Main

Lake surface water temperature can increase considerably in response to greenhouse warming1,2,3, leading to unprecedented shifts in lake thermal habitats and consequently in lake ecosystem functioning4,5,6. The implications of lake warming are particularly severe when temperatures increase above the thermal tolerance limit of key aquatic species7,8,9. One potential severe consequence of long-term future warming in lakes is the emergence of thermal conditions that are wholly outside the range of historical variability and not analogous to conditions observed either today or in the past10,11. In other words, future climate change could lead to the emergence of no-analogue conditions (that is, when lake temperatures become increasingly new) and likewise exceed temperatures that organisms will be able to adapt to. Future lake temperatures with no current analogue (that is, not found today or in the past) and the disappearance of some extant climates could lead to the extinction of some species and the redistribution of others at the global scale12,13. Projecting the emergence of no-analogue lake temperatures is thus fundamental for adaptation, planning and future risk assessments.

A key challenge for projecting the emergence of no-analogue conditions is to partition the uncertainties introduced by natural variability of local climates and, specifically, to assess when temperatures will increase outside the upper natural variability range. With climate projections using an individual realization of an Earth system model, one is faced with the challenge of deconvolving the forced signal from natural variability, with this becoming particularly pronounced at local scales. With large-ensemble simulations, where the only difference between the individual simulations lies in the initial conditions, the forced signal can be identified through the ensemble mean14. Thereby, this method facilitates a clear identification of natural variability as deviations from the ensemble mean. Previous studies have investigated the emergence of no-analogue conditions in both terrestrial and marine ecosystems11,15,16. In lakes, however, the use of ensemble modelling is less common17,18,19—particularly the use of large ensembles20—leading to a dearth of knowledge regarding the emergence of no-analogue conditions in one of Earth’s most critical ecosystems. In this Article, we aim to fill this knowledge gap by calculating the emergence of no-analogue conditions in lakes using projections from a 100-member ensemble of historical (1850–2014) and future (2015–2100) simulations conducted with a state-of-the-art Earth system model: the Community Earth System Model version 2 Large Ensemble (CESM2-LE)21, which includes a fully coupled lake model (see Methods).

Using the CESM2-LE, we investigated the forced (anthropogenic) and natural variability components of depth-resolved lake temperature changes during the open-water, ice-free (that is, warm) season (see Methods), enabling identification of: (1) the forced climate change signal itself; and (2) a timescale over which such changes will emerge over natural variability. Conceptually, no-analogue conditions represent unprecedented thermal environments that have not been observed within the historical record. Understanding these conditions is important as they signal a shift beyond the adaptive capacities of current aquatic ecosystems, potentially leading to ecological disruptions. The emergence of no-analogue conditions is subsequently communicated relative to global warming levels (calculated from CESM2-LE). In Fig. 1, we show for illustrative purposes the method for calculating the emergence of no-analogue conditions at the surface of one modelled lake, but the same method is then applied to all simulated lakes, encompassing both surface and interior conditions. In this study, we excluded all model grid points at which lakes experienced at least 8 months of annual ice cover during the historical (1850–1900) period (Supplementary Fig. 1). The CESM2-LE lake temperature projections analysed in this study have been validated against in situ and satellite data, as well as against other process-based lake models (Supplementary Figs. 2–10 and Supplementary Table 1).

Fig. 1: Methodology for calculating the emergence of no-analogue conditions in lakes.
figure 1

a,b, Shown for one example lake (situated at 42.9° N and 111.3° W) is the method used to estimate the emergence of no-analogue conditions. In a, each grey line represents the simulated warm season surface water temperature from the individual ensemble members (n = 100). The black line indicates the ensemble mean. The red lines represent two standard deviations (\(\sigma\)) around the mean (\(\mu\)). The blue horizontal lines represent the natural variability range in lake surface temperature, defined as 2\(\sigma\) around the \(\mu\) of the ensemble (1850–1900). The emergence of no-analogue conditions, shown by the vertical dashed line, is estimated as the time when lake temperatures will permanently exceed the natural variability range. b, Global average surface air temperature anomalies (relative to 1850–1900) from the ensemble mean, which the emergence of no-analogue conditions (a) is compared against.

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No-analogue conditions in lake surface waters

The emergence of no-analogue conditions at the surface of lakes is projected to occur under different levels of future global warming, with strong regional dependence (Fig. 2a). These conditions indicate a considerable shift in lake thermal conditions that surpasses historical variability, potentially leading to notable ecological and biological impacts. Low-latitude lakes are projected to experience no-analogue conditions first (that is, under lower levels of global warming; Fig. 2 and Supplementary Fig. 11). This suggests that these ecosystems, which are already adapted to narrower thermal ranges, may be more vulnerable to early changes, highlighting the importance of considering regional differences in climate change impacts. To investigate further the influence of lake location on the emergence of no-analogue conditions, we grouped lakes by the thermal regions in which they are found22. Within each thermal region, we calculated the average and standard deviation of the global mean surface air temperatures under which no-analogue conditions occur at the lake surface (Fig. 2c). Our results suggest that no-analogue conditions at the lake surface will emerge under lower levels of global warming within the warmest thermal lake regions (for example, northern warm, tropical hot and southern hot lakes). For the colder lakes situated in, for example, northern frigid or southern temperate regions, the emergence of no-analogue conditions is projected to occur only after global warming reaches ~4.0 °C (Fig. 2c). Our analysis also suggests that a proportion of the studied lakes—primarily those situated at higher latitudes—are unlikely to experience no-analogue warm season temperature conditions during this century (Fig. 2a), at least under the warming scenario considered.

Fig. 2: Emergence of no-analogue conditions at the lake surface.
figure 2

a, Projected emergence of no-analogue conditions at the lake surface under global warming. This illustrates the magnitude of projected global warming that our simulations suggest will result in no-analogue conditions. b, Distribution of lake thermal regions worldwide. c, Emergence of no-analogue conditions across the thermal regions during the warm season. The data represent means ± s.d. NC, northern cool; NF, northern frigid; NH, northern hot; NT, northern temperate; NW, northern warm; SH, southern hot; ST, southern temperate; SW, southern warm; TH, tropical hot.

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Role of anthropogenic forcing and natural variability

The emergence of no-analogue conditions in lakes is determined by both the anthropogenic trend and the range of natural variability in lake water temperature, both of which vary with latitude (Supplementary Fig. 12) and thus across lake thermal regions (Fig. 3). It is the ratio of these quantities that determines when no-analogue conditions emerge. When the ratio of the trend to the natural variability is high, no-analogue conditions will occur sooner as lake temperatures can reach the natural upper bounds earlier. In contrast, if this ratio is low, no-analogue conditions will occur later. In Fig. 3, we compare the trend (2000–2100) and natural variability (1850–1900) in lake surface water temperature. Our projections suggest that during this century lakes situated in colder climates (northern frigid and northern cool) will experience strong surface temperature trends ~1.5 times higher than lakes situated in warmer regions (for example, northern hot and tropical hot). However, these cold lakes also experience the largest natural variability, which is approximately twice that projected in the climatologically warmer lakes. Both the trend and natural variability in lake surface water temperature closely follow those projected for surface air temperature (Supplementary Fig. 13). This is expected, given the degree to which surface air temperature variations influence lake surface temperature. However, the amplified response of lake surface temperature to air temperature changes is also influenced by lake depth, with deeper lakes typically shown to experience greater long-term change23,24. Other atmospheric drivers can also influence lake surface temperatures, including wind speed25 and solar radiation26, among others27, all of which are included in our model projections (see Methods). There is also a lag between air and water temperature, particularly for large lakes28, which can result in a partial decoupling of air and water temperature at seasonal timescales. These factors, as well as the influence of lake morphometry29 and the presence of winter ice cover1, account for some of the variability in air–water temperature relationships and partly explain why natural variability and warming rates can differ somewhat between air and surface water temperature (Supplementary Fig. 13). Overall, our results suggest that although warmer tropical lakes experience lower temperature trends, their level of background natural variability is proportionally even lower, so they can experience relatively early emergence of no-analogue conditions.

Fig. 3: Across-lake differences in the trend and natural variability of surface water temperature.
figure 3

a,b, Rate of change in lake surface water temperature across the studied lakes from 2000–2100 (a) and differences in these trends across lake thermal regions (b). c,d, Natural variability (1850–1900) in surface water temperatures worldwide (c) and differences in this variability across thermal regions (d). The trends in surface water temperature were calculated from an average across the 100 ensemble members using a linear regression model. The data in b and d represent means ± s.d.

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Novel conditions in subsurface waters

Understanding the emergence of no-analogue conditions at the lake surface will be critical for assessing the impacts of climate change on lake ecosystems, particularly for organisms and aquatic species that cannot shift their vertical distributions to track a suitable thermal habitat. However, some aquatic species have adapted to light and thermal conditions at depth and hence will not be directly influenced by surface water temperature changes. It is therefore important to also consider the emergence of no-analogue conditions in subsurface layers, and to identify when the natural range of variations in temperature will be exceeded throughout the water column. We investigated differences in the emergence of no-analogue conditions by depth in our global simulations. For consistency, we initially focused on the subsurface layers ranging from 0–8.5 m depth. Lakes that are 8.5 m deep (that is, in terms of average depth) or shallower represent 96% of the global lake distribution30. In some lake thermal regions, our simulations suggest clear differences across depths in the emergence of no-analogue conditions (Fig. 4). The most apparent variations with depth were found in northern lakes (northern frigid to northern hot) where the emergence of no-analogue conditions is projected to occur much later for deeper waters. For example, in northern temperate lakes, no-analogue conditions at the lake surface will emerge under a projected global warming of 2.7 ± 0.6 °C. However, at a depth of ~8.5 m, no-analogue conditions become emergent only for a global temperature increase of 4.5 °C (corresponding to ~2100 ce) (Fig. 4). Several lakes in this thermal regimen are unlikely to experience no-analogue conditions in deeper waters before 2100 ce under the projected levels of global warming considered in this study. However, in tropical hot and many southern lake thermal regions (southern hot, southern warm and southern temperate), there are only marginal differences in the projected emergence of no-analogue conditions with varying depth (Fig. 4f–i). In tropical hot lakes, no-analogue conditions will emerge under a global warming of 2.5 ± 0.5 °C at the surface or 2.6 ± 0.7 °C at a depth of 8.5 m.

Fig. 4: Emergence of no-analogue conditions in subsurface waters.
figure 4

a–i, Vertical profiles of the calculated emergence of no-analogue conditions across thermal lake regions. Subsurface patterns are shown for lakes in northern frigid (a), northern cool, (b) northern temperate (c), northern warm (d), northern hot (e), tropical hot (f), southern hot (g), southern warm (h) and southern temperate regions (i). For each thermal region, we selected lakes that were at least 8.5 m deep and calculated the average (solid line) and s.d. (dashed lines) in the emergence of no-analogue conditions during the warm season.

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Our simulations also suggest clear differences in the emergence of no-analogue conditions in bottom water temperature (Fig. 5a). Notably, warmer low-latitude lakes experience no-analogue conditions first and cooler lakes situated at higher latitudes (that is, cooler lake thermal regions) experience no-analogue conditions at depth last, if at all. An ordinary least-squares analysis (sample size = 1,084) suggested that, in lakes with a depth of 8.5 m (and in which no-analogue conditions emerge), 87.7% of the variance in the emergence of no-analogue conditions can be explained by the ratio of the trend to the natural variability. Our simulations suggested that the calculated trends in bottom water temperature during the twenty-first century will be highest at low latitudes and the natural variability will be lowest at low latitudes (Fig. 5 and Supplementary Fig. 14). The trend in deep-water temperature is primarily determined by the trend in surface water temperature and, critically, the warming signal that is transferred vertically within a water body. The latter is influenced by the frequency of overturning days during the ice-free season. Specifically, the trend and natural variability in bottom water temperatures follow closely those projected at the surface in tropical hot lakes and shallow polymictic lakes worldwide. In our simulations, 65% of lakes (with a depth of 8.5 m; 590 lakes) in the tropics overturn for more than 182 d annually. However, the trend of bottom water in lakes that stratify has a weak relationship with the trends in surface water temperature. In northern temperate and northern cool lakes with a mean depth of 8.5 m and where no-analogue conditions of the bottom water are projected to emerge this century, the frequency of overturning days explains 73.1% of the variance (sample size = 294) in the trend of bottom water temperature, which outweighs the impacts of the trend in surface water. These lakes are dimictic and experience ice coverage annually, and the amount of downward heat penetration increases along with the frequency of overturning across lakes. In lakes that experience intermittent mixing or stratify permanently, bottom waters will, to a large extent, be shielded from much of the influence of surface temperature, although deep mixing31,32 and the downward diffusion of heat33,34 are able to introduce heat into deeper water. The slow increase in bottom water temperature in these lakes, however, would lead to a delayed emergence of no-analogue conditions at depth.

Fig. 5: Emergence of no-analogue conditions in deep water.
figure 5

a, Projected emergence of no-analogue conditions by bottom water temperature increase under global warming. Lakes where no-analogue conditions are unlikely to occur this century, under the global warming levels considered, are shown in black. b, Rate of change (2000–2100) in bottom water temperature during the warm season, calculated from the average of the 100-member ensemble. c, Natural variability in bottom water temperature during the warm season, estimated as twice the standard deviation (\(\sigma\)) around the mean (\(\mu\)) of the large ensemble between 1850 and 1900. d, Percentage of overturning (that is, mixed) days during the warm season (1850–1900), calculated as the average of the 100-member ensemble.

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Impact of no-analogue conditions on lake ecosystems

The ecological responses expected from the emergence of no-analogue conditions at the surface or at depth are likely to be idiosyncratic and will depend on attributes such as species adaptive capacity, the ability of aquatic species to migrate and the disruption of ecological interactions. Nevertheless, the emergence of no-analogue lake temperatures over the twenty-first century implies that there will be a substantial disruption of the normal lake conditions that have shaped lake ecosystems in the past. Lake ecosystems are already being threatened by several anthropogenic stressors35, including over-fishing36, eutrophication37,38 and water abstraction39,40. Climate change exacerbates the degradation of lake ecosystems by pushing organisms to adapt to warmer waters. In addition, extreme events such as lake heatwaves are expected to increase under persistent anthropogenic perturbations41, with potentially devastating effects on lake ecosystems. Indeed, the occurrence of extreme events in recent years has highlighted the serious consequences of reaching historically unprecedented conditions7,9,42,43,44.

Although our study focuses on the emergence of no-analogue conditions relative to natural variability, it is crucial to consider the absolute tolerances of organisms inhabiting lakes. Even temporary deviations in temperature beyond these absolute tolerances can have ecological impacts, including stress, mortality and disruption of ecosystem services7,8. For instance, species adapted to specific thermal niches may face critical thresholds beyond which survival and reproductive success are compromised, regardless of whether such conditions are unprecedented within the historical context of variability. Cold water fish species such as lake trout (Salvelinus namaycush), which have optimal environmental temperatures of less than ~12 °C, could be particularly susceptible to no-analogue conditions, or even to changes that are not considered to be outside of the bounds of natural variability. In lakes experiencing no-analogue warming, temperatures could exceed these limits for a sustained duration, potentially leading to decreased growth rates, increased susceptibility to disease and higher mortality rates. Similarly, for aquatic plants such as the water lily (Nymphaea odorata), which thrive in temperatures up to ~30 °C, mean warming of lakes might push temperatures beyond this threshold, impacting their photosynthesis and growth. Several uncertainties must also be considered when evaluating these impacts, including that species’ thermal tolerances vary45,46, genetic and phenotypic variability can influence adaptability47,48 and ecological interactions may amplify or mitigate effects49,50. For example, changes in predator–prey dynamics, competition for resources and symbiotic relationships can influence how species respond to altered thermal conditions. Shifts in community composition and trophic interactions may have cascading effects throughout the ecosystem, altering nutrient cycling and productivity. Additionally, the effects of no-analogue conditions may be influenced by habitat complexity, further complicating predictions of ecological responses. Thus, although our study provides a framework for identifying no-analogue conditions, the actual ecological impacts will depend on a multitude of factors, requiring comprehensive assessment for accurate predictions and mitigation strategies.

The simulations employed in this study demonstrate the value of scrutinizing climate change perturbations on ecosystem thermal environments across the water column with respect to surface conditions, which has been the focus of previous studies exploring future warming impacts on lakes. Our results thus shed light on a complex picture of the impacts of climate change on lake ecosystems by adding the vertical dimension and recognizing the importance of natural variability. We find that ongoing climate change will induce changes across the water column, particularly in low-latitude lakes, leading to the emergence of unparalleled climates with no modern counterparts. If anthropogenic emissions continue to rise, we project that the natural variability in water temperature will be exceeded and no-analogue conditions will become ubiquitous in lakes this century, probably affecting their habitability. Assuming that aquatic organisms are adapted to the current thermal environment, no-analogue conditions may lead to substantial rearrangements of freshwater habitats this century.

Methods

Lake temperature projections

We evaluated the influence of climate change on the thermal environment of lakes by analysing simulations from CESM2-LE21. Most notably, we investigated lake temperature projections generated by the Lake, Ice, Snow, and Sediment Simulator (LISSS)51, which is a one-dimensional (1D) thermodynamic lake model embedded within and coupled to the land surface module of CESM (that is, the Community Land Model; version 5)52. The CESM2-LE lake simulations have been used, and described in detail, in previous studies20,53. LISSS is a thermal diffusion model—it is an adapted version of the Hostetler 1D model—and was developed specifically for simulating lakes in Earth system models. Compared with other lake models, LISSS has lower computational expense and requires minimal lake-specific calibration. More complex models, such as the General Lake Model54 or SimStrat55, improve the characterization of deep lakes, but also often require lake-specific data or calibration and have not yet been integrated into Earth system models. LISSS was developed to accurately simulate lakes in Earth system models, but also to be computationally efficient. In brief, LISSS simulates the thermal environment of lakes by balancing the surface energy budget and solving the 1D thermal diffusion equation for lake water temperature, then it simulates vertical mixing, including diffusion of wind-driven eddies, convective mixing, molecular diffusion and enhanced mixing due to unresolved 3D processes. LISSS has been tested extensively in previous studies investigating lake responses to climate change20,51,56,57. LISSS has been shown to provide an accurate representation of water temperature, surface fluxes and the thickness of ice and snow in previous studies for which observational data were available20,51,58,59,60.

LISSS was used to simulate depth-resolved lake water temperatures at a longitude–latitude resolution of ~1° by ~1° and a 30 min time step. Lakes simulated within each grid in CESM2-LE are based on the depth and surface area of all known lakes in that region61,62. The projections thus represent a typical lake for each grid cell57,63,64. Each lake grid has ten vertical layers in the simulation. A piecewise cubic Hermite interpolation method65 was applied to interpolate lake water temperatures onto desired depths. The CESM2-LE simulations include historical projections from 1850–2014 and future (2015–2100) projections simulated under the Shared Socioeconomic Pathways forcing scenario SSP3-7.0 (ref. 66). An ensemble approach was used in CESM2-LE including 100 members, with each member initialized from a set of different combinations of initial states of the atmosphere and ocean21.

Although previous studies have validated lake temperature simulations from LISSS20,51,56,57, here we performed an additional validation of the outputs from CESM2-LE (Supplementary Figs. 2–10 and Supplementary Table 1). Most notably, we compared the lake temperature simulations with satellite-derived surface water temperatures from ARC-Lake version 3.0 (ref. 67) and depth-resolved in situ temperatures from ref. 68. All comparisons were made between the observations and simulations by extracting the water temperature time series from the grid in which each lake was located. In the case of satellite-derived lake surface temperatures, we highlight that the obtained value is sensitive to the skin temperature of the water, which is the temperature of a layer <0.1 mm thick from which thermal radiation is emitted by the lake. Thus, the satellite datum is an estimate of this skin temperature, which may differ from the temperature as measured by a thermometer, or as simulated by a lake model, a few centimetres below the air–water interface. Typically, the difference between skin and sub-skin lake surface temperature is of the order of a few tenths of a degree69,70,71. This temperature difference is commonly known as the cool skin effect72,73, the magnitude of which is influenced by air–water surface heat fluxes70,71. Satellite lake surface temperatures have been used to quantify worldwide aspects of lake thermal dynamics22,74,75. Regarding our depth-resolved lake temperature observations, these are mostly only available for lakes in the Northern Hemisphere, but also include a few tropical systems68. In turn, our depth-resolved lake temperature simulations are not as well validated at low latitude but do provide a reasonable validation of our modelled data when available. To verify that our simulations were able to simulate multidecadal variations in lake temperature (and would therefore also be informative with respect to future climate change impacts), we compared the CESM2-LE simulations with long-term (1910–2018) in situ water temperature observations from Wörthersee, Austria (Supplementary Fig. 8), available from ref. 76.

We also compared the CESM2-LE water temperature simulations with global-scale projections from the Intersectoral Impact Model Intercomparison Project phase 2b (ISIMIP2b) Lake Sector18. Specifically, we repeated the model validation exercise described above for CESM2-LE, but for the ISIMIP2b projections, then compared the validation summary statistics. Here we compared the CESM2-LE simulations with those simulated by more complex models, including: (1) SimStrat-UoG, a modified version of the buoyancy-extended k–ε model SimStrat, which is a k–ε turbulence model with buoyancy and internal seiche parameterization77,78; (2) LAKE, an extended one-dimensional model of thermodynamic, hydrodynamic and biogeochemical processes in lakes79,80 that has been tested extensively with respect to thermal and ice regimens under contrasting climate conditions81,82,83,84; and (3) VIC-LAKE, a 1D model derived from the Variable Infiltration Capacity Macroscale Hydrologic Model85. These models were included in ISIMIP2b to simulate lakes worldwide at a 0.5° by 0.5° grid resolution using climate projections from GFDL-ESM2M, HadGEM2-ES, IPSL-CM5A-LR and MIROC5 as input. The ISIMIP2b Lake Sector simulations have been used extensively to investigate the impact of climate change on lakes57,63,64. The model validation exercise demonstrated that despite the spatial resolution of CESM2-LE being coarser (1° by 1°) than that of ISIMIP2b (0.5° by 0.5°), the simulations provide comparable performance for the lakes tested. We also note that in the lakes tested the standard deviations of the observations and simulations from CESM2-LE are comparable at the lake surface, but the difference typically (although not always) increases in deeper water.

The CESM2-LE simulations were also used in this study to estimate the number of overturning (that is, mixed) days in lakes worldwide. Although there is no universal definition of stratification/mixing in lakes86,87, here we define an overturning day as the day that has at least one full water column overturning during a 24-h period.

Emergence of no-analogue conditions

The emergence of no-analogue conditions was estimated from the 100-member CESM2-LE as the time when an increase in lake temperature is permanently above its natural variability. In this study, we considered the natural variability in lake temperature to be twice the standard deviation (\(\sigma\)) around the mean (\(\mu\)) of the ensemble between 1850 and 1900. This period was chosen to represent the pre-industrial period when the influence of anthropogenic emissions was considered minimal. Thus, we took lake temperatures of all of the ensembles (n = 100) and all of the years between 1850 and 1900 as a sample set that was formed under a pre-industrial climate. The natural variability range was defined as twice the standard deviation around the mean of the pre-industrial sample set. Along with continuous warming, no-analogue conditions emerge when \(\mu\) − 2\(\sigma\) (the lower red solid line in Fig. 1a) of the 100-member ensemble permanently exceeds the natural variability range (that is, when the upper threshold is exceeded). The calculated emergence of no-analogue conditions was subsequently communicated relative to global warming levels, which provided a way to reference change in climatic conditions independent of the emissions scenario used in the simulations.

In this study, we only considered the open-water, ice-free (that is, warm) season when estimating the emergence of no-analogue conditions (Supplementary Fig. 1). We define the warm season as January to March in the Southern Hemisphere (90° S–23.5° S) and July to September in the Northern Hemisphere (23.5° N–90° N). In tropical lakes (23.5° S–23.5° N), the warm season refers to the entire year. However, we note that our definition of a warm season does not strictly include the warmest months in all of the studied lakes, with some lakes experiencing, for example, higher surface water temperatures in June compared with September. In this study we also excluded all model grid points where lakes experienced at least 8 months of annual ice cover during the 1850–1900 period (Supplementary Fig. 1). Finally, the lake temperature for the warm season was calculated for each lake and used to estimate the natural variability and emergence of no-analogue conditions.

To investigate across-lake differences in the emergence of no-analogue conditions, we grouped the studied lakes according to the lake thermal region in which they are found22. This classification allowed us to better understand the varying capacities of different lake types to cope with thermal changes, and the potential onset of no-analogue conditions serves as an indicator of when and where these ecosystems may face unprecedented thermal stress.

Limitations of the model projections

Although we consider our results to be robust and believe that they bridge an important knowledge gap in climate change assessments, there are some limitations to consider when interpreting our key findings. First, our simulations are for representative lakes for each CESM2-LE grid. Individual lakes within a grid will behave in a different way from the typical lake considered as, for example, lake surface area and depth are known to influence both lake surface and bottom water temperatures due to differences in their thermal inertia23,29 and thus could also influence the computed emergence of no-analogue conditions. We also note that as our projections were generated with a 1D process-based lake model, which largely represents lake mean conditions88,89, horizontal features in lakes (for example, lateral advection) and the intra-lake responses to climate change will not have been captured23,24.

In this study, we also calculated the emergence of no-analogue conditions based on the results of SimStrat-UoG model simulation from the local lake sector of ISIMIP. Instead of simulating virtual lakes based on average depth in individual grids, this project configured the lake model with actual bathymetry for 59 lakes. Of these, 56 had corresponding lake grids in CESM2-LE. The calculation of emergence of no-analogue conditions for the ISIMIP local lake simulation was based on the single realization as the meteorological forcing for the lake simulation was achieved from the output of the GFDL-ESM2M model under the RCP8.5 scenario in CMIP5. In the calculation, the natural variability range was calculated as twice the standard deviation around the mean of water temperature during 1850–1900. The forcing signal was identified as the fourth-order polynomial fit of the raw data and the natural variability (that is, the envelope denoted by the two red solid lines in Fig. 1a) was calculated as the two standard deviations of temperature anomalies (by retracting the fourth-order polynomial fit values from the raw data) in a sliding window of 30 years. After calculating the emergence of no-analogue conditions, we compared the year of no-analogue conditions emerging against the magnitude of projected global warming. To maintain consistency in the calculation method, we applied the same method to individual members of the CESM2-LE. The results indicated that the emergence of no-analogue conditions in the surface water estimated by the ISIMIP local project is close to the CESM2-LE-based estimations, except for four lakes (that is, Annie, Biel, Kinneret and Sau) in the northern mid- and high latitudes that have a difference of about 1 °C in warming magnitude. Notably, despite the difference in the model configuration of depth, the emergence of no-analogue conditions projected by the CESM2-LE shares the same vertical pattern with the emergence estimated by the ISIMIP local project, which uses the actual depths of lakes. For example, in Lake Kivu, which is in the tropics and has a maximum depth of more than 490 m, the CESM2-LE projects the same pattern of emergence as the ISIMIP local project for the upper 50 m layer. Indeed, there exists a distinct difference in one of the 56 lakes (that is, Lake Rotorua, New Zealand), in which the vertical patterns of emergence are opposite to the two simulations. Although the model configuration of virtual lake depth induces bias in the projection of emergence of no-analogue conditions, the CESM2-LE-based projections are in the same range of uncertainty as the estimations based on the simulation of actual lakes.

Another limitation of the lake temperature simulations is that the light attenuation coefficient (Kd) does not vary temporally but is assumed to be constant for a given lake (but does vary from one lake to another). Although this is common in 1D global lake simulations18,57,59, it means that changes in water transparency during the twentieth and twenty-first century are not considered in the historic and future projections of lake temperature. Transparency can either increase or decrease in the future, as it has during the historic period, due to changes in—among other things—land management practices and precipitation patterns90. These changes in transparency can either amplify or suppress lake surface temperatures under climate change91. Although it is unclear how transparency will change during the twenty-first century, we now discuss how some of the potential changes could influence our long-term projections of water temperature. Regarding surface water temperature, stronger light attenuation can lead to higher temperatures in spring and summer (due to higher absorption of solar radiation) but result in faster cooling in autumn due to the presence of a shallower thermocline92,93.

As suggested by our results, the influence of climatic change on bottom water temperature will differ across lakes depending on their mixing regimen, with, for example, bottom temperatures experiencing a stronger response to climatic warming in lakes that frequently mix. An increase in transparency in these lakes will probably result in an even greater increase in bottom temperature, due to an increase in the depth at which solar radiation can penetrate through the water column. Conversely, a decrease in transparency could result in a weaker relationship between air and bottom temperature, or even a cooling of the deeper layers, due to well-mixed lakes potentially shifting to a more stable mixing regimen94,95. However, such transparency-induced alterations in mixing regimens are most likely to occur in marginal lakes (that is, those that historically transition between two mixing regimen types)75,95. In seasonally stratifying lakes, a change in transparency could influence how solar radiation is absorbed in the water column, essentially altering the vertical partitioning of heat. A scenario of increasing water transparency could result in further amplification of bottom warming compared with those projected in this study91, leading to an earlier emergence of no-analogue conditions. Conversely, a decrease in transparency could result in cooler bottom water temperatures in summer due to thermal shielding42,91,96,97, thus leading to a later emergence of no-analogue conditions. The modelling protocol followed in this study assumed no temporal change in water transparency nor changes in topography (for example, wind sheltering), both of which can influence lake temperature98, but instead focused solely on the more robust future projections of changes in climate.

It is important to consider that our study was based on simulations from a single lake model coupled to an Earth system model. Recent studies have highlighted the benefit of investigating climate change impacts in lakes with the use of lake model ensembles17,18. Indeed, multi-lake model ensemble simulations are increasingly used to obtain robust assessments of freshwater ecosystem responses to climate change. A lake model ensemble approach was not feasible within CESM2-LE, given its large computational requirements. Future studies could benefit from considering multiple lake model simulations when investigating lake responses to climate change within a large ensemble. Despite these limitations, our results provide an important step forward in understanding changes in lake thermal conditions within a warming world.