Model Calculations

Early estimates (Haeberli 1985) already clearly indicated that latent heat effects would cause complete melting of perennially frozen rock glacier debris rich in ice to require many centuries, even with instantaneous atmospheric warming by several °C. Increasing temperatures over time and complicated effects from snow cover (Lutschg et al. 2003, 2004; Lutschg and Haeberli 2005) could easily extend such time scales beyond the millennium. In contrast to small and medium-size mountain glaciers, mountain permafrost will, therefore, continue to exist for long time periods into the future, though in a state of growing disequilibrium with respect to thermal conditions at the surface and with extreme heat-flow anomalies (reversal) down to depths of several tens of meters or more.

The same is true for permafrost in rock summits with steep slopes and walls. Time-dependent spatial heat diffusion modelling of idealized topographies provides fundamentally important insights (Fig. 14.7; Noetzli et al. 2007). After 100 years already, i.e., after twenty-first century warming, permafrost conditions may no longer exist at the surfaces of sun-exposed slopes, but frozen rocks may still be present at some depth below, as influenced by colder temperatures from both earlier centuries as well as colder slopes facing away from the sun. Roughly the 500 top meters of sharp mountain peaks are effectively decoupled from geothermal heat, and undergo changes influenced by multilateral warming as well as by strongly asymmetrical and often sub-horizontal heat flow through the mountain from warm to cold sides.

Inhomogeneities such as the occurrence of ice-filled cracks and fissures certainly cause more complex developments in reality. Penetration of surface water into such linear features, with almost stepwise increasing hydraulic permeability when thawing, is likely to lead not only to strong acceleration of deep warming but also to highly irregular structures of the thermal field inside mountain peaks. Together with modelling snow-cover effects, realistic simulation of the influence from ice-containing heterogeneities constitutes one of the primary challenges in climate-change-related research about mountain permafrost.

Fig. 14.7 2D-temperature field (top) and heat flow (bottom) for an idealized high mountain peak with a cold and a warm side and with a linear warming of 3°C/100 years. From Noetzli et al. (2007)
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