Water temperature and discharge data as well as physiographic characteristics are provided by the Swiss Federal Office for the Environment , by the Canton of Bern Office of Water and Waste Management and by the Canton of Zurich Office of Waste, Water, Energy and Air . The discharge and water temperature data from FOEN are provided at a daily time step, whereas the AWA and AWEL water data are provided at an hourly time step. For most of the FOEN stations, hourly data also exist (see Table ). While discharge measurements exist for some stations since the beginning of the 20th century (mainly installed in the context of hydropower infrastructure projects), water temperature records only begin from the 1960s. In the present study, stations with sufficiently long times series of water temperature and discharge are selected (observations available since before 1980 for FOEN data and before 2000 for AWA and AWEL data). Some stations that fulfil these a priori conditions have been removed for other reasons, which are detailed in Table S1 in the Supplement. Data from other Swiss cantons have been investigated, but to the best of our knowledge, no other Swiss canton provides water temperature measurements before 2000. In particular, no data from the canton of Ticino could be used (because temperature measurements by the canton only started after 2000); therefore, only one catchment is located on the southern side of the Alps in this study. Note that a recent study has already discussed the river warming in Ticino .

The 52 selected watersheds, presented in Table  and Fig. , cover a wide range of catchment areas (from a few square kilometres to tens of thousands of square kilometres) and mean elevations (from 450 m to more than 2500 m). Due to the complex topography of the country, the partitioning between solid and liquid precipitation can vary strongly over small distances. Combined with the presence of glaciers in some catchments, this factor naturally influences the hydrological response characterized via the hydrological regime . The selected catchments are representative of all natural hydrological regimes found in Switzerland except the southern Alps regimes; they can also be influenced by human activities (hydropower production, lake regulation, and water intake or release). The basins are classified into four different categories :

Swiss Plateau/Jura regime (SPJ): in the lower part of the country, most of the precipitation falls as rain. The hydrological response is driven by precipitation and evapotranspiration. The annual cycle with respect to discharge is moderate with a minimum in summer and exhibits high interannual variability depending on regional precipitation patterns.

One or more meteorological stations, operated by the Federal Office of Meteorology and Climatology (MeteoSwiss), have been associated to each hydrometric gauging station . These meteorological stations were selected according to the proximity of the catchments in order to be representative of the local meteorological conditions. Only stations with sufficiently long data records at a daily timescale were kept.

Daily measurements of air temperature and precipitation were compiled, and homogeneous time series were used whenever available. Homogenization carried out by MeteoSwiss consists of adjusting historic measured values to current measuring standards and locations. Figure  shows a map detailing all of the hydrological measurement sites and the associated MeteoSwiss stations. In total, 41 MeteoSwiss stations are associated with one or several catchments. Details on the stations are given in Table S2.

Monthly snow water equivalent maps of Switzerland are used as a proxy for snow melt. These maps are provided by the WSL Institute for Snow and Avalanche Research SLF. They are generated using a temperature-index model in which observational SWE data are assimilated using an ensemble Kalman filter . Glacier annual and seasonal (summer and winter) mean local mass balance and surface extent are available for selected glaciers from the GLAMOS data set . The mass balance is estimated based on in situ biannual measurements and then extrapolated to the whole glacier area using distributed modelling and point measurement homogenization techniques to retrieve the mean local mass balance. The total mass balance is obtained in this study by multiplying the mean annual and seasonal mass balance (in millimetres water equivalent per year) by the glacier area.

In the analysis below, only complete calendar years are retained; sparse or missing data are allowed as long as gaps do not exceed 2 weeks. For daily averaging, missing data are propagated (i.e. one missing data point during a day results in a missing day), but they are ignored for seasonal and annual averaging. Seasonal and annual time series are used for all interannual comparisons and for inter-variable correlation studies. Daily time series are used for the trend analysis. Indeed, more points are available for daily values than for annual values, leading to more robust trends (see Sect. ).

Before applying linear regression to daily data, the seasonal signal is removed using a method called seasonal-trend decomposition based on “loess” (STL) , where loess stands for “locally weighted regression” . This method is robust with respect to outliers in the time series, able to cope with missing data and with any seasonal signal shape, and is computationally efficient. In addition, the seasonality is allowed to change over time and this rate of change is parameterized by the user. The STL method has been widely used in other fields; examples of application in hydrology include the work of , , or .

Here, only the main ideas of the method are presented; full details are given in . The loess fitting method is a local fitting with weights applied to the points that are fitted. The fitting can be locally linear or locally quadratic, here we use the locally linear fitting following . For any xi in the neighbourhood of x, the loess, or the weight applied to the points before carrying out a local fitting, is defined as follows: 1v(x)=Wxi-xλq(x). Note that xi is the position of the point, not its value. λq(x) is defined as the distance to the qth furthest point, with q being a parameter of the model discussed below. W(x) is defined by the tricubic function: 2W(x)=1-x33for0⩽x<10,otherwise. Therefore W(x) is large for xi close to x and becomes zero for xi further than the qth farthest point. We can see that q will act as a smoothing parameter on the fit obtained with this method.

In the STL algorithm, vectors of data Y are decomposed as follows: 3Yi=Ti+Si+Ri, where Ti is the trend term, Si the seasonal term, and Ri the residual term. The algorithm is composed of two iterative loops, called inner and outer loops. In the inner loop, the time series is first de-trended: Ti is extracted and smoothed with a loess fitting as explained above. Then, the seasonal component is extracted using a low-pass filter, and the remaining time series is again smoothed by loess. This process is repeated iteratively and encapsulated in an outer loop. In this second loop, a weight is attributed to each point based on its residual (i.e. Yi-Ti-Si) such that the weight is low when the residual term is large. These weights are used for the loess fitting in the next round of the inner loop. As the outliers are given a low or zero weight, the method is robust to the presence of outliers. At the end of the loop, Ri is obtained by subtracting the final Ti and Si from the raw data. Note that the trend term obtained here is a locally fitted function, so it is completely different from the regression parameters obtained by a linear regression, which will later be called the trend.

The STL method has five algorithmic parameters: the number of iterations in the inner loop (ni), the number of iterations in the outer loop (no), the smoothing parameter of the low-pass filter (nl), the smoothing parameter of the trend component (q), and the seasonal smoothing parameter (ns). The value of parameter nl is imposed by the time series sampling frequency and is set here to 365, which is the least odd integer greater than or equal to the time series frequency. The parameters ni and no are set to the recommended values, i.e. ni=1 and no=15 . Following the same recommendation, the parameter q is defined as the first integer respecting the following condition: 4q≥1.5np1-1.5ns-1, where np is the time series frequency.

For the seasonal smoothing parameter ns, no formal recommendation based on previous mathematical analyses exists . This parameter determines the variation of the seasonal signal over time and thus the fraction of the data variation that is included in the seasonal component. If set to a small value, the seasonal component will vary greatly from year to year, including interannual variability. If set to an overly large value, the seasonal component will be exactly the same from year to year, and the method is no longer superior to a simple periodic removal of the seasonal signal (as classically done in hydrological time series analysis, e.g. in ). The method proposed by to adjust this parameter is not applicable here: it would require an assessment based on 365 different plots per catchment. We propose here to use the autocorrelation function (ACF) and the partial autocorrelation (PACF) of the residuals' time series to select an appropriate ns. In fact, the ACF and the PACF can be used to ensure that no seasonality remains in the residuals. In particular, the ACF and the PACF of the residuals should not show any significant correlation at the biannual (183 d) or the annual scale (365 d), as this would be indicative of seasonal components being left in the residuals.

Therefore, the following method is applied to all water temperature, discharge, air temperature, and precipitation time series: the STL is run for ns ranging from 7 to 99 (note that ns has to be odd and ≥7), and the ACF and PACF are computed for all residuals' time series. The mean ACF and PACF values for lags between 360 and 370 are plotted against the ns value and the plots are checked individually by visual inspection to determine the best ns. Visual inspection is justified by the fact that for some catchments and variables, the PACF decreases monotonically and tends to a constant value, whereas in other cases, it reaches a minimum before increasing again, making an automated decision process difficult. Based on this analysis, the value retained for this study is ns=37, for all variables and all catchments. A single value for all catchments and variables is preferable. Indeed, as this value defines how the signal can evolve over time, and thus influences the trend and the residual terms, different values would make the comparison of linear regression output between catchments and variables less relevant.

Some example outputs of the STL method and additional details are given in Sect. S1.3 of the Supplement. It is noteworthy that the de-seasonalization with the STL method has almost no effect on precipitation. However, in Fig. S4 in the Supplement, we show that the seasonality in precipitation time series is weak.

The temporal trends are explored using linear regressions over different time periods, which has been shown to be a suitable approach and is commonly used . A linear regression is applied to all four de-seasonalized variables (i.e. Ti+Ri from the STL method, for the water temperature, discharge, air temperature, and precipitation variables) against time with the classical least-squares estimation technique. The linear model is applied, when possible, for the 1979–2018 and 1999–2018 periods.

As expected, the correlation determination R2 values are relatively low, because the daily and interannual variability is still present in the time series and the linear model cannot represent these components. However, the p values are all very small, and the residuals of the linear model show that, for all periods, the linear regression against time only is a suitable estimator of the trend.

The robustness of the trends is assessed using two independent methods. The first method compares the results from the simple linear model to a robust linear model . This model, which is less sensitive to outliers, is well suited for de-seasonalized temperature time series, but has shown problems with the remaining variability in the de-seasonalized discharge and precipitation time series, including convergence problems for precipitation. For our case study, this method fails to converge for all precipitation time series. The differences in trends obtained by the simple and robust linear models for the four variables are shown in Figs. S9 and S10. The only notable difference is for discharge during the 1999–2018 period.

The second method, which assesses the sensitivity to boundary effects, consists of removing 1 year at the beginning or at the end of the period and recompute the trends (removing 2 years leads to similar results). Figure S11 shows the analysis for the 1999–2018 period. The trends for water and air temperature are indeed lower when the last year (2018, which was extremely warm in Switzerland) is removed, whereas for discharge and precipitation the negative trends are less pronounced when the first year (1999) is removed. These differences are notable, but do not change the main message of the study. For the 1979–2018 period, removing 1 year, both at the beginning or at the end of the time interval, leads to negligible differences, showing the overall robustness of the trends computed over 40 years (see Fig. S12).

The root-mean-square error (RMSE) of the trends obtained over a shorter period is used as a measure of the uncertainty of the mean trend values (the largest RMSEs between trends obtained by removing 1 year at the beginning or at the end are used as the uncertainty value). For single trend uncertainty, the largest difference between the normal linear model trend and trends obtained by removing 1 year at the beginning or at the end is used as the uncertainty value (indicated in Tables , , S4, and S5).

The linear regressions are also applied to seasonal and annual mean time series. In this case, the R2 values are clearly higher, as there is less variance in the input data, but the p values increase. Indeed, only 20 or 40 points are used depending on the time period, reducing the robustness of the method. Some p values are even above the significance threshold. As a consequence, the long-term trends presented in this paper only use de-seasonalized time series, with p values < 0.05. Seasonal trends, obtained from seasonal mean values, must be interpreted cautiously. As a consequence, most of the seasonal analysis is based on raw seasonal means instead of trends due to their low significance level.

For catchments with more than one meteorological station attributed to them, the trends used in the analysis for air temperature and precipitation are the mean of the trends of all the catchment's stations. For precipitation and discharge, they are expressed in relative changes to allow for a comparison between catchments. Unless stated explicitly, trends are expressed per decade.

Two important ecological indicators are used to quantify the impact of river warming and its evolution: the number of days on which stream temperature reaches or exceeds the value of 25 ∘C, and the number of consecutive days during which the hourly temperature remains above 15 ∘C.

The 25 ∘C threshold is a legal limit in Switzerland above which heat release in rivers is forbidden; this is important, for example, for nuclear power plant cooling. The indicator is computed as follows: based on hourly data, when the water temperature reaches 25 ∘C for at least 1 h, the day is flagged as being above 25 ∘C. Then, the number of such days per year are summed in order to investigate the evolution over time.

The 15 ∘C threshold is important for fish health. Indeed, proliferative kidney disease (PKD) affecting salmonid fish is caused by a parasite that proliferates when the water temperature remains above 15 ∘C for a few weeks . Thus, water temperature affects the impact of PKD and its prevalence .

The indicator is computed following a simple approach inspired by the more complex model proposed in the work of . First, the days on which the water temperature remains above 15 ∘C for the whole day are computed (a 3 h moving window average is applied beforehand). Then, data are filtered to keep only series longer than 28 consecutive days. Finally, the number of days above 28 days in the remaining series are summed for each year. The results indicate the number of days in the year for which the temperature was above 15 ∘C for at least 28 consecutive days. As the process behind PKD is far more complex, this method does not pretend to be exact in determining the presence or absence of PKD in the rivers monitored; however it is an indicative approach to assess the exposure evolution of the river system. A sensitivity analysis has been performed and the qualitative evolution is not dependent on the chosen values for the period length and for the moving average window size.

The water temperature evolution for all gauging stations used in the current study is shown in Fig. a. In spite of the high natural variability, a warming trend is visible in most rivers. To investigate this evolution in detail, catchments with temperature measurements available since 1970 are selected (14 catchments). Figure b shows the temperature anomalies per decade with respect to the 1970–2018 mean for these catchments. A two-sided t test is performed to assess if the differences in decadal means are significant. Except between the 1970s and 1980s, where no significant difference is found (p value = 0.17), all of the other respective anomaly means are shown to be significantly different (p values < 5×10-5 for the three tests) which confirms the important rise observed since 1980 (Fig. b). The shift occurring at the end of the 1980s reported by and discussed in and is not observed in all rivers (see Fig. a). Indeed, the shift is clearly visible in catchments located in the Swiss Plateau/Jura regions and downstream lakes, but not necessarily in alpine catchments or catchments strongly influenced by hydro-peaking. Note that this shift is also present in air temperature records (see Fig. S13). The shift between the 1980s and 1990s is more important than previous or subsequent shifts, but contrary to the statement in , the warming trend continues after the shift. Looking at the 30-year anomaly difference, the mean anomaly difference over the 14 catchments for the 1970–2000  period is 0.59 ∘C and for the 1990–2018 period it is 0.55 ∘C. A partially overlapping samples two-sided t test finds no significant difference between these two values (p value = 0.59, this test is used instead of a classic t test as the two samples overlap). Consequently, the “end-of-80s” shift might be interpreted as a hiatus in the long-term trend. The apparent acceleration of the warming seen over recent years is due to the extreme year 2018, which pulls up the running mean.

A long-term analysis is also performed on discharge data (Fig. ). In this case, catchments with measurements ranging back to at least 1920 (20 catchments) are kept for anomaly analysis. Figure  shows that there is almost no trend in the long term for annual mean discharge and precipitation (for the discharge, the mean trend obtained by linear regression over the 26 catchments available between 1970 and 2018 is -0.5 % per decade). However, recent decades have shown a clear negative trend. The 1980s exhibited a positive runoff anomaly with a decrease toward the end of the decade. A 7- to 8-year cycle in the runoff annual mean can be seen in Fig. . This is related to the cycle found in the North Atlantic Oscillation (NAO) and the Atlantic Multi-decadal Oscillation (AMO) which has already been discussed in the literature . These cycles also have an influence on water temperature as shown by . The time series are presented in Fig. S15.

A longer multi-decadal variation can be seen in discharge data (see Fig. ). However, 1 century of data is not long enough to assess if there is a real 30- to 40-year cycle, which could be related to the 34- to 36-year cycle found in the Atlantic Meridional Overturning Circulation (AMOC) , or if there is only some statistical variation. As a consequence, it is not possible to assess if the decrease over the last decade is part of a long-term cycle, if it results from climate change, or both.

The decades from 1970 to 1980 and 1980 to 1990 show a more marked anomaly (negative first and then positive, see Fig. ) for discharge than for precipitation. This is explained by the glacier melt evolution, which reaches a minimum in the decade from 1970 to 1980 followed by a sharp increase in the next decade .

The trends in stream temperature and discharge have been computed using linear regression over the 1999–2018 period for all 52 catchments and over the 1979–2018 period when possible. All trend values are presented in the Appendix in Tables  and  for water temperature and discharge, and in Tables S4 and S5 for air temperature and precipitation. The plots shown in this section are for the 1999–2018 period, where more catchments are available. Similar plots for the 1979–2018 period are shown in Sect. S2.1. Note that results presented in this section, except for the trends in runoff over the last few decades, also hold for the longer time period, and the results are even more evident over this longer time period. This can be explained by the lower sensitivity to boundary effects and the generally higher robustness of linear regressions over longer time periods.

Trends in stream temperature and discharge are compared to trends in air temperature and precipitation in Fig. . There is a clear increase in water temperature and a reduction in discharge observed in Swiss rivers over the 1999–2018 period. The mean trends for the last 20 years are +0.37±0.11 ∘C per decade for water temperature (with a large spread in the distribution), +0.39±0.14 ∘C per decade for air temperature, -10.1±4.6 % per decade for discharge, and -9.3±3.4 % per decade for precipitation. However, the trends in precipitation and runoff have to be considered with caution regarding the long-term variation discussed above. For the 1979–2018 period, the mean trends are as follows: +0.33±0.03 ∘C per decade for water temperature (again with a large spread in the distribution), +0.46 ∘C ± 0.03 ∘C per decade for air temperature, -3.0±0.5 % per decade for discharge, and -1.3±0.5 % per decade for precipitation.

The water temperature and discharge trends for the four different regimes are shown in Fig. . Similar plots for air temperature and precipitation are shown in Fig. S14. A two-sided Wilcoxon test is used to assess whether differences between regimes are significant in terms of temperature trends (results shown in Table S3). As some categories only have a few observations and normal distribution can not be assumed, this test is used instead of a t test. Two groups can clearly be identified: the downstream lakes (DLA) regime and the Swiss Plateau/Jura (SPJ) regime on the one hand, and the alpine (ALP) and hydro-peaking-influenced (HYP) regimes on the other hand. Indeed, for both pairs of regimes, the hypothesis of different mean values is clearly rejected with p values > 0.15 (i.e. testing the hypothesis of a different mean between SPJ and DLA and between HYP and ALP). The water temperature trends are significantly lower for alpine catchments and catchments strongly influenced by hydro-peaking. The impact of lakes is discussed in Sect. .

The catchment area is not correlated with trend values (see Fig. ) despite the fact that area is clearly correlated with the regime (Table ). To infer the isolated effect of area, only catchments from the Swiss Plateau/Jura regime are used (largest sample of rivers and no major disturbance), but no correlation between water temperature or discharge trends and area can be found (see Fig. S19).

Elevation and the fraction of glacier coverage in the catchment (which are strongly correlated) clearly correlate with water temperature and discharge trends (see Fig. , bottom row). The smaller positive trends in water temperature and reduced negative trends in discharge observed for highly glaciated catchments can be attributed to cold water coming from glacier melt (as discussed in ), as air temperature trends for alpine catchments are similar to lowland catchments (see Fig. S14). For these reasons, discharge and temperature of alpine streams have been the least impacted by climate change to date. However, if this buffer effect induced by glaciers and seasonal snow cover disappears due to the continuation of temperature rise in the future , the alpine catchments will be amply impacted (see Sect. ). Lowland catchments, mostly located in the Swiss Plateau/Jura regions, experience the most important decrease in discharge.

Unsurprisingly, rivers strongly influenced by hydro-peaking show lower temperature trends compared with undisturbed waterways. This results from large volumes of cold water being released from reservoirs located at high elevation to lowland rivers as discussed, for instance, in .

In conclusion, for Swiss Plateau/Jura catchments, air and water temperature trend distributions are similar, and the mean of the trends for this type of catchment is close to the mean air temperature trend (see Figs.  and S14). Figures S20 and S21 show water temperature trends for each catchment plotted against trends in air temperature for the 1999–2018 and 1979–2018 periods. Single values (i.e. water and air temperature trends for a given catchment) are poorly correlated. Over the 1979–2018 time period, a better correlation for DLA and SPJ catchments is visible, suggesting that part of the poor correlation in Fig. S20 is due to the noise in the trends obtained with a linear model (boundary effects). For ALP and HYP catchments, the general poor correlation suggests that additional factors, such as snow and glacier melt and anthropogenic disturbances, become predominant in the energy balance, decoupling the mean air temperature and water temperature trends.

In the previous section, it was shown that rivers located downstream of lakes have water temperature trends similar to the Swiss Plateau/Jura catchments, in spite of a higher mean elevation and a larger glacier-covered fraction (see Table ), which typically attenuate the water temperature increase.

The effect of lakes located at the foot of mountain ranges on stream temperature is well known . The input water originates from alpine rivers (potentially disturbed by hydro-peaking), which are colder than the surrounding environment and not in equilibrium with local air temperature. As water has a certain residence time in the lake, its temperature increases due to atmospheric forcing and the main driver for the outflow water temperature is the air temperature. However, it has currently not been demonstrated if the effect of lakes on river temperature trends is similar. In , it is shown that lake temperature trends can exceed air temperature trends due to solar brightening.

To investigate the effect of lakes on water temperature trends, five lake systems with measurements at the inflow and the outlet are selected: the Thun–Brienz lake system, Lake Biel, Lake Luzern, Lake Walen, and Lake Geneva. Temperature anomalies with respect to the 1979–2018 period and trends are plotted for water temperature at each station and air temperature at meteorological stations representative of the catchment. The results are shown in Fig.  for Lake Geneva and in Figs. S22 to S25 for the other four lakes. The trends for the different inflow and outflow rivers and for air temperature are presented in Table .

For Lake Walen and Lake Geneva, the effect is obvious: the outlet trend is almost equal to the co-located air temperature trend. Even if trends in inflows are much smaller, they do not significantly influence the outlet waters (see Table ). The lake acts as catalyst and the system reaches a quasi-equilibrium. For Lake Geneva, the water temperature of the Arve River is also shown. The Arve River originates from the Mont Blanc massif (France) and flows for about 100 km through the Arve Valley before joining the Rhône in Geneva. Despite flowing through low-lying land, the Arve keeps its alpine characteristics, whereas these characteristics are completely lost in the Rhône River after the lake.

In Lake Luzern, a similar effect is observed. Indeed, the three rivers feeding the lake (the Reuss, Muota, and Engelberger Aa rivers) show trends that are considerably lower than that for the Reuss River in Luzern (see Table ). However, the Kleine-Emme River, which joins the Reuss just after Luzern, shows a similar trend without the presence of a lake along its course; this demonstrates that, for a mid-elevation stream, flowing a certain distance on the Swiss Plateau leads to a similar effect to that induced by lakes. For the Thun–Brienz lake system, the water temperature trend is enhanced as a result of the two subsequent lakes and it gets closer to the air temperature trend.

For Lake Biel, no effect is observed. This is not surprising as the Aare input water already has a trend similar to the local air temperature. In addition, the residence time in Lake Biel is very short (58 d, whereas for the five other lakes it ranges from 520 to 4160 d; ), limiting the exposure time of lake waters to atmospheric forcing. This has been described in more detail in .

In conclusion, despite their higher mean catchment elevation, water temperature trends for stations at lake outlets are similar to Swiss Plateau trends. As lakes have much longer residence times for water than rivers, they smooth out local effects such as snow or glacier melt or precipitation. As a consequence, water temperature trends at the outlet of lakes are generally similar to air temperature trends, which seem to be the main forcing.

In this section, stream temperature and discharge trends and anomalies are analysed at a seasonal scale. The relation between these two variables and the meteorological conditions (air temperature and precipitation) are also discussed on a seasonal basis. Particular seasonal features are then addressed. Finally, the evolution of the intra-annual variability along with the inter-seasonal correlation, or system memory, are discussed. Even if the inter-variable correlation and system memory are not directly linked to observed changes, they are key factors with respect to understanding the system dynamics and, thus, are essential for inferring the impacts of climate change on water temperature and discharge. The analysis below is mostly based on the 1999–2018 period. Seasons are defined as follows: winter is December–January–February (DJF), spring is March–April–May (MAM), summer is June–July–August (JJA), and autumn is September–October–November (SON).

Long-term evolution of the seasonal anomalies are shown in Figs.  and  for water temperature (decades from 1970 to 2010) and discharge (decades from 1960 to 2010). Air temperature and precipitation are shown in Figs. S26 and S27 and exhibit similar behaviour. For all seasons, the water temperature has been significantly rising since 1980. The warming is more important in summer and less pronounced in winter. For discharge, spring and autumn do not show an obvious trend in the long term. There is a clear decrease in summer since 1980, whereas winter shows a slight increase.

Annual and seasonal trends for stream and air temperature, discharge, and precipitation are presented in Fig.  for the 1999–2018 period. They confirm the tendencies described above. Mean water temperature trends are slightly smaller than air temperature trends for all seasons except for spring, when they are notably larger. This shows that rivers do not react linearly to a general warming of the atmosphere and additional factors control these complex systems. For discharge, negative trends are found in all seasons except for winter, when they are almost zero. Discharge trends follow precipitation trends in all seasons. In general, precipitation determines the discharge trend; consequently, snow and glacier melt play a minor role in the observed trends. However, for specific catchments, this can be different. When looking at individual catchments, there is only a insignificant correlation between trends in air and water temperature, and between trends in discharge and precipitation (see Table S6). This absence of a correlation results from the noise in the individual trend values due to the short time period available. This is a limitation of the method applied and, thus, trends can not be used for an inter-variable interaction study.

To explore the correlation between variables, raw values are used. Table  shows the correlation between main variables on a yearly and seasonal basis. These values are obtained by computing the correlation of two variables for individual catchments and then averaging these correlations. As a measure of the robustness of the method, the number of catchments where correlations are insignificant (p value > 0.05) is indicated. At an annual scale, air temperature is the main driver of water temperature. The negative correlation between water temperature and discharge is rather weak and is not significant in almost half of the catchments. As expected, discharge and precipitation are strongly correlated.

In this section, two ecological indicators based on water temperature are presented. The first one is the number of days per year when the stream temperature exceeds 25 ∘C for at least 1 h during the day. Rivers reaching this threshold at least once in the past are shown in Fig. . The summer discharge anomaly for these catchments is shown in Fig. S38.

There is a noticeable increase in warm water events over the few last decades. The extreme years of 2003 and 2018 are clearly highlighted. The occurrence of warm days is often related to discharge deficit, i.e. low flow conditions. However, while peaks above 25 ∘C were only occurring along with a discharge reduction in the 1970s and 1980s, this is no longer the case in the last few decades (see e.g. years 1994, 2007, and 2012), indicating that the Swiss river system is becoming more sensitive and more exposed to these extreme temperature events with ongoing climate change.

The second threshold is the consecutive number of days above 28 d for which the temperature constantly remains above 15 ∘C, which is critical with respect to the spread of the proliferative kidney disease (PKD). Figure  shows the number of days per year during which fish would be exposed to PKD. There is a clear increase over the past few decades (see Fig. b), and some rivers that were almost preserved before 1990, such as the Aare in Bern (Aar-Ber) or the Broye in Payerne (Bro-Pay) have become increasingly affected over the last 2 decades. During extremes years, such as 2003 and 2018, the increase is particularly visible.

Most of the measurement sites where such warm water events were observed are located downstream of lakes and in relatively large catchments, or at low elevation on the Swiss Plateau (e.g. the Broye or the Glatt rivers). Some catchments at higher elevation are also affected (e.g. the Linth in Weesen – Lin-Wee, which has a mean basin elevation of 1584 m). Looking at the temporal distribution of days above the 15 ∘C threshold (not shown), they mostly occur between June and mid-October. Over time, there is a clear shift to earlier occurrences in the year, although the temporal conclusion of these events remains constant.