Modelling borehole temperatures in Southern Norway – insights into permafrost dynamics during the 20 th and 21 st century

Introduction Conclusions References


Conclusions References
Tables Figures

Back Close
Full of snow cover and different types of surficial material and bedrock.
In Scandinavia and especially in Northern Norway, Iceland and Svalbard, multiple shallow boreholes have been drilled to continuously monitor ground thermal regimes and the relation between atmosphere and ground in terms of energy exchange since 1999 (Christiansen et al., 2010;Etzelm üller et al., 2007;Farbrot et al., 2007;Isaksen et al., 2000Isaksen et al., , 2003)).In 2008 12 new boreholes have been established at three different mountain areas in Southern Norway.This monitoring network addresses environmental gradients in Southern Norway related to elevation and continentality (Farbrot et al., 2011), and provides the basis for calibrating and validating transient heat flow models.
The objective of this study is to assess the ground thermal response of permafrost to historical and future air temperature (T AIR ) variation in different environmental settings in terms of elevation, snow and sediment cover for mountain sites in Southern Norway.The study aims for quantifying subsurface warming and changes in active layer thickness (ALT) over a c. 250 yr period from the approx.end of the Little Ice Age (LIA) in the mid 19th century to 2100 in the high-mountain environment of Southern Norway.Over this period, significant warming occurred and is expected to continue.In relation to these changes, we intend to identify the possible zonations of former, present and future permafrost.Finally, we aim to characterise these responses for different environmental settings in terms of bedrock properties, sediment-cover and snow.We suggest that these assessments are fundamental prerequisites for spatially distributed Introduction

Conclusions References
Tables Figures

Back Close
Full permafrost modelling in Scandinavia, and for understanding geomorphological process patterns and ultimately landscape development (Berthling and Etzelm üller, 2011).
In this study, we apply a 1-D heat flow model (Etzelm üller et al., 2011;Farbrot et al., 2007) to simulate GTs and ALT for the time period of 1860 until 2100.The model was first calibrated and validated for each of totally 13 sites, where records of GT, GST and T AIR exist.Forcing the calibrated model using reconstructed and projected T AIR series, we assess how sensitive GT and ALT react to warming at the investigated sites, including an assessment of model limitations and related uncertainties of our approach.

Setting, instrumentation and climate at the study sites
We use borehole measurements from three locations in Southern Norway in this study (Fig. 1a): Juvvasshøe ( 61• 40 N, 08 • 22 E, 1894 m a.s.l.), Jetta ( 61• 53 N, 9 • 17 E, 1640 m a.s.l.) and Tron ( 62• 10 N, 10 • 41 E, 1560 m a.s.l.).At these sites, ground temperature records are available for 13 boreholes at 2-h intervals covering the period August 2008 to July 2011.At Juvvasshøe, the PACE borehole ground temperature data is available from 1999 (Isaksen et al., 2001(Isaksen et al., , 2007)).An overview of the geomophologic and climatic setting as well as the permafrost conditions at the study sites are given here, while a more detailed description of the sites and the instrumentation is given by Farbrot et al. (2011).

Conclusions References
Tables Figures
Tron (Fig. 1d) is located further east in a more continental climate setting.Two boreholes were drilled 10 m into fine-grained morainic material, while the uppermost borehole (Tro-BH1, 1640 m) was drilled 30 m into a block field.
At all boreholes GST, T AIR and snow depth (SD) are recorded.Maxim © iButton temperature loggers (±0.5 • C accuracy) at fixed heights above the ground surface (10, 20, 30, 40, 50, 60, 80, 100, 120 cm) were used to extract the snow depth using the daily temperature variance (Lewkowicz, 2008).At PACE and Tron automatic weather stations record several meteorological variables to characterize the surface energy balance.

Climate and ground thermal conditions at the study sites
The three sites are situated along a continentality gradient from a more maritime influenced climate at Juvvasshøe to a more continental climate setting at Tron (Farbrot et al., 2011).The entire period was divided in three seasons    Full  (Farbrot et al., 2011).At higher elevations snow cover is strongly variable and generally thin (< 20 cm) due to strong redistribution by wind.A thick snow cover, however, is found at lower elevations (70-140 cm) (Table 1).Permafrost is present at BH4 at 1559 m a.s.l. and the lower limit of permafrost along the instrumented slope was c. 1450 m a.s.l.(Farbrot et al., 2011).Permafrost thickness at the PACE borehole was estimated to be approximately 380 m (Isaksen et al., 2001).During the study period, observed ALT varied between 1.6 (Juv-BH1) and 8.6 m (Juv-BH4) and seasonal frost depths between 0.5 m and > 6 m (not shown).The mean annual ground temperature  (Farbrot et al., 2011).Seasonal frost dominates at the lower boreholes with freezing depths of c. 1.5 m to 4 m.Similarly an increase of freezing depths was observed during S2 and S3 (Fig. 3d).At Jetta, MAATs between −2.2 • C to −0.2 • C and −3.7 • C to −1.6 • C were measured during S1 and S2, respectively.A long-lasting, thick snow cover (> 140 cm) is recorded at the uppermost two boreholes, while Jet-BH3 had no significant snow cover due to strong wind drift.Therefore, despite the lower elevation, the GST recorded at Jet-BH3 is lower than at Jet-BH2 (Table 1).The uppermost (1560 m a.s.l.) borehole record shows permafrost with a MAGT 10 of −0.8 • C and an ALT decreasing from c. 8.0 m to c.
6.9 m during the observation period (Table 3).While at Jet-BH2 the depth of seasonal Introduction

Conclusions References
Tables Figures

Back Close
Full frost remains at c. 6.5 m due to a constant snow cover, an increase from c. 6 m to c. 9 m depth was observed at Jet-BH3 (Fig. 3f).

Seasonal variations
The air temperature records for different sites and seasons display the influence of continentality as well as a strong inter-annual variation.To better analyse these differences, we calculated anomalies of mean monthly air temperatures (MMAT) for all three sites and for 2008-2011 with respect to the reference period 1961-1990 (Fig. 2, see Sect.3.2 for details).Due to the lower elevation, Jetta shows higher summer and winter temperatures.However, although Tron is about 250 m lower than Juvvasshøe, T AIR is similar or even lower (Fig. 2a).Using altitudinal lapse rates derived from observations (Farbrot et al., 2011), MAAT at 1640 m a.s.l. is −2.3, −2.2 and −3.8 • C at Juvvasshøe, Jetta and Tron, respectively.Two different seasonal patterns have been observed (Fig. 2b).Compared to the normal period S1 was warmer by 1.0 The MAAT of S2, however, was −0.The borehole temperatures show different susceptibilities to inter-annual variability depending on the strength of coupling between GST and T AIR (Fig. 4).Boreholes having a close atmosphere-ground coupling show much lower GSTs and GTs in S2.The GSTs of S2 at Juv-BH3 and the bedrock site Juv-BH4 were by 0.6 • C and 2.1 • C lower, respectively, than during S1 (Table 1).While Jet-BH2 shows a constant MAGST of +0.9 • C during both seasons due to extensive snow cover, strong variations at Jet-BH3 with +0.5 • C during S1 and −1.0 • C during S2 (Table 1) demonstrate closer coupling between atmosphere and ground surface (Fig. 4).Introduction

Conclusions References
Tables Figures

Back Close
Full

1-D numerical heat flux model
For this study we used a one-dimensional transient heat flow model, which was previously applied in similar studies (Farbrot et al., 2007;Etzelm üller et al., 2011).Assuming heat conduction as the only process of energy transfer the model is solving the heat conduction equation (Williams and Smith, 1989) describing the evolution of the ground temperature T over time t and depth z, where specific heat capacity c eff , thermal conductivity k and density ρ are the main thermal properties of the ground.All borehole stratigraphies were implemented in the model at a spatial resolution of ∆z = 0.1 m by assigning ground thermal properties according to the observed stratigraphy (Table 2).The heat conduction equation ( 1) is then solved using finite differences along the borehole profile to a depth of 150 m.The volumetric water content (VWC) is considered in the model as a constant.The effect of latent heat due to freezing and thawing of the ground is accounted for by using a temperaturedependent effective heat capacity c eff , which is strongly increased in a temperature interval of ±0.1 • C around the freezing temperature of the pore water (Etzelm üller et al., 2011).Any effects related to the advection of heat due to flow of ground water or of air in coarse-grained block fields are not considered in the model formulation.
The individual standardized series are presented as anomalies in terms of standard deviations σ T m,i relative to the 1961-1990 average µ T m,i (Hanssen-Bauer, 2005): where T m,i is the observed temperature series at station i in region m.
For the entire mainland Norway MDATs are available as 1-km-resolution maps (MDAT grid ) for the period 1 September 1957 until present (provided by the Norwegian Meteorological Institute -met.no,available at http://senorge.no,from hereon referred to as seNorge dataset).These grids are interpolated (kriging) from recorded temperatures at synoptic weather stations (Mohr, 2009).Daily air temperatures from 1957 to 2008 were generated for the boreholes PACE, Jet-LB1 and Tro-BH1 using linear regressions between measured temperatures and those extracted from seNorge for the corresponding location.This procedure worked well for PACE with r 2 = 0.8 and a RMSE of 3.1 • C. For Jet-LB1 and Tro-BH1, however, the relation between observed air temperature and the corresponding seNorge value is non-linear, displaying a sharp bend at low temperatures.This characteristic is associated with the frequent occurrence of temperature inversions during winter (Farbrot et al., 2011), which are not captured by the seNorge dataset.To cope with this problem two separate linear regressions were performed for each site, one above and one below a threshold temperature (−10 • C and −5 • C for Tro-BH1 and Jet-BH1, respectively).
For the normal period 1961-1990 mean monthly values (MAT i ,1961(MAT i , −1990 ) and monthly standard deviations (σ 1961−1990 ) were calculated from these daily air temperatures.ST m was used to construct a time series of monthly air temperatures at the station i (MAT i ) from the early 1860ies until today at the station i by (Hanssen-Bauer, 2005):

Conclusions References
Tables Figures

Back Close
Full The observed temperature lapse rates during 2008-2010 of 0.5, 0.6 and 0.8 • C/100 m at Juvvasshøe, Jetta and Tron, respectively (Farbrot et al., 2011), were used to transfer the so-constructed MAT i time series locally to the other borehole locations.The historic air temperature series used as input data for the modelling therefore consists of monthly values until 2008 and measured daily values for 2008-2011.
Concerning the future air temperature series for the climate change model runs, the rather moderate A1B emmission scenario was chosen.The A1B scenario assumes balanced use of all energy sources with an increase in renewable energy sources, therefore assuming a decrease of CO 2 emissions by the mid of the 21st century (IPCC, 2007).The likely range of the global mean temperature change from 1990 to 2100 of the A1B scenario is between +1.7 • C and +4.4 • C, with a best estimate of +2.8 • C (IPCC, 2007).Temperatures from an ensemble of > 30 different GCMs were empirically-statistically downscaled to the weather station Fokstugu (Benestad, 2011(Benestad, , 2005)), which is located between the Jetta and Tron sites, and used to drive the ground heat flux model.The measured daily air temperatures at each borehole were correlated to Fokstugu yielding r 2 -values of > 0.9.This allowed the construction of air temperature scenarios for each individual borehole from 2010 until 2100 by correcting for a constant bias, specific for each site (Fig. 8a).

Model initialization and boundary conditions
The finite-difference scheme for solving Eq. ( 1 factors are considered as transfer functions relating T AIR to GST during freezing (n F ) and thawing (n T ) conditions (Smith and Riseborough, 2002;Lunardini, 1978).The nfactors were derived from measured daily GST and T AIR at each borehole by calculating the ratios of annual sums of freezing (FDD) and thawing degree days (TDD) of GST to those of T AIR : where indices S and A refer to the temperature at the ground surface and the air, respectively (Riseborough, 2007).FDD and TDD were calculated for the whole year and not based on freezing and thawing seasons at the ground surface, using average daily air temperatures.Sites having a thick snow cover are characterized by a GST > T AIR during large parts of the winter and therefore n F < 1. n T > 1 indicates a higher GST than T AIR during summer, which can be the case at bedrock sites in the absence of vegetation or on south-facing slopes.
The reconstruction of historic permafrost conditions employs monthly air temperatures whereas n-factors were determined from diurnal data.We investigated the possible effect of this inconsistency in temporal resolution on the n-factor values by recalculating n-factors based on monthly data.We found that the values deviate by less than 9 % and therefore, we use the same n-factors throughout our study, regardless of whether they were applied to monthly or daily temperatures.For the long term modelling, mean values of n F and n T of S1 and S2 were used (Table 1), assuming representativeness of our observation period.n F -values range from 0.2 and 0.4 at boreholes with a thick snow cover (Tr-BH1, Tr-BH2, Jet-BH1, Jet-BH2 and Juv-BH6) and from 0.8 to 1.0 where snow cover was moderate ( Full The model was initialised in two different ways, one for the calibration and validation procedure and the other one for the historical permafrost modelling.Simulations of S1 and S2 were initialised from observed profiles of GT which were extrapolated to the full depth assuming a linear gradient.Longterm simulations were started from steady-state corresponding to the mean air temperature of the decade 1860-1869.To account for seasonal variations a second degree Fourier curve function, is fitted to the observed daily T AIR of S1 (fit parameters a i , b i , ω).The higher degree function was chosen to appropriately represent the asymmetric seasonal cycle introduced by the long and cold winter season.Using (a 1 , a 2 , b 1 , b 2 , ω) from the fit and a 0 = MAT 1860−1869 , we generate a time series of air temperatures, which the model is forced with until no more changes in GTs occur.

Model calibration
In absence of detailed data on the thermal properties of the subsurface (in terms of c, k, ρ and VWC), we empirically determined the values by adjusting until satisfying agreement between model results and available observations over the calibration period.We selected S1 as calibration period, while S2 and S3 were kept as independent control for subsequent model validation (see following section).For calibration, the model was forced by using measured ground surface temperature as upper boundary condition.A careful, stepwise optimization procedure was applied to avoid erroneous parameter calibration which may result from compensating effects.As such, for example, a wrong choice for heat capacity may cause an exaggerated phase shift of GT with respect to GST which in turn may partly be compensated for by enhanced heat conduction.Our approach to deal with this problem was to preselect ranges of plausible values for the parameters from literature (Williams and Smith, 1989).Previous sensitivity testing revealed that within the given bounds, modelled GT were most sensitive to Introduction

Conclusions References
Tables Figures

Back Close
Full changes in heat conductivity and water content, while heat capacity and density are robustly constrained by literature values.Therefore, after assignment of plausible starting values to the parameters, calibration was performed by systematically changing k and VWC over the given ranges aiming for improving the agreement between modelled and observed GTs at different depth levels.Subsequently, minor adjustments were made to c and ρ to fine-tune the model performance.The agreement between model and observation was quantified at each individual depth in terms of the Nash-Sutcliffe model efficiency coefficient (ME) (Nash and Sutcliffe, 1970).For bedrock, values for thermal conductivity and density were measured at Juv-BH4 and at all sites at Jetta by the Norwegian Geological Survey (NGU), and these observations served as initial guesses for the calibration.A time series of measured soil moisture (O.Humlum, 2011, personal communication) in the vicinity of some sites (Juv-BH1, Tro-BH1) served as an estimate for the water content in the near-surface sediments.Adopted values for the different materials are shown in Table 2, while depth-averaged values of the ME for each borehole are presented in Table 3.
In total, only slight changes to the starting values had to be applied to achieve satisfactory agreement between modelled and observed GT.We defined satisfaction as ME > 0.7 and/or when further changes of parameter values did not yield better model performance.Nevertheless, we emphasize that the obtained set of parameter values for each site represent one possible set that yields satisfactory agreement between model and observations.However, as symptomatic for calibrating numerical models, different sets may exist and calibrated values may be erroneous.Therefore, transferability of parameter values to other regions is restricted and site-specific calibration is necessary.

Model validation
For our validation procedure we followed Rykiel's (1996) suggestion that the meaning of validation is that a "model is acceptable for its intended use because it meets specified performance requirements" in terms of operational validation.For our study Introduction

Conclusions References
Tables Figures

Back Close
Full the correspondence between measured and observed GT is expressed by the depthaveraged values of the Nash-Sutcliffe model efficiency coefficient (ME).Again, we require ME > 0.7.
To validate the reliability of the GST model, it was run for each season individually using the average n-factors from S1 and S2 (Table 1).For most boreholes a good correspondence between modelled and measured GSTs was achieved with ME > 0.8 (Table 3, Fig. 5).Since S3 was not included in the average n-factor calculation, it represents an additional independent validation period.Despite some differences in the snow conditions, the model reproduced GSTs of S3 equally well (Table 3).The highest values of ME > 0.9 were achieved at bedrock sites with negligible winter snow cover (Juv-BH4, Jet-BH3).The measured GTs of the validation period (S2-S3) are well reproduced by the calibrated model yielding ME-values ranging from 0.81 to 0.93 (Table 3).
To better estimate the model performance on a long-term scale, the model was run from 1860 until 2009 using the reconstructed T AIR series and results compared to the measured GTs of S1.In the case of the PACE borehole modelled and measured GTs of the entire series 1999-2009 were compared down to a depth of 100 m.The measured MAGTs were reproduced with a RMSE of 0.6-0.7 • C in the uppermost part (0 to 1 m depth) and 0.1-0.3 • C at a depth between 5 and 10 m (Fig. 7).

Historical and future air temperature trends
The historical air temperature series show temperature increases of 1.4 • C to 2.1 both sites.The more continental site Tron, however, shows strong increases of air temperature both in winter as well as in spring with +1.8 and +1.9 • C, respectively.
The median of the downscaled future temperatures indicates a further warming of +2.8 • C of the decadal means 2001/2010 until 2091/2100.The 10th percentile shows the same warming trend, the 90th percentile, however, shows an increase of +3.3 • C (Fig. 8a).The deviation of the median to the climate normal 1961-1990 amounts to +3.8 • C and +4.2 • C at Juvvasshøe (Fig. 8b) and Tron (Fig. 8c), respectively.

Mountain permafrost after the Little Ice Age
From the initial situation in 1860 rough estimates on the lower altitudinal limit of mountain permafrost after the LIA can be made.The model results suggest the presence of permafrost at Juvvasshøe at c. 1300 m a.s.l.(Juv-BH6).The modelled ALT range from 0.5 m at 1900 m a.s.l.(Juv-BH1) to c. 3 m at 1300 m a.s.l (Juv-BH6).The greatest ALT (close to 4 m) was modelled for the bedrock site (Juv-BH4).At Tron, permafrost thicknesses of up to 90 m and ALT of c. 1.3 m to 6 m were modelled.According to the model results, the altitudinal zone of the lower limit of permafrost at this site was below c. 1300 m a.s.l.

Ground temperatures
According to the model results for the period from 1860 to 2009, GTs were increasing at all depths.At all boreholes, most significant increases in GT occurred in the last two decades (since 1990).The model results show an increase in GT at 10 m depth since the 1860s by about 0.9 • C to 1.

Active layer thickness
Depending on location, elevation and stratigraphy, different ALT behaviour is indicated by the model results.A characteristic pattern is observed at all boreholes, with a comparatively slow ALT increase until the end of the 20th century (1995/1999) and accelerated increase in ALT during the decade 2000-2009.
Trends of ALT increase were derived for the two periods 1860/64-1995/1999 and 2000-2010.The non-parametric Mann-Kendall test was used to test these trends for significance (1 % level).At Juvvasshøe and Jetta all trends of ALT increase during both periods have been proven significant, while at Tron only the trend for the later period (1990-2010) is significant.
At Juvvasshøe the lowermost borehole (Juv-BH6) shows a very rapid ALT increase and permafrost degradation prior to the end of the 19th century.The 20th century increase in ALT at the other boreholes was only +0.2 m (24 %, +0.1 cm yr −1 ) and +0.7 m (54 %, +0.5 cm yr −1 ) at Juv-BH1 and PACE (Fig. 9a), respectively.At the lower boreholes (Juv-BH3 and Juv-BH4) an ALT increase of +2.3 m (68 %, +1.6 cm yr −1 ) and +2.4 m (65 %, +1.7 cm yr −1 ) was modelled, respectively.The model results indicate a stronger ALT increase at all boreholes during the last 10 yr in the range of +0.2 to +2.6 m (20-46 %, 2-26 cm yr −1 ).The PACE borehole shows higher mean interannual variation of ALT than Juv-BH1 with +40 cm yr −1 and +20 cm yr −1 , respectively.Although Juv-BH3 was drilled in coarse material and Juv-BH4 in bedrock they show a similar ALT evolution, the latter however, having continuously larger ALT (average +0.4 m) and a much higher mean inter-annual variation of 70 cm yr −1 compared to 30 cm yr −1 .As all boreholes are drilled in bedrock at Jetta, the ALT is more sensitive to climate variations, and a more rapid increase during the last 150 yr was modelled.Until mafrost degradation was modelled for Jet-BH3 (Fig. 9b).
At Tron the strongest increases in ALT were modelled with +1.1 m (110 %, +0.8 cm yr −1 ) until the end of the 20th century (Fig. 9c).Within the last decade only, the model indicates a rapid warming of permafrost with an ALT reaching a depth of 10-11 m as measured today.This indicates an ALT increase of nearly +9 m (430 %, +87 cm yr −1 ) since 1990.This development agrees well with observations indicating the possible beginning of a talik development (Fig. 3c) (Farbrot et al., 2011).

Ground temperatures
According to modelled GT until 2100, warming will continue beyond that found for 2000-2009.The model suggests that GTs at Juv-BH1 will increase by +1.9 • C and +1.1 • C at 30 m and 100 m depth until 2100, respectively.Juv-BH4 shows the same warming at 100 m depth, but a more pronounced increase in GT at 30 m with +2.6 • C.

Active layer thickness
The model results are indicative for permafrost degradation also above 1800 m a.s.l.
until 2100.Permafrost at lower elevations (Juv-BH3 and Juv-BH4) degrades completely before 2050 (Fig. 9a).At the bedrock site at Jetta the rapid AL thickening rates at Jet-BH1 will continue and the development of a talik until the end of the 2020s is predicted by the model (Fig. 9b).
While the air temperature increase in the climate change scenario shows a linear development and even a decrease in the warming rate (Fig. 8a), the ALT displays a non-linear response at most sites (Fig. 9).The ALT of Juv-BH1 increases linearly by another 70 cm from 2010 until mid 2070s.Although the climate change scenario includes a decrease in the warming rate at this point, a rapid degradation of permafrost subsequently takes place until the end of this century, with a linear increase of ALT by Introduction

Conclusions References
Tables Figures

Back Close
Full > 40 cm yr −1 .A similar development can be observed at the PACE borehole with higher thickening rates and a permafrost degradation at the mid 2060s.
Running the model with the 90th and 10th percentiles of the downscaled temperature ensemble yields an estimation of the possible range of developments.The 90th percentile causes a fast degradation of permafrost at all boreholes by latest mid of this century (Fig. 9a).Considering the moderate warming projections (10th percentile), permafrost at Juv-BH1 and PACE is warming at a slow rate without degradation occurring.

Probable future of permafrost at the PACE and Juv-BH1 boreholes
Concerning the projected air temperate, there are uncertainties related to the different formulations of the GCMs themselves, as well as to the empirical-statistical downscaling procedure (Benestad, 2011).Although only one emission scenario is considered here (A1b), the uncertainties lead to considerable spread of projected temperature.In order to quantify the effects of this uncertainty on modelled ALT and GT, the development of GT and ALT until 2100 were simulated for all percentiles of the projected T AIR -ensemble in steps of 5 %.From these results, we identify the percentiles which are associated with disappearance of an AL in the years 2050 and 2100, respectively.This analysis is used to estimate the probabilities for transition of permafrost to talik at Juv-BH1 and PACE in the years 2050 and 2100 (Fig. 10).
For the PACE borehole, a talik evolution until 2100 was modelled already using the 25th percentile resulting in a high probability of 70-75 % (Fig. 9).According to the classification proposed by the IPCC (IPCC, 2007), this situation is therefore likely to occur for the given emission scenario.However, at Juv-BH1 a talik will have developed in 2100 with a probability of 50-55 %, and is classified as likely to occur as not.The probabilities for talik evolution until 2050 is 35-40 % for PACE and 20-25 % for Juv-BH1, respectively and therefore unlikely (Fig. 10).According to these model results, above 1800 m a.s.l,where stable and continuous mountain permafrost is found today, Introduction

Conclusions References
Tables Figures

Back Close
Full discontinuous mountain permafrost is to be expected by the end of the 21st century.

Model uncertainties due to snow cover, soil water content variability and model approach
A major source of uncertainty is related to the parameterisation of using constant nfactors.It is uncertain how well the snow conditions of the historic and future model period are represented by the average n-factor from S1 and S2.A 10-yr record (1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008) of GST and T AIR is available at the PACE borehole (Isaksen et al., 2011), which enables an estimate for the decadal variation of n-factors and put the period 2008-2010 into context.A mean n F -factor of 0.91 (0.89-0.98) and n T -factor of 1.12 (1.02-1.26)was derived from the records.The mean n F -and n T -factors for 2008-2010 (Table 1) therefore are within the variation of the period 1999-2009.Additionally, based on these minimum and maximum values an uncertainty analysis was conducted to give a quantitative estimate on the error that can be expected from n-factors that do not accurately represent the actual snow cover.For that purpose, the model was run for the PACE that the n-factors assumed in the model runs are a good representation of long-term average n-factors.Some deviations of modelled from observed GTs are observed during periods of thawing and freezing, presumably caused by our assumption of constant VWC.At sites where VWC > 15 %, the model typically underestimates the pronounced zero-curtain effect observed.(Fig. 5).Further, our model neglects advective heat transport, and changes of ice-content in the ground are not recognised in the model.The degradation of permafrost would remove ice and enhance water drainage, leading to an increased warming in the ground.This process is observed at Juv-BH5 and discussed in more detail by Farbrot et al. (2011) (see also Isaksen, 2011).Our modelling does not account for this process and therefore, rather represents a minimum estimate for the increase of GT.
A third process not included in the model are 3-D-effects due to lateral variation of either topography or snow cover.Farbrot et al. (2011) suggests that 3-D-effects may affect BH5 due to variable snow cover.In our 1-D modelling this effect is probably compensated for by the calibration parameters, so that the performance of the model is relatively good.Hence, the results for BH5 in deeper soil layers should be treated with caution.
The aim of this study are to assess the long-term trends of permafrost temperature and its altitudinal distribution.We assume conduction and latent heat effects as main factors, which is in agreement with studies showing that conduction and latent heat effects attribute for most of the heat flow processes (Kane et al., 2001;Weism üller et al., 2011).Both soil water/ice content and snow conditions on the long-term are afflicted with uncertainties.For this study we suggest that the average n-factor value we used provides a useful approximation to address the snow influence on GST.The constancy of soil water content may be responsible for slight deviations during periods of zero-curtain.Nevertheless, observed GT, ALT and GT amplitudes were reproduced reasonably well according to the ME measure used in this study.Long-term data are not available, which e.g. could aid possible trends of n-factors or soil water content, so

Conclusions References
Tables Figures

Back Close
Full we do not know if and how trends and inter-annual variations would interfere with each other and affect our result.Moreover, at our sites and generally in most high-mountain settings in Scandinavia, coarse-grained near-surface material or bedrock is dominating.Thus, the soil water content is relatively low and the effect of water flow on GT is considered minor.Furthermore, the boreholes have been drilled in flat topography, in doing so, 3-D-effects are largely avoided.Processes of lateral heat transfer along a slope and air convection within the pore space of block fields seem not important.
Even with the stated simplifications, modelled GTs agree well with observations and the present borehole temperature distributions are reproduced when simulating the evolution since 1870.These results suggest therefore, that our simple approach is capable of capturing the dominating processes within the time scale considered.

Uncertainties of reconstructed and projected air temperature series
The method by Hanssen-Bauer and Nordli (1998) has proven useful in reconstructing reliable air temperature time series (Farbrot and Hanssen-Bauer, 2009).However, it introduces uncertainty due to the spatial and temporal interpolation of air temperatures.
Before daily values become available in 1957, the model is run with monthly data.To test the possible error introduced by the discontinuity in temporal resolution, the period 2008-2010 was simulated with monthly means.The model result does not show any significant deviation to those obtained when using the daily resolution input data.
Uncertainties related to the interpolation in mountain topography arise from unknown lapse rates during inversions (Tveito and Førland, 1999), which are observed frequently, especially during calm winter days.The temperature fields used in this study for the long-term record are based on constant lapse rates, which may produce too cold SAT in high elevations (e.g., Tveito and Førland, 1999).However, generally a good fit has been achieved when comparing measured and interpolated air temperature, indicating the mean temperature trends being well represented (Tveito and Førland, 1999).
In our study we employ ensemble estimates of future T AIR evolution to illustrate and assess the uncertainty of the future GT evolution.Ensemble analysis has proven pow-

Conclusions References
Tables Figures

Back Close
Full erful in assessing uncertainties of projected T AIR evolution.However, there are several ways to define an ensemble, each of which refers to a different cause of uncertainty.In detail, the ensemble may consist of GCM realizations for a multitude of emission scenarios, thereby uncovering the range of expected outcomes for the discrete emission scenarios defined by IPCC (2007).Furthermore, a T AIR ensemble may also consist of many realizations for one single emission scenario but from a multitude of GCMs.The combination of both would also be possible, though we regard that possibility as little instructive.Here, we have focused on illustrating the uncertainty related to the choice of GCM for a given scenario rather than on the uncertainty related to future emissions.Namely, we have chosen the A1b scenario for which empirically-statistically downscaled time series of T AIR are available for a multi-model ensemble (Benestad, 2011).

Influence of ground properties on thermal regime
GTs respond differently to warming, depending on the surface material, ground properties and soil water content.The inter-annual change of ALT was calculated and averaged for the period 1860-2009 for all boreholes at Juvvasshøe.Borehole Juv-BH4, which does not have significant snow cover and is located in bedrock, shows the highest variation of 0.7 m yr −1 .Much lower inter-annual ALT variations of 0.2-0.3m yr −1 were modelled for boreholes covered by block fields.This reflects how the block fields act as a buffer dampening the effect of the air temperature fluctuations on GT (Harris and Pedersen, 1998;Juliussen and Humlum, 2008).At Juv-BH4, however, no such buffer layer exists causing a more direct response of the ALT to changes in T AIR .Despite their proximity, the boreholes PACE and Juv-BH1 show different thermal regimes and ALT developments in past and future due to differences in volumetric water content.A large part of the energy transferred into the ground at Juv-BH1 is consumed for melting ground ice.This explains the reduced inter-annual variability of ALT and the less pronounced increase in ALT in the past and future.Furthermore, the non-linear response in ALT is attributed to the melting of ice within the ground.

Conclusions References
Tables Figures

Back Close
Full After melting of ground ice, more energy is available to efficiently warm the ground.Similar effects have been observed in North-America (Smith et al., 2010) and Russia (Romanovsky et al., 2010), where the non-linear response of GT and ALT to warming are clearly attributable to water content.Similar results have been found comparing the impact of the extreme summer of 2003 on the ALT of bedrock and block field sites in the Swiss Alps (Vonder M ühll et al., 2007).
Several other studies have attempted to quantify the impact of climate change on permafrost conditions, distribution and ALT.Stendel and Christensen (2002) predicted a general increase of ALT of up to 30-40 % until the end of the 21st century in the Northern Hemisphere.Zhang et al. (2008) estimated the ALT increase in Canada to 14-30 % by 2050 compared to a permafrost baseline in the 1990s.For Svalbard, similar changes for the ALT evolution during the 21st century were modelled (Etzelm üller et al., 2011).In our study the ALT increased by 65 % to 180 % at the boreholes where permafrost still is expected by 2050.Even the results using the 10th percentile of the climate change models indicate an ALT increase of 44 % at the PACE borehole.This implies a high sensitivity of warm mountain permafrost to climate change, comparable to coastal areas e.g. on Svalbard (Etzelm üller et al., 2011).Furthermore, many of the assessments mentioned above were made for Arctic lowlands, where large areas with fine-grained and organic-rich sediments are present.Organic components in the nearsurface layer are known to effectively damp the GT response to warming (Williams and Smith, 1989).In mountain areas, significant accumulation of organic material is seldom and restricted to special topographic and geomorphic settings.However, block fields may have an effect similar to that of organic material in Arctic lowlands, i.e. retarding the GT-response to climate signals and cooling the ground, as discussed above.
In summary our modelling study shows a high sensitivity of mountain permafrost and high probabilities of degradation at elevation levels below c. 1800 m a.s.l. in Southern Norway.Simulated GTs at bedrock sites are generally more sensitive to climate change than those at sites within block fields or finer-grained sediment cover.Introduction

Conclusions References
Tables Figures

Back Close
Full At that time, sporadic to discontinuous permafrost conditions seem to have been more widespread at elevations of around 1300 m a.s.l., where we only find permafrost as isolated patches at present (Sollid et al., 2003).This translates to the lower permafrost zone being approximately 200 m lower during the LIA than at present.At Juvvasshøe, this zone between 1300 m a.s.l. up to 1500 m a.s.l. is dominated by block lobes, which may be inactive today, but are shaped by an earlier high-active periglacial environment.Further climate warming would move this zone up-slope.The model results of this study indicate that the lower limit of the discontinuous permafrost zone may rise up to above 1800 m a.s.l., thus, c. 250 m higher than today.With such a scenario, major changes in periglacial processes are expected.
As our results are derived from 1-D modelling at the point scale, these implications on the spatial distribution of mountain permafrost have to be treated with care.The large spatial heterogeneity of parameters that strongly influence permafrost distribution such as snow cover, surface cover and ground parameters can not be considered in these estimations, as recently documented by Gubler et al. (2011) for sites in Switzerland and Etzelm üller et al. (2007) in Iceland.Therefore, a simple point-to-area extrapolation is problematic.However, we have three main reasons to consider this set-up as sufficient to give estimations on the altitudinal changes of mountain permafrost since the LIA in these very particular mountain areas: (1) The 13 boreholes cover a large altitudinal range from 1900 m a.s.l. to c. 1200 m a.s.l., today ranging from continuous permafrost to no permafrost, (2) Farbrot et al. (2011) clearly documented consistent altitudinal trends in GT on an annual average and (3) even if a borehole location is not representative for the local variability of surface characteristics, the GT signal in greater depth will be integrated over a larger surface area.Figures

Back Close
Full From this study we draw the following conclusions: -Forcing the model with reconstructed T AIR over 1860-2009 yielded vertical profiles of GT close to those observed in 2009, thereby suggesting validity of our approach.
-During the Little Ice Age the altitudinal zone covering the lower limit of permafrost was approximately 200 m lower than today in the field area.A future warming according to the A1B scenario would further lift this zone by c. 250 m towards the end of the 21st century, depending on site characteristics and snow cover development.
-Model results suggest that GT at 10 m depth increased by +0.9 • C to +1.5 • C over 1860-2009.The largest part of this warming occurred after 1990.
-From 1860 until c. 1990 a comparatively small increase in active layer thickness was modelled where permafrost exists, with values ranging from 0.1 cm yr −1 to +2 cm yr −1 (20-68 %).tia of ice-containing ground material.In our sites, this response is related mainly to block fields and coarse ground moraine sites containing ice.
The modelled past and possible future changes in GT and ALT have geomorphologic and geotechnical implications since the ground thermal regime is a major controlling factor for geomorphologic processes and landscape development (Berthling and Etzelm üller, 2011).As alpine rock faces are widespread in the study area between 1900 and 2400 m a.s.l, our study suggests major impacts on the geotechnical properties and stability of rock walls.This relationship is well-documented in literature (Davies et al., 2001;Gruber et al., 2004a) and has to be evaluated in future research.Especially the modelled long period of stable permafrost and a subsequent sudden and quick degradation results in challenges for engineering, natural hazard prediction and mitigation.Finally, our study provides important insights in the range of thermo-physical parameters in a wide range of bedrock and surficial material relevant for mountain areas in Southern Norway.These provide important constraints for spatial numerical permafrost modelling.

TCD Introduction
Full  Full  Full  Full Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | in addition to the existing PACE borehole along an altitudinal transect from 1894 m a.s.l.
(S1 -September 2008 to August 2009; S2 -September 2009 to August 2010; S3 -September 2010 to July 2011) to analyze the inter-annual variation ( Discussion Paper | Discussion Paper | Discussion Paper | At Juvvasshøe MAATs during S1 and S2 ranged from −3.4 • C to −0.6 • C and −4.5 • C to −2.3 • C, respectively, resulting in an average altitudinal lapse rate of 0.5 • C/100 m at 10 m depth (MAGT 10 ) ranges from −2.4 • C to −0.5 • C within permafrost and reaches up to +1.7 • C (Juv-BH6) in non-permafrost areas.At Tron, MAAT during S1 and S2 ranged from −3.6 • C to −0.9 • C and −4.5 • C to −2.3 • C, respectively.Tro-BH1 and Tro-BH2 show thick and long-lasting snow cover during both seasons (> 90 cm).Permafrost was found at the uppermost borehole with GTs only slightly below 0 • C down to a depth of 30 m.Despite lower MAAT and MAGST in S2, the ALT at Tron-BH1 slightly increased from 10.7 m to 11.1 m (Fig. 3c).Along the north slope of Tron, comparatively low MAGST of −0.4 • C to −0.7 • C were recorded by miniature temperature loggers down to 1450 m a.s.l., indicating the possible presence of permafrost Discussion Paper | Discussion Paper | Discussion Paper | 5 • C lower at Juvvasshøe and 0.3 • C to 0.4 • C higher at the other sites.The MAAT during S2 was on average by 1.4 • C to 1.1 • C lower than during S1.At PACE the winter 2008-2009 did not show any strong deviation from the period 1961-1990, but positive deviations of up to +5 • C were recorded during spring and summer.The winter 2009/2010 was much colder than the normal period, with negative deviations of up to −4.5 • C during December to February (Fig. 2b).

3. 2
Historic and future temperature data Analyzing available long-term temperature records (starting in the 1860s), Hanssen-Bauer (2005) and (Hanssen-Bauer and Nordli, 1998) identified six temperature regions, each of which characterized by similar long-term variability of air temperature.For each region monthly standardised temperature series ST m are derived by averaging Discussion Paper | Discussion Paper | Discussion Paper | the standardized temperature series ST m,i of each individual station i in the region m: Discussion Paper | Discussion Paper | Discussion Paper | ) requires boundary conditions at the upper and lower ends of the domain.Here, we used a geothermal heat flux of Q geo = 33 mW m −2 (Isaksen et al., 2001) as lower boundary condition and GST as upper boundary condition.The atmosphere-ground coupling is an important factor for prescribing appropriate upper boundary conditions for the heat flow model.The relation between T AIR and GST varies strongly from borehole to borehole, depending on snow and surface cover (Fig. 4).Historical and future time series of GST were generated from the reconstructed T AIR and downscaled future temperatures, respectively, using n-factors.n-Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 9 • C/100 yr and +1.4 • C/100 yr) between 1860/1870 and 2008/2009 at Juvasshøe and Tron, respectively.During the last decade (2000-2010) only positive deviations of T AIR to the climate normal 1961-1990 were observed all sites (Fig. 8b,c).In the period 1860s until 2000/2009 the strongest warming occurred during spring with +2.1 • C at Discussion Paper | Discussion Paper | Discussion Paper | 5 • C at Juvvasshøe and 0.1 • C to 0.7 • C at Tron.GTs at 100 m depth increased in the range of 0.4 • C to 1.0 • C at Juvvasshøe and 0.1 • C to 0.4 • C at Tron.Modelled warming was strongest for the bedrock borehole (Juv-BH4) with +1.5 • C and +0.5 • C at 10 m and 100 m depth, respectively.Discussion Paper | Discussion Paper | Discussion Paper | 1990 the ALT increased by +1.1 m (26 %, +1 cm yr −1 ) and +2.2 m (40 %, +2 cm yr −1 ) at Jet-BH1 and Jet-BH3, respectively.During the period 1990 until 2010 the strongest increase of ALT of +2.7 m (50 %, +14 cm yr −1 ) was modelled at Jet-BH1, while per-Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | borehole for 1999-2010 separately both with the minimum and maximum n-factors.This implies running the model with the coldest (n F = 0.98; n T = 1.02) and warmest (n F = 0.89; n T = 1.26) possible GST conditions.The differences in GTs expressed in the absolute error between the two model runs were calculated for each depth individually.A change in ALT of < 50 cm and changes in MAGT of 0.7• C to 0.4• C at the surface and 10 m depth, respectively, were introduced.The PACE borehole represents a site with relatively constant n F -factors due to the negligible snow cover.At sites with higher snow cover and thus smaller n F -factors (particularly Tr-BH2, Jet-BH1 and Tr-BH6), our measurements suggest a higher interannual variability of the n F -factors (Table1), most likely caused by different wind redistribution of snow.However, the good agreement of modelled long-term subsurface temperatures with measured GT gives us confidence 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 |5.4 Altitudinal changes of mountain permafrost during the modelling periodThis study indicates a major change in ground thermal regime since the end of the LIA.

-
Since c. 1990 ALT-change rates of +2 cm yr −1 to +87 cm yr −1 (20-430 %) were modelled.The model results indicate permafrost degradation at boreholes below c. 1450-1500 m at Juvvasshøe and Jetta and below c. 1600 at Tron.Throughout the 21st century degradation of permafrost at most of the sites below c. 1800 m a.s.l. is suggested by the model.By the end of this century the highest locations (Juv-BH1, PACE) will experience pronounced ALT-increases of up to 10 m or the development of taliks.This implies an upward shift of the lower permafrost zone to around 1800 m a.s.l. by the end of the 21st century, again depending on sediment characteristics and snow cover development.-Our study successfully simulated the non-linear response of ground temperature and active layer thickness to increasing air temperatures, due to the thermal iner-Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Fig. 1 .Fig. 4 .Fig. 5 .Fig. 6 .
Fig. 1.Location of the study sites and boreholes in Norway (a).As a rough estimate of possible permafrost distribution all areas with MAAT < −3 • C during the last normal period 1961-1990 are shown in blue (Etzelm üller et al., 2003).Local site overview of (b) Juvvasshøe, (c) Jetta and (d) Tron, each indicating the locations of boreholes (BH), where GST measurements (MTD) and T AIR , GST and snow depth measurements are performed.

Fig. 8 .
Fig. 8. (a) Historic air temperature series at the uppermost borehole at Juvvasshøe (black) and Tron (blue).The bold line represents the 7-yr Gaussian-filtered series.For 2010 onwards, the figure shows the median (bold black), 90 percentile (red) and 10 percentile (blue) of the downscaled T AIR ensemble for Juv-BH1.The lower panels show the deviations of MAAT from the 1961-1990 climate normal at Juvvasshøe (b) and Tron (c).

Table 1 .
Thermal conditions at individual boreholes included in the modelling study, showing mean annual air temperature (MAAT), mean annual ground surface temperature (MAGST) and ground temperature at 10 m depth (MGT 10 ).N F -and n T -factors for the two seasons 2008/2009 (S1) and 2009/2010 (S2) and the average (AVG) used in the modelling are shown.For 2010/2011 (S3) only n F -factors could be calculated due to missing data for the summer months.

Table 2 .
Ground properties for different substrates, surface cover and bedrock type, used in the model.Variations within these generalised surface and subsurface classes at different sites can still be found, thus, ranges of parameter values are given.Here, k is thermal conductivity, c is specific heat capacity, VWC is the volumetric water content and ρ is the density.

Table 3 .
Model performance in terms of ground surface temperature (GST), ground temperature (GT) and active layer thickness (ALT) at boreholes included in the modelling study.Model performance for GST and GT is expressed in terms of Nash-Sutcliffe model efficiency.Modelled and observed ALT are presented in absolute values.For GT, both the calibration (C) and the validation (V) periods are listed.For the GST the model was run with the averaged n-factors and ME calculated for each season individually.