Permafrost monitoring using time-lapse resistivity tomography

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1 Permafrost monitoring using time-lapse resistivity tomography Permafrost, Phillips, Springman & Arenson (eds) 2003 Swets & Zeitlinger, Lisse, ISBN C. Hauck 1 Graduiertenkolleg Natural Disasters & Institute for Meteorology and Climate Research, University of Karlsruhe, Germany D. Vonder Mühll University of Basel & Institute for Geography, University of Zurich, Switzerland 1 formerly at: Laboratory for Hydraulics, Hydrology and Glaciology (VAW), ETH Zurich, Switzerland ABSTRACT: Time-lapse direct-current (DC) resistivity tomography is shown to be a useful method for permafrost monitoring in high-mountain areas. Resistivity changes are related to subsurface freezing and thawing processes using a fixed-electrode array throughout a full year at a high elevation site in the Swiss Alps. The 2-dimensional tomographic approach yields information about spatially variable transient processes, like the advance and retreat of freezing fronts. In combination with borehole temperature data the temporal evolution of the unfrozen water content was calculated showing a strong decrease during winter months in the near-surface layer and quasi-sinusoidal behaviour at greater depths. A comparison between borehole temperatures, resistivity and energy balance data emphasizes the dominant role of the snow cover evolution in winter and net radiation in summer for the ground thermal regime. A combination of radiation, snow cover and resistivity measurements seems promising for long-term monitoring programmes of the permafrost evolution at low cost. 1 INTRODUCTION In view of a warming climate and the recent retreat of most Alpine glaciers, the need for a continuous monitoring of the permafrost evolution in mountainous regions has been identified in recent years (Fitzharris et al. 1996). This should include long-term temperature monitoring programmes (such as the EU-funded PACE (Permafrost and Climate in Europe) project), as well as improved process understanding and impact assessment. This is specifically important in the context of thawing permafrost slopes, which may induce natural hazards such as rock falls and debris flows (Harris et al. 2001). However, as most mountain permafrost sites are situated in remote and rather inaccessible regions, drilling operations and therefore temperature monitoring programmes in deep boreholes are very costly and often impossible to conduct. In contrast, surface geophysical measurements using electric, electromagnetic and seismic methods present a cost-effective alternative and are applicable even in harsh and remote environments (Scott et al. 1990, Vonder Mühll et al. 2001). In addition, they allow the determination of 2- and 3-dimensional spatial variability compared to the single point measurements in boreholes. In this study a 2-dimensional geophysical monitoring approach introduced in Hauck (2002) is used in combination with energy balance data to determine the permafrost evolution at Schilthorn, Swiss Alps. Changes in subsurface electrical resistivity were monitored using a fixed-electrode array, which allows measurements independent of the snow cover thickness. The resistivity changes are related to changes in the subsurface unfrozen water content, which can be used to determine the amount of freezing and thawing. Energy balance data and temperature data from a nearby borehole are used to verify the results. This work serves as a pilot study for long-term monitoring programmes for permafrost changes in the shallow subsurface. 2 THEORY AND METHODS 2.1 DC resistivity tomography The DC resistivity technique is based on electrical resistivity differences between different subsurface materials. For typical permafrost material a marked increase in resistivity at the freezing point was shown in several field and laboratory studies (Hoekstra et al. 1975, King et al. 1988). Consequently, the application of 1-dimensional vertical electrical has a long tradition in the study of permafrost. With the development of fast, commercially available 2-dimensional inversion schemes for DC resistivity surveys (e.g. Res2DINV, Loke & Barker 1996), 2-dimensional resistivity tomography is increasingly applied, especially in mountainous terrain (Hauck & Vonder Mühll 1999, Kneisel et al. 2000, Hauck 2001). As the heterogeneous surface and subsurface characteristics of mountain permafrost terrain often prohibit the application of plane-layer approximations used in standard data processing for 1-dimensional soundings, the tomographic method greatly improves the quality of data interpretation in resistivity studies on permafrost. 361

2 However, most applications are restricted to single measurements at one time instant (mostly in summer), which may lead to ambiguous interpretations. Resistivity depends mainly on the unfrozen water content of the subsurface, which can be influenced not only by the presence or absence of permafrost, but also through changes in temperature, geologic material, water input through precipitation and snow melt and the occurrence of subsurface air cavities. 2.2 Archie s law for partially frozen soils In most Earth materials electric conduction takes place through ionic transport in the liquid phase. A well known empirical relationship called Archie s law relates the resistivity of a 2-phase medium (rock matrix, liquid) to the resistivity of the water, the porosity and the fraction of the pore space occupied by liquid water: only in so far as the resistivity of the pore water is changed. A decrease in temperature increases the viscosity of water, in turn decreasing the mobility of the ions in the water, which increases the resistivity. A relationship between r and temperatures T above the freezing point is given by: r0 r 1 a( T T ), 0 (3) where r 0 is the resistivity measured at a reference temperature T 0 and a is the temperature coefficient of resistivity, which has a value of about K 1 for most electrolytes (Telford et al. 1990). For temperatures below the freezing point resistivities increase exponentially until most of the pore water is frozen. Using an exponential relationship of the form (e.g. Hauck 2001, 2002) r ar w m S n w, (1) r r 0e bt ( f T), (4) where r is the resistivity of the material, r w is the resistivity of the water in the pore spaces, is the porosity, S w is the fraction of the pore space occupied by liquid water and a, m and n are empirically determined parameters (Telford et al. 1990). In partly frozen material, ionic transport still takes place in the liquid phase. Therefore, the resistivity depends not directly on temperature or ice content, but on the unfrozen water content S, that is the fraction of water remaining unfrozen at subfreezing temperatures, which can be substantial even at relatively low temperatures (Anderson & Morgenstern 1973). Assuming the pore space of the material was completely filled with water prior to freezing (S S w 1 for temperatures above the freezing point) and using Equation 1, Daniels et al. (1976) showed that the ratio of the resistivity of a partially frozen material r f to that unfrozen r i is related to the unfrozen water content by r f r i S 1 n. (2) King et al. (1988) estimated the so-called saturation exponent n between 2 and 3 (for sands) and 5 8 (for clays) using permafrost samples from the North American Arctic. 2.3 Dependence on temperature The dependence of resistivity on temperature differs for temperatures above and below the freezing point. At temperatures above the freezing point, a decrease in temperature changes the resistivity of the material where r 0, b (in K 1 ) are constants and substituting into Equation (2), S can be expressed as bt ( f T) S exp, 1 n (5) where T f is the temperature of the freezing point. For a saturation exponent of n 2 (commonly used for rock, Telford et al. 1990) and T f 0, Equation 5 describes simply an exponential decrease of the unfrozen water content with decreasing temperature. The factor b controls the rate of decrease and can easily be determined from Equation (4) if resistivity data for different subzero temperatures are available. By choosing appropriate values for n and b, the temporal evolution of the unfrozen water content can be determined in a qualitative way. 3 FIELD SITE AND DATA ACQUISITION The Schilthorn (46 33 N, 7 50 E at 2970 m a.s.l.) is located in the Bernese Oberland in the Northern Swiss Alps. Due to the high amount of precipitation and additional snow input through wind transport, the snow cover usually persists from October to June (Imhof et al. 2000). Permafrost temperatures measured in a borehole are comparatively warm, reaching 0.7 C at 14 m depth. Consequently, the unfrozen water content is high leading to low resistivity values compared to typical mountain permafrost occurrences (Hauck & Vonder Mühll 1999). The ground consists of a 5 m thick weathered layer (small to medium size debris) over firm bedrock (micaceous shales) with no vegetation cover. 362

3 A fixed-electrode array allowing resistivity tomography measurements along a 58 m survey line throughout the year was permanently installed at Schilthorn in September 1999 (Hauck 2002). A 2-dimensional inversion algorithm (Res2DINV, Loke & Barker 1996) is used to determine specific resistivities within a finite-element block model from the surface resistance measurements. Ground temperatures were measured within a 14 m borehole drilled in 1998 (Vonder Mühll et al. 2000). Snow height, longwave and shortwave radiation balance were measured 1.50 m above the surface at the energy balance station completed in 1999 (Mittaz, 2002). 4 RESULTS 4.1 Resistivity Between September 15, 1999 and August 28, 2000 eleven sets of DC resistivity tomography measurements were conducted with the fixed electrode array at Schilthorn. The time span between measurements was roughly 1 month except for the thawing season 2000, where measurements were conducted every 2 weeks (June/July). Instead of analysing the resulting resistivity tomograms in terms of absolute values, the cumulative resistivity differences per day based on the September measurement are shown in Figure 1. Largest resistivity increases (white colors) were observed in October, when the snow cover was not yet established and heat loss at the surface resulted in a reduction of near-surface ground temperature (Fig. 1b). Freezing extended along the whole survey line and reaches a depth of 2 m. From October 1999 to April 2000 resistivities increased only slowly due to the insulating snow cover, which arrived in October and effectively decoupled the subsurface thermal regime from the atmosphere. Heat conduction allowed a reduction in temperature at greater depths, subsequently freezing deeper layers. This gradual downshift of the freezing front can be visualised by plotting ratios of successive resistivity measurements instead of cumulative differences (Hauck 2002, not shown here). During the phase transition, the temperatures remained close to 0 C (the so-called zero-curtain effect), while the resistivities increased as the unfrozen water content diminished. From the borehole temperature data shown in Figure 2 it is seen that the zero-curtain effect started at the end of October and lasted until end of December at 0.4 m depth and until beginning of February at 4 m depth. Figure 1. (a) Resistivity model for the measurement on as determined by the inversion. (b) (k) Resistivity difference per day based on the September measurement (a). White and dark shading denote resistivity increase and decrease, respectively. 363

4 Figure 2. Borehole temperatures with time at 4 different depths (PACE borehole 51/1998). In the beginning of May the temperatures near the surface approached 0 C and melting of the uppermost layer started. Again, temperatures remained almost constant at 0 C during the phase transition. At the time of the first summer resistivity measurement (June 2000), most of the frozen water in the uppermost 23 m had already melted which led, together with additional water input by rain, to a wet soaked surface layer, decreasing the resistivity strongly near the surface (grey colors in Figure 1g). Between June and July 2000, temperatures increased at all depths down to 10 m with a corresponding resistivity decrease throughout the major part of the survey area. This decrease continued until end of August 2000, thereby almost totally equalizing the resistivity increase of the winter months (Figure 1k). A more detailed analysis of the resistivity results can be found in Hauck (2001). Comparing all resistivity measurements at the borehole location versus the corresponding temperatures a small but linear increase is found for decreasing but still positive temperatures, showing good agreement with the values calculated from Equation (3) (see Hauck (2002) not shown here). Below the freezing point resistivities increase exponentially with cooling. However, as the data originate from different depths, the rate of increase is not uniform for all data points. Using equation (4) different values for the factor b ( rate of increase) can be determined for different depths. These values can then be used to calculate the unfrozen water content S (see below). 4.2 Comparison between energy balance, ground temperature and resistivity evolution The dominant role of snow cover evolution can be revealed by comparing it to temperature change in the borehole, the radiation balance and the total resistivity variation at the borehole location (Figure 3). A permanent snow cover was established at the end of October (Figure 3c) and persisted until mid-june. During that time the temperature within the uppermost 10 m of the borehole remained almost constant (Figure 3a), as the ground temperature regime was effectively decoupled from atmosphere and temperatures stayed at the freezing temperature of the ground. The net radiation (being the dominant energy flux, see Hoelzle et al. (2001)) during that time is negative, meaning that cooling takes place at the snow surface (Figure 3b). But as the energy flux through the snow cover is negligible during winter (less than 1 W/m 2, Figure 3e), the freezing processes in the subsurface can only be induced by the cold October temperatures, which penetrated into the ground before the snow cover arrived and propagated to larger depths through heat conduction. After the melting of the snow cover in June, temperature variability in the borehole is high, coinciding well with the observed variability of the radiation balance (Figure 3b). This agreement confirms again the dominant role of the radiation balance for ground temperatures in mountain permafrost terrain. Figure 3d shows the evolution of the unfrozen water content, which was calculated using Equation (5). The parameter b was chosen from the respective resistivity temperature relation as introduced in Hauck (2002). The results for two different values for the saturation exponent n and for four depths are shown. In the uppermost layer (0.5 m) the unfrozen water content starts to decrease at the end of October, corresponding to the onset of the negative radiation balance seen in Figure 3b. The minimum is reached in February and subsequently later at greater depth (beginning of June at 8.7 m depth). At larger depths the evolution of S is nearly sinusoidal, corresponding to the seasonal variation of ground temperature. The minimal value of S is smallest at larger depths ( below 6 m for n 2) and largest at intermediate depths ( at 2 4 m for n 2), but depends on the choice of parameters b and n. The larger n, the smaller the variations of S. King et al. (1988) examined a large number of permafrost samples from the North American Arctic. At 2 C they found unfrozen water contents as high as 0.9 (clay) and as low as 0.2 (sands) depending on the material type. Finally, Figure 3f shows the total resistivity variation at the borehole location, calculated as weighted vertical mean ( (r i h i )/z, where z is the model depth and h i is the thickness of the individual resistivity model layers). Total resistivities increase steadily until a maximum is reached for the April measurement. From there, resistivities decrease again until September 2000, where a slightly larger value than the initial value in September 1999 is reached. It is notable that the strong 364

5 Figure 3. Comparison between borehole temperatures, energy balance parameters and resistivity. (a) Total temperature difference per day in the uppermost 10 m in the borehole, (b) net radiation at the energy balance station, (c) snow height, (d) calculated unfrozen water content (Equation (5)), (e) energy flux through the snow cover and (f) total resistivity variation at the borehole location (weighted vertical mean). resistivity increase during winter coincides with an almost zero total temperature change in the borehole (Figure 3a). 5 CONCLUSION Time-lapse resistivity tomography measurements at a mountain permafrost site have been presented in combination with borehole temperature and energy balance data. A set of eleven DC resistivity tomography measurements were performed between September 1999 and September 2000 using a fixed electrode array at Schilthorn, Switzerland. The resulting resistivity changes were analysed in terms of subsurface freeze and thaw processes. Key results from this multiparameter data set include: Temporal resistivity changes in high Alpine environments can be accurately determined using a fixed electrode array, which is accessible throughout winter. Maximum resistivity changes were observed in autumn (September October), before a permanent snow cover was established, and in late spring (May June), when the thawing snow cover and additional water from precipitation greatly decreased the resistivity values in the active layer. During winter, the snow cover effectively decouples the ground from atmospheric influences. The heat flux through the snow cover was less than 1 W/m 2, estimated from energy balance measurements. Consequently, the small but steady resistivity increase observed during winter was solely due to temperature reduction by heat conduction from upper to lower layers. From December to May the freezing front moved gradually downward, reaching 6 m in mid-april. After the start of the melting season the resistivities decreased until the previous September values were reached again at the end of August Resistivity temperature relationships between the resistivity values at the borehole location and 365

6 borehole temperatures show good agreement with theory. The increase of resistivity with decreasing temperature is small and linear for temperatures above the freezing point and exponential for temperatures below freezing. The calculated temporal evolution of the unfrozen water content shows a strong decrease during the winter months in the active layer and a quasisinusoidal behaviour below. A comparison between borehole temperatures, resistivity and energy balance data emphasizes the dominant role of the snow cover evolution in winter and net radiation in summer. In addition, resistivity monitoring may be used to determine the amount of freezing and thawing in the subsurface in future long-term monitoring programmes. ACKNOWLEDGEMENTS The authors would like to thank the Schilthornbahn AG for logistic support and C. Mittaz and M. Hoelzle (Glaciology and Geomorphodynamics Group, University of Zurich) for supplying the energy balance data. This study was financed by the PACE project (Contract Nr ENV4-CT and BBW Nr ). C. Hauck acknowledges a grant by the German Science Foundation (DFG) within the Graduiertenkolleg Natural Disasters (GRK 450). REFERENCES Anderson, D.M. & Morgenstern, N.R Physics, chemistry and mechanics of frozen ground: a review. Proceedings 2nd International Conference on Permafrost, Yakutsk, Russia: Daniels, J.J., Keller, G.V. & Jacobson, J.J Computerassisted interpretation of electromagnetic soundings over a permafrost section. Geophysics 41: Fitzharris, B.B. & 27 authors The cryosphere: changes and their impacts. Climate Change Contribution of Working Group II to the 2nd Assessment Report of the IPCC. Cambridge University Press, Cambridge: Harris, C., Haeberli, W., Vonder Mühll, D. & King, L Permafrost monitoring in the high mountains of Europe: the PACE project in the global context. Permafrost and Periglacial Processes 12(1): Hauck, C Geophysical methods for detecting permafrost in high mountains. Mitt. Versuchsanstalt Wasserbau, Hydrologie u. Glaziologie 171, Zürich, Switzerland. Hauck, C Frozen ground monitoring using DC resistivity tomography. Geophysical Research Letters (in press). Hauck, C. & Vonder Mühll, D Using DC resistivity tomography to detect and characterise mountain permafrost. In: Proceedings of the 61. Europ. Association of Geoscientists and Engineers (EAGE) conference, June 1999, Helsinki, Finland: 2 15, 4pp. Hoekstra, P., Sellmann, P.V. & Delaney, A Ground and airborne resistivity surveys of permafrost near Fairbanks, Alaska. Geophysics 40: Hoelzle, M., Mittaz, C., Etzelmüller, B. & Haeberli, W Surface energy fluxes and distribution models of permafrost in European mountain areas: An overview on current development. Permafrost and Periglacial Processes 12: Imhof, M., Pierrehumbert, G., Haeberli, W. & Kienholz, H Permafrost investigation in the Schilthorn Massif, Bernese Alps, Switzerland. Permafrost and Periglacial Processes 11(3): King, M.S., Zimmerman, R.W. & Corwin, R.F Seismic and electrical properties of unconsolidated permafrost. Geophysical Prospecting 36: Kneisel, C., Hauck, C. & Vonder Mühll, D Permafrost below the timberline confirmed and characterized by geoelectric resistivity measurements, Bever Valley, Eastern Swiss Alps. Permafrost and Periglacial Processes 11: Loke, M.H. & Barker, R.D Rapid least-squares inversion of apparent resistivity pseudosections using a quasi-newton method. Geophysical Prospecting 44: Mittaz, C Energy balance over alpine permafrost. PhD-thesis, University of Zurich, Switzerland. Scott, W., Sellmann, P. & Hunter, J Geophysics in the study of permafrost. In (ed. S. Ward): Geotechnical and Environmental Geophysics, Soc. of Expl. Geoph., Tulsa. pp Telford, W.M., Geldart, L.P. & Sheriff, R.E Applied geophysics. 2nd edition, Cambridge University Press. Vonder Mühll, D., Hauck, C. & Lehmann, F Verification of geophysical models in Alpine permafrost using borehole information. Annals of Glaciology 31: Vonder Mühll, D., Hauck, C., Gubler, H., McDonald, R. & Russill, N New geophysical methods of investigating the nature and distribution of mountain permafrost with special reference to radiometry techniques. Permafrost and Periglacial Processes 12(1):