We use the 1-D lake model Simstrat v2.1 to model 54 Swiss lakes or reservoirs (see Appendix A for details of modeled lakes) in an automated way. Simstrat was first introduced by Goudsmit et al. (2002) and has been successfully applied to a number of lakes (Gaudard et al., 2017; Perroud et al., 2009; Råman Vinnå et al., 2018; Schwefel et al., 2016; Thiery et al., 2014). Recently, large parts of the code were refactored using the object-oriented Fortran 2003 standard. This version of Simstrat provides a clear, modular code structure. The source code of Simstrat v2.1 is available via GitHub at https://github.com/Eawag-AppliedSystemAnalysis/Simstrat/releases/tag/v2.1 (last access: 29 August 2019). A simpler build procedure was implemented using a docker container. This portable build environment contains all necessary software dependencies for the build process of Simstrat. It can therefore be used on both Windows and Linux systems. A step-by-step guide is provided on GitHub.

In addition to the improvements already described by Schmid and Köster (2016), Simstrat v2.1 includes (i) the possibility to use gravity-driven inflow and a wind drag coefficient varying with wind speed – both described by Gaudard et al. (2017) – and (ii) an ice and snow module. The ice and snow module employed in the model is based on the work of Leppäranta (2014, 2010) and Saloranta and Andersen (2007), and is further described in Appendix B.

A Python script was developed to (i) retrieve the newest forcing data directly from data providers and integrate them into the existing datasets, (ii) process the input data and prepare the full model and calibration setups, (iii) run the calibration of the model for the chosen model parameters, (iv) provide output results, and (v) update the Simstrat online data platform to display these results. The script is controlled by an input file written in JavaScript Object Notation (JSON) format, which specifies the lakes to be modeled together with their physical properties (depth, volume, bathymetry, etc.) and identifies the meteorological and hydrological stations to be used for model forcing. The overall workflow is illustrated in Fig. 1.

Table 1 summarizes the type and sources of the data fed to Simstrat. For meteorological forcing, homogenized hourly air temperature, wind speed and direction, solar radiation, and relative humidity from the Federal Office of Meteorology and Climatology (MeteoSwiss, Switzerland) weather stations are used. For each lake, the closest weather stations are used. Air temperature is corrected for the small altitude difference (see Appendix A) between the lake and the meteorological station, assuming an adiabatic lapse rate of -0.0065 ∘C m-1. This correction is a source of error in high-altitude lakes like Daubensee for which dedicated meteorological station would be needed. The cloud cover needed for downwelling longwave radiations are estimated by comparing observed and theoretical solar radiation (Appendix C). For hydrological forcing, homogenized hourly data from the stations operated by the Federal Office for the Environment (FOEN) are used. For each lake, the data from the available stations at the inflows are aggregated to feed the model with a single inflow. The aggregated discharge is the sum of the discharge of all inflows, and the aggregated temperature is the weighted average of the inflows for which temperature is measured. Inflow data are often missing for small or high-altitude lakes (Appendix A). Missing inflows and more generally watershed data are a source of error in small alpine lakes, yet such error can be compensated during the calibration process. The light absorption coefficient εabs (m-1) is either obtained from Secchi depth zSecchi (m) measurements (for Inkwilersee, Lake Biel, Lake Brienz, Lake Geneva, Lake Neuchâtel, lower Lake Zurich, Oeschinen Lake, upper Lake Constance, and Sihlsee) or set to a constant value based on the lake trophic status. In the first case, the following equation is applied: εabs=1.7/zSecchi (Poole and Atkins, 1929; Schwefel et al., 2016). In the second case, εabs is set to 0.15 m-1 for oligotrophic lakes, 0.25 m-1 for mesotrophic lakes, and 0.50 m-1 for eutrophic lakes. The values correspond to observations of Secchi depths in Swiss lakes (Schwefel et al., 2016) and fall into the decreasing range of transparency from an oligotrophic to eutrophic system (Carlson, 1977). For glacier-fed lakes (typical above 2000 m) rich in sedimentary material, εabs is set to 1.00 m-1.

The timeframe of the model is determined by the availability of the meteorological data (air temperature, solar radiation, humidity, wind, precipitation). Initial conditions for temperature and salinity are set using conductivity–temperature–depth (CTD) profiles or using the temperature information from the closest lake. We apply different data patching methods to remove data gaps from the forcing depending on the length of the data gap. For small data gaps with duration not exceeding 1 d, the dataset is linearly interpolated. In total, < 1 % of the dataset is corrected using this approach. Longer data gaps of up to 20 d are replaced by the long-term average values for the corresponding day of the year. Only ∼ 1.5 % of the dataset is corrected using this approach.

Model parameters are set to default values, and four of them are calibrated (see Table 2). The parameters p_radin and f_wind scale the incoming longwave radiation and the wind speed, respectively, and can be used to compensate for systematic differences between the meteorological conditions on the lake and at the closest meteorological station. The parameter a_seiche determines the fraction of wind energy that feeds the internal seiches. This parameter is lake-specific, as it depends on the lake's morphology and its exposure to different wind directions. Finally, the parameter p_ albedo scales the albedo of ice and snow applied to incoming shortwave radiation, which depends on the ice/snow cover properties. The calibration parameters were selected according to their importance for the model (e.g., based on previous sensitivity analysis), and their number was deliberately kept small in order to keep the calibration process simple and focused. Calibration is performed using PEST v15.0 (see http://pesthomepage.org, last access: 29 August 2019), a model-independent parameter estimation software (Doherty, 2016). As a reference for calibration, temperature observations from CTD profiles are used. Calibration is performed on a yearly basis, unless significant changes are made either to the model, the forcing data, or the observational data (e.g., release of a new version of Simstrat or delivery of a large amount of new observational data). For the eight lakes without observational data, parameters are set to their default value (see Table 2) with no calibration performed, and the lack of calibration is indicated on the online platform.

The online platform (accessible at https://simstrat.eawag.ch, last access: 29 August 2019) is automatically fed every week with model results, metadata, and plots for all the 54 modeled lakes (see Fig. 2). It allows for efficient display and open sharing of the model results for interested users. While the framework is here restricted to Swiss lakes, the code could be easily adapted to other lakes outside Switzerland and used at the global scale. From the model results, we directly obtain time series of several model output variables. Those datasets include temperature, salinity, Brunt–Väisälä frequency, vertical diffusivity, and ice thickness. In addition, we use the following known physical and lake-related properties: the acceleration of gravity (g=9.81 m2 s-1), the heat capacity of water (cp=4.18×103 J K-1 kg-1), the volume of the lake V (m3), the area Az (m2), temperature Tz (∘C), and density ρz (kg m-3) at depth z (m), and the mean lake depth z‾=1V∫zAzdz (m) to calculate time series of derived values:

mean lake temperature: T‾=1V∫TzAzdz (∘C);

From these results, we create static and interactive plots. The latter are created using the Plotly Python library (see https://plot.ly/python, last access: 29 August 2019). The plots can be categorized as follows:

history (e.g., contour plot of the whole temperature time series, line plot of the whole time series of Schmidt stability);

Over the period 1981–2015, yearly averaged simulated surface temperatures in Lake Brienz increased with a significant (p<0.001) trend of +0.69 ∘C decade-1 (Fig. 4a). For the same period, monthly in situ observations indicate a similar trend of 0.72 ∘C decade-1 (p∼0.07), while the trend of air temperature at the meteorological station in Interlaken is lower (+0.50 ∘C decade-1, p<0.01). Based on physical principles, lake surface temperature is expected to increase less than air temperature (Schmid et al., 2014); however, Schmid and Köster (2016) also observed a higher trend in lake surface temperature than in air temperature for lower Lake Zurich and assigned the excess warming to a positive trend in solar radiation. For the period of 1981–2015, the ascending trend in solar radiation is 5 W m-2 decade-1, which corresponds to an equilibrium temperature increase of about 0.2 ∘C decade-1. The warming rate at the surface of Lake Brienz is larger than observed trends in neighboring lakes with reported increases of +0.46 ∘C decade-1 for upper Lake Constance (1984–2011; Fink et al., 2014), +0.41 ∘C decade-1 for lower Lake Zürich (1981–2013, Schmid and Köster, 2016; 1955–2013, Livingstone, 2003), and +0.55 ∘C decade-1 for lower Lake Lugano (1972–2013; Lepori and Roberts, 2015). This can be explained by the lower light penetration in Lake Brienz (ranging from ∼ 1 to ∼ 10 m) compared to other lakes, the increase in solar radiation being distributed into a shallower layer and thereby warming the lake surface slightly more. This low light penetration results from upstream hydropower operation on the glacier-fed river (Finger et al. 2006).

The temperature increase was significantly smaller in the hypolimnion, with a minimum trend at the lake bottom of 0.16 ∘C decade-1 (p<0.001), leading to a depth-averaged rate of temperature increase of 0.22 ∘C decade-1 (p<0.001). The temperature difference between the inflow and the outflow also contributes to the heat budget. While no significant change in the yearly total discharge was observed at the gauging stations of FOEN for the inflows of the Aare and of the Lütschine rivers for the period 1981–2015, the weighted inflow temperature increased by 0.26 ∘C decade-1. The riverine temperature remains colder than the lake surface temperature, leading to a yearly average loss of energy by throughflow of ∼-40 W m-2 for 2015. This result is consistent with the recent observations of Råman Vinnå (2018), suggesting that tributaries significantly affect the thermal response of lakes with residence time up to 2.7 years (as Lake Brienz). The contribution of the river to the heat budget of Lake Brienz is also ∼ 4 times larger than that previously estimated for upper Lake Constance (Fink et al., 1994), a lake with a longer residence time. The increasing difference over time between the inflow temperature and the outflow temperature (taken as the lake surface temperature) leads to a non-negligible cooling contribution from the river of ∼ 0.14 ∘C decade-1 (p<0.05). The temporal change in the discharge and its temperature resulting from climate change should therefore be taken into account in studies attempting to predict the change in lake thermal structure.

The vertically heterogeneous warming modeled in Lake Brienz is consistent with previous observations showing that the difference in warming between the surface and the bottom increases the strength and duration of the stratified period (Zhong et al., 2016; Wahl and Peeters, 2014). We simulate an earlier onset of the stratification in spring of -7.5 d decade-1 (p<0.001) and a later breakdown of the stratification by +3.7 d decade-1 (p<0.001) (Fig. 4c). Both the warming trend and the increase in length of the stratified period increase the Schmidt stability (Fig. 4d) and heat content (Fig. 4f). Finally, the yearly maximum stratification strength (Brunt–Väisälä frequency; Fig. 4e) gradual increases over the investigated period with a rate of 3.3×10-4 s-2 decade-1. The simulated increase in overall stability (Fig. 4d–f) reduces vertical mixing and affects the vertical storage of heat with less heat transferred immediately below the thermocline causing a slight decrease in temperature observed in autumn at ∼ 30 m depth (Fig. 4b). This effect is even more clearly seen in other lakes like Lake Geneva (https://simstrat.eawag.ch/LakeGeneva, last access: 29 August 2019) with the surface waters warming strongly (+1 ∘C decade-1 in June), resulting in a cooling layer between 20 and 60 m (-0.2 ∘C decade-1) in late summer. Such a reduction of vertical exchange is self-strengthening and enhances the differential vertical warming.

Such analyses can be extended to all modeled lakes. An intercomparison of the temporal extent of summer stratification and winter ice cover period is illustrated in Fig. 5. An altitude-dependent decrease of the duration of summer stratification is observed, along with a stronger corresponding increase in the duration of the inverse winter stratification from 1200 m a.s.l. This is possibly linked to an altitude dependency of climate-driven warming in Swiss lakes, first reported by Livingstone et al. (2005), which may be caused by a delay in meltwater runoff (Sadro et al., 2018). Here, this process is not directly resolved but incorporated through the calibration procedure spanning all seasons.

In conclusion, the online platform provides all the data to estimate the past warming rate of lakes and evaluate how the different external processes contribute to their heat budgets. The change in the thermal structure depends mostly on the change in atmospheric forcing, yet other factors such as the changes in discharge and temperature from the tributaries and the light absorption into the lake should also be taken into account. We specifically show that the warming rate of the lake surface temperature significantly differs from that of depth-averaged temperature, thereby highlighting the benefit of using either in situ observations resolving the thermal structure over the water column or hydrodynamic model output for assessing climate change impacts on lake thermal structure.

A major drawback of traditional lake monitoring programs in Switzerland is the coarse temporal resolution, with measurements often performed on a monthly basis. This resolution only allows to detect long-term trends when measurements are conducted over an extended period typically longer than 30 years. However, traditional monitoring programs cannot resolve the impact of short-term events and their consequences for the ecosystem. This is a strength of high-frequency (hourly timescale) lake modeling, which allows for simulation and comparison of the effects associated with rapid and often severe events such as storms. Based on high-frequency observations, Woolway et al. (2018) showed the effects of a major storm on Lake Windermere. They observed a decrease in the strength of the stratification, a deepening of the thermocline and the onset of internal waves oscillations ultimately upwelling oxygen-depleted cold water into the downstream river. Furthermore, Perga et al. (2018) illustrated how storms could be just as important as gradual long-term trends for changes in light penetration and thermal structure in an alpine lake.

Here, we demonstrate how high-frequency model output can be used to study the influence of specific events on the thermal dynamics of lakes. As an example, we focus on 28 June 2018, when Switzerland experienced a strong but by no means exceptional storm with northeasterly winds mainly affecting the northwestern part of the country – the mean wind speed during that day is shown spatially in Fig. 6a. The evolution of the stratification strength, illustrated here by the Schmidt stability, is given in Fig. 6b for one of the most affected lakes, Lake Neuchâtel (https://simstrat.eawag.ch/LakeNeuchatel, last access: 29 August 2019; Fig. 2). This lake, with the main axis well aligned to synoptical winds, experienced a ∼ 8 % decrease in the Schmidt stability over this half-day event. Yet, the effects were not long-lasting and the Schmidt stability reverted to its pre-storm value within ∼ 5 d (Fig. 6b). This also resulted in a total increase of the lake heat content by ∼1.4×1016 J from the start of the storm to the time of recovery. We used the Schmidt stability recovery duration as a way to assess the short-term effect of the storm on the different modeled lakes. In Fig. 6a, lakes are colored based on the delay in Schmidt stability increase (in days) caused by the storm. The impact of the storm was not limited to Lake Neuchâtel but rather showed a regionally varying pattern. Particularly small- to medium-sized lakes in the northwestern parts of Switzerland were more affected than large lakes or lakes located in the southern part of Switzerland. However, the thermal structure of these lakes quickly reverted to the seasonal early summer warming trend.

So far, climate-driven warming has been recognized to cause an overall increase in lake stratification strength and duration, and a gradual warming of the different layers (Schwefel et al., 2016; Zhong et al., 2016; Wahl and Peeters, 2014). Air temperature trend was the most studied forcing parameter. Yet, the dynamics of extreme events (such as heat waves, drought spells, storms), including their changes in strength and distribution, has been comparatively overlooked. Scenario exploration, climate change studies, or historical forcing reanalysis should be integrated in such web-based hydrodynamic platforms to assess their roles in modifying the lake thermal structures and heat storage.