1. Introduction
Lakes and reservoirs have significantly different radiative and thermal properties than the surrounding land surfaces (Subin et al. 2012). Their energy balance modulates their impact on the local climate. For example, the ability of reservoirs to store net radiation delays the release of heat to the atmosphere (Leppäranta et al. 2016; Schmid and Read 2022). The energy balance also controls the surface temperature of the reservoirs and thus the sensible and latent heat fluxes (Blanken et al. 2011; Momii and Ito 2008). The energy balance also determines the onset/disappearance of ice cover (Cheng et al. 2021; Leppäranta et al. 2019), with direct consequences on the surface albedo (Kirillin et al. 2012) and the rate of greenhouse gas emissions (Denfeld et al. 2018; Jammet et al. 2015). Several studies have attempted to integrate the effects of open water bodies into regional and global climate models, focusing on moisture, heat, and momentum fluxes (MacKay 2012; MacKay et al. 2009; Nazemi and Wheater 2015). However, the contribution of advective fluxes (Rodríguez-Rodríguez and Moreno-Ostos 2006), which remains a fundamental aspect in the study of water bodies mass and energy balances, is often neglected due to the lack of direct measurements. Yet, some studies have confirmed the need to consider these terms in regional climate modeling. Almeida et al. (2022) stated that it is critical to adequately model lateral heat and mass inputs/outputs to reservoirs, as well as water levels for the benefit of climate modeling.
Hydropower reservoirs differ from lakes in that their water level and residence time are largely controlled by human intervention over the course of the year. As a result, their thermal regime can also differ substantially from that of a natural lake. For example, fluctuations in reservoir temperature profiles can be triggered by internal currents resulting from turbine operation, thereby attenuating thermal stratification (Çalışkan and Elçi 2009; Olsson 2022). In addition, large water level fluctuations can induce shoreline transformation and erosion, which increase turbidity (Dirnberger and Weinberger 2005), reduce light penetration, strengthen stratification, and ultimately enhance heat exchanges with the atmosphere (Heiskanen et al. 2015; Saros et al. 2016). Depending on geographic location, regional climate, and hydroelectric demand, reservoirs have specific characteristics that affect their thermal energy and water balances. At mid- and high latitudes, ice and snow cover reservoirs and their watersheds for several months of the year, reducing inflows from shoreline hillslopes, as well as suppressing heat exchanges with the atmosphere. High winter energy demand from human activities, especially for home heating, requires substantial water release, which in turn lowers reservoir levels. During the spring freshet, reservoir inflows increase, sharply raising water levels. The management of reservoirs alters the seasonality of streamflow, which sets them apart from lakes. Moreover, such water inflows and outflows can represent a significant contribution to the reservoir’s energy balance, and thus affect their interactions with the atmosphere. Studies on energy balance of water bodies have been conducted in various regions of the world including high latitudes (Leppäranta et al. 2016; Ragotzkie and Likens 1964), tropical and equatorial regions (MacIntyre et al. 2014; Vallet-Coulomb et al. 2001), and high altitudes (Rodríguez‐Rodríguez et al. 2004), but almost exclusively on lakes and rarely on reservoirs.
Net advective fluxes are driven by heat carried by net water flows, which, in the case of a cascade of reservoirs, include upstream inflows (natural or turbined/discharged) and downstream outflows (through spillways and turbines). From a thermodynamic point of view, to obtain the net advection flux, we need to take the sum of the products of the inflows/outflow and the associated water temperatures (Han and Wright 2022; Venkateshan 2021). Therefore, it is impossible to consider the energy balance of a reservoir without including a water balance. In the absence of direct measurements, lateral contributions are estimated using proxies or empirical relationships. For example, to estimate lateral inputs, several studies have relied on relationships with atmospheric predictors such as mean sea level pressure, air and dewpoint temperatures, and wind speed (George et al. 2019), precipitation, and soil moisture (Long et al. 2019), or multiple linear regression models with wavelet and bootstrap techniques (Bashir et al. 2019). Some rare studies have quantified lake inflows and outflows using direct measurements (Leach et al. 2021), but, to the best of our knowledge, this is rare for a reservoir, in part because turbine flow data are often undisclosed by operators. As a result, studies are typically conducted on a one-dimensional basis, neglecting lateral inflows and energy fluxes (e.g., Elo 2007; Momii and Ito 2008; Kallel et al. 2024). Conducting a full water balance of a hydropower reservoir can help quantify and verify the importance of advection terms in the thermal energy balance, particularly when compared to surface turbulent heat fluxes (Xing et al. 2012). In one of the only studies that have considered lateral inputs, Moreno-Ostos et al. (2008) showed that the thermal dynamics of the Sau reservoir in Spain (mean depth of 25 m) were controlled by the advection fluxes induced by water management. Xing et al. (2012) showed that inflow advective heat fluxes of a shallow tropical reservoir were a critical component of the heat budget, with a magnitude equivalent to 71% of the net radiation budget. On the other end, Winter et al. (2003) highlighted that energy advected by precipitation and streams into Mirror Lake (a 49-ha lake in New Hampshire) had little effect on the measured evaporation rates.
The annual heat budgets of water bodies (mostly lakes) were initially measured using simple instruments such as evaporation pans, resistance thermometers, and pyrheliometers (Juday 1940; Saur and Anderson 1956). As a result, early analyses were subject to considerable uncertainties that often led to misinterpretations. More recently, flux (eddy covariance) towers have improved our understanding of the thermal energy balance of water bodies (Metzger et al. 2018; Nordbo et al. 2011; Wilson et al. 2002). Thus, using net radiometers and eddy covariance instruments is now standard practice for measuring surface heat fluxes (Blanken et al. 2000; Rouse et al. 2003, 2005). However, assessing the thermal energy balance of a water body remains complex. First, eddy-covariance-based fluxes suffer from edge effects when taken from the shore—some studies have circumvented this issue by using rafts to deploy instruments on water (Spank et al. 2020; Spence et al. 2003). Second, the oscillations of the measurement system associated with raft motions caused by waves contaminate the recorded data. This can be corrected by using the raft motion data obtained with an accelerometer (Miller et al. 2008; Pierre et al. 2023). Finally, the footprint of the turbulent heat flux measurement tends to differ from that of the other energy balance terms, preventing the thermal energy balance from closing (Pierre et al. 2022).
Studies on the energy balance of deep cascade reservoirs in northern environments are still lacking, and the goal of this paper is to fill this gap through the assessment of (i) the hydrological and thermal energy balances of a midlatitude hydroelectric reservoir at monthly and annual scales, including a thermal regime analysis, characterized by two mixing periods and two stratification periods; (ii) the closure of the energy balance, using direct measurements of the majority of the terms, identifying the dominant processes and the main sources of uncertainty; and (iii) the effect of reservoir management (advective fluxes, water levels) on the thermal regime.
2. Methods
a. Research site
The research site is located at the southern end of the Romaine-2 hydropower reservoir (50.68°N, 63.25°W) in eastern Quebec, Canada [see Fig. 1 in Pierre et al. (2023)], and is characterized by a subarctic Dfc climate (Beck et al. 2018). The 640-MW hydropower reservoir is operated by Hydro-Québec, the provincial government–owned power utility. It is part of the La Romaine hydroelectric complex, which consists of four cascade reservoirs (from Romaine-4 upstream to Romaine-1 downstream) with a full power capacity of 1550 MW (Hydro-Québec 2007). Each reservoir includes a penstock that delivers water to the hydropower plant and a spillway. The Romaine-2 and Romaine-3 penstocks are located at depths of 40 and 35 m, respectively. The inflows into the Romaine-2 reservoir include the upstream inflow of the Romaine-3 reservoir outflow, the lateral inflow consisting of three rivers (Bernard, L’Abbé-Huard, and Mista) and more than 60 small tributaries. The Romaine-2 reservoir discharges into the Romaine-1 reservoir via the Romaine River.
The Romaine-2 and Romaine-3 reservoirs were flooded in 2014 and 2017, respectively. The Romaine-2 reservoir has a maximum surface area of 85.6 km2, with a mean depth of 44 m, and a maximum depth of 101 m (Fig. 1). It is typically ice-free from May to December, with a mean annual water level fluctuation of 14 m. The catchment area upstream of Romaine-2 reservoir has a surface area of 9987 km2, which represents 70% of the total catchment area of the Romaine River. More details about the study site can be found in Pierre et al. (2022). The study period extended from 27 June 2018 to 31 December 2022.
(a) Location of the southern end of Romaine-2 reservoir [blue and brown isolines represent bathymetry (m) and topography (m MSL), respectively]. (b) Southern edge of the Romaine-2 reservoir with the locations of the experimental setup. (c) Overview of the entire Romaine-2 reservoir with bathymetry in blue and topography in other colors; the black rectangle indicates the area represented in (a). TC refers to the thermistor chains.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0149.1
b. Energy budget
1) Turbulent heat fluxes
An accelerometer [attitude and heading reference system (AHRS); Lord Sensing MicroStrain, United States] installed near the IRGASON recorded raft oscillations by capturing all linear acceleration components, angular velocities and the three Euler angles at a frequency of 10 Hz. Raw data were corrected following Miller et al. (2008). Then, the data were processed using EddyPro (R) software, version 7.0 (LI-COR Biosciences, United States). Flux time series of the raft and shore stations were subsequently merged according to the best quality criteria of Mauder et al. (2013). More details on the EC data processing can be found in Pierre et al. (2023). Overall, 43% of the turbulent heat flux data had to be gap filled: most of the missing fluxes were in winter, when raft data were not available. The dataset was gap filled using a marginal distribution sampling approach (Reichstein et al. 2005).
2) Net radiation
3) Thermal regime
(i) Water temperature
Temperature profiles were measured using two thermistor chains (HOBO TidBit UTBI-001, Onset, United States; Fig. 1a), providing high-resolution data near the surface and lower resolution data at greater depths. More precisely, sensors were spaced 0.2 m apart from the surface to 1 m deep, 0.4 m from 1 to 3 m, 1 m from 3 to 10 m, 2.5 m from 10 to 32.5 m, 8.5 m from 32.5 to 40 m, and 10 m from 40 to 70 m. The first chain, TC1 (Fig. 1), was 15 m long and was deployed in a 30-m-deep zone of the reservoir between two islands. The second chain, TC2 (Fig. 1), was 70 m-long and was deployed in a 100-m-deep area of the reservoir, 1 km south of TC1. The chains were deployed to withstand water level fluctuations. The surface temperature sensors were shielded from solar radiation by a piece of white polystyrene floating on the surface. The observations from the two thermistor chains were averaged for each measurement level to produce a single dataset. Pressure sensors (HOBO water level logger u20-001-03, Onset, Canada) were attached to the chains to confirm that they remained vertical and that the sensors were at their nominal depth. To monitor the presence of the ice cover, time-lapse images of Romaine-2 were also taken on an hourly basis using automated cameras (Reconyx HP2X, United States).
We removed the data when the chain was not vertical or when suspicious temperature spikes were observed. Spikes were defined as a temperature difference of more than 5°C over a two-day period or a difference of more than 2°C over a 12-h period. Then, gaps were filled with several techniques applied in the following order: (i) water surface temperature was derived from linear regression with lower sensors, (ii) water temperature were derived from a linear regression with temperature above and below target, (iii) remaining missing data were filled with yearly mean temperature to which a linear detrending was applied to ensure reconnection with measurements at both ends of the gap, and (iv) remaining missing data were filled with linear interpolation.
Water transparency was measured with a Secchi disk twice a year, usually in June or August and in October, under sunny conditions and in presence of a smooth water surface. The mean Secchi depth (SD) was 4 ± 0.04 m and was used to assess the vertical attenuation coefficient of light (Kd). According to Koenings and Edmundson (1991), the suggested SD × Kd value for water of moderate transparency is 2.28, leading to an approximate Kd value for the Romaine-2 reservoir of 0.57 m−1. As a result, 50% of the absorption of incident solar radiation took place in the first 1.2 m of the water column, while the aphotic zone, defined as the region where solar radiation penetration is only 1% or less, began at a depth of 8.1 m.
The following thermal phases were identified and characterized in terms of duration and timing: the vernal and fall turnovers, the reverse winter stratification, and the summer stratification. Summer stratification was divided into two subperiods, that is the epilimnion growth phases from 0 to 15 m and from 15 m to the start of the fall turnover period. Phase identification was performed using the mean daily temperature profile. For example, the onset of mixing periods (i.e., vernal and fall turnovers) coincided with the homogenization of the temperature from top to bottom, while the onsets of summer and reverse stratifications were detected by slope changes in the vertical water temperature profile.
(ii) Heat storage
(iii) Thermocline characteristics
A key feature of a reservoir’s thermal regime is the position of its thermocline. The metalimnion, the classic thermocline of Birge (1897), corresponds to a range of depths where a rapid decline in temperature occurs. It separates two regions of nearly homogeneous temperatures, the epilimnion (Te) and hypolimnion (Th), respectively. Hence the metalimnion is bounded by upper (he) and lower (hh) depths and has a thickness defined by Δz = hh − he, a temperature amplitude (ΔTw) and a mean temperature gradient (ΔTw/Δz) (see Fig. 2). The thermocline lies within this zone and is defined as the water depth ht (m) at which the maximum change in temperature occurs. Its temperature is Tt. The transition depths he and hh are characterized by radii of curvature that indicate the transition from one layer to another. A simple algorithm was implemented to determine he and hh. We iteratively compared the mean temperature of progressively thicker layers (from the surface/bottom) with the temperature of the next sensor until we encountered a difference greater than 0.5 K, at which point the depth was identified as either the beginning or the end of the metalimnion. Moreover, if the temperature amplitude ΔTw was less than 1 K, we considered that there is no thermocline. Finally, ht and Tt were calculated as the mean of he and hh, and Te and Th, respectively, assuming that the temperature gradient was constant across the thickness of the metalimnion. The uncertainty associated with he, hh, and ht was estimated to be ±2 m.
Schematic of a vertically stratified temperature profile (blue line) showing the thermocline (red line) depth ht (m), the metalimnion thickness Δz = hh − he (m), and the temperature amplitude ΔTw (°C), as well as the epilimnion and hypolimnion zones. The term he is defined as the depth of the intersection between the temperature lines of the epilimnion and the metalimnion, and hh is defined as the depth of the intersection between the metalimnion and hypolimnion. The green arcs represent the radii of curvature delineating the beginning and end of the metalimnion.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0149.1
4) Heat budget
Schematic of (a) the water balance, where VP is the precipitation, Ve is the volume of evaporation, ΔV is the internal volume change,
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0149.1
A thermal year from 1 March to 28 February was used to calculate heat budgets, as it was at this time of the year where the cumulative change in heat storage approached zero. Three thermal years were used in this study: 2019/20, 2020/21, and 2021/22. Note that, the reservoir water level was slightly different between the beginning and the end of each thermal year. Additional or reduced volumes were accounted for in the heat budget calculations, to ensure budget closure. The temperature chosen for these volumes was that of the lateral inflow. Table 1 presents ΔV and the corresponding heat storage term for each thermal year.
Internal volume and heat storage changes for each thermal year of the study period. The Δh and ΔV values represent the difference between the last day and the first day of the periods under consideration.
c. Water budget
Daily ΔV was obtained by multiplying daily reservoir area, taking from the storage curve, by the daily water level change Δh that was measured with a constant flow bubble gauge (Sutron Accubar dual orifice, Virginia, United States). Finally, the natural tributary inflow volume (
3. Results and discussion
a. Hydropower and meteorological conditions
Figure 4 shows a subset of the meteorological variables recorded at the southern edge of the Romaine-2 reservoir. Summers were more humid but less windy than winters [wind speed (WS) up to 15 m s−1]. Mean daily net radiation peaked in June at about 300 W m−2 and reached a minimum of −80 W m−2 in December. Ice breakup occurred during a period of rapidly increasing radiation, which greatly accelerated thawing. Precipitation varied slightly from year to year (1008, 1153, 1339, and 1151 mm in 2019, 2020, 2021, and 2022, respectively).
Daily means of (a) WS, (b) Rn, (c) Ta, (d) RH collected at the raft and shore sites, and (e) P observed at the shore station and recorded at the nearest weather station. Shaded areas indicate the ice cover periods, which were identified using time-lapse photos of the southern end of the reservoir surface.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0149.1
b. Water budget
Throughout the study period (2018–22), hydropower generation involved large water level drops, up to 17 m in winter and 2 m during the ice-free period (Fig. 5a), resulting in a smaller surface area during these seasons. Romaine-2 and Romaine-3 reservoirs turbine flow rates also fluctuated throughout the year, with peaks in winter when energy demand was high and during the freshet to avoid spillage (Figs. 5b,c). During the ice-free period (May–December), the mean turbine flow rate out of the Romaine-2 reservoir was 220 m3 s−1, while the mean flow rate out of Romaine-3 (and into Romaine-2) was only 140 m3 s−1, hence the gradual decline in the Romaine-2 water level during that period. The spillway flow is not represented in Fig. 5 as it remained close to zero most of the year except in spring when it was used to release excess spring freshet water.
Romaine-2 daily (a) water levels and (b) turbine outflow rate Qo (m3 s−1), and (c) Romaine-3 reservoir turbine flow rate
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0149.1
In general, the water level variation in the reservoir was cyclical, that is, the maximum level of 100 m was reached in mid-June, followed by slight fluctuations around 98 m until the end of December; then, a significant decline of 3 m per month occurred from January to mid-April, leading to an average minimum level of 89 m. The average hydraulic residence time is 5.4 months ± 10 days, and was obtained by dividing the average reservoir volume over a year by the total outflow volume over the same period. Note that this annual cycle varied from one year to another. From July to November 2020, the water level of the Romaine-2 reservoir dropped sharply by about 10 m due to the impoundment of the upstream Romaine-4 reservoir. This affected the Romaine-2 thermal regime, as discussed in section 3e. Figure 6 shows the monthly water balance of the Romaine-2 reservoir.
Mean monthly volumes of the water budget for the Romaine-2 reservoir from June 2018 to December 2022. The term
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0149.1
The largest water budget fluxes occurred in May and June, as much of the upstream and lateral inflow took place during the spring freshet. The
On an annual basis, upstream and downstream flows were the main drivers of water movement within the reservoir. The outflow mainly consisted of turbine flow (∼91.5%), while spilled flow contributed less than 8%. The same can be said for the water inflows, which were mostly turbine flow from the upstream Romaine-3 reservoir (69.5%), with spill and lateral inflow accounting for 10% and 20%, respectively. Direct precipitation and evaporation had a much smaller impact, with precipitation accounting for only 1% of inflows and evaporation amounting to only 0.5% of outflows. Evaporation and precipitation were two orders of magnitude smaller than the other terms, which was expected given the large volume of water passing through the turbines. Nevertheless, it is noteworthy that due to evaporation, less water was available for use downstream of the reservoir, including for power generation. If we compare the mean annual evaporative volume (50 hm3) with the mean annual turbine volume (≈8200 hm3), the corresponding power loss represented almost two days of turbine operation.
c. Annual heat budget
Figure 7 shows the annual heat budget of the Romaine-2 reservoir for the three thermal years of this study period (2019/20, 2020/21, 2021/22). The Hc [Eq. (10)], the energy required to melt the snow and ice cover (estimated at 283 MJ m−2), was subtracted from the net radiation. We assumed that this value was approximately the same for each year, which obviously introduced some uncertainty. Depending on the year, Hc accounted for between 14% and 15% of the net radiation.
Pie charts of the overall annual energy balance of the Romaine-2 reservoir from 1 Mar to 28 Feb for (top) 2019/20, (middle) 2020/21, and (bottom) 2021/22. The entering energy is in incoming terms, while the leaving energy refers to outgoing terms. The term Rn is the net radiation; Hadv,n is the net advection of heat; H and LE are the sensible and latent heat fluxes, respectively; ΔHS is the heat storage calculated over the top 70 m; and “Residual” refers to the missing energy reflecting the nonclosure. Note that Hc (fraction of net radiation energy used to melt the ice and snow cover) is removed from Rn.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0149.1
For these three thermal years, net radiation accounted for the majority of the total energy input, ranging from 62.2% to 79.1%, while the net advection of heat (Hadv,n) ranged from 16.2% to 37.5%. Regarding the outgoing terms, the latent heat flux amounted to 43.7% to 51.2% and represented about 3 times the energy released by the sensible heat flux, which ranged from 12.5% to 20.1%. The rate of change of heat storage, ΔHS, was either a small source or sink term depending on its sign due to its imbalance on these periods. Finally, the heat budgets exhibited a nonclosure term in the form of output energy, the residual, varying from 26.3% to 39.4%, which represented a significant value, indicating the presence of uncertainties on some of the terms. In other words, we measured more incoming energy into the reservoir than outgoing energy for each year of the whole study period.
Meanwhile, it has been shown that the eddy-covariance approach does not close the energy balance (Foken 2008) when solely measuring the turbulent heat fluxes. Based on the energy balance ratio introduced in Eq. (10), we obtained annual EBR values ranging from 0.6 to 0.72. Consequently, we can close the heat budget by adjusting the turbulent heat fluxes by preserving the Bowen ratio (Mauder et al. 2018), so that the residual term is nullified. When doing so, the contribution of LE is revised to 72.1%, 80.4%, and 67%, and H to 27.9%, 19.6%, and 28% for years 2019/20, 2020/21, and 2021/22, respectively. Now, if we refer to these values, more than two thirds of the incoming energy was released to the atmosphere in the form of latent heat flux, which remained the dominant way of dissipating heat, and less than 30% was lost through sensible heat. A similar result was obtained by Xing et al. (2012), who reported that latent heat flux accounted for 83% of the net radiation on the Kranji tropical reservoir (Singapore). Moreover, Rouse et al. (2005) showed that latent and sensible heat fluxes accounted for 80% and 20% of the net radiation for medium and large boreal lakes, respectively. For Great Slave Lake in northwestern Canada, Blanken et al. (2000) reported that latent and sensible heat fluxes varied between 50% and 75% and between 5% and 15% of net radiation from August to September. In Japan, Momii and Ito (2008) found that the latent flux accounted for 90% of the net radiation, while the sensible flux was about 10%. For the boreal Lake Mendota (United States), Ragotzkie (1978) showed that the latent heat flux was about 80% of the net radiation, while the sensible heat flux was about 20%. Finally, it appears that in more northern regions, latent heat flux decreases and sensible heat flux increases relative to net radiation due to colder temperatures (Leppäranta et al. 2016). Xing et al. (2012) also showed that the advected heat fluxes could be an important component of the heat budget. They estimated the mean net advective heat fluxes to be −4 W m2. In our study, the net advective heat flux, Hadv,n, was much higher and varied from 11 to 29 W m−2. This emphasizes that the net advective heat flux varies from one reservoir to another, as it is primarily governed by climate and operating rules. It appears that on annual time scales, the net advected heat was a major source of energy to the reservoir and thus to the turbulent heat fluxes. Moreover, on smaller time scales, advective fluxes can also contribute substantially to surface temperature and thus indirectly to turbulent heat fluxes (Schmid and Read 2022).
d. Monthly heat budget
Figure 8 shows the monthly heat budgets. Contrary to the annual scale, we did not consider the energy used for ice melting at the monthly time step. Therefore, in May, the high residual (∼180 MJ m−2) was approximately equivalent to the amount of energy used for ice and snow cover melting. This value is not so far from the Hc value computed (283 MJ m−2). We can clearly see that there was little energy exchange from January to April, when all terms were around 50 MJ m−2. This was due to the very low evaporative demand, the low net radiation, and the ice and snow cover that impeded the energy exchange between the reservoir and the atmosphere. Advective heat fluxes remained low as well because of the low water temperatures (below 4°C) entering and leaving the reservoir. However, from May to September, energy rapidly went into the reservoir mainly in the form of net radiation, and this energy was stored in the water column (negative ΔHS, that is away from the water surface). The other major source of heat was through net advective fluxes, which were low from January to April, but in excess of 50 MJ m−2 the rest of the year. More precisely, Hadv,n was sustained in July and August (200 MJ m−2), while it remained positive and lower than 80 MJ m−2 from September to December. This positive Hadv,n was explained by the higher
Average monthly energy balance of the Romaine-2 reservoir for the 1 Mar 2019–28 Feb 2022 period. The entering terms (incoming) are positive while the leaving energy term (outgoing) are negative. The term Rn is the net radiation (black); Hadv,n is the net advection of heat (green); H and LE (red and blue) are the sensible and latent heat flux, respectively; ΔHS (orange) is the heat storage calculated over the top 70 m; and Residual (gray) refers to the missing energy reflecting the heat budget nonclosure. Note that, the radiative energy used for ice and snow cover, Hc, was subtracted from Rn. Green arrows represent the minimum and maximum for each term over the three years. Background colors refer to mean thermal phases (see section 3e). The sign convention used here is the following: fluxes are positive (negative) when they come toward (away) from the water surface.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0149.1
As described in Pierre et al. (2023), the turbulent heat fluxes had the following pattern: H contributed to the reservoir heat (positive flux, i.e., toward the water surface) from February to July before increasingly releasing heat from August to January on average (negative flux, or away from the water surface). On the other hand, LE remained negative (away from the water surface) throughout the year, with small and persistent values from January to June and from July to December, respectively. Note that in December, the Bowen ratio (H/LE) reached 1.5, meaning that, at that time of the year, the main means by which the reservoir released heat to the atmosphere was through the sensible heat flux, due to the cold air above. Vernal turnover occurred when Rn was maximal, injecting large amounts of energy into the reservoir and homogenizing the temperature of the water column. Similarly, the fall turnover occurred when ΔHS, H, and LE were sustained, returning heat stored in the reservoir back into the atmosphere.
Monthly heat content nonclosure was also determined, as a large residual was observed at certain times during the year: May (ice-off and vernal turnover), in July (high Hadv,n), in September (transition from heat stored and heat released), in November (fall turnover and sustained H and LE) and in December (sustained H and LE). Variability of the heat budget terms was moderate from year to year. In September and October, corresponding to the transition between the energy storage and release phases (ΔHS changing sign), ΔHS variability was great as it changed depending on the timing of that transition.
In 2020/21, the late summer 9-m drop in water level (see Fig. 5a) was responsible for variations in turbulent heat fluxes compared to other years. Namely, the sensible heat flux was 275 MJ m−2, compared to a 430 MJ m−2 mean for 2019/20 and 2021/22. This lower H occurred simultaneously with lower water temperatures Tw during the open-free season. In 2020/21, the higher output advection flow, Ho, resulted in a drop in the water level of the reservoir, but more importantly in an increase in the energy extracted from the reservoir by turbines. As a result, the temperature of the reservoir’s water column was reduced, as was its surface temperature. The substantial 9-m drop in 2020 had a dual impact as it (i) represented a significant loss of thermal energy (see Fig. 11 below) and water and (ii) led to conditions altering the thermal structure and energy fluxes of the reservoir.
e. Thermal regime
The heat fluxes presented in the previous section are highly dependent on mixing and stratification processes in the reservoir water column.
The fall turnover in November–December lasted on average 28 days, while the vernal turnover from mid-May to mid-June typically lasted 22 days (Fig. 9). The vernal turnover displayed more variability in the start and end dates than the fall turnover did. For example, in 2021 and 2019, vernal turnover started on 5 May and on 12 June, respectively, and ended on 7 June and on 27 June, respectively. The beginning of fall turnover occurred on 15 and 17 November, and the end took place on 7 and 14 December in 2021 and 2019, respectively. During the vernal turnover, the temperatures of the upper layers dropped to those of the deep layers (thermal homogenization). In spring, snowmelt runoff injected cold water into the reservoir, with temperatures below 4°C, which maintained the heat budget in a low state during several weeks before growing in mid-June. This cold water remained at the surface, on top of the warmer (and denser) water below, until it warmed up to 4°C and allowed vernal mixing to begin. On average, we observed a 31-day delay between ice-off and the start of the summer stratification.
Average length of each thermal phase of the Romaine-2 reservoir for the whole study period. Phases include vernal turnover, summer stratification, fall turnover, and reverse stratification. Numbers indicate the mean length (in days) of each thermal phase and bars indicate the standard deviations of start and end for each phase. Summer stratification is split in two phases: the epilimnion growth from surface to 15 m (black) and from 15 m to fall turnover (white hatched).
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0149.1
On average, the reverse stratification lasted from mid-December to mid-May, for a total of 160 days (>5 months). The onset occurred between 5 and 21 December, while the end took place between 10 May and 15 June. The water temperature dropped to 1.5°, 2°, and 2.3°C at 20, 30, and 40 m deep, respectively, between March and the beginning of May (Fig. 10) while at depth it remained above 2.3°C. Hence, the minimum heat storage occurred at the beginning of March.
The 30-min time series of temperature profiles from 1 Jan 2020 to 31 Dec 2022. Data beyond this period have gaps in time or in information from the thermistor chain.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0149.1
Summer stratification began on average in June (between 6 and 27), ended in mid-November (between 4 and 20), and lasted about 155 days (Fig. 9). It took 89 days for the epilimnion to grow from the surface (0 m) to a depth of 15 m between mid-June and mid-September, and 66 days for the epilimnion to grow from a depth of 15 m to about 40 m (roughly corresponding to the onset of fall turnover) between mid-September and mid-November. These two subperiods had a ±16 and ±18 days variation in length, respectively. Finally, we note that the top 1-m temperature peaked in mid-August, reaching 20°C or higher each year for about 10 days before starting to decline. We identified that the maximum amount of energy stored within the reservoir occurred around mid-September, about a month after the maximum temperature in the upper layers of the reservoir. In other words, the reservoir needed about 6.5 months to achieve its maximum energy state and about 5.5 months to return to its lowest level, which suggests that heat was removed from the reservoir slightly faster than it was stored. For comparison, Oswald and Rouse (2004) showed that the dimictic Great Slave Lake in the boreal region began to stratify in the second week of July with a thermocline formed at a depth of 9 m. However, due to its high latitude, the lake started to cool down mid-August instead of mid-September for the Romaine-2 reservoir, with low radiation and high wind helping to cool down the lake afterward.
The year 2020 represented a special case, with a cooler temperature profile than in 2021 and 2022 (Fig. 10). A maximum water temperature of 18°C was observed at 15 m in 2020, while it was recorded at 20 and 23 m in 2021 and 2022, respectively. Also, since the amount of heat stored was lower, the amount of heat to be dissipated was smaller and the fall turnover appeared 12 days sooner than in all the other years. This was directly attributable to the sharp decline in the reservoir level between July and November. Indeed, the high outflow resulted in a large amount of energy extracted from the Romaine-2 reservoir, which was not balanced by the low upstream inflow entering Romaine-2. Accordingly, it shows that the Romaine-2 reservoir management directly contributed to the thermal regime (Fig. 11).
The 30-min heat storage over the 70-, 15-, and 5-m-deep water column of the Romaine-2 reservoir for the entire study period. The reference point representing no storage (0 MJ m−2) was chosen as the mean of the lowest heat storage between each year.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0149.1
The heat storage (Fig. 11) followed an annual cycle with a mean maximum of 1950 MJ m−2 in September and around 0 MJ m−2 in March. About 20% and 60% of the total heat storage was within the top 5 and 15 m, respectively. It also indicated that the deeper the water column, the stronger fluctuations in heat storage. Finally, the total amount of stored energy varied between years: in 2020, it reached a 1600 MJ m−2 while in 2021 it peaked at more than 2000 MJ m−2 over the 70-m water column, corresponding to a 20% difference. Moreover, in 2020, minimum storage coincided with a 10-m drop in the reservoir water level during the summer. Indeed, Romaine-2 turbine flow was lower than those of the other years and upstream inflow was very low with values closed to 0 m3 s−1. This confirmed that the hydrology imposed through reservoir management substantially affects heat storage and, thus, the thermal regime.
f. Thermal structure and thermocline
Changes in the thermal regime of a reservoir indirectly affect the timing of the heat budget and, in particular, the release of energy to the atmosphere through turbulent fluxes. Figure 12 presents the daily characteristics of the thermocline for the ice-free period from 2018 to 2022. In general, during the summer stratification, the epilimnion starts to grow from the surface of the top layer while the thermocline moves deeper at a steady rate of approximately 0.2 m day−1 from end of June until November. On average, from mid-June to mid-August (2 months), Tt rose from 6° to 12°C before declining until mid-November (3 months). The growth of the epilimnion is more irregular than the decline. The metalimnion temperature amplitude ΔT follows the same pattern with a maximum of 14°C in mid-August due to high surface water temperatures (approximately 20°C) and low subsurface temperatures (6°C). It then declines more steadily with a mean rate of approximately −1.3°C week−1 before vanishing in November (fall turnover).
Daily (a) thermocline temperature (Tt), (b) thermocline depth (ht), (c) metalimnion temperature amplitude, and (d) metalimnion temperature gradient, for the ice-free period from 2018 to 2022.
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0149.1
The ht starts between 3 and 6 m on 20 June and increases steadily in open water, typically reaching 10 m in early July, 20 m in late August, 30 m in October, and 40 m in early November before the fall turnover. The temperature gradient ΔTw/Δzmeta evolved differently: it increases until September, when it stabilizes at a maximum value of approximately 0.8°C m−1 on average. Thereafter, the temperature gradient decayed at a mean rate of −0.15°C m−1 week−1 until the onset of the fall mixing phase.
The summer thermocline lasts on average 155 days between 9 June and 10 November. Overall, the thermocline initially has a strong amplitude and a weak temperature gradient, then a weaker amplitude and a more intense temperature gradient. Similar results were found by Read et al. (2011), who showed that the metalimnion of Lake Mendota (43.1°N, 89.4°W; 39.4 km2, maximum depth of 25 m) (Wisconsin) decreased in thickness between August and October. The thermal regime of the Romaine-2 reservoir is very comparable to that of water bodies at the same latitude and with the same climate (Bolsenga 1975; Nordbo et al. 2011; Vincent et al. 2008).
The lag between the maximum temperature amplitude (August) and the maximum temperature gradient (September) is about one month. Between these two dates, the metalimnion thickness decreases faster than the thermal amplitude, increasing the temperature gradient. From mid-September to November, the temperature gradient gradually declines, allowing wind mixing to take place and thus increasing the thickness of the epilimnion.
Once again, we confirm the connection between the water management regime and the thermal structure of the Romaine-2 reservoir. For example, in 2020, the 9-m decline in the water level, due to low outflow and almost no upstream flow, resulted in a 10-m rise in the thermocline, from −20 to −10 m, a colder thermocline temperature than for the other years, and a thermal gradient exceeding 1°C m−1 from the end of August to mid-September (Fig. 12). In November 2021, water level dropped by 2 m, resulting in a change of the thermocline from −22 to −35 to −20 m. This also caused an increase in the thermal gradient due to a stagnation of the temperature of the epilimnion over 8 days, from 8 to 16 October, and a decrease in the thickness of the metalimnion. Finally, mid-September 2022 (from 17 to 23), the outflow fluctuated between 150 and 250 m3 s−1 and the thermal gradient rose when the metalimnion thickness decreased.
The thermal regime of this large hydropower reservoir varies significantly over the course of the year because of the downstream water release. Figures 5 and 10 offer an insight between the thermal structure and the outflow of the Romaine-2 reservoir. The main period of water level variation (associated with hydroelectric production) occurs between January and May, when the reservoir is either inversely and weakly stratified (January–April), or in a mixing period (April–May). From June to December, the reservoir is in a steady state in terms of water level, which remains relatively constant (lower water release). At this time, however, the thermal regime undergoes a major transformation (summer stratification) in intensity and depth. Finally, the great drop in water level in 2020 made the heat storage weaker, modified the thermocline depth, and preserved the thermal structure’s integrity. Consequently, the influence of Romaine-2 reservoir operation on the thermal structure appears moderate.
4. Uncertainties
a. Nonclosure problem of the energy budget
The energy balance is affected by the problem of nonclosure due to the various uncertainties present throughout its calculation procedure. The main measurement errors are as follows. First, not all variables were measured directly. Indeed, some were derived from models or approximated by indirect methods. For example, the water temperature featured in the
Thus, to establish an energy balance of a reservoir or lake, it is strongly recommended to, first, carry out in situ measurements of each of the terms at the appropriate scale, and then, for as long as possible, using the most appropriate measurement method. This requires overcoming certain difficulties inherent to field work in a cold environment (presence of ice, etc.), which is not always feasible or even realistic. We detail two aspects of these shortcomings below, namely, the estimation of water temperatures and turbulent heat fluxes.
b. Water temperatures
The temperature of the lateral inflow is the only term of the energy budget for which we do not have direct measurement and could be therefore considered as one of the most uncertain. The
Sensitivity analysis of the change in water temperature of lateral inflows
Citation: Journal of Hydrometeorology 25, 3; 10.1175/JHM-D-23-0149.1
Another source of uncertainty in the water temperature is due to the coarse resolution of the measurements performed in the reservoir water column. Measurements made beyond 10 m had a coarser resolution (one sensor every 2.5 m up to 32.5 m and every 10 m deeper), with an accuracy of 0.1°C. This means that beyond 10 m, each sensor was assumed to be representative of a 2.5-m-thick layer at best. A mischaracterization of the water temperature by 0.1°C over the 70-m-deep water column would lead to a difference of 0.029 MJ m−2. We also assumed that the reservoir was constituted of several water layers homogeneous in temperature, which was not exactly the case. An intercomparison of the two thermistor chains separated by 1 km showed that the two temperature profiles deviated by less than 0.1°C from one another at most when considering monthly averages but can reach 2°C when looking at more frequent data.
While the temperature measurement of the water going through the turbines is less prone to error, the amount of water is harder to determine precisely. It cannot be measured directly, but only inferred from the power generated by the turbines, knowing the efficiency of each turbine. Moreover, the temperature of water exiting via the spillway was assumed to be the same as the deeper turbine water temperature whereas the former is from surface water. But this hypothesis is supported by the spilled water occurring mainly in May and June when the water column was homogeneous in temperature.
The processes involving heat exchange with water are also prone to uncertainty. For instance, the calculation of the net advection of heat was challenging since the Romaine-2 reservoir was not under a steady-state regime. To achieve a pseudo-steady-state regime, the excess energy corresponding to the additional volume was evaluated using the hypsometric curve and the temperature of the water going through the Romaine-2 turbines. The heat exchange between water and the banks was not considered in this study because it is difficult to quantify but is likely to have a minor influence in the energy budget as the reservoir is deep and compact.
c. Turbulent heat fluxes
Eddy covariance is a state-of-the-art technique to estimate turbulent heat flux, but the measurements are nonetheless affected by several sources of uncertainty. The most important one is probably that the eddy-covariance method tends to underestimate turbulent heat fluxes as the technique may fail to capture exchanges for the smallest and largest eddies (Foken 2008). The literature reports that up to 35% of the energy imbalance can be attributed to this technical limitation, which approaches the annual residual term that varies between 26.3% and 39.4% in this study.
The motion of the raft contaminates the measurement of atmospheric turbulence, which was corrected using data collected from an accelerometer installed on the raft [section 2b(1)]. This added an extra step of data acquisition and flux calculation, and thus another source of uncertainty. These oscillations are also likely to affect radiation measurements, as it was not possible to keep the net radiometer in a stable position. This can then affect the net radiation estimates Rn. However, this uncertainty is expected to be small as the overall measurement should not be biased. Indeed, the radiometer oscillates with the raft about a horizontal position and deviations from this position should cancel out over sufficiently long periods.
Fluxes measured by the eddy-covariance towers may not be fully representative of the fluxes at reservoir scale, as the measurement footprint does not exceed 3% of the reservoir area. This implies that, without additional measurements, we must assume that the reservoir is spatially homogeneous over its extent, which it is assuredly not. This might have an effect on the magnitude of the turbulent fluxes and underlines the need to take measurements at broader scales with instruments such as scintillometers (Pierre et al. 2022). Random sampling uncertainty (Finkelstein and Sims 2001) is another source of error in this study, and it accounts for about 2% for sensible and latent heat fluxes. Finally, several algorithms were applied to filter out turbulent fluxes of lower quality (Pierre et al. 2022), resulting in gaps in the time series. These gaps were filled with a standard procedure (Reichstein et al. 2005), but despite a good performance, it introduces some uncertainty in the heat budget (Mahabbati et al. 2021).
5. Conclusions
In this study, we showed that the dam management operations performed at the Romaine-2, which is part of a cascading reservoir system located in the subarctic region, alter its thermal regime and thus its interactions with the atmosphere. We analyzed the thermal regime of a deep dimictic hydroelectric reservoir in eastern Canada from June 2018 to 2022. Thanks to this unique dataset built using two eddy-covariance installations, two thermistor chains, and inflow and outflow data provided by the operator of hydroelectric reservoir, we assessed the water and heat budgets at various time scales.
The reservoir water balance was dominated by the upstream inflow of the Romaine-3 reservoir and the outflow from the Romaine-2 reservoir. The input volume from the reservoir tributaries was estimated to be 20% of the total inflow, as a residual of the water budget. On the other hand, evaporation and precipitation were very small in volume. Spilled and turbine flow maxima occurred in spring due to the release of water from spring freshet. The hydraulic residence time was 5.4 months ± 10 days.
The annual heat budget indicated that on average 73.3% of the inputs came from net radiation and 25% from the direct lateral inflow net advection, while the outputs were mainly dominated by latent heat flux (73.2%) and sensible heat flux (25.1%). These results highlight the importance of the lateral inflow and the latent heat fluxes in the heat budget of a cascading reservoir system. From a monthly perspective, heat advection occurred mainly in summer due to higher upstream and lateral inflow temperatures than outflow temperatures. It confirms the importance of advection flows in the heat budget and the calculation of the turbulent heat fluxes.
The thermal phases of the reservoir varied in duration and timing. Reverse stratification lasted approximately 160 days, from mid-December to mid-May, while summer stratification lasted approximately 155 days, from mid-June to early November. These time intervals separated two mixing episodes, one in the spring that lasted about 22 days and one in the fall that lasted about 28 days. Surface and deep-water temperatures differed in time as well as in annual amplitude, with the with the maximum surface temperature observed in August, while deeper layers reached their maximum in September. The thermocline lasted on average 155 days, with a strong amplitude ΔT and a weak temperature gradient ΔT/Δz in August that inversed in September and October (weak amplitude and stronger temperature gradient).
Finally, during a period when water storage was drawn down for power production, the heat storage of the water column declined by 20% in response to the large removal of thermal mass from the reservoir. This highlighted the influence of the hydrological regime on the thermal structure of the reservoir. Water management governed variations in the thermocline, both in terms of depth and temperature, and ultimately changes in the energy balance, particularly turbulent fluxes that reflected the amount of heat stored in the reservoir. In sum, we showed that advective fluxes made a significant contribution to the reservoir’s water and heat balances and should therefore not be ignored in climate modeling.
Acknowledgments.
The authors would like to acknowledge Paul del Giorgio for sharing the Bernard River database. They are also grateful to Annie-Claude Parent, Dany Crépault, Denis Jobin, and Benjamin Bouchard for their contribution to this work. This research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) through Grant RDCPJ508080-16 entitled “Observation and modelling of net evaporation from a boreal hydroelectric complex (water footprint).”
Data availability statement.
Data are available upon request.
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