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Modeled impacts of changes in tundra snow thickness on ground thermal regime and heat flow to the atmosphere in Northernmost Alaska
Global and Planetary Change 57 (2007) 235 – 246 www.elsevier.com/locate/gloplacha
Modeled impacts of changes in tundra snow thickness on ground thermal regime and heat flow to the atmosphere in Northernmost Alaska Feng Ling a,⁎, Tingjun Zhang b a b
Department of Computer Science, Zhaoqing University, Zhaoqing, Guangdong 526061, P. R. China National Snow and Ice Data Center, Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO 80303–0449, USA Received 12 March 2006; received in revised form 3 October 2006; accepted 14 November 2006 Available online 29 December 2006
Abstract Seasonal snow covers the tundra surface for up to nine months of each year on the Alaskan North Slope. Variations in the snow thickness could strongly influence the thermal regime of the underlying soil and permafrost, and the surface energy balance. The impacts of increases and decreases in the tundra snow thickness on the thermal regime of snow surface, active layer, and permafrost, and on the conductive heat flow to the atmosphere were investigated numerically, by using an improved surface energy balance approach based onedimensional heat transfer model. The baseline inputs for the numerical model are mean daily meteorological data and surface albedos collected at Barrow, Alaska from 1995 through 1999. Based on a study for the long-term mean daily maximum and minimum snow thickness distributions at Barrow in the snow season of 1948 through 1997, a snow thickness factor was defined and five simulation cases were run for the snow season of 1997–1998 by changing the snow thickness factor. The modeled results indicate that changes in snow thickness have significant impacts on ground thermal regimes and conductive heat flow to the atmosphere. Decreasing the snow thickness by 50% led to the maximum ground temperature decrease of 1.48 °C at 0.29 m depth, and 0.72 °C at 3.0 m depth; the magnitude of the mean conductive heat flow to the atmosphere for December increase of 4.3 Wm− 2. Increasing the snow thickness by 50% resulted in the maximum ground temperature increase of 1.44 °C at 0.29 m depth, and 0.66 °C at 3.0 m depth; the magnitude of the mean conductive heat flow to the atmosphere for December decrease of 1.57 W m− 2. On an annual basis, variation in the snow thickness by 50%, the ground temperature variations of more than 0.25 °C occurred as deep as 8.0 m below the ground surface. The modeled results also show that changes in snow thickness have a relatively small influence on the snow surface temperature. © 2006 Elsevier B.V. All rights reserved. Keywords: Snow thickness; Energy balance; Ground thermal regime; Conductive heat flow; Modeling
1. Introduction Owing to the low air temperature and high wind speed, the thickness of tundra snow on the North Slope of Alaska can vary substantially over distances of a few meters, and ⁎ Corresponding author. Tel.: +86 758 275 2208; fax: +86 758 271 6586. E-mail address: [email protected] (F. Ling). 0921-8181/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.gloplacha.2006.11.009
large year-to-year variations in snow thickness at a specific location can be found (Zhang et al., 1996; Sturm and Holmgren, 1998; Taras et al., 2002). In addition, changes in the arctic shrubs also can significantly modify snow thickness and other snow-related characteristics, because shrubs are taller than other tundra vegetation and can capture and hold more snow (Liston and Sturm, 1998; Sturm et al., 2001; Liston et al., 2002).
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Variations in the snow thickness could strongly influence the thermal regime of the underlying soil and permafrost, and the conductive heat flow to the atmosphere, because the low thermal conductivity of snow insulates the ground, preventing the escaping of heat from the warm ground to the cold atmosphere, or conversely, damping out the cold wintertime temperature signal in the snowpack well before it reaches the ground (Goodrich, 1982; Sturm and Johnson, 1992; Lynch-Stieglitz, 1994; Zhang et al., 1996; Sturm et al., 1997; Zhang et al., 2001;
Ling and Zhang, 2003b, 2004b, 2005; Zhang, 2005; Ling and Zhang, 2006), and because changes in the thickness of tundra snow can significantly affects the length and timing of the snow-free period, and the structural and thermal characteristics of snow cover (Sturm et al., 2001; Liston et al., 2002). Field measurements during 1968–1973 at Garry Island, Northwest Territories, Canada, showed that the snow ground interface temperature varied significantly from site to site within a few hundred meters owing to thickness variations of the seasonal snow cover (MacKay
Fig. 1. Mean daily meteorological conditions collected at Barrow, Alaska, during June 1995 through July 1998.
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and MacKay, 1975). Smith (1975) reported that in the east-central part of the Mackenzie Delta, Northwest Territories, Canada, the seasonal snow cover was the major factor controlling the permafrost temperature during the winter and thus the mean annual permafrost surface temperature. On the Alaskan North Slope, snow covers the tundra surface for up to nine months of each year (Benson and Sturm, 1993; Zhang et al., 1996), the impacts of such change could be significant. Snow cover is the most variable land surface conditions in both time and space in the Northern Hemisphere (Gutzler and Rosen, 1992; Cohen, 1994; Cohen and Entekhabi, 2001), and a crucial parameter in studies of ground freezing/thawing processes, climate change, and weather forecasting (Walsh et al., 1985; Groisman et al., 1994; Gustafsson et al., 2001). The impacts of changes in the extent, timing, duration, accumulation and melting processes, density and structure of seasonal snow cover on the thermal regime of the active layer and permafrost have captured the interest of many investigators (Outcalt et al., 1975; Goodrich, 1982; Foster, 1989; Dutton and Endres, 1991; Foster et al., 1992; Sturm and Johnson, 1992; Zhang et al., 1996, 1997; Leathers and Luff, 1997; Dye, 2002; Stone et al., 2002; Taras et al., 2002; Strack et al., 2003; Ling and Zhang, 2003b, 2004b, 2005; Zhang, 2005; Ling and Zhang, 2006). However, a quantitative understanding of the consequences of changes in snow thickness on the ground thermal regime and conductive heat flow to the atmosphere is limited. The goal of this paper is to estimate numerically the effects of increases and decreases in thickness of tundra snow on thermal regime of snow surface, active layer, and permafrost, and the conductive heat flow to the atmosphere in the northernmost Alaska by using an improved numerical model describing surface energy balance components and thermal regimes of snow and ground. 2. Numerical model and data sources The numerical model used in the present study is composed of a surface energy balance model and a heat conduction model with phase change for the subsurface system of snow-active layer-permafrost. A detailed description of the model development, validation, and improvement procedures can be found in Ling and Zhang (2004b, 2006). Only a brief introduction is given here with a particular emphasis on the treatment for the arctic tundra snow. The meteorological data used as baseline inputs for the numerical model include mean daily air temperature, dew point temperature, snow cover thickness, wind speed, and atmospheric pressure measured at the National Weather
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Table 1 The five snow thickness factors used in this study and the corresponding mean daily maximum snow thicknesses Snow thickness factor
1.0
0.25
0.5
1.5
1.75
Mean daily maximum snow thickness (m)
0.41
0.10
0.21
0.62
0.72
Service (NWS) station at Barrow, Alaska (Fig. 1a–e), and the incident solar radiation measured at the NOAA Climate Monitoring and Diagnostics Laboratory (CMDL) at the Barrow site (Fig. 1f). This study focuses on the impacts of changes in the thickness of arctic tundra snow on the ground thermal regime and conductive heat flow to the atmosphere in the snow season of 1997–1998. In order to minimize the effect of the initial temperature distribution, the simulation was conducted from January 1995. The daily snow thickness in the snow season of 1997–1998 is set to change as follows: Hs ðt Þ ¼ f d Hm ðt Þ
ð1Þ
Where Hs(t) is the snow thickness used in this study, Hm(t) is the measured mean daily snow thickness in the snow season of 1997–1998, f is a snow thickness factor. The stable seasonal snow cover appeared on September 22, 1997, and disappeared on May 28, 1998, in the snow season of 1997–1998 at NWS at Barrow, Alaska, with a mean daily maximum snow thickness of 0.41 m (Fig. 1(a)). Previous studies indicate that the total depth of tundra snow rarely exceeds 0.7 m in the northern Alaska (Zhang et al., 1996; Sturm and Holmgren, 1998). The long-term (1947–1997) mean daily maximum and minimum snow depth at the Barrow NWS station are 0.76 and 0.10 m, respectively, as reported by Zhang and Jeffries (2000). Based on these results, the snow thickness factor f is set for five values in this study. The values of f and the corresponding mean daily maximum snow thicknesses are summarized in Table 1, the corresponding mean daily snow distributions for different snow thickness factors are presented in Fig. 2. Snow cover was regarded as multiple layers in the current model. The number of layers, Ns, was determined by the following formula: 8 1 0bHs V0:07 > > > > 2 0:07bHs V0:15 > > > > < 3 0:15bHs V0:24 ð2Þ Ns ¼ 4 0:24bHs V0:34 > > 5 0:34bH V0:45 > s > > > > > 6 0:45bHs V0:57 : 7 0:57bHs
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Fig. 2. Distributions of mean daily snow thickness with time for the snow thickness factors f =0.25, 0.5, 1.0, 1.5, and 1.75 in the snow season of 1997–1998.
The effective thermal conductivity of snow, ks, in W m− 1 °C− 1, is given by the following quadratic equation (Sturm et al., 1997): keff ¼
0:138−1:01qs =1000 þ 3:233ðqs =1000Þ2 0:023 þ 0:234qs =1000
156bqs V600 qs V156
ð3Þ where ρs is the density of snow in kg m− 3. Based on a previous study, the time-density curve for tundra snow hardly change at all over the winter at a specific location in northernmost Alaska, and a constant snow density can be used for a certain location (Sturm and Holmgren, 1998). In this study, the calibrated snow density value of 362 kg m− 3 (Ling and Zhang, 2006) is chosen as the baseline input of snow density. The volumetric heat capacity of snow, Cs, in J m− 3 −1 °C , is also related to snow density, ρs, using the following formula (Goodrich, 1982): Cs ¼ 2:09 103 qs
ð4Þ
The surface albedo is a skin phenomenon, 1 cm of new snow will drive the albedo of aged snow right back up to 0.86 in the northern Alaska. Due to the lack of the observed data, the albedos for the stable snow cover surface and peat surface respectively are set to 0.86 and 0.17 during the periods from January 1995 through April 1997, and from July 1997 through April 1998 in the current study, based on the previous studies (Maykut and Church, 1973; Stone et al., 2002). While during the snowmelt and snow-free periods from May 1 through June 30 in 1997 and 1998, the surface albedos were derived from measurements of upwelling and downwelling solar irradiance at NOAA Climate Monitoring and Diagnostics Laboratory Barrow Observatory. The derived snow and ground surface albedos are shown in Fig. 3.
3. Results 3.1. Snow surface temperature Fig. 4 shows the simulated temperature differences at snow surface between snow thickness factor f = 0.5 and 1.5 respectively and f = 1.0 (Fig. 4a); and between f = 0.25 and 1.75 respectively and f = 1.0 (Fig. 4b) during the snow season of 1997–1998. Because the low thermal conductivity of snow insulates the ground, preventing the escaping of heat from the warm ground to the cold atmosphere, an increase in snow thickness leads to a decrease in snow surface temperature. In the contrary to increases in snow thickness, a decrease in snow thickness results in an increase in snow surface temperature. During the period from late September 1997 through early March 1998, increases in the snow thickness by 50% and 75%, the decreases in the average snow surface temperature are 0.03 and 0.04 °C, respectively. Alternatively, decreases in the snow thickness by 50% and 75%, the increases in the average snow surface temperature are 0.09 and 0.13 °C (Table 2). The impact of decrease in snow thickness on the snow surface temperature is greater than that of increase in snow thickness, because the greater temperature gradient increases when snow thickness reduces, although changes in snow thickness on the snow surface temperature is in general small. During the period from the middle of March to late of May in 1998, snow surface temperature rise significantly with time in the Alaskan Arctic, and can be higher than the ground surface temperature, owing to the significant increases in mean daily air temperature (Fig. 1b) and solar radiation (Fig. 1f). Changes in the snow thickness could either increase or decrease the snow surface temperature. 3.2. Ground thermal regime An increase in snow thickness could damp out the cold temperature signal in the snowpack well before it reaches
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Fig. 3. Snow and ground surface albedos derived from measurements of upwelling and downwelling solar irradiance at NOAA/Climate Monitoring and Diagnostics Laboratory Barrow Observatory (CMDL-BRW) from May 1 through June 30 in 1997 and 1998.
the ground, reducing the heat transfer between the snow surface and the ground surface, and thus increasing the ground temperature. Consequently, an increase in the snow thickness factor from 1.0 to 1.5 and 1.75 respectively during the snow season of 1997–1998 results in the
simulated maximum ground temperature increased at 0.01 m depth by 2.01 °C and 2.12 °C (Fig. 5a); at 0.29 m depth by 1.44 °C and 1.85 °C (Fig. 5b); at 1.0 m depth by 1.14 °C and 1.50 °C (Fig. 5c), and at 3.0 m depth by 0.66 °C and 0.84 °C (Fig. 5d), respectively. A decrease in
Fig. 4. Simulated temperature differences at snow surface (a) between f = 0.5, 1.5 respectively, and f = 1.0; and (b) between f = 0.25, 1.75 respectively, and f = 1.0 during September 1997 through June 1998.
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Table 2 The simulated average temperature differences at snow surface between snow thickness factors f = 0.25, 0.5, 1.5 and 1.75, respectively, and f = 1.0 during the period from September 22, 1997 through March 10, 1998 Snow thickness factor
0.25
0.5
1.5
1.75
Average temperature difference (°C)
0.13
0.09
− 0.03
− 0.04
the snow thickness factor from 1.0 to 0.5 and 0.25 respectively leads to the simulated maximum ground temperature decreased at 0.01 m depth by 2.0 °C and 5.51 °C; at 0.29 m depth by 1.48 °C and 4.50 °C; at 1.0 m depth by 1.21 °C and 3.58 °C, and at 3.0 m depth by
0.72 °C and 2.12 °C, respectively. Fig. 5 also shows that from the middle of April, decreasing the snow thickness factor could increase ground surface temperature and ground temperature at 0.29 m depth rather than decrease on several days. And contrarily, increasing the snow thickness factor could decrease ground surface temperature and ground temperature at 0.29 m depth. This is because on a daily basis, snow cover can either warm or cool the ground surface from late spring in the Alaskan Arctic, depending upon variations in air temperature, solar radiation, and the previous thermal history of the ground surface. Fig. 6 is the simulated differences of mean annual ground temperature with depth between the snow
Fig. 5. Simulated temperature differences at a depth of (a) 0.01 m; (b) 0.29 m; (c) 1.0 m; and (d) 3.0 m between f = 0.25, 0.5, 1.5 and 1.75, respectively, and f = 1.0 during September 1997 through June 1998.
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Table 3 The simulated mean annual ground temperature differences (MAGTD) at various depths during September 1997 through August 1998 between the snow thickness factors f = 0.25, 0.5, 1.5 and 1.75, respectively, and f = 1.0
Fig. 6. Simulated differences of annual mean ground temperature with depth between f = 0.25, 0.5, 1.5 and 1.75, respectively, and f = 1.0 during September 1997 through August 1998.
thickness factor f = 0.25, 0.5, 1.5, and 1.75, respectively, and f = 1.0 during the snow season of 1997–1998. Increases in the snow thickness factor from 1.0 to 1.5 and 1.75 respectively resulted in an increase of the mean annual ground surface temperature by about 0.5 °C and 0.6 °C. Decreases in snow density factor from 1.0 to 0.5 and 0.25 led to a decrease of the mean annual ground surface temperature by approximately 0.6 °C and 1.7 °C, respectively. The impact of changes in the snow thickness factor on ground temperature decreases gradually with depth. For instance, decrease in the snow thickness by 50%, ground temperature variation at 3.0 m depth is great than 1.0 °C, at 8.0 m depth below the ground surface less than 0.4 °C. In order to further investigate the impact of changes in snow thickness on the thermal regime of ground, Fig. 7 presents the simulated mean ground temperature at a depth of 1.0 m for each month for different snow thickness factors during the period from October 1997 through May 1998. The impact of changes in the snow thickness on the thermal regime of ground in the snow cover formation period and snow melt period is smaller than that in the
Snow thickness factor
0.25
0.5
1.5
1.75
MAGTD at MAGTD at MAGTD at MAGTD at MAGTD at
− 1.67 − 1.55 − 1.51 − 1.41 − 1.05
− 0.58 − 0.53 − 0.51 − 0.48 − 0.35
0.51 0.49 0.47 0.44 0.33
0.62 0.57 0.55 0.52 0.39
0.01 m (°C) 0.29 m (°C) 0.5 m (°C) 1.0 m (°C) 3.0 m (°C)
snow accumulation period from November to next April. For example, increases in snow thickness factor from 0.25 to 1.75, the modeled differences of mean values of ground temperature at 1.0 m depth for October, January, February, and May are −0.51, −4.71, −4.56, and −1.14 °C, respectively. This is because the temperature difference between ground surface and snow surface is greater in the snow accumulation period. Table 3shows the simulated mean annual ground temperature differences at various depths during September 1997 through August 1998 between the snow thickness factors f = 0.25, 0.5, 1.5 and 1.75, respectively, and f = 1.0. On an annual basis, the ground temperature difference caused by decreasing the snow thickness is greater than that caused by increasing the snow thickness. For example, decreasing the snow thickness by 75% ( f = 0.25), the ground temperature decreases at depths of 0.01, 0.29, 0.5, 1.0, 3.0 m are 1.67, 1.55, 1.51, 1.41, and 1.05 °C, respectively. While increase the snow thickness by 75% ( f = 1.75), the corresponding ground temperature increases are 0.62, 0.57, 0.55, 0.52, and 0.39 °C, respectively. 3.3. Conductive heat flow to the atmosphere The conductive heat flow to the atmosphere was calculated using the thermal conditions at the bottom of the
Fig. 7. A comparison of simulated mean values of ground temperature at a depth of 1.0 m for every month for different snow thickness factors during the snow season of 1997–1998.
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Fig. 8. A comparison of simulated mean values of conductive heat flux to the atmosphere for every month for different snow thickness factors during the snow season of 1997–1998.
top node layer, which is 0.03 m in depth. The energy fluxes toward the ground surface were defined as positive. Fig. 8 is a comparison of the simulated mean conductive heat flux for every month for different snow thickness factors during the snow season of 1997–1998. Increasing the snow thickness factors from 0.25 to 1.75 results in decreases in the magnitude of the mean conductive heat flux through ground to snow surface, due to the decreases in the temperature differences between the snow surface and ground surface. Decreases in the snow thickness can increase the conductive heat flux substantially, while increases in the snow thickness have relatively small influence on the conductive heat flow to the atmosphere. For instance, decreasing snow thickness factor from 1.0 to 0.5 and 0.25, respectively, the magnitude of the mean conductive heat flow to the atmosphere for December increases from 5.87 to 10.17 and 14.58 W m− 2, respectively, while increasing snow thickness factor from 1.0 to 1.5 and 1.75, respectively, the magnitude of the mean conductive heat flow to the atmosphere for December decreases from 5.87 to 4.30 and 3.77 W m− 2, respectively. The mean conductive heat flux for every month period from October 1997 to March 1998 was positive, and for the two-month period from April through May in 1998 was negative, reflecting the release and absorption processes of the active layer and permafrost. 4. Discussion Numerical modeling is generally regarded as the most effective method to simulate and forecast the thermal regime of the active layer and permafrost (e.g., Brown et al., 1964; Harlan, 1973; Nixon, 1975; Miller, 1979; Jame and Norum, 1980; Guymon et al., 1984; Kane et al., 1991; Zhang and Stamnes, 1998; Ling and Zhang, 2003a,b, 2004a). The modeling studies for the influence of the seasonal snow cover on the ground thermal regime
have received considerable attention during the past few decades (e.g., Lachenbruch, 1959; Goodrich, 1982; Lachenbruch and Marshall, 1986; Zhang et al., 1996; Zhang and Stamnes, 1998; Zhang et al., 2001). The most widely used upper boundary condition for numerical simulation is the snow surface temperature when seasonal snow cover was present, and the ground surface temperature when seasonal snow cover was absent. And the surface temperatures are observed values derived directly or indirectly from air temperatures. An accurate description for surface temperature should use physically based models that account for the relevant processes occurring within, and at the boundaries of permafrost, snow, and atmospheric components of the natural system. The surface energy balance approach is a reasonable method of establishing surface temperature boundary conditions because it tends to preserve the cause and effect relationship between surface temperatures and heat fluxes (e.g., Myrup, 1969; Outcalt, 1972; Miller, 1979). There have been used, but relatively fewer in number, for simulating the ground thermal regime by using the surface energy balance approach to estimate surface temperature conditions. Several surface energy balance models, which are forced with daily weather information, have been developed and used to simulate the snowmelt and tundra soil thermal regime (Outcalt et al., 1975; Miller, 1979), and to investigate the effect of tundra vegetation and climate change on ground temperature (Ng and Miller, 1977; Smith and Riseborough, 1983). However, these models do not include the effect of unfrozen water on soil thermal properties. Hinzman et al. (1998) developed a spatially distributed surface energy balance model for calculating soil temperature profiles and thaw depth in permafrost regions. The model performs quite well with one-day time increments, but seasonal snow cover was not included in the model.
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Based on a surface energy balance approach for lake ice evolution (Liston and Hall, 1995) and a heat conduction model with phase change for freezing and thawing of permafrost containing unfrozen water (Osterkamp, 1987), Ling and Zhang developed a numerical model for the subsurface system of snowactive layer-permafrost (Ling and Zhang, 2004b). The surface energy balance approach was used to estimate the upper boundary condition for numerical thermal conduction calculations. The heat conduction model is a one-dimensional finite difference model for the active layer and permafrost containing unfrozen water. The influence of unfrozen water on the thermal properties of soils was accounted for in the heat conduction model. And the impact of snow was included in the combined model by extending the heat conduction solution into the snow layer and computing the surface heat balance components and the snow surface temperature. The model was validated against field measurement the observed ground temperatures at Barrow, Alaska, and the results show that the simulated soil temperatures track the measured soil temperatures well in the active layer, near the permafrost surface, and in shallow permafrost. On the basis of the developed model with some modifications (Ling and Zhang, 2006) and field measurements, Ling and Zhang conducted several investigations on the impact of variations in thickness, timing and duration, and density of the seasonal snow cover on surface energy fluxes and the thermal regime of the active layer and permafrost on the North Slope of Alaska in previous studies (Ling and Zhang, 2003b, 2005, 2006) and the present study. The primary consequences and implications from the previous studies can be summarized as follows: 1) the thermal regime of the active layer and permafrost in the Alaskan Arctic is sensitive to variations in the timing and duration of seasonal snow cover, due to variations in surface conditions and the associated ground surface energy balance. Delaying the snow cover onset date in autumn results in a decrease in ground temperatures, advancing the snow cover disappearance date in spring leads to an increase in ground temperatures, and delaying the snowpack disappearance date in spring results in a decrease in ground temperatures. The active layer thickness also has a corresponding response to variations in the timing and duration of seasonal snow cover, but the change is very limited. Previous studies show that much of the Arctic has already warmed significantly (Serreze et al., 2000) and Arctic permafrost is thawing (Osterkamp and Romanovsky, 1999).
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These results suggest that the earlier disappearance of spring snow cover (Stone et al., 2002) has an important contribution to Arctic warming and permafrost thawing. 2) varying the snowpack disappearance date by 10 days in spring can strongly affect the mean annual net solar radiation, sensible heat flux, and latent heat flux, and can slightly affect the mean annual net longwave radiation and conductive heat flux. Groisman et al. (1994) suggested that there is a strong positive feedback between spring snow cover and the radiative balance over northern extratropical land. The global warming that has occurred in the spring during the twentieth century is likely to have been significantly enhanced by corresponding changes in snow-cover extent. Thus, the transient effects of external climate forcing, such as greenhouse warming, may be especially prominent during spring in the Northern Hemisphere, where snow-cover variations substantially affect the radiative balance. The simulated results from our model agree well with their result. 3) changes in snow density have significant influences on ground surface temperature and near-surface ground temperature because snow density determines the snow thermal conductivity and volumetric heat capacity. But changes in snow density have very limited impact on the snow surface temperature and the active layer depth, as the ground surface temperature is higher during snow-free periods due to the significant increase in the net radiative forcing following the last day of snowmelt (Stone et al., 2002) and the higher mean daily air temperature, the ground temperature differences caused by variations in snow density reduced very quickly after the ground surface became snow free. 4) variations in snow density can influence the conductive heat flux considerably in northern Alaska, reflecting the variations in snow thermal properties. But variations in snow density have insignificant influence on the sensible and latent heat fluxes, reflecting the very limited variation in mean daily snow surface temperature. Snow cover was regarded as multiple layers in the current model and the number of layers was determined by snow thickness using formula (2). Based on the conclusion that time-density curve for tundra snow hardly change at all over the winter at a specific location in northernmost Alaska because pulverized drift snow tends to be dense right from the start (Sturm and Holmgren, 1998), this study sets the snow density to a
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constant value of 362 kg m− 3, which was determined by fitting the calculated ground temperatures at different depth to the measured values using the trial and error method. However, this is an ideal assumption to simplify the modeling study. The structure of seasonal snow cover usually consists of hard, higher-density, wind-packed slab layers at the top with coarse, lower-density depth hoar layers at the base, due to high wind speeds and low air temperatures (Benson and Sturm, 1993). Variations in the snow cover thickness would result in changes in the depth hoar fraction, thus lead to changes in snow density. A previous study has shown that in permafrost regions, variations in depth hoar fraction can affect ground surface temperature and the mean annual ground surface temperature, and delay the active layer freeze-up (Zhang et al., 1996). Further studies for model improvement to include the impact of depth hoar layer are needed. Properties of seasonal snow cover, such as density, albedo, thermal conductivity, emssivity, and roughness length, have obvious distinctions in autumn, winter, and spring, particularly during the snow melt period. This can affect the surface energy balance significantly, and thus the thermal regime of the active layer and permafrost. Besides, the time step used in the presented model is daily rather than an hourly or a shorter time scale, because the hourly observed data are not available. This also can affect the simulation precision. In order to better simulate the combined influence of seasonal snow cover on the thermal regime of the active layer and permafrost, systematic field measurements of the variations in snow properties with time and further studies for model validation using hourly time step and observational snow surface temperature and surface energy balance components are needed, and the variability of snow cover parameters should be taken into account in the model. During the soil thawing period, the infiltration of snow melt water and rainfall increases the soil temperature sooner than the model would predict, as has been observed in field studies at Barrow (Kane et al., 1991; Hinkel et al., 2001; Ling and Zhang, 2003b). Convective heat transfer becomes progressively more important as the soil warms and remains unfrozen longer. In addition to the effect of convective heat transfer in the active layer, convective heat transfer in seasonal snow cover could also play a role (Sturm and Johnson, 1991). This nonconductive heat transfer could effectively reduce the insulating effect of the seasonal snow cover (Stein and Kane, 1983; Hinkel et al., 1997, 2001; Kane et al., 2001). However, the numerical model used in this study does not include the nonconductive heat transfer of the convection. Based on Russian historical soil
temperature and snow depth data, Frauenfeld et al. (2004) found that maximum snow depth by the end of winter has a significant impact on the thaw depth in the following summer. They hypothesize that the impact of snow depth on active layer depth in the following summer may be due to the influence of snow cover on soil moisture. The development of a one-dimensional conductive-convective heat transfer model considering the nonconductive heat transfer processes in seasonal snow cover and the active layer are needed. Permafrost changes mainly refer to changes in active layer thickness and permafrost temperature. In northern Alaska, changes in active layer thickness are mainly controlled by summer air temperature, while permafrost temperature is mainly controlled by winter air temperatures and snow conditions. The overall impact of snow cover on the ground thermal regime depends on the timing, duration, accumulation, and melting processes of seasonal snow cover; density, structure, and thickness of seasonal snow cover; and interactions of snow cover with micrometeorological conditions, local microrelief, vegetation, and the geographical locations. Climate change may lead to decreases in soil temperatures and increases in soil freezing because of lack of an insulating snow cover and changes in soil water dynamics during the important snowmelt period Zhang, 2005). The feedback of increased soil freezing to the climate system is poorly understood and needs further investigation. 5. Conclusions The primary results from this modeling study can be summarized as follows: 1) Changes in snow thickness can significantly influence the near-surface ground temperature in northernmost Alaska. During the snow season of 1997– 1998, a decrease in the snow thickness factor from 1.0 to 0.5 leads to the maximum ground temperature decreased at 0.01 m depth by 2.0 °C, at 0.29 m depth by 1.48 °C, at 1.0 m depth by 1.21 °C, and at 3.0 m depth by 0.72 °C. An increase in the snow thickness factor from 1.0 to 1.5 results in the maximum ground temperature increased at 0.01 m depth by 2.01 °C, at 0.29 m depth by 1.44 °C; at 1.0 m depth by 1.14 °C, and at 3.0 m depth by 0.66 °C. On an annual basis, variation in the snow thickness by 50%, the ground temperature variation of more than 0.25 °C occurs as deep as 8.0 m below the ground surface. 2) Decreases in the snow thickness can strongly increase the conductive heat flow to the atmosphere, while increases in the snow thickness have relatively
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small influence on the conductive heat flow. For instance, decreasing snow thickness by 50% and 75%, respectively, the magnitude of the mean conductive heat flow to the atmosphere for December increases from 5.87 to 10.17 and 14.58 W m− 2, while increasing snow thickness by 50% and 75%, the magnitude of the mean conductive heat flow to the atmosphere for December decreases from 5.87 to 4.30 and 3.77 W m− 2, respectively. 3) The effect of changes in snow thickness on the snow surface temperature is very limited. Decreases and increases in snow thickness by 75%, the corresponding increase and decrease in the average snow surface temperature for the period before snowmelt from September 22, 1997 through March 10, 1998 are just 0.13 °C and 0.04 °C, respectively. Acknowledgments We would like to express our gratitude to the two anonymous reviewers for their constructive criticisms, helpful comments and insightful suggestions on the original version of this paper. Financial support for this study was provided by the Guangdong Natural Science Foundation of the People's Republic of China (Grant No. 04011600); the Scientific Research Foundation for the Returned Overseas Chinese Scholars, the State Education Ministry; the US National Science Foundation through the NSP OPP-0352910 and OPP-0229766; and the International Arctic Research Center, University of Alaska Fairbanks, under the auspices of the NSF cooperative agreement number OPP-0327664. Any opinions, findings, and conclusions or recommendations expressed in this article are those of the authors and do not necessarily reflect the views of the funding institutes and agencies. We are grateful to Robert Stone for providing the measurements of upwelling and downwelling solar irradiance at NOAA/Climate Monitoring and Diagnostics Laboratory Barrow Observatory (CMDL-BRW) used in Fig. 3a and b. References Benson, C.S., Sturm, M., 1993. Structure and wind transport of seasonal snow on the Arctic slope of Alaska. Annals of Glaciology 18, 261–267. Brown, W.G., Johnson, G.H., Brown, R.J., 1964. Comparison of observed and calculated ground temperatures with permafrost distribution under a northern lake. Canadian Geotechnical Journal 1 (3), 147–154. Cohen, J., 1994. Snow cover and climate. Weather 49, 150–156. Cohen, J., Entekhabi, D., 2001. The influence of snow cover on Northern Hemisphere climate variability. Atmosphere-Ocean 39 (1), 35–53.
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change in the northern high-latitude environment. Climatic Change 46, 159–207. Smith, M.W., 1975. Microclimatic influence on ground temperatures and permafrost distribution, Mackenzie Delta, Northwest Territories. Canadian Journal of Earth Sciences 12, 1421–1438. Smith, M.W., Riseborough, D.H., 1983. Permafrost sensitivity to climatic change. Proceedings of 4th International Conference on Permafrost, Fairbanks, Alaska. National Academy Press, Washington, pp. 1178–1183. Stein, J., Kane, D.E., 1983. Monitoring the unfrozen water content of soil and snow using time domain reflectometry. Water Resources Research 19, 1573–1584. Stone, R.S., Dutton, E.G., Harris, J.M., Longenecker, D., 2002. Earlier spring snowmelt in northern Alaska as an indicator of climate change. Journal of Geophysical Research 107 (D10), 1–15 (ACL10). Strack, J.L., Pielke Sr, R.A., Adegoke, J., 2003. Sensitivity of modelgenerated daytime surface heat fluxes over snow to land-cover changes. Journal of Hydrometeorology 4 (1), 24–42. Sturm, M., Holmgren, J., 1998. Differences in compaction behavior of three climate classes of snow. Annals of Glaciology 16, 125–130. Sturm, M., Johnson, J.B., 1991. Natural convection in the subarctic snow cover. Journal of Geophysical Research 96 (B7), 11657–11671. Sturm, M., Johnson, J.B., 1992. Thermal conductivity measurement of depth hoar. Journal of Geophysical Research 97 (82), 2129–2139. Sturm, M., Holmgren, J., Konig, M., Morris, K., 1997. The thermal conductivity of seasonal snow. Journal of Glaciology 43 (143), 26–41. Sturm, M., McFadden, J.P., Liston, G.E., Chapin, F.S., Racine, G.H., Holmgren, J., 2001. Snow-shrub interactions in arctic tundra: a hypothesis with climatic implications. Journal of Climate 14, 336–344. Taras, B., Sturm, M., Liston, G.E., 2002. Snow-ground interface temperatures in the Kuparuk River basin, Arctic Alaska: measurements and model. Journal of Hydrometeorology 3, 377–394. Walsh, J.W., Jasperson, H., Ross, B., 1985. Influences of snow cover and soil moisture on monthly air temperature. Monthly Weather Review 113, 756–769. Zhang, T., 2005. Influence of the seasonal snow cover on the ground thermal regime: an overview. Review of Geophysics 43, RG4002. Zhang, T., Jeffries, M.O., 2000. Modeling interdecadal variations of lake-ice thickness and sensitivity to climatic change in northernmost Alaska. Annals of Glaciology 31, 339–347. Zhang, T., Stamnes, K., 1998. Impact of climate factors on the active layer and permafrost at Barrow, Alaska. Permafrost and Periglacial Processes 9 (3), 229–246. Zhang, T., Osterkamp, T.E., Stamnes, K., 1996. Influence of the depth hoar layer of the seasonal snow cover on the ground thermal regime. Water Resources Research 32 (7), 2075–2086. Zhang, T., Osterkamp, T.E., Stamnes, K., 1997. Effect of climate on the Active layer and permafrost on the North Slope of Alaska, U.S.A. Permafrost and Periglacial Processes 8 (1), 45–67. Zhang, T., Barry, R.G., Haeberli, W., 2001. Numerical simulation of the influence of the seasonal snow cover on the occurrence of permafrost at high latitudes. Norsk Geografisk Tidsskrift 55, 261–266.
Modeled impacts of changes in tundra snow thickness on ground thermal regime and heat flow to the atmosphere in Northernmost Alaska Feng Ling a,⁎, Tingjun Zhang b a b
Department of Computer Science, Zhaoqing University, Zhaoqing, Guangdong 526061, P. R. China National Snow and Ice Data Center, Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO 80303–0449, USA Received 12 March 2006; received in revised form 3 October 2006; accepted 14 November 2006 Available online 29 December 2006
Abstract Seasonal snow covers the tundra surface for up to nine months of each year on the Alaskan North Slope. Variations in the snow thickness could strongly influence the thermal regime of the underlying soil and permafrost, and the surface energy balance. The impacts of increases and decreases in the tundra snow thickness on the thermal regime of snow surface, active layer, and permafrost, and on the conductive heat flow to the atmosphere were investigated numerically, by using an improved surface energy balance approach based onedimensional heat transfer model. The baseline inputs for the numerical model are mean daily meteorological data and surface albedos collected at Barrow, Alaska from 1995 through 1999. Based on a study for the long-term mean daily maximum and minimum snow thickness distributions at Barrow in the snow season of 1948 through 1997, a snow thickness factor was defined and five simulation cases were run for the snow season of 1997–1998 by changing the snow thickness factor. The modeled results indicate that changes in snow thickness have significant impacts on ground thermal regimes and conductive heat flow to the atmosphere. Decreasing the snow thickness by 50% led to the maximum ground temperature decrease of 1.48 °C at 0.29 m depth, and 0.72 °C at 3.0 m depth; the magnitude of the mean conductive heat flow to the atmosphere for December increase of 4.3 Wm− 2. Increasing the snow thickness by 50% resulted in the maximum ground temperature increase of 1.44 °C at 0.29 m depth, and 0.66 °C at 3.0 m depth; the magnitude of the mean conductive heat flow to the atmosphere for December decrease of 1.57 W m− 2. On an annual basis, variation in the snow thickness by 50%, the ground temperature variations of more than 0.25 °C occurred as deep as 8.0 m below the ground surface. The modeled results also show that changes in snow thickness have a relatively small influence on the snow surface temperature. © 2006 Elsevier B.V. All rights reserved. Keywords: Snow thickness; Energy balance; Ground thermal regime; Conductive heat flow; Modeling
1. Introduction Owing to the low air temperature and high wind speed, the thickness of tundra snow on the North Slope of Alaska can vary substantially over distances of a few meters, and ⁎ Corresponding author. Tel.: +86 758 275 2208; fax: +86 758 271 6586. E-mail address: [email protected] (F. Ling). 0921-8181/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.gloplacha.2006.11.009
large year-to-year variations in snow thickness at a specific location can be found (Zhang et al., 1996; Sturm and Holmgren, 1998; Taras et al., 2002). In addition, changes in the arctic shrubs also can significantly modify snow thickness and other snow-related characteristics, because shrubs are taller than other tundra vegetation and can capture and hold more snow (Liston and Sturm, 1998; Sturm et al., 2001; Liston et al., 2002).
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Variations in the snow thickness could strongly influence the thermal regime of the underlying soil and permafrost, and the conductive heat flow to the atmosphere, because the low thermal conductivity of snow insulates the ground, preventing the escaping of heat from the warm ground to the cold atmosphere, or conversely, damping out the cold wintertime temperature signal in the snowpack well before it reaches the ground (Goodrich, 1982; Sturm and Johnson, 1992; Lynch-Stieglitz, 1994; Zhang et al., 1996; Sturm et al., 1997; Zhang et al., 2001;
Ling and Zhang, 2003b, 2004b, 2005; Zhang, 2005; Ling and Zhang, 2006), and because changes in the thickness of tundra snow can significantly affects the length and timing of the snow-free period, and the structural and thermal characteristics of snow cover (Sturm et al., 2001; Liston et al., 2002). Field measurements during 1968–1973 at Garry Island, Northwest Territories, Canada, showed that the snow ground interface temperature varied significantly from site to site within a few hundred meters owing to thickness variations of the seasonal snow cover (MacKay
Fig. 1. Mean daily meteorological conditions collected at Barrow, Alaska, during June 1995 through July 1998.
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and MacKay, 1975). Smith (1975) reported that in the east-central part of the Mackenzie Delta, Northwest Territories, Canada, the seasonal snow cover was the major factor controlling the permafrost temperature during the winter and thus the mean annual permafrost surface temperature. On the Alaskan North Slope, snow covers the tundra surface for up to nine months of each year (Benson and Sturm, 1993; Zhang et al., 1996), the impacts of such change could be significant. Snow cover is the most variable land surface conditions in both time and space in the Northern Hemisphere (Gutzler and Rosen, 1992; Cohen, 1994; Cohen and Entekhabi, 2001), and a crucial parameter in studies of ground freezing/thawing processes, climate change, and weather forecasting (Walsh et al., 1985; Groisman et al., 1994; Gustafsson et al., 2001). The impacts of changes in the extent, timing, duration, accumulation and melting processes, density and structure of seasonal snow cover on the thermal regime of the active layer and permafrost have captured the interest of many investigators (Outcalt et al., 1975; Goodrich, 1982; Foster, 1989; Dutton and Endres, 1991; Foster et al., 1992; Sturm and Johnson, 1992; Zhang et al., 1996, 1997; Leathers and Luff, 1997; Dye, 2002; Stone et al., 2002; Taras et al., 2002; Strack et al., 2003; Ling and Zhang, 2003b, 2004b, 2005; Zhang, 2005; Ling and Zhang, 2006). However, a quantitative understanding of the consequences of changes in snow thickness on the ground thermal regime and conductive heat flow to the atmosphere is limited. The goal of this paper is to estimate numerically the effects of increases and decreases in thickness of tundra snow on thermal regime of snow surface, active layer, and permafrost, and the conductive heat flow to the atmosphere in the northernmost Alaska by using an improved numerical model describing surface energy balance components and thermal regimes of snow and ground. 2. Numerical model and data sources The numerical model used in the present study is composed of a surface energy balance model and a heat conduction model with phase change for the subsurface system of snow-active layer-permafrost. A detailed description of the model development, validation, and improvement procedures can be found in Ling and Zhang (2004b, 2006). Only a brief introduction is given here with a particular emphasis on the treatment for the arctic tundra snow. The meteorological data used as baseline inputs for the numerical model include mean daily air temperature, dew point temperature, snow cover thickness, wind speed, and atmospheric pressure measured at the National Weather
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Table 1 The five snow thickness factors used in this study and the corresponding mean daily maximum snow thicknesses Snow thickness factor
1.0
0.25
0.5
1.5
1.75
Mean daily maximum snow thickness (m)
0.41
0.10
0.21
0.62
0.72
Service (NWS) station at Barrow, Alaska (Fig. 1a–e), and the incident solar radiation measured at the NOAA Climate Monitoring and Diagnostics Laboratory (CMDL) at the Barrow site (Fig. 1f). This study focuses on the impacts of changes in the thickness of arctic tundra snow on the ground thermal regime and conductive heat flow to the atmosphere in the snow season of 1997–1998. In order to minimize the effect of the initial temperature distribution, the simulation was conducted from January 1995. The daily snow thickness in the snow season of 1997–1998 is set to change as follows: Hs ðt Þ ¼ f d Hm ðt Þ
ð1Þ
Where Hs(t) is the snow thickness used in this study, Hm(t) is the measured mean daily snow thickness in the snow season of 1997–1998, f is a snow thickness factor. The stable seasonal snow cover appeared on September 22, 1997, and disappeared on May 28, 1998, in the snow season of 1997–1998 at NWS at Barrow, Alaska, with a mean daily maximum snow thickness of 0.41 m (Fig. 1(a)). Previous studies indicate that the total depth of tundra snow rarely exceeds 0.7 m in the northern Alaska (Zhang et al., 1996; Sturm and Holmgren, 1998). The long-term (1947–1997) mean daily maximum and minimum snow depth at the Barrow NWS station are 0.76 and 0.10 m, respectively, as reported by Zhang and Jeffries (2000). Based on these results, the snow thickness factor f is set for five values in this study. The values of f and the corresponding mean daily maximum snow thicknesses are summarized in Table 1, the corresponding mean daily snow distributions for different snow thickness factors are presented in Fig. 2. Snow cover was regarded as multiple layers in the current model. The number of layers, Ns, was determined by the following formula: 8 1 0bHs V0:07 > > > > 2 0:07bHs V0:15 > > > > < 3 0:15bHs V0:24 ð2Þ Ns ¼ 4 0:24bHs V0:34 > > 5 0:34bH V0:45 > s > > > > > 6 0:45bHs V0:57 : 7 0:57bHs
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Fig. 2. Distributions of mean daily snow thickness with time for the snow thickness factors f =0.25, 0.5, 1.0, 1.5, and 1.75 in the snow season of 1997–1998.
The effective thermal conductivity of snow, ks, in W m− 1 °C− 1, is given by the following quadratic equation (Sturm et al., 1997): keff ¼
0:138−1:01qs =1000 þ 3:233ðqs =1000Þ2 0:023 þ 0:234qs =1000
156bqs V600 qs V156
ð3Þ where ρs is the density of snow in kg m− 3. Based on a previous study, the time-density curve for tundra snow hardly change at all over the winter at a specific location in northernmost Alaska, and a constant snow density can be used for a certain location (Sturm and Holmgren, 1998). In this study, the calibrated snow density value of 362 kg m− 3 (Ling and Zhang, 2006) is chosen as the baseline input of snow density. The volumetric heat capacity of snow, Cs, in J m− 3 −1 °C , is also related to snow density, ρs, using the following formula (Goodrich, 1982): Cs ¼ 2:09 103 qs
ð4Þ
The surface albedo is a skin phenomenon, 1 cm of new snow will drive the albedo of aged snow right back up to 0.86 in the northern Alaska. Due to the lack of the observed data, the albedos for the stable snow cover surface and peat surface respectively are set to 0.86 and 0.17 during the periods from January 1995 through April 1997, and from July 1997 through April 1998 in the current study, based on the previous studies (Maykut and Church, 1973; Stone et al., 2002). While during the snowmelt and snow-free periods from May 1 through June 30 in 1997 and 1998, the surface albedos were derived from measurements of upwelling and downwelling solar irradiance at NOAA Climate Monitoring and Diagnostics Laboratory Barrow Observatory. The derived snow and ground surface albedos are shown in Fig. 3.
3. Results 3.1. Snow surface temperature Fig. 4 shows the simulated temperature differences at snow surface between snow thickness factor f = 0.5 and 1.5 respectively and f = 1.0 (Fig. 4a); and between f = 0.25 and 1.75 respectively and f = 1.0 (Fig. 4b) during the snow season of 1997–1998. Because the low thermal conductivity of snow insulates the ground, preventing the escaping of heat from the warm ground to the cold atmosphere, an increase in snow thickness leads to a decrease in snow surface temperature. In the contrary to increases in snow thickness, a decrease in snow thickness results in an increase in snow surface temperature. During the period from late September 1997 through early March 1998, increases in the snow thickness by 50% and 75%, the decreases in the average snow surface temperature are 0.03 and 0.04 °C, respectively. Alternatively, decreases in the snow thickness by 50% and 75%, the increases in the average snow surface temperature are 0.09 and 0.13 °C (Table 2). The impact of decrease in snow thickness on the snow surface temperature is greater than that of increase in snow thickness, because the greater temperature gradient increases when snow thickness reduces, although changes in snow thickness on the snow surface temperature is in general small. During the period from the middle of March to late of May in 1998, snow surface temperature rise significantly with time in the Alaskan Arctic, and can be higher than the ground surface temperature, owing to the significant increases in mean daily air temperature (Fig. 1b) and solar radiation (Fig. 1f). Changes in the snow thickness could either increase or decrease the snow surface temperature. 3.2. Ground thermal regime An increase in snow thickness could damp out the cold temperature signal in the snowpack well before it reaches
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Fig. 3. Snow and ground surface albedos derived from measurements of upwelling and downwelling solar irradiance at NOAA/Climate Monitoring and Diagnostics Laboratory Barrow Observatory (CMDL-BRW) from May 1 through June 30 in 1997 and 1998.
the ground, reducing the heat transfer between the snow surface and the ground surface, and thus increasing the ground temperature. Consequently, an increase in the snow thickness factor from 1.0 to 1.5 and 1.75 respectively during the snow season of 1997–1998 results in the
simulated maximum ground temperature increased at 0.01 m depth by 2.01 °C and 2.12 °C (Fig. 5a); at 0.29 m depth by 1.44 °C and 1.85 °C (Fig. 5b); at 1.0 m depth by 1.14 °C and 1.50 °C (Fig. 5c), and at 3.0 m depth by 0.66 °C and 0.84 °C (Fig. 5d), respectively. A decrease in
Fig. 4. Simulated temperature differences at snow surface (a) between f = 0.5, 1.5 respectively, and f = 1.0; and (b) between f = 0.25, 1.75 respectively, and f = 1.0 during September 1997 through June 1998.
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Table 2 The simulated average temperature differences at snow surface between snow thickness factors f = 0.25, 0.5, 1.5 and 1.75, respectively, and f = 1.0 during the period from September 22, 1997 through March 10, 1998 Snow thickness factor
0.25
0.5
1.5
1.75
Average temperature difference (°C)
0.13
0.09
− 0.03
− 0.04
the snow thickness factor from 1.0 to 0.5 and 0.25 respectively leads to the simulated maximum ground temperature decreased at 0.01 m depth by 2.0 °C and 5.51 °C; at 0.29 m depth by 1.48 °C and 4.50 °C; at 1.0 m depth by 1.21 °C and 3.58 °C, and at 3.0 m depth by
0.72 °C and 2.12 °C, respectively. Fig. 5 also shows that from the middle of April, decreasing the snow thickness factor could increase ground surface temperature and ground temperature at 0.29 m depth rather than decrease on several days. And contrarily, increasing the snow thickness factor could decrease ground surface temperature and ground temperature at 0.29 m depth. This is because on a daily basis, snow cover can either warm or cool the ground surface from late spring in the Alaskan Arctic, depending upon variations in air temperature, solar radiation, and the previous thermal history of the ground surface. Fig. 6 is the simulated differences of mean annual ground temperature with depth between the snow
Fig. 5. Simulated temperature differences at a depth of (a) 0.01 m; (b) 0.29 m; (c) 1.0 m; and (d) 3.0 m between f = 0.25, 0.5, 1.5 and 1.75, respectively, and f = 1.0 during September 1997 through June 1998.
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241
Table 3 The simulated mean annual ground temperature differences (MAGTD) at various depths during September 1997 through August 1998 between the snow thickness factors f = 0.25, 0.5, 1.5 and 1.75, respectively, and f = 1.0
Fig. 6. Simulated differences of annual mean ground temperature with depth between f = 0.25, 0.5, 1.5 and 1.75, respectively, and f = 1.0 during September 1997 through August 1998.
thickness factor f = 0.25, 0.5, 1.5, and 1.75, respectively, and f = 1.0 during the snow season of 1997–1998. Increases in the snow thickness factor from 1.0 to 1.5 and 1.75 respectively resulted in an increase of the mean annual ground surface temperature by about 0.5 °C and 0.6 °C. Decreases in snow density factor from 1.0 to 0.5 and 0.25 led to a decrease of the mean annual ground surface temperature by approximately 0.6 °C and 1.7 °C, respectively. The impact of changes in the snow thickness factor on ground temperature decreases gradually with depth. For instance, decrease in the snow thickness by 50%, ground temperature variation at 3.0 m depth is great than 1.0 °C, at 8.0 m depth below the ground surface less than 0.4 °C. In order to further investigate the impact of changes in snow thickness on the thermal regime of ground, Fig. 7 presents the simulated mean ground temperature at a depth of 1.0 m for each month for different snow thickness factors during the period from October 1997 through May 1998. The impact of changes in the snow thickness on the thermal regime of ground in the snow cover formation period and snow melt period is smaller than that in the
Snow thickness factor
0.25
0.5
1.5
1.75
MAGTD at MAGTD at MAGTD at MAGTD at MAGTD at
− 1.67 − 1.55 − 1.51 − 1.41 − 1.05
− 0.58 − 0.53 − 0.51 − 0.48 − 0.35
0.51 0.49 0.47 0.44 0.33
0.62 0.57 0.55 0.52 0.39
0.01 m (°C) 0.29 m (°C) 0.5 m (°C) 1.0 m (°C) 3.0 m (°C)
snow accumulation period from November to next April. For example, increases in snow thickness factor from 0.25 to 1.75, the modeled differences of mean values of ground temperature at 1.0 m depth for October, January, February, and May are −0.51, −4.71, −4.56, and −1.14 °C, respectively. This is because the temperature difference between ground surface and snow surface is greater in the snow accumulation period. Table 3shows the simulated mean annual ground temperature differences at various depths during September 1997 through August 1998 between the snow thickness factors f = 0.25, 0.5, 1.5 and 1.75, respectively, and f = 1.0. On an annual basis, the ground temperature difference caused by decreasing the snow thickness is greater than that caused by increasing the snow thickness. For example, decreasing the snow thickness by 75% ( f = 0.25), the ground temperature decreases at depths of 0.01, 0.29, 0.5, 1.0, 3.0 m are 1.67, 1.55, 1.51, 1.41, and 1.05 °C, respectively. While increase the snow thickness by 75% ( f = 1.75), the corresponding ground temperature increases are 0.62, 0.57, 0.55, 0.52, and 0.39 °C, respectively. 3.3. Conductive heat flow to the atmosphere The conductive heat flow to the atmosphere was calculated using the thermal conditions at the bottom of the
Fig. 7. A comparison of simulated mean values of ground temperature at a depth of 1.0 m for every month for different snow thickness factors during the snow season of 1997–1998.
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Fig. 8. A comparison of simulated mean values of conductive heat flux to the atmosphere for every month for different snow thickness factors during the snow season of 1997–1998.
top node layer, which is 0.03 m in depth. The energy fluxes toward the ground surface were defined as positive. Fig. 8 is a comparison of the simulated mean conductive heat flux for every month for different snow thickness factors during the snow season of 1997–1998. Increasing the snow thickness factors from 0.25 to 1.75 results in decreases in the magnitude of the mean conductive heat flux through ground to snow surface, due to the decreases in the temperature differences between the snow surface and ground surface. Decreases in the snow thickness can increase the conductive heat flux substantially, while increases in the snow thickness have relatively small influence on the conductive heat flow to the atmosphere. For instance, decreasing snow thickness factor from 1.0 to 0.5 and 0.25, respectively, the magnitude of the mean conductive heat flow to the atmosphere for December increases from 5.87 to 10.17 and 14.58 W m− 2, respectively, while increasing snow thickness factor from 1.0 to 1.5 and 1.75, respectively, the magnitude of the mean conductive heat flow to the atmosphere for December decreases from 5.87 to 4.30 and 3.77 W m− 2, respectively. The mean conductive heat flux for every month period from October 1997 to March 1998 was positive, and for the two-month period from April through May in 1998 was negative, reflecting the release and absorption processes of the active layer and permafrost. 4. Discussion Numerical modeling is generally regarded as the most effective method to simulate and forecast the thermal regime of the active layer and permafrost (e.g., Brown et al., 1964; Harlan, 1973; Nixon, 1975; Miller, 1979; Jame and Norum, 1980; Guymon et al., 1984; Kane et al., 1991; Zhang and Stamnes, 1998; Ling and Zhang, 2003a,b, 2004a). The modeling studies for the influence of the seasonal snow cover on the ground thermal regime
have received considerable attention during the past few decades (e.g., Lachenbruch, 1959; Goodrich, 1982; Lachenbruch and Marshall, 1986; Zhang et al., 1996; Zhang and Stamnes, 1998; Zhang et al., 2001). The most widely used upper boundary condition for numerical simulation is the snow surface temperature when seasonal snow cover was present, and the ground surface temperature when seasonal snow cover was absent. And the surface temperatures are observed values derived directly or indirectly from air temperatures. An accurate description for surface temperature should use physically based models that account for the relevant processes occurring within, and at the boundaries of permafrost, snow, and atmospheric components of the natural system. The surface energy balance approach is a reasonable method of establishing surface temperature boundary conditions because it tends to preserve the cause and effect relationship between surface temperatures and heat fluxes (e.g., Myrup, 1969; Outcalt, 1972; Miller, 1979). There have been used, but relatively fewer in number, for simulating the ground thermal regime by using the surface energy balance approach to estimate surface temperature conditions. Several surface energy balance models, which are forced with daily weather information, have been developed and used to simulate the snowmelt and tundra soil thermal regime (Outcalt et al., 1975; Miller, 1979), and to investigate the effect of tundra vegetation and climate change on ground temperature (Ng and Miller, 1977; Smith and Riseborough, 1983). However, these models do not include the effect of unfrozen water on soil thermal properties. Hinzman et al. (1998) developed a spatially distributed surface energy balance model for calculating soil temperature profiles and thaw depth in permafrost regions. The model performs quite well with one-day time increments, but seasonal snow cover was not included in the model.
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Based on a surface energy balance approach for lake ice evolution (Liston and Hall, 1995) and a heat conduction model with phase change for freezing and thawing of permafrost containing unfrozen water (Osterkamp, 1987), Ling and Zhang developed a numerical model for the subsurface system of snowactive layer-permafrost (Ling and Zhang, 2004b). The surface energy balance approach was used to estimate the upper boundary condition for numerical thermal conduction calculations. The heat conduction model is a one-dimensional finite difference model for the active layer and permafrost containing unfrozen water. The influence of unfrozen water on the thermal properties of soils was accounted for in the heat conduction model. And the impact of snow was included in the combined model by extending the heat conduction solution into the snow layer and computing the surface heat balance components and the snow surface temperature. The model was validated against field measurement the observed ground temperatures at Barrow, Alaska, and the results show that the simulated soil temperatures track the measured soil temperatures well in the active layer, near the permafrost surface, and in shallow permafrost. On the basis of the developed model with some modifications (Ling and Zhang, 2006) and field measurements, Ling and Zhang conducted several investigations on the impact of variations in thickness, timing and duration, and density of the seasonal snow cover on surface energy fluxes and the thermal regime of the active layer and permafrost on the North Slope of Alaska in previous studies (Ling and Zhang, 2003b, 2005, 2006) and the present study. The primary consequences and implications from the previous studies can be summarized as follows: 1) the thermal regime of the active layer and permafrost in the Alaskan Arctic is sensitive to variations in the timing and duration of seasonal snow cover, due to variations in surface conditions and the associated ground surface energy balance. Delaying the snow cover onset date in autumn results in a decrease in ground temperatures, advancing the snow cover disappearance date in spring leads to an increase in ground temperatures, and delaying the snowpack disappearance date in spring results in a decrease in ground temperatures. The active layer thickness also has a corresponding response to variations in the timing and duration of seasonal snow cover, but the change is very limited. Previous studies show that much of the Arctic has already warmed significantly (Serreze et al., 2000) and Arctic permafrost is thawing (Osterkamp and Romanovsky, 1999).
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These results suggest that the earlier disappearance of spring snow cover (Stone et al., 2002) has an important contribution to Arctic warming and permafrost thawing. 2) varying the snowpack disappearance date by 10 days in spring can strongly affect the mean annual net solar radiation, sensible heat flux, and latent heat flux, and can slightly affect the mean annual net longwave radiation and conductive heat flux. Groisman et al. (1994) suggested that there is a strong positive feedback between spring snow cover and the radiative balance over northern extratropical land. The global warming that has occurred in the spring during the twentieth century is likely to have been significantly enhanced by corresponding changes in snow-cover extent. Thus, the transient effects of external climate forcing, such as greenhouse warming, may be especially prominent during spring in the Northern Hemisphere, where snow-cover variations substantially affect the radiative balance. The simulated results from our model agree well with their result. 3) changes in snow density have significant influences on ground surface temperature and near-surface ground temperature because snow density determines the snow thermal conductivity and volumetric heat capacity. But changes in snow density have very limited impact on the snow surface temperature and the active layer depth, as the ground surface temperature is higher during snow-free periods due to the significant increase in the net radiative forcing following the last day of snowmelt (Stone et al., 2002) and the higher mean daily air temperature, the ground temperature differences caused by variations in snow density reduced very quickly after the ground surface became snow free. 4) variations in snow density can influence the conductive heat flux considerably in northern Alaska, reflecting the variations in snow thermal properties. But variations in snow density have insignificant influence on the sensible and latent heat fluxes, reflecting the very limited variation in mean daily snow surface temperature. Snow cover was regarded as multiple layers in the current model and the number of layers was determined by snow thickness using formula (2). Based on the conclusion that time-density curve for tundra snow hardly change at all over the winter at a specific location in northernmost Alaska because pulverized drift snow tends to be dense right from the start (Sturm and Holmgren, 1998), this study sets the snow density to a
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constant value of 362 kg m− 3, which was determined by fitting the calculated ground temperatures at different depth to the measured values using the trial and error method. However, this is an ideal assumption to simplify the modeling study. The structure of seasonal snow cover usually consists of hard, higher-density, wind-packed slab layers at the top with coarse, lower-density depth hoar layers at the base, due to high wind speeds and low air temperatures (Benson and Sturm, 1993). Variations in the snow cover thickness would result in changes in the depth hoar fraction, thus lead to changes in snow density. A previous study has shown that in permafrost regions, variations in depth hoar fraction can affect ground surface temperature and the mean annual ground surface temperature, and delay the active layer freeze-up (Zhang et al., 1996). Further studies for model improvement to include the impact of depth hoar layer are needed. Properties of seasonal snow cover, such as density, albedo, thermal conductivity, emssivity, and roughness length, have obvious distinctions in autumn, winter, and spring, particularly during the snow melt period. This can affect the surface energy balance significantly, and thus the thermal regime of the active layer and permafrost. Besides, the time step used in the presented model is daily rather than an hourly or a shorter time scale, because the hourly observed data are not available. This also can affect the simulation precision. In order to better simulate the combined influence of seasonal snow cover on the thermal regime of the active layer and permafrost, systematic field measurements of the variations in snow properties with time and further studies for model validation using hourly time step and observational snow surface temperature and surface energy balance components are needed, and the variability of snow cover parameters should be taken into account in the model. During the soil thawing period, the infiltration of snow melt water and rainfall increases the soil temperature sooner than the model would predict, as has been observed in field studies at Barrow (Kane et al., 1991; Hinkel et al., 2001; Ling and Zhang, 2003b). Convective heat transfer becomes progressively more important as the soil warms and remains unfrozen longer. In addition to the effect of convective heat transfer in the active layer, convective heat transfer in seasonal snow cover could also play a role (Sturm and Johnson, 1991). This nonconductive heat transfer could effectively reduce the insulating effect of the seasonal snow cover (Stein and Kane, 1983; Hinkel et al., 1997, 2001; Kane et al., 2001). However, the numerical model used in this study does not include the nonconductive heat transfer of the convection. Based on Russian historical soil
temperature and snow depth data, Frauenfeld et al. (2004) found that maximum snow depth by the end of winter has a significant impact on the thaw depth in the following summer. They hypothesize that the impact of snow depth on active layer depth in the following summer may be due to the influence of snow cover on soil moisture. The development of a one-dimensional conductive-convective heat transfer model considering the nonconductive heat transfer processes in seasonal snow cover and the active layer are needed. Permafrost changes mainly refer to changes in active layer thickness and permafrost temperature. In northern Alaska, changes in active layer thickness are mainly controlled by summer air temperature, while permafrost temperature is mainly controlled by winter air temperatures and snow conditions. The overall impact of snow cover on the ground thermal regime depends on the timing, duration, accumulation, and melting processes of seasonal snow cover; density, structure, and thickness of seasonal snow cover; and interactions of snow cover with micrometeorological conditions, local microrelief, vegetation, and the geographical locations. Climate change may lead to decreases in soil temperatures and increases in soil freezing because of lack of an insulating snow cover and changes in soil water dynamics during the important snowmelt period Zhang, 2005). The feedback of increased soil freezing to the climate system is poorly understood and needs further investigation. 5. Conclusions The primary results from this modeling study can be summarized as follows: 1) Changes in snow thickness can significantly influence the near-surface ground temperature in northernmost Alaska. During the snow season of 1997– 1998, a decrease in the snow thickness factor from 1.0 to 0.5 leads to the maximum ground temperature decreased at 0.01 m depth by 2.0 °C, at 0.29 m depth by 1.48 °C, at 1.0 m depth by 1.21 °C, and at 3.0 m depth by 0.72 °C. An increase in the snow thickness factor from 1.0 to 1.5 results in the maximum ground temperature increased at 0.01 m depth by 2.01 °C, at 0.29 m depth by 1.44 °C; at 1.0 m depth by 1.14 °C, and at 3.0 m depth by 0.66 °C. On an annual basis, variation in the snow thickness by 50%, the ground temperature variation of more than 0.25 °C occurs as deep as 8.0 m below the ground surface. 2) Decreases in the snow thickness can strongly increase the conductive heat flow to the atmosphere, while increases in the snow thickness have relatively
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small influence on the conductive heat flow. For instance, decreasing snow thickness by 50% and 75%, respectively, the magnitude of the mean conductive heat flow to the atmosphere for December increases from 5.87 to 10.17 and 14.58 W m− 2, while increasing snow thickness by 50% and 75%, the magnitude of the mean conductive heat flow to the atmosphere for December decreases from 5.87 to 4.30 and 3.77 W m− 2, respectively. 3) The effect of changes in snow thickness on the snow surface temperature is very limited. Decreases and increases in snow thickness by 75%, the corresponding increase and decrease in the average snow surface temperature for the period before snowmelt from September 22, 1997 through March 10, 1998 are just 0.13 °C and 0.04 °C, respectively. Acknowledgments We would like to express our gratitude to the two anonymous reviewers for their constructive criticisms, helpful comments and insightful suggestions on the original version of this paper. Financial support for this study was provided by the Guangdong Natural Science Foundation of the People's Republic of China (Grant No. 04011600); the Scientific Research Foundation for the Returned Overseas Chinese Scholars, the State Education Ministry; the US National Science Foundation through the NSP OPP-0352910 and OPP-0229766; and the International Arctic Research Center, University of Alaska Fairbanks, under the auspices of the NSF cooperative agreement number OPP-0327664. Any opinions, findings, and conclusions or recommendations expressed in this article are those of the authors and do not necessarily reflect the views of the funding institutes and agencies. We are grateful to Robert Stone for providing the measurements of upwelling and downwelling solar irradiance at NOAA/Climate Monitoring and Diagnostics Laboratory Barrow Observatory (CMDL-BRW) used in Fig. 3a and b. References Benson, C.S., Sturm, M., 1993. Structure and wind transport of seasonal snow on the Arctic slope of Alaska. Annals of Glaciology 18, 261–267. Brown, W.G., Johnson, G.H., Brown, R.J., 1964. Comparison of observed and calculated ground temperatures with permafrost distribution under a northern lake. Canadian Geotechnical Journal 1 (3), 147–154. Cohen, J., 1994. Snow cover and climate. Weather 49, 150–156. Cohen, J., Entekhabi, D., 2001. The influence of snow cover on Northern Hemisphere climate variability. Atmosphere-Ocean 39 (1), 35–53.
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