Freezing n-factors in discontinuous permafrost terrain, Takhini River, Yukon Territory, Canada

Permafrost, Phillips, Springman & Arenson (eds) 23 Swets & Zeitlinger, Lisse, ISBN 9 589 582 7 Freezing n-factors in discontinuous permafrost terrain, Takhini River, Yukon Territory, Canada K.C. Karunaratne & C.R. Burn Department of Geography and Environmental Studies, Carleton University, Ottawa, Canada ABSTRACT: Air, near-surface ground temperatures, and snow depths were measured for three consecutive years at five sites in Takhini River valley. At two of the sites snow cover was manipulated either by clearing or with a snow fence. The effect of snow cover on the freezing n-factor, a ratio of surface to air freezing index, was assessed. The mean n-factor was high at sites where the snow cover was thin or absent, and low at sites where the snow cover was thick, and ultimately depended upon the snow-depth-days for each season. Inter-annual variation in the freezing n-factors was up to 3%, and between site variation was 2%. 1 INTRODUCTION Numerical models of permafrost distribution predict the ground thermal regime at a site (Jorgenson & Kreig 1988; Henry & Smith 22), and commonly such models use estimates of ground surface temperature as an upper boundary condition (Smith & Riseborough 1996). However, ground surface temperature has greater local spatially variability than air temperature, and has only been monitored at a few sites with permafrost (Taylor 1995; Klene et al. 21). As a result, surface temperatures are often estimated from air temperatures through the use of n-factors, ratios of the ground surface freezing or thawing index to the air freezing or thawing index (Lunardini 1978). The n-factor summarizes the surface energy balance for a site, and is affected by the surface conditions which control microclimate (Klene et al. 21). While n-factors are attractive due to the simplicity inherent in their determination and application, their physical relation to surface conditions remains undefined. In the discontinuous permafrost zone, correct application of n-factors is critical in predicting permafrost presence. In this paper, air and near-surface temperatures measured at five sites in the discontinuous permafrost of Takhini River valley, Yukon Territory, will be used to examine the effect of snow on the freezing n-factor (n f ). The purposes of this paper are (1) to examine the relation between air and surface temperature during winter; (2) to present data on n f for five sites of varying surface characteristics over three consecutive winters; and (3) to show that site-to-site and inter-annual variation in n f are caused by variation in snow cover. 2 STUDY AREA The study area is 5 km west of Whitehorse in Takhini River valley, southern YT. The sides of the 8-km-wide valley have a morainic cover, while the valley floor is a glaciolacustrine plain (Klassen 1979). The glaciolacustrine deposits, up to 12 m thick, are underlain by sand (Rampton et al. 1983). Whitehorse Airport, which has an mean annual temperature of 1. C, is slightly warmer than Takhini River valley, possibly because of cold-air pooling in the valley floor during winter (Burn 1998). Takhini River valley lies in the sporadic discontinuous permafrost zone (Heginbottom et al. 1995); about 2% of the terrain is underlain by permafrost (Rampton et al. 1983). The valley lies in the rain shadow of Coast Mountains, and the climate is relatively dry (Wahl et al. 1987). In July 1958, much of Takhini River valley was burned by forest fires that destroyed the spruce forest and soil organic horizon. A few stands of spruce were not burned, but in other areas vegetation regeneration has been slow due to the severity of the fires and the aridity of the climate (Burn 1998). 2.1 Study sites In summer 1994, two sites were established to study the relation between air and ground surface temperature in unburned forest and in an adjacent burned area, hereafter called the forest site and the burned site respectively. The forest site is dominated by mature Picea glauca, and has a 1-cm thick organic horizon. Permafrost underlying the forest site is in equilibrium with the surface conditions, because the temperature profile is linear (Burn 1998). The active layer is 1.4 m thick and the base of permafrost is at a depth of 18.5 m (Burn 1998). The mean annual ground temperature at the site is.8 C (Smith et al. 1998). The burned site is now unevenly covered with Populus tremuloides, Pinus contorta, Picea glauca, and Salix spp. saplings, and the organic horizon has not yet redeveloped (Burn 1998). The forest fire initiated permafrost degradation and the active layer is now nearly 4 m thick. 519

A snow manipulation experiment to examine the effect of snow cover on the relation between air and ground surface temperature, was initiated in an open meadow 2 km from the forest site in summer 1997. The meadow is covered with grasses and is not underlain by permafrost. There are three experimental sites in the meadow. The snow conditions are not manipulated at a control site called the meadow site. Each winter since 1997 98 snow has been removed every two weeks from a 15 m by 15 m plot, adjacent to the meadow site. A snow fence was erected at a third site to increase the snow depth. These sites are referred to as the cleared and snow fence sites respectively. 2.2 Snow conditions at the study sites Snow characteristics for the five study sites are summarized in Table 1. The maximum snow depth has been greatest at the burned site due to willows that break the wind but do not intercept the snowfall. There has been considerable inter-annual variation in the maximum snow depth at this site (22 34 cm). The trees at the forest site intercept much of the snowfall resulting in a relatively low snow depth, which has been more consistent than at the other sites (18 21 cm). The maximum snow depth at the meadow site is greater than in the forest and, as at burned site, is variable from year to year (18 33 cm). Near the snow fence, the snow depth has been similar to the meadow site during the first part of the season, but has regularly been higher later in the season. After mid-february the snow depth at the meadow and forest sites has declined, but at the snow fence and burned sites the thick snow cover has persisted for another month. 3 FIELD METHODS Air temperature was measured at the forest and burned sites in a radiation shield 1.8 m above the ground surface and ground temperature was measured 2 cm below the surface. Data were collected five times daily (at 4 h 48 min intervals) on HOBO TM miniature data loggers. The precision of the measurements was.11 C. At the cleared, snow fence, and meadow sites, thermistors were installed to measure ground temperature at 2 cm depth five times daily. These measurements were also recorded on HOBO TM data loggers. We have assumed that air temperature at the burned site represented conditions in the meadow, because both sites were unshaded and were 5 m apart. However, the burned site is 1 C warmer than the shaded forest site throughout the year (Burn 1998). Snow depth was measured at each site every two weeks beginning in winter 1997 98. 4 RELATION BETWEEN AIR AND NEAR-SURFACE TEMPERATURE Figure 1 is a scatter plot of daily mean near-surface ground temperature and daily mean air temperature at the forest site for winter 1999. This relation can be summarized through the functional fit, in this case the principal axis, because the measurements of air and near-surface temperature have equal precision (Mark & Church 1977): T sfc.28t a 3.4 (1) where T sfc is the near-surface temperature and T a is the air temperature. Due to the large sample size (n 15) the correlation between near-surface and air temperature is significant at the 98% confidence level, but there is considerable scatter about the principal axis. The scattered points can be divided into two subseasonal groups: early and late winter. The elliptical pattern of the data in Figure 1 indicates conduction of heat through the snow pack and phase lag of ground temperature at depth (Beltrami 1996). Since snow characteristics change throughout the winter, the influence of snow on the relation between air and near-surface ground temperature is variable. Table 2 presents the slopes of the principal axes, and Table 1. Summary of snow characteristics at study sites in the Takhini valley for winters 1997 98, 1998 99, 1999. Data are the means for the period of record. Snow characteristics Forest Burned Meadow Snow fence Cleared Mean maximum snow depth (cm) 19 28 24 26 Mean snow depth Dec (cm) 11 16 11 11 Mean snow depth Mar (cm) 1 24 17 2 Mean duration of snow cover (wks) 21 2 21 21 Mean snow depth Dec to Feb 1997 98 (cm) 11 23 15 19 Mean snow depth Dec to Feb 1998 99 (cm) 17 29 28 28 Mean snow depth Dec to Feb 1999 (cm) 3 18 7 12 52

the coefficients of determination (r 2 ), for the relations between air and near-surface ground temperature at the five study sites. Snow depth is associated with the slope of the principal axis: the slope of the line is high at the forest and cleared sites where the snow cover is thin, and low at the burned and snow fence sites where the snow cover is thick. The slopes are higher in the forest than at the cleared site due to the greater soil heat flux in the meadow, supplied by latent heat released by frost penetration throughout the winter. This heat flux maintains a higher ground temperature. Burn (1998) proposed that the slope of the principal axis for the relation between air and near-surface temperature would be analogous to the n-factor if the intercept of the function was close to the origin, perhaps within 1 C. Estimating the n-factor by the principal axis then indicates its precision via r 2. This method yields a summary of the relation between air and ground surface temperature on a daily, rather than a seasonal, basis, which may be accomplished through the use of air and surface freezing indices. Near-surface ground temperature (ºC) -4-8 -12-16 -2 T sfc =.28 T a - 3.4 r 2 =.25-4 -3-2 -1 1 Air temperature (ºC) Figure 1. Air (T a ) and near-surface ground temperatures (T sfc ) at the forest site winter 1999, Takhini River valley, YT. The fitted line is the principal axis of these data. 5 CALCULATION OF FREEZING N-FACTORS Freezing n-factors were computed for the study sites using accumulated seasonal air and near-surface freezing degree-days (FDD): n f FDDs FDD a (2) where FDD s is the freezing degree-days for the nearsurface ground temperature, and FDD a is the freezing degree-days for the air temperature. Freezing degreedays were computed using daily mean air temperature and daily mean near-surface temperature. Ideally, n-factors should be computed using surface temperature, however an appropriate depth at which to estimate surface temperature is slightly beneath the surface, e.g. 1 5 cm. During the winter the near-surface has a high diffusivity, which results in similar daily mean temperatures at 5 cm and 2 cm. Therefore, we assume that ground temperatures measured at 2-cm depth are a reasonable estimate of the surface temperature, although the 2 cm temperature will overestimate T sfc at the beginning of winter. For this paper, calculation of FDD only used days within the season when the air and near-surface temperature were both below C; any temperature measurements above C were not included in the FDD total. Since air and near-surface temperature rarely drop below C or rise above C simultaneously, the beginning and the end of the n-factor season must be defined. The near-surface temperature was used to define the season, rather than air temperature, because of the high variability in air temperature. The season was defined when near-surface temperatures were below C. The calculated value of n f changes by no more than.2, or 4%, when air temperature was used to define the season, because temperatures at the beginning and end of the season are of low magnitude and contribute little to the total FDD. 5.1 Seasonal evolution of the freezing n-factor The value of n f evolves over the winter as FDD a and FDD s totals progressively increase. To illustrate the Table 2. Slopes of the principal axis for the relation between air and near-surface temperatures and corresponding coefficient of determination (r 2 )*, for the five study sites, Takhini River valley. Forest Burned Meadow Snow fence Cleared 97 98.35 (.54).16 (.47).26 (.51).15 (.45).35 (.48) 98 99.31 (.65).19 (.54).8 (.37).25 (.31) 99.28 (.25).11 (.21).18 (.22).4 (.4).21 (.26) Mean.31.14.21.9.27 521

evolution of n f, daily cumulative n-factors and daily cumulative FDD a and FDD s are presented in Figure 2 for winter 1998 99 from the meadow site. At the beginning of the season n f often fluctuates because both FDD a and FDD s totals are low and therefore sensitive to any added value. As the FDD total increases, the oscillations in n f are damped and the ratio begins to increase. The relative increase in FDD s total is higher than in FDD a, causing n f to rise quickly. If the ground surface experiences a zero curtain, the n f decreases during initial ground freezing because the FDD a increases faster than the FDD s. This decrease is short-lived and n f begins to rise after the zero curtain has lifted. Towards the end of the season the rate of increase in n f declines and eventually the value becomes constant. The stabilization of n f at the end of the season is caused by a decrease in the rate of growth in FDD a as the air temperature rises. In addition, at the end of the season, n f becomes insensitive to additions of daily temperature because of the large FDD a and FDD. Freezing n-factors computed using FDD a and FDD s are presented for the study sites from 1997 to 2 (Table 3). The n f for 1998 99 at the burned site cannot be reported due to failure of the ground temperature sensor. Given similar air temperatures, low n f indicate.6 3 warm surface temperatures, and high n f indicate relatively cold surface temperatures. 6 SNOW COVER AND FREEZING N-FACTORS Although the freezing n-factor varies inter-annually, each study site has a different mean n-factor. The differences in n f, both inter-annually and among the sites, are dominated by variations in snow characteristics. The maximum depth, and duration of a snow cover, as well as the timing and rate of the snow cover development, have been shown to greatly influence the ground thermal regime (Goodrich 1982). The effect of snow on the seasonal evolution of n f can be explored through data from the snow manipulation sites (Fig. 3). At the beginning of the season during initial ground freezing, n f at the cleared and snow fence sites are similar. By mid-winter n f at the snow fence site decreases as low air temperatures are experienced without correspondingly low surface temperatures due to a relatively thick snow cover. In contrast, n f at the cleared site continues to increase because near-surface ground cooling is uninhibited by.6 Cleared.4 2.4 n f n f FDD a FDD n f Snow Fence.2 1.2 FDD s 1999 1998 Figure 2. Daily n-factors and daily cumulative FDD a and FDD s for winter 1998 99 at the meadow site, Takhini River valley. 1998 1999 Figure 3. Daily cumulative n-factors at the cleared and snow fence sites for winter 1998 99. Table 3. Freezing n-factors computed using air and near-surface FDD for the five study sites, Takhini Valley. Forest Burned Meadow Snow fence Cleared 97 98.56.3.45.31.53 98 99.48.4.32.56 99.57.34.55.33.57 Mean.54.32.47.32.55 522

snow cover. At the end of the season n f is higher at the cleared site than at the snow fence site due to the absence of a snow cover. 6.1 Site to site variations in n f as a result of different snow characteristics The rank order of snow depths is inverse to the rank order of mean n f for the five study sites (Table 1,3). The thick snow cover at the burned and snow fence sites keeps the near-surface temperatures warm, resulting in low n f (Table 3). The mean n f is highest for the cleared site where snow is absent. At the three sites with natural snow cover, the spatial variation in n f was 2% of the mean. In contrast, the sites with manipulated snow cover had a similar absolute variation in n f, but little inter-annual change. 6.2 Inter-annual variation of n f due to inter-annual changes in snow conditions The inter-annual variation of n f in the Takhini Valley can be explained through examination of yearly differences in snow characteristics. Although the snow depth at the meadow site is slightly lower than at the burned and snow fence sites, and slightly greater than at the forest site, inter-annual differences in snow cover characteristics at the meadow site are representative of those experienced at the other sites (Fig. 4). Each winter had different snow cover characteristics. In winter 1997 98 the snow cover began early in October but remained thin until January when it rapidly increased to 17 cm. The following winter the 35 3 1998-1999 snow cover began later, but was almost twice as deep by February. In 1999 a thick snow cover developed early in the season but diminished by the end of December. A longer period of snow cover or a higher snow depth may decrease n f by inhibiting heat loss. However, at the meadow and forest sites n f was lower for winter 1998 99 than for winter 1997 98 even though the duration of snow cover was 6 weeks longer in 1997 98, and n f was higher in 1999 than in 1997 98 even though the maximum snow depth was higher in 1999. Rather, n f is a function of both the duration and depth of the snow cover. Throughout the season n f is inversely related to cumulative snow-depth-days (similar to degree-days). The relation can be identified through examination of daily cumulative snow-depth-days and cumulative n f (Figs 5, 6). The cumulative n f during December was lowest in 1999 and highest in 1998 99 due to each year s respective snow-depth-days at this time. As the season progressed the rate of increase of snow-depth-days declined in 1999, and resulted in a rapid increase in n f. In 1998 99 the snow-depth-days increased after December and caused n f to remain relatively constant through the rest of the season. In December 1997 98 the accumulated snow-depth days were fairly high because of the early snow season, and by January the rate of increase of snowdepth-days was almost constant. This caused n f to rise gradually over the season. Overall, Table 3 indicates inter-annual variations in n f of 2, 3, and 1% at the forest, meadow, and burned sites respectively. The inter-annual variation was 8 and 6% at the cleared and snow fence sites respectively. 3 1998-1999 25 Snow depth (cm) 2 15 1 1997-1998 1999-2 Snow-depth-days (cm d) 2 1 1997-1998 1999-2 5 Figure 4. Snow depths at the meadow site for winters 1997 98, 1998 99, and 1999. Figure 5. Daily cumulative snow-depth-days at the meadow site for winters 1997 98, 1998 99, and 1999. 523

n f.6.4.2 7 CONCLUSION This study shows that: 1. variations in snow cover within a small area caused by differences in vegetation, result in variations for n f of 2%; 2. n f varies inter-annually by between 1 and 3%; 3. throughout the season n f is inversely related to snow-depth-days. The freezing n-factor is a manageable parameter as it is primarily controlled by snow cover, which is easily measured or estimated from standard meteorological records. ACKNOWLEDGEMENTS Engineering Research Council of Canada, and the Northern Research Institute, Yukon College. Winter fieldwork by Diana, Karen, and Gary White of Whitehorse has been critical to the investigation. The helpful comments of the referees improved the paper. REFERENCES 1997-1998 19 98-1999 19 99-2 Figure 6. Daily cumulative n-factors at the meadow site for winters 1997 98, 1998 1999, and 1999. Beltrami, H. 1996. Active layer distortion of annual air/soil thermal orbits. Permafrost and Periglacial Processes 7: 11 11. Burn, C.R. 1998. The response (1958 1997) of permafrost and near-surface ground temperatures to forest fire, Takhini River valley, southern Yukon Territory. Canadian Journal of Earth Sciences 35: 184 199. Goodrich, L.E. 1982. The influence of snow cover on the ground thermal regime. Canadian Geotechnical Journal 19: 421 432. Heginbottom, J.A., Dubreuil, M.A. & Harker, P.A. 1995. Canada-Permafrost. In National Atlas of Canada 5th Edition. National Atlas Information Service, Natural Resources Canada, Ottawa. Plate 2.1 MCR 4177. Henry, K.A. & Smith, M.W. 22. A model-based map of ground temperatures for the permafrost regions of Canada. Permafrost and Periglacial Processes 12: 389 398. Jorgenson, M.T. & Kreig, R.A. 1988. A model for mapping permafrost distribution based on landscape component maps and climatic variables. In Proceedings, 5th International Conference on Permafrost, Trondheim, Norway, Tapir Publishers. August 2 5, 1988. 1: 176 182. Klene, A.E., Nelson, F.E. & Shiklomanov, N.I. 21. The N-factor in natural landscapes: variability of air and soil-surface temperatures, Kuparuk river basin, Alaska, U.S.A. Arctic, Antarctic and Alpine Research 33 (2): 14 148. Klassen, R.W. 1979. Thermokarst terrain near Whitehorse, Yukon Territory. In Current Research, Part A. Geological Survey of Canada, Paper 79 1A, 385 388. Lunardini, V.J. 1978. Theory of n-factors and correlation of data. In Proceedings, 3rd International Conference on Permafrost, Edmonton, Alberta, July 1 13, 1978. National Research Council of Canada. Ottawa, ON. 1: 4 46. Mark, D.M. & Church, M. 1977. On the misuse of regression in earth science. Mathematical Geology 9: 63 75. Rampton, V.N., Ellwood, J.R. & Thomas, R.D. 1983. Distribution and geology of ground ice along the Yukon portion of the Alaska Highway gas pipeline. In Proceedings, 4th International Conference on Permafrost, Fairbanks, Alaska, July 17 22, 1983. National Academy press, Washington, D.C., Vol. 1: 13 135. Smith, M.W. & Riseborough, D.W. 1996. Permafrost monitoring and detection of climate change. Permafrost and Periglacial Processes 7: 31 39. Smith, C.A.S., Burn, C.R., Tarnocai, C. & Sproule, B. 1998. Air and soil temperature relations along an ecological transect through the permafrost zones of Northwestern Canada. In Proceedings, 7th International Conference on Permafrost, Yellowknife, Canada, June 23 27, 1998. National Research Council of Canada: 19 115. Taylor, A.E. 1995. Field measurements of n-factors for natrural forest areas, Mackenzie Valley, Northwest Territories. In Current Research 1995-B; Geological Survey of Canada. 89 98. Wahl, H.E., Fraser, D.B., Harvey, R.C. & Maxwell, J.B. 1987. Climate of Yukon. Environment Canada, Atmospheric Environment Service, Climatological Studies 4. 524