Regional-scale permafrost mapping using the TTOP ground temperature model

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1 Permafrost, Phillips, Springman & Arenson (eds) 2003 Swets & Zeitlinger, Lisse, ISBN Regional-scale permafrost mapping using the TTOP ground temperature model J.F. Wright, C. Duchesne & M.M. Côté Geological Survey of Canada, Ottawa, Canada ABSTRACT: The TTOP model predicts the mean annual ground temperature at the base of the seasonal freeze/ thaw layer, using relatively simple parameters representing key climate and terrain factors influencing the ground thermal regime. The technical performance of TTOP is evaluated through a comparison of its outputs to those of a finite-element heat conduction model. The TTOP model was calibrated for the Mackenzie region using observations of permafrost occurrence and thickness at 154 geotechnical borehole sites along the Norman Wells Pipeline right-of-way. The calibrated model correctly predicts the occurrence of permafrost at 87% of geotechnical borehole sites. TTOP-based estimates of permafrost thickness are in general agreement with estimates of permafrost thickness derived from ground temperature profiles at 26 borehole sites instrumented with temperature cables. Given its computational simplicity, the TTOP model is well suited for regional-scale GIS-based mapping applications, and investigations of the potential impacts of climate change on permafrost. 1 INTRODUCTION The permafrost regions of Canada encompass more than 50% of Canada s landmass. The current benchmark publication Permafrost in Canada (Hegginbottom et al., 1995) depicts broad contiguous zones of either continuous or discontinuous permafrost. However, for the vast majority of Canada s northern territories, little direct information exists regarding the actual distribution and thickness of permafrost. While informative in a general sense, the permafrost map of Canada is of limited utility for practical engineering applications or as a basis for assessing the regional/sub-regional impacts to terrain as a consequence of climate warming in Canada. Modeling of the ground thermal regime provides a means for assessing the likely extent of permafrost, and for predicting permafrost response climate change. In this context, a useful model must link ground thermal conditions to atmospheric (climatic) forcing factors, which ultimately determine ground temperatures. In most natural settings this linkage is indirect, subject to the modulating influences of intervening surface vegetation and winter snow cover: the buffer layer (Luthin and Guymon, 1974). There have been a number of efforts towards the development of a generalized physical model for describing ground thermal conditions at regional and sub-regional scales. A simple relation offered by Carlson (1952) as the approximate criteria for permafrost formation considers thawing and freezing degree-day indices and the seasonal (frozen and unfrozen) thermal conductivities of the substrate. Nelson and Outcalt (1983) delineated permafrost boundaries using a Stefan-based frost index number, which employs seasonal (thawing and freezing) degree-day indices, snow cover, and the thermal properties of the substrate. Jorgenson and Kreig (1988) improved Carlson s relation by incorporating seasonal n-factors (Lunardini, 1978) to represent the influences of surface vegetation and snow cover, and a potential insolation index (Lee, 1964) to account for topographic situation. However, index methods are of little utility for addressing the impacts of climate change, as they do not explicitly define relations between climate and ground temperature. 2 THE TTOP MODEL Smith and Riseborough (1996) and Riseborough and Smith (1998) have presented an explicit formulation of the climate-permafrost system that provides a functional framework for analyzing the influence of climate, terrain and lithologic factors on the temperature condition and distribution of permafrost (TTOP model). Henry and Smith (2001) applied the TTOP model at national scale to map ground temperatures in the permafrost regions of Canada. While Smith and Riseborough (2002) have used the TTOP model to define the climatic and environmental conditions that determine the limits of permafrost zones under conditions of thermal equilibrium. The TTOP model links ground temperatures to the atmospheric temperature regime through the use of seasonal n-factors (Lunardini, 1981), which provide a highly simplified representation of the influence of the buffer layer in modulating heat exchange between the atmosphere and the ground surface. The model assumes a homogeneous substrate and that a state of thermal equilibrium exists (on a year to year basis) between the atmosphere and the ground thermal regime. 1241

2 The TTOP Relation: TTOP Kt Kf ( nt DDT nf DDF) Where: TTOP Temperature at the top of permafrost K t Thermal conductivity of unfrozen ground K f Thermal conductivity of frozen ground DDT Air thawing index (degree days) DDF Air freezing index (degree days) n t Thawing n-factor n f Freezing n-factor P Annual period (365 days) 2.1 The technical performance of the TTOP P The technical performance of the TTOP model was evaluated through comparison of its outputs with predictions of the temperature at the top of permafrost generated by a TONE, a one-dimensional finite-element heat conduction model (Goodrich, 1982). An equilibrium solution may be obtained by allowing the TONE to run until no further changes in ground temperature occur at successive time steps. Note that TONE may be configured to utilize climate and terrain parameters that are virtually identical to those employed in the TTOP relation. Analysis of TONE outputs indicates that the mean annual temperature at the top of permafrost corresponds closely to the minimum temperature observed in the mean annual ground temperature (MAGT) profile (Figure 1). Below this point, the ground temperature profile is linear (assuming a homogeneous substrate), and thus an estimate of permafrost thickness may be obtained by extrapolating along the geothermal gradient to 0 C. ground temperature (ºC) active layer active layer A series of twinned model runs were executed in which sets of identical parameter values (represented a broad range of hypothetical climate and terrain conditions) were employed in both models. Results indicate that TTOP outputs are virtually identical to predictions of the equilibrium temperature at the top of permafrost generated by TONE (Wright et al., 2001). This comparison suggests that the TTOP model can reliably predict the equilibrium temperature at the top of permafrost, provided that the parameter values employed adequately represent local site conditions. 3 MODEL PARAMETERIZATION The establishment of model parameter values that adequately reflect actual site conditions is critical for the successful utilization of TTOP for regional/sub-regional permafrost modeling and mapping. Reliable information about local terrain and ground thermal conditions must be acquired for a sufficient number of sites to support calibration of the model for application within any given geographic area. A set of 154 geotechnical borehole records was selected from a database describing 270 boreholes drilled as part of Interprovincial Pipe Lines (1982a) program to acquire stratigraphic data along the Norman Wells Pipeline right-of-way (Figure 2). Selected boreholes were situated well within the discontinuous permafrost zone in undisturbed terrain between KP 270 and KP 700, to ensure an equitable distribution of permafrost bearing versus non-permafrost sites. Permafrost was observed at 85 of 154 sites (55%). Maximum borehole depth was typically about 10 meters, so it was not possible to determine the depth of permafrost beyond borehole limits. KP 0 Norman Wells Great Bear Lake 65 N Depth below surface (m) mean annual ground temperature at the top of permafrost (TTOP) point of zero annual amplitude Base of active layer occurs where maximum ground temperature = 0ºC permafrost unfrozen km Wrigley Fort Simpson Liard R.Mackenzie River KP N W 120 W Figure 1. Generalized representation of a ground temperature profile through permafrost. Figure 2. Site map showing the approximate location of the Norman Wells Pipeline right-of-way. 1242

3 Borehole records provided information about the dominant surficial soil unit and the presence or absence of permafrost at each site. A generalized description of vegetation cover at each borehole location was obtained from Interprovincial Pipe Lines (1982b) geophysical survey. 3.1 Degree-day indices A simple method for describing the atmospheric temperature regime along the pipeline right-of-way (ROW) was adopted for the borehole modeling. Mean annual air temperatures (MAAT) for Norman Wells, Wrigley and Fort Simpson (at KP 0, KP 270 and KP 531 respectively) were converted to thawing and freezing degreeday indices by integration of a sinusoidal annual temperature wave having an amplitude of 23 C. This reflects the regional range in annual temperatures as indicated in the Canada Climate Normals (Environment Canada, 1982). Linear fitting of the data produced equations describing relations between seasonal degreeday indices and kilometer post (KP) location. Degreeday indices for individual borehole sites were obtained through interpolation or extrapolation of these relations. 3.2 Thermal conductivity and soil moisture This modeling adopts Johansen s (1975) equations for estimating frozen and unfrozen thermal conductivity (K f, K t ) of the substrate based on specifications of soil texture, dry bulk density, quartz content, and soil water content. Dry density values for the various surficial units reflect average values determined from borehole records. Quartz contents of 18% and 50% were assumed for fine-grained and coarse-grained soils respectively. However, Riseborough and Smith (1998) showed that the conductivity ratio is largely insensitive to soil mineralogy. Soil moisture content is expressed in terms of the saturation ratio (S r ). Jorgenson and Kreig (1988) provide guidelines for determining relations between vegetation cover and soil moisture conditions. Note that any given surficial soil unit may exhibit a range of seasonal thermal conductivity values, depending on local soil moisture conditions (Table 1). Table 1. geology. Model parameters associated with surficial Dry Density K t K f Surficial unit Kg/m 3 W/m/ C W/m/ C Colluvial Lacustrine Aeolian Glaciofluvial Alluvial Glacial till Organic N-factors and model calibration Surface vegetation and winter snow cover modulate heat exchange between the atmosphere and the ground surface. In the modeling, this effect is accommodated through modification of thawing and freezing air indices (DDT, DDF) according to the values of seasonal n-factors (n t, n f ). This affords a highly simplified expression of the combined influences of a variety of heat transfer processes (e.g. conduction, convection, transpiration) occurring continuously and/or seasonally within the buffer layer (Lunardini, 1981). In this work the influence of snow cover in winter is assumed to be implicit in n f. Limited n-factor data for vegetated surfaces are presented in Lunardini (1981) and Jorgenson and Kreig (1988), but neither source is specific to the Mackenzie valley. Unfortunately, n-factors calculated from shortterm air/ground temperature data exhibit a high degree of spatial and temporal variability (e.g. Taylor 1995), and so are unlikely to adequately reflect the long-term influence of vegetation and snow cover on ground temperatures. An initial model run employed n-factor values suggested by Jorgensen and Kreig (1988) for vegetated surfaces in an Alaskan sub-arctic environment (Table 2). These initial values were iteratively adjusted in successive model runs to obtain an optimum number of correct model predictions. Assuming that Johansen s (1975) equations provided reasonable estimates of frozen and unfrozen thermal conductivities, then the derived n- factors may be considered as effective long-term values, which satisfactorily reproduce the observed distribution of permafrost within the geotechnical borehole dataset. 4 RESULTS OF BOREHOLE MODELING The calibrated model correctly predicted the occurrence of permafrost at 134 of 154 geotechnical borehole sites Table 2. Model parameters associated with vegetation cover. Vegetation Jorgensen & Kreig Derived Cover nt nf nt nf Sr Upland spruce Open black spruce Closed blk. spruce Pine Poplar (aspen) Birch Alder (shrub) Sedge fens* Peat bog Mixed forest* Tundra* * class not represented in borehole dataset. 1243

4 (87%). The model also performed well within individual categories of vegetation cover and surficial geology (Table 3a, b). Correct predictions were obtained in % of cases within the various categories of surficial geology, with the exception of glaciofluvial deposits (75% correct). It should be noted that there were only 8 boreholes situated on glaciofluvial deposits, and only 6 sited on alluvial deposits. The comparatively modest prediction accuracy within the glacial till category (80%) is probably due to the relatively high degree of spatial variability with respect to physical/thermal properties of different till deposits. Model predictions of the presence/absence of permafrost were better than 85% correct for all vegetation categories except deciduous forests, for which 15 of 20 cases (75%) were correctly predicted. Note that the presence of permafrost was indicated at 8 of 20 deciduous sites. It is possible that some of these sites may have been incorrectly categorized in the field due to the presence of deep seasonal frost. Of the 20 prediction errors overall, the TTOP model failed to predict the presence of permafrost (as indicated by borehole records) at 12 sites. In the other 8 cases, TTOP predicted the presence of permafrost at sites where no permafrost was observed. 4.1 Predictions of permafrost thickness Limited information about permafrost thickness was obtained from temperature profiles at 26 boreholes Table 3a. Borehole modeling results by surficial soil unit. Observed TTOP predictions Surficial # of unit sites F U # correct % correct Colluvial Lacustrine Aeolian Glaciofluvial Alluvial Glacial till Organic Overall F Frozen, U Unfrozen. Table 3b. Borehole modeling results by vegetation category. Observed TTOP predictions # of Vegetation sites F U # correct % correct Upland spruce Black spruce Pine Deciduous Sedge fens Peat bogs Overall instrumented with 20 m temperature cables, and located in undisturbed terrain adjacent to the pipeline ROW (Pilon et al., 1991). TTOP modeling employed parameter values consistent with those established for the larger set of 154 geotechnical boreholes. Figure 3 presents TTOP predictions of permafrost occurrence and thickness at these sites. Estimate permafrost thickness were obtained by extrapolating from the predicted MAGT at the top of permafrost, along the geothermal gradient to 0 C. The geothermal gradient is a function of the thermal conductivity of the substrate, and an assumed regional geothermal heat flux of 0.04 Wm 2 (Williams and Smith, 1989). The TTOP model correctly predicted the presence or absence of permafrost at 24 of 26 borehole sites (92%). The pattern of TTOP predictions of permafrost thickness is in good general agreement with estimates of permafrost thickness interpreted from ground temperature logs. A tendency for under-prediction of thick permafrost in the northern portion of the ROW may be explained by a general state of thermal disequilibrium existing between regional climate and ground temperatures at depth (reflecting a cooler regional climate prevailing a century or more ago, perhaps during the Little Ice Age), while thinner permafrost in southern portion of the transect would have responded more quickly to a regional warming during the intervening time period. 5 SPATIAL MODELING WITH TTOP The TTOP model correctly predicted the presence/ absence of permafrost at 158 of 180 borehole sites (87.8%) within the combined borehole datasets. Modeling parameters were keyed to highly simplified classifications of surficial geology and vegetation cover, at a level of detail comparable to that generally inherent in regional-scaled maps. Such maps constitute core Permafrost Thickness (m) TTOP Prediction Estimated From Temperature Logs Approximate KP Location Figure 3. TTOP predictions of permafrost thickness at 26 instrumented borehole sites. 1244

5 elements of the available spatial data that can practically be brought to bear on the problem of estimating the distribution of permafrost over extensive areas. Modeling results suggest that this level of detail adequately differentiates terrain conditions along the borehole transect, with respect to the generalized influences of terrain on the presence or absence of permafrost. The TTOP model was implemented within ArcView and ArcInfo spatial analysis platforms and subsequently applied to regional-scale modeling of ground thermal conditions within the broader Mackenzie River valley, and the prediction of the geographic extent of permafrost (see Wright et al., 2001). A brief summary of this work follows. A 1 km resolution database compiled in support of geothermal modeling within the broader Mackenzie River Valley between 60 N (Alberta border) and 70 N (Beaufort Sea), consisted of: 1 Landcover classification for Canada based on 1 km 2 multi-spectral AVHRR imagery acquired by the NOAH series of geostationary orbiting satellites (CCRS, 1999). 2 Digital version of 1:1,000,000 surficial geology maps of the Mackenzie Valley and adjacent areas (Aylsworth et al., 2000). 3 Digital versions of 1:2,000,000 maps showing the distribution of organic terrain in the Mackenzie Valley (Aylsworth and Kettles, 2000). 4 A digital elevation model (DEM) of the broader Mackenzie River valley compiled from NTDB (National Topographic Database) products and resampled to 1 km resolution (Wright et al., 2001). 5 Spatial interpolation of thawing and freezing degreeday indices for the Mackenzie Valley (Wright et al., 2001) based on Climate Normals (Environment Canada, 1982). Reclassification and integration of the primary map layers produced a classification scheme consistent with that employed in the borehole modeling, thus facilitating utilization of the parameter values established in Table 1. Note that some vegetation classes encountered in the spatial modeling (sedge fens, mixed forest and tundra) were not represented in the borehole dataset. Topographic influences were represented by the potential insolation index (Ip) calculated on basis of local slope and aspect determined from the regional DEM. TTOP predictions of ground temperature were subsequently used for estimating the distribution and thickness of permafrost within the broader Mackenzie River valley (Figure 4). The modern (active) Mackenzie delta was excluded from the modeling due to the presumed dominance of non-conductive heat fluxes, as was all terrain above 700 m elevation. TTOP predictions of ground temperature ranged from between 0.5 to 2 C at the Figure 4. TTOP predictions of the distribution and thickness of permafrost in the Mackenzie River Valley. southern boundary (at the Alberta/NWT border, to colder than 10 C at the northern edge of Richards Island and the Tuktoyaktuk Peninsula. In general terms, the north-south distribution of ground temperatures agrees very favorably with limited ground temperature data for the Mackenzie valley presented by Judge (1973), and with a larger number of ground temperature measurements in the GSC s Ground Temperature Database for Northern Canada (Smith and Burgess, 2000). Visual interpretation of Figure 4 suggests that the transition between the discontinuous and continuous zones occurs somewhere between Norman Wells and Fort Good Hope. This is in good agreement with the boundary as placed by Hegginbottom et al. (1995). 6 CONCLUSIONS A simple functional relation (TTOP) has been shown to provide estimates of the equilibrium temperature at the top of permafrost nearly identical to those generated 1245

6 by sophisticated finite-element methods. A set of model parameter values representing the dominant climate and terrain factors influencing the ground thermal regime in the Mackenzie River valley was established by optimizing the performance of the TTOP model using a dataset of 154 geotechnical boreholes located along the Norman Wells Pipeline right-of-way. These parameter values were assumed to be transferable to the broader Mackenzie valley, given that the range of terrain conditions encountered at borehole sites are generally representative of the surficial geology and vegetation cover types in the broader region. Spatial modeling at 1km 2 resolution produced a map of permafrost distribution and thickness in the broader Mackenzie River valley, north of 60 N that is in good general agreement with currently available information. REFERENCES Aylsworth, J.M., Burgess, M.M., Desrochers, D.T., Duk-Rodkin, A., Robertson, T., and J.A. 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