Introduction

Permafrost regions, which cover approximately 22% of the Northern Hemisphere land area, store more than 50% of the world’s soil organic carbon1,2. The onset of global warming is triggering widespread abrupt permafrost thaw3, which serves as a substantial source of land-atmosphere carbon exchange and has the potential to act as a positive feedback to climate warming4. Thermokarst lakes, are characteristic features of abrupt permafrost thaw resulting from the melting of underground ice5. These lakes play a crucial role in climate feedback due to their methane (CH4) emission potential compared to surrounding soils, yet they remain the most uncertain source of CH4 emissions in the global permafrost zone6,7,8. Notably, large quantities of CH4 are produced in the anaerobic environments of thermokarst lakes, becoming trapped in lake ice and the water body beneath the ice9,10. Upon the melting of lake ice, CH4 undergoes sudden release. However, due to the harsh alpine environment and high monitoring costs, in-situ measurements of lake CH4 release, particularly during ice-covered and ice-melting periods are sparse, posing a significant challenge and hindering our understanding of CH4 release dynamics from thermokarst lakes.

The Tibetan Plateau represents the largest alpine permafrost region globally, covering an area of 1.05 million km2, which accounts for roughly 75% of the total alpine permafrost regions in the Northern Hemisphere11,12. This region stores an estimated 15.3–46.2 Pg of organic carbon in the top 3 meters of soil13. Similar to the Arctic region, the Tibetan Plateau is experiencing rapid climate warming14 and substantial permafrost thaw2. Presently, it hosts over 160,000 thermokarst lakes, spanning approximately 2825 km2 in total area15. The expansion of these lakes is expanding across the plateau. Over the past three decades, the number and area of thermokarst lakes near the Qinghai-Tibet Highway have increased by 59% and 83%, respectively16. Changes in lake ice phenology, influencing the duration of ice cover, are undergoing significant alterations by modifying freeze-up and break-up times17. Thermokarst lakes emerge as important CH4 sources on the Tibetan Plateau18,19. However, uncertainty persists regarding CH4 emissions during ice-melting periods compared to the Arctic region, resulting in the underestimation of current CH4 emissions on the Tibetan Plateau. Additionally, the absence of thermokarst lake simulations for CH4 release in Earth system models stems from a poor understanding of CH4 release dynamics, obscuring projections regarding future changes in CH4 release from thermokarst lakes3,20. These knowledge gaps impede the accurate prediction of carbon-climate feedback in alpine permafrost regions under forthcoming climate scenarios.

In this study, we conducted field observations of 56 thermokarst lakes during ice-covered periods (March-April) in 2023 and synthesized our previous measurements of CH4 release from 162 thermokarst lakes during ice-free periods (May-October) on the Tibetan Plateau from 2019 to 202118 (Fig. 1a, Supplementary Fig. 1, Supplementary Table 1). In this field survey, we collected the samples of lake ice and water beneath the ice by cutting a hole in the lake ice with a diameter of 30–50 cm (Fig. 1b-e). We measured dissolved CH4 and CO2 concentrations and their stable carbon isotopes to study CH4 production pathways. Subsequently, we illustrated the patterns of CH4 release during both ice-melting (including ice bubble and water storage) and ice-free periods (including ebullition and diffusion) on the whole plateau, thereby estimating the CH4 emissions from thermokarst lakes. Finally, by integrating changes in the susceptibility distribution of thermokarst lake simulated by machine learning models, we predicted the expansion of thermokarst lakes and future changes in CH4 emissions during the ice-melting and ice-free periods under Shared Socioeconomic Pathways (SSPs). We also separately presented future projections of CH4 emissions from thermokarst lakes with and without considering the loss of lake ice.

Fig. 1: Field observations of thermokarst lakes during ice-covered period on the Tibetan Plateau.
figure 1

a Distribution of the 56 monitored thermokarst lakes during ice-covered period (this study) and 162 thermokarst lakes during ice-free period18. A total of 409 field observations were conducted from June 2019 to April 2023. Permafrost and vegetation distribution data are sourced from existing distribution dataset12,69. b–e The images depict field observations during the ice-covered periods from March to April, captured by P. L and M. M. f Density frequency of dissolved CH4 concentrations and their comparison between the ice-covered period and ice-free period. The lines indicate CH4 concentrations of individual samples during ice-free and ice-covered periods. g The relationships of dissolved CH4 concentrations between the ice-covered and ice-free periods under vegetation types of alpine swamp meadow (ASM), alpine meadow (AM), alpine steppe (AS) and alpine desert (AD). Notably, the circles represent the individual lakes observed during both the ice-free and ice-covered periods. The corresponding values indicate the average CH₄ concentration within the same lake during the two periods. The shaded area represents the 95% confidence interval. *P < 0.05, **P < 0.01, ***P < 0.001.

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Results and Discussion

CH4 emission pathways

To explore the difference in dissolved CH4 concentrations between ice-free and ice-covered periods on the Tibetan Plateau, we conducted field observations in March-April 2023 and integrated our published data from thermokarst lakes during 2019–202318. The same sampling method was used in two periods in order to narrow the uncertainty (See Methods). Results indicate that during ice-covered period, the median concentration of dissolved CH4 in the water body beneath lake ice is 2.61 μmol/L (n = 151; Fig. 1f), with a wide range from 0.03–280.47 μmol/L. Conversely, during ice-free period, the median dissolved CH4 concentration in lake water is 0.88 μmol/L, ranging from 0.01–39.98 μmol/L (n = 353; Fig. 1f). Dissolved CH4 concentrations during ice-covered period significantly surpass those in the ice-free period (p < 0.001), with concentrations within the same thermokarst lake reaching up to 100 times higher in the ice-covered period. It is attributable to that methanogenesis continues under the lake ice due to the anaerobic environment and the barrier effect of lake ice9,21, leading to the accumulation and entrapment of CH4 in ice-covered thermokarst lakes. Interestingly, dissolved CH4 concentrations during ice-covered and ice-free periods exhibit significantly positive correlations (Fig. 1g, Supplementary Table 2).

Additionally, dissolved CH4 concentrations are closely related to sediment organic carbon content in thermokarst lakes with different vegetation types on the Tibetan Plateau (Supplementary Fig. 2). This is attributable to that methanogenesis primarily occurs in the lake sediments, where organic carbon provides crucial substrate for microbial CH4 production22,23,24. The gradient of sediment organic carbon contents in thermokarst lakes is controlled by soil organic carbon around the lakes within the watersheds, which is transported into the thermokarst lakes through hydrological processes25,26. Thus, the highest CH4 concentrations are found in thermokarst lakes under the vegetation of alpine swamp meadows (ASM) and meadows (AM), followed by alpine steppe (AS) and desert (AD), evident both ice-covered and ice-free periods (Supplementary Fig. 3). It was shown that sediment organic carbon contents in the thermokarst lakes is closely related to vegetation types on the Tibetan Plateau18,25. The results suggest that large amounts of CH4 are trapped in ice-covered thermokarst lakes, exhibiting similar patterns to those during ice-free period.

Furthermore, to elucidate the pathways of CH4 production in thermokarst lakes during ice-covered periods on the Tibetan Plateau, we calculated the carbon fractionation factor (αC) using δ13C values of dissolved CO2 and CH4. The αC values greater than 1.055 indicate CH4 origin predominantly via CO2 reduction, while values between 1.040 and 1.055 suggest acetate fermentation27,28. The αC values below 1.040 are likely associated with CH4 oxidation29 (see Methods). Results show that the observed δ13C-CH4 in the water body beneath lake ice has a median value of −57.9‰ (ranging from −89.6‰ – −26.7‰) (Supplementary Fig. 4a), similar to that of diffusion during ice-free periods on the Tibetan Plateau. The median αC value of water storage during ice-covered periods is 1.038 (n = 140) (Supplementary Fig. 4b), which indicates that acetate fermentation is the primary pathway for CH4 production during ice-covered periods, accompanied by significant oxidation27,29,30,31. This finding further implies that CH4 production continues throughout the winter in the Tibetan Plateau thermokarst lakes. Meanwhile, this pathway aligns with that of CH4 emissions via diffusion during ice-free periods18, but contrasts with that via ebullition during ice-free periods, which is predominantly driven by CO2 reduction on the Tibetan Plateau19. Similarly, high-emission point sources and hotspots in Siberian lakes are primarily driven by CO2 reduction, while lower-emission processes are influenced by acetate fermentation27. However, in Western Greenland, it was shown that the primary production pathway for CH4 released through ebullition is acetate fermentation32, whereas in Finland, CH₄ emissions via diffusion are mainly driven by CO2 reduction33. The discrepancy is attributed to that the different composition of microbial communities in aquatic systems can control the CH4 production pathways34,35. Additionally, the environmental factors, such as temperature36, salinity19, and substrates available for methanogenesis37, can further influence the pathway of CH4 production.

Under future climate scenarios, shorter ice-covered periods and warmer lake water are expected to enhance the proportion of CH4 ebullitive emissions from thermokarst lakes on the Tibetan Plateau. Particularly, changes in lake water temperature and dissolved oxygen content can shift the methanogenic pathway, with more CH4 likely released through ebullition driven by CO2 reduction36, potentially increasing future total CH4 emissions from thermokarst lakes. Although regional divergence exists in the CH4 accumulation during ice-covered periods38,39,40, potentially affecting future CH4 emission prediction, the results shed light on the mechanistic understanding of CH4 release dynamics in the Tibetan Plateau thermokarst lakes. Our study highlights the need to account for winter CH4 production in thermokarst lakes, which may substantially contribute to future annual CH4 emissions under ongoing climate warming.

CH4 flux in ice-melting and ice-free periods

To systematically evaluate the total annual CH4 release from thermokarst lakes on the Tibetan Plateau, we quantified the water storage and ice bubble storage by conducting the field observations during ice-cover periods and synthesizing our published fluxes during ice-free period18 (see Methods). During ice-melting periods, we calculated the proportions of CH4 flux between ice bubble and water storage with different vegetation types (Supplementary Fig. 5). The result shows that during the ice-melting period, CH4 release from thermokarst lakes primarily originates from water storage (Fig. 2a). The median CH4 release flux from water storage is 0.8 (0.01–39.9) g m−2 yr−1, while CH4 release from ice bubble occurs at a rate of 0.3 (0–17.0) g m−2 yr−1 (Fig. 2a), corroborating recent observations38. Combined, the total CH4 release from ice bubble and water storage ranges from 0.01–56.9 g m−2 yr−1, with a median of 1.1 g m−2 yr−1. Similarly, we observed a distribution pattern of CH4 release flux from thermokarst lakes under different vegetation type within the watershed (Fig. 2b). Our study reveals that water storage and ice bubble are estimated to contribute 71.1% and 28.9% to the CH4 release from thermokarst lakes during the ice-melting periods, respectively.

Fig. 2: CH4 emission flux from thermokarst lakes during ice-melting and ice-free periods on the Tibetan Plateau.
figure 2

a Density distribution of CH4 release flux from water storage and ice bubble storage during ice-melting period. The lines indicate CH4 fluxes of individual sampling points from water storage and ice bubble storage. b Total CH4 flux from thermokarst lakes during ice-melting under the vegetation types of alpine swamp meadow (ASM), alpine meadow (AM), alpine steppe (AS) and alpine desert (AD). The violin plot illustrates the magnitude and distribution density of CH4 fluxes of individual samples, in which the boxes represent the 25th and 75th percentiles; the black line indicates the median value, and the black diamond represents the mean value. c Density distribution of CH4 release flux in diffusion and ebullition ways during ice-free period. The lines indicate CH4 fluxes of individual sampling points from ebullition and diffusion. d Total CH4 flux from thermokarst lakes during ice-free period with vegetation types. e The proportions of annual CH4 release in the ways of water storage, ice bubble, ebullition and diffusion for the whole year under different vegetation types on the Plateau. The number at centers of the circle indicates the annual CH4 emissions from thermokarst lakes (Gg C yr−1). One-way analysis of variance (ANOVA) with Tukey’s HSD post hoc comparisons are used to test differences in concentrations across different vegetation types and periods at a significance level of P < 0.05.

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To estimate the proportions of ebullition and diffusion release for annual CH4 emissions, we collected and analyzed the previous data of CH4 emissions during ice-free period19 (Supplementary Fig. 6). Our results show that the median CH4 release flux is 13.6 (0.1–481.4) g m−2 yr−1, with 2.0 (0.01–71.5) g m−2 yr−1 for diffusion and 11.2 (0.1–422.6) g m−2 yr−1 for ebullition (Fig. 2c). The highest CH4 fluxes are also found in thermokarst lakes under vegetation type of ASM with a median of 30.7 g m−2 yr−1, followed by AM, AS and AD (Fig. 2d). The proportions of CH4 release from thermokarst lakes through diffusion and ebullition are 15.6% and 84.4%, respectively. By comparing CH4 release flux between the ice-melting and ice-free period, we show that the contribution of CH4 release during ice-melting is essential for the annual estimation, accounting for 5.2–25.8% of the total release from these lakes (Fig. 2e). Although lower water temperatures and reduced external hydrological inputs typically limit the CH4 production, microbial activity continues in both the water column and sediments, even when fully covered by ice9,41. Additionally, significant inputs of allochthonous organic matter during the early and late ice-covered periods42, promote the decomposition of organic matter, leading to a high proportion of CH4 emissions during the ice-melting period. Notably, the lake ice covered period account for approximately 40% for a year on the Tibetan Plateau43.

Annual emissions

To estimate the extent of previously underestimated CH4 release on the Tibetan Plateau, we used a Monte Carlo approach to randomly sample thermokarst lake CH4 flux for each vegetation type. We then obtained the total annual CH4 emissions by multiplying the area of thermokarst lakes and mean CH4 flux under each vegetation type. Results indicate that during ice-free period, thermokarst lakes emit CH4 at a rate of 54.2 ± 9.9 Gg C yr−1, with 46.9 ± 9.8 Gg C yr−1 from ebullition and 7.3 ± 1.4 Gg C yr−1 from diffusion. During ice-melting period, CH4 emission is estimated at 11.2 ± 1.6 Gg C yr−1, with 3.3 ± 0.6 Gg C yr−1 released from bubbles trapped within lake ice, and 7.9 ± 1.5 Gg C yr−1 from the water body beneath lake ice. The total annual CH4 emissions from thermokarst lakes on the Tibetan Plateau are estimated to be 65.5 ± 10.0 Gg C yr−1. Our study reveals that previously overlooked CH4 emissions during ice-melting period account for 17.1% (13.5–20.7%) of the annual CH4 emissions, with 5.0% (3.8–6.2%) attributed to ice bubbles and 12.1% (9.2–15.0%) from water storage (Table 1, Supplementary Fig. 7a). The contributions of CH4 emissions during ice-melting period to the whole year vary with vegetation types of alpine swamp meadow (25.8%), alpine meadow (16.9%), alpine steppe (11.5%) and alpine desert (5.2%) (Fig. 2e, Supplementary Fig. 7b). Compared with the Arctic region, where the contribution of CH4 release during ice-melting was 20–74%7,44,45,46, the proportion of CH4 release during ice-melting period on the Tibetan Plateau is relatively lower. This is attributable to that the Arctic permafrost regions have higher SOC contents47,48 and longer ice-covered durations43,45. Our study shows the magnitude of CH4 emissions during thermokarst lake ice melting on the Tibetan Plateau, providing essential monitoring data for alpine permafrost carbon cycling.

Table 1 Annual CH4 and CO2-equivalent emissions from thermokarst lakes during ice-free and ice-melting periods on the Tibetan Plateau
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To better illustrate the magnitude of carbon release from thermokarst lakes, we converted the CH4 emissions into CO2 equivalent using the 100-year global warming potential49. Result show that CH4 emissions from Tibetan Plateau thermokarst lakes are estimated at 2362.0 ± 360.8 Gg CO2-eq yr−1 (Table 1). Remarkably, although the area of thermokarst lakes accounts for only 0.2% of the Plateau permafrost regions11,15, our estimated total amount of CH4 release from thermokarst lakes offsets approximately 6.4 ± 1.0% of the alpine grasslands carbon sink on the Plateau50. Hence, we underscore the CH4 release from thermokarst lakes for the future climate feedback in alpine permafrost region. Despite overcoming challenges such as harsh climatic conditions during the ice-covered period and limited accessibility in high-altitude permafrost regions, our estimation has possible uncertainties due to field observations. On the one hand, the sampling focuses on a specific depth of the water body beneath lake ice, resulting in the vertical difference in CH4 concentrations is neglected. On the other hand, the duration of ice-covered and ice-melting periods was estimated using remote sensing43, which might not represent all small thermokarst lakes. Therefore, enhancing more observations, especially for changes in lake ice phenology on the Tibetan Plateau, is crucial for a comprehensive understanding of CH4 emissions from thermokarst lakes.

Expansion of thermokarst lake

To predict future changes of thermokarst lakes on the Tibetan Plateau, we used the Random Forest (RF) model to assess the susceptibility distribution of thermokarst lakes and calculate the actual area of thermokarst lake based on the lake area density under different vegetation types (Supplementary Table 5) (see Methods). The results show that thermokarst lakes on the Tibetan Plateau are expected to increase under SSP scenarios. By 2100, the total area of thermokarst lakes is projected to reach 3912 km2 (increase by 85.9% compared with 2020) under SSP1-2.6, 3926 km2 (86.5%) under SSP2-4.5, and 4102 km2 (94.9%) under SSP5-8.5 (Supplementary Fig. 8). These changes correspond with the previous remote sensing observations that showing an increase of 14.7% per-decade between 1969 and 2010 and 20.0% per-decade between 2010 and 201951. Our results forecast thermokarst lakes area will increase by 33.2% per decade between 2020–2040, which is higher than the previous increasing rate due to future warming and wetting in the alpine region (Supplementary Fig. 9). Although future prediction of thermokarst lakes relies more on the process model and need more verification, abrupt permafrost thaw cannot be simulated by Earth System Models (ESMs). Our results show the response of these lakes on the Tibetan Plateau to future climate change through considering the influencing factors of climate, topography, hydrology, soil, permafrost, and human activity (Supplementary Table 3). Our study highlights the future changes of alpine thermokarst lakes and their ecological and environmental impacts.

Future CH4 emissions

To show the effects of future lake expansion and ice loss on CH4 release, we projected future CH4 emissions both with and without considering changes in thermokarst lake ice (see Methods). Our findings indicate significant increases in CH4 emissions from Tibetan Plateau thermokarst lakes even if lake ice loss is not considered (Supplementary Table 6). Specifically, CH4 emissions during the ice-melting period are expected to rise by 76.7%–77.8% by 2050 and 93.8%–105.8% by 2100 under the SSP1-2.6, SSP2-4.5, and SSP5-8.5 (Fig. 3a). During the ice-free period, the emissions could increase by 95.9%–107.9% by 2100 (Fig. 3c), with total annual emissions potentially reaching 116.7–117.3 Gg C yr−1 by 2050 and 128.0–135.9 Gg C yr−1 by 2100 (Fig. 3e). However, over the past 40 years, the average ice-covered duration on the Tibetan Plateau has decreased at a rate of 0.2 days per year (Supplementary Fig. 10)43. Taking the loss of lake ice into account, by 2100, a shorter ice-covered duration could reduce the increase in CH4 emissions during ice-melting periods but enhance it during ice-free periods (Fig. 3b, d). This is because the shortened ice-covered period means less CH4 accumulation in the water beneath the ice40,52 and more emissions during ice-free periods53. Moreover, a longer ice-free period can boost methanogenic activity, further enhancing CH4 emissions54,55. Taken together, future CH4 emissions from the Tibetan Plateau thermokarst lakes could reach 135.5–143.8 Gg C yr−1 by 2100 (Fig. 3f), and considering the CO2-equivalent emissions of CH4, this could potentially offset about 14.1% of the carbon sink in alpine grasslands50.

Fig. 3: Simulated future CH4 emissions from Tibetan Plateau thermokarst lakes by 2100.
figure 3

The projected CH4 emissions from thermokarst lakes up to 2100 during ice-melting (a-b) and ice-free periods (c-d) under Shared Socioeconomic Pathways (SSPs). a, c depict the trends in CH4 emission from thermokarst lakes without considering the changes of ice-covered duration. Conversely, b, d show future changes of CH4 emissions after considering the changes of ice duration, reflecting a dynamic modeling of ice impacting on CH4 emissions. e The predicted annual CH4 emissions from thermokarst lakes up to 2100, without accounting for changes in the duration of ice cover. f The predicted annual CH4 emissions from thermokarst lakes with future lake ice loss. g The bar charts show the past, present, and future CH₄ emissions. The charts with white bars represent CH₄ emissions during the ice-melting period, and color bars show the annual emissions. Data are reported as mean ± standard error (SE).

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The future increase of CH4 emissions on the Tibetan Plateau is possibly different with the Arctic lakes7. This is attributable to the different trends of thermokarst lake areas between the Arctic and Tibetan Plateau, specifically the Arctic is undergoing the extensive draining of thermokarst lakes56,57, whereas thermokarst lakes on the Tibetan Plateau are expanding rapidly in response to climate change16,51,58,59. To date, the estimate of CH4 release rarely involves the changes in areas and ice phenology of thermokarst lakes. The advantage of this study is that we fully consider the changes of thermokarst lake based on the remote sensing monitoring and future climate scenarios. However, our simulations did not fully incorporate dynamic vegetation changes. The variations of vegetation and permafrost stability highlight that not all thermokarst lakes respond uniformly, underscoring the need for more detailed vegetation change data to improve the projections, particularly under warming-driven shifts in vegetation types. Future increase in CH4 emissions from thermokarst lakes on the Tibetan Plateau highlights the growing importance in global greenhouse gas inventory data. Our study demonstrates that the expansion of thermokarst lakes and shortening of lake ice-covered duration accelerate CH4 emissions, playing a crucial role in predicting permafrost carbon feedback to climate change.

Our study offers advantages in simulating CH4 emissions from thermokarst lakes. Firstly, by integrating the distribution of thermokarst lakes and environmental factors, we predicted the future changes in thermokarst lake area on the Tibetan Plateau. Secondly, although our simulations do not include dynamic vegetation changes expected in Tibetan Plateau permafrost regions with warming, we consider the effects of vegetation and climate on the current distribution of thermokarst lakes in order to reduce the uncertainty in estimating CH4 emissions. Furthermore, given that thermokarst lakes affect small areas within the permafrost region, changes in vegetation may not be the primary determinant of CH4 emissions compared to widespread gradual permafrost thaw emissions3. Finally, by integrating field observations of CH4 release, analysis of dissolved δ13C-CH4 and CO2, and future predictions, we provide current and future changes in previously underestimated CH4 release during ice-melting from thermokarst lakes (Fig. 4). Our study also identifies additional important knowledge gaps, such as the verification of lake expansion and spatial heterogeneity of lake ice phenology, that will require further research before carbon release from thermokarst lakes can be simulated by ESMs.

Fig. 4: Schematic of annual CH4 release from thermokarst lakes during ice-melting and ice-free periods on the Tibetan Plateau.
figure 4

The total annual CH4 release includes the four parts shown in the formula. During ice-melting, CH4 release from thermokarst lakes is through both ice bubble and water storage beneath lake ice. During ice-free period, CH4 release is from diffusion and ebullition. The percent data is from the integrated analysis of field observations, showing the proportion of CH4 release from the ice bubble (5.0%), water storage (12.1%), ebullition (71.7%) and diffusion (11.2%) for the whole year. The dotted black line represents the future expansion of thermokarst lakes.

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Implications

The exploration into the dynamics of thermokarst lakes and their impact on climate change yields invaluable insights with far-reaching implications for both scientific understanding and proactive mitigation strategies. This study delves into the significance of these research findings and outlines potential strategies to address the challenges posed by thermokarst lake dynamics in the context of climate change. First and foremost, the research on thermokarst lakes underscores their pivotal role in the carbon cycle and climate feedback loop. By quantifying previously underestimated CH4 emissions, particularly during ice-melting periods, studies have illuminated a critical aspect of permafrost thaw dynamics. This enhanced understanding not only refines our knowledge of regional carbon dynamics but also highlights the urgency of addressing these emissions to mitigate climate change.

One of the key values of this research lies in its contribution to improving ESMs and climate projections. By integrating field observations, machine learning modeling, and projections from climate models, researchers have laid the groundwork for more accurate simulations of thermokarst lake dynamics and their implications for future climate scenarios. This advancement is instrumental in informing climate policy decisions and developing adaptive strategies to mitigate the impacts of permafrost thaw. Furthermore, the insights gleaned from thermokarst lake research offer valuable guidance for policymakers and stakeholders seeking to address the challenges posed by climate change. From enhancing monitoring efforts to implementing targeted mitigation measures, there are several avenues for action. Investing in enhanced monitoring permafrost thaw and remote sensing techniques is essential to capture the spatial variability of thermokarst lakes and track their evolution over time60,61. This comprehensive data collection is crucial for refining climate models and improving the accuracy of future projections.

Moreover, proactive mitigation strategies are imperative to mitigate the impacts of thermokarst lake dynamics on the climate system62. This includes measures to reduce anthropogenic greenhouse gas emissions63, as well as targeted interventions to mitigate CH4 emissions from thermokarst lakes64. Strategies such as lake management techniques, habitat restoration, and land-use planning can help minimize the release of CH4 and mitigate the climate feedback effects of thermokarst lakes. Research on thermokarst lakes offers invaluable insights into the complex dynamics of permafrost thaw and its implications for global climate change. By enhancing our understanding of CH4 emissions from thermokarst lakes and refining climate models, this research provides a foundation for informed decision-making and proactive climate mitigation strategies. Moving forward, continued investment in research, monitoring, and mitigation efforts is essential to address the challenges posed by thermokarst lakes and safeguard the stability of the global climate system.

Methods

Study area and field observations

Permafrost is widely distributed across the Tibetan Plateau, covering approximately 50% of the Plateau12. The annual mean ground temperature has increased by 0.43 °C per decade65, resulting in a significant deepening of the active layer66,67,68. Thermokarst lakes are widely distributed on the permafrost regions and are dominated by lakes with small surface areas (<10,000 m2), which account for ~80% of the total. In this study, we measured the dissolved CH4 concentrations in 56 alpine thermokarst lakes during ice-covered period in 2023. Furthermore, we integrated CH4 concentrations data from 162 thermokarst lakes during ice-free period on the Tibetan Plateau (Fig. 1a)18, all located within the same study area. The observed lakes are primarily located in the continuous permafrost regions with elevations between 4210 and 5127 m (Fig. 1a). The area of thermokarst lakes ranges from 373 m2 to 648,966 m2, with the majority being less than 100,000 m2 (Supplementary Fig. 1b, Supplementary Table. 1).

Based on the dataset of vegetation type distribution on the Tibetan Plateau69, the observed thermokarst lakes are mainly distributed in the regions with four vegetation types: alpine swamp meadow (ASM), alpine meadow (AM), alpine steppe (AS) and alpine desert (AD). These regions exhibit distinct differences in vegetation composition, soil characteristics, and organic carbon content. ASM is characterized by sedges and rushes, with saturated soils rich in organic matter and high moisture levels, which supports significant carbon sequestration70,71. AM features grasses and herbs, with well-drained loamy soils and moderate organic carbon content, experiencing seasonal freeze-thaw cycles71. AS comprises drought-tolerant grasses and shrubs, with dry, coarse soils and low organic carbon content, showing significant spatial variability71. AD is characterized by sparse vegetation, very dry rocky soils, and minimal organic carbon, with high pH levels and significant wind erosion72. During ice-covered period from March to April 2023, the dissolved CH4 in lake water was collected using the headspace equilibrium method (Fig. 1e)73,74. In each lake, 3–6 sampling points were distributed from the edge to the center of lake. Briefly, 400 mL of surface water from a depth of 15 cm was collected with a 500 mL syringe after removing surface ice with a chainsaw (Fig. 1b), Subsequently, 100 mL of pure N2 was injected into the syringe, and the syringe was immediately shaken for 3 minutes to equilibrate the headspace in the field. A 100 mL of the headspace gas was transferred from the syringe into a specialized aluminum foil gas sampling bag, which was then sealed for preservation. At each sampling point, two gas samples were collected for parallel comparison. The sample collection techniques employed during ice-free period19, were in line with the methodologies used in this study. The collection period for CH4 during ice-free period spanned from May to October in the years 2019 –2021. The concentration of dissolved CH4 was measured using a gas chromatograph, with a measurement precision of ±2.2%.

At each sampling point, we also measured water quality parameters, including water temperature, dissolved oxygen and conductivity, using a multi-parameter water quality meter (Fig. 1d). Meteorological data, including air temperature, atmospheric pressure, and wind speed, were sourced from automated field weather stations located at Liangdao River, Tanggula, and Beilu River, as well as from the National Meteorological Science Data Center (NMSDC; http://data.cma.cn/) for the Maduo, Wudao Liang, and Tuotuo River.

Calculation of dissolved CH4 concentrations

Dissolved CH4 concentration in water was calculated by integrating the principles of the ideal gas law and Henry’s law with the concentration of CH4 in the headspace of the syringe18,19,75,76. This methodological approach allowed for the precise calculation of CH4 levels in the aquatic environment, providing accurate results for gas solubility in lake water under varying atmospheric and temperature conditions. The dissolved CH4 concentration in water was calculated using Eq. (1):

$${C}_{{{\rm{w}}}}=\frac{({C}_{{{\rm{h}}}}\times {V}_{{{\rm{h}}}}+S\times {V}_{{{\rm{w}}}})}{{V}_{{{\rm{w}}}}^{-1}}$$
(1)

where Cw is dissolved CH4 concentration in water (μmol L−1). S is the CH4 solubility in water when equilibrium is reached between the air and water phases (μmol L−1)77. Vh is the volume of headspace gas in the syringe (L). Vw is the volume of water in the syringe (L). Ch is CH4 concentration in the headspace gas of the syringe, calculated using Eqs. (2) and (3).

$${C}_{{{\rm{h}}}}=\frac{n}{{V}_{{{\rm{h}}}}}$$
(2)
$$n=\frac{{P}_{{{\rm{m}}}}\times {V}_{{{\rm{h}}}}}{R\times {T}_{{{\rm{air}}}}}$$
(3)

where n represents the molar quantity of CH4 in the headspace gas when equilibrium is reached between the air and water phases (mol). Pm is CH4 partial pressure in the headspace gas (atm), determined by the CH4 volume concentration in the headspace gas and the actual atmospheric pressure at the sampling location. R is the ideal gas constant (L atm K−1 mol−1). Tair is the air temperature in degrees Kelvin (K)22.

Calculation of CH4 flux during ice-free period

Based on the collected CH4 concentration data during the ice-free period, a thin boundary layer method was used to calculate the CH4 diffusion fluxes from thermokarst lakes18,19,22. It is important to note that the data measured in this study is the same with our previous study. Consequently, this study did not account for potential differences that might arise from variations in sampling or calculation methods between data from ice-free period and ice-covered period. The diffusion fluxes from surface water to the atmosphere are correlated with the concentration gradient of CH4 between the water and the atmosphere, as well as the gas transfer velocity78. The diffusion fluxes were calculated using Eq. (4):

$${F}_{{{\rm{diffusion}}}}=K\times ({C}_{{{{\rm{w}}}}_{{{\rm{ice}}}-{{\rm{free}}}}}-{C}_{{{{\rm{eq}}}}_{{{\rm{ice}}}-{{\rm{free}}}}})\times {n}_{{{\rm{ice}}}-{{\rm{free}}}}\times m$$
(4)

where Fdiffusion is the CH4 diffusion fluxes from surface water to the atmosphere during ice-free period (g m−2 yr−1). K is the gas transfer velocity (cm h−1). \({C}_{{w}_{{ice}-{free}}}\) is the concentration of dissolved CH4 in water during ice-free period (μmol L−1)79. \({C}_{{{eq}}_{{ice}-{free}}}\) is the dissolved CH4 concentration in water at equilibrium with the atmosphere (μmol L−1)77. The CH4 concentration in the atmosphere was obtained from the Waliguan Baseline Observatory (https://gaw.kishou.go.jp/). nice-free is the duration of the ice-free period (200 days)43. m is the molar mass of CH4, which is 16.04 g/mol.

The gas transfer velocity is correlated with wind speed and water temperature, it was calculated using Eqs. (5) and (6):

$$K={\left(\frac{{S}_{{{\rm{c}}}}}{600}\right)}^{-{{\rm{X}}}}\times {K}_{600}$$
(5)
$${S}_{c}=1897.8-114.28{T}_{{{\rm{water}}}}+3,2902{{T}_{{{\rm{water}}}}}^{2}-0.039061{{T}_{{{\rm{water}}}}}^{3}$$
(6)

where Sc is the Schmidt number of CH480. Twater is water temperature (°C). If the wind speed is at most 3 m/s, x = 0.66; for wind speeds exceeding 3 m/s, x = 0.581. K600 refers to the value of K when the Schmidt number is 600.

Different studies employ various methods to calculate this value, leading to discrepancies. To reduce uncertainty, this study adopts the average value derived from three different calculation methods82,83,84. The calculation is given in Eqs. (7) and (8).

$${K}_{600}=\frac{(2.07+0.215{{U}_{10}}^{1.7})+0.45{{U}_{10}}^{1.64}+(1.68+0.228{{U}_{10}}^{2.2})}{3}$$
(7)
$${U}_{10}={U}_{{{\rm{Z}}}}\times \left(1+\frac{{{C}_{{{\rm{d}}}10}}^{0.5}}{K}\times \,{\mathrm{ln}}\,\frac{10}{{{\rm{Z}}}}\right)$$
(8)

where U10 represents the wind speed at a height of 10 m (m/s). Uz represents the wind speed at a height of Z m (m/s). In this study, the wind speed data, measured at a height of 2 m, was obtained from automated field weather stations and the National Meteorological Science Data Center. Cd10 is the drag coefficient measured at 10 meters above the ground, and K denotes the von Kármán constant.

Through Eqs. 1 to 8, the fluxes of CH4 emission from surface waters into the atmosphere during ice-free period were determined. Besides diffusion, ebullition is another primary pathway for CH4 emissions from thermokarst lakes22,46. Compared to diffusion, ebullition is typically intermittent and can exhibit significant fluctuations in CH4 emissions over short periods. However, it contributes substantially to the total CH4 emissions from these lakes19,22,85. We collected published data on the proportion of CH4 emissions via ebullition from thermokarst lakes on the Tibetan Plateau. Additionally, the proportion of ebullition in CH4 emissions does not show significant differences across regions with different vegetation types (P > 0.05)19. We calculated the average proportion of CH4 emissions via ebullition from thermokarst lakes under the vegetation type of alpine swamp meadows (n = 48), alpine meadows (n = 52), and alpine steppe (n = 20). Since there was no data available for alpine desert, the average value from the other three vegetation types was used (Supplementary Fig. 6). The ebullition flux during ice-free period from thermokarst lakes under different vegetation types was calculated using Eqs. (9) and (10):

$${F}_{{{\rm{ebullition}}}}=\frac{M\times {F}_{{{\rm{diffusion}}}}}{1-M}$$
(9)
$${F}_{{{\rm{ice}}}-{{\rm{free}}}}={F}_{{{\rm{diffusion}}}}+{F}_{{{\rm{ebullition}}}}$$
(10)

where M represents the proportion of total CH4 emissions through ebullition corresponding to the type of vegetation underlying the lake. Fbubblition is the CH4 ebullition flux during ice-free period (g m−2 yr−1), Fice-free is the total CH4 flux from thermokarst lakes during ice-free period (g m−2 yr−1).

Calculation of CH4 flux during ice-melting period

The ice cover on thermokarst lakes acts as a barrier during frozen periods, preventing CH4 release into the atmosphere. As the lake ice melts during the spring season, the accumulated CH4 is released at a higher flux86. The sealed CH4 can be divided into two segments during ice-covered period: water storage and ice bubble storage7,10,81,87,88. Water storage refers to dissolved CH4 in water, remaining confined within the lake water until the ice breaks. During this process, a portion of the CH4 undergoes oxidization, with roughly half of it being transformed87. During ice-melting period, CH4 is released into the atmosphere through diffusion. Throughout these periods, as the CH4 concentration in the lake water steadily decreases, the diffusion flux correspondingly diminishes as well. When calculating the CH4 flux, we consider the 14 days before and after ice-free period as the high and low emission periods76. CH4 flux from water storage were calculated using Eqs. (11), (12), and (13):

$${F}_{{{\rm{water}}}\; {{\rm{storage}}}}=({F}_{{{\rm{high}}}\; {{\rm{emission}}}}+{F}_{{{\rm{low}}}\; {{\rm{emission}}}})\times 14$$
(11)
$${F}_{{{\rm{high}}} \; {{\rm{emission}}}}={K}_{{{\rm{high}}}}\times ({C}_{{{{\rm{w}}}}_{{{\rm{ice}}}-{{\rm{covered}}}}}-{C}_{{{{\rm{eq}}}}_{{{\rm{ice}}}-{{\rm{covered}}}}})\times m$$
(12)
$${F}_{{{\rm{low}}}\;{{\rm{emission}}}}={K}_{{{\rm{low}}}}\times ({C}_{{{{\rm{w}}}}_{{{\rm{ice}}}-{{\rm{melting}}}}}-{C}_{{{{\rm{eq}}}}_{{{\rm{ice}}}-{{\rm{melting}}}}})\times m$$
(13)

where Fwater storage represents the CH4 flux from water storage (g m−2 yr−1). Fhigh emission is the CH4 flux during high emission periods (g m−2 yr−1). Flow emission is the CH4 flux during low emission periods (g m−2 yr−1). \({C}_{{w}_{{ice}-{covered}}}\) and \({C}_{{w}_{{ice}-{melting}}}\) are dissolved CH4 concentration in water at the end of ice-covered period (late April) and the end of ice-melting periods (early May) (μmol L−1), respectively. \({C}_{{{eq}}_{{ice}-{covered}}}\) and \({C}_{{{eq}}_{{ice}-{melting}}}\) are dissolved CH4 concentration in water when equilibrium with the atmosphere (μmol L−1)77. For lakes that were sampled during ice-covered period but lacked data for the end of ice-melting period, we employed an interpolation method to estimate the missing data. This method involved establishing linear relationships between dissolved CH4 concentrations at the end of ice-covered period and those at the end of ice-melting period across various vegetation types in thermokarst lakes.

The formation process of ice bubble storage is as follows: Bubbles released from the lakebed sediment cannot escape into the atmosphere due to the barrier created by the lake ice. Instead, they are gradually encased by the ice as it grows from the top down. Before being completely sealed within the lake ice, approximately 80% of this CH4 ultimately dissolves back into the lake water. The remaining 20% remains trapped within the lake ice in the form of bubbles87 and is directly released into the atmosphere during the early stages of ice melting. By integrating the principles of ice bubble storage and water storage, and considering the proportion between ebullition and diffusion in thermokarst lakes, a simple numerical approach was used to estimate CH4 production and storage during ice-covered period. The derivation process for the numerical relationship between water storage and ice bubble storage is outlined in Eqs. (14), (15), and (16):

$${S}_{{{\rm{ebullition}}}}=\frac{M\times {S}_{{{\rm{diffusion}}}}}{1-M}$$
(14)
$${S}_{{{\rm{water}}}\; {{\rm{storage}}}}=0.5({S}_{{\rm{diffusion}}}+0.8{S}_{{\rm{ebullition}}})$$
(15)
$${S}_{{{\rm{ice}}}\; {{\rm{bubble}}}\; {{\rm{storage}}}}=0.2{S}_{{{\rm{ebullition}}}}$$
(16)

where Sebullition and Sdiffusion are the total CH4 production through bubbling and diffusion from the thermokarst lakes during ice-covered period, respectively. Swater storage is the total CH4 emission from water storage. Sice bubble storage is the total CH4 emission from ice bubble storage. We obtained the numerical relationship between Swater storage and Sice bubble storage, as shown in Eqs. (17) and (18). (Supplementary Fig. 5):

$${S}_{{{\rm{ice}}}\; {{\rm{bubble}}}\; {{\rm{storage}}}}=\frac{2M}{5-M}\times {S}_{{{\rm{water}}}\; {{\rm{storage}}}}$$
(17)
$${F}_{{{\rm{ice}}}\; {{\rm{bubble}}}\; {{\rm{storage}}}}=\frac{2M}{5-M}\times {F}_{{{\rm{water}}}\; {{\rm{storage}}}}$$
(18)

where Fice bubble storage is the CH4 fluxes from ice bubble storage during ice-melting period (g m−2 yr−1). M represents the proportion of CH4 emissions through ebullition from thermokarst lakes, corresponding to the type of vegetation.

The total CH4 fluxes during ice-melting period (g m−2 yr−1) were calculated using Eq. (19):

$${F}_{{{\rm{ice}}}-{{\rm{melting}}}}={F}_{{{\rm{water}}}\; {{\rm{storage}}}}+{F}_{{{\rm{ice}}}\; {{\rm{bubble}}}\; {{\rm{storage}}}}$$
(19)

Pathway of CH4 production

To evaluate the pathway of CH4 production, we measured the δ13C isotope abundance of both CO2 and CH4 and calculated the apparent fractionation factor (αC). Stable carbon isotope analysis of CO2 and CH4 was conducted using an isotopic ratio mass spectrometry. The αC was calculated from δ13C of CH4 and CO2 using Eq. (20)18. The δ13C isotope abundance of CO2 and CH4 released from diffusion and ebullition during ice-free period were analyzed from published data18,19.

$${\alpha }_{{{\rm{C}}}}=\frac{{\delta }^{13}{{{\rm{CO}}}}_{2}+1000}{{\delta }^{13}{{{\rm{CH}}}}_{4}+1000}$$
(20)

If αC is between 1.040 and 1.055, it suggests that CH4 production in thermokarst lakes is mainly through acetate fermentation (AM); and αC is greater than 1.055, it indicates that CH4 production is primarily driven by CO₂ reduction27,28. When αC is less than 1.040, it indicates that CH4 oxidation is the dominant process in thermokarst lakes29.

Regional upscaling

Based on 409 CH4 fluxes data during ice-free and ice-melting period, this study uses Monte Carlo analysis to estimate the annual CH4 emissions and their uncertainties from thermokarst lakes on the Tibetan Plateau. For each vegetation type (including alpine swamp meadow, alpine meadow, alpine steppe, and alpine desert)69, 1000 iterations were performed for both the ice-melting period and ice-free period. In each iteration, a random value was sampled from the thermokarst lake CH4 flux data and multiplied by the total area of thermokarst lakes for each vegetation type15. Finally, the annual CH4 emissions from thermokarst lakes under different vegetation type were calculated to determine total CH4 emissions. We used the mean value of the results from the Monte Carlo analysis as the total CH4 emissions from thermokarst lakes on the Tibetan Plateau.

Thermokarst lake susceptibility

We analyzed a total of 161,341 thermokarst lakes15. Prior to machine learning modeling, we used the ENMTools to filter out redundant samples, ensuring that only one lake was present in each 0.0083° × 0.0083° grid. Ultimately, we selected 71164 thermokarst lakes as training samples for the model. Meanwhile, we selected nine environmental factors influencing the distribution of thermokarst lakes. These factors include topography, hydrology, soil, human activities, permafrost and climate (Supplementary Table 3). The topographic factors, including elevation and slope, was derived from the high-precision Global Digital Elevation Model (DEM) (ETOPO Global Relief Model, National Centers for Environmental Information (NCEI) (noaa.gov)). The elevation data was directly obtained from the DEM, while the slope was calculated based on the DEM. The Topographic Wetness Index (TWI) was calculated using DEM89. Soil factors, including sand and silt, were obtained from the Harmonized World Soil Database version 2.0 (https://doi.org/10.4060/cc3823en). The human footprint was from Last of the Wild, v290. To simulate the current susceptibility distribution of thermokarst lakes, climatic factors, including monthly maximum air temperature and precipitation, were obtained from WorldClim. The permafrost factor of active layer thickness (ALT) was sourced from a published dataset91.

Prediction of thermokarst lake

To predict future changes in thermokarst lake susceptibility under SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5, we used monthly air temperature, precipitation (https://www.worldclim.org/), and ALT92 data from five general circulation models (GCMs). We refined the resolution to 1 km using the delta approach. All data were masked to the study area and resampled to a spatial resolution of 0.0083° × 0.0083°. Our study used six machine learning models to assess the susceptibility of thermokarst lakes: Random Forest (RF), Generalized Additive Model (GAM), Generalized Boosted Regression Model (GBM), Classification and Regression Tree Analysis (CTA), Artificial Neural Network (ANN), and MaxEnt. We evaluated the performance of these models using Receiver Operating Characteristic (ROC) curves, Kappa statistics, and true skill statistics (TSS) (Supplementary Table 4). Based on these evaluations, we select the RF model, which performed best, for modeling. We set thresholds at 0.2, 0.4, 0.6, and 0.8 to classify susceptibility into five levels: very low, low, medium, high, and very high93. We identified the regions with moderate to very high levels as thermokarst lake affected areas. Then we estimated the lake area density (i.e., the area of lakes within a pixel) to calculate the future actual area of thermokarst lakes under different vegetation types. The standard error of the area density was used to quantify the uncertainty in these future projections (Supplementary Table 5).

Statistical analyses

In this study, we utilized one-way analysis of variance (ANOVA) with Tukey’s HSD post hoc comparisons to test differences in dissolved CH4 concentrations and emission fluxes in thermokarst lakes among different vegetation types and during different periods at a significance level of P < 0.05. Regression analysis was employed to establish a linear relationship of dissolved CH4 concentrations between the end of ice-covered and ice-melting period. This approach was used to interpolate concentration for lakes in our dataset lacking on-site sampling at the end of ice-melting period. These statistical analyses were performed using Python 3.11 (available at https://www.python.org/). The regional estimates from Monte Carlo analysis were carried out using R v4.2.3 (available at https://www.R-project.org/).