To understand the level variations of Lake Paiku over the last 40 years (1980–2019 period), we develop an approach at the catchment scale. Because the catchment is hydrologically closed, the lake receives water input via direct precipitation, land surface and subsurface runoff, and glacier runoff. Conversely, it loses mass via evaporation. Because the quantification of water flows between the lake and potential aquifers surrounding it is difficult (Rosenberry et al., 2015), our approach assumes that these flows are negligible. The present study requires quantification of the different terms of the hydrological balance. Under these assumptions, the hydrological balance of the lake is given by the following equation: 1ΔzLake=PrecipitationLake+RunoffLandSurf+RunoffLandSub+RunoffGlacier-EvaporationLake.

The production of forcing data for the catchment (including precipitation) is detailed in Sect. 3.2.2. The land hydrology processes are quantified using the CryoGrid community model (version 1.0) (Westermann et al., 2023), as described in Sect. 3.2.3. Distributed 1D simulations are used to quantify land evaporation and runoff. The routing of water in the catchment is not represented, and the runoff computed for a given simulation is directly accounted for as a water input for the lake. The evaporation from the lake is simulated using the CryoGrid3-Flake model (Langer et al., 2016), as described in Sect. 3.2.5. Glacier melt is not modeled but is estimated for the study period (1980–2019) from remote sensing observations. From these observations, glacier yield is calculated as described in Sect. 3.2.6. Our catchment-scale approach to represent the hydrological balance of the lake is summarized in Fig. 2. Based on this approach, we can evaluate the performance of our framework (Sect. 4.1.2) by comparing the simulated lake balance with the one derived from the detailed observations of lake level variations over the study period (Lei et al., 2018, 2021).

In high-mountain environments, topography creates strong spatial variability in temperature and incoming radiation, which impact the surface energy balance (Klok and Oerlemans, 2002) and the ground thermo-hydrological regime (Magnin et al., 2017). Our approach requires forcing data that (i) capture this variability; (ii) include numerous variables such as air temperature, incoming long- and shortwave radiation, wind speed, specific humidity, rain, and snowfall; and (iii) cover the 40-year study period at a sub-daily time step. The TopoSCALE approach (Fiddes and Gruber, 2014) was developed for this purpose and allows us to downscale reanalysis products like ERA5 (Hersbach et al., 2020) at a high resolution (here ∼100m×100m).

Additionally, because working at a 10-2 km2 spatial resolution over a 2400 km2 catchment would require more than 200 000 forcing files and simulations, we rely on the TopoSUB method (Fiddes and Gruber, 2012) to reduce computational costs. This method uses a SRTM30 digital elevation model to explore redundancies in physiographic parameters of the study area such as elevation, aspect, slope and sky-view factor and to identify groups of high-resolution pixels (100m×100m) sharing similar values for these parameters. From there, all the high-resolution pixels belonging to such a group are only described as a single TopoSUB point, for which climatic variables can be downscaled to create one single dataset of climatic time series. The degree of similarity required by TopoSUB to identify groups of high-resolution pixels with redundant physiographic parameters can be adjusted by choosing the final number of TopoSUB points (and thus climate datasets) that should be used to cover the area corresponding to one ERA5 pixel. The Paiku catchment intersects eight ERA5 pixels at 30 km resolution, and we chose to use 50 TopoSUB points within each ERA5 pixel to cover the spatial variability created by the topography in small-scale climate. Ultimately, 368 TopoSUB points are used to cover the catchment. The average level of redundancy (i.e., the average number of high-resolution pixels represented by a single TopoSUB point) is 723 ± 745 (1σ, median: 506, min: 1, max: 4347). Figure C1 shows the distribution of the TopoSUB points and a reconstruction of the topography of the catchment based on this approach. The period covered by the forcing datasets starts on 1 January 1980 and ends on 31 August 2020 (40 years and 8 months).

In the TopoSCALE statistical downscaling approach, we do not rely on the AWS data, and thus the downscaled ERA5 data can be biased, as is often the case over Asia (Jiang et al., 2021, 2020; Jiao et al., 2021; Orsolini et al., 2019). Comparison against the available AWS observations (Fig. D1) indeed highlights notable differences in variables such as air temperature and precipitation. From these differences, we derived monthly bias correction factors that we applied systematically to all 368 of the climate forcing datasets. The catchment averages for precipitation and air temperature are shown in Fig. 3. In this figure and across the rest of the study, we use p values to evaluate the significance of linear trends in the temporal evolution of certain variables (temperature, precipitation, evaporation  etc.). This p value tests the null hypothesis which supposes that the value of the slope is equal to zero. The hypothesis is tested using Student's t test by comparing the distance between the estimated slope and 0 relative to the standard error of the slope. We did not report trends when this p value (probability of a null slope) was higher than 0.005.

To simulate the ground thermo-hydrological regime, we use the CryoGrid community model (Westermann et al., 2023). The CryoGrid community model (CG) is a land surface model designed for applications in cold regions where seasonal frozen ground or permafrost may occur. The model implements heat transfer in a 1D soil column, accounting for freeze–thaw processes of soil water using effective heat capacity (Nakano and Brown, 1972). To do so, soil-freezing curves are based on Dall'Amico et al. (2011), as detailed in Westermann et al. (2013). Vertical water movement in the soil column is based on Richards' equation (Richardson, 1922; Richards, 1931). The soil matric potential and hydraulic conductivity follow van Genuchten (1980) and Mualem (1976). Additionally, to represent the obstruction of connected porosity by ice formation, the hydraulic conductivity is reduced by a factor dependent on the local ice content, following Dall'Amico et al. (2011). The model features the snowpack module called CG Crocus described in Zweigel et al. (2021), which adapts the snow physics parameterizations from the CROCUS scheme (Vionnet et al., 2012) to the native snow module of CryoGrid3 (Westermann et al., 2016). At the surface, the model uses a surface energy balance module to calculate the ground surface temperature and water content. The turbulent fluxes of sensible and latent heat are calculated using a Monin–Obukhov approach (Monin and Obukhov, 1954). Evaporation is derived from the latent heat fluxes using the latent heat of evaporation and is adjusted to the available water in the soil. It occurs in the first grid cell only, but water can be drawn upwards due to matric potential differences. Because vegetation is very scarce in the catchment, we do not expect transpiration to have a strong imprint on evapotranspiration, and our calculations do not unravel evaporation from transpiration.

The setup of the CryoGrid community model for the land is presented in Fig. 4. To capture the high spatial variability of mountainous climate, our approach relies on the 368 climate forcing datasets to cover the catchment (see Sect. 3.2.2). This approach enables us to perform spatially distributed modeling. All 368 of the simulations are independent and use the same parameterization. In the absence of direct observations of the soil stratigraphy within the catchment, the soil column was designed to agree with field observations in the region (Yuan et al., 2020; Wang et al., 2009; Hu et al., 2020; Luo et al., 2020; S. Yang et al., 2014; Wang et al., 2008), to be consistent with similar modeling approaches across Tibet (Chen et al., 2018; Song et al., 2020) and to be consistent with input datasets (Shangguan et al., 2013, 2017). Thus, the soil stratigraphy is divided into three units: a top soil (0.3 m thick), a bottom soil (1.7 m thick) and a bedrock unit (extending beyond the depth of interest of the study). An overview of the parameters for each unit, their source and the way they are calculated is presented in Table A1 in the Appendix.

Regarding the processes implemented in the model (Sect. 3.2.3), infiltration according to Richards' equation only occurs in the top and bottom soil units. The bedrock unit has a static water content. Unraveling surface from subsurface flow is an ongoing challenge in catchment-scale hydrology (McDonnell, 2013), and this distinction is important in mountain terrains where these two flows can behave differently due to the complex topography (Seibert et al., 2003; Gao et al., 2014; Hu et al., 2020). For this study, we rely on a simple approach that is based on thresholds regarding the soil water content (porosity and field capacity). These kinds of approaches are thus based on soil properties and have often been used in hydrological modeling studies (Vörösmarty et al., 1989; Shaman et al., 2002; Kelleners et al., 2010; Kampf, 2011; Samuel et al., 2008). In detail, we compute surface and subsurface flow as follows.

On the one hand, surface runoff is computed relative to the saturation level of the soil column. When the entire soil column is saturated (WC = porosity), additional water input from precipitation or snow melt is directly counted as surface runoff. On the other hand, subsurface runoff is computed relative to the field capacity of the ground, which is an input parameter of the model. When the water content (WC) of a ground cell exceeds this field capacity (FC), the amount of water corresponding to WC minus FC is available to produce subsurface runoff. We use the lateral boundary condition LAT_WATER_RESERVOIR from the CryoGrid community model (Westermann et al., 2023) to account for this subsurface runoff. The speed at which this available water exits the soil column towards the lake is calculated with Darcy's law, using the hydrological conductivity of the ground and the mean slope of the catchment as hydraulic slope. Because the model couples thermal and hydrological fluxes, all of these changes in the soil water content can be driven by precipitation input and evaporation but also by water phase change in the ground, such as ice melt.

Because we do not have knowledge of the distributed thermal state with depth over the catchment at the beginning of the simulations, we assume that temperature profiles were in equilibrium with the climate of the 5 first years of modeling (1980–1984). To do so, we start our simulations with a 60-year spin-up of these first 5 years (12 repetitions), which is sufficient to establish a stable temperature profile over the first 9 to 80 m, depending on the simulations, extending beyond the hydrologically active part of the ground (the first 2 m).

To validate model simulations, the simulated ground surface temperatures (GSTs) are compared to the two temperature logger time series acquired in the vicinity of the AWS (Sect. 3.1). We used this comparison to calibrate the surface roughness used for the surface energy balance calculations in the model.

The following method is used to produce area-averaged evaporation and runoff (in mm, water equivalent) in a zone of interest. For a given TopoSUB point in this zone, the model produces hydrological values (in m3) using the area of a TopoSUB pixel on the catchment map. Then these values are multiplied by the number of pixels in the zone corresponding to this TopoSUB point in particular, and this is for all the relevant TopoSUB points covering the zone (e.g., evaporation in warm permafrost). Then the area of interest is calculated by counting the number of pixels in the zone of interest and multiplying this number by the area of a pixel. Then the total volume is divided by the total surface for the zone of interest to obtain the final value (in mm).

The lake thermo-hydrological response to the climatic forcing data is simulated using the CryoGrid3-Flake model (Langer et al., 2016). The two models were coupled by Langer et al. (2016) to simulate the thermal regime of thermokarst lakes (including surficial water freezing and melting) and underlying ground. Here, we use the coupled models mainly to quantify evaporation at the lake surface. In the coupled model, the native surface energy balance module of CryoGrid3 (Westermann et al., 2016) was amended to account for processes tied to free water surface energy balance: (i) the dependence of the albedo of a water surface on solar angle (and thus time of the day) and wind speed (and wave formation), (ii) the dependence of the surface roughness length on wind speed (and wave formation), and (iii) the exponential decay of incoming radiation with depth in the water column. Similarly to the land simulations, the lake simulations were forced by the downscaled ERA5 data (with the TopoSUB and TopoSCALE methodology), with the corrections being derived from the AWS data (Sect. 3.2.2). The simulations were initiated with a 20-year spin-up of the 1980–1984 climate. The simulation results corresponding to the four ERA5 tiles covering the lake were then averaged using the respective spatial footprint of each tile on the lake.

Multiple studies quantified the volume change of the glaciers located within the Paiku catchment in the recent past (1970s to 2020). To our knowledge, there are no field-based measurements of glacier mass balance available in this catchment. As a consequence, we rely solely on geodetic mass balance studies (Brun et al., 2017; Maurer et al., 2019; King et al., 2019; Shean et al., 2020; Hugonnet et al., 2021). All these studies estimated glacier volume changes over periods of 20–30 years from satellite-derived DEMs. As a consequence, we can only estimate the average annual glacier mass balance and not the year-to-year variability. Glaciers occupy approximately 113 km2 in the Paiku catchment. They have shrunk over the past 50 years at a rate of 0.44 %yr-1 from an area of 132 km2 in 1975 to 122 km2 around 2000 and to their current extent (King et al., 2019; Bolch et al., 2019). The average mass balances for the period 1975–2000 and 2000–2020 are -3.9 ± 2.1×1010 and -5.4 ± 2.4×1010 kgyr-1, respectively (-4.6 ± 2.5×107 and -6.4 ± 2.8×107 m3 with a 850 kgm-3 density). These mass balances correspond to specific mass balances of -0.31 ± 0.17 m of water equivalent per year (w.e.yr-1) and -0.47 ± 0.21 mw.e.yr-1, respectively.

Regarding glacial runoff, it was estimated to be 320 ± 4 mmyr-1 for the 2001–2010 period by Biskop et al. (2016) using a temperature index approach for ice melt. For the 2000–2018 period, X. Zhang et al. (2020) derived a runoff value of 52 ± 12 mmyr-1 (1.24 ± 0.29×108 m3yr-1, which we scaled to the basin area). The value we derive of 39 ± 13 mmyr-1 is thus found to have good consistency with the latter one (Sect. 4.1.1).

Simulated daily ground surface temperatures are in good agreement with the observed ones, showing a bias of -0.2 and 0.6 ∘C and an RMSE of 1.4 and 1.6 ∘C for loggers 15 and 13, respectively (Fig. 5a and c). Most of this RMSE is explained by a mismatch between the model and observations in the tails of the temperature distribution, whereas intermediate temperatures exhibit the best agreement with observations.

Annual lake evaporation mainly ranges between 800 and 900 mmyr-1 (Fig. 5b), with a mean value of 870 ± 23 mm (1σ). Lake evaporation does not exhibit a linear trend of increasing or decreasing and is mostly dominated by year-to-year variability. Though slightly lower, our evaporation results are in good agreement with the values from Lei et al. (2021), which are derived from local and regional meteorological observations and lake budget calculations (Fig. 5b). We used the simulated evaporation together with the lake level data and lake area data from Lei et al. (2018) and Lei et al. (2021) and the precipitation forcing datasets (3.2.2) to derive the total runoff (land + glacier) required as an input to the lake budget to reproduce the lake variations. This required runoff corresponds to the red line of Fig. 5d. The required runoff volumes are scaled to the land area of the catchment to be comparable with the other variables. Figure 5d also presents the runoff values derived from the land cryo-hydrological modeling and from the glacier remote sensing investigations. Annual volumes are expressed (in mm) over the land part of the catchment (excluding the lake). As presented in Sect. 3.2.6, glacier mass balance values are considered to be constant for the 1980–2000 period and the 2000–2019 period and are, respectively, equal to -4.6 ± 2.5×107 and -6.4 ± 2.8×107 m3yr-1. The addition of annual precipitation to these values to quantify the total glacier runoff introduces year-to-year variability to the glacier runoff. At the catchment scale, the average glacier runoff over the 40 years is 39 ± 13 mmyr-1.

Over the 40 years, the average annual land runoff value (surface + subsurface) we model is 24 ± 8 mm. Summed together, the land and glacier runoff are in partial agreement with the runoff that is required to close the lake water balance. Annual values are compatible within error bars for 28 out of the 40 years of simulations. The glacier and land runoff are slightly too small to close the lake water balance during the first 20 years and slightly too large for the last 20 years of simulation. Over the whole period, the sum of the glaciers + land runoff produces 95 % of the required runoff. Land runoff is further described in Sect. 4.3, and lake results are described in the following section.

Our observations, climate data, simulations, geodetic data and the lake level data from Lei et al. (2018, 2021) enable us to quantify the different terms of the lake hydrological budget. We present these results in meters for lake level change based on the average slope of the volume = f (level) relationship (Fig. 6). As the unique output term, evaporation dominates the lake budget with an average annual value of 0.86 m (34.6 m per 40 years; Fig. 6a). Direct precipitation in the lake is the dominant input, with an average annual value of 0.31 m (12.3 m per 40 years), followed by glacier runoff (0.28 myr-1, 11.3 m per 40 years) and land runoff (0.18 myr-1, 7.0 m per 40 years). When compared with lake volume observations over the 40 years of the simulation, the simulated lake budget is 1.04 m too negative.

Based on our results, we also reconstructed lake level variations that we compare with the observed variations (Fig. 6b). Following our framework, our values are presented at an annual time step. They qualitatively reproduce the overall lake level decrease but tend to overestimate this decrease and show an increasing mismatch with the observations from 0 in 1980 to 2 m in 2005. This mismatch is later compensated for by an increasing lake level trend in our simulation from 2005 to 2019. At the end of the simulation period, the mismatch is 1.04 m, which is consistent with the budget values (Fig. 6a) and the fact that our approach provides 95 % of the required runoff to close the lake budget (Sect. 4.1.1). This pattern of a too-strong decrease followed by an increase is consistent with the comparison between simulated and required runoff presented in Fig. 5d.

Our approach relies on a variety of data with regard to their scientific focus (glaciers, ground, lake, atmosphere), their type (in situ observations, remotely sensed data, reanalysis data), their characteristics (pointwise data, distributed data, constant or with various time resolutions) and the way they interact with our models (model parameters, forcing data, validation data, result data in the case of the glacier runoff). Such a diversity arises from our goal to quantify both the ground thermo-hydrological regime and the different terms of the lake budget. This variety also makes it challenging to consistently merge these data into a unique framework. For example, our quantification of the glacier mass change reconstruction is made of two constant values for the study period (1975–2000 and 2000–2020), which limits the relevance of the comparison between the observed lake level variations and the simulated ones.

Yet, the lake level variations are the only hydrological observations available to evaluate the robustness of the runoff we compute. Therefore, we had to combine lake level observations with our precipitation forcing data and lake evaporation quantifications in a simple mass conservation calculation to derive the land runoff to the lake required to reproduce the level variations (red curve in Fig. 5d). In this regard, the sum of the glacier and land runoff we derive over the 40 years corresponds to 95 % of the required runoff to the lake, indicating that the magnitude of our reconstruction is correct. Year-to-year comparison is less accurate, and we suggest that this is the consequence of the aforementioned limitations and also of our modeling strategy, as detailed below.

A main limitation regarding our usage of the data is related to the limited amount of available field observations required to provide robust model parameterizing, climate forcing and in-depth validation of the simulations, both hydrologically and thermally. Regarding climatic forcing data, our AWS measurement offers sound observations to evaluate and adjust the ERA5 data processed with TopoSUB and downscaled with TopoSCALE. Yet, a period of observations longer than 2 years would have enabled more robust corrections and could have allowed us to perform a more advanced statistical downscaling approach, e.g., quantile mapping (Themeßl et al., 2011). As such, the spatiotemporal domain of relevance of these corrections is insufficient to correct data for the whole catchment and for the 40 years of simulations. Overall, considering the strong bias we observe in the raw ERA5 data (Fig. D1), these corrections do represent an important first-order improvement.

Additionally, in the absence of borehole data that would allow us to anchor our parameters into observations, we rely on gridded values designed for hydrological and/or land surface modeling (Sect. 3.2.4 and Appendix A). Because these values might be less reliable than field observations, we chose to average them over the catchment to derive some more robust values. Altogether, this scarcity of field observations is likely to bring significant uncertainties to our analysis. Future efforts should focus on acquiring additional data or developing validation methods based on remotely sensed observations.

A limitation in our study is that lateral water flows between land simulation units is ignored. By giving access to the timing of water transport across the catchment, water routing would allow us to investigate temporal hydrological patterns at a monthly or seasonal scale. Because we work at annual and decadal timescales, this limitation has limited consequences for our results. The main consequence is to ignore potential storage effects on the land that would delay the arrival of runoff to the lake. We suggest that it is possible that this limitation partly explains the limited match between computed and required runoff at the annual timescale (Fig. 5). Yet, our subdivision of the catchment based on the different cryological states of the ground allows us to work with hydrological units that are smaller than the catchment and thus present shorter hydrological response times to precipitation.

Additionally, our approach regarding the modeling of runoff is relatively simple, i.e., partition between subsurface and surface runoff based on comparison between the soil water content and field capacity and porosity, respectively. More complex approaches split runoff into more sophisticated categories such as Horton overland flow, Dunne overland flow, subsurface storm flow, etc. (e.g., Savenije, 2010; Gao et al., 2014; Mirus and Loague, 2013). However, over the last decade, the relevance of this type of partitioning between different types of runoff has been questioned (McDonnell, 2013; Gao et al., 2023). In the frame of our study, we find it important to distinguish between surface and subsurface runoff because they generate flows with very contrasted speeds. From a general perspective, this significant difference in flow velocities impacts the hydrological system as a whole (e.g., river discharge, evaporation) and has various consequences throughout the catchment, such as for the water availability for vegetation, erosion and sediment transport.

In the particular case of a cryo-hydrological study, separating surface from subsurface runoff is particularly relevant because both flows do not react in the same way to ground temperature changes. As such, we see our approach as a middle way that allows us to make this distinction based on simple hydrological considerations. Yet, we acknowledge that the classification and quantification of the different types of runoff represent a valuable direction for future investigation of catchment-scale cryo-hydrology in Tibet. Another potential improvement in our modeling approach could be to unravel evaporation from transpiration. However, since vegetation is extremely scarce in the Paiku catchment, which is largely dominated by barren lands, we suggest that this would not significantly affect our results. However, this limitation should be explored in future field and modeling studies.

Conversely, our approach also conveys several important advantages regarding our goal to describe and quantify the ground thermo-hydrological regime of the catchment. The use of TopoSUB enables us to produce results at a resolution of 100m×100m over an area of nearly 2400 km2, with calculation costs 700 times lower than if each 100m×100m pixel was treated individually. Yet, thanks to the clustering method used to produce the forcing dataset (Sect. 3.2.2), the strong spatial variability of the physiography and its impact on the climate and incoming radiations are significant in the forcing data and have a major influence on the ground thermo-hydrological results, as exemplified by the strong spatial variability of ground temperatures (Fig. 7). Beyond elevation, other physiographic parameters such as aspect also influence the results. The mean values of 2 m deep temperature and evaporation over the 40 years for north-facing areas (averaged over the whole catchment and over the 40 years) are 1.3 ∘C and 163 mm, while they reach 2.9 ∘C and 197 mm for the south-facing ones. This strong dependence of modeled results on physiography highlights the necessity of taking this into account when modeling the thermo-hydrological regime of the ground in high-mountainous environments. Finally, our approach allows us to couple the physical processes governing both energy and water fluxes at the surface and subsurface and to highlight their interplay, as developed in Sect. 5.3.1.

The total lake level change we simulate is a decrease of 4.11 m. This is qualitatively consistent with the overall observed trend. The mismatch with the observations is limited to a 1.04 m excess in the simulated level drop (Fig. 9a). Our reconstruction shows a decrease of 4.66 m from 1980 to 2007, which is an overestimation of the initial drop. Afterwards, while observations indicate a gradual slowdown of the lake level decrease, we simulate a stabilization followed by a slight increase (0.55 up between 2013 and 2019). The reason for the overall mismatch of 1.04 m can arise from bias (i) in the forcing data (and mainly in the precipitation) used for the land and lake simulations, (ii) in the glacier mass balance estimate, and/or (iii) in the quantification of hydrological processes for the land or for the lake (evaporation, runoff). On top of these potential biases, the difference in trends for the end of the simulation time can be influenced by (i) our estimates of glacier mass changes, which are made of two time averages (one for the 1980–2000 period and one for the 2000–2020 period) and therefore produce very smoothed glacier runoff values that cannot capture variations at the scale of a decade or less, and (ii) the absence of water routing that prevents us from accounting for delays in storage effects on the water supply from the land to the lake.

Additionally, our approach ignores potential water fluxes between the lake and a surrounding aquifer. This can be a possible reason for this mismatch. In the context of a decreasing lake level, an aquifer surrounding the lake can create an additional water inflow when the lake level passes below the piezometric level of the aquifer (Yechieli et al., 1995). We suggest that such an inflow could mitigate the lake level decrease and thus explain the missing water in our reconstruction (Fig. 6b). It could also explain the gradual stabilization of the lake level that our model does not reproduce. This flow is not part of our conceptual hydrological framework even though it likely exists in reality, especially since there is no permafrost near the lake (as we simulate it here), allowing for the existence of such an aquifer (Walvoord and Kurylyk, 2016). Groundwater has been identified as a potential contributor to lake level rise in other regions of the QTP (Lei et al., 2022). In the long run, lake–aquifer systems commonly follow oscillations of the net atmospheric flux of water (precipitation–evaporation) and of the runoff that forces its mass balance (Watras et al., 2014). During these oscillations, the lake can pump water from the aquifer or feed it, depending on the relative difference in the piezometric level between them (Almendinger, 1990; Liefert et al., 2018). Yet, this potential effect is difficult to account for, and its magnitude remains unclear. Therefore, the reasons for the mismatch between observed and simulated lake levels could also be connected to other aspects of our methodology, such as bias in the climatic forcing data and other shortcomings arising from the lack of field data, or hydrological processes, as developed in Sects. 5.1.1 and 5.1.2.

Our reconstruction of the lake budget is informative regarding the contributions of the different inputs and outputs. Regarding lake evaporation, our mean value of 870 ± 23 mm is close to the one modeled by Yang et al. (2016) with the Flake model for Lake Nam (832 ± 69 mm) for the period 1980–2014, but we do not report a significant increasing trend in our results. Yet for the same lake (Nam Co) and a similar period (1980–2016), Zhong et al. (2020) reported an average value of 1149 ± 71 mm (along with an increasing temporal trend) using the Penman formula (Penman, 1948), thus highlighting the potential dependence of the results on the methodology. In our results, direct precipitation to the lake represents 40 % of the inputs, followed by glacial runoff (35 %) and land runoff (25 %). Glaciers are therefore a particularly important contributor to the runoff towards the lake (60 % of the total runoff vs. 40 % for land runoff), which is in contrast to the results from Biskop et al. (2016), who calculated that the runoff input to Lake Paiku was dominated by land runoff (70 % vs. 30 % for the glacier contribution). Here again, these differences likely arise from important differences in input data and methodologies to quantify the different hydrological processes (evaporation, runoff, snow and glacier melt). Yao et al. (2018) reported that, at the QTP scale, the balance between precipitation and evaporation (over land and lake) was dominant over glacier melt for understanding both lake storage increases and decreases. Our reconstruction does not give us access to significant temporal variations of the glacier contribution, but the abovementioned proportions in the contributions to the lake (40 %, 35 % and 25 %) show that the glacier contribution does not dominate the input terms. At the catchment scale, these proportions can vary significantly depending on the glacier coverage. For Lake Selin, Zhou et al. (2015) reported that runoff towards the lake, evaporation from the lake and on-lake precipitation altogether explained 90 % of the lake storage variations for the 2003–2012 period. The catchment of Lake Selin has a very limited glacier coverage, corresponding to 0,63 % of its area (Lei et al., 2013), compared to the Paiku (5 %).

Our results indicate that permafrost coverage in the Paiku catchment evolved from 27 % to 22 % of the land area during the simulated period. Such a coverage corresponds to sporadic permafrost (10 %–50 % of the area) and is consistent with recent large-scale estimates of permafrost in the Northern Hemisphere (Obu et al., 2019) and across the QTP (Zou et al., 2017; Ran et al., 2018). This decrease corresponds to a 19 % shrinkage of the 1980 permafrost area, which is higher than the 9 % reported by Gao et al. (2018), a value determined by catchment-scale numerical modeling in the upper Heihe catchment (northeastern QTP) over a similar period. It is also slightly higher than the 13 % decrease modeled by Wang and Gao (2022) from 1971 to 2015 for the Qinghai Lake catchment using a similar approach. Yet, it is smaller than the 34 % loss modeled by Qin et al. (2017) from 1981 to 2015 for the Yellow River Source Region (YRSR, northeastern QTP).

Active-layer (AL) evolution is contrasting throughout the catchment, and a deepening signal is only visible for the locations with limited evaporation (<150 mmyr-1). Given the strong drive of summer climate in relation to ALT, this overall lack of a deepening trend highlights how evaporation can act as an energy intake at the surface (K. Yang et al., 2014), limiting the surface and subsurface heat fluxes and thus AL deepening. In this regard, our results fall in line with the conclusions of Fisher et al. (2016) when observing evapotranspiration and ALTs in boreal forests and also confirm the modeling experiments of Zhang et al. (2021b) on permafrost wetting in arid regions of the QTP. Besides, the lack of an overall deepening trend is consistent with observations from Luo et al. (2018) in the YRSR over the last decade and with the modeled AL from Zhang et al. (2019) at the scale of the QTP for the last 40 years. Where evaporation is limited, we report an AL-deepening trend of 2.7 cm per decade, which is smaller than the 4.8 cm per decade trend modeled by Song et al. (2020) for the YRSR for the same period and smaller than the 4.3 cm modeled by Gao et al. (2018) in the upper Heihe catchment. Yet, it is comparable to the 2 cm per decade value modeled by Wang and Gao (2022) for the Qinghai Lake catchment from 1971 to 2015. Connections between AL deepening and evaporation are discussed in Sect. 5.3.1.

In no-permafrost areas, our simulations show that the thickness of seasonally frozen ground shrinks at a rate of 6.8 cm per decade. This rate is faster than the rate of 3.1 cm per decade quantified by Qin et al. (2018) using the Stefan solution for the YRSR (1961–2016) and faster than the 3.2 cm per decade modeled by Gao et al. (2018, Heihe catchment). However, it is similar to the 6 cm per decade rate modeled by Wang and Gao (2022) in the Qinghai Lake catchment from 1971 to 2015 and smaller than the 12 cm per decade modeled by Qin et al. (2017) for the YRSR (1981–2015). All these values fall within the wide range of 3 to 29 cm per decade reported by C. Wang et al. (2020) when studying seasonally frozen ground over the whole QTP with in situ observations. Regarding timing, we report a decreasing trend of 5.3 d for frozen conditions (70 cm deep) per decade. which is consistent with the decrease of 6.7 d per decade reported by C. Wang et al. (2020) just below the surface.

Regarding the timing of seasonal ground thaw, our results highlight that the increase in the duration of the seasonal ground thaw (at 70 cm) is mostly driven by a progressive delay of the end date of the thaw period. This result contrasts with those from Song et al. (2020) for the same period in the YRSR; they also modeled an increase of the seasonal thaw (at a 2 cm depth), although this was driven by an advancing trend of the start date of the seasonal thaw.

Our warming trends at 4 m depth for permafrost areas is 0.1 ∘C per decade, which is substantially smaller than the 0.43 ∘C per decade observed at this depth between 1996 and 2006 in permafrost boreholes along the Qinghai–Tibetan Highway in the northeast of the QTP (Wu and Zhang, 2008). Zhang et al. (2019) reported a 0.13 ∘C warming per decade of the permafrost top during winter, which is consistent with the trend of 0.14 ∘C per decade we observe at 2 m depth (mean AL between 1.4 and 1.7 m in our simulations) for the months of December, January and February.

Our results are characterized by (i) an increase in both evaporation and runoff (Fig. 9a and b), mainly driven by an increase in precipitation (Fig. 3 bottom); (ii) a runoff/(runoff + evaporation) ratio exhibiting an increasing trend as a result of ground warming and permafrost disappearance, both of which enable more subsurface runoff over time (Figs. 9c and 10d); and (iii) an increase in the proportion of liquid water in the ground compared to ice (Fig. 9d). Regarding all these points, our results show good consistency with the evolution reported by Gao et al. (2018) for the upper Heihe catchment (northeastern QTP) using a similar approach for a comparable period (1971–2013). The increasing trends in evaporation and runoff they report for the thawing season (dominant period for both processes) are comparable with the annual values we report: +10.0 mm per decade for evaporation (our study: +10.1 mm per decade) and +3.3 mm per decade for runoff (our study: +4.8 mm per decade). Similar evolutions are also reported by Wang and Gao (2022) for the Qinghai Lake catchment and by Qin et al. (2017) for the YRSR (1981–2015). These increases in runoff (especially surface runoff) are likely to have an influence on sediment transport. For instance, Li et al. (2021) showed that the current precipitation increase over High Mountain Asia is driving a runoff increase, which contributes to a significant rise in fluvial sediment fluxes. Regarding differences, Qin et al. (2017) modeled a stronger evaporation increase (14.3 mm per decade) linked to a decreasing runoff coefficient. Similarly to Li et al. (2019), we see that an important part of snow melt (49 %) infiltrates the ground and later contributes to runoff and evaporation.

Our simulation results enable us to explore the interplay between the fluxes of energy and water at the surface and subsurface. In this regard, we tested the correlation of evaporation with the proportions of liquid water and total water in the ground for cold and warm permafrost, as well as the correlation between evaporation and the duration of seasonal thaw at 70 cm depth (Fig. 11a and b). For permafrost areas (cold permafrost and warm permafrost), evaporation shows a strong correlation with the seasonal distribution between liquid and frozen water, similarly to previous modeling works for the region (Cuo et al., 2015). As such, this correlation suggests that the intensity of seasonal ground thaw plays a role in enabling higher or lower evaporative fluxes. This is likely due to cold surface temperatures strongly reducing water loss from the surface and because moisture delivery to the surface is inhibited when the ground is frozen. We suggest that this dependence is particularly important in the Paiku catchment because evaporation is strong (88 % of the precipitation input to the surface evaporates on average) and because frozen water is the dominant form of water in the ground in permafrost areas (Fig. 11a; the calculation includes the first 2 m below the surface).

Similarly, evaporation in no-permafrost areas shows a significant correlation with the duration of the seasonal thaw (Fig. 11b). We suggest that this result arises from the fact that frozen ground limits the evaporative fluxes, and thus, years during which the subsurface seasonal thaw is shorter are associated with reduced evaporative fluxes. We also tested the relationship between the linear trend of active-layer deepening and the mean evaporation (over the 40 years of simulation) for warm-permafrost areas (Fig. 11c). Thus, this graph does not present annual values, and one point corresponds to one of the 92 TopoSUB points classified as warm permafrost (values averaged over the 40 years). The graph highlights that TopoSUB points showing an active-layer (AL) deepening trend are associated with low evaporation and precipitation. From there, TopoSUB points with stronger evaporation show no deepening trend or even a shrinkage of the AL. This relationship is contradicted by the highest level of evaporation (>240 mmyr-1) observed for warm permafrost, for which AL deepening is observed again (dark-blue points of the graph). These TopoSUB points with the highest levels of evaporation also correspond to those receiving the largest amount of precipitation.

Runoff also shows a strong connection with the ground thermal regime (Fig. 11d). At the beginning of the simulation, years with an average 2 m deep temperature below 0 ∘C are associated with limited subsurface runoff (<5 mmyr-1). Over the years, as the ground warms up and permafrost disappears, subsurface runoff increases and can reach 20 to 45 mmyr-1. This result is consistent with the increased subsurface connectivity expected when permafrost thaws (Kurylyk et al., 2014; Gao et al., 2021), which has been both observed (Niu et al., 2016) and modeled (Lamontagne-Hallé et al., 2018; Huang et al., 2020; Gao et al., 2018). We suggest that these substantial changes in subsurface runoff, associated with changes in the ground temperature in Fig. 11d, support the hypothesis of a modification in the hydrological pathways as permafrost thaws.

Altogether, these results suggest a dependence of key variables quantifying the catchment hydrological balance (evaporation, runoff) on the seasonal characteristics and interannual trends of the ground thermal regime (temperature, liquid vs. frozen water content). Similarly to previous studies (Ding et al., 2020; Wang and Gao, 2022), we think these results advocate for the necessity of coupling thermal and hydrological modeling to improve our ability to understand and quantify changes in the hydrological balance of high-mountain catchments. To our best knowledge, along with Gao et al. (2022), our study represents to date the most complete effort to include the variety of coupled climatological, surface and subsurface processes characterizing the climate, hydrology and ground thermal regime of high-mountain catchments in Tibet at a small scale with a high spatial resolution.

Our results indicate that evaporation is particularly strong in the Paiku catchment. Over the 40 years of simulation, 10 % of the total precipitation is converted into runoff, and the rest of the water is either directly returned to the atmosphere from the snowpack via snow sublimation or from the ground surface via evaporation. Comparatively, Gao et al. (2018) observed and modeled a ratio of around 35 % for the Heihe catchment; Qin et al. (2017) reported an average ratio of 33 % for the YRSR, and Li et al. (2014) reported a ratio of 83 % for the Qugaqie catchment (central QTP) but modeling hydrological fluxes only.

Our sensitivity test on evaporation and runoff for slightly different climates (Sect. 4.4) highlights the fact that the role of permafrost regarding the runoff–evaporation distribution is a complex question, as has already been discussed in the literature (e.g., Bring et al., 2016). Some studies have suggested that landscape-scale permafrost thaw would trigger more evaporation (Walvoord and Kurylyk, 2016). This phenomenon was modeled by Wang et al. (2018) in the upper Heihe River catchment, for which they reported that the thickening of the active layer increased the ground storage capacity and led to a decrease in runoff and an increase in evapotranspiration. G. Wang et al. (2020) also reported that permafrost thawing accelerated evapotranspiration (1961–2014).

Conversely, Zhang et al. (2003) and Carey and Woo (1999) reported that shallow frozen-ground conditions (such as a shallow active layer) maintain higher water contents close to the surface, promoting higher evaporation. Sjöberg et al. (2021) modeled this phenomenon with a fully coupled cryo-hydrological model including surface energy balance calculation. They modeled a slope with a simplified geometry in 2D for different permafrost coverages. They found that hillslopes with continuous permafrost have rates of evapotranspiration that are twice as high compared to hillslopes with no permafrost.

As such, the interplay between the runoff–evaporation distribution and the ground thermal regime in areas where permafrost coverage shows a spatiotemporal variability is difficult to apprehend (Fig. 10). This complexity is most likely to be due to a strong sensitivity to the drainage conditions (fast flows of steep mountain environments vs. slow flows of lowland catchments) and to the climate setting, both at the annual scale (arid regions vs. wet regions) and at the seasonal timescale (relative timing of temperature variations, rainfall, snowfall, snow melt and ground freeze–thaw).

Because it can both promote evaporation or runoff depending on the setting, the ground thermal regime of the catchment seems to have the possibility to create a positive feedback towards both lake level decreases or increases. Further studies should therefore focus on comparing the thermo-hydrological regime of different Tibetan catchments with contrasting lake level changes and permafrost coverage to test to which extent these differences can contribute to explaining the spatial patterns of lake level changes across the QTP.