1 INTRODUCTION

In view of a warming climate and the recent retreat ofmost Alpine glaciers, the need for a continuous moni-toring of the permafrost evolution in mountainousregions has been identified in recent years (Fitzharriset al. 1996). This should include long-term temperaturemonitoring programmes (such as the EU-funded PACE(Permafrost and Climate in Europe) project), as wellas improved process understanding and impact assess-ment. This is specifically important in the context ofthawing permafrost slopes, which may induce naturalhazards such as rock falls and debris flows (Harris et al.2001).

However, as most mountain permafrost sites are situ-ated in remote and rather inaccessible regions, drillingoperations and therefore temperature monitoring pro-grammes in deep boreholes are very costly and oftenimpossible to conduct. In contrast, surface geophysicalmeasurements using electric, electromagnetic and seis-mic methods present a cost-effective alternative andare 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-dimensionalspatial variability compared to the single point meas-urements in boreholes.

In this study a 2-dimensional geophysical monitor-ing approach introduced in Hauck (2002) is used incombination with energy balance data to determinethe permafrost evolution at Schilthorn, Swiss Alps.Changes in subsurface electrical resistivity were moni-tored using a fixed-electrode array, which allows mea-surements independent of the snow cover thickness. The

resistivity changes are related to changes in the subsur-face unfrozen water content, which can be used to deter-mine the amount of freezing and thawing. Energybalance data and temperature data from a nearby bore-hole are used to verify the results. This work serves asa pilot study for long-term monitoring programmesfor permafrost changes in the shallow subsurface.

2 THEORY AND METHODS

2.1 DC resistivity tomography

The DC resistivity technique is based on electricalresistivity differences between different subsurfacematerials. For typical permafrost material a markedincrease in resistivity at the freezing point was shownin several field and laboratory studies (Hoekstra et al.1975, King et al. 1988). Consequently, the applicationof 1-dimensional vertical electrical has a long tradi-tion in the study of permafrost. With the developmentof fast, commercially available 2-dimensional inversionschemes for DC resistivity surveys (e.g. Res2DINV,Loke & Barker 1996), 2-dimensional resistivity tomo-graphy is increasingly applied, especially in moun-tainous terrain (Hauck & Vonder Mühll 1999, Kneiselet al. 2000, Hauck 2001). As the heterogeneous sur-face and subsurface characteristics of mountain per-mafrost terrain often prohibit the application ofplane-layer approximations used in standard data pro-cessing for 1-dimensional soundings, the tomo-graphic method greatly improves the quality of datainterpretation in resistivity studies on permafrost.

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Permafrost monitoring using time-lapse resistivity tomography

C. Hauck1

Graduiertenkolleg Natural Disasters & Institute for Meteorology and Climate Research, University of Karlsruhe, Germany

D. Vonder MühllUniversity 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 per-mafrost monitoring in high-mountain areas. Resistivity changes are related to subsurface freezing and thawingprocesses 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 theadvance and retreat of freezing fronts. In combination with borehole temperature data the temporal evolution ofthe unfrozen water content was calculated showing a strong decrease during winter months in the near-surfacelayer and quasi-sinusoidal behaviour at greater depths. A comparison between borehole temperatures, resistivityand energy balance data emphasizes the dominant role of the snow cover evolution in winter and net radiation insummer for the ground thermal regime. A combination of radiation, snow cover and resistivity measurementsseems promising for long-term monitoring programmes of the permafrost evolution at low cost.

Permafrost, Phillips, Springman & Arenson (eds)© 2003 Swets & Zeitlinger, Lisse, ISBN 90 5809 582 7

However, most applications are restricted to singlemeasurements at one time instant (mostly in summer),which may lead to ambiguous interpretations. Resis-tivity depends mainly on the unfrozen water contentof the subsurface, which can be influenced not only bythe presence or absence of permafrost, but also throughchanges in temperature, geologic material, water inputthrough precipitation and snow melt and the occur-rence of subsurface air cavities.

2.2 Archie’s law for partially frozen soils

In most Earth materials electric conduction takes placethrough ionic transport in the liquid phase. A wellknown empirical relationship called Archie’s law relatesthe resistivity of a 2-phase medium (rock matrix, liq-uid) to the resistivity of the water, the porosity and thefraction of the pore space occupied by liquid water:

(1)

where r is the resistivity of the material, rw is theresistivity of the water in the pore spaces, $ is theporosity, Sw is the fraction of the pore space occupiedby liquid water and a, m and n are empirically deter-mined parameters (Telford et al. 1990).

In partly frozen material, ionic transport still takesplace in the liquid phase. Therefore, the resistivitydepends not directly on temperature or ice content,but on the unfrozen water content S, that is the fractionof water remaining unfrozen at subfreezing tempera-tures, which can be substantial even at relatively lowtemperatures (Anderson & Morgenstern 1973).

Assuming the pore space of the material was com-pletely filled with water prior to freezing (S Sw 1for temperatures above the freezing point) and usingEquation 1, Daniels et al. (1976) showed that the ratio of the resistivity of a partially frozen material rf to that unfrozen ri is related to the unfrozen watercontent by

(2)

King et al. (1988) estimated the so-called saturationexponent n between 2 and 3 (for sands) and 5–8 (for clays) using permafrost samples from the NorthAmerican Arctic.

2.3 Dependence on temperature

The dependence of resistivity on temperature differsfor temperatures above and below the freezing point.At temperatures above the freezing point, a decreasein temperature changes the resistivity of the material

only in so far as the resistivity of the pore water ischanged. A decrease in temperature increases the vis-cosity of water, in turn decreasing the mobility of theions in the water, which increases the resistivity. Arelationship between r and temperatures T above thefreezing point is given by:

(3)

where r0 is the resistivity measured at a referencetemperature T0 and a is the temperature coefficient ofresistivity, which has a value of about 0.025 K�1 formost electrolytes (Telford et al. 1990).

For temperatures below the freezing point resistivi-ties increase exponentially until most of the pore wateris frozen. Using an exponential relationship of the form(e.g. Hauck 2001, 2002)

(4)

where r0, b (in K�1) are constants and substitutinginto Equation (2), S can be expressed as

(5)

where Tf is the temperature of the freezing point. For a saturation exponent of n 2 (commonly used for rock, Telford et al. 1990) and Tf 0, Equation 5describes simply an exponential decrease of the unfrozen water content with decreasing temperature.The factor b controls the rate of decrease and can eas-ily be determined from Equation (4) if resistivity datafor different subzero temperatures are available. Bychoosing appropriate values for n and b, the temporalevolution of the unfrozen water content can be deter-mined in a qualitative way.

3 FIELD SITE AND DATA ACQUISITION

The Schilthorn (46°33�N, 7°50�E at 2970 m a.s.l.) islocated in the Bernese Oberland in the Northern SwissAlps. Due to the high amount of precipitation and addi-tional snow input through wind transport, the snowcover usually persists from October to June (Imhof et al.2000). Permafrost temperatures measured in a boreholeare comparatively warm, reaching �0.7°C at 14 mdepth. Consequently, the unfrozen water content is highleading to low resistivity values compared to typicalmountain permafrost occurrences (Hauck & VonderMühll 1999). The ground consists of a 5 m thick weath-ered layer (small to medium size debris) over firmbedrock (micaceous shales) with no vegetation cover.

Sb T T

nf

�

�exp

( ),

1

r r� �

0e b T Tf( ) ,

rr

a

� �

0

01 ( ),

T T

r

r

f

i

nS �1 .

r r $� �a Swm

wn ,

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A fixed-electrode array allowing resistivity tomo-graphy measurements along a 58 m survey line through-out the year was permanently installed at Schilthorn in September 1999 (Hauck 2002). A 2-dimensionalinversion algorithm (Res2DINV, Loke & Barker 1996)is used to determine specific resistivities within afinite-element block model from the surface resist-ance measurements.

Ground temperatures were measured within a 14 mborehole drilled in 1998 (Vonder Mühll et al. 2000).Snow height, longwave and shortwave radiation bal-ance were measured 1.50 m above the surface at theenergy balance station completed in 1999 (Mittaz,2002).

4 RESULTS

4.1 Resistivity

Between September 15, 1999 and August 28, 2000eleven sets of DC resistivity tomography measure-ments were conducted with the fixed electrode arrayat Schilthorn. The time span between measurementswas roughly 1 month except for the thawing season2000, where measurements were conducted every

2 weeks (June/July). Instead of analysing the resultingresistivity tomograms in terms of absolute values, thecumulative resistivity differences per day based on theSeptember measurement are shown in Figure 1.

Largest resistivity increases (white colors) wereobserved in October, when the snow cover was not yetestablished and heat loss at the surface resulted in areduction of near-surface ground temperature (Fig. 1b).Freezing extended along the whole survey line andreaches a depth of 2 m. From October 1999 to April2000 resistivities increased only slowly due to the insu-lating snow cover, which arrived in October and effec-tively decoupled the subsurface thermal regime fromthe atmosphere. Heat conduction allowed a reduction intemperature at greater depths, subsequently freezingdeeper layers. This gradual downshift of the freezingfront can be visualised by plotting ratios of successiveresistivity measurements instead of cumulative differ-ences (Hauck 2002, not shown here). During the phasetransition, the temperatures remained close to 0°C (theso-called zero-curtain effect), while the resistivitiesincreased as the unfrozen water content diminished.

From the borehole temperature data shown in Figure 2it is seen that the zero-curtain effect started at the end ofOctober and lasted until end of December at 0.4 mdepth and until beginning of February at 4 m depth.

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Figure 1. (a) Resistivity model for the measurement on 15.9.1999 as determined by the inversion. (b)–(k) Resistivity differenceper day based on the September measurement (a). White and dark shading denote resistivity increase and decrease, respectively.

In the beginning of May the temperatures near thesurface approached 0°C and melting of the uppermostlayer started. Again, temperatures remained almost con-stant at 0°C during the phase transition. At the time ofthe first “summer” resistivity measurement (June 2000),most of the frozen water in the uppermost 23 m hadalready melted which led, together with additional waterinput by rain, to a wet soaked surface layer, decreasingthe resistivity strongly near the surface (grey colors inFigure 1g). Between June and July 2000, temperaturesincreased at all depths down to 10 m with a correspon-ding resistivity decrease throughout the major part ofthe survey area. This decrease continued until end ofAugust 2000, thereby almost totally equalizing theresistivity increase of the winter months (Figure 1k).A more detailed analysis of the resistivity results canbe found in Hauck (2001).

Comparing all resistivity measurements at the bore-hole location versus the corresponding temperatures a small but linear increase is found for decreasing butstill positive temperatures, showing good agreementwith the values calculated from Equation (3) (seeHauck (2002) not shown here). Below the freezingpoint 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 differentdepths. These values can then be used to calculate theunfrozen water content S (see below).

4.2 Comparison between energy balance, groundtemperature and resistivity evolution

The dominant role of snow cover evolution can berevealed by comparing it to temperature change in theborehole, the radiation balance and the total resistivity

variation at the borehole location (Figure 3). A perma-nent snow cover was established at the end of October(Figure 3c) and persisted until mid-June. During thattime the temperature within the uppermost 10 m of theborehole remained almost constant (Figure 3a), as theground temperature regime was effectively decoupledfrom atmosphere and temperatures stayed at the freez-ing temperature of the ground. The net radiation(being the dominant energy flux, see Hoelzle et al.(2001)) during that time is negative, meaning thatcooling takes place at the snow surface (Figure 3b).But as the energy flux through the snow cover is neg-ligible during winter (less than 1 W/m2, Figure 3e),the freezing processes in the subsurface can only beinduced by the cold October temperatures, which pene-trated into the ground before the snow cover arrivedand propagated to larger depths through heat conduc-tion. After the melting of the snow cover in June, tem-perature variability in the borehole is high, coincidingwell with the observed variability of the radiation bal-ance (Figure 3b). This agreement confirms again thedominant role of the radiation balance for groundtemperatures in mountain permafrost terrain.

Figure 3d shows the evolution of the unfrozen watercontent, which was calculated using Equation (5). Theparameter b was chosen from the respective resistivity–temperature relation as introduced in Hauck (2002).The results for two different values for the saturationexponent n and for four depths are shown. In the upper-most layer (0.5 m) the unfrozen water content starts to decrease at the end of October, corresponding tothe onset of the negative radiation balance seen inFigure 3b.

The minimum is reached in February and subse-quently later at greater depth (beginning of June at8.7 m depth). At larger depths the evolution of S isnearly sinusoidal, corresponding to the seasonal vari-ation of ground temperature. The minimal value of Sis smallest at larger depths (0.2–0.3 below 6 m forn 2) and largest at intermediate depths (0.6–0.8 at2–4 m for n 2), but depends on the choice ofparameters b and n. The larger n, the smaller the vari-ations of S. King et al. (1988) examined a large numberof permafrost samples from the North American Arctic.At �2°C they found unfrozen water contents as highas 0.9 (clay) and as low as 0.2 (sands) depending onthe material type.

Finally, Figure 3f shows the total resistivity variationat the borehole location, calculated as weighted verti-cal mean (�(rihi)/z, where z is the model depth and hiis the thickness of the individual resistivity model lay-ers). Total resistivities increase steadily until a maxi-mum is reached for the April measurement. Fromthere, resistivities decrease again until September 2000,where a slightly larger value than the initial value inSeptember 1999 is reached. It is notable that the strong

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Figure 2. Borehole temperatures with time at 4 differentdepths (PACE borehole 51/1998).

resistivity increase during winter coincides with analmost zero total temperature change in the borehole(Figure 3a).

5 CONCLUSION

Time-lapse resistivity tomography measurements at amountain permafrost site have been presented in com-bination with borehole temperature and energy bal-ance data. A set of eleven DC resistivity tomographymeasurements were performed between September1999 and September 2000 using a fixed electrode arrayat Schilthorn, Switzerland. The resulting resistivitychanges were analysed in terms of subsurface freezeand thaw processes. Key results from this multi-parameter data set include:

• Temporal resistivity changes in high Alpine envi-ronments can be accurately determined using a fixedelectrode array, which is accessible throughoutwinter.

• Maximum resistivity changes were observed inautumn (September–October), before a perma-nent snow cover was established, and in late spring (May–June), when the thawing snow cover andadditional water from precipitation greatly decreasedthe resistivity values in the active layer.

• During winter, the snow cover effectively decou-ples the ground from atmospheric influences. Theheat flux through the snow cover was less than1 W/m2, estimated from energy balance measure-ments. Consequently, the small but steady resistiv-ity increase observed during winter was solely dueto temperature reduction by heat conduction fromupper to lower layers. From December to May thefreezing front moved gradually downward, reach-ing 6 m in mid-April. After the start of the meltingseason the resistivities decreased until the previousSeptember values were reached again at the end ofAugust 2000.

• Resistivity–temperature relationships between the resistivity values at the borehole location and

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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 atthe borehole location (weighted vertical mean).

borehole temperatures show good agreement withtheory. The increase of resistivity with decreasingtemperature is small and linear for temperaturesabove the freezing point and exponential for tem-peratures below freezing.

• The calculated temporal evolution of the unfrozenwater content shows a strong decrease during the winter months in the active layer and a quasi-sinusoidal behaviour below.

• A comparison between borehole temperatures,resistivity and energy balance data emphasizes thedominant role of the snow cover evolution in winterand net radiation in summer. In addition, resistivitymonitoring may be used to determine the amount offreezing and thawing in the subsurface in futurelong-term monitoring programmes.

ACKNOWLEDGEMENTS

The authors would like to thank the SchilthornbahnAG for logistic support and C. Mittaz and M. Hoelzle(Glaciology and Geomorphodynamics Group,University of Zurich) for supplying the energy bal-ance data. This study was financed by the PACE pro-ject (Contract Nr ENV4-CT97-0492 and BBW Nr97.0054-1). C. Hauck acknowledges a grant by theGerman Science Foundation (DFG) within theGraduiertenkolleg Natural Disasters (GRK 450).

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