Past climate changes and permafrost depth at the Lake El’gygytgyn site: implications from data and thermal modelling

We present results of numerical simulations of the temperature ﬁeld of the subsurface around and beneath the crater Lake El’gygytgyn in NE Russia, which is subject of an interdisciplinary drilling campaign within the International Continental Drilling Program (ICDP). This study focuses on determining the permafrost depth and the transition be-5 tween talik and permafrost regimes, both, under steady-state and transient conditions of past climate changes. Thermal properties of the subsurface are deduced from measurements on three representative core samples taken from the quaternary sediments and the underlying impact rock. Further information is derived from the available geo-physical logs and literature data. The temperature data from the lake borehole ICDP 10 site 5011-1 down to 400 m depth below lake bottom are dominated by thermal perturbations related to the drilling process, and thus only give reliable values for the low-ermost value in the borehole. Undisturbed temperature data recorded over more than two years in the 140 m deep land-based borehole ICDP site 5011-3 allow to determine the mean annual ground surface temperature (GST), as well as its history (GSTH) to 15 a certain extent. Although the borehole’s depth is by far not su ﬃ cient for a complete reconstruction of past temperatures back to the last glacial maximum (LGM), the temperature data and our modelling results show that there is still an inﬂuence of the LGM on the thermal regime, and thus on the permafrost depth. Whereas the latter result is

The crater Lake El'gygytgyn in NE Russia (67 • 30 N, 172 • 5 E, 492 m a.s.l.) was formed by an Asteroid impact 3.6 Myr ago (Fig. 2).In 2008, an interdisciplinary drilling campaign was carried out that is part of the International Continental Drilling Program (ICDP).Detailed information on this project re described by, while the most important paleoclimatological were published by Melles et al. (2012).The primary aim is to obtain the currently longest time-continuous sedimentary record of climate change in the terrestrial Arctic, which will improve the understanding of the Arctic climate evolution in the late Cenozoic, when related to data from other marine and terrestrial sites.Additionally, the collection of meteorite impact rocks from a metavolcanic bedrock terrain are expected to produce unique insights on the impact processes that might be found on other planets.In accordance with these goals, boreholes were drilled at two sites, one near the deepest part of the lake (ICDP site 5011-1), and the other on land close to its shoreline (ICDP site 5011-3).From borehole 5011-1 315 m of sediment cores were retrieved, complemented by 200 m from the underlying volcanic bedrock, while from 5011-3 a 141.5 m long permafrost core composed of frozen deposits was recovered (Fig. 2).
In this paper, we focus on the characterization of the thermal field beneath and around the lake, studying the influence of variations of thermal properties and past ground surface temperature changes by numerical modelling (e.g.Osterkamp and Gosink, 1991;Galushkin, 1997;Mottaghy and Rath, 2006;Holm én et al., 2011).In the recent years, the impact of climate change on permafrost formation and evolution has become a particular subject of interest.The understanding of the response of permafrost regimes to transient changes in surface temperatures is a key issue regarding the prediction of the influence of global warming on permafrost areas (Saito et al., 2007;Lemke et al., 2007;Serreze et al., 2007;Miller et al., 2009Miller et al., , 2010b;;Serreze and Barry, 2011, amongst many others).Introduction

Conclusions References
Tables Figures

Back Close
Full When studying heat transfer in the Earth's upper crust, the upper boundary condition of heat transport is determined by the local climatic conditions.The variations of this condition induces a transient signal which diffuses into the subsurface.Thus, ground temperatures may be seen as an archive of past climate signals.Reconstructing the past changes is of major interest since one of the most important components of climatic change is the variation of temperature at the Earth's surface.However, the diffusive character implies that the older the signal is, the more it is attenuated, with a corresponding larger uncertainty in magnitude and timing.Analysing the variation of temperature with depth, past fluctuations at the Earth's surface can be reconstructed to a certain extent (see, e.g. the recent review by Gonz ález-Rouco et al., 2009, and the references therein).This reconstruction can be performed by numerical forward modelling with models of varying complexity, or inverse methods in the narrow sense (Shen and Beck, 1991;Beltrami and Mareschal, 1991;Beck et al., 1992;Rath and Mottaghy, 2007, amongst others).A prerequisite for such a reconstruction is sufficient available data, most relevant temperature data.Here, we limit ourselves to forward modelling for determining the present day temperature profile, because the available temperature data is not sufficient for a reliable reconstruction of the ground surface temperature history (GSTH) at the study area.Nevertheless, we propose that the combination of forward modelling and sensitivity studies allow some meaningful conclusions concerning the local GSTH.
As our approach relies on forward modelling, we must assume a certain GSTH driving the simulations.In particular, it has been shown (Rath et al., 2012) that the amplitude of the last glacial maximum and the following warming from Pleistocene to Holocene influence the temperature distribution even in the upper surface.However, in the arctic region the values of this amplitude are not well known, but the available data suggest a 18 ± 7 K cooler mean temperature than today (Miller et al., 2010a,b).There have been some efforts to determine the spatial distribution of this parameter (Demezhko et al., 2007) whose results also enter our models, but the available data in the area is sparse.In order to do justice to these uncertainties, we perform Monte Introduction

Conclusions References
Tables Figures

Back Close
Full Carlo simulations with an ensemble of GSTHs as boundary conditions for the transient forward modelling.At middle and high latitude sites like the Lake El'gygytgyn, freezing and thawing processes may create a considerable effect on subsurface temperature-depth profiles when climatic changes take place in time-scales of glaciations.Therefore, latent heat effects must be included in modelling studies in such areas.Depending on the amount of pores and fractures in rocks, and the fluids filling them, freezing and thawing will play an important role in controlling the subsurface thermal conditions when climatic changes take place in the ground surface temperature (Mottaghy and Rath, 2006;Rath and Mottaghy, 2007).This implies that the reconstruction of past temperatures by forward or inverse methods must include the freezing and thawing processes.

Available data
The data used for this study originate from the aforementioned boreholes, one in the deepest part of the lake (ICDP site 5011-1, depth 517 m below lake bottom), and one close to its shoreline (ICDP site 5011-3, depth 140 m below surface).Figure 1 shows the location of the Lake El'gygytgyn as well as a panorama view.Figure 2 gives an schematic sketch of the basin, and of the site and the boreholes' locations.Our investigations rely on (a) temperature measurements in both boreholes; (b) determination of thermal properties from laboratory measurements on cores and γ-ray logging in borehole 5011-1.
The temperature data from the lake borehole ICDP site 5011-1 are considered disturbed, and only the value from the lowermost part is supposed to approximate the undisturbed temperature of the surrounding bedrock (see Sect. 4).Temperature measurements in the permafrost hole 5011-3 started shortly after its drilling in November-December 2008.The earliest recordings were expected to reflect conditions undisturbed by the physical effects of the drilling process.However, temperatures around −6 • C were determined at depths which are not affected by daily or seasonal variations.Introduction

Conclusions References
Tables Figures

Back Close
Full Subsequently, during the years from 2008 to 2010, temperatures were continuously recorded by an automatic data logger in this borehole, in order to monitor the approach of the subsurface temperatures to conditions in equilibrium with the ambient rock.These measurements confirm the first measurements, showing that the value obtained earlier was already rather near to the equilibrium value.In Fig. 3, a selection of the recorded temperatures in the year 2010 is plotted.It can be seen that in depth ranges between 15 and 20 m annual variations disappear.Our modelling studies target at the impact of long term climate changes on the temperature field, and in consequence annual variations in the uppermost layers are not taken into account.At a depth 20 m the average temperature for this year was estimated to −5.9 ± 0.1 • C.
This estimate was on turn used to extrapolate a value for the upper boundary condition of the modelling studies of −6.7 • C at the surface.
Regarding the thermal properties of the prevailing sediments and rocks in frozen condition, we performed thermal conductivity measurements on one core sample retrieved from borehole 5011-3: No. 28(2) at 28.15-28.35m depth.This sample consists of sandy gravel, and is representative for much of the material from the permafrost core (Schwamborn et al., 2012) associated with the model's unit 2 in Fig. 2. We used the full space and half space line source measuring device (TK-04, TeKa, Berlin), the measurement procedures is described by Erbas (2001).Other studies (e.g.Putkonen, 2003) show that the determination of frozen soil thermal properties by a needle probe yields reasonable results.The work flow, elaborated together with the manufacturer, was as follows: first, a part of the frozen core, which consists of loose sand and gravel as well as the ice fraction, was cut off and put in a jar where it was left to thaw.Then, thermal conductivity was determined with the needle probe in the common procedure.To ensure reliable results, several heating cycles were applied.This allowed to pick only stable solutions, and also made it possible to determine a mean value along with a standard deviation.
After finishing the measurements on the thawed material the mixture was frozen with the needle probe remaining in it.Then, thermal conductivity was determined for Introduction

Conclusions References
Tables Figures

Back Close
Full the frozen mixture.Finally, the mixture was unfrozen once more and put in the half space line source.In contrast to the full-space line source there is less triggering of possible convection since the heating source lies on top of the sample mixture.The results shown in Table 1 confirm this assumed bias: whereas the "unfrozen" values of the full-space line source feature quite some variation as seen by the standard variation, the values of the frozen mixture is more stable.Furthermore, thermal conductivity measured by the half-space probe is slightly lower.Porosity was determined by using a defined volume and weighing the saturated and dry sample.This allows to determine the matrix thermal conductivity, using the geometric mixing law, which proved to be a good theoretical description of the effective thermal conductivity of rocks with different components (e.g.Hartmann et al., 2008).Further measurements were performed in order to determine thermal conductivity of the impact rocks of unit 4 (polymictic and suevitic breccia) and unit 5 (monomictic breccia and fractured bedrock).Two samples were chosen, originating from 334 m (No.C104) and 491 m (No.C170) below lake bottom, respectively.We used the optical scanning method (TCS).A detailed description and comparison with other methods can be found in Popov et al. (1999).Thermal conductivity was determined in the original dry state of the sample, after being completely dried, and after being saturated again.The latter two measurement procedures allowed to estimate the porosity of the sample.Table 2 lists the result.

Numerical model
The finite difference (FD) code SHEMAT SUITE (Rath et al., 2006) was used for the 2-D numerical simulation of heat transport processes at the Lake El'gygytgyn site.As mentioned above, in addition to assuming all thermal properties to be functions of temperatures, latent heat effects due to freezing and thawing of subsurface fluids are accounted for in the code.Particularly, the freezing range can be adapted, taking into account that the phase change occurs over a temperature range in the subsurface, Introduction

Conclusions References
Tables Figures

Back Close
Full assuming a functional relationship between unfrozen water content an temperature given by Lunardini (1988).Water and ice properties in the freezing domain were calculated using the formulations of Fukusako (1990) and Ling and Zhang (2004).A detailed description of this approach is found in Mottaghy and Rath (2006).

Conceptual model
For building the numerical model, the basin scheme shown in Fig. 2 is used as a basis.This scheme is based on seismic basin profiling (Gebhardt et al., 2006).
The thermal properties of the different zones were derived from our own measurements (see Sect. 2), as well as literature data.Core sample 28( 2) is assumed to be representative for the lacustrine sediments of unit 2 in Fig. 2. We deduced some information from the available studies such as Asikainen et al. (2007) on grain size, clay mineralogy, and crystallinity to assess the thermal properties of the lake sediments.Together with a γ-ray log from borehole ICDP site 5011-1 (Gebhardt et al., 2010), and using literature data we estimate thermal conductivity as summarized together with other properties in Table 1.The lacustrine sediments are likely to exhibit lower values of bulk thermal conductivity which is mainly due to high porosities around 35 % (Melles, 2006).The impact rocks in unit 3 and unit 4 show higher γ-ray values (around 150 gAPI) which implies some quartz content of the suevite bedrock.This is confirmed by the measurements of the two samples from the impact bedrock, and is consistent with results on comparable rocks (Popov et al., 2003;Mayr et al., 2008).Bulk thermal conductivity becomes higher along with lower porosity in the impact rocks.For the transient simulations, additionally volumetric heat capacity must be considered.Here, we use the general mean value of 2.3 MJ m −3 K −1 as given in Beck (1988).With respect to internal heat generation of the rocks, we assume a general value of 0.5 µW m −3 for the lake sediments and 1 µW m −3 for the impact rock.However, this parameter plays only a secondary role since our model only considers the upper few hundred metres of sediments and bedrock which is not enough for a significant influence of heat generation on the temperature field.Table 3 summarizes some properties of the numerical model.Introduction

Conclusions References
Tables Figures

Back Close
Full All thermal properties, in particular thermal conductivity, represent initial values for the subsequent modelling studies, but had to be slightly adapted for the simulations presented in Sect. 5 in order to fit the observations.

Boundary conditions
The current mean annual air temperature (MAAT) in the area is −10.3 • C (Nolan and Brigham-Grette, 2007;Nolan, 2012), which is a lower boundary condition for the mean annual ground surface temperature (GST).The coupling between air and ground surface temperature is not trivial and has been studied for some decades now (e.g.Smerdon et al., 2004Smerdon et al., , 2006;;Stieglitz and Smerdon, 2007).In particular in areas with varying snow cover, several parameters play a role (Kukkonen, 1987).Generally, the mean annual GST is some degrees above the mean annual air temperature.A recent study (Ge et al., 2011) presents numerical modelling of the different coupling mechanisms between air, soil, and groundwater flow in a permafrost area, the Northern Central Tibet Plateau.Although this site is not directly comparable to the Lake El'gygytgyn area, the available data confirms a 3-4 K higher mean annual GST compared to the MAAT: as explained in Sect.2, the long term measurements in borehole 5011-3 allow to determine the mean annual GST at the study site, it is about −6 • C at 20 m depth.
For the transient simulations we use a ground surface temperature history (GSTH) as discussed in Sect. 5.At the lake floor, a mean temperature of 5.5 • C is set, which is supported by some temperature data (see Sect. 3).Whereas the bottom lake water approaches 4 • C, the value where water density is highest, the higher temperature value in the uppermost lake sediment layers may point to a seasonal signal that has been preserved from previous warmed up summer water masses.It is known from subglacial lakes in Antarctica without seasonal cycling that water temperatures at the bottom of this kind of lakes remain at 4 • C at maximum with only slight variation (Vincent and Laybourn-Parry, 2008).Water levels change on long-term scales.For instance, it is well documented that the level was some 10 m lower at the LGM (Juschus et al., 2011).However, when comparing this range of water level change with the total water Introduction

Conclusions References
Tables Figures

Back Close
Full depth of up to 175 m in Lake El'gygytgyn it is negligible to account for that in terms of changing water mass circulation during the last 125 kyr which are studied here.Instead, we accept the measured value of 5.5

Steady-state simulations
In order to determine the temperature field near and beneath lake, we performed steady state simulations as a first step.All the parameters described in Sect.3.2 enter the numerical modelling.In particular, both the temperature profile in the permafrost borehole as well as the lake borehole give valuable constraints to the upper and lower boundary conditions.However, the data from the lake do not represent undisturbed conditions.Thus, the data is restricted to some general temperature gradient, because the temperature measured in the lowermost part (400 m below lake surface) should be most reliable (Kueck, 2010, personal communication).The different logs and the assumed gradient are shown in Fig. 4. Therefore, we used this value (about 25 • C) to test the initially assumed basal heat flow (see Sect. parameters of our model represent a reasonable basis for the subsequent modelling studies. In contrast to the lake hole temperature data, the long term record in borehole 5011-3 reflects undisturbed conditions, but the shallow depth (140 m) only allows a limited calibration with respect to the thermal properties of the layers beneath.Furthermore, transient effects such as paleoclimatic ground surface temperature changes are likely to have a significant influence on the temperature field, as described in Sect. 5. Thus, the measurements on thermal conductivity give valuable constraints for a reliable temperature modelling.
Figure 5 shows the modelled temperature profiles in comparison with the data plotted in Fig. 4 at borehole 5011-1 in the lake, as well as at the land location, borehole 5011-3.The dashed and dotted lines show the strong sensitivity to thermal conductivity.The values are varied within the ranges given in Table 4.The lower and higher thermal conductivity values yield a higher and lower temperature gradient, respectively.This variation in thermal conductivity is rather large: due to our measurements, the actual values are likely to be close the mean values, represented by the solid lines in Fig. 5.
It is important to notice that steady-state simulations can explain temperature distribution beneath the lake, applying thermal conductivity values determined in the lab and from the literature.As explained in Sect.3.2, the lowermost temperature value is considered to be representative and can be well reproduced by the model.However, the steady-state simulations are not able to explain the temperature profile of the permafrost borehole 5011-3 (Fig. 5).Even with a variation within a rather large uncertainty range of ±20 % is insufficient to match the measured data.Therefore, transient surface temperature changes must be taken into account. In

Transient simulations
In order to study the influence of past climate variations, we performed transient simulations, applying a simple boxcar model for the climate changes in the past 125 000 yr (Fig. 7).For this, we used the available information on the past climate as described in Sect. 1. From pollen records only vegetation and thus information on summer climate conditions can be reconstructed, which is obviously only a partial contribution to the mean annual air temperature.Furthermore, the duration, thickness and kind of snow cover play a role in the coupling between air and ground surface temperatures (see Sect. 3.2).As the study site seemed to remain without glacier cover, very low temperatures during the LGM are likely to have prevailed (e.g.Miller et al., 2010a).Therefore, a rather large amplitude of the Pleistocene-Holocene temperature step is likely and confirmed by our modelling results: in order to explain the temperature variation with depth in the lower part of the measured profile, the amplitude of the LGM (denoted as PGW Fig. 7) is estimated to be around 14 K, which is in agreement with the results from other studies (see Sect. 1).
The results are shown in Fig. 8.This figure also shows the situation at the end of the LGM when permafrost depth was obviously much larger.Today, our modelling results suggest a permafrost base of approximately 340 m depth at the borehole 5011-3.Compared to the results from the steady-state simulations, it becomes evident that the past changes in GST have a significant influence on the temperature distribution today.Table 5 summarises the different results for this value at the permafrost borehole 5011-3.
The upper part of the measured profile in borehole 5011-3 shows some strong curvature (see blue lines Fig. 8), which was thoroughly investigated by sensitivity studies in terms of more recent surface temperature changes.Other possible influences are unknown heterogeneities in thermal parameters, porosity changes, or fluid flow.However, these can be largely excluded due to several reasons: on the one hand thermal properties have been determined by different approaches (indirect as well as measurements), Introduction

Conclusions References
Tables Figures

Back Close
Full one the other hand permafrost has been present for at least some ten thousand years.
The warmer period during the Allerød (13.3-13.1 kyr BP), when the lake level was some 5 m higher than modern and flooded the coring site at that time (Schwamborn et al., 2008(Schwamborn et al., , 2012)), was studied by different model runs and showed that there is no influence on the current temperature field anymore.
Therefore we conclude that past surface temperature changes are most like to be responsible for the temperature variation with depth.As a result we propose a possible large amplitude of the Little Ice Age (LIA) of 3.5 K lower temperature during the 1500-1900 period GST than today's mean GST.A subsequent still cool period until 1950 of 2.5 K lower than today is able to approximately explain the observed temperature profile.Though data are sparse in this area of Siberia, there are some other indications for low LIA temperatures.Mann et al. (2009) includes some tree ring density reconstructions from Northern Siberia, which indicate temperature differences of more than −2.5 K with respect to the modern.In addition, the recently published CRUTEM4 the 10-yr averaged land surface temperature anomalies (Jones et al., 2012), now including many more sites from Siberia, show a strong warming of more than 1 K since 1970 in this area.
To obtain a overview on the uncertainties of prediction, we performed a Monte Carlo (MC) experiment.The setup was as following: as in the simulation presented above, the last glaciation cycle was parametrised as simple as possible, in this case a boxcar function.As the time of the postglacial warming is rather well constrained, we choose to vary only three parameters, the preglacial average temperature (PAT), the average glacial temperature (GAT) and the timing of the glacial initiation (TGI).Concerning the PAT it is well known, that due to the strong attenuation of temperature perturbations with time, only the temperature changes of the last glacial cycle play a significant role.Older variations may safely be approximated by an appropriate average temperature (see, e.g.Majorowicz et al., 2008).For the purposes followed here, even the variations during the glacial are accommodated easily this way.Though nearer to the present, even the steepness of the temperature rise during the glacial-interglacial transition plays Introduction

Conclusions References
Tables Figures

Back Close
Full a detectable but minor role.In particular, Rath et al. (2012) have shown that for very shallow boreholes as the one considered here, the joint effect of the glacial-interglacial complex is indistinguishable from an additional linear trend, or, more physically, to an additional heat flow density.Thus, we think this simple parametrisation as reasonable.We assumed independent normal distributions for all three parameters, implying that they are characterized by their means μi and standard deviations σi .The values assumed are given in Table 6, while the generated distributions can be found in Fig. 9.
The results are shown in Fig. 10.From these results we conclude that the uncertainties assumed for the more ancient GSTH produce a considerable spread in temperatures already in the first few hundreds of metres.This spread carries over to the depths of the lower limit of permafrost, which can be found in Fig. 11.Unfortunately the existing geophysical surveys do not extend beyond the lake area and its immediate surroundings, so that recent undisturbed permafrost extent could not be observed.However, the values in Fig. 11 largely agree with the values found in the literature for this area (Yershov, 1998).

Conclusions and outlook
Our below the active zone remained frozen at least for the last 10 kyr.The talik below the lake basin is pervasive and follows a normal temperature gradient of 3 • C per 100 m starting at 5.5 • C in the uppermost lake sediment layers.
Future studies are necessary to improve the interpretation of the very shallow temperature field.In particular, these will include additional forward modelling in order to improve our conceptual model, and assess the sensitivities of our results with respect to subsurface heterogeneity or possibly subsurface flow.Using more sophisticated inverse techniques will not only enable us to obtain a better characterization of the past surface temperature changes, but also to characterize the uncertainties involved.The annual variation visible in the high quality temperature monitoring data of the top 20 m was not investigated in this study.However, these observations could be used to retrieve valuable constraints for the very shallow subsurface properties.Introduction

Conclusions References
Tables Figures

Back Close
Full  Full  Full Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 3.2).However, it only slightly varied, changing from initial value of 66 mW m −2 to 70 mW m −2 , which is still within the uncertainty range given in Goutorbe et al. (2011).Therefore we can conclude that the input Discussion Paper | Discussion Paper | Discussion Paper | Fig. 6 the units and the temperature field of the whole model are shown, again applying different thermal conductivity values in order to demonstrate the sensitivity of the temperature field to this parameter.The lower boundary of permafrost (0 • C isoline) is highlighted in order to visualise the sensitivity to thermal conductivity.Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | results of 2-D numerical simulations of the temperature field in El'gygytgyn Crater indicate the permafrost depth and the talik dimensions around and below the lake basin, as well as the influence of past temperature changes.The temperature model suggests a permafrost depth surrounding the lake of 330-360 m.This result depends on the assumption of an ancient transient signal present in the temperature distribution that evolved from low temperatures during the last glacial maximum.MC simulations permitted a crude characterization of the uncertainties in permafrost depth.More recent signals in the temperature distribution presumably originate from the Little Ice Age and the recent global warming.In particular regarding the LIA, our comparison between data and modelling suggests a significant and persistent cooling during that time period.A possible bias by fluid flow can probably be excluded, because the regime Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Yershov, E. D.: General Geocryology, Cambridge University Press, Cambridge, UK, 1998.2616Discussion Paper | Discussion Paper | Discussion Paper | Table 1.Summary of the different measured thermal conductivity values λ (W m −1 K −1 ) of the sample No. 28(2) from the permafrost borehole 5011-3.φ is porosity, which can be estimated from the ratio of volume and mass of the sample (φ a ), or from thermal conductivity (φ b ).Based on these, the corresponding matrix thermal conductivities λ a,b m can be determined.FSLS: full space line source, HSLS: half space line source.Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Fig. 6 .
Fig. 6.(a) The model and its units.The temperature field using (b) the mean value, (c) lower thermal conductivity, and (d) higher thermal conductivity.

Fig. 8 .Fig. 9 .
Fig. 8. Results from the transient simulations.Temperature profiles at borehole 5011-3 showing (a) the whole model depth, and (b) only the upper part.The temperature field of the model (c) today, and 20 kyr BP (d).
• C as a reasonable value for the upper lake sediment environment (see Sect. 4).The lower boundary condition is an estimated basal heat flow, there is no data in the vicinity of the study area.The compilation of global heat flow data of Pollack et al. (1993) lists a few data, which originate from boreholes some 500 km away.Yershov (1998), referring to Russian sources, presents a heat flow map with values between 40 mW m −2 and 80 mW m −2 for this area.Recently Goutorbe et al. (2011) published a new compilation of global heat flow, combining the data of Pollack et al. (1993) with geological proxies, applying different interpolation techniques.From their findings the surface heat flow in the area is 66 ± 8 mW m −2 .Therefore, we initially set the lower boundary condition to this value and compare the results to the available temperature data (see Sect. 4).

Table 2 .
Summary of the different measured thermal conductivity values λ (W m −1 K −1 ) for the two samples from unit 3 and 4, respectively.Porosity φ is determined from saturated and dry thermal conductivity measurements.λ dry λ min−max,dry λ sat λ min−max,sat φ from λ (−) λ matrix

Table 5 .
Depth of permafrost base for the different simulations at borehole 5011-3.S-S: steadystate.