Exploring and quantifying the impact of climate change on surface water temperature of a high mountain lake in Central Europe.

Lake surface water temperature (LSWT) is a key indicator which drives ecosystem structure and function. Quantifying the impact of climate change on LSWT variations is thus of great significance. In this study, observed data of LSWT during the period 1969–2018 in a high mountain lake (Morskie Oko Lake, Central Europe) were analyzed. The results showed that the prominent warming of the LSWT and air temperature began around 1997. A logistic non-linear S-curve function was used to model monthly average LSWT. The non-linear model performed well to capture monthly average LSWT and air temperature relationships (Nash-Sutcliffe efficiency coefficient 0.86 and the root mean squared error 1.63 °C). Using the 2009–2018 period as base scenario, a sensitivity analysis was conducted. The results showed that the annual mean LSWT will likely increase about + 1.29 °C and + 2.64 °C with air temperature increases of + 2 °C and + 4 °C respectively at the end of the twenty-first century. If realized, such a scenario will cause serious consequences on lake ecosystem.

Keywords: High mountain lake; Surface water temperature; Climate change; S-curve; Poland

Lake surface water temperature (LSWT) is one of the most important indicators for lake ecosystem. It impacts lake water chemistry, thermal structure, food webs, etc. (Åberg et al. [1]; Posch et al. [38]; Beaulieu et al. [4]; Ptak et al. [40]). Thus, its variation, especially warming, may cause serious consequences on aquatic system. For example, Verburg et al. ([49]) indicated that warming slowed vertical water mixing and reduced primary production in Tanganyika Lake; Baulch et al. ([6]) found that warming increased metabolic rates of the epilithon in a boreal lake; Deng et al. ([15]) found that earlier and warmer springs increased cyanobacterial blooms in Taihu Lake.

In the past decades, LSWT in the globe presented rapid and highly variable warming trends (Schneider and Hook [42]; Dokulil [16]; O'Reilly et al. [35]). For example, O'Reilly et al. ([35]) indicated that LSWT in summer season rose rapidly in the period 1985–2009 with a global mean warming rate of 0.34 °C dec−1. LSWT warming is mainly induced by natural and anthropogenic activities (Ptak et al. [40]), and with the uncertainties of climate conditions, how will the LSWT evolve in the future is critical for sustainable lake management. Thus, exploring and quantifying the impact of climate change on LSWT are of great significance.

Due to inconsiderable human pressure, high mountain lakes constitute a natural indicator of climate changes. According to Moser et al. ([32]), "Mountain lakes are eyes on global environmental change." The necessity of detailed knowledge concerning water temperature in the lakes is emphasized in numerous studies covering many issues in the scope (Novikmec et al. [34]; Roberts et al. [41]; Debnath et al. [14]; Christianson et al. [12]; Matulla et al. [25]).

In this study, long-term observed data of LSWT in the period 1969–2018 in a high mountain lake in Central Europe (Morskie Oko Lake) were analyzed. The Morskie Oko Lake is one part of the UNESCO World Biosphere Reserve, and thus, it is devoid of human impacts. To date, the discussed lake has been a subject to many analyses (Cabała [9]; Choiński et al. [10]; Dynowski et al. [17]), and one of the main issues addressed was water temperature (Choiński et al. [10]; Choiński and Strzelczak [11]), constituting the subject of research already in the nineteenth century (Świerz [45]). Nonetheless, no attempts of the assessment of future changes in the thermal regime have been taken so far.

Different types of models have successfully developed and applied to quantify the impact of climate change on LSWT, which include process-based physical models (Li et al. [22]; Weinberger and Vetter [50]; Gu et al. [18]), hybrid physically statistically based models (Piccolroaz et al. [36]; Toffolon et al. [47]), and simple statistical models (Sharma et al. [44]; Czernecki and Ptak [13]). Sharma et al. ([44]) indicated that multiple regression was able to provide the best solution considering model performance and computational complexity. Czernecki and Ptak ([40]) applied the empirical-statistical downscaling regression model to assess the impact of global warming on LSWT, and the results showed that the statistical model is reliable.

We tested the applicability of a non-linear logistic model for LSWT forecasting. This model has been widely used for stream water temperature forecasting in local, regional, and global studies (Mohseni et al. [28], [29]; Morrill et al. [31]; Mantua et al. [23]; van Vliet et al. [48]; Kelleher et al. [21]; Arismendi et al. [2]; Segura et al. [43]; Basarin et al. [5]; Zhu et al. [53]), and the results showed that it outperformed the simple linear regression models. However, it has never been assessed for LSWT forecasting. The objectives of this study are to (1) detect and quantify trends and fluctuations of LSWT and air temperature time series, (2) assess the applicability of the non-linear logistic model for LSWT forecasting; and (3) quantify the impact of climate change on LSWT in Morskie Oko Lake.

The Morskie Oko Lake is a high mountain lake (1395 m a.s.l.) in the Tatra Mountains (the highest mountain range in the Carpathians) of Central Europe (Fig. 1). It has a mean water depth of 29.7 m and a lake area of 0.33 km2. Its water volume is 9.9 × 106 m3 with a watershed area of 5.9 km2. The lake is within the Tatra Mountains National Park and is well protected and devoid of human activity since it is a part of a World Biosphere Reserve of UNESCO. Mountain pine and grassy vegetation are the main vegetation types in the lake watershed, and rock outcrops and debris are ubiquitous (Fig. 1).

Graph: Fig. 1 Morskie Oko Lake and Kasprowy Wierch meteorological station (upper) and natural landscape of Morskie Oko Lake (lower)

In this study, long-term observed data from the Institute of Meteorology and Water Management in the period 1969–2018 (50 years), including monthly average air temperature and LSWT, were studied. LSWT were measured at a depth of 0.4 m under the water surface with a frequency of 5 days (particularly in the autumn-winter period) and daily (in the summer period). Air temperature data were obtained from the nearby meteorological station Kasprowy Wierch (Fig. 1).

The widely used rescaled adjusted partial sums (RAPS) approach was used to detect and quantify trends and fluctuations of LSWT and air temperature time series (Bonacci et al. [7]; Bonacci and Oskoruš [8]; Zhu et al. [54]). It can highlight trends, shifts, irregular fluctuations, and periodicities of the time series and is given by:

Graph

where Tmean is the mean value of the time series, STD is the standard deviation of the time series, Tj is the value of a sample, j = 1, 2, N, N is the number of samples in the time series.

Mohseni et al. ([27]) proposed the non-linear regression model for stream water temperature based on a logistic S-shaped function, which is given as:

2 $$T_w\left(t\right)=\mu +\frac{\alpha -\mu }{1+e^{\gamma \cdot \left(\beta -T_a\left(t\right)\right)}}$$

Graph

where Tw(t) and Ta(t) are monthly water temperature and air temperature, respectively; α is a coefficient which estimates the maximum water temperature; μ is a coefficient which estimates the minimum water temperature; β represents the air temperature at the inflection point; and γ represents the steepest slope of the logistic S-shaped function. The four parameters (α, μ, β, and γ) can be estimated using the least squares method as described in Mohseni et al. ([27]). The criterion is to minimize the sum of squared errors between the observed and fitted water temperatures (Mohseni et al. [27]).

The linear regression model is a simple form to represent LSWT and air temperature relationships. It uses the following form:

3 $$T_w\left(t\right)=a+b\cdot T_a\left(t\right)$$

Graph

where a and b are regression parameters.

Two indicators were used to assess the model performance: the Nash-Sutcliffe efficiency coefficient (NSE) and the root mean squared error (RMSE). NSE has a maximum of 1.0 and no minimum, and NSE = 1.0 indicates a perfect fit. RMSE value is used to represent the fitting error. They are defined as:

4 $$\mathit{NSE}=1-\frac{\sum _{i=1}^N{\left(T_M-T_O\right)}^2}{\sum _{i=1}^N{\left(T_O-T_{\mathit{AV}}\right)}^2}$$

Graph

5 $$\mathit{\text{RMSE}}=\sqrt{\frac{1}{N}\sum _{i=1}^N{\left(T_M-T_O\right)}^2}$$

Graph

where N is the number of samples, TO and TM are the observed and modeled water temperature at time i, and TAV is the average value of TO.

The relationships of annual averaged monthly LSWT and air temperature in the period 1969–2018 are presented in Fig. 2. Here, data from successive 10 years were averaged respectively: 1969–1978, 1979–1988, 1989–1998, 1999–2008, and 2009–2018. Due to the effect of decadal averaging, LSWT values are 1 °C or less with air temperatures well below zero (Fig. 2). As seen, LSWT and air temperature presented clear hysteresis in Morskie Oko Lake. The hysteresis between the LSWT and air temperature has also been reported in other lakes, such as Tahoe Lake (Piccolroaz et al. [37]), Mara Lake, and Sparkling Lake (Toffolon et al. [47]).

Graph: Fig. 2 Hysteresis cycles of the lake surface water temperature (LSWT) and air temperature (Ta) in the period 1969–2018

The RAPS values of the mean annual LSWT and air temperature time series are shown in Fig. 3. The data sets were divided into two sub-periods: (1) 1967–1996 and (2) 1997–2018 (Fig. 3). The trends in the mean annual air temperature and LSWT in the two sub-periods are shown in Fig. 4. Air temperature in the second sub-period showed clearer warming trend than the first sub-period (Fig. 4a), and the prominent warming of the air temperature began around 1997 (Fig. 3). Average air temperature values are − 0.76 °C and 0.17 °C for the two sub-periods, respectively. Mean annual LSWT did not show clear warming trend for the two sub-periods (Fig. 4b). However, raising of the base value is clear: average LSWT values are 4.8 °C and 5.6 °C for the two sub-periods, respectively. This can explain the previous research result, which showed that the mean annual LSWT in Morskie Oko Lake increased by 0.3 °C dec−1 (Ptak et al. [39]).

Graph: Fig. 3 Rescaled adjusted partial sums (RAPS) values of lake water temperature (Tw) and air temperature (Ta)

Graph: Fig. 4 Trends in mean annual air temperature (Ta) and lake surface water temperature (LSWT) in the two sub-periods: Ta (a) and LSWT (b)

Previous study showed that variation of the mean annual LSWT in Morskie Oko Lake is mainly determined by air temperature (Ptak et al. [39]). The correlations between the LSWT and air temperature in May and June and the annual ice duration are shown in Fig. 5. Except air temperature, we found that ice duration also played an important role in controlling LSWT dynamics. As seen, the LSWT in May and June increased with the decrease of the ice duration. This is because ice-melt process within the lake water body and the watershed could release cold water, which can reduce the impact of air temperature warming on LSWT. The impact of the ice duration on LSWT in May is stronger than that in June since the air temperature is the main controller for LWST in June, as can be seen from the coefficients of determination in Fig. 5. However, the duration of ice phenomena and ice cover was reduced by 10 day dec−1 in the lake with the warming of air temperature (Ptak et al. [39]). Under the impacts of warming of air temperature and reduction of ice cover, LSWT warming may be exacerbated in the future in the Morskie Oko Lake.

Graph: Fig. 5 Relationships between lake surface water temperature (LSWT), air temperature and ice durations: a LSWT and air temperature in May, b LSWT in May and ice duration, c LSWT and air temperature in June, and d LSWT in June and ice duration

The performance of the linear and non-linear logistic models is presented in Fig. 6. It is clearly shown that the non-linear logistic model outperformed the linear regression model (Fig. 6a, c). For the non-linear and linear regression models, the NSE values are 0.86 and 0.80, and the RMSE values are 1.63 °C and 1.92 °C, respectively. Additionally, all the LSWT values produced by the non-linear model are above 0.0 °C, which is more applicable compared with the observed data and the linear regression model (Fig. 6a, b). The parameter values are α = 18.17 °C, μ = 0.37 °C, β = 5.77 °C, and γ = 0.23 °C−1, which are all within the ranges in Mohseni et al. ([27]) for 584 stream gauges. The reason for the formation of the non-linear S-curve is that at higher air temperatures, the vapor pressure deficit above a water surface increases drastically, which will cause strong evaporative cooling and result in a flatter lake surface water temperature/air temperature relationship, while at low air temperatures, lake surface water temperatures often reach 0 °C as an asymptote (Mohseni and Stefan [26]).

Graph: Fig. 6 Performance of the linear and non-linear logistic models for monthly lake surface water temperature (LSWT) and air temperature (Ta) relationships: a linear regression model, b non-linear regression model, and c comparison of the modeled and observed LSWT using the non-linear model

Due to the better performance of the non-linear logistic model, in this study, we used this model to assess the impact of climate change on LSWT. The original observed air temperature series for 2009–2018 (10 years) were augmented incrementally with air temperature increases of + 2 °C and + 4 °C, respectively. The choice increments in air temperature are within the likely range of the projected global average surface air temperature increase at the end of the twenty-first century (van Vliet et al. [48]). The results showed that the annual mean LSWT will likely increase about + 1.29 °C and + 2.64 °C for the two scenarios, respectively. The results in this study are almost the same as those in global stream temperature forecasting in van Vliet et al. ([48]), and in their study, the annual mean stream temperature increased about + 1.3 °C and + 2.6 °C for the two scenarios, respectively.

As shown in Figs. 3 and 4, an evident change in the thermal regime occurred in the second half of the 1990s. The situation is different than that observed in the case of lakes located in the lowland part of the region, where the change occurred in the second half of the 1980s (Woolway et al. [51]). The progressing faster decline of the ice cover (Ptak et al. [39]) contributed to a longer time of water heating. The shift by a decade in comparison with lowland lakes and changes in the course of temperature are associated with substantial effect of local conditions. Their role is emphasized by among others Wrzesiński et al. ([52]) who determined inconsiderable effect of North Atlantic Oscillation on selected hydrological characteristics. Inflow of cold water from melting snow from the surrounding peaks and alimentation from screes (southern shore of the lake) inhibited such fast increase as in the case of air temperature.

As emphasized by Thompson et al. ([46]), even small changes in future air temperatures will lead to serious transformations of the temperature of lakes and therefore affect their ecological state. Here, the impact of climate change on LSWT in lakes around the globe is summarized in Table 1. Some details, such as name of lakes, part of the world where it is situated, the LWST warming rate, major factors influencing the LWST, and expected consequences, are introduced. As seen from Table 1, LSWT in many lakes around the globe showed significant warming trends. The warming rate of LSWT for the Morskie Oko Lake is 0.3 °C dec−1 according to Ptak et al. ([39]), which are comparable with lakes in other regions, such as lowland lakes in Poland (Ptak et al. [40]), eight lakes in Europe (Woolway et al. [51]), 235 lakes in the globe (O'Reilly et al. [35]), and three shallow lakes in the Netherlands (Mooij et al. [30]) (Table 1). Also, as seen in Table 1, warming of LSWT in these lakes is mainly controlled by the local climate (e.g., air temperature). This can also be revealed by the quantitative relationship between the LSWT and air temperature using the non-linear logistic model in this study (Fig. 6).

Summary of the impact of climate change on lake surface water temperature (LSWT) in lakes around the globe

The warming of the LSWT will lead to potentially serious consequences, as listed in Table 1. In the context of a substantial increase in water temperature (its elementary characteristic), changes in the trophic status may be accelerated (Ptak et al. [40]). For example, Jeppesen et al. ([20]) showed that the warming of the LSWT in 24 European lakes (mean annual, 0.15–0.3 °C dec−1) has resulted in profound changes in either fish assemblage composition, biomass, abundance, body size, and/or age structure of key species in these lakes. Hampton et al. ([19]) found that in the Lake Baikal, the largest freshwater lake by volume in the world, the warming of the LSWT (mean annual, 0.2 °C dec−1) has increased the levels of chlorophyll and cladocerans. The quantitative results in this study showed that the mean annual LSWT will likely increase about + 1.29 °C and + 2.64 °C with air temperature increases of + 2 °C and + 4 °C respectively at the end of the twenty-first century for the Morskie Oko Lake, which may bring serious consequences to the lake ecosystem, as listed in Table 1. The results in this study may support policy-makers to plan an effective and sustainable future management of this important water resource in Poland.

In this study, long-term observed LSWT and air temperature data for a high mountain lake in Central Europe were analyzed, and the non-linear logistic model was used to assess the impact of climate change on LSWT. The following conclusions can be drawn:

• The prominent warming of air temperature and LWST began around 1997 in the Morskie Oko Lake;
• Except air temperature, ice duration also played an important role in controlling LSWT dynamics in the lake;
• The non-linear logistic model outperformed the linear regression model for LSWT modeling with higher NSE and lower RMSE values;
• The annual mean LSWT increased about + 1.29 °C and + 2.64 °C with potential air temperature increases of + 2 °C and + 4 °C respectively at the end of the twenty-first century at the Morskie Oko Lake.

This work was jointly funded by the National Key R&D Program of China (2018YFC0407200), the China Postdoctoral Science Foundation (2018M640499), Yellow River Institute of Hydraulic Research Scientific Development Fund (201910), and the research project from Nanjing Hydraulic Research Institute (Y118009).

The authors acknowledge the Institute of Meteorology and Water Management–National Research Institute in Poland for providing the data used in this study.

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