A climate change scenario experiment conducted with the state-of-the-art coupled atmosphere-ocean general circulation model ECHAM4/OPYC3 is analysed with the objective to quantify changes in present-day Arctic permafrost conditions. An efficient procedure is adopted which overcomes the many problems associated with an explicit treatment of soil freezing and thawing processes. The zero degree soil temperatures as well as induced permafrost index characteristics simulated by the model for present day conditions match well the observed permafrost zonation. For a future scenario of greenhouse gas emissions (SRES A2 issued by IPCC), we estimate the amounts that the permafrost zones moves poleward and how the thickness of the active layer deepens in response to the global warming by the end of the 21st century. The simulation indicates a 30–40% increase in active-layer thickness for most of the permafrost area in the Northern Hemisphere, with largest relative increases concentrated in the northernmost locations.
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 Permafrost currently underlies nearly one fourth of the exposed land area of the Northern Hemisphere (NH) [Zhang et al., 1999]. Under warmer climatic conditions much of this terrain would be vulnerable to subsidence, particularly in ice-rich areas of relatively warm, discontinuous permafrost [Osterkamp et al., 2000]. Studies based on coupled ocean-atmosphere general circulation models (OAGCMs) have revealed that the area of the NH occupied by permafrost could eventually be reduced quite substantially in a warmer climate [Anisimov et al., 1997; Smith and Burgess, 1999]. Thawing of ice-rich permafrost is, however, subject to a considerable lag resulting from large latent heat of fusion of ice. It could therefore persist in relict form for centuries or millennia. The present formulation of state-of-the-art OAGCMs prohibits a detailed description of these processes as even the most advanced schemes applied to treat subsurface soil processes do not reach far into the ground. Only rarely depths below 5 meters are treated explicitly. It therefore seems necessary to diagnose the presence or absence of permafrost by other methods than deduced from direct model output. [Anisimov and Nelson, 1997] assessed the permafrost distribution in the NH under scenarios of climate change adopting a simple permafrost model based on the concept of a ’surface frost index‘. Recently, [Christensen and Kuhry, 2000] applied this index to a high-resolution present day climate simulation over the Arctic part of European Russia. They found that the index offers a powerful tool in diagnosing permafrost zonation in climate models. In applying it to simulated soil rather than air temperature, complications associated with the treatment of the wintertime snowcover explicitly parameterized in [Anisimov and Nelson, 1997] can be avoided, and the inherent problem in many GCMs related to the lack of a specific description of freezing and thawing processes can be overcome.
 Another important feature of areas underlaid by permafrost is summer time thawing of the upper soil layers, the so-called ‘active layer’. This phenomenon has for obvious reasons practical implications in the regions where it occurs. The direct modelling approach to estimate changes in active layer thickness seems to be to treat specifically the thawing and freezing of the soils. However, as present-day OAGCMs operate at scales coarser than 300 km by 300 km, the rather fine scale heterogeneous soil structures in the Arctic cannot be treated realistically. Hence, the bulk change estimates from such simulations would offer little practical advances compared to more simple modelling efforts, such as using also here a ‘frost index’ or rather ‘thaw index’ [Anisimov et al., 1997] based an assessment of NH climate change impacts on the active layer thickness on a relatively advanced model of the active layer. This formulation, however, also requires a parameterization of winter time snow pack. The most straight-forward approach to estimate the thickness of the active layer is based on a simple version of Stefan's solution [Stefan, 1891] for the heat transfer problem in a solid medium. Here we will demonstrate that our approach, which is based on model soil temperatures rather than air temperatures, offers a methodological shortcut. Therefore, improvements to the diagnostics of simulated permafrost-related properties are possible.
2. Model and Simulation Configuration
 The OAGCM that is used for this study consists of the atmospheric component ECHAM4 [Roeckner et al., 1996] and the oceanic component OPYC3 [Oberhuber, 1993]. Both have a horizontal resolution of about 2.8° poleward in the extratropics. [Roeckner et al., 1999] give a detailed description. For the climate change experiment, described in [Stendel et al., 2000], the model has been forced by observed concentrations of well-mixed greenhouse gases for 1860 to 1990, whereas for 1990 to 2100, greenhouse gas concentrations and sulfur emissions are derived from the IPCC SRES scenario A2 [Nakicenovic et al., 2000].
 The soil model comprises the budgets of heat and water in the soil, the snow pack over land and the heat budget of land ice as prognostic equations. Vegetation effects such as the interception of rain and snow in the canopy are parameterized in an idealized way. Land surface parameters, such as background albedo, roughness length, vegetation type, leaf area index and soil parameters, such as water holding and heat capacities and thermal conductivity are given by [Claussen et al., 1994]. Snow can melt if there is sufficient energy available to raise the temperature of the top of the snow cover above the melting point. However, thawing and melting of the soil are not treated specifically. For brevity, we refer to [Roeckner et al., 1996] for further details.
 Temperature is calculated as a prognostic variable for five soil layers whose thickness increases with depth (0.065, 0.254, 0.913, 2.902, and 5.7 m, respectively). At the lowest layer, a zeroux lower boundary condition is prescribed in order to ensure that the energy balance is not affected by artificial heat sources or sinks.
3. Permafrost and Active Layer Indices
 Based on the work of [Nelson and Outcalt, 1987], a ‘normalized’ permafrost index F can be defined as , where DDF (DDT) stands for the annual degree-days of freezing (thawing), i.e. the sum of daily mean temperatures below (above) 0°C. F is normally applied to 2 m air temperatures because observations of soil temperatures are generally not available. Here we calculate F on the deepest model soil layer, thus relating the frost index directly to quantities significant for permafrost, avoiding empirical approaches as in e.g., [Anisimov and Nelson, 1996, 1997] that relate surface to air temperatures and additional factors that take into account snow cover, vegetation, organic layers etc.
 Following [Christensen and Kuhry, 2000], the daily values are approximated by monthly means. Sporadic, discontinuous and continuous permafrost are then given by F values of 0.5, 0.6, and 0.67, respectively. Using a value of 0.67 for continuous permafrost may appear as a problem, since values smaller than 1 imply there is thawing at depth, so per definition permafrost does not exist. However, contemporary GCMs cannot resolve the fine structure of permafrost soils adequately due to their coarse resolution, so that the value of 0.67 is rather a gridbox average than a point value (see also the discussion in [Nelson and Outcalt, 1987]). When the index is applied to soil temperatures (which are prognostic quantities in the GCM), no special treatment of the insulation effects due to snow cover is required, as this is handled implicitly by the GCM itself.
 The active layer thickness can be derived from the Stefan equation [Stefan, 1891]:
with active layer thickness H, thermal conductivity λ, density ρ, latent heat of fusion L, freezing temperature Tf and temperature at the uppermost soil level Ta. This equation, originally derived for the description of the growth of sea ice, is only a simplification. The adaptation of Stefan's theory to the treatment of soil thawing and freezing is discussed in detail in [Andersland, 1994]. However, these more advanced descriptions do not substantially alter the ideas we present in this paper. Here we use the uppermost soil layer to obtain a good approximation for the amount of heat entering the frozen soil from the atmosphere. The simple analog between freezing and melting can be applied if we assume that the soil is not saturated with water. When evaluated for Δt = 1 day, the integral gives the number of thawing-degree days. Following [Anisimov et al., 1997], we can then estimate the active layer thickness for specific soil types.
 The effect of the buffer layer (vegetation and organic layer) which modulates the transfer of air temperature changes to the ground is calculated by the model and does not need to be approximated (compare [Nelson et al., 1997]). Obviously, this procedure gives only an approximation of the active layer thickness, since in general different soil types may be present within a grid box, and the effect of vegetation on top of the active layer is rather crudely parameterized in GCMs. Therefore this estimate will give us a lower boundary of the active layer thickness. This approach does not take into account that actual layer thickness can vary over short distances due to variations in soil type, moisture content and vegetation cover. Therefore the ratio of active layer thicknesses at different times, discussed next, is probably a more useful parameter. It should also be stressed that the estimation of actual layer thickness could be extended here by taking into account additional terms referring to thaw consolidation etc.
 Under climate change conditions, many uncertainties due to soil properties can be avoided by calculating the ratio of the active layer thicknesses from equation (1) at different times, i.e., , where t1 stands for present-day climate and t2 is calculated from scenario A2. This quantity is independent of density, conductivity and soil type and depends only on temperature. In contrast to the calculations based on air temperatures in [Anisimov et al., 1997], A is calculated here from the uppermost soil layer. We assume that the soil thermal properties are constant with depth and also with time. This simplification appears reasonable because under warming conditions, the soil would become drier so that thaw consolidation is not a major factor. It should be noted that warming may not necessarily result in significant changes in active layer thickness, especially when ice-rich soil is present [Wolfe et al., 2000; Smith et al., 2001]. Thaw settlement in ice-rich soils may occur as the deeper soil layers thaw with warming. Maximum summer thaw penetration measured from above the surface may therefore show a steady increase over time which may not be rejected in a similar increase in active layer thickness due to thaw consolidation.
3.1. Present-Day Permafrost Zonation and Active Layer Thickness
Figure 1 shows in blue the zonation of permafrost calculated from the deepest model soil layer (5.7 m) under present-day climate conditions. A detailed elevation map is underlaid in gray for guidance. Compared to observations ([Brown et al., 1997; Heginbottom et al., 1995]), the index captures the large-scale distribution of permafrost. Regional details in at areas, such as northeast Asia, are also reproduced well. Due to the coarse model resolution, the unrealistic model topography (not shown) causes less similarity to observations in areas with steep elevation gradients, such as Scandinavia and the Canadian Rockies, where high-elevation permafrost is not covered well.
 The thickness of the active layer under present-day climate conditions is shown in Figure 2 for several soil types and water contents with values for density and thermal conductivity taken from [Anisimov et al., 1997]. The thickness of the active layer is typically 20 to 40 cm in sand (not shown), silt or clay and 40 to 90 cm in peat. The absolute values in the present study are somewhat lower that those of [Anisimov et al., 1997], while the geographical variation is similar.
4. Climate Change Scenario
4.1. Temperature and Snow Cover
Figure 3 shows the geographical distribution of winter (DJF) temperature change in the deepest soil layer in scenario A2, expressed as the difference of the periods 2071–2100 and 1961–1990. Warming of more than 5 K is simulated for most regions where we find permafrost today. According to the scenario, a general decrease in the number of days with snow cover is simulated (not shown). Under present-day climate conditions, the ground is covered with snow more than 70% of the time everywhere in northern Russia poleward of 60°N except in the lowland areas west of the Jenissej river. In the simulation, this area will shrink by 50% by the end of the century. Changes further to the south (snow cover disappears in summer already under present-day conditions) and in Canada (elevated terrain with perennial snow cover) are smaller.
4.2. Permafrost Zonation
Figure 1 shows in red the distribution of permafrost in scenario A2, calculated by means of the frost index F. According to this calculation, permafrost retreats below the lowest soil level in most of the Russian and Canadian Arctic. However, this approach does not take into account that heat transfer in frozen soils is mainly achieved by conduction and therefore very slow and the lack in reaction between reaction of the upper layer and deep permafrost is not taken into account. Following [Anisimov and Nelson, 1996], the map is therefore best interpreted as representing the potential permafrost distribution realisable only after a long and steady period under the new climatic conditions.
4.3. Active Layer Thickness
 The ratio of the active layer thicknesses for scenario A2 (2071 to 2100) and present-day climate (1961 to 1990) is shown in Figure 4. For most of the Russian Arctic, we find an increase in active layer thickness by 30 to 40%. The largest values are found in northeast Siberia and in Western Canada. Further south, in northern China and Mongolia, in parts of Canada and Alaska, the active layer deepens so much that the permafrost retracts into deeper layers and disappears from the surface. This does not necessarily imply that a talik forms, but that the permafrost moves below the lowest model layer. Small permafrost “domes”, however, would disappear completely, since permafrost not only moves into the ground, but also retreats sideward.
 Because most exchange of energy, moisture, and gases between the atmospheric and terrestrial systems occur through the active layer, thickening of this order most likely would have important effect on geomorphic, hydrological and biological processes. When the upper layer is rich in ice, such a thickening may have severe destabilizing effects on inadequately constructed infrastructure ([Smith and Burgess, 1999]). It could also trigger the release of additional amounts of greenhouse gases to the atmosphere [Michaelson et al., 1996]. Given such possible severe consequences of climate change in the circumpolar North, the present relatively crude analysis of an state-of-the-art OAGCM simulation of the SRES A2 scenario provides good qualitative and reasonable quantitative estimates of the possible changes which can be expected under such a scenario. Our findings are in qualitative agreements with [Anisimov et al., 1997], who had to go through a more complicated analysis of climate change simulations with OAGCMs, as the data readily available for such an analysis only would be monthly mean air temperature and precipitation values. In the present study, we have shown that the soil temperatures simulated by the climate model can provide similar estimates of similar quality, albeit at a course resolution, but with much less assumptions and parameterization for post-processing of the data.
 We propose that this technique can be applied to dynamical downscaling experiments as well. The better resolved surface structures in such models will enable a more detailed analysis of the geographical variations in these changes. In general, the analysis has revealed that regions which at present have a relative shallow active layer (e.g., at high latitude or high altitude) will experience the largest relative changes in a warmer world. The consequences can, however, be more damaging in areas where the change is relatively small if the absolute change is high. According to the present analysis, this would be the case within the perimeter of the present day permafrost limits.
 The authors would like to thank Dr. P. Kuhry for introducing us to permafrost research. This work also benefitted from useful discussions with Dr. O. Anisimov on simple approaches that can be adopted to process GCM data in a meaningful way.