Introduction

Lakes, numbering more than 100 million worldwide, play a vital role in land-atmosphere interactions and regional climates1,2,3. Amid ongoing climate change, lakes—especially those in colder regions—are undergoing rapid and dramatic changes4,5,6, characterized by the loss of lake ice7,8 and significant warming of water temperatures9,10,11, both of which raise substantial concern.

Ice cover on lakes acts as a natural insulator. However, the reduction of lake ice under climate change decreases surface albedo, allowing for a greater influx of solar energy4,11. As a result, lake temperatures rise typically as lake ice cover diminishes12. Additionally, the absence of ice effectively removes the barrier between the warmer water and the colder atmosphere above, creating a crucial opportunity for the exchange of energy and material. This process has the potential for considerable heat and gas transfer with the atmosphere13,14,15,16,17, as exemplified by the increased release of methane from warming lakes18,19,20. Despite its significance, uncertainty persists regarding the exact role of lake ice, largely due to the lack of a comprehensive assessment of lake heat release. Furthermore, rising water temperatures represent a substantial increase in energy storage within lakes, which could further amplify heat release to the atmosphere21,22,23. Additionally, warmer water contributes to shifts in the timings of ice-off and ice-on4. Overall, the global quantification of heat released from lakes to the atmosphere remains largely unknown.

The role of lake ice cover in lake-atmosphere interactions is analogous to the well-documented Arctic amplification phenomenon24. The Arctic region has experienced rapid warming, driven by diminishing sea ice and temperature feedback mechanisms24,25,26,27. This amplified warming in high latitudes will impact the thermal dynamics and ice phenology of lakes, with the potential to considerably alter energy exchange between lakes and the atmosphere. However, studies from a land-surface perspective have primarily focused on the warming effects of vegetation and the ice-snow albedo feedback28,29,30, often overlooking the impact of lake changes on the local atmospheric energy budget. Additionally, alterations in lakes not only influence surface albedo but also lead to complex seasonal patterns of heat storage and release, driven by thermal inertia and seasonal freeze-thaw cycles, similar to processes observed in oceans1,4,14,16.

In this study, we investigate changes in lake heat release (LHR) globally, which we define as the sum of upward longwave radiation (lake-emitted longwave radiation, LWup), upward shortwave radiation (lake-reflected shortwave radiation, SWup), sensible heat flux (SH) and latent heat flux (LH) (see Methods). LHR is defined as the first-order energy transfer from lakes to the atmosphere, describing the process through which lakes release absorbed energy back into the atmosphere. Lake energy budget variables from three lake models forced by four general circulation models (GCMs)31 are employed to estimate LHR. We compare LHR between the present-day and pre-industrial periods to assess the impact of historical anthropogenic forcing, and subsequently project future changes under different anthropogenic greenhouse gas concentration pathways.

Results

Amplified LHR changes in northern mid-high latitudes

Our results indicate a significant relative increase in LHR across the majority of global lakes (Fig. 1a). The average increase is 1.5 ± 0.8% globally in the present-day period (1991–2020) compared to pre-industrial conditions (Fig. 1a). Approximately 64% of lakes with increasing LHR are concentrated at mid-high latitudes (>45°N). The relative increase in LHR at these latitudes, with an average rise of 1.8 ± 0.8%, is approximately double that of lakes at low latitudes (30°S–30°N), which show an average increase of 0.9 ± 1.0%. The peak of this relative increase (2.8 ± 0.8%) occurs around 75–80°N (Fig. 1b).

Fig. 1: Historical changes in lake heat release (LHR).
figure 1

Relative changes in spatial pattern (a) and latitudinal average (5° bins) (b) of LHR. Absolute changes in spatial pattern (c) and latitudinal average (5° bins) (d) of LHR. e Latitudinal sum (5° bins) of ∆LHR times lake area. Latitudinal averages are weighted by lake area, and the shaded regions represent the ensemble standard deviation. The text in (a) indicates the global average change, weighted by lake area. The grid cells in spatial maps correspond to representative lakes (see Methods). All changes refer to differences between present-day (1991–2020) and pre-industrial conditions. Source data are provided as a Source Data file.

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In terms of absolute changes, our analysis suggests that 93% of lakes within the mid-high latitudes experience a LHR increase of more than 4 W·m–2, with 70% exceeding 6 W·m–2 and 19% surpassing 8 W·m–2 (Fig. 1c, d). Although lakes at low latitudes also exhibit a discernible increase in LHR (with a median change of 7.1 W·m–2), their overall contribution to total heat release is overshadowed by mid-high latitude lakes, which dominate due to their extensive surface area (Fig. 1e and Supplementary Fig. 2). Specifically, when weighted by lake area and then summed latitudinally, the total heat release at northern mid-high latitudes is significantly higher than that at low latitudes (Fig. 1e). The regional totals amount to 10.0·106 ± 4.4·106 W for mid-high latitudes and 2.7·106 ± 1.5·106 W for low latitudes. These findings underscore a pronounced amplification of LHR change at northern mid-high latitudes, emphasizing the substantial role of these regions plays in the global dynamics of lake-atmosphere interactions.

We investigate historical changes in four contributors (LWup, SWup, SH, and LH) to LHR (Fig. 2a, b and Supplementary Fig. 3). The results show that LWup and LH are the primary contributors to the increase in LHR. In contrast, SWup and SH generally exhibit a decreasing trend, though with a smaller magnitude compared to LWup and LH. Notably, the dominance of these contributors varies substantially by latitude (Fig. 2a). The change in LHR is predominantly driven by LWup at mid-high latitudes, with 97% of lakes in this region identifying LWup as the major contributor. However, this pattern differs at low latitudes, where 59% of lakes is primarily governed by LH. The latitudinal average further confirms this variability, with LWup dominating in northern regions and LH dominating in southern regions (Fig. 2b). These results suggest that the intensified increase in LWup is responsible for the amplified LHR change at mid-high latitudes.

Fig. 2: Dominant contributors to the change in lake heat release (LHR) and the sensitivity of upward longwave radiation (LWup) to lake surface water temperature (LSWT).
figure 2

a Spatial pattern of dominant contributors driving LHR. b Latitudinal average (5° bins) of changes in each contributor. The contributors include LWup, upward shortwave radiation (SWup), sensible heat flux (SH) and latent heat flux (LH). Spatial pattern (c) and latitudinal average (5° bins) (d) of the sensitivity of LWup to LSWT. e Latitudinal average (5° bins) of LSWT changes. Latitudinal averages are weighted by lake area, and the shaded regions represent the ensemble standard deviation. The grid cells in spatial maps correspond to representative lakes (see Methods). All changes compare present-day (1991–2020) with pre-industrial conditions. Source data are provided as a Source Data file.

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According to the Stefan–Boltzmann equation, a warmer physical body emits more radiation, which, in lakes, manifests as longwave radiation. We use the mean annual lake surface water temperature (LSWT) for all days to characterize lake thermal conditions. We find that mid-high latitude lakes show a more pronounced increase in LWup per °C increase in LSWT (Fig. 2c). This indicates a higher sensitivity of LWup to LSWT at mid-high latitudes. Sensitivity values indicate that 59% of mid-high latitude lakes experience an increase in LWup of >12 W·m–2, with 25% exceeding 16 W·m–2 and 10% surpassing 20 W·m–2 per °C increase in LSWT. The latitudinal average further highlights the elevated sensitivity of LWup to LSWT at mid-high latitudes (Fig. 2d), where lakes experience a widespread increase in LSWT (Fig. 2e). However, the well-established theoretical relationship between longwave radiation and temperature suggests a decoupling between LWup and LSWT at mid-high latitudes. Given the cold climate in these regions, lake ice phenology may contribute to this high sensitivity.

Loss of ice cover results in amplified LHR changes

We further investigate the intensified increase in LWup, the primary driver of amplified LHR at mid-high latitudes, from the perspectives of lake thermal conditions and ice phenology. The results indicate that the spatial pattern of LSWT changes closely resembles that of LWup (Fig. 3a and Supplementary Fig. 3a). Specifically, mid-high latitude lakes, which show amplified LWup increases (with a median change of 7.5 W·m–2), exhibit noticeable increases in LSWT (with a median change of 0.65 °C) during the present-day compared to pre-industrial conditions. Conversely, regions experiencing a decrease in LWup, such as central North America and Southeast Asia, show clear decreases in LSWT. Since ice cover substantially impacts the lake-air surface energy budget15,16,32,33, we employ mean annual ice thickness (MAIT) to describe changes in lake ice phenology. MAIT represents the ratio of daily accumulated lake ice thickness to 365 or 366 days, accounting for ice duration and ice thickness during the ice-covered period (see Methods). We find a strong agreement between the spatial patterns of changes in MAIT and LWup (Fig. 3b and Supplementary Fig. 3a). Changes in LWup show a positive correlation coefficient (R = 0.79) with changes in MAIT (Supplementary Fig. 4). Hence, our findings suggest a joint influence of LSWT and ice phenology on changes in LWup.

Fig. 3: Explanation for amplified lake heat release (LHR) changes at mid-high latitudes.
figure 3

Spatial pattern of changes in mean annual lake surface water temperature (LSWT) (a) and mean annual ice thickness (MAIT) (b). c Relationship between changes in upward longwave radiation (LWup) (y-axis) and LSWT (x-axis). d Relationship between ∆LWup / ∆LSWT (y-axis) and ∆MAIT (x-axis). The red and blue colors of points in (c) indicate the ice-free and ice-covered lakes. The light shades on the right and top of (c) show marginal distributions of LWup and LSWT changes, the overlapped black lines show the median, and the dark shaded boxes show the interquartile range. The x-axis in (d) is the logarithm of MAIT changes, with an offset applied to make all points positive. The color of points in (d) shows the multi-year averaged ice duration of lakes. The texts in (c) and (d) show slopes (α), correlation coefficients (R) and corresponding confidence intervals at the 99% confidence level. Points in (c) and (d) correspond to lakes in Northern Hemisphere. The grid cells in spatial maps correspond to representative lakes (see Methods). All changes compare present-day (1991–2020) with pre-industrial conditions. Source data are provided as a Source Data file.

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We then categorize lakes based on whether they experience ice cover (see Methods). Our analysis reveals high correlations between changes in LSWT and LWup for both ice-free (R = 0.997) and ice-covered (R = 0.75) lakes (Fig. 3c), illustrating that LSWT governs the changes in LHR. However, the slope of the regression curve for ice-covered lakes (α = 8.7) is approximately 1.4 times steeper than that for ice-free lakes (α = 6.2), indicating a heightened sensitivity of LWup to LSWT in ice-covered lakes. This heightened sensitivity is further supported by the fact that lakes with longer ice duration tend to become more sensitive (R = 0.76) (Supplementary Fig. 5). These results demonstrate the decoupling between LWup and LSWT in ice-covered lakes, where the temperature of the ice/snow surface being additional control on LWup. Additionally, we find that ice-covered lakes experience more pronounced increases in LSWT (with a median change of 0.65 °C) compared to ice-free lakes (with a median change of 0.47 °C) (Fig. 3c). Collectively, ice-covered lakes experience greater increases in LWup (with a median change of 7.2 W·m–2) compared to ice-free lakes (with a median change of 2.7 W·m–2) (Fig. 3c).

These findings suggest that changes in lake ice phenology play a pivotal role in amplifying LHR increase in mid-high latitudes. It primarily decouples LWup from LSWT, which increases the sensitivity of LWup to LSWT, and drives additional LSWT increases. Existing research has already indicated that ice-covered lakes have experienced more substantial warming compared to ice-free lakes in recent decades10,11,12,34. Our results corroborate this hypothesis by establishing a significant correlation between changes in lake ice phenology and the sensitivity of LWup to LSWT (R = 0.65) (Fig. 3d). Both thinner ice during the ice-covered period and shorter ice duration contribute to the increase in LWup, with the former exerting a more dominant influence (Supplementary Fig. 6). In total, simulated changes in MAIT explain 62% (R2 = 0.62) of the spatial variation in LWup changes for ice-covered lakes (Supplementary Fig. 4).

Overall, changes in LSWT and ice phenology both contribute to the observed increase in LWup, resulting in the amplified LHR change at mid-high latitudes. Changes in lake ice phenology play a critical role in this amplification by increasing the sensitivity of LWup to LSWT (decoupling LWup from LSWT) and contributing to the amplified LSWT increase.

Seasonality of LHR changes

The global strengthening of LHR, as well as the amplified LHR at mid-high latitudes, is also evident at the seasonal scale (Supplementary Figs. 7, 8). Changes in LHR exhibit considerable seasonality, highlighting how lakes redistribute energy across seasons. To quantify this seasonality, we calculate the difference in LHR changes (∆LHR) between during the boreal summer and winter in the Northern Hemisphere, which we refer to as the seasonal difference in ∆LHR. We find that 56% of lakes in the Northern Hemisphere show positive seasonal differences in ∆LHR (Fig. 4a). This percentage increases to 71% for ice-free lakes (Fig. 4b), suggesting that LHR increases more intensively during the warm season than the cold season for these lakes. This positive seasonal difference in ∆LHR in ice-free lakes is attributed to higher LH increase in summer compared to winter (Supplementary Figs. 9, 10). For ice-covered lakes, the seasonal difference in ∆LHR is centered around zero (Fig. 4b), primarily due to the opposing effects of LWup and LH. Specifically, ice-covered lakes experience a greater increase in LWup in winter (Fig. 4c), which offsets the higher LH increase in summer (Supplementary Fig. 10d).

Fig. 4: Seasonal lake heat release (LHR) changes.
figure 4

Spatial pattern (a) and cumulative distribution function (CDF) (b) of seasonal difference (boreal summer minus winter) in ∆LHR. c The CDFs of seasonal difference in upward longwave radiation (LWup) changes. d Boxplots show the sensitivity of LWup to lake surface water temperature (LSWT) and the purple line shows the percentage of lakes with ice cover. In each boxplot, the central line represents the median, the box indicates the interquartile range, the whiskers extend to the non-outlier minimum and maximum, and the dots denote outliers. The red and blue colors in (b–d) indicate the ice-free and ice-covered lakes. The light shades on the top of (b) and (c) show marginal distributions, the overlapped black lines show the median, and the dark shaded boxes show the interquartile range. The CDFs in (b) and (c) and boxplots in (d) are based on outputs of lakes in Northern Hemisphere. The grid cells in the spatial map correspond to representative lakes (see Methods). All changes compare present-day (1991–2020) with pre-industrial conditions. Source data are provided as a Source Data file.

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Greater increases in LH during summer for both ice-free and ice-covered lakes (Supplementary Fig. 10d) are primarily driven by more pronounced lake warming in this season compared to winter (Supplementary Fig. 11). The opposing seasonal shift in LWup changes is largely due to seasonal freeze-up. We analyze the seasonal-scale sensitivity of LWup to LSWT (Fig. 4d and Supplementary Fig. 12) and find that only ice-covered lakes exhibit clear seasonal variability in this sensitivity. Specifically, ice-covered lakes exhibit the lowest sensitivity in summer (with a median change of 5.4 W·m–2·°C–1) and the highest sensitivity in winter (with a median change of 13.9 W·m–2·°C–1). This is primarily because nearly half of the ice-covered lakes lose their ice cover in summer (Fig. 4d and Supplementary Fig. 13), resulting in a sensitivity similar to that of ice-free lakes in this season (with a median change of 6.2 W·m–2·°C–1). As a result, most ice-covered lakes exhibit larger LWup increases in winter due to the seasonal variations in its sensitivity.

To further validate these findings, we calculate the spatial distribution of the seasonal freeze-up of lakes, where lakes experience ice cover annually but have open water in summer (Supplementary Fig. 14). The results show that most lakes with a larger LWup increase in winter compared to summer are seasonal freeze-up lakes (Supplementary Fig. 9a).

Future changes in LHR

Towards the end of this century (2070–2099), LHR increases globally, with a global average rise of 2.1 ± 0.8%, 4.5 ± 1.4%, and 7.5 ± 2.5% relative to the present-day (1991–2020) for representative concentration pathways (RCPs) 2.6, 6.0, and 8.5, respectively (Fig. 5a and Supplementary Figs. 15, 16). The amplified response of LHR to climate change at mid-high latitudes persists under all considered emission scenarios, with average increases of 2.4 ± 1.0%, 5.2 ± 1.8%, and 8.7 ± 3.3% for RCPs 2.6, 6.0, and 8.5, respectively (Fig. 5b). The intensified increase in LWup continues to drive the amplified LHR at mid-high latitudes (Supplementary Fig. 17). Furthermore, the sensitivity of LWup to LSWT across the three emission scenarios remains consistent in both spatial patterns and latitudinal averages (Fig. 5c, d, and Supplementary Fig. 18). Additionally, these sensitivities in future projections align well with those observed in the present day (Fig. 5c, d, and Fig. 2c, d). These findings suggest that the decoupling of LWup from LSWT and its high sensitivity at mid-high latitudes is an inherent characteristic, independent of external climate forcing.

Fig. 5: End-of-century changes in lake heat release (LHR) and the sensitivity of upward longwave radiation (LWup) to lake surface water temperature (LSWT).
figure 5

Relative changes in spatial pattern (a) and latitudinal average (5° bins) (b) of LHR, with the spatial pattern (a) based on representative concentration pathway (RCP) 8.5. Spatial pattern (c) and latitudinal average (5° bins) (d) of the sensitivity of LWup to LSWT, with the spatial pattern (c) based on RCP 8.5. e Latitudinal average (5° bins) of LSWT changes. Latitudinal averages are weighted by lake area, and the shaded regions represent the ensemble standard deviation. The grid cells in spatial maps correspond to representative lakes (see Methods). All changes compare end-of-century (2070–2099) with present-day (1991–2020) conditions. Source data are provided as a Source Data file.

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Changes in lake MAIT continue to explain the higher sensitivity at mid-high latitudes, with correlation coefficients ranging from 0.57 to 0.70 (Supplementary Figs. 19, 20). Additionally, changes in MAIT account for 38% (R2 = 0.38), 52% (R2 = 0.52), and 59% (R2 = 0.59) of the spatial variations in LWup changes for ice-covered lakes under RCPs 2.6, 6.0, and 8.5, respectively (Supplementary Fig. 21).

Changes in LSWT for ice-free lakes remain highly correlated with changes in LWup (correlation coefficients ranging between 0.93 and 0.99), while ice-covered lakes show much weaker correlations (below 0.28) (Supplementary Fig. 22). Furthermore, LSWT increases for ice-covered lakes are no longer higher than those for ice-free lakes (Supplementary Figs. 22, 23). These model results suggest that future amplified LHR in mid-high latitude lakes will be primarily driven by changes in lake ice phenology.

In terms of seasonal difference in ∆LHR, both ice-free and ice-covered lakes release more heat during the warm season than the cold season due to higher LH increase during the warm season in the future projections (Supplementary Figs. 24, 25). Ice-covered lakes continue to experience greater LWup increase in winter, but they can no longer offset the higher LH increase in summer (Supplementary Fig. 25).

Discussion

Our results indicate an amplified LHR change at mid-high latitudes (>45°N), with LWup as the dominant contributor and the loss of lake ice cover as the primary driver. This pattern is reminiscent of the Arctic amplification phenomenon, which centers on diminishing sea ice and temperature feedback24,25,26,27. The loss of lake ice extends the open water period, allowing more heat to transfer from lakes to the atmosphere13,14,15,16 (Supplementary Fig. 26a). The thinning ice cover also pushes the lake surface into a new energy balance, resulting in increased heat release35,36,37,38,39. Reduced snow cover duration decreases thermal insulation, opening a window for this new energy balance40,41 (Supplementary Fig. 26b). Additionally, the decrease in ice duration allows more solar radiation to enter the lake (Supplementary Fig. 27a), as reflected by the reduction in SWup observed at mid-high latitudes (Fig. 2b). This increased solar energy uptake leads to more pronounced warming for ice-covered lakes11,12,33 (Supplementary Fig. 27b). Such excess warming not only contributes to higher LHR increase but also creates positive feedback on lake ice loss4.

However, we observe a paradox: while ice-covered lakes show an excess LSWT increase when comparing present-day to pre-industrial conditions, this trend is not seen in future projections (Fig. 3c and Supplementary Fig. 22). This indicates uncertainty in the role of ice cover in regulating lake temperature6,10,34. Although the loss of ice cover can increase incoming energy, it can also lead to greater energy loss4. This complexity of ice-lake interactions is further reflected in the low correlation between changes in LWup and LSWT for ice-covered lakes in future projections (Supplementary Fig. 22). Illuminating the mechanisms behind ice-LHR provides further evidence of this paradox and improves our understanding of how lakes respond to climate change, suggesting a need to prioritize mid-high latitude lakes in developing mitigation strategies.

We highlight the distinct responses to climate change between lakes at mid-high and low latitudes. Low-latitude lakes can mitigate warming through enhanced LH42,43,44, driven in part by the increased saturated vapor pressure of the warming atmosphere45. Although SH decreases synchronously due to the Bowen ratio (the ratio of SH to LH)43, the increase in LH significantly outweighs the reduction of SH (Fig. 2b). In contrast, colder conditions limit the rise in LH for mid-high latitude lakes43. As a result, lake energy is primarily transferred to the atmosphere by thermal radiation. The decline in lake ice cover exacerbates this, amplifying LHR changes. This distinction suggests that lakes in cold and warm regions exhibit different energy release patterns in response to global warming, which may lead to contrasting risks to the local climate and the lakes themselves. Since the climatic effect of lakes is generally more pronounced at regional scale2,3, LHR would have a stronger impact on the overlying and adjacent atmosphere. For example, rising regional atmospheric temperatures could promote snow melt around lakes, contributing to the warming feedback on regional temperatures28,29. Given the essential services of ice-covered lakes provide to northern communities46, the regionally intensified warming effect could expose populations and economies to local warming risks15,16,47. Moreover, large lakes experiencing cold waves without ice cover may intensify LHR, which could enhance lake-effect snow in downwind areas48,49. For low-latitude lakes, increased lake evaporation could lead to water storage loss in the catchment44,50, potentially threatening aquatic ecosystems.

Although we provide a quantitative estimate of the LHR globally, the absence of atmospheric feedback is a limitation of this assessment. Air temperature is the main driver of LSWT42,51, but without atmospheric feedback, the heated atmosphere cannot further warm the lakes. Therefore, LHR may be underestimated in long-term simulations. GCMs with fully coupled lake models could address this issue52. However, even large lakes are often absent or poorly represented in coarse GCMs53,54, and the uneven distribution of subgrid-scale lakes is commonly disregarded55. Current high-resolution GCMs are inadequate for fully representing lake-atmosphere interactions56. Given the amplified LHR increase of ice-covered lakes at mid-high latitudes shown by our first-order results, we call for the development of high-resolution GCMs coupled with fully tested lake models to enable a more realistic investigation of lake-driven warming on the regional atmosphere.

Regarding the suitability of global lake simulations, the lack of LHR observations makes it challenging to directly evaluate simulated LHR at the global scale. However, the lake models included in our study show reasonable agreement with both ERA5-Land and satellite/in-situ observations. The models represent key features of lake thermodynamics and provide informative insights into snow and ice processes, particularly in capturing their variability worldwide (Supplementary Note 1 and Supplementary Figs. 28–31). Nonetheless, current lake simulations are still influenced by limitations in model structures and limited input data, though these biases do not preclude the models from effectively responding to climate scenarios6 (Supplementary Note 1).

Moreover, lake models account for only a small fraction of the total LHR uncertainty (less than 11% on average globally across all scenarios), indicating a reasonable agreement across the lake models (Supplementary Note 2, Supplementary Figs. 32, 33, and Supplementary Tables 2, 3). In contrast, LHR uncertainty is primarily driven by GCMs, reflecting differences in their simplifications and parameterization schemes57,58,59. Despite these uncertainties, GCMs remain state-of-the-art tools for analyzing the impacts of climate change31.

Methods

Definition of LHR

We define LHR as the primary energy transfer from lakes to the atmosphere, describing how lakes release the absorbed energy back into the atmosphere. As expressed in Eq. (1), LHR is derived from four sources: LWup, SWup, SH and LH. SH and LH include both upward (positive) and downward (negative) fluxes. LHR quantifies the first-order energy transfer from lakes to the atmosphere, representing the lake’s capacity to alter the atmospheric energy budget.

$${{{\rm{LHR}}}}={{{\rm{LWup}}}}+{{{\rm{SWup}}}}+{{{\rm{SH}}}}+{{{\rm{LH}}}}$$
(1)

where LHR denotes the lake heat release to the atmosphere, LWup represents the longwave radiation emitted from the lake, SWup represents the shortwave radiation reflected from the lake, and SH and LH represent the sensible and latent heat flux between the lake and atmosphere, respectively.

Inter-sectoral impact model intercomparison project

Ensemble data for the lake surface energy budget is obtained from global-scale lake model simulations conducted under the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP) phase 2b Lake Sector31. The ISIMIP 2b Lake Sector simulates climate change impacts on lakes using an ensemble of lake models and climate change scenarios. These global lake model simulations have been widely used to assess the influence of anthropogenic forcing on, lake temperatures6, seasonal variations60, stratification patterns61, bottom water methane production62, and global heat uptake21,22. Our study uses simulations from three lake models: Arctic Lake Biogeochemistry Model63 (ALBM), LAKE64, and SIMSTRAT-UoG65.

ALBM is a one-dimensional process-based lake model originally developed for Arctic lakes, but has recently been applied to simulate lake environments worldwide63,66,67. The thermal regimes for both water and sediment columns in ALBM are simulated using one-dimensional thermal diffusion equations. ALBM includes one snow layer, one gray ice layer, and multiple ice layers. The gray ice layer forms when excess snow accumulates, leading to the conversion from snow to white or slush ice. Snow dynamics are driven by accumulation from precipitation, compaction, sublimation, and melting. Ice dynamics are determined by the energy balance and can grow or decay at the ice-water interface, snow-ice interface, and within the ice layer63,67.

LAKE is an extended one-dimensional model that simulates thermodynamic, hydrodynamic, and biogeochemical processes in lakes31,64. It includes multilayers snow and ice modules. Snow dynamics depend on precipitation during the cold season, snow melting/freezing, and densification due to gravity. An initial ice cover forms when the surface temperature drops below 0 °C. Ice dynamics are governed by the heat balance at the top boundary of the ice layer, and melted water is added to the underlying water layer68,69.

SIMSTRAT-UoG is a one-dimensional model based on turbulence closure schemes65. It simulates snow and ice formation using a formulation proposed by Patterson and Hamblin70. Snow and ice dynamics depend on precipitation accumulation, ice buoyancy, and melting/freezing at the interfaces. Rainfall over snow or ice is added as an equivalent amount of snow. Snow thickness is limited by the ability of floating ice to support the weight of snow, and excess snowfall is added to the existing ice cover70.

Although the models used in this study are based on different structures and parameterization schemes, LHR is generally a result of energy balance at the lake surface. It is influenced by downward radiation, heat fluxes through water/ice/snow, and energy involved in phase changes31,63,64,65,66,67. All models use default parameters and coefficient values based on prior study experience for each model31. The integration time step is 24 h for ALBM and LAKE, and 3 h for SIMSTRAT-UoG. Model outputs are detailed in ref. 31.

All the lake models simulate at a 0.5° × 0.5° horizontal resolution over grid cells with non-zero lake area fractions. Each simulated grid cell is termed a representative lake, as it represents the combined properties of the real lakes within the grid cell31. Specifically, a representative lake is modeled as a cylindrical bucket, with its shape determined by the weighted mean depth and total area of all real lakes within the grid cell. Both surface area and mean depth of lakes are derived from the Global Lake Database (GLDB) with a horizontal resolution of 30 arc seconds31,71,72. GLDBv1 contains real data for over 13,000 lakes, assigning a default depth of 10 m when actual depth is unknown71. GLDBv2 provides indirect estimates of mean depth for unknown lakes in boreal regions based on their geological origin72. ALBM and SIMSTRAT-UoG use GLDBv1, while LAKE uses GLDBv2. Consequently, although the lake models share the same horizontal resolution, LAKE has a slightly different set of grid cells due to the use of different GLDB versions. Specifically, ALBM and SIMSTRAT-UoG contain 17,436 grid cells based on GLDBv1, while LAKE contains 15,503 grid cells based on GLDBv2. As a result, there are 18,586 available grid cells, of which 77% are overlapped by all three lake models, 17% by two, and 6% by one (Supplementary Fig. 1). Additionally, some future projections for LAKE and SIMSTRAT-UoG are missing (Supplementary Table 1), accounting for 5% of total future projection data.

Each of the three lake models is forced by four bias-corrected GCM simulations: GFDL-ESM2M, HadGEM2-ES, IPSL-CM5A-LR and MIROC531,73,74,75. The bias-corrected GCMs share the same horizontal resolution (0.5° × 0.5°) as the lake models. Input climate variables include downward shortwave and longwave radiation, surface air temperature, specific humidity, surface wind, surface pressure, and precipitation. ALBM additionally takes snowfall as an input. Historical simulations cover 1861–2005, using historical climate data. Future projections cover 2006–2099 under three RCPs: low (2.6), medium-high (6.0), and high (8.5) greenhouse gas emission scenarios. Pre-industrial simulations represent a scenario without anthropogenic influence using an assumed pre-industrial climate. These simulations cover 1661–1860 for all lake models except ALBM, spans 2006–2099 but is driven by pre-industrial forcings rather than future forcings. Despite differences in time periods, all simulations represent pre-industrial climate conditions. We stitch the historical simulations with RCP 6.0 simulations to generate the present-day period (1991–2020)21,22,74. The differences between present-day (1991–2020) and pre-industrial conditions represent the impact of ongoing climate change caused by anthropogenic forcing. We also analyze the differences between end-of-century (2070–2099) and present-day (1991–2020) projections.

Post-processing of lake model outputs

To attain homogenized and stable results, we exclude ensemble grid cells with LSWT changes of less than 0.05 °C when calculating the sensitivity of LWup to LSWT. The removed ensemble grid cells account for 2.1% during the present-day period and 0.2–2% during the future period. The excluded grid cells make up 41.6%, 19.2%, 1.8%, and 2.1% of the total ensemble member grid cells in boreal winter, spring, summer, and autumn for the present-day period, respectively.

We define ice-covered lakes as those where more than half of the ensemble members show a multi-year average ice duration longer than 1 day·year–1 or 1 day·season–1 at the annual or seasonal scale. A lake is considered frozen when the ice thickness exceeds 0.1 cm for a single day. It should be noted that the quoted multi-year average ice duration represents the average of the two periods (either between present-day and pre-industrial or between present-day and end-of-century) to reflect a stable ice phenology property. Additionally, ice-free days are included in the calculation of MAIT. MAIT is the ratio of daily accumulated lake ice thickness to 365 or 366 days, reflecting both ice thickness and ice cover duration over the annual cycle. The calculation of mean seasonal ice thickness follows the same method as MAIT.

We use an ensemble of 12 members (3 lake models × 4 GCMs) to quantify the uncertainty and provide more robust assessments. Each index is first calculated for each ensemble member and then averaged to capture a reasonable spatial pattern. Lake fractions from the HydroLAKES dataset are used to weight grid cells when calculating regional averages76. The HydroLAKES polygons are converted to lake area fractions on a 0.5° × 0.5° grid to match the resolution of the lake models (Supplementary Fig. 2).