Comparison of hydrogeochemical characteristics of thermokarst lake water in the Qinghai–Tibet Plateau under active layer freeze–thaw conditions

As the ‘Third Pole’ of the earth, the Qinghai–Tibet Plateau (QTP) is mainly underlain by high-altitude permafrost (Ran et al. 2018). Thermokarst lakes are common landscape features in the QTP, and they developed as a result of the thawing of ice-rich permafrost or melting of massive ground ice (Brown & Grave 1979; Hinzman et al. 1997). Climate change has a significant impact on water resources and the eco-environment in cold and arid regions of China (Wang et al. 1996; Toniolo et al. 2009). As a result, the occurrence of active thermokarst lakes may indicate that permafrost is warming and unstable (Zhou et al. 1996; Serreze & Walsh 2000). The thermokarst is mainly experienced in four stages of development, which include formation, expansion, stopping of expansion, water body drainage, and formation of another permafrost (Niu et al. 2008). The size, depth of the lake, and water temperatures are important factors determining the permafrost configuration around and beneath them (Lin et al. 2011). The mean annual temperature at the lake bottom may influence the configuration of the permafrost and talik further (Burn 2005).

Under the impact of warming climate and increasing precipitation, lake areas in the interior of the QTP have been increasing over the past few decades (Zhang et al. 2017). The number of thermokarst lakes in the Beiluhe River basin of the QTP has increased approximately by 534, amounting to an augment in an area of 410 ha during the past four decades (Luo et al. 2015). The expansion of these lakes has fatally led to a series of environmental issues, such as changes in soil, ecology hydrology, and caused instability of important basic projects such as the Qinghai–Tibet highway and railway in the basin. In addition, thermokarst lakes threaten the stability of the ecosystem and hinder the sustainable development of the social economy (Gao et al. 2017a, 2017b).

The hydrogeochemical characteristic of the thermal melting lakes will change inevitably along with a series of material and energy exchanges in the thaw–freeze process. From the study on the hydrogeochemical genesis of some saltwater lakes, such as Qinghai Lake and Qarhan Salt Lake, showing the hydrogeochemical characteristics of typical salt lakes are mainly affected by the supply source and the evaporation (Sun et al. 1991; Zhang 2009; Zhang et al. 2010; Gou 2011). Numerous new thermokarst lakes were formed because of the disturbance of natural conditions after the construction of the Qinghai–Tibet railway (Li et al. 2020). The hydrogeochemical composition of lakes along the railway in the Beiluhe region was found to be lower than that of other regions which may be related to the formation conditions of lakes (Yang et al. 2016).

Stable isotope geochemistry plays a critical role in monitoring climate change (Li et al. 2012, 2013). As the common stable isotope, δD and δ¹⁸O have a wide range of applications in evaluating the source and recharging of surface water. It can also indicate the interaction between surface water, groundwater, and rainfall in different regions. The values of ion concentrations of δD and δ¹⁸O were proven to be useful tools for studying the hydrological processes of lakes on the Tibetan Plateau (Yang et al. 2016; Gao et al. 2017a, 2017b). Furthermore, Yang et al. (2016) demonstrated that thermokarst lake water was contributed 61.3% of the melting of ice-rich permafrost by using the isotopic method.

The active layer is the layer above the permafrost that freezes in the cold season and melts in the warm season (Zhang et al. 2015). It is the interface between the permafrost and the atmosphere for heat exchange. The seasonal freezing–thawing process of the active layer has an important impact on surface energy balance, water migration, and groundwater runoff (Anisimov et al. 1997; Hollesen et al. 2011). Based on the observation data, the melting of the active layers in the Wudaoliang area first began in late April, achieved the maximum depth in September melt, and quickly completed all the freezing processes in late October (Hu 2020).

In this study, the regimes of hydrogeochemical composition, δD and δ¹⁸O, in lakes and groundwater during the freezing–thawing process in the active layer were analyzed by using hydrogeochemical theory and mathematical statistics. The objectives of this paper are: (i) to determine the hydrogeochemical components of lake water in different freezing–thawing processes; (ii) to analyze the possible hydrogeochemical reactions in lake water; and (iii) to determine the recharge relationship between lake water and atmospheric precipitation and underground meltwater.

The Beiluhe basin, a main part of the Hoh Xil Nature Reserve Region, lies in the interior of the QTP (Lin et al. 2011). This primary area of QTP experiences permafrost basin is 350 km away from Golmud City with an altitude of 4,600 m (Figure 1). The Beiluhe basin is located in an extremely continental climate zone and high solar radiation. The data recorded from 2005 to 2014 indicated that the mean annual air temperature is about −3.4 °C, while the precipitation is about 369.8 mm yr⁻¹ (Yin et al. 2017). Over 90% of precipitation falls between May and September. The mean annual potential evaporation is about 1,317 mm yr ⁻¹, much higher than the precipitation (Yin et al. 2017). Meanwhile, the annual variation of air temperature in the study area (+0.027 °C/annum) over the past 60 years has shown increasing trends, similar to that of precipitation processes (+154 mm/annum) (Gao et al. 2017a, 2017b). Permafrost is widely distributed in the study area because the multi-year ground temperature is −1.8 to −0.5 °C (Huang et al. 2011). The active layer thickness is 1.8–3.0 m, and the permafrost is generally 20–80 m thick; the geothermal gradient is 1.5–4.0 °C/100 m (Huang et al. 2011).

The regional strata consisted predominantly of lacustrine deposits of the upper Tertiary and diluvium of the Quaternary Holocene Series (silty clay). The ground surface, which is generally sparse in vegetation, is covered by fine sand with gravel (0.5–2.1 m in thickness), while the underlying layers include silty clay (up to 8 m in thickness in some places) and mudstone with sandstone interlayer (Lin et al. 2011).

Thermokarst lakes are widely distributed in the study area. The mean lake area in the region is 8,500 m², the largest lake is greater than 60,000 m², and the smallest one is less than 1,200 m² (Lin et al. 2011). The permafrost thickness ranges from 20 to 80 m, with an active layer of 1.8 to 3.0 m in thickness (Lin et al. 2011). The lakes in the study area are relatively small compared with those in the Kunlun mountainous region, Chumaerhe High Plain, and Beiluhe basin, whereas they are much deeper. Almost all the lakes in the study area have a depth of >1 m, and one of them is almost 3 m deep. The thermokarst lakes developed in the low-lying ground where ice-rich permafrost or massive ground ice exists.

The water samples of the Beiluhe River were collected in June, July, August, and October in 2019, and the sampling locations are shown in Figure 2. The freezing–thawing stages of the active layer that corresponds to the time of the four samples include the early thawing, middle thawing, late thawing, and freezing periods of the active layer.

There are over 15 lake samples and nine groundwater samples were collected, while part of the water sample may be missing because of the high degree of difficulty of sampling in some sampling sites. The water samples were sealed in PVC bottles and then taken back to the room for testing. Three bottles of water samples were collected at each sampling point. Two bottles of 500-ml water samples were used for general hydrogeochemical analysis and detection, while one bottle of 50-ml water sample was used for isotope detection.

The temperature and pH of the samples can be measured directly by a portable water quality analyzer (6,250 °C) at the water sampling site. The contents of ⁠, ⁠, ⁠, NH₄⁺, and Cl⁻ in the lake water sample were determined by using the conventional titration method. Na⁺ and K⁺ were determined by flame color reaction and flame atomic absorption spectrometry (TAS990). EDTA titrimetric methods were adopted for analyzing Ca²⁺ and Mg²⁺. The total dissolved solids are obtained by steaming the water sample dry and measuring its weight. F⁻ was determined by the ion-selective electrode (ICS-90A), and and were measured mainly by ion chromatography (precision ion meter).

The detection of hydrogen and oxygen stable isotopes were carried out by the Hebei University of Geosciences, which mainly measured the 1,000 deviation value of hydrogen and oxygen stable isotopes in lake water, underground water, and rainwater samples. The measurement is mainly performed by the newest L214-i instrument in the United States, and the accuracy of δD and δ¹⁸O can reach 0.5 and 0.1‰.

The isotopic thousandth deviation (⁠⁠) is a dimensionless value that clearly reflects the size and trend of an isotope content in a sample

The evaporation-to-inflow (E/I) of lakes is estimated at different stages for a particular lake in the study area. The amount of water that flows into the lake and the amount of water lost by the lake should be balanced dynamically within a certain period. However, it is difficult to calculate the lake water balance by using traditional hydrology methods due to the high altitude in the study area. Therefore, many scholars have adopted the E/I ratio of the lake as an important index to evaluate the balance process of lake water.

The value of h_s is between 0 and 1, and C_K is the relevant parameter used to calculate the dynamic fractionation coefficient. The C_K of ¹⁸O is 14.2‰, whereas that of D is 12.5‰ (Gonfiantini 1986).

Therefore, the values of relative humidity h_s, temperature T, and hydrogen and oxygen isotopes δD and δ¹⁸O should be determined and substituted in atmospheric precipitation during the melting and freezing of the active layer. So, the E/I of the lake at different stages can be calculated. Temperature and h_s are available from the National Meteorological Data Network.

Simple statistics were carried out on the test results of lake water samples in the freezing–thawing process of the active layer (Table 1). Table 1 shows that the content distribution of each ion in different lakes varies to some extent. Meanwhile, most of the variation coefficient between 10 and 100% shows that the ions in the lakes are not evenly distributed in the region.

The content of each ion in the water sample in the study area was plotted as a boxplot (Figure 3). The contents of anions Cl⁻ and and the cation such as Na⁺ − K⁺ in lake water are at a high level at different freezing–thawing stages in the active layer. The distribution of Ca²⁺, Mg²⁺, ⁠, and is relatively uniform, whereas the extreme values of Na⁺ and Cl⁻ concentrations vary greatly with significant regional differences from the perspective of regional characteristics.

Moreover, the average concentrations of ⁠, ⁠, and Cl⁻ in the lake changed greatly in the freezing–thawing process of the active layer. During the melting process of the active layer to refreezing, pH concentration showed an increasing trend from 8.4 to 9.11 under the influence of aquatic plants' photosynthesis. The concentration also increased gradually from 10.11 mg/L at the initial melting stage of the active layer to 49.29 mg/L, while the concentration decreased to 156.43 from 249.00 mg/L. Obviously, the decreased range of concentration is greater than the increased range of concentration, which may be due to the conversion of part of to other forms of carbon in the lake.

In this study, Shukalev classification was employed to clarify the water types of thermokarst lakes. The classification results show that the hydrogeochemical types of lake water have certain regional differences (Figure 4).

Na⁺, Ca²⁺, and Mg²⁺, which are located in Zones B and D, are predominant among cations. The anions, including and Cl⁻, are mainly located in the E and G regions. Besides, the sample in October is all distributed with the right of the sample points except for the lakes in the central region. The results obtained by the Piper graph indicated that the hydrogeochemical types of lakes in the study area were mainly mixed water samples of HCO₃·Cl − Na·Ca·Mg and Cl − Na·Mg.

The Gibbs graphs indicate that the source of the hydrogeochemical composition of surface water is mainly affected by rock weathering, evaporation and concentration, and meteoric precipitation. The Gibbs diagram of the lake is shown in Figure 5 during the melting of the active layer to the freezing process.

Figure 5 shows that Na⁺/(Na⁺ + Ca²⁺) in the lake is between 0.3 and 0.9, while Cl⁻/(Cl⁻ + ⁠) is between 0.1 and 0.9. Lake water sample points are mostly distributed in the middle and upper parts of the Gibbs chart, which is controlled by evaporation and rock weathering. The hydrogeochemical compositions of the lakes in the north, central, and south of the study area were significantly different from one another. The hydrogeochemical compositions of the lakes in the north of the study area were significantly affected by rock weathering, whereas those in the central and south were mainly affected by evaporation and concentration.

Furthermore, the water chemistry of each lake in the Gibbs diagram shows a trend of migrating to the right during the thawing–freezing process of the active layer. This phenomenon indicates that the concentration of ions in the unfrozen water is increased by the freezing desalination of the active layer in the thawing–freezing process of the active layer, which has an important effect on the hydrogeochemical composition of the lake.

Through analyzing the ratio of ion normality, we can study the formation process of hydrochemical characteristics; otherwise, the characteristics of water quality on regional and temporal scales can be reflected. Eight thermokarst lakes in the study area were selected as the research objects to investigate the changes in the relevant ion proportionality coefficients on the time and regional scales (Figure 6).

The magnitude of γNa/γCl can determine the sources of Cl⁻ and Na⁺ and the level of salinity in lakes. Figure 6(a) shows that γNa/γCl in the northern lakes was greater than 1, whereas in most of the central and southern lakes was less than 1. Such a result was consistent with the TDS content in the lakes. The coefficient of γNa/γCl in the northern and central lakes fluctuated greatly on a time scale which indicates the freezing and thawing process had an influence on γNa/γCl. The γNa/γCl coefficient of the lakes in the southern part of the study area fluctuated less, which may be related to the hydrogeochemistry of the active layer.

The magnitude of γHCO₃/γCa is often used to analyze the sources of Ca²⁺ and in water. Figure 6(b) shows that magnitude of γHCO₃/γCa in most lakes was between 1.5 and 3 at the initial melting time of the active layer, which may be caused by the dissolution of calcite. The magnitude of γHCO₃/γCa showed a slow decline over time, which may be mainly caused by the change in concentration. As the active layer began to melt, the photosynthesis of aquatic organisms at the bottom continued to increase which eventually leads to the reduction of ⁠.

In Figure 6(c), the γCa/γMg coefficients of all lakes except lake H07 were less than 1 and gradually showed a decreasing trend in the different stages from the active layer melting to freezing. This phenomenon may be related to the decrease in Ca²⁺ concentration with the increase of concentration in the lake. However, due to the time of H07 lakes formed earlier, resulting in the activities of the lake bottom layer is completely melt wear, this may lead to the gamma coefficient of Ca/Mg in gamma anomalies.

The γCa/γCl coefficient is used to describe the dynamic characteristics of lake water. The lower the coefficient of γCa/γCl, the worse the water flow alternations in the lakes. When the coefficient of γCa/γCl is small, the water will flow slowly. In Figure 6(d), the γCa/γCl coefficients of all lakes water except the northern lake L07 at different stages were less than 1 and basically did not change with time, indicating that the alternative effect between lake water and groundwater flow was poor. The reason for the difference in L07 lake may be that the active layer at the bottom of the lake is melted through, which leads to the enhanced exchange between lake water and groundwater. Moreover, the γCa/γCl coefficient of L07 increased with time, which may be caused by the hydraulic connection enhanced between lake water and groundwater due to the warmer temperatures.

The SI can use to analyze chemical reactions that may occur in the lake. As shown in Figure 7, the SI of the calcite and dolomite in the lake water are all greater than 0 and will continuously increase in freezing–thawing stages, indicating that the dissolution reaction of minerals occurs in the lake water.

The SI of the salt rock and gypsum rock are less than 0, which indicates these two rocks do not exist at the bottom of the lake. The SI of gypsum rock in some lakes is getting lower on the time scale due to the reduction in Ca²⁺ concentration. Overall, the SI of salt rock does not change significantly with time.

The alternation of cation adsorption in lake water mainly occurs on the surface of lake bottom minerals. Some of the cations in lake water will be adsorbed on the soil particles to replace the originally adsorbed ions. Conventional ion adsorption ability from strong to weak is: H⁺ > Fe³⁺ > Al³⁺ > Ca²⁺ > Mg²⁺ > K⁺ > Na⁺. The positive and negative relationship between γ(Na⁺ − Cl⁻) and γ(⁠ + − Mg²⁺ − Ca²⁺) is usually used to evaluate whether cationic alternate adsorption occurred in lake water (Figure 8). Only both of them are greater than 0 and Na⁺ and Ca²⁺ have cation alternate adsorption.

As shown in Figure 8, Na⁺ − Cl⁻ and (⁠ + − Mg²⁺ − Ca²⁺) in the northern lakes are all greater than 0 during the melting and freezing of the active layer, which indicates that cationic alternate adsorption may exist in the northern lakes. From the perspective of time, cationic alternate adsorption occurred in the L07 and L08 lakes at the initial melting stage of the active layer, whereas it only occurred in the L08 lake in the middle melting stage to the freezing stage. The cationic alternation adsorption in the L08 lake was the Na⁺ replaced by Ca²⁺ due to the concentration of Na⁺ in the northern lakes being higher than that of Ca²⁺.

Generally, lake water hydrogeochemical characteristics are mainly influenced by aquatic plants, groundwater runoff, temperature, and other conditions. Lake L06, which is located in the middle of the study area, is chosen as the representative lake to analyze the reasons for the changes in the hydrogeochemical characteristics of the lake water during the melting–freezing process of the active layer. The changes in the ion concentration in Lake L06 are shown in Figure 9.

The concentrations of ⁠, ⁠, and Cl⁻ and pH in Lake L06 showed significant differences during the melting–freezing process of the active layer, whereas ⁠, Na⁺, Ca²⁺, and Mg²⁺ showed rarely differences over time. The reasons for the changes in the concentration of major ions in Lake L06 were analyzed.

In the early stage of the melting of the active layer, the lake surface had almost melted. At this stage, the surface water thawed the top of the active layer, whereas the bottom of the active layer was mostly frozen.

In the later period of the melting of the active layer, the melting speed of the active layer reached the maximum. Compared with the initial melting stage of the active layer, the contents of pH, Cl⁻, ⁠, and Na⁺ in the lake increase, whereas the content of continued to decrease. In this stage, the changes in ⁠, ⁠, and pH were mainly caused by the photosynthesis of aquatic organisms at the bottom of the lake. Although the effect of groundwater on the runoff of lake water enhanced and the groundwater with a high content replenished into the lake water, the in the lake water was not sufficient to balance the consumption of photosynthesis due to the strong photosynthesis of aquatic plants in the lake water. As a result, the concentration in the lake water continued to decrease, while the concentration and pH continued to increase. The slight increase in Cl⁻ and Na⁺ contents may be due to the following reasons: First, the discharge of groundwater with high Cl⁻ and Na⁺ concentrations into lake water had a certain effect on the Cl⁻ and Na⁺ contents in lake water. Secondly, the evaporation of the active layer was strong in the later period of melting which may increase the contents of Cl⁻ and Na⁺.

During the freezing period of the active layer, the temperature and the precipitation of the lake water decrease. The water began to freeze simultaneously from the surface and the top surface of the active layer to the center. Compared with the previous stage, the concentration changes of each ion in the lake were reflected by the increase in the concentrations of ⁠, ⁠, Na⁺, and Mg²⁺, whereas the decrease in the pH of the lake. From the thawing to the freezing stage of the active layer, the precipitation decreased significantly, and evaporation and crystallization played an obvious control role on the concentration of all ions in the lake. At the same time, the concentration of almost all ions increased under intense evaporation. The decrease in temperature increased the solubility of CO₂ in the lake and reduced the intensity of photosynthesis. The decrease in pH is affected by the carbonic acid equilibrium system. As the consumption of CO₂ decreases, the equilibrium in Equation (11) moved to the left and increased the concentration.

Isotopes of lakes and groundwater in the study area were collected in June (early thawing period of active layer), July (middle thawing period of active layer), August (late thawing period of active layer), and October (freezing period of active layer). Among them, rainwater samples were collected in June and August, which was helpful to understand the relationship between lake water and groundwater in the study area.

Table 2 shows that during the melting to refreezing of the active layer, δD and δ¹⁸O in the groundwater and the lake water were less than 0. Furthermore, δD and δ¹⁸O in the groundwater were always less than the lake water, which indicated that the heavy isotope content in the former was higher than in the latter. In addition, the content of δD in the lake water and groundwater was lower than that of δ¹⁸O, which also indicated that the degree of fraction of heavy isotopes was lower than light isotopes.

The E/I of lakes at different stages for a particular lake in the study area was estimated. The amount of water flowing into the lake and the amount lost by the lake should be in dynamic balance at set times. However, calculating the lake water balance by using traditional hydrology methods was difficult due to the high altitude in the study area. Therefore, many scholars adopt the E/I ratio of the lake as an important index to evaluate the lake water balance process.

To facilitate the description of the calculation results, the eight lakes in the study area were named as 1–8 in the order from north to south. The calculation results of E/I at different stages were statistically analyzed (Table 3).

Table 3 shows that the E/I of the lakes in June, July, and August has rarely difference, whereas in October was large. The temperature dropped significantly in October, thereby enhancing the fractionation effect of isotopes. The atomic mass of hydrogen was much lighter than that of oxygen atoms, so the fractionation effect was significantly stronger than that of oxygen atoms, thereby resulting in some differences in the calculation results.

Furthermore, the value of E/I reached the maximum in the initial melting stage and the active layer freezing stage, whereas reached the minimum in the middle and late periods of the melting of the active layer.

With increasing evaporation in July and August, the precipitation and the depth of the melting of the active layer both reach the maximum which will increase recharge to the lake. Therefore, the E/I ratio of the lake is the minimum in July and August. On the contrary, the E/I is relatively large in June and October due to the weakly runoff effect of groundwater. The E/I characteristics of lakes at different stages verified the influence of freezing–thawing on groundwater runoff in the study area from the perspective of isotopes. Since the main drainage mode of the lake is evaporation, the evaporation of the lake in July and August is smaller than that of the groundwater, indicating that the lake is expanding when the active layer begins to melt until it is completely melted.

With the warming of the global climate, the expansion of hot melt lakes has become irreversible. It will lead to a series of environmental issues, including soil, ecology, and hydrology changes. The formation and development of lakes will release sodium from permafrost into the soil system, producing sodic or locally salinized soil, and subsequently degrading alpine vegetation.

Although the processes governing the formation and thawing of lake ice depend on multiple interacting meteorological and limnological factors (Gu & Stefan 1990), air temperature is considered to be the dominant factor. Toniolo et al. (2009) found that natural factors, which generally refer to the climatic environment, are major factors affecting the formation of hot melt lakes. The increase of temperature will lead to the increase of active-layer thickness, the melting of underground ice, and then the formation of hot melt lake in low terrain. Moreover, climate change directly causes lake temperatures, water levels, and the formation of water chemistry (Adrian et al. 2009).

In the form of global warming, it is a fact that the temperature of the QTP has generally increased. In this case, the rise of temperature will accelerate the development of hot karst lakes so that the number and area of hot karst lakes will change greatly. This paper studies the formation mechanism and evolution process of hot karst lakes under climate change conditions, which is helpful to grasp the water cycle process and future expansion direction of the lakes, and provides corresponding theoretical basis for harm reduction.

This paper clarified the water chemistry types of the hot melt lakes in the Wudaoliang area of Beiluhe and analyzed the reasons affecting the chemical composition of the water, and the E/I of different stages of hot melt.

1. The hydrogeochemical types of lakes showed regional differences. The northern lakes were mainly HCO₃·Cl − Na·Ca·Mg mixed water samples, whereas the central and southern lakes in the study area were Cl − Na·Mg evaporated water samples. And hydrogeochemical types of lakes are affected by evaporation and concentration and rock weathering.

2. The ion proportional coefficient at different stages reflects that the main ions in lake water may be related to the dissolution of salt rock, calcite, and dolomite. The SI of dolomite and calcite show that they control the components of hydrogeochemistry of lakes. The SI of salt rock and gypsum rocks indicate these two minerals are basically completely dissolved.

3. Atmospheric precipitation, evaporation, thawing of permafrost water, freezing desalination of the active layer, and the photosynthesis of aquatic plants are the main factors that cause the changes in pH, ⁠, ⁠, Ca²⁺, Na⁺, Cl⁻, and Mg²⁺ concentrations in the lake.

4. With the influence of air temperature, E/I values show regular changes in different stages. The E/I of the lake and the recharge of groundwater to the lake both reach the maximum when the thickness of the unfrozen layer reaches the maximum in the middle and late stages of the melting of the active layer.

The melting and freezing of the active layer is a relatively complicated process, accompanied by the conversion of material energy. Although the four sampling times are in different stages, the four sampling times are relatively little. It is recommended to increase the number of samplings and to sample and analyze the water samples in the study area in different seasons to improve the existing conclusions.

We acknowledge the Beiluhe Scientific Research Station of CAS and the China University of Geosciences for their technical support during the experiment. This research was funded by the National Science Foundation of China, Grant No. 41730640 – Environmental and Hydrological Effects of the thermokarst Lakes in the Permafrost Region of the QTP – and the Fundamental Research Funds for the Central Universities, CHD, Grant No. 300102290401. This research was mainly supported by Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences. We are grateful to the anonymous reviewers for their helpful comments and constructive suggestions.

Y.F., W.W., and Z.L. designed the test and wrote the manuscript; H.H. and Q.L. analyzed the data, drew pictures, and checked the manuscript. All authors gave comments and contributed to the final version of the manuscript.

The authors declare that they have no conflict of interest.

All relevant data are included in the paper or its Supplementary Information.