Permafrost Analysis for the Alpine Monitoring Station at Zugspitze (Bavaria, Germany): Measurements, Modeling and Climate Impacts

doi:10.21203/rs.3.rs-3142479/v1

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Permafrost Analysis for the Alpine Monitoring Station at Zugspitze (Bavaria, Germany): Measurements, Modeling and Climate Impacts

https://doi.org/10.21203/rs.3.rs-3142479/v1

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Permafrost degradation due to global warming, particularly in mountainous regions, can be responsible for an increase in mass movements such as rockfalls, slides and subsidence. Therefore, preventive measures, based on a simulation of permafrost degradation, should be planned in advance. Consequently, modeling of permafrost in the high Alpine region of Bavaria is the main objective of this study. At first, this paper evaluates a permafrost temperature (T) database for the Permafrost Monitoring Station (PMS), located between 2,922 and 2,907 m a.s.l. at the ridge of the highest mountain of the Bavarian Alps (Zugspitze, 2,962 m a.s.l.). The compiled T data along the oblique (20°) 44.5 m long borehole reveals a warming trend over the period from 2010 to 2020, resulting in a noticeable permafrost degradation. After that, a transient permafrost model was developed and calibrated using collected T records. Then, the model was applied to PMS meteorological data from 1900 to 2015. The permafrost simulations showed a considerable decrease in permafrost along the borehole by the length of about 9.5 m, mainly at the southern side. Lastly, calculation of potential permafrost changes, up to 2100, was performed for two different climate scenarios (RCP8.5 and RCP2.6) with 13 different climate realizations (model runs), obtained from the statistical regional climate model WETTREG2013. The RCP8.5 scenario (9 realizations) is based on the assumption of a linear increase of CO₂ emissions with time. The RCP2.6 scenario (4 realizations) assumes no further increase in CO₂ emissions. In conclusion, the modeling results for the RCP8.5 scenario imply a permafrost disappearance at the Zugspitze by the end of the 21st century. Yet, in the case of the RCP2.6 scenario, today’s permafrost will remain essentially unchanged.

Geology

Climate Analysis and Modeling

Permafrost

Modeling

Rock temperature

Climate scenarios

Zugspitze

Bavaria

A significant decrease of permafrost has been observed in the Alpine region over the last two decades (Krautblatter et al., 2018). Also, permafrost is known to be very sensitive to climate change, i.e., its size responds to noticeable changes in air T (Czekirda et al., 2019). Thus, retreat of permafrost coincides with trends of climate warming in the European Alps (Nogués-Bravo et al., 2007). Retreating permafrost results in reduced slope stability, especially in mountainous regions, which in turn leads to mass movements such as rockfalls, land subsidence and slides (e.g. Ravanel and Deline, 2011; Krautblatter et al., 2013, Mamot et al., 2021). Subsequently, these processes can also deteriorate the stability of building foundations (Gruber et al., 2004a; Gude and Barsch, 2005). Therefore, it is important to foresee climate change effects on the permafrost extent and character. Consequently, to evaluate potential risks of a permafrost degradation, permafrost monitoring stations (PMS) have been established and mathematical models have been developed.

To address the above issues for the European scale, the PermaNET project (Permafrost Long-Term Monitoring Network) was launched in 2007 (Mair et al., 2011). The main objective of this project was to establish a research network for monitoring permafrost in the European Alps and to produce, by mathematical modeling, a permafrost distribution map (Boeckli et al., 2012). A classical example is the PMS at Zugspitze, which was established in 2007. Additionally, similar stations were created in Switzerland at Gemsstock (Phillips et al., 2016), in France at Aiguille du Midi (Magnin et al., 2015) and in Austria at Kitzsteinhorn (Keuschnig et al., 2017). Moreover, a permafrost index map, showing possible permafrost presence, was generated by Boeckli et al. (2012). This map is applicable mainly to surficial deposits and is of limited use for the specific local conditions, such as occurrence of rock faces. Consequently, more specific permafrost models, accounting for local conditions and geometries, were developed and applied to the sites, e.g., the PMS, and compared with recorded permafrost data (e.g. Noetzli et al., 2010, Magnin et al., 2015). For the site of the Zugspitze PMS, Noetzli et al. (2010) concluded that the modeling could predict permafrost presence with an accuracy of about 0.5 to 1 degrees Celsius.

Permafrost extent is very sensitive to changes in air T. Therefore, reliable projections of the dynamics of climate change on permafrost extent require transient models that can predict the rock T evolution in the range of the accuracy of T sensors (about 0.1°C). Permafrost modeling in Alpine environments is well understood (e.g. Hoelzle et al., 2001; Gruber et al. 2004b, Noetzli et al., 2010, Magnin et al., 2015) but there is a lack of permafrost models with such accuracy applied to specific sites.

Consequently, the main objective of this study concentrated on a development of a versatile transient permafrost model, specifically adapted to the site of the Zugspitze PMS. This model is able to analyze the following: (i) Rock T trends influenced by air T, solar and rock radiation, and snow depth. (ii) Better understanding of the past permafrost extent (prior to 2007), based on the available meteorological database. (iii) Potential scenarios for the future permafrost presence at the Zugspitze, using available climate models.

Zugspitze Permafrost Monitoring Station

The borehole of the PMS at the Zugspitze (2,962 m a.s.l.) is located below the Eibsee Cableway Mountain Station (“Eibseebahn East”, Fig. 2), at an altitude between 2,907 (northern end) and 2,922 m a.s.l. (southern end). It is situated in the Northern Calcareous Alps; the immediate surroundings of the peak consist of massy, fine-grained dolomised limestone of the Triassic Wetterstein Formation (“Wettersteinkalk”) (Krautblatter et al., 2010; Hornung and Haas, 2017). First permafrost data in that area was reported by Knauer (1933). He described “ice stalactites” in a vertical rock crevice at 2,400 m a.s.l. during the construction of a tunnel for the Zugspitze cogwheel railway. Later, permafrost presence was found during construction of the Zugspitze Cableway Mountain Station (Ulrich and King, 1993). More recently, the permafrost in the Zugspitze ridge at 2,800 m a.s.l. (“Kammstollen gallery”) has been studied using electrical resistivity tomography (Krautblatter et al. 2010).

For the PMS construction, a borehole (diameter 125 mm) was drilled in August 2007 through the permafrost-affected ridge, about 30 m below the cableway mountain station, in a S-N direction over a length of 44.5 m with an inclination of 20° (Fig. 1). The borehole goes entirely through the mountain, i.e. it had two open ends. The drilling was carried out with the down-the-hole-hammer technique, which only produces cuttings. Therefore, no drill cores are available from the borehole. Subsequently, the northern end was sealed by a concrete filling, while the southern end is covered by a control cabinet that connects the T sensors to the data logger.

The borehole was equipped with an airtight measurement chain consisting of 16 T sensors. This chain was made by Stump ForaTec AG, Russikon, Switzerland. It is equipped with “YSI 44031RC Precision Epoxy NTC” sensors located at the following distances from the southern end of the borehole (in m): 0, 0.5, 4.0, 8.85, 13.65, 18.65, 21.15, 23.65, 28.65, 31.15, 33.65, 35.65, 37.65, 39.65, 41.65, 43.55 (see Fig. 2b for positions in the PMS borehole). The sensor accuracy is 0.1°C. Calibration and recalibration were carried out in 2007 and 2012, and no problems with drift or shift of the sensors were detected. The T is measured at hourly intervals and recorded with a data logger.

Figure 2 shows the location of the Zugspitze PMS. The topographic map of the Zugspitze summit is depicted in Fig. 2a with an enlargement of the area marked in red showing the Zugspitze summit buildings and position of the PMS borehole. Figure 2b shows a schematic profile section through the summit ridge along the borehole. Here the summit buildings and the borehole geometry with the positions of the T sensors and the numerical grid for the modeling are given. The southern side of the borehole has a smaller slope and is more exposed to solar radiation, while the north side has a steep rock face that does not receive direct sunlight all year round. Due to this specific topography, there is a snow cover on the southern side of the borehole during a cold season, while the north side is largely free of snow.

The PMS is listed as a climate indicator for the Bavarian Climate Adaptation Strategy (LfU, 2017b). Specifically, the T sensor at 23.65 m from the southern end of the borehole (as shown in scale of Fig. 2b) is used as an indicator of permafrost development because it has the lowest annual T amplitude and thus represents the point with the least short-term influence of weather in the ridge.

Permafrost thermal state: transient modeling

In the permafrost model development the following processes were considered: heat conduction through rocks, heat convection at rock surfaces, shortwave solar radiation on rock surfaces, long-wave heat radiation from the rock surfaces and ice/water phase changes.

A transient 3-D model of heat conduction in solids (rocks) can be written as follows (Groeber et al., 1988, Baehr and Stephan, 2019):

$$c \bullet \rho \bullet \frac{dT}{dt}= \lambda (\frac{{d}^{2}T}{d{x}^{2}}+\frac{{d}^{2}T}{d{y}^{2}}+\frac{{d}^{2}T}{d{z}^{2}})$$

where

c = heat capacity of the (porous) rock

ρ = rock density

x = distance x

y = distance y

z = distance z

T = rock temperature

t = time

λ = thermal conductivity of (porous) rock

For the one-dimensional (1-D) case, the conduction heat transport equation has the following form:

$$\frac{dT}{dt}= a\bullet \frac{{d}^{2}T}{d{x}^{2}}$$

where a is a rock thermal diffusivity: a = λ ⁄ (c ∙ ρ)

Values for density ρ, heat capacity c and thermal conductivity λ are obtained from weighted volume contents of respective rock fractions, water/ice contents and air-filled pores. In addition, different rock λ can also be considered. When modeling latent water/ice phase changes, the temperature in the respective node is kept constant at phase change temperature, while any heat fluxes only cause the water/ice to freeze or thaw. When the phase change process is complete, the temperatures change again. The fraction of time-dependent water/ice phase changes φ_fl during the freezing/thawing process is calculated as follows:

$$\frac{{d{\phi }}_{fl}}{dt}= \frac{\lambda }{h \bullet \rho \bullet {\Phi }} \bullet \frac{d²T}{dx²}$$

where

φ_fl = fraction of liquid phase

h = enthalpy of phase change ice/water

Φ = rock porosity

Finite difference numerical model

The section of the PMS borehole could be described by a fitted 2-D or 3-D finite difference grid. However, due to numerous unknown physical parameters (such as the distribution of rock thermal parameters) and boundary conditions, it would be too difficult to achieve the required accuracy of T calculations in the borehole. This was one of the main reasons for the decision to proceed with a much simpler and easier to control 1-D model.

The finite difference domain is shown in Fig. 2c, where the x-axis closely follows the 20° inclined borehole. The T distribution, along the permafrost borehole, was calculated for an equally spaced grid length of 0.5 m over the total length of 44.5 m (Fig. 2c). Time steps of 60 minutes were used for all simulation runs. The spatial increments and time steps used for the numerical model were optimised to obtain stable model results with reasonable computational effort. No numerical stability problems occurred under these spatial and temporal conditions (see also Press et al., 2007). Accordingly, rock T was obtained using the 1-D finite difference method (Crank-Nicholson scheme) (Baehr and Stephan, 2019).

Rock properties, starting and boundary conditions

Initial thermal parameters of the Wetterstein formation were taken from literature (Cermák and Rybach, 1982 in Noetzli et al., 2010): thermal conductivity λ = 2.5 W/(m K), volumetric heat capacity c · ρ = 2 ∙ 10⁶ J/(m³ K), porosity of the rock Φ = 5 Vol.-%. Uncertainties for those parameters were taken into account in the calibration process (see chapter model calibration). For the phase-change T (water/ice) of the Wetterstein limestone at the Zugspitze, Krautblatter et al. (2010) determined a value of -0.5°C, for the porosity 4,4 Vol.-%.

For modeling the past permafrost condition, the starting conditions for the T distribution in the PMS borehole are unknown. Since a complete T equilibration of the Zugspitze permafrost borehole requires a period of about 10 years (LfU, 2017a), the model results were evaluated only after a simulation period of 15 years from the starting point. The data from the Zugspitze automatic weather station (AWS) of the DWD (2021) were used for the boundary conditions of the energy balance: air T, snow presence and incoming solar radiation. The AWS is located near to the summit of the Zugspitze (see Fig. 2a) at 2,960 m a.s.l., about 45 m above the permafrost borehole (between 2,922 and 2,907 m a.s.l.). The radiation data for the borehole surfaces on the southern and northern sides were adjusted to their exposure. For this purpose, the orientation and inclination of the rock surfaces at the borehole ends were measured with a Freiberg geological compass.

Model calibration

Heat flow in the rocks at Zugspitze is influenced by several factors whose exact values remain largely unknown, such as for example: spatial variability of rock thermal parameters, convective heat fluxes due to precipitation and heat flows transverse to the direction of measurement (Noetzli, 2010). Therefore, to achieve the required accuracy of the model (approx. 0.1°C difference between measured and modeled T) the model was calibrated by fitting obtained data to measured T sensor data. For this purpose, the two calibration factors z1 and z2 were introduced into the 1-D equation of heat transfer:

$$\frac{dT}{dt}=z1+z2 ·a\bullet \frac{{d}^{2}T}{d{x}^{2}}$$

In the first step, z1 and z2 were determined for each node (i.e., approximately 170 adjustment factors) using a least squares method for a calibration period from 2013 to 2014. Then, z1 and z2 were iteratively varied until the deviations of calculated and measured T reached a minimum. In this way, information from the measured data was implemented into the model. As applied in Eq. 4, z1 takes into account unknown heat sources and sinks and z2 unknown variations of rock thermal diffusivity. In the second step, heat transfer parameters between the rock surfaces and the atmosphere were also optimized using a least squares approach based on a comparison of measured and calculated T.

The snow cover has a strong influence on the distribution of permafrost (Hoelzle et al. 2001, Krautblatter, 2009). On the southern exposure snow can accumulate due to the less steep terrain. In turn, on the north side, an insulating effect of snow is expected to be less relevant due to the steep rock surface. Therefore, an insulating effect of snowpack was taken into account in the modeling for the southern exposure based on the snow depths provided by the Zugspitze AWS.

Meteorological data

Meteorological data from the Zugspitze AWS of the German Weather Service (DWD) were used for past permafrost modeling at the Zugspitze. The DWD-measurements at this station began in August 1900 and the following data relevant for permafrost modeling were collected: air T, snow depth, cloud cover and global radiation (measured since January 2013). The 30-year moving average of air T was minus 4.9°C in 1930, while in 2015 it was minus 4.0°C; i.e. 0.9 K rise in 85 years.

Station data from global climate projections (Table 1) were used to model future development of permafrost. Representative Concentration Pathway (RCP) scenarios of the 5th IPCC report (IPCC, 2014: Climate Change) include an additional radiative forcing, i.e. atmospheric warming caused by increased CO₂ concentrations. The RCP8.5 represents a scenario without climate change mitigation, while the RCP2.6 denotes a scenario for compliance with the 2 K cap of atmospheric warming. These two scenarios are considered in this study to project future permafrost development through the end of the 21st century.

Table 1

Global climate models and associated forcing scenarios for the WETTREG2013 realizations (last two columns show the scenarios covered by the models).
Abbreviation global model	Long name global model	RCP8.5	RCP2.6
CA2	CCCMa-CanESM2_r1	x
CM5	CNRM-CERFACS-CNRM-CM5_r	x
ECE	ICHEC-EC-EARTH_r12	x
HG2	MOHC-HadGEM2-ES_r1	x
MI5	MIROC-MIROC5_r1i1p1	x
MP1	MPI-M-MPI-ESM-LR_r1	x	x

The abbreviations originate from the project “Regionale Klimaprojektionen Ensemble fuer Deutschland” (Regional Climate Projections Ensemble for Germany) (ReKliEs-DE, Huebener et al., 2017).

For the specific Bavarian conditions, the Bavarian Climate Projection Ensemble was compiled, which is based on the most plausible representation of measured climate by the models (LfU, 2020). Regarding the climate data, the permafrost modeling is based exclusively on WETTREG2013 (CEC, 2015) because only for this model generation, Zugspitze station data are available. In total, WETTREG2013 provides 60 realizations with RCP8.5 (10 realizations each with 6 different global model drives) and 10 realizations with RCP2.6 (10 realizations with one global model drive) (Table 1). For the permafrost modeling presented here, a total of 9 realizations were chosen for the RCP8.5 scenario and 4 realizations for the RCP2.6 scenario. For the differences between the realizations see “Meaning of symbols of the station data” as explained in the caption of Fig. 3. The different realizations of the scenarios were chosen to visualize the uncertainty ranges and to reflect the temperature signal of the Bavarian Ensemble.

Figure 3 displays the thermopluviogram of realizations selected for the "far future" period (30-year normal period to the end of the century 2071 to 2100). The figure shows changes of T and precipitation signals for the RCP8.5 and RCP2.6 scenarios of the Bavarian Ensemble (+ and x signatures). In addition, the position of the 13 WETTREG2013 realizations used for the future modeling is depicted by the colored symbols. The symbols indicate the criteria used to select the realizations (e.g., triangle = minimum/maximum in hydrologic year, Figure 3). To reflect the bandwidth of the models, the realizations representing the minimum, maximum and median T signal changes were selected. As expected, the RCP8.5 scenarios show a much larger T increase of +3.5 to +5.3 K than the RCP2.6 with a range between +0.8 and +1.1 K.

Measured vs. simulated T data during the observation period

The measured T, along the borehole axis, for a period from June 2010 to May 2020 is shown in Fig. 4. The spatial T distribution was determined from the T values by interpolation between the T sensors using the inverse distance method. Daily averaged data from the T sensors (hourly measurements) were used.

The T course over time shows the warming trend of the ridge. This can be clearly seen from the 0°C boundary marked in green. The 0°C boundary moves toward the interior of the ridge, from the southern and northern sides of the borehole.

For the T sensor at 23.65 m from the southern end of the borehole, the highest temperature is reached around the turn of March/April. Measured and modeled peak T values for the respective years are shown in Table 2. The measured and calculated results of the T sensor at 23.65 m in Fig. 5 show a clear warming trend in rock T during the observation period, corresponding to an upward trend of annual mean air T as also shown in Fig. 5. The differences between measured and calculated values are at most 0.06 K and thus within the range of measurement accuracy.

Table 2

Maximum annual rock T at 23.65 m distance from the southern end and 20.85 m from the northern end of the borehole: measurement vs. modeling. For location of T sensors see Fig. 2b.
	Measurement [°C]	Modeling [°C]
2013	-1.04	-0.98
2014	-0.99	-1.04
2015	-0.90	-0.96
2016	-0.86	-0.88
2017	-0.82	-0.84
2018	-0.80	-0.81
2019	-0.78	-0.76

The time course of rock T as shown in Fig. 5 exhibits a considerable T increase of about 0.4 K within six years. This agrees well with the observed trends in annual air T patterns.

Modeling past permafrost data (1915–2015)

The calibrated model was used to simulate the evolution of permafrost from 1900, i.e. the beginning of the AWS data recording. Modeling results were not evaluated until 1915 to allow equilibrium with the (unknown) initial conditions at the start of modeling in 1900.

Figure 6 shows the number of days per year that the daily mean rock T exceeds 0°C in a specific path segment. Thus, sections with zero days above 0°C per year indicate the permafrost area of the borehole. So, while in 1915 permafrost existed in a range between 7.5 and 41.5 meters borehole length - i.e., over the length of 34 meters - in 2015 it is only observed in the range between 14.5 and 39 meters (24.5 meters length). Therefore, the permafrost area has shifted into the ridge interior by about 7 meters on the southern side of the borehole and by about 2.5 meters on the north side during the 100-year period. This corresponds to a total loss of permafrost (in the borehole) of 9.5 m. The differences in permafrost degradation may be attributed to the different site topography: while the southern side has a flatter terrain slope with snow cover in winter and incoming solar radiation, the north side is a steep rock face with no snow cover and no direct solar radiation all year round.

Calculated future permafrost data (until 2100)

Modeling of T in the borehole to the year 2100 was performed using meteorological data based on two scenarios (RCP8.6 and RCP2.6). Since no projection data are available for global radiation and snow depths, measured DWD data for 2015 are used. Simulated rock T is shown at 23.5 and 31.0 m from the southern end of the borehole. The T sensor at 23.5 m has the lowest seasonal amplitude; the T sensor at 31.0 m is in the area where model calculations indicate permafrost will last occur if rock T continues to rise. Figure 7 shows the curves for the realization HG2_RCP85_00, from 1971 to 2100. This is a realization with a particularly strong T rise. As can be seen, the increase in rock T over time follows the increase in air T. The rock T at a distance of 31.0 m from the southern end of the borehole reaches the zero-degree limit in the 50s of the 21st century. Figure 8 shows the corresponding T curves for the MPI_RCP26_11 realization. This realization roughly corresponds to the mean T range of the realizations used for the RCP2.6 scenario.

The annual maxima of rock T at 23.5 m from the southern end of the borehole show a clear warming trend for all realizations RCP8.5 in the period 1971 to 2100. In Fig. 9, the values at the end of the period are clearly above the 0°C limit.

For the RCP2.6 realizations, increasing rock T into the early 50s result in nearly constant T levels at 23.5 m from the southern end. In no case does the maximum T reach the 0°C limit by 2100 (Fig. 10).

Figures 11 to 14 show the rock T along the borehole for the different realizations for the end of the years 2019 and 2100. Figure 11 shows the rock T along the borehole for the RCP8.5 scenario realizations of the year 2019. At 31 m from the southern end of the borehole, T values ranging from − 2.05 to -0.68°C are obtained for the RCP8.5 realizations on December 31, 2019, while the measured value (at 31.15 m) is -1.22°C.

The corresponding plot of simulated rock T for RCP8.5 realizations at the end of 2100 (Fig. 12) no longer shows permafrost in the borehole, with values at 31 m ranging from 0.49 to 2.31°C.

For the RCP2.6 realizations, the simulated rock T at 31 m from the southern end of the borehole at the end of 2019 are between − 1.55 and − 1.79°C, slightly lower than the measured value of -1.22°C (Fig. 13).

At the end of the year 2100, the calculations for RCP2.6 realizations at 31 m result in values between − 1.02 and − 1.90°C (Fig. 14). Accordingly, no permafrost thawing is expected in these realizations with the RCP2.6 scenario.

The T trends are analyzed for the 30-year future periods 2021–2050 (near future), 2041–2070 (middle future), and 2071–2100 (far future), and for the reference period 1971–2000. Table 3 lists the mean values of air T and calculated rock T at 23.5 m for the three time periods and the individual realizations.

Table 3

30-year mean values of air and rock T (23.5 m distance from the southern end of the borehole and 21 m from the northern end)
[°C]	1971–2000		2021–2050		2041–2070		2071–2100
	Air	Rock 23.5 m	Air	Rock 23.5 m	Air	Rock 23.5 m	Air	Rock 23.5 m
HG2_RCP85_00	-4.30	-1.36	-1.79	-0.07	-0.74	0.72	0.97	1.88
HG2_RCP85_11	-4.42	-1.35	-1.86	-0.05	-0.68	0.79	0.90	1.89
MP1_rcp85_00	-4.14	-1.42	-2.64	-0.72	-1.73	-0.08	-0.31	1.06
MP1_rcp85_44	-4.05	-1.22	-2.65	-0.48	-1.66	0.17	-0.37	1.04
CA2_RCP85_77	-4.11	-1.06	-1.90	0.04	-0.99	0.72	0.67	1.40
CM5_rcp85_77	-4.25	-1.31	-3.06	-0.81	-2.09	-0.16	-0.75	0.44
CM5_rcp85_88	-4.26	-1.36	-3.13	-0.90	-2.20	-0.32	-0.71	0.38
ECE_RCP85_88	-4.34	-1.34	-2.55	-0.46	-1.62	0.18	-0.06	0.79
MI_RCP85_55	-4.40	-1.14	-1.73	0.29	-0.78	0.90	0.75	1.64
MPI_RCP26_00	-4.14	-1.64	-3.29	-1.07	-3.13	-0.96	-3.07	-0.73
MPI_RCP26_11	-4.16	-1.60	-3.31	-1.01	-3.11	-0.91	-3.28	-0.79
MPI_RCP26_55	-4.14	-1.40	-3.33	-0.84	-3.15	-0.77	-3.13	-0.82
MPI_RCP26_88	-4.13	-1.49	-3.29	-0.86	-3.04	-0.80	-3.31	-1.16

The T data from Table 3 and corresponding linear trend lines are shown in Fig. 15. Accordingly, a 1 K increase in mean air T during the 30-year period results in a 0.65 to 0.7 K increase in rock T at 23.5 m. Data for the 1971 to 2000 reference period confirm the validity of the trend lines for the future periods (green dots/circles).

Figure 16: Calculated number of days in 2100 with rock T above 0°C along the PMS borehole for the four different realisations of the RCP2.6 scenario. The segments with zero days for T above 0°C indicate the respective permafrost area in the borehole.

Permafrost model limitations

Heat transport processes along the permafrost borehole were simulated using a transient 1-D finite difference model. As a result, it was possible to project potential permafrost trends in response to climate changes. According to Hoelzle et al. (2001), air T, solar radiation and snow conditions, as well as rock properties, are the most important factors affecting permafrost presence. However, these parameters are not completely available at the Zugspitze site. For example, solar radiation data has only been collected since 2013. Consequently, there is some uncertainty about possible solar radiation data trends over the last hundred years or, as well, through the end of the 21st century. So, it was assumed that variations in observed solar radiation (over the last two decades) were about ± 5%. This value was observed in the Swiss Alps by Gruber et al. (2004b). However, a sensitivity analysis (LfU, 2017b) showed, that these variations have a negligible impact on permafrost extent.

Additional shortcomings include missing rock surface radiation properties, such as short- and long-wave radiation factors. According to Krautblatter (2009), local variations in radiation values due to different meteorological conditions, such as snow cover, solar exposure and shading, are essential for modeling permafrost dynamics. According to Hoelzle et al. (2001) and Krautblatter (2009) snow cover is a very important factor affecting permafrost formation and existence. However, no reliable snow cover data are available for the rock surface next to the permafrost borehole ends. Therefore, an empirical approach as described in LfU (2017b) was chosen for snow modeling. This approach was validated by comparing measured and calculated T of the T sensors next to the rock surface.

Also, rock inhomogeneities at Zugspitze influence the conduction heat transport (Noetzli et al., 2010). Such inhomogeneities were exemplarily found by Koerner and Ulrich (1965) below the Zugspitze peak in the form of larger, partly clay-filled fissures. Ulrich & King (1993) report of year-round frozen weathered loam and up to 10 cm thick ice lenses filling cleavages at an 8 m deep and 7 m wide opening of the entranceway for the Glacier cable car (Fig. 2a) near to the Zugspitze PMS. Values of the thermal rock parameters (thermal conductivity, heat capacity, porosity, and void fraction filled with water or ice) are strongly influenced by the ice presence in fissures. Thus, the distribution and volume fraction of the fissures (cracks) as well as their water content are random and largely unknown. Consequently, these issues had to be omitted from the finite difference model.

In addition to the heat flow along the borehole, there is also a heat flow along a vertical axis to the borehole, e.g. from the mountain top above with the mountain station of the cableway. Also, it is difficult to assess a convective heat flow that may occur due to groundwater flow in the unfrozen area as well as possible moisture movement of unfrozen water in the permafrost area. This is because porous systems can contain significant amounts of unfrozen water even at T well below the freezing point (Burt and Williams, 1976; Tarnawski and Wagner, 1996).

Modeling issues

In earlier modeling approaches at the Zugspitze area (Noetzli et al., 2010), the deviations of measured and simulated temperatures in the Zugspitze borehole were in the range of about 0.5 to 1°C for a transient simulation in 2008. The deviation between measured and calculated T is attributed to the inaccurate knowledge of the rock thermal parameters and the existing inhomogeneities. As the permafrost is very sensitive to temperature changes, it was necessary to calibrate the model to a deviation in the range of the measurement accuracy of the T sensors (about 0.1°C). Therefore, a new modeling approach was introduced to compensate these limitations with regard to the parameter uncertainties as discussed above. This was achieved by introducing two calibration parameters z1 and z2 into the underlying equation for calculating conductive heat transport. The z1 considers heat sinks and sources that are not accounted for in the 1-D heat conduction model. Examples include convective heat flows due to groundwater flow or conductive heat flow perpendicular to the borehole. The z2 accounts for variations of the rock physical parameters relevant for 1-D heat conduction over the borehole depth (e.g. thermal conductivities and void fractions). In this way, irregularities in the geometry (inclination of the borehole, irregular surface above the borehole) are also taken into account to a certain extent. Consequently, this is a hybrid (empirical/physical) approach that ensured good agreement between calculation and experimental data. The approach was also validated by the good agreement between simulated and measured data outside the calibration period (i.e., before 2013 and after 2014). It should be noted that the calibrated model is valid only for the specific location of the borehole section. Therefore, application to other sites would require a complete recalibration of the model.

Finally, the possible future development of permafrost at the Zugspitze PMS depends on the actual climate development. While the permafrost model allows a very accurate simulation of the permafrost response to climate change, the greatest uncertainty lies in the future climate development. Therefore, the range of possible permafrost development at the Zugspitze PMS until the end of the century, for different realizations of the two climate scenarios RCP8.5 und 2.6, lies between disappearance and persistence of permafrost.

The main objective of this study was to determine the permafrost reaction to current climate changes in a high Alpine environment until 2100. The focus was on Mt. Zugspitze, where trends during the measurement period (10 years, 2010 to 2020) and 100 years into the past, as well as possible future trends based on available climate projections, were analysed.

A new transient permafrost model was developed, calibrated, and tested. The model was applied to T measurements during the calibration period (2013 and 2014) and to T data outside the calibration period with a relatively high prediction accuracy. Then, the model was applied to meteorological data since 1900 to quantify the permafrost occurrence over the past 100 years.

Finally, based on available regional climate models, the calibrated model was applied for estimating potential future permafrost development. Its status strongly depends on a selected climate path: for the scenarios without climate protection measures (RCP8.5), the disappearance of permafrost ranges from 2040 to 2080. Then, for a significant reduction in CO₂ emissions (RCP2.6), permafrost presence will persist over the projected period to 2100.

The outcome of this research coincides with findings of other studies (e.g. Nogués-Bravo et al., 2007; Krautblatter et al., 2018) and permafrost monitoring programs (e.g. PERMOS, 2022) regarding a general permafrost degradation trend in the Alpine region. It was shown that the developed transient permafrost model is capable of providing accurate projections of permafrost response to climate change. Therefore, it is concluded that to mitigate negative impacts of climate change on permafrost environments, it is necessary to collect more permafrost data and to continue development of versatile transient permafrost models.

The developed transient model was based on a calibration procedure valid only for the specific site. However, spatial approaches are required for mitigation planning. This means, that future research on permafrost development should consider a spatial approach. However, this requires development of highly accurate multidimensional models (2-D or 3-D), which could be based on approaches such as of Nötzli et al. (2010) for the Zugspitze.

Funding Statement

The PMS Zugspitze was jointly funded by the Bavarian State Ministry for the Environment and Consumer Protection and the European Union’s Interreg IV B, Alpine Space program in the period December 2007 – July 2011 as part of the PermaNet-BY project. The continued operation of the PMS after this project has been funded by the Bavarian State Ministry for the Environment and Consumer Protection.

Conflict of interest disclosure

The authors declare that they have no conflicts of interest.

Acknowledgements

The authors would like to thank the Zugspitzbahn AG for logistic support in the operation of the PMS. The project runs under the umbrella of the Environmental Research Station Schneefernerhaus (UFS). We thank Prof. Emeritus Dr. V.R. Tarnawski from Saint Mary’s University in Halifax (Canada) for proofreading and constructive criticism of the manuscript. Also, many valuable suggestions and comments from the anonymous reviewers are highly appreciated.

Author contributions BW: Conceptualization; methodology; supervision; validation; writing-original draft; writing-review and editing. TG: Validation; methodology; data curation; formal analysis; investigation; software; visualization; writing-original draft. MF: Climate data validation; writing-original draft. MJ: Supervision; climate data validation; review-original draft. MM: Model development and calibration; model simulations; writing-original draft.

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Affiliations

Bavarian Environment Agency, Geological Survey, Hof, 95030, Germany

Bernhard Wagner, Thomas Gallemann

Bavarian Environment Agency, Climate Centre, Hof, 95030, Germany

Maria Foltyn, Michael Joneck

Dr. Mahr Ingenieurbuero, Wallgau, Germany

Michael Mahr

Corresponding author

Correspondence to Bernhard Wagner

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Permafrost Analysis for the Alpine Monitoring Station at Zugspitze (Bavaria, Germany): Measurements, Modeling and Climate Impacts

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Abstract

Figures

Introduction

Zugspitze Permafrost Monitoring Station

Permafrost thermal state: transient modeling

Finite difference numerical model

Rock properties, starting and boundary conditions

Model calibration

Meteorological data

Results

Measured vs. simulated T data during the observation period

Modeling past permafrost data (1915–2015)

Calculated future permafrost data (until 2100)

Discussion

Permafrost model limitations

Modeling issues

Conclusions

Declarations

References

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