a). The Romaine-2 reservoir is a dimictic water body that
is ice-free from May to December. The regional climate has a mean annual
air temperature and precipitation of 1degC and 852 mm (52\% as rain),
respectively (Hydro-Quebec, 2007). This is typical of the subarctic
(Dfc) Koppen-Geiger climate classification type (Beck et al., 2018). The
reservoir, which flooded in 2014, drains a
14,351-km\textsuperscript{2}area that is mostly covered with a
spruce-moss forest. At its southern end, the reservoir is about 1
km-wide, and sits at an elevation of 244 m above mean sea level. When
full, it has a surface area of 85.6 km\textsuperscript{2} and a maximum
depth of 101 m (mean depth of 44 m). It has an elongated north-south
shape that channels the near-surface winds. Hydropower production
imposes large water level fluctuations, up to 17 m in winter and 2 m in
summer and fall (Fig. 2a), resulting in a smaller surface area during
these seasons when the water is shallow. Turbine flow rates also
fluctuate yearly, with maximum values in winter when the demand for
energy is at its maximum (Fig. 2b) and during freshet to avoid spillage.
The study period extended from 27 June 2018 to 12 June 2022.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Figure 1: (a) Location of the Romaine-2 reservoir in North America (red
square). (b) Satellite image (Sentinel-2A, 2022-01-26) of the Romaine-2
reservoir in winter. The black rectangle indicates the area of the
experimental setup (c). (c) Elevation map indicating precisely where the
spillway, intake, flux towers and thermistor chains (indicated by TC)
are located.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

Figure 2: (a) Romaine-2 daily water levels (Above Sea Level) and (b)
turbine outflow rate. Both plots feature the average (black solid line)
and the full range of observed values (grey shaded area) for the 2018 to
2021 period. No data were collected in 2022.

\textbf{2.2 Raft and Shore Flux Tower}

Figure 3 shows the two flux towers that were deployed on the research
site: a 3 \selectlanguage{ngerman}× 3-m raft (measurement height of 2.0 m) deployed from June to
October each year and a permanent shore tower (measurement height
fluctuating between 11 and 28 m depending on the water level) (Fournier
et al., 2021; Pierre et al., 2022). At both sites, the eddy covariance
technique was used to calculate turbulent heat fluxes from raw 10-Hz
turbulence data.

The raft was anchored between two islands to offer protection against
large waves, in a 30-m deep section of the reservoir. The raft hosted a
fast-response sonic anemometer coupled with an infrared gas analyzer
(IRGASON, Campbell Scientific, USA), a net radiometer (Kipp \& Zonen,
The Netherlands) and a temperature probe, all mounted 2 m above the
water surface. Turbulence sensors were oriented eastward to capture the
prevailing wind directions while minimizing flow distortion by the mast.
The raft slowly oscillated along its three Euler angle axis due to
wave-induced motions. To decontaminate raw wind measurements, an
accelerometer (AHRS, Lord Sensing MicroStrain, USA) was attached
adjacent to the anemometer to record pitch, yaw, and roll angles at a
frequency of 10 Hz.

At the shore site, the flux tower was equipped with a combined sonic
anemometer and infrared gas analyzer (IRGASON, Campbell Scientific,
USA), installed 11 m above the maximum water level and pointing toward
the reservoir in the NNW direction. A complete meteorological setup was
also deployed: a TB4 tipping bucket (Hyquest Solutions, USA) for
rainfall measurement, a propeller anemometer (05103, R.M.Young, USA),
and a four-component net radiometer (CNR4, Kipp \& Zonen, The
Netherlands). The last two instruments were installed at heights of 10.3
m and 12.3 m, respectively. The radiometer measured all terms of the
radiation budget, namely incoming and outgoing shortwave and longwave
radiation, but since the instrument was installed on the shore, it did
not report the radiation emitted/reflected by the reservoir.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

Figure 3: The two eddy covariance measurement setups deployed on and
around the Romaine-2 reservoir. Raft station (left, photo taken looking
west) and shore station (right, photo taken looking north) with the
following instruments: (a) net radiometer, (b) air temperature probe,
(c) accelerometer, (d) sonic anemometer and infrared gas analyzer, and
(e) propeller anemometer. Photos were provided by Hydro-Qu\selectlanguage{ngerman}ébec and taken
on 13 June 2019, at approximately 2 m below the maximum reservoir level.

A complete year-long net radiation time series was created using the
following strategy. We used the net radiation that was measured on the
raft when it was deployed (June\selectlanguage{english}-October). When ice was present on the
reservoir, it was typically covered in snow. We therefore assumed that
the emitted/reflected radiation measured at the shore station during
that time was equivalent to what would have been measured on the
reservoir. During the transition periods, we estimated the reflected
radiation on the reservoir with a simple albedo formula based on that by
Patel and Rix (2019). The longwave radiation emitted during the
transition periods was estimated from the Stefan\selectlanguage{english}-Boltzmann law. This was
done by taking an emissivity of 0.995 and extrapolating the water
temperature profile in the top first meter of water to estimate the
water skin temperature for periods when no direct measurements were
available.

\textbf{2.3 Turbulent Heat Fluxes}

Sensible (\emph{H} ) and latent heat fluxes (\emph{LE} ) (both in W
m\selectlanguage{english}\textsuperscript{-2}) were calculated using the covariance between the
vertical wind speed \emph{w} (m s\selectlanguage{english}\textsuperscript{-1}) and air
temperature \emph{T} (K), as well as between w and the specific
humidity\emph{q} (kg kg\selectlanguage{english}\textsuperscript{-1}), such that:

\(H=\ \rho_{a}\ c_{\text{pa}}\ \overset{\overline{}}{w^{{}^{\prime}}\ T^{{}^{\prime}}}\)(1)

\(\text{LE}=\ \lambda\rho_{a}\ \overset{\overline{}}{w^{{}^{\prime}}\ q^{{}^{\prime}}}\)(2)

where \selectlanguage{greek}\emph{ρ\textsubscript{a}}\selectlanguage{english} is the humid air density (kg
m\textsuperscript{-3}), \emph{c\textsubscript{pa}} is the specific heat
of humid air (J kg\textsuperscript{-1} K\textsuperscript{-1})
and\selectlanguage{greek}\emph{λ} \selectlanguage{english}is the latent heat of vaporization (J
kg\textsuperscript{-1}). Here, primes denote fluctuations from the
30-min average, indicated by an overbar.

Raw wind velocity data from the raft were first corrected for
wave-induced motion, using the accelerometer data, following the method
proposed by Miller et al. (2008). In short, the apparent wind measured
by the sonic anemometer was corrected to account for Euler angles,
angular velocities and linear accelerations monitored by the
accelerometer. Then, for the shore and raft flux towers, we processed
the turbulence data using the EddyPro\selectlanguage{ngerman}® software, version 7.0 (LI-COR
Biosciences, USA). In doing so, we applied time-lag compensation, linear
detrending, double rotation approach (Baldocchi et al., 1988; Wilczak et
al., 2001), density fluctuation compensation (Webb et al., 1980), spike
removal (Papale et al., 2006), and other statistical tests (Vickers \&
Mahrt, 1997). Poor-quality data were flagged (Mauder \& Foken, 2011) and
removed. Data from the raft and shore stations were aggregated into one
dataset by favoring data with the best quality criteria (Mauder et al.,
2013). Note that shore data were retained only when winds originated
from the reservoir. To complete the final dataset, gap-filling was
implemented based on the method developed by Reichstein et al. (2005).

Over the whole study period (1447 days), 57 \% of the turbulent flux
data had to be gap-filled due to the fact that the raft was only
deployed from June to October and the shore flux tower was frequently
exposed to winds from the surrounding land. We assessed flux errors by
applying the Finkelstein and Sims (2001) random uncertainty method.

\textbf{2.4 Water Temperature and Transparency}

The vertical water temperature profile was continuously measured with
two chains of temperature probes (HOBO TidBit UTBI-001, Onset, USA) that
were designed with a higher resolution near the surface and a coarser
resolution deeper in the water (Figs 3c and 4). These are referred to as
thermistor chains (TCs). The first measurement site,
TC\textsubscript{1}, consisted of a 15-m chain deployed in a 30-m deep
section of the reservoir, in the vicinity of the raft. The second
measurement site, TC\textsubscript{2}, consisted of a 70-m chain located
in a 100-m deep section of the reservoir, 1 km south of the raft. At
both sites, skin temperatures were obtained using floating sensors
sheltered from incoming solar radiation by a white piece of foam. The
chains were designed to withstand variations in water levels by using
additional rope. A pressure sensor (HOBO water level logger u20-001-03,
Onset, USA) was added to each chain to correct for the effects of rope
tilt on the exact vertical position of the probes.

Water transparency was also periodically measured using a Secchi disc.
The mean Secchi depth (\emph{SD} ) was 4 ± 0.04 m. Assuming a mean
product \emph{SD} × \emph{K\textsubscript{d}} of 2.28 for water of
moderate transparency following Koenings and Edmundson (1991), the
vertical attenuation coefficient \emph{K\textsubscript{d}} becomes 0.57
m\textsuperscript{--1}. Consequently, 50\% of the incident energy flux
density is absorbed in the first 1.2 m of water and 99\% over the first
8.1 m of water.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Figure 4: (a) Schematic of the thermistor chain (TC) components, (b)
TidBit temperature probes (HOBO TidBit UTBO-001, Onset, USA) installed
on the chains, and (c) the resolution of temperature measurements
presented on a logarithmic scale (in m).

\textbf{2.5 Energy Balance Ratio}

The energy balance ratio (Feng et al., 2016) allows us to quantify the
energy balance closure and therefore to correct underestimated turbulent
heat fluxes (see Sect. 3.3). It is defined as follows:

\(\text{EBR}=\frac{H+\text{LE}}{R_{n}-{H}_{S}}\ \times 100\)(3)

where \emph{R\textsubscript{n}} is the net radiation and
\selectlanguage{greek}Δ\selectlanguage{english}\emph{H\textsubscript{S}} is the heat storage variation along the water
column, defined as

\({H}_{S}=\ \int_{0}^{h}{\rho_{w}\ c_{\text{pw}}\ \frac{\overset{\overline{}}{{T}_{w}}}{t}\ \text{dh}}\)(4)

where \selectlanguage{greek}\emph{ρ\textsubscript{w}}\selectlanguage{english} is the water density (kg
m\textsuperscript{-3}), \emph{c\textsubscript{pw}} is the specific heat
of water (J kg\textsuperscript{-1} K\textsuperscript{-1}),
\selectlanguage{greek}Δ\selectlanguage{english}\emph{T\textsubscript{w}} is the water temperature difference between
two time steps (K), \selectlanguage{greek}Δ\selectlanguage{english}\emph{t} is the time period (30 min), and
\emph{h}is the water layer thickness (m). To determine the EBR,
\selectlanguage{greek}Δ\selectlanguage{english}\emph{H\textsubscript{S}} was calculated over the entire depth of the
epilimnion, which is the distance between the surface (0 m) and the
position of the thermocline (\emph{h} ). Note that the epilimnion
thickness varies over the year. On average, \emph{h} = 15 m from June to
October, \emph{h} = 30 m from November to December, and \emph{h} = 0 m
from January to May.

\textbf{2.6 Ice Cover}

Ice cover was monitored using a time-lapse camera (Reconyx, Holmen, WI,
USA) that took hourly photos of the southern edge of the reservoir.
Water temperatures were also used to identify the solar radiation
penetration into the water column and as such, ice formation, as ice and
snow cover reduce or prevent radiation from entering the water column.

Figure 5 illustrates the key phases of the reservoir regime. The
ice-free period (Fig. 5a) and the ice-cover period (Fig. 5c) are
separated by the onset (Fig. 5b) and break-up (Fig. 5d) of ice.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

Figure 5: Photographs (looking north) illustrating some key phases of
the reservoir regime: (a) open-water period (12 September 2018), (b)
start of freeze-up (23 December 2018), (c) full ice and snow cover (7
February 2019), and (d) ice breakup (23 May 2019).

\textbf{3. RESULTS \& DISCUSSION}

\textbf{3.1 Meteorological Conditions}

The overall meteorological conditions observed over the Romaine-2
reservoir were typical of a subarctic climate (Fig. 6), with cool and
humid summers along with cold and dry winters. Wind speed (\emph{WS} )
was generally quite high, particularly in the fall and winter when daily
averages occasionally reached 15 m s\textsuperscript{--1}, but showed a
marked decline in summer. The reservoir was mostly colder than the air
above it between May and July (the heat storage period). The vapour
pressure deficit (VPD) values were high from mid-spring to mid-autumn.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

Figure 6: Daily means of (a) 2-m air (\emph{T\textsubscript{a}} ) and
near-surface water temperatures (\emph{T\textsubscript{w}} ), (b) vapor
pressure deficit (VPD), and (c) wind speeds (\emph{WS} ) collected at
the raft and shore sites. The period with ice cover (shaded area) was
determined from time-lapse photos.

The distribution of the wind direction measured from the raft flux tower
followed a bimodal pattern, aligned along the SSW-NNE axis of the
reservoir. Wind measured from the reservoir at the shore flux tower
showed the same pattern. The 30-min mean wind speed was 5.6 m
s\textsuperscript{-1} while the maximum wind speed reached 19.4 m
s\textsuperscript{-1}.

\textbf{3.2 Heat Fluxes}

3.2.1 Daily Scale

Figure 7 illustrates the average diurnal cycles of \emph{H} and\emph{LE}
during ice cover (January to mid-May), the heat storage phase (mid-May
to August), and heat release (September to December). The last two
phases are defined based on the heat storage curve presented in Figure
13. The 70-m heat storage peaked in early September, marking a
transition from the storage period to the release period. In fact, it is
important to note that the storage and release phases of the reservoir
overlap during August, as heat release starts in early August while heat
storage continues to grow in the water column until early September.

During the ice cover periods, \emph{LE} remained low (\textless{} 20 W
m\textsuperscript{-2}) and positive, which is indicative of sublimation,
while \emph{H} was negative (\textless{} --10 W m\textsuperscript{-2}).
Both turbulent heat fluxes had diurnal cycles with an amplitude lower
than 10 W m\textsuperscript{-2}. The corresponding Bowen ratios were
small and negative when \emph{LE} was between 5 W
m\textsuperscript{-2}and 10 W m\textsuperscript{-2}. These results were
expected, as ice and snow covered the water surface from early January
until mid-May, suggesting low albedo and preventing the surface from
heating up enough to produce stronger turbulent heat fluxes.

From mid-May to August, \emph{LE} values remained low, with an average
of nearly 30 W m\textsuperscript{-2} and a maximum of up to 60 W
m\textsuperscript{-2} at 14:00. H then showed a clear diurnal cycle, at
-30 W m\textsuperscript{-2} at 15:00 and close to 0 W
m\textsuperscript{-2} at night. A value of -60 W
m\textsuperscript{-2}was reached in early afternoon. As a result, the
Bowen ratio also exhibited a diurnal cycle.

During the heat release phase (September to December), \emph{LE}remained
larger than \emph{H} at all times, meaning that energy was mainly
released through phase change (evaporation). One striking feature is
that \emph{LE} and \emph{H} had opposite daily patterns: (i)\emph{LE}
reached a maximum at around 15:00 while \emph{H} reached a minimum, and
(ii) \emph{LE} reached a minimum at 00:00 while \emph{H}peaked at 5:00.
\emph{LE} peaked in the afternoon when the incident solar radiation
reached its maximum value, warming up the water surface during the day.
Maximum \emph{H} values occurred at night, when the maximum water-air
temperature difference was observed. At a similar temporal scale, Nordbo
et al. (2011) observed fluxes over the small, boreal Lake Valkea-Kotinen
in Finland and showed that the highest values of \emph{LE} and \emph{H}
occurred in June, peaking at 15:00 and at 06:00 respectively. Therefore,
in this study, the Bowen ratio exhibited an explicit diurnal cycle. The
highest values were around 0.95 at night because of high \emph{H} and
low \emph{LE} values. The lowest values were around 0.40 in the day
because of low \emph{H} and high \emph{LE}values. As a result, heat was
released by two different mechanisms depending on the time of the day:
through both turbulent heat fluxes at night and mainly through
evaporation during the day. Overall, the sensible heat fluxes \emph{H}
contributed to the heat stored by the water body early in summer, that
will later be released as latent heat flux.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

Figure 7: Average diurnal cycle of (top) latent heat flux, (middle)
sensible heat flux, and (bottom) Bowen ratios, with the interquartile
(dark shading) and the 10 to 90 quantile zones (light shading). The left
column are data for January to mid-May (ice cover), the central column
covers mid-May to August (heat storage), and the right column covers
September to December (heat release). Note that the range of the
ordinate values varies from one plot to the other. All times are local.

Condensation episodes (\emph{LE} \textless{} 0 W m\textsuperscript{-2})
occurred occasionally throughout the study period. During winters, small
and short condensation episodes occurred almost every day. However,
during the vernal turnover, conditions became very stable and the
atmosphere was much warmer than the water surface, which was nearly
constant at 4\selectlanguage{ngerman}°C. Consequently, only a few condensation events were
recorded between 1 May and 17 July, with cumulative amounts of 2.2 mm,
0.6 mm and 3.4 mm in 2019, 2020 and 2021, respectively. Figure 8
presents examples of condensation events that occurred in June,
temporarily reaching --10 W m\selectlanguage{english}\textsuperscript{-2} or 0.35 mm
day\selectlanguage{english}\textsuperscript{-1}.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

Figure 8: Daily mean latent heat flux for 2019 (light blue), 2020
(purple) and 2021 (blue), illustrating the occurrence of condensation
episodes between 13 and 30 June.

The reservoir was exposed to many episodes of sustained evaporation,
defined as consecutive 24-h periods with a daily mean \emph{LE} [?] 100 W
m\textsuperscript{-2} (i.e., daily mean \emph{LE} [?] 3.5 mm), ranging
from one to several days. Of those, the most modest episode caused 3.5
mm of evaporation in one day (obviously), while the largest episode
caused 29.3 mm of evaporation in 6 days ([?]5 mm
day\textsuperscript{--1}). Figure 9 presents the number of sustained
evaporation events for each month and their durations. Most events were
of short duration but had high evaporation rates: 80\% of events lasted
2 days or less. The mean rate of evaporation was 0.2 mm
h\textsuperscript{--1} for all events. As a comparison, Blanken et al.
(2011) reported that most of the evaporation from Lake Superior occurred
in 2.5- to 3-day episodic pulses.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

Figure 9: Sustained evaporation events, defined as consecutive days with
at least 3.5 mm of daily evaporation. (a) Number of occurrences per
month: A (August), S (September), O (October), N (November), D
(December); and (b) number of occurrences for different durations.

Figure 10 presents several variable time series during two strong
evaporative events. These episodes occur when air becomes drier (decline
of at least 50\% of the specific humidity) in conjunction with high wind
speeds. This may be due to the passage of a low pressure system (Figure
10, left) or a high pressure system (Figure 10, right).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image10/image10}

\end{center}
\end{figure}

Figure 10: Three sustained evaporation episodes (left, 1-day and 5-day
episodes in September 2018, and right, 2-day episode in August 2020)
with 30-min time series of (a, b) latent heat fluxes, (c, d) specific
humidity, (e, f) wind speed, (g, h) atmospheric pressure, and (i, j)
vapor pressure deficit. Shaded zones indicate high evaporation events.

3.2.2 Monthly Scale

Figure 11 displays monthly averaged turbulent heat fluxes over the whole
study period. Latent heat fluxes always remained positive despite some
condensation events in June (Sect. 3.2.1). \emph{LE} peaked in
September, when the heat storage reached its maximum (Fig. 13). It
remained above 70 W m\textsuperscript{-2} from August to
October.\emph{LE} began to rise in July when stratification in the
reservoir set in. It then sharply increased in August all the way to
December, during which 84\% of the annual evaporation occurred. This is
consistent with the findings from Blanken et al. (2011) for Lake
Superior, where 89\% of the annual evaporation occurred when there was
unstable atmospheric stratification. It is also consistent with the
Rouse et al. (2003) study at Great Slave Lake, where 85\% to 90\% of
evaporation occurred during a period when the atmosphere was unstable.
However, in our study,\emph{LE} decreased gradually due to the declining
vapour pressure deficit that followed the decline in air temperature. In
winter and spring, \emph{LE} stayed below 20 W m\textsuperscript{-2} and
reached its minimum in June, during the ice-free period (Fig. 6).

Sensible heat fluxes were negative from February to July, with values
less than -10 W m\textsuperscript{-2} and reaching as low as -20 W
m\textsuperscript{-2} when the reservoir was colder than the air. On
average, values remained positive from August to January. In June, the
reservoir was ice-free while the water column was under vernal
transition, with upper layers that were not warm enough to stratify
(i.e., below 3.98\selectlanguage{ngerman}°C, the temperature of maximum water density). The
water surface temperature stayed far below the air temperature,
preventing \emph{H} from becoming positive and enabling \emph{LE} to
become negative. Despite the high net radiation term around the summer
solstice, the heat content of the water body only slowly rose because of
the high specific heat and density of water. In summer and fall, the
surface layers were warmer than the air above the water.
\emph{H}increased steadily until December, reaching 80 W
m\selectlanguage{english}\textsuperscript{-2}, and then decreased abruptly in January as the
water surface froze. From May to August, net radiation
(\emph{R\textsubscript{n}} ) was high, contributing mostly to the
storage of heat in the reservoir (\selectlanguage{greek}Δ\selectlanguage{english}\emph{H\textsubscript{S}} ), while
turbulent heat fluxes were relatively low. Nearly all the energy brought
in by\emph{R\textsubscript{n}} was used to increase the heat storage
term. During the fall and early winter, \emph{R\textsubscript{n}}
declined rapidly while \emph{LE} and \emph{H} increased, fuelled by the
energy stored in the reservoir, firmly establishing the heat release
period of the reservoir. We observed a three-month delay between the
maximum summer net radiation that occurred in June and the maximum
latent heat flux. The delay was six months between the peak net
radiation and the maximum sensible heat flux. We also observed different
delays between the maximum surface water temperature and the maximum
\emph{LE} and\emph{H} , which were delayed by one and four months,
respectively.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image11/image11}

\end{center}
\end{figure}

Figure 11: (a) Monthly sensible heat flux (red), latent heat flux (blue)
and net radiation (black) from June 2018 to December 2021. Bars indicate
monthly minimum and maximum average values. (b) Monthly Bowen ratio. The
error bars indicate the maximum and minimum values observed for each
month.

The Bowen ratios exhibited high negative values during the first seven
months of each year due to low \emph{LE} values. After the onset of the
heat release period (end of July), it stayed around zero before
gradually increasing to about 1.5 in December. This indicates that the
reservoir was mostly releasing heat through sensible heat flux, as
evaporation was constrained by the small vapour pressure deficit induced
by the cold air temperatures.

The energy state of the reservoir is closely tied to the stability
regime of the overlying atmosphere. During heat release (August to early
January), the overlying atmosphere was unstable, while it remained
mostly stable during the heat storage (mid-May to August) and ice-cover
periods. Figure 12 explores the relationship between daily \emph{LE} and
atmospheric stability \selectlanguage{greek}\emph{ζ} \selectlanguage{english}for heat storage and release. The figure
confirms that larger daily evaporation occurs under near-neutral
(\selectlanguage{greek}\emph{ζ} \selectlanguage{english}[?] \selectlanguage{english}0) and unstable conditions (\selectlanguage{greek}\emph{ζ} \selectlanguage{english}\textless{} 0), and
that stable conditions (\selectlanguage{greek}\emph{ζ} \selectlanguage{english}\textgreater{} 0) are related to low
evaporation rates. Note that condensation occurred primarily under
near-neutral and stable conditions.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image12/image12}

\end{center}
\end{figure}

Figure 12: Daily latent heat flux as a function of atmospheric stability
(\selectlanguage{greek}\emph{ζ}\selectlanguage{english}=\(\frac{z}{L_{\text{Ob}}}\) where z is the measured height
and\emph{L\textsubscript{Ob}} refers to the Obukhov length) for the
ice-free periods (15 May to 31 December) from 2018 to 2021.

Figure 13 presents the 2018, 2020 and 2021 cumulative heat storage
\selectlanguage{greek}Δ\selectlanguage{english}\emph{H\textsubscript{S}} calculated over the 70-m water column. Heat
storage started in spring and ended in early September (a 3.5-month
period), with maximum values of 2000 MJ m\textsuperscript{-2} for 2018
and 2021 and 1700 MJ m\textsuperscript{-2} for 2020. Heat release
followed and lasted about 4 months until ice-on. The heat release rate
was lower from September to mid-November compared to mid-November to the
end of December: 13 MJ m\textsuperscript{-2}
day\textsuperscript{-1}compared to 21.7 MJ m\textsuperscript{-2}
day\textsuperscript{-1} for 2018. Overall, heat storage exhibited larger
day-to-day fluctuations than heat release.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image13/image13}

\end{center}
\end{figure}

Figure 13: Cumulative heat storage in the upper 70 m of the water column
for years 2018, 2020 and 2021. There are no data shown for 2019 due to a
major thermistor chain malfunction. Calculations start from 24 June as
no data were recorded before this date for 2018 and 2020. For the
purposes of the figure, to create a reference point based on our data
availability, we set the annual cumulative heat storage at the end of
the year to zero (\selectlanguage{greek}Δ\selectlanguage{english}\emph{H\textsubscript{S}} = 0 MJ
m\textsuperscript{-2}).

Note that Romaine-2 experienced a sharp drop in heat storage in
September 2020. This is linked to the approximately 10 m decline in
water level in August and September. Indeed, the epilimnion moved closer
to the water intake and therefore the accumulated heat within the top
layers was drained out as turbine flow. The year 2020 was therefore
unusual in terms of heat storage.

When looking at the monthly layer energy balance of the reservoir using
equation 3, we noted that there was a significant non-closure. This is
due to the time scale difference between the heat storage in the water
column and the remaining terms (turbulent heat fluxes and net
radiation). Indeed, due to the high thermal inertia and the high
specific heat of water, the net radiation that was received in summer
accumulated in the water column and was only released in autumn. This
feature makes it difficult to calculate the EBR on a monthly scale.
Within this context, correcting turbulent heat fluxes to account for the
energy imbalance (Foken, 2008) using the monthly EBR is problematic,
unless accurate measurements of lateral energy inputs are available
(sect. 3.3).

3.2.3 Annual Scale

Calculating annual reservoir evaporation values is challenging. It is
well understood that eddy covariance data underestimate turbulent heat
fluxes (Foken, 2008), and in addition, the calculation of the heat
storage term is especially difficult for a deep water column. For this
reason, an alternative approach was used: the corrected turbulent heat
fluxes were obtained by redistributing the missing energy according to
the annual EBR over a so-called ''energy year,'' from March 1 to
February 28 of the next year. Since energy storage is typically at its
minimum value at this time of year, this allowed us to discard that
variable and make \emph{R\textsubscript{n}} = \emph{H} +\emph{LE} .
Since\emph{R\textsubscript{n}} \textgreater{} \emph{H} + \emph{LE} , the
missing energy can then be redistributed by preserving the observed
Bowen ratio, as discussed in Mauder et al. (2018). By doing so, the EBR
was 80\%, 69\%, and 76\% for the years 2019-20, 2020-21, and 2021-22,
respectively.

Figure 14 illustrates the yearly cumulative evaporation for three energy
years, from 2019 to 2022. The mean annual non-corrected evaporation was
439 \selectlanguage{ngerman}± 23 mm and did not vary much from year to year. When correcting for
the energy imbalance using the annual EBR values, the annual evaporation
values reached 555 mm, 656 mm and 559 mm for 2019\selectlanguage{english}-20, 2020\selectlanguage{english}-21 and
2021\selectlanguage{english}-22, respectively (refer to Table 1). Note that the inter-annual
variabilities of cumulative evaporation were 7.2\% and 18\% for
non-corrected and corrected values, respectively. In fact, 50\% of the
total measured evaporation occurred over 24\%, 27\% and 26\% of the days
for 2019\selectlanguage{english}-20, 2020\selectlanguage{english}-21 and 2021\selectlanguage{english}-22, respectively. This is consistent with
Blanken et al. (2000), who found a mean value of 22.5\% for the Great
Slave Lake.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image14/image14}

\end{center}
\end{figure}

Figure 14: Cumulative annual evaporation from 1 March to 28/29 February
of the following year, for 2019-20, 2020-21 and 2021-22. Pale green,
red, blue and grey bars represent the duration of the respective ice
cover periods. Horizontal bars at the end of the energy period represent
corrected annual evaporation, compensating for the lack of closure of
the energy balance based on the annual EBR (see Table 1).

Few studies have focused on annual scales of lake or reservoir
evaporation in the boreal biome. In Canada, Strachan et al. (2016)
reported that the evaporation rate at the Eastmain-1 reservoir was 595
mm yr\textsuperscript{--1}, reaching 100 mm month\textsuperscript{--1}in
summer and 3.1~mm d\textsuperscript{--1} from August to October. Rouse
et al. (2003) found the annual evaporation at Great Slave Lake to be
between 384 mm and 506 mm yr\textsuperscript{-1} and daily evaporation
ranged from 2 mm d\textsuperscript{--1} in summer to 5 mm
d\textsuperscript{--1} in December. For Lake T\selectlanguage{ngerman}ämnaren in Sweden,
Heikinheimo et al. (1999) reported 281 mm of evaporation from May to
October. Finally, Blanken et al. (2011) found the annual evaporation at
Lake Superior to be up to 645 mm. However, it is important to note that
these studies were all based on eddy-covariance measurements and did not
take into consideration the non-closure of the energy balance, meaning
that they did not correct for cumulative evaporation values. This
appears to be one major shortcoming in the annual estimation of
turbulent heat fluxes.

Table 1 presents important meteorological characteristics for each year
of the study period. Note that 2020 experienced the lowest turbine
volume in the study, probably due to the upstream flooding of the
Romaine-4 reservoir, which might explain the slightly higher
evaporation. The highest temperature anomaly by a fair margin occurred
in 2021, while wind speed anomalies remained low and constant throughout
the study period.

Table 1: Annual characteristics from 2018 to 2021. Non-corrected and
corrected total of evaporation, ice cover period, turbine outflow
volume, temperature and wind speed anomalies compared to 1991\selectlanguage{english}-2020 (ERA5
values) and total net radiation.\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
Years & 2018 - 19 & 2019 - 20 & 2020 - 21 & 2021 - 22\tabularnewline
\midrule
\endhead
Non-corrected total evaporation (mm) & - & 446 & 456 &
423\tabularnewline
Corrected annual evaporation (mm) see Sect. 3.3 & - & 555 & 656 &
559\tabularnewline
Ice cover period (days) & - & 145 & 133 & 119\tabularnewline
Turbine outflow volume (km\textsuperscript{3}) & 6.1 & 7.4 & 5.6 &
8.5\tabularnewline
Temperature anomaly (\selectlanguage{ngerman}°C) & -0.4 & -0.4 & +0.7 & +3.5\tabularnewline
Wind speed anomaly (m s\textsuperscript{-1}) & +0.01 & +0.2 & +0.03 &
+0.03\tabularnewline
Total net radiation (MJ m\textsuperscript{-2}) & - & 1844 & 2046 &
1970\tabularnewline
\bottomrule
\end{longtable}

When examining the inter-annual variation of cumulative evaporation, we
noted that the seasonal onset and the break-up of ice cover did not have
a large impact on total yearly evaporative losses. The longer ice cover
period in 2019 (145 days) than that of 2020 (133 days) resulted in lower
cumulative evaporation. This trend is not repeated in 2021, which
featured the shortest ice cover period (119 days) and lower cumulative
evaporation compared to 2020 (Fig. 14). We also noted that the timing of
ice onset was very consistent, as it began around January 1 of each
year, while ice break-up was more variable between years. As for
duration, the onset of ice lasted between two and three weeks while ice
break-up lasted five to seven weeks prior to the reservoir becoming
completely ice-free.

\textbf{3.3 Uncertainties}

There are uncertainties that affected the EC measurements that were used
in this study. Random sampling uncertainties were calculated following
Finkelstein and Sims (2001) and amounted to [?] 2\% for both sensible and
latent heat fluxes over the whole study period. In addition, the error
associated with gap-filling was noteworthy for \emph{H} , \emph{LE} and
Rn because of the difficulty of measuring fluxes over an inland water
body. The use of a raft results in oscillations that must be considered
in the calculation process, while the use of a flux tower on the shore
limits the measurement period over the reservoir.

EC measurements were also subject to underestimations linked to the lack
of energy balance closure (Foken, 2008), which is best described in
terms of the energy balance ratio (EBR, equation 3). Figure 15
illustrates the monthly EBR values in the reservoir for 2019 to 2021.
This confirms that the energy budget layer was subject to non-closure.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image15/image15}

\end{center}
\end{figure}

Figure 15: Monthly EBR from March 2019 to December 2021. Note that \selectlanguage{greek}Δ\selectlanguage{english}HS
were calculated over a 15-m depth except for November and December 2020
and 2021, for which it was calculated for an h of 30-m and 44-m depths
respectively.

Some uncertainties lie in the evaluation of \selectlanguage{greek}Δ\selectlanguage{english}\emph{H\textsubscript{S}} .
The monthly EBR was calculated using a \selectlanguage{greek}Δ\selectlanguage{english}\emph{H\textsubscript{S}} for
depths of 0-15 m, 0-30 m or 0-44 m, which correspond to the average
depths of the thermocline for January to October, November and December,
respectively. The water between the surface and these depths represent
good approximations of heat storage in the water column. This is because
the thermal mixing is spatially constrained by the thermocline. However,
there is uncertainty in estimating these thermocline depths, which may
lead to errors in the evaluation of \selectlanguage{greek}Δ\selectlanguage{english}\emph{H\textsubscript{S}} .

Note that for 2019, there were no data for depths below 15 m. When we
calculated \selectlanguage{greek}Δ\selectlanguage{english}\emph{H\textsubscript{S}} for a 30-m and a 44-m depth, the
EBR for November and December 2020 was 101\% and 138\% respectively.
This was less that the 150\% and 440\% calculated for the water between
the surface and 15-m depth.

\textbf{4. CONCLUSION}

This study quantified the temporal dynamics of evaporation over a deep,
boreal, dimictic hydroelectric reservoir using two eddy-covariance
setups, one mounted on a raft and one onshore. Data were collected for
four years, from June 2018 to June 2022, in order to examine the daily,
monthly and annual patterns of the turbulent heat fluxes.

Turbulent heat fluxes revealed opposite diurnal cycles of \emph{H}
and\emph{LE} during heat storage and heat release periods, and the
absence of a diurnal pattern during the rest of the year. \emph{LE}
reached its maximum at 15:00 when \emph{H} reached its minimum, and
\emph{LE} was minimal at night at 00:00 while \emph{H} peaked at 05:00
in the morning. Our monthly analysis showed that most of the latent and
sensible heat fluxes occurred from August to December. The cumulative
latent heat flux amounted to 84\% of the annual evaporation. Three- and
six-month delays occurred between maximum summer net radiation and
maximum values of\emph{LE} and \emph{H} , respectively, suggesting the
impact of the heat storage release. Moreover, one- and four-month delays
were observed between the maximum surface water temperature and maximum
\emph{LE} and\emph{H} , respectively.

Results showed an annual evaporation of 590 \selectlanguage{ngerman}± 66 mm
yr\textsuperscript{--1} that was quite constant from year to year, with
frequent 1-day to 2-day sustained events. Latent heat flux increased
earlier than the sensible heat flux but also decreased before the
sensible heat flux, resulting in a Bowen ratio that varied from a
near-zero negative value in July to 1.5 in December. Vapour
pressure-controlled evaporation induced a steady decline from September
to December due to decreasing air temperature.

The large time lag and the magnitude of the energy storage within the
water column made it difficult to close the energy balance. Therefore,
in this study, we have taken that issue into account by correcting the
annual cumulative evaporation while preserving of the measured Bowen
ratio.

Moreover, monthly and seasonal patterns of evaporation can be related to
the energy state of the reservoir. Indeed, depending on the time of
year, the reservoir was either under ice cover or in heat storage or
heat release conditions, which drives the magnitude of evaporation.

Results clearly illustrate that water loss through evaporation has a low
impact on hydroelectricity production and water availability downstream.
However, because evaporation is likely to increase in the region due to
climate change, the assessment of this energy and the associated
hydraulic components remains topical and essential to understanding
future trends.

\textbf{ACKNOWLEDGEMENTS}

The authors would like to acknowledge Hydro-Québec for their
collaboration, and more specifically François Bilodeau. They are also
grateful to Annie-Claude Parent, Dany Crépault, Denis Jobin, Jaril
Deschamps, Philippe Richard, Benjamin Bouchard, Habiba Kallel, Alexis
Trottier-Paquet, and Gonzalo Leonardini Quelca for their help in
field-related activities. This research was funded by the Natural
Sciences and Engineering Research Council of Canada (NSERC) through
grant RDCPJ508080-16 titled, ``Observation and modelling of net
evaporation from a boreal hydroelectric complex (water footprint)''.

\textbf{DATA AVAILABILITY:} Data available upon request.

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