This paper provides a review of permafrost modelling advances, primarily since the 2003 permafrost conference in Zürich, Switzerland, with an emphasis on spatial permafrost models, in both arctic and high mountain environments. Models are categorised according to temporal, thermal and spatial criteria, and their approach to defining the relationship between climate, site surface conditions and permafrost status. The most significant recent advances include the expanding application of permafrost thermal models within spatial models, application of transient numerical thermal models within spatial models and incorporation of permafrost directly within global circulation model (GCM) land surface schemes. Future challenges for permafrost modelling will include establishing the appropriate level of integration required for accurate simulation of permafrost‐climate interaction within GCMs, the integration of environmental change such as treeline migration into permafrost response to climate change projections, and parameterising the effects of sub‐grid scale variability in surface processes and properties on small‐scale (large area) spatial models. Copyright © 2008 John Wiley & Sons, Ltd.

This paper defines the climatic and environmental conditions that determine the limits and continuity of permafrost occurrence, in the Canadian context. The analysis utilizes a functional model that links air, surface and permafrost temperature through seasonal surface transfer functions and subsurface thermal properties. The temperature of permafrost (TTOP) results from the interplay between the air temperature, the nival (snow) offset and the thermal offset. These offset values vary systematically and geographically with freezing and thawing indices, snow cover conditions and ground thermal properties. These effects are analysed by calculating offset and TTOP values using Canadian climate station data for air temperature and snowfall. Whilst permafrost is ultimately a climatic phenomenon, the ground thermal conductivity ratio, via the thermal offset, is shown to be the critical factor in determining the southernmost extent of (discontinuous) permafrost. In contrast, snow cover, via the nival offset, is the critical factor in determining the northern limit of discontinuous permafrost (i.e. southern limit of continuous permafrost). Calculated TTOP values increase gradually southwards towards the limit of permafrost occurrence, as the effect of a rising mean annual air temperature (MAAT) is counteracted by an increasing thermal offset. This results in a diffuse geographical transition in the disappearance of permafrost. In contrast, there is a more abrupt transition to continuous permafrost at the northern limit of the discontinuous zone, associated with geographical changes in snow cover and the associated nival offset. The transition from discontinuous to continuous permafrost occurs between a MAAT of −6° to −8°C. This may explain the air temperature limit for continuous permafrost cited by previous authors. Copyright © 2002 John Wiley & Sons, Ltd.

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[1] Most climate records and climate change scenarios projected by general circulation models are for atmospheric conditions. However, permafrost distribution as well as ecological and biogeochemical processes at high latitudes is mainly controlled by soil thermal conditions, which may be affected by atmospheric climate change. In this paper, the changes in soil temperature during the twentieth century in Canada were simulated at 0.5°latitude/longitude spatial resolution using a process-based model. The results show that the mean annual soil temperature differed from the mean annual air temperature by À2°to 7°C, with a national average of 2.5°C. Soil temperature generally responded to the forcing of air temperature but in complex ways. The changes in annual mean soil temperature during the twentieth century differed from that of air temperature by À3°to 3°C from place to place, and the difference was more significant in winter and spring. On average, for the whole of Canada the annual mean soil temperature at 20 cm depth increased by 0.6°C, while the annual mean air temperature increased by 1.0°C. Three mechanisms were investigated to explain this differentiation: air temperature change, which altered the thickness and duration of snow cover, thereby altering the response of soil temperature; seasonal differences in changes of air temperature; and changes in precipitation. The first two mechanisms generally buffer the response of soil temperature to changes in air temperature, while the effect of precipitation is significant and varies with time and space. This complex response of soil temperature to changes in air temperature and precipitation would have significant implications for the impacts of climate change.