Changes in the thermal structure and mixing regimes of lakes are connected to changes in several climatic factors such as air temperature, solar radiation, cloud cover, wind speed, and humidity (Woolway and Merchant, 2019). The alteration of lake hydrodynamic properties has consequences for lake chemistry, biology, and ultimately the ecosystem services that lakes provide (Adrian et al., 2009; Vincent, 2009). Since climatic conditions have changed markedly in the last century and are expected to change considerably in the next decades (IPCC, 2013), the importance of evaluating how freshwater bodies are affected by climate change becomes evident. A direct assessment of how lakes have already been affected by climate change is to analyse historical trends in lake water temperature data. However, the availability of long-term data of lake water temperature is still scarce. For example, there are very few lakes around the world with a long-term record (defined here as >50 years) of water temperature profiles (e.g. Jankowski et al., 2006; Skowron, 2017). Instead, the availability of long-term historical data is often limited to surface water temperature of one or a few lakes (e.g. Livingstone and Dokulil, 2001; Kainz et al., 2017), and the time frame of surface temperature data available for the majority of lakes is limited to 2–3 decades. For example, Sharma et al. (2015) compiled a worldwide database with lake surface water temperature between 1985 and 2009. The same time frame was used by Schneider and Hook (2010) that reported an average warming trend of 0.045±0.011 ∘C/year of lake surface water temperature in 167 large lakes (>500 km2) using satellite-derived measurements; similarly O'Reilly et al. (2015) reported an average warming trend of 0.34 ∘C per decade for lake summer surface water temperature in 235 lakes worldwide retrieved from both in situ and satellite data. Even though these studies have demonstrated a rapid warming trend among lakes, the analysis of only surface water temperature is not sufficient to obtain a complete evaluation of the changes in the thermal structure that encompass, for example, temperature trends in the water column and phenology of thermal stratification. Moreover, the scarcity of water temperature data before the 1980s makes it difficult to assess earlier thermal conditions for the majority of lakes. A longer record of historical data provides more background information, allows better documentation of the changes that have already taken place, and leads to more accurate predictions of lake thermal conditions in future decades. One of the best arguments to counter climate change sceptics is well-documented long-term records of the ongoing effects of climate change.

For this reason, the aim of this study was to use a hydrodynamic model to extend records of lake water temperature back in time, in order to provide a longer and more consistent picture of the changes in the thermal structure of lakes. We tested this approach on Lake Erken, which has been studied extensively over the past 70 years (Pettersson, 2012). Automated hourly measurements of water temperature and meteorological data have been collected from the lake since October 1988. Before 1988, water temperature measurements were taken manually during periodic sampling campaigns or recorded using strip chart recorders from a limited number of depths during several years (1961–1963). As a consequence, information about the thermal state of the lake before 1988 was missing or infrequent for most of the time, and even after 1988 there are large gaps in the measured temperature data. Thus, the information available for Lake Erken made it a good study case for testing the methodological approach of this study. Here, we created a complete daily time-step water temperature record for Lake Erken, extending the information on its thermal structure further back in time until 1961, in order to provide a longer and more consistent picture of the changes that have occurred in the lake over the last 5 decades. The hydrodynamic GOTM (General Ocean Turbulence Model) used here is driven by meteorological data collected from Uppsala University's field station at Lake Erken (http://www.ieg.uu.se/erken-laboratory/, last access: 11 April 2019) and from nearby stations to create daily time-step water temperature profiles for the entire period 1961–2017. In this work we evaluated (1) the validity of using modelled temperature to reconstruct the past water temperature of Lake Erken for the period 1961–2017, providing a valuable method that can be extended to other lakes, and (2) how water temperature and other metrics of lake stratification have changed over the study period. Finally, the creation of a reliable, consistent, and complete 57-year dataset of daily water temperature profiles will be a valuable source of information for future research on Lake Erken that will help to better our understanding of many ecological processes that can be affected by changes in thermal conditions.

The model used in this study revealed a good match between observed and simulated water temperature during the entire study period 1961–2017 (RMSE =1.089 ∘C, MAE =0.753 ∘C, bias =-0.047). In particular, the GOTM was able to reproduce past water temperature with a high level of accuracy not only when meteorological driving data were available from the Erken meteorological station (1988–2017), but also during the period 1961–1988, when most of the meteorological data were estimated using artificial neural network analysis. Indeed, the model was able to well describe water temperature during the 3-year period 1961–1963, when it was possible to compare frequent water temperature measurements recorded from several depths by strip chart recorders (Figs. 3–4).

The model performance was very similar at 0.5 and 5 m depths, with a RMSE of 0.827 and 0.840 ∘C respectively. Slightly greater errors were found at 10 and 15 m depth, with a RMSE of 1.187 and 1.155 ∘C respectively. Since Erken is subjected to internal seiche movements, it is likely that higher errors found at deeper points (especially when a thermocline is present) between modelled and observed temperature could be at least partially explained by the limitation of a 1-D model like the GOTM in describing seiche movements. On a seasonal basis, the model performed well in all the season (winter is excluded from the calibration). In spring (April–May), the model showed a RMSE of 0.952 ∘C, a MAE of 0.721 ∘C, and a very low temperature bias (-0.008 ∘C). These values revealed that, despite the lack of a fully functioning ice module in the GOTM version used here, the model performed very well during a period in which ice cover could still occur in some years at Lake Erken. The good model performance during spring also adds confidence to the onset of stratification calculated from the modelled water temperature profiles, which often starts in April or May. In summer (June–August), the model showed slightly higher errors (RMSE =1.240 ∘C, MAE =0.903 ∘C, and bias =-0.027 ∘C). Lake Erken is always stratified during summer and, similarly to higher errors found at deeper points, higher errors of the model in this season could be related to seiche movements around the thermocline that are hard to predict with a 1-D model. This is corroborated by the fact that in autumn (September–November), when the lake is fully mixed, the model performed better (RMSE =0.530 ∘C, MAE =0.361 ∘C, bias =-0.005 ∘C).

The Pettitt test showed that an abrupt change in air temperature occurred in 1988, which is consistent with the results of Temnerud and Weyhenmeyer (2008), who found that the most abrupt changes in air temperature (interval 1961–2005) occurred in 1988 and 1989 across different sites in Sweden. The similarity of these findings to the present work demonstrates the consistency of air temperature data used to drive the GOTM to that previously evaluated by Temnerud and Weyhenmeyer (2008) and also supports our finding that trends in water temperature were strongest during the period 1989–2017 and that this interval plays the most important role in defining the trend's water temperature warming. Since the majority of the increasing trends were detected only in this sub-interval, it is apparent that most of the increase in Erken water temperature has occurred during the last 3 decades rather than during the entire study period. Overall, autumn is the season that showed the highest increase in water temperature between 1989 and 2017 (whole-lake: 0.789 ∘C per decade, epilimnion: 0.792 ∘C per decade, hypolimnion: 0.816 ∘C per decade). A lesser trend was detected during spring between 1989 and 2017 for whole-lake and epilimnetic temperature (0.404, and 0.444 ∘C per decade respectively). Summer whole-lake and epilimnetic temperature showed a constantly increasing trend throughout the entire study period, with a significant increase since 1961 (0.239 and 0.351 ∘C per decade respectively) but no significant increase in the sub-intervals, suggesting that the first and most persistent effects of global warming have occurred during summer. Otherwise, the more recent and more significant trends are most apparent in spring and autumn. These results also showed that while epilimnetic temperature increased in each season, hypolimnetic temperature showed a significant increase in autumn between 1989 and 2017 (0.816 ∘C per decade) in autumn and in spring, even though the trend detected in this season is pretty low (0.148 ∘C per decade over the interval 1961–2017), while no significant trends were detected in summer. The marked trend detected in autumn could result from the entrainment of warmer epilimnetic waters into the hypolimnion as the seasonal thermocline deepens. In general, however, the lower and fewer increasing trends detected in the hypolimnion compared to epilimnion and whole-lake temperature could be related to the fact that hypolimnetic temperature is less affected by meteorological variability than epilimnetic temperature (Adrian et al., 2009).

A large-scale study carried out by O'Reilly et al. (2015) found that a mean trend of increasing summer surface water temperature (0.34 ∘C per decade) was detected in 235 lakes worldwide between 1985 and 2009, with trends from individual lakes ranging from -0.7 to +1.3 ∘C per decade. The study reports a surface water temperature trend for Lake Erken derived from measured data of 0.61 ∘C per decade (see O'Reilly et al., 2015, Supplement), while in the present work the trend of the surface summer modelled temperature calculated over the same time period (1985–2009) is somewhat greater: 1.145 ∘C per decade. The trend detected by O'Reilly et al. (2015) is calculated using a dataset with temporal gaps in the summer water temperature record (14 years with recorded data between 1985 and 2009), while in the present work the trend was calculated using a complete long-term dataset of simulated summer surface water temperatures. Furthermore, the same article indicates that water temperature trends detected for lakes with data gaps might have been underestimated, suggesting that the trend detected in the present study for Lake Erken could be more accurate. This illustrates the value of using more complete and consistent modelled data to calculate trends and also indicates that the lake is warming at a rate near the global maximum. The rapid rate of warming estimated from our work is also consistent with the conclusions of O'Reilly et al. (2015) that lakes located in northern Europe are warming more rapidly than the global average and also of Kraemer et al. (2017) that lakes at high latitudes are warming faster than tropical lakes. Temperature trends obtained in the present study are consistent with these findings.

A prolonged duration of high surface water temperature and an increase in epilimnetic temperature can have impacts on lake mixing dynamics, leading to a higher thermal stability (Jankowski et al., 2006; Butcher et al., 2015). Such increases in water temperature can explain why Schmidt stability has also increased over the period 1961–2017 (5.365 J m-2 per decade) and why the duration of stratification has also increased by about 40 d since 1961, shifting both the onset and the loss of the stratification. Compared to 1961, the present onset of thermal stratification occurs on average 16 d earlier. However, the higher thermal stability has an even greater effect on the loss of stratification. From the simulated temperature, the end of the stratification now occurs on average 26 d later if compared with the 1960s. Very similar results were reported by Arvola et al. (2009), who used less frequently measured temperature data to estimate that the loss of stratification in Lake Erken was delayed by almost 1 month since the 1960s, further verifying the reliability of the model-based approach used in this study for detecting such variation. However, Arvola et al. (2009) did not detect the trends in the onset and duration of stratification or lake warming that were detected here. That these trends are now further detected shows the value of using model simulations to provide long-term consistent temperature records that are more amenable to trend analysis.

Higher surface temperature also increased the difference between surface and bottom temperature over the period 1961–2017 (0.253 ∘C per decade), thereby increasing the gradient of the thermocline while reducing the mean thermocline depth (-0.236 ∘C per decade). This could in part be due to a lower wind speed in recent times. Trend analyses of mean annual wind speed have revealed that there is a significant decreasing trend in wind speed over the study period. Since 1961, the wind speed has decreased on average by 0.775 m s-1 (Sen's slope =-0.136 m s-1 per decade, p < 0.001). Another possible explanation for a shallower thermocline could be related to a reduction in heat fluxes from water to air, which might have weakened the convective mixing of the upper layers (Monismith and MacIntyre, 2009). However, heat fluxes have not been analysed in this study, and further research is needed to better understand the causes behind reductions in thermocline depth.

A known limitation of the GOTM version used in this work is the lack of an ice module to simulate the onset, the loss, and the duration of the lake ice cover. Simulated and observed temperature close to the surface is similar throughout the entire year. However, during winter months (December–March) the model does not take into account the heat loss from sediment during ice cover, which causes an increase in bottom water temperature. Despite the lack of simulated ice cover, it was possible to analyse the duration of ice cover thanks to yearly observations of the onset and loss of ice cover made at Lake Erken since 1941. Ice-cover duration has decreased since 1941 by 7.343 d per decade. A step change in ice-cover duration was detected in 1988, consistent with the step change in air temperature detected in the present study and by Temnerud and Weyhenmeyer (2008). When trend analysis was performed on the two sub-intervals 1941–1988 and 1989–2017, no significant trends in ice-cover duration were detected. However, the ice-cover duration showed a greater interannual variability in the sub-interval 1989–2017 compared to the sub-interval 1941–1988. Within the sub-interval 1941–2017, the variability in ice-cover duration ranges from a minimum of 68 d in 1961 to a maximum of 168 d in 1958, while in the sub-interval 1989–2017 the ice-cover duration ranges from 12 d in 2008 to 142 d in 2011. Such an increase in the variability of ice-cover duration could be related to warming of climatic conditions (Magnuson et al., 2000). Sadro et al. (2019) found that decline of snowpack in mountain lakes in the Sierra Nevada (California) causes a warming response in lake temperature. Since Lake Erken and most lakes in Scandinavia are always ice-covered during winter and snowfall occurs every year, understanding the dynamics of snowfall and ice-cover phenology could be of extreme importance to better understand thermal response of lakes to climate change.

Changes in lake water temperature and stratification patterns can have a broad influence on many aspects of lake ecosystems, both biotic and abiotic. For example, a longer duration of thermal stratification could lead to a depletion in hypolimnetic oxygen (Jankowski et al., 2006; Butcher et al., 2015), potentially reducing the natural range of lacustrine fish (Jones et al., 2008), or otherwise influence the vertical distribution of living organisms (Woolway et al., 2014). Moreover, an earlier onset of thermal stratification and warmer lake temperature could change the seasonal dynamics of phytoplankton (Thackeray et al., 2008). A previous model simulation conducted by Blenckner et al. (2002) on the ecology of Lake Erken concluded that warmer water temperature and changes in mixing dynamics due to climate change are likely to boost nutrient concentrations and phytoplankton production, with consequences for the entire lake ecosystem in the coming decades. Given the relatively long retention time of Lake Erken (7 years), the importance of internal phosphorus loading due to changes in thermal stratification could make the lake more susceptible to climate change than other Swedish lakes with shorter retention times and higher levels of external nutrient loading (Malmaeus et al., 2005). Another potential impact could be an increase in carbon emission from the lake, since a recent study has shown that an increase in nutrient concentration coupled with a rise in water temperature can have a positive and synergistic effect on methane ebullition (Davidson et al., 2018), and in a warmer world not only methane, but also CO2 emissions from boreal lakes are likely to increase (Weyhenmeyer et al., 2015). Finally, a general indicator of the effects of warmer conditions on the biological dynamics of Lake Erken is the growing season indicator of Håkanson and Boulion (2001). Our simulations showed a significant increase in the number of days in which epilimnetic temperature was greater than the suggested 9 ∘C threshold during the 1961–2017 study period (3.793 d per decade).

The present study has shown that the use of the GOTM to reconstruct the past 57 years of thermal conditions of Lake Erken provided a valuable source of information that could be used to detect changes in its thermal structure. This methodology can be extended to other lakes that have incomplete records of water temperature data. The use of local meteorological data to drive model simulations such as those demonstrated here can be used to extend water temperature records further back in time or fill data gaps where they exist. This work also shows that water temperature has been rising faster in the last 3 decades compared to the previous decades in both the epilimnion and hypolimnion and that other metrics describing thermal stratification have changed over the entire 57-year study period.

It is likely that increasing water temperature will cause many secondary effects with serious and to some extent unpredictable repercussions for lake ecosystems. This work can be seen as a baseline for future research on Lake Erken that involves climate-related investigations. A further step towards a better understanding of how the lake ecosystems will respond to climate change is to couple a biogeochemical model with the GOTM physical model using FABM – Framework for Aquatic Biogeochemical Models (Bruggemann and Bolding, 2014). Then parameters such as chlorophyll, nutrients, and dissolved organic carbon concentrations can be simulated and analysed. The coupling of physical and biogeochemical models could, therefore, be a valuable tool to facilitate the mitigation of detrimental effects of a warmer world on lake ecosystems.