Deepwater Renewal in a Large, Deep Lake (Lake Geneva): Identifying and Quantifying Winter Cooling Processes Using Heat Budget Decomposition

Wintertime deepwater renewal, which is important for heat–oxygen–nutrient exchange in lakes, is traditionally considered to be mainly driven by 1D vertical convective cooling. However, differential cooling between shallow and deep waters can produce density currents that flow into deep layers. In order to determine the role that these two cooling processes play in deepwater renewal, field measurements and 3D numerical modeling were combined to investigate heat content dynamics in Lake Geneva's large basin, the Grand Lac (maximum depth 309 m), during an exceptionally cold air spell in early 2012 where complete overturning had been reported. In a novel approach, the heat budget of the lake was decomposed, which allowed the identification and quantification of the heat budget components. The heat budget decomposition revealed that vertical convective cooling only penetrated to 200 m and that lateral advection was not only caused by density currents being discharged from the shallow littoral zone of the Grand Lac, but also from the Lake's shallow Petit Lac basin (maximum depth 75 m); the latter was found to be the main driver of heat content decrease in the deep layers of the Grand Lac below ∼200‐m depth. These findings provide unique insight into heat exchange processes that cannot be obtained from field data or numerical simulations alone. Heat budget decomposition proved to be a powerful, universally applicable tool for quantifying the contribution of alternative deepwater renewal processes. This is important, since deepwater renewal by convective cooling is weakening due to persistent global warming.


Introduction
Deepwater renewal during winter cooling is an important process in the annual cycle of mid-latitude lakes, and mainly occurs due to temperature differences between the atmosphere and the lake surface.This process controls the exchange of heat, oxygen, and nutrients between the surface and deeper layers, and thus can significantly affect the lake ecosystem and its biodiversity (Posch et al., 2012).Traditionally, one-dimensional (1D) vertical convection is considered to be the main driver of deepwater renewal (e.g., Winder, 2012;Woolway et al., 2020), with complete overturning occurring when temperatures become homogeneous over the full water depth.In deep oligomictic lakes, however, vertical convective cooling is often not sufficiently strong to reach the lake's deepest layers (Coats et al., 2006;Livingstone, 1993;Perroud et al., 2009) and complete overturning only occurs during exceptionally cold winters (Livingstone, 1993).Climate change has already resulted in increased water temperatures and lower Dissolved Oxygen (DO) concentrations, which affects the lake's ecological state (e.g., Butcher et al., 2015;Friedrich et al., 2013;Golub et al., 2022).In particular, vertical convective cooling is expected to further weaken during warmer winters (Adrian et al., 2009;Ambrosetti & Barbanti, 1999;O'Reilly et al., 2015), thereby reducing the frequency and intensity of deepwater renewal (Peeters et al., 2002;Schwefel et al., 2016;Wahl & Peeters, 2014).Here, we investigate whether and under what conditions alternative processes can contribute to deepwater renewal in deep lakes.To this aim, we developed a three-dimensional (3D) heat budget decomposition methodology.
In addition to vertical convective cooling, two types of lateral advection, usually caused by differential cooling, can significantly contribute to deepwater renewal: (a) density currents from littoral zones and (b) density currents from shallow basins.In the first case, during wintertime, water in shallow littoral zones cools more rapidly than in deeper pelagic zones (e.g., Fer et al., 2002;Ulloa et al., 2022).Driven by gravity, the colder, denser water from the littoral zones then flows down the sloping lakebed.This kind of density-driven lateral advection is sometimes called a thermal siphon (Monismith et al., 1990).Experiments carried out by Wells and Sherman (2001) showed that lateral advection can change the stratification when shallow regions account for at least 50% of the lake's surface area.Based on a linear model, Farrow and Patterson (1993) derived asymptotic solutions for currents driven by differential cooling and quantified the flow transition process.Ulloa et al. (2022) used analytical scaling to determine a transition timescale for the triggering of lateral advection, as well as velocity scales for the associated cross-shore water exchange.
Lateral advection is important for the transport of heat, oxygen, nutrients and pollutants from the littoral to the pelagic zones of lakes.In the deepest part of Lake Garda (Italy, depth 346 m), a pronounced temperature decrease detected during early 2018 was attributed to lateral advection (Biemond et al., 2021).Peeters et al. (2003) suggested that cold-water density currents due to differential cooling are one of the reasons for the short residence time of Lake Issyk-Kul's deep waters (Kirghizstan, ∼670-m deep).Fer et al. (2002) estimated that the volume flux discharged by lateral advection from the littoral zone of Lake Geneva (France/Switzerland) in winter could be 11.5 times greater than the total river inflow.
Lakes are often composed of several basins of different sizes and depths.A second category of lateral advection occurs when shallow basins cool down more rapidly than adjacent deeper basins, producing a horizontal interbasin density gradient that drives cold-water density currents from shallower to deeper basins.In Lake Biwa (Japan), for example, strong density currents generated by more rapid cooling in the small shallower south basin were observed in winter (Okubo, 1995).In Lake Tanganyika (Burundi/Democratic Republic of the Congo/Tanzania/Zambia), Verburg et al. (2011) observed that large-scale convective inter-basin circulation due to differential cooling supplied oxygen below the permanent thermocline.Sherman et al. (2001) found that in Chaffey Reservoir (Australia), stronger cooling in a broad shallow region drove lateral exchange with the deep part, and was the second-most significant transport process after circulation by artificial destratification (bubble plume injection).
Frequently, a lake's physical, biochemical and ecological state is determined by analyzing 1D vertical profile measurements.In this approach, the maximum depth of vertical convective cooling, also called overturning depth, is usually obtained from oxygen and temperature profiles (e.g., Amaral et al., 2018;CIPEL, 2022;Coats et al., 2006;Schwefel et al., 2016).However, based on long-term measurements in the hypolimnion of Lake Geneva, Lemmin (2020) found that, during cold winters, temperatures in the lake's deepest layers were often lower than in the shallower layers above.Furthermore, he observed that DO concentrations near the bottom, at ∼300-m depth, increased every winter and were occasionally higher than further up in the water column (e.g., at ∼200-m depth), even during mild winters when vertical convective cooling did not reach below 200-m depth.These and similar observations led Lemmin (2020) to conclude that deepwater renewal in Lake Geneva is the result of complex 3D transport processes.Recently, Reiss et al. (2020); Reiss et al. (2022Reiss et al. ( , 2023) ) investigated the contributions of wind-driven coastal upwelling processes and wind-driven interbasin exchange to deepwater renewal in Lake Geneva.It was demonstrated that water discharged from the Lake's shallow basin (Petit Lac) can penetrate down to ∼200-m depth into the hypolimnion of its deep basin (Grand Lac), again emphasizing the importance of 3D advective processes in deepwater renewal.Cimatoribus et al. (2019) showed that wind-induced coastal downwelling can also transport coastal water downslope to ∼200-m depth, thus contributing to the renewal of intermediate hypolimnion layers.Ever present basin-scale gyres and mesoscale eddies (Hamze-Ziabari, Lemmin, et al., 2022) spread these advected water masses in the intermediate hypolimnion layers throughout the basin.However, these processes do not reach the deepest layer (∼300-m depth) of the Grand Lac.
In deep, oligomictic lakes, the total heat content generally increases during milder winters due to climate change (e.g., Ambrosetti & Barbanti, 1999;Michalski & Lemmin, 1995;Ye et al., 2019).Given that both vertical topdown convective cooling and lateral advection of cold waters impact a lake's heat content, it is essential to determine whether and under what conditions differential cooling processes can compensate for, or perhaps aggravate, climate change effects.However, thus far, no studies quantified the contribution of differential cooling to the lake heat budget.Such information is crucial, particularly in deep lakes, where the lake's ecological state depends on its heat content (e.g., Ambrosetti & Barbanti, 1999;Weinberger & Vetter, 2014).Ye et al. (2019) demonstrated that the lake heat content, which is proportional to the depth-integrated water temperature, is a more appropriate indicator of climate-induced warming than surface temperatures.
In the present study, we investigate how vertical convection and, in particular, lateral advective processes during winter contribute to deepwater renewal of large, deep lakes using, as an important archetype, Lake Geneva.In such lakes, the total heat content is primarily controlled by hypolimnetic temperatures (e.g., Ambrosetti & Barbanti, 1999;Michalski & Lemmin, 1995), not by the temperature of shallower layers.Specifically, our goal is to quantify the contribution of the different lateral advective processes and vertical convective cooling to the heat budget of Lake Geneva during winter.We focus on an exceptionally cold air spell during winter 2012, a year when complete overturning was reported to have taken place (e.g., CIPEL, 2013).Furthermore, the underlying driving mechanisms of deepwater renewal are scrutinized, highlighting the need for consideration of 3D processes, instead of drawing conclusions based only on 1D observations.The following questions are addressed: • Did Lake Geneva (maximum depth 309 m) actually completely overturn during early 2012, as was previously reported?If not, what was the maximum overturning depth reached by vertical convective cooling?• Did lateral advective processes affect deepwater cooling in Lake Geneva during early 2012?Can they explain the observed vertical profiles of temperature and DO concentrations?• If so, can the contributions of cold-water density currents from the Petit Lac and from the littoral zone to the heat budget of the Grand Lac's deep layers be quantified?
To answer these questions, field observations are combined with detailed 3D hydrodynamic modeling.In a novel approach, Lake Geneva's heat budget was decomposed, which made possible not only the identification, but also the quantification of the contributions from: (a) vertical convection, (b) lateral advection from the shallow littoral regions, and (c) lateral advection from the shallow side basin (Petit Lac).
A Supporting Information (SI) section, with texts, figures, tables, and movies prefixed S, provides additional details on certain topics mentioned in the text.

Study Site
Lake Geneva (local name: Lac Léman), located between Switzerland and France, is the largest freshwater lake in Western Europe (Figure 1a).It is a deep, oligomictic perialpine lake with a volume of 89 km 3 , a surface area of 580 km 2 , a length of 73 km along its major axis, a maximum width of 14 km, and a surface elevation of ∼372 m.The lake is crescent-shaped and consists of two basins: a small, narrow western basin called the Petit Lac (maximum depth 75 m) and a large, deep eastern basin called the Grand Lac (mean and maximum depths of 170 and 309 m, respectively).The two main river inflows are the Rhône and the Dranse, and the sole river outflow is the Rhône.The theoretical (water) residence time of the lake is 11.3 years (CIPEL, 2022), indicating that riverinduced advective flow, which is at its minimum during winter, is a small contributor to the lake heat budget (Rahaghi et al., 2018, Text S1.1 in Supporting Information S1).Lake Geneva's deep Grand Lac remains stratified during most years; the deepest thermocline depth is reached in late February/early March.In contrast, the shallow Petit Lac completely overturns annually.Occasionally, during sufficiently cold winters, complete overturning, that is, uniform temperatures from top-to-bottom, can occur in the Grand Lac.It was reported that the last complete overturning in the Grand Lac occurred during early 2012 (CIPEL, 2013).This period will be analyzed in the present study.Since 2012, temperatures in the lake's deepest layers have gradually increased, while the oxygen content has decreased (CIPEL, 2022).Temperatures in the deepest layers take the form of a multi-year "saw-tooth" pattern in which sudden deepwater cooling in 1 year is followed by several years of continuous temperature increase.This behavior is characteristic of Lake Geneva's deepwater dynamics as documented since the 1960s, well before climate change impacts on winter cooling dynamics were observed in the lake (e.g., CIPEL, 2022; Lemmin, 2020;Lemmin & Amouroux, 2013).Similar saw-tooth patterns were observed in other deep lakes (Livingstone, 1997).
Given the lake bathymetry, two potential lateral transport processes are considered: lateral advection originating from the Petit Lac and that from the littoral zone of the Grand Lac.For the heat budget analysis, Lake Geneva was divided into three parts (Figure 1b): (a) the Petit Lac (PL), (b) the shallow Littoral Zone of the Grand Lac (LZ), and (c) the deep Pelagic Zone of the Grand Lac (PZ).The littoral zone is defined as the shallow, gently sloping nearshore area of the Grand Lac with a maximum depth of 25 m.The pelagic zone is the remaining area of the Grand Lac.
Approximate volumes of the Petit Lac, the littoral zone and the pelagic zone are 4, 0.3 and 85 km 3 , respectively.

Field Observations
Temperature time series measured at three locations from January-April 2012 are used: (a) Midlake Mooring (MM in Figure 1a, details given in Lemmin ( 2020)), located on the central Grand Lac plateau (maximum depth 309 m), where water temperatures were recorded at 309, 240, 180 and 120-m depth every 10 min; (b) EPFL Buchillon Mast station (BM in Figure 1a (Graf et al., 1984)), located in the littoral zone of the Grand Lac near Buchillon (Switzerland), where hourly near-surface temperatures at 1-m depth, near-bottom temperatures at 36-m depth and air temperatures at 10-m height are available; and (c) the Vengeron Water Intake (VWI in Figure 1a), located in the south-westernmost part of the Petit Lac, where water temperatures at 45-m depth were recorded every 5 min by the Services Industriels de Genève (SIG, provider of Geneva's drinking water).
In addition, we analyzed full-depth profiles taken by the Commission Internationale pour la Protection des Eaux du Léman (CIPEL) at stations SHL2 (309-m depth) located near MM in the Grand Lac (temperature and dissolved oxygen concentrations), and GE3 (70-m depth) located in the Petit Lac (temperature) (for locations, see Figure 1a).

3D Hydrodynamic Simulations
We employed a 3D numerical model based on the Massachusetts Institute of Technology General Circulation Model (Marshall et al., 1997), which solves the incompressible, hydrostatic Boussinesq Navier-Stokes equations.
The nonlinear equation-of-state proposed by McKinley et al. (2004) was adopted to consider thermobaricity, with salinity kept constant at 0.05 psu since conductivity in Lake Geneva is small (see Text S2 in Supporting Information S1).The present study is based on a model set-up that was adapted for Lake Geneva (Cimatoribus et al., 2018) and extensively compared with field observations under a variety of conditions (Cimatoribus et al., 2018(Cimatoribus et al., , 2019;;Hamze-Ziabari, Lemmin, et al., 2022;Hamze-Ziabari, Razmi, et al., 2022;Reiss et al., 2020Reiss et al., , 2022Reiss et al., , 2023)).It consistently gave good agreement.A horizontal Cartesian grid size of ∼115 m was used along with 100 vertical z-layers, ranging from 0.35 m at the surface to 4.8 m near the deepest point of the Grand Lac.The model was forced by hourly meteorological reanalysis data from the MeteoSwiss COSMO-2 model (Voudouri et al., 2017), which covers the lake surface with a ∼2-km grid resolution.River inflows and outflows are not included, because their impact on the heat budget and deepwater renewal are small (for details, see Text S1.1 in Supporting Information S1).
To determine the contribution of vertical convection and the two different lateral advective processes to winter cooling in Lake Geneva, three different model configurations were employed (see Table 1): (a) The Entire Lake (EL) model (Figure 1c), (b) the Grand Lac (GL) model (Figure 1d), and (c) the Pelagic Zone (PZ) model (Figure 1e).The GL model only contains the Grand Lac, whereas the PZ model is limited to the pelagic zone of the Grand Lac.In the GL model, there is no lateral advection from the Petit Lac, and in the PZ model, only vertical convection is considered.The EL model was initialized from rest at 12:00 (CET) on 3 March 2008 with a horizontally homogeneous temperature field derived from the SHL2 temperature profile on that day (for location, see Figure 1a) and was run until 31 December 2012, with a spin-up time of ∼4 years.Both the GL and PZ models were initialized from the results of the EL model at 12:00 on 24 January 2012 and ran until 24:00 on 31 March 2012; the remaining model parameters were identical to the EL simulation.

Heat Budget and Decomposition
Deepwater renewal can be quantified by considering the heat budget of a lake.At a given horizontal location (x, y) and time t, the heat content in a depth layer z 1 ≤ z ≤ z 2 (0 ≤ z ≤ z max ; z increases from the surface to the bottom) is given by: where θ [°C] is the water temperature with θ 0 = 273.15,ρ [kg m 3 ] is the water density and C p = 3994 J kg 1 °K 1 is the specific heat capacity of water at constant pressure (Jamieson et al., 1969).The lake's total heat content, is related to the total surface heat flux Q Surf = ∬ q Surf (x, y, t) dxdy by (Ragotzkie, 1978): where q Surf (x, y, t) is the local surface heat flux.In the above formulation, the heat content changes resulting from water inflows and outflows (rivers, precipitation, groundwater), and geothermal heat fluxes are neglected (e.g., Michalski & Lemmin, 1995;Rahaghi et al., 2018, details in Text S1 in Supporting Information S1).
The heat budget in the Pelagic Zone (PZ) of the Grand Lac is quantified by its total heat content variation ΔH C,PZ (t) = H C,PZ (t) H C,PZ (t 0 ), determined by integrating from a given initial time t 0 to an arbitrary time t, and can be expressed as (for details, see Text S3.1 in Supporting Information S1): where F Surf→PZ is the contribution of vertical convection due to surface heat loss, F PL→PZ is the contribution of lateral advection from the Petit Lac, and F LZ→PZ is the contribution of lateral advection from the littoral zone (Figure 1b).Heat exchange between the Petit Lac and the littoral zone of the Grand Lac is neglected due to the small contact area (Figure 1b).
Similarly, the heat budget of an arbitrary layer, L, of thickness 2δ (i.e., z δ ≤ z ≤ z + δ) in the pelagic zone between times t 0 and t is given as (for details, see Text S3.2 in Supporting Information S1): where F Surf→L is the contribution of vertical convection and F PL→L and F LZ→L are the contributions of the two lateral advective processes (Figure 1c).These three terms (Figures 1c-1e) are obtained from the heat budgets in the numerical models (Table 1).Based on the above, water renewal driven by winter cooling is represented by negative values of the heat budgets ΔH C,PZ (for the pelagic zone of the Grand Lac; Equation 4) and ΔH C,L (for a given layer; Equation 5).

Heat Budget Contributions by Different Processes
By taking the layer thickness δ → 0 limit in Equation 5, the vertical heat budget distribution for the depth layer over the entire lake, is composed of contributions from vertical convection ϕ Surf , and the two lateral advective processes from the Petit Lac (ϕ PL ) and from the littoral zone (ϕ LZ ).
Similar to Equation 6, at an arbitrary point G (x, y), the vertical distribution of the heat budget is decomposed based on the three different components as: Water Resources Research 10.1029/2023WR034936 PENG ET AL.
The different terms in Equations 6 and 7 are quantified using the results of the numerical simulations for the three different models (for details, see Text S3.3 in Supporting Information S1).

Time Series
Air temperatures over Lake Geneva typically drop to 3 or 5°C almost every winter during events lasting three to 5 days.An exceptionally cold air spell occurred in early 2012.Representative for the situation over the whole lake, air temperatures at Buchillon Mast (BM) in the littoral zone of the Grand Lac (for location, see Figure 1a) dropped to 10°C from 3 to 8 February (Figure 2a).Thereafter, air temperatures remained lower than water temperatures.Water temperatures at BM continuously decreased shortly after the onset of the cold spell.Nearbottom temperatures at 36-m depth decreased from 6.5 to 5°C between 29 January and 12 February, and were below 5.2°C until early March (Figures 2a and 2b).Temperatures at VMI (in the Petit Lac; Figure 1a) at 45-m depth (Figure 2c) decreased from 6.4 to 4°C between 29 January and 12 February, and low temperatures (below 5°C ) then persisted until 8 March.From mid-February to early March, temperatures of ∼5°C at VMI and BM were close to or even lower than the bottom temperatures at mooring MM (Figure 2d) and station SHL2 (Figure 3a).This suggests that cooling in the bottom layer at SHL2 (below 270 m, Figure 3a) was probably affected by lateral advection of cold water from the Petit Lac and from the littoral zone.This will be further addressed below in Section 4.2 using numerical modeling.
At Midlake Mooring (MM; Figure 1a), water temperatures at different depths cooled from early February (temperatures 5.6-5.8°C) to early March (4.8-5.5°C)(Figure 2d).Around 12 February 2012, temperatures at all four depths at MM were close to 5.5°C, suggesting that the lake had completely overturned by convective cooling.However, the lake's deepest layers continued to cool after 12 February.Thus, vertical, top-to-bottom convection cannot be the cause of this apparent complete overturning (further discussed in Section 4.2).
At the lake bottom (309-m depth), temperatures were nearly constant (5.6°C) until 10 February, after which they increased slightly due to the downward movement of the thermocline driven by surface cooling (analyzed in Section 4.2).This temperature increase was more obvious at shallower depths.Then, as noted above, temperatures at 309-m depth decreased rapidly on 25 February by 0.9°C.Between 12 and 25 February, cold temperature spikes were recorded, indicating that, initially, cold-water advection occurred in bursts.After 29 February, temperatures remained at ∼4.9°C, although some fluctuations were still present.These temperatures are noticeably colder than those in the layers above.
At 120-m depth, temperatures gradually decreased from ∼12 February (Figure 2d), consistent with continuous vertical convective cooling.At 180 and 240-m depth, a clear temperature decrease was seen after 3 March, 7 days later than at the lake bottom.At the same time, temperatures at 120-m depth remained unchanged.This temperature pattern can only be due to lateral intrusion of cold water into the deep hypolimnion, since temperatures at BM and VMI are colder than those measured in the intermediate water column at MM. Overall, these measurements (Figure 2d) cannot be explained by vertical convection alone.Thus, lateral advection contributed to the cooling observed in Lake Geneva's deepest layers, as previously suggested by Lemmin (2020).This conclusion is supported by the dissolved oxygen (DO) measurements discussed below.

Full-Depth Profiles
The temperature full-depth profiles at CIPEL station SHL2 (for location, see Figure 1a) during early 2012 (Figure 3a) indicated that the lake was stratified on 11 January.On 23 February, temperatures were significantly lower, and its profile became more complex.Temperatures were nearly uniform (∼5.5°C) down to 180-m depth, and slightly decreased to a minimum of ∼5.4°C below that.However, between 220 and 270-m depth, temperatures (∼5.6°C) still match the profile of 11 January.Below 270-m depth, the water was noticeably colder (∼5.2°C ) than that measured on 11 January and in the layers above 220 m on 23 February.Thus, the colder water below 270 m cannot be the result of vertical convection, and instead suggests lateral advection.On 8 March, temperatures below 270 m further decreased to <5°C.They increased to ∼5.15°C on 19 March.These burst-like changes were not related to the temperature pattern in the shallower layers between 70 and 220-m depth, which changed little, thus again indicating that lateral advective processes affect deep layer dynamics.
In addition to temperature profiles, DO concentration profiles can be indicators of deepwater renewal (Figure 3b).DO concentrations decreased gradually with depth on 11 January.The remaining three profiles showed similar values down to ∼200-m depth, with a slight DO increase due to convective cooling.On 23 February, a minimum DO concentration was observed between 220 and 270-m depth.The DO concentration in this layer did not change since 11 January.Temperatures in this layer likewise remained unchanged since 11 January (Figure 3a).Below ∼270-m depth, however, DO concentrations increased significantly, with values near the bottom close to those at the surface.These profiles cannot be explained by the traditional 1D concept of convective cooling from the surface down, implying cold water with high DO concentrations was directly transported into deep layers by lateral advection.

Numerical Simulations
The Entire Lake (EL) model simulations were compared to temperature measurements taken at: (a) 45-m depth at VWI in the Petit Lac (blue in Figure 2c), (b) the lake bottom at BM in the littoral zone of the Grand Lac (blue in Figure 2b), and (c) MM in the pelagic zone of the Grand Lac (red in Figure 4e).Model results and field observations agree well for all three stations in the different zones of the lake (additional comparisons in Text S4 in Supporting Information S1 and in summary Table S1 in Supporting Information S1).Furthermore, the good agreement between model results (salinity kept constant) and field observations indicates that compared to temperature, salinity has a negligible effect on water density variations in Lake Geneva (Text S2 in Supporting Information S1).
The total surface heat flux (Q Surf , Equation 3) from the EL model, integrated over the entire lake surface, decreased rapidly after 24 January and remained strongly negative until 16 February (Figure 4a).The negative surface heat flux in this period was caused by extremely low air temperatures (Figure 2a), and accounts for the above discussed rapid cooling of Lake Geneva after the onset of the cold air spell.Simulated temperatures at station SHL2 during early 2012 obtained from the EL model (Figure 4b) show relatively strong stratification until 4 February, with a thermocline at 60-90-m depth and minimum temperatures of 5.5°C at the lake bottom that are similar to the measured profile on 23 January (Figure 3a).Thereafter, driven by vertical convective cooling from the surface, the thermocline weakened and began to descend, leading to transient warming below (Figure 2d).On 12 February, a full-depth uniform temperature profile appeared (as already observed in Figure 2d).However, this was not caused by complete vertical convective cooling since temperatures in the deepest layers increased.Analysis of the model results shows that the uniform temperature profile in the upper part of the water column was "matched" by the intrusion of a warm water mass driven by lateral advection from the Petit Lac into the near-bottom layers (details in Text S5 in Supporting Information S1) and indicates that processes in the hypolimnion are strongly 3D.
Starting on 14 February, a cold-water mass reached the lake bottom, with temperatures lower than the lowest temperature observed during the previous stratification period (5.5°C; contour marked by the white line in Figure 4b).After 16 February, the stratification disappeared and temperatures down to ∼200-m depth were approximately uniform.Moreover, the cold water advected into the lake bottom boundary (below 5.2°C) formed a new thermocline at ∼270-m depth (see isotherms in Figure 4b); this pattern is identical to the measured temperature profile on 23 February (Figure 3a).The cold layer near the lake bottom persisted and even grew in thickness, as illustrated by a newly formed thermocline at ∼250-m depth in mid-March (analyzed in Section 5.1).  1) and field observations (cf. Figure 2d).Colorbar legend: temperature range.All dates refer to 2012 and are indicated on the abscissa of plot (e).
Unlike the EL model results (Figure 4b), the Grand Lac (GL) simulation (Petit Lac removed; Figure 4c) only sporadically showed temperatures below 5.5°C (contour marked by the white line in Figure 4c; [15][16][17][18][19][2][3][4][5][6][23][24][25].Instead, near-bottom temperatures remained close to those before 15 February, indicating that the observed change in the deepwater temperatures are mainly related to processes originating in the Petit Lac.In the Pelagic Zone (PZ) simulation, which only accounts for convective cooling because the Petit Lac and the littoral zone are removed, near-bottom temperatures did not decrease (Figure 4d), and the water column remained stratified most of the time, with vertical convective cooling reaching down to ∼200-m depth by around 20 February.
The differences between the bottom temperatures of the EL model, and the GL and PZ models (Table 1) during early 2012 (Figure 4e) reveal the impact of the two different lateral advective processes on the deepwater dynamics in Lake Geneva.Only the EL model, which included the two zones from where lateral advection can originate (Petit Lac and the littoral zone of the Grand Lac), reproduced the strong temperature decrease observed near the bottom after 16 February and seen in the measured profile on 8 March (Figure 3a).The GL model showed only a modest temperature decrease over 4 days and the bottom temperature remained almost unchanged in the PZ model results.This occurred because the Petit Lac, which generates most of the cold water that is laterally advected into the hypolimnion of the Grand Lac, is not part of the GL and PZ models (see Section 5.2).
The potential contribution from river inflows and geothermal heat flux are small compared to the heat content of the littoral zone (Text S1 in Supporting Information S1) and were not included in the analysis.

Discussion
It was previously reported that full-depth convective overturning occurred during winter 2012 and resulted in deepwater renewal in Lake Geneva.However, field measurements and numerical modeling results analyzed in Section 4 above demonstrate that three different processes actually contributed to lake cooling during the cold air spell in February 2012, that is, (a) convective cooling, and density currents from (b) the Petit Lac and (c) the littoral zone of the Grand Lac, both flowing into the deep hypolimnion of the Grand Lac.The results make evident that convective overturning did not reach the deepest layers of the Grand Lac, and that density currents played a major role in deepwater renewal.Below, we will discuss this and quantify the contribution of each of these three cooling processes.

LCDCs From the Petit Lac
The results show that the cold-water density current from the Petit Lac is an important contributor to deepwater temperature dynamics in the deep hypolimnion of the Grand Lac of Lake Geneva.Modeled near-bottom temperatures (Figure 5) indicate that a Lateral Cold Density Current (LCDC, temperature below 5.5°C) was generated in early February 2012 in the westernmost (shallowest) part of the Petit Lac (Figure 5a); measurements at VWI confirm this temperature drop (Figure 2c).As cooling continued (Figures 2a and 4a), the LCDC grew in volume and moved along the southeast shore of the Petit Lac due to Coriolis force.After occupying nearly the entire length of the Petit Lac's bottom layer, the LCDC "spilled over" into the Grand Lac, where it continued flowing eastward and was deflected to the right into the large embayment (Figure 5b).There, the LCDC evolved into a Cold Cyclonic (counterclockwise rotating) Circulation (CCC) in mid-February (Figure 5c).This CCC then moved eastward along the lake bottom and finally reached station SHL2 in late February (Figure 5d), in agreement with the rapid temperature decrease at 309-m depth observed at mooring MM (Figure 2d).The advection of the CCC, which originated in the shallow Petit Lac region and is therefore rich in dissolved oxygen (DO), explains the cold temperatures measured at station SHL2 at the lake bottom on 8 March (Figure 3a), as well as the increase in DO concentrations in the deep layers (Figure 3b).Model results show that LCDCs were continuously generated in the Petit Lac and subsequently discharged into the Grand Lac until mid-March, thereby maintaining the CCC and causing it to increase in thickness.Moreover, the CCC also produced pelagic upwelling, extending the cold-water layer (temperatures below 5.2°C) to ∼250-m depth in mid-March (Figure 4b; more details in Movie S1).

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10.1029/2023WR034936 PENG ET AL.

LCDCs From the Littoral Zone
Although weaker than the outflow from the Petit Lac, LCDCs were also discharged from the littoral zone, contributing to the CCC in the deepest pelagic zone (Figure 5).The littoral-zone areas near Ouchy (Switzerland), St. Sulpice (Switzerland), Buchillon (Switzerland) and Excenevex (France) generated the strongest LCDCs (Figure 6a).These areas have two common features: (a) wide shallow (<10 m) nearshore shelves and gradually sloping lakebeds (see Figure 1a), and (b) embayments oriented in the cyclonic direction, which favor the accumulation of cold water that form LCDCs.The largest embayment in the littoral zone, found near Excenevex (Figures 5b and 6a), provides a clear example of how the generation and accumulation of cold water in a littoralzone area forms a LCDC.When the cold-water flow outside the embayment due to the outflow from the Petit Lac was stable, a backward-facing step flow formed inside the embayment with a recirculation zone (Armaly et al., 1983), generating a Cold Local Anti-cyclonic (clockwise rotation) Circulation (CLAC).Since the recirculation zone was essentially closed, little to no momentum or heat was exchanged with the Petit Lac outflow, resulting in a strengthening of the CLAC (Figure 6b).Thereafter, the Petit Lac outflow became unstable and penetrated into the recirculation zone (Figure 6c) where it entrained the CLAC, transported it out of the embayment and into the CCC (Figure 5c), which subsequently reached the deep pelagic zone (Figure 5d).Details of the LCDC dynamics can be found in the continuous time evolution of the near-bottom temperatures obtained from the Entire Lake (EL) model simulations (Movie S2), highlighting the formation and movement of LCDCs from the Petit Lac and from the littoral zone as described above.In particular, it can be seen that LCDCs are not steady flows.Instead, all LCDCs in the Grand Lac showed significant time variability alternating between strong pulses and weak flow during the cooling event.This explains the bursts in the recorded temperatures at 309-m depth between 12 and 25 February (Figure 2d).Such pulses were already observed by Fer et al. (2002) in density currents from the littoral zone.Most strong LCDCs formed eddy-like cold circular motions soon after they started flowing downslope (Movie S2).Compared to the LCDCs in the EL model, the LCDCs were much weaker in the Grand Lac (GL) model results and almost disappeared in the Pelagic Zone (PZ) model simulation (Movies S3 and S4, respectively).These movies illustrate the important contribution made by LCDCs generated in shallower regions (Petit Lac and littoral zone) to deepwater renewal in the deepest Grand Lac layers.

Quantification of Deepwater Renewal by Different Processes
Based on the equations given in Section 3.1, the heat budget was decomposed into the three components, that is, convective cooling, lateral advection from the Petit Lac and lateral advection from the littoral zone; each contribution was quantified using the model results.The initial time for the calculation of the heat content variations and the integration of heat fluxes (t 0 in Equations 4 and 5) was set to 24 January 2012 12:00.This was the beginning of the continuous cooling period in the lake (Figures 2a and 4a) and heat fluxes from vertical convection and the two lateral advective processes were continuously negative (not shown).Below, the analysis will first be applied to the entire pelagic zone and then the heat budget of specific layers will be investigated: The heat budget decomposition in the entire pelagic zone ΔH C,PZ (Equation 4) was considered during early 2012 (Figure 7a), including the contributions by vertical convection and lateral advection from the Petit Lac and from the littoral zone.Due to the large surface area of the pelagic zone, vertical convection is responsible for most of the total heat budget.However, the contribution of lateral advection from the Petit Lac gradually increased and reached 16% of the total heat budget by the end of March, whereas lateral advection from the littoral zone contributed 5%.Considering that the volumes of the Petit Lac and the littoral zone are only 4.48% and 0.35%, respectively, of the pelagic zone's volume, lateral advection contributed significantly to the heat content decrease in the entire pelagic zone.Rahaghi et al. (2018) found that heat content variation at station SHL2 by lateral advection May-October 2010 resulted in almost no accumulation because during summer and autumn, lateral advection brought alternately positive and negative heat fluxes.In winter, however, we found that continuous negative heat fluxes due to lateral advection generated accumulative contributions and caused the observed heat content decrease (Figure 7a).
The heat budget of specific layers (Equation 5) of the deep hypolimnion was calculated in order to determine the contributions to each layer of vertical convection, and lateral advection from the Petit Lac and from the littoral zone (Figures 7b-7e).Layers at four depths (300, 250, 190 and 150 m) were considered, with layer thickness (2δ) set to 10 m.At all four depths, the surface area at 260-m depth (region inside the green contour line in Figure 1a) was used so that the comparison was unaffected by the basin shape (surface area reduces with increasing depth); at the same time, the considered area covered almost the entire area affected by the dynamics of the CCC (e.g., Figure 5d).In the deep layers at 300 (Figures 7b) and 250-m (Figure 7c) depths, the total lateral advection by the LCDCs from the Petit Lac and the littoral zone contributed more than 100% of the entire heat content decrease, since vertical convective cooling from the surface down did not reach those layers.Instead, vertical convection led to warming of the deep layers due to the descent of the original thermocline (discussed in Section 4.2).At 190m depth (Figure 7d), the warming resulting from vertical convection became insignificant by the end of March, implying that this layer was close to the maximum depth of vertical convective cooling at that time.At 150-m depth (Figure 7e), vertical convective cooling appeared after 18 February and eventually became comparable in strength to lateral advection from the Petit Lac.
For all depth layers considered, lateral advection from the littoral zone varied little.It made its strongest contribution to the 250-m depth layer.The total littoral zone area (∼33.13 km 2 ) that contributed to this cooling accounts for ∼5.7% of the lake surface (∼580 km 2 ).Note that this is much less than a littoral zone area of 50% that Wells and Sherman (2001) suggested is required to make an important contribution to changes in stratification.On the other hand, the contribution of the lateral advection from the Petit Lac was significant for all depths below 150 m.These results emphasize that the contribution of interbasin lateral advection to deepwater renewal in 309m-deep Lake Geneva is important.

Determination of the Convective Overturning Depth
In order to determine the actual overturning depth of convective cooling during the February 2012 cooling event, we used Equation 6to analyze the vertical heat budget contributions of the three different processes (Section 3.2), that is, (a) vertical convection, and lateral advection from (b) the Petit Lac and (c) from the littoral zone of the Grand Lac, all calculated using the same surface area (green contour in Figure 1a) as in Section 5.2 (Figures 8a-8c).The three corresponding local contributions at station SHL2 were calculated in the same way, using Equation 7(Figures 8d-8f).From this analysis, it is evident that vertical convection did not cool the deepest layers of the lake (Figures 8a and 8d).Instead, it caused a downward movement of the thermocline that resulted in warming below the maximum convective cooling depth (Section 4.2).Thus, the overturning depth, defined by the maximum depth of vertical convective cooling, averaged over the entire lake basin, was 190 m (Figure 8a); locally, at station SHL2, it was 200 m (Figure 8d).Short-term convective cooling below 200-m depth from 11 to 17 March (Figure 8d) is due to transient advection of cold waters surrounding SHL2, indicating that winter cooling is a strongly 3D process that cannot be accurately described by 1D concepts.It had, however, a negligible effect on the overall cooling of that layer, since it did not last long enough to cause stable cooling below 200-m depth.
On the other hand, lateral advection from the Petit Lac appeared first on 16 February near the lake bottom and then spread gradually upwards into depth range 100-200 m by the end of March (Figures 8b and 8e).Furthermore, lateral advection from the littoral zone started in the upper layers and reached the lake bottom on 16 February (Figures 8c and 8f).In particular, the LCDCs discharged from the wide littoral-zone area at Excenevex (Figures 6b  and 6c) spread to the deep pelagic zone together with the CCC that originated from the Petit Lac (analyzed in Section 5.1).Thereafter, the whole lake cooled, as indicated by the negative heat budget values in all layers.
These results (Figures 7b-7e and 8a-8f) confirm that deepwater cooling and renewal in Lake Geneva during early 2012 were mainly controlled by lateral advection (Lemmin, 2020).The present analysis allowed identifying the strong LCDCs discharged from the Petit Lac as the dominant contributor to deepwater renewal.Since LCDC water masses originate from the surface layers and are rich in oxygen, DO concentrations in the deepest layers of the Grand Lac increased.They actually reached near-surface values due to the rapid transport by the LCDCs and minimal mixing along the pathway, and were higher than in the layers above ∼200-m depth, which were controlled by convective cooling (Figure 3b).This further demonstrates the importance of LCDCs for maintaining the ecological health of the deep hypolimnion.
The complex temperature profiles measured at station SHL2 on 23 February (blue profile in Figure 3a) can be explained by heat budget contributions from vertical convection and the combined lateral advection at station SHL2 (Figure 8g).Model results show that the vertical convection contribution was negative from the surface down to ∼180 m, where it became zero.This depth is also the maximum depth where the measured profile showed uniform temperatures (Figure 3a).Advection contributions from the lakebed to ∼180-m depth were negative and sufficiently strong to impose a small amount of cooling between 180 and 220 m, even though vertical convection was positive over this depth range (Figure 3a).Between 220 and 270 m, the positive heat budget contribution of vertical convection increased and offset the negative contribution of advection.Thus, the temperature remained unchanged and was close to that of 11 January (Figure 3a).Note that the temperatures in this layer were higher than those above 220 m, potentially leading to weak instabilities.Below 270 m, the total advective contribution became increasingly negative due to LCDCs discharged from the Petit Lac (Figure 8e), which cooled this layer and resulted in a rapid temperature decrease (Figure 3a).
The present heat budget decomposition methodology makes it possible to identify and, in particular, to quantify the contributions of different processes to the heat budget of the different layers of the deep hypolimnion.The analysis provides new findings and shows that full overturning did not occur in 2012, as was previously reported in the literature based on traditional 1D temperature or DO-concentration profile interpretation.

Summary and Conclusions
Wintertime deepwater renewal is an important process for heat-oxygen-nutrient exchange in lakes and is essential for maintaining a healthy lake ecosystem.This study investigated deepwater renewal in 309-m deep Lake Geneva during an exceptionally cold air spell in early 2012 by combining field measurements and detailed 3D numerical modeling.In a novel approach, a heat budget decomposition methodology was developed and applied to numerical simulation results.This made it possible to identify and quantify three different processes that primarily contribute to the Lake's deepwater renewal: (a) vertical convection, (b) lateral advection from the lake's shallow Petit Lac basin, and (c) lateral advection from the littoral zone of its deep Grand Lac basin.Furthermore, • Field observations in the center of the lake indicated that during early 2012, vertical convection only reached layers above 200-m depth.Continued cooling of the deeper hypolimnion of the deep Grand Lac (maximum depth 309 m) suggested that lateral advective processes contribute to deepwater renewal in the deeper layers.• 3D numerical simulation results showed that this lateral advection was due to cold density currents whose origins in the nearshore zone and in the shallow Petit Lac (max depth 75 m) could be identified and their trajectories into the deep hypolimnion made evident.Density current flow was affected by Coriolis force.Such insight cannot be derived from 1D models.• Heat budget decomposition provided additional insight into these density currents and made it possible to quantify the contribution of each of these deepwater renewal processes to different layers of the deep hypolimnion of the Grand Lac. Integral contributions over the whole cold air spell, as well as details of time and depth development were obtained.• Heat budget decomposition revealed that, averaged over the whole Grand Lac, convective cooling was limited to ∼200-m depth and that deepwater renewal in the deeper hypolimnion of the Grand Lac (below ∼200 m) was due to lateral advective processes, which were dominated by density currents discharged from the Petit Lac.Below ∼270-m depth, lateral advection was the sole driver of deepwater renewal.• Complete overturning did not occur in Lake Geneva during winter 2012.Instead, alternative cooling processes renewed and thus re-oxygenated the deep hypolimnion layers of the Grand Lac bringing oxygen levels to saturation.
Vertical convective cooling is expected to continue weakening due to climate change-induced warmer winters.This will result in an increasingly shallower overturning depth and a decreasing frequency of complete overturning.Thus, it is essential to understand how alternative processes such as lateral advection from different origins can contribute to deepwater renewal.The heat budget decomposition methodology presented here for Lake Geneva provided important new insights into winter cooling and deepwater renewal that could not be obtained from field data and numerical simulations alone.Heat budget decomposition is conceptually straightforward and can be applied to other lakes under similar conditions.

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Deepwater renewal in a large, 309-m deep lake during a very cold air spell is investigated by field observations and 3D numerical modeling • A novel heat budget decomposition methodology allows for quantification of contributions of different processes to deepwater renewal • Lateral advection by density currents from shallow areas and a side basin was identified as the governing process in deepwater renewal Supporting Information: Supporting Information may be found in the online version of this article.

Figure 1 .
Figure 1.(a) Bathymetric map of Lake Geneva, including the surrounding topography, adapted from a public domain satellite image (NASA WorldWind, 2004) and bathymetry data (SwissTopo, 2022).Depth is given in meters in the colorbar legend, with isobaths at 260 and 300-m depths shown in green and red, respectively.Five measurement locations: SHL2, Midlake Mooring (MM), Buchillon Mast (BM), GE3 and Vengeron Water Intake (VWI), are denoted by circles.The red dasheddotted line delimits the narrow, shallow western Petit Lac basin from the large, deep eastern Grand Lac basin.River inflows and outflow (Rhône and Dranse) are marked by red and blue arrows, respectively.(b) Partitioning of Lake Geneva used in the heat budget analysis: (i) Petit Lac (blue), (ii) the littoral zone (green) and (iii) the pelagic zone (red) of the Grand Lac, with heat exchanges between the Petit Lac and the pelagic zone (white arrows) and between the littoral zone and the pelagic zone (orange arrows).Schematics of the three numerical model configurations: (c) Entire Lake (EL) model, (d) Grand Lac (GL) model, and (e) Pelagic Zone (PZ) model (see Section 2.3 for model details), with heat budget contributions to an arbitrary layer (regions with gray slanted lines) by different processes: convective cooling (red arrows), and lateral advection from the Petit Lac (blue arrow) and from the littoral zone (green arrows).

Figure 2 .
Figure 2. Time series of: (a) air temperature at 10-m height (black) compared to water temperature at 36-m depth (gray) measured at Buchillon Mast (BM in the littoral zone, Figure 1a), and water temperatures measured (black) and modeled (blue) at (b) BM at 36-m depth, and (c) Vengeron Water Intake (VWI in the Petit Lac, Figure 1a) at 45-m depth; (d) water temperatures measured at Midlake Mooring (MM in pelagic zone, Figure 1a) at different depths (legend), during early 2012.The horizontal gray dashed line in (a) marks 10°C, the air temperature during the cold spell starting on 3 February.Vertical dashed lines in (d): dates when CIPEL SHL2 profiles were taken (same colors as the corresponding profiles in Figure 3a).All dates refer to 2012 and are indicated on the abscissa of plot (d).

Figure 3 .
Figure 3. Profiles of: (a) water temperatures and (b) dissolved oxygen (DO) concentrations measured by CIPEL at station SHL2 on different dates (legend) during early 2012.Depths with significant changes in temperature and DO concentrations discussed in the text are shown with dashed lines.

Figure 4 .
Figure 4. (a) Total surface heat flux (Q Surf , Equation 3) in the Entire Lake (EL) model (b)-(d) Temporal evolution of temperature profiles at station SHL2 computed by the different models; isotherms of 5.5 and 5.2°C are marked by white and orange lines, respectively, in each panel.(e) Temperatures at the lake bottom (309-m depth) at Midlake Mooring (MM) obtained from the three different model simulations indicated in the panel (for details, see Table1) and field observations (cf.Figure2d).Colorbar legend: temperature range.All dates refer to 2012 and are indicated on the abscissa of plot (e).

Figure 5 .
Figure 5. Sequence of bottom temperatures during early 2012 (dates and times are indicated in bottom right corner of the panels) as simulated by the Entire Lake (EL) model, showing the evolution of the Lateral Cold Density Currents (LCDCs) that formed in and were discharged from the shallow Petit Lac: (a) First, LCDCs were generated at the shallowest (southwest) corner of the Petit Lac.(b) LCDCs grew and moved along the southern shore of the Petit Lac, and discharged into the deep Grand Lac. (c) In the large embayment (see (b)), a Cold Cyclonic Circulation (CCC) formed and moved along the lake bottom.(d) Finally, the CCC reached and remained in the deepest pelagic zone around stations Midlake Mooring (MM) and SHL2, and significantly cooled the deep hypolimnion layers.Note that, at the same time, LCDCs are still flowing from the Petit Lac into the Grand Lac. Colorbar legend: temperature range.

Figure 6 .
Figure 6.(a) Bottom temperatures simulated by the Entire Lake (EL) model, showing the dynamics of Lateral Cold Density Currents (LCDCs) discharged from the littoral zone, in particular near Ouchy, St. Sulpice, Buchillon and Excenevex.(b) and (c) Close-ups of the dashed-dotted lined box area near Excenevex in (a).In (b), the stable LCDC outflow from the Petit Lac created a Recirculation Zone (RZ) inside the embayment, where a Cold Local Anti-cyclonic Circulation (CLAC; marked by red circle) formed, (c) After the CLAC strengthened, it was entrained into the LCDC outflow from the Petit Lac and moved into the pelagic zone.Horizontal velocity vectors at 20 m above the lake bottom are shown by black arrows in (b) and (c).Colorbar legend: temperature range.

Figure 7 .
Figure 7. Heat budget decomposition into vertical convection (red), and lateral advective processes from the Petit Lac (blue) and the littoral zone of the Grand Lac (green) during early 2012 (for details, see Section 3.1): (a) in the entire pelagic zone of the Grand Lac, and (b)-(e) in different depth layers (depth given in the bottom left corner of each panel) of thickness 10 m.Negative values indicate cooling, and positive values, warming.Vertical axes: heat content variation.All dates refer to 2012.

Figure 8 .
Figure 8.Time development of the heat budget contributions of the three cooling processes during early 2012 at each depth layer for the entire lake (a)-(c) and at SHL2 (d)-(f) (details in Section 3.2).(a) and (d) vertical convection, (b) and (e) lateral advection from the Petit Lac, and (c) and (f) lateral advection from the littoral zone of the Grand Lac. Negative values (blue) indicate cooling and positive values (red), warming.In (a) and (d), respectively, overturning depths of 190 and 200 m, are marked by horizontal dashed-dotted lines.Colorbars: parameter ranges.Dates refer to 2012.(g) Vertical distributions of vertical convection and total lateral advection from the Petit Lac and the littoral zone of the Grand Lac at station SHL2 on 23 February (vertical gray dashed lines in (d-f)).

Table 1
Summary of the 3D Numerical Models: Entire Lake (EL), Grand Lac (GL) and Pelagic Zone (PZ) The model domains are given schematically in Figures1c-1e, respectively.VC denotes Vertical Convection, LA-PL is the Lateral Advection from the Petit Lac, and LA-LZ, the Lateral Advection from the Littoral Zone.