## The effect of boundary conditions on the permafrost thickness and temperature regime

The depth of the perennial freezing cper, the thickness of permafrost formed as a result of harmonic temperature fluctuations on its surface, is

South

North

7"pLr = 10 years

North

7"pLr = 10 years

defined by the upper (7^,., Apei, t^an) and lower (g) boundary conditions as well as by specific lithological features: heat conduction A; heat capacity C and moisture content Wof the materials:

It follows from this dependence that the processes controlling permafrost thickness are in many respects analogous but not identical to the processes in seasonal ground freezing. Given the similarity of thermal-physical processes in seasonally and perennially frozen ground, the development of the latter depends on a more complicated interaction of geological and geographical conditions. As follows from the equation (1.35), the depth of perennial freezing appears to be directly proportional to the period of the fluctuation:£per oc i.e. it increases with the increase of the duration of the fluctuation. This dependence still applies under any change of the other parameters (Qph, Aper, i^eeran, X, C). At the same time, as in the case of seasonal ground freezing with T = 1 year, the process of the perennial freezing proper lasts usually during a third part of the period (t « 1/3 7). As an example we can consider the results of calculations (using a hydrointegrator) for perennial freezing of the upper layers of the lithosphere under the following conditions: Cean = 0°C, Tpei = 100000 years, Apei = 6°C,g = O.OlTm"1, A = 2.89 kJ (m hr °C)"1, Qph = 99,219 kj m " 3 (Fig. 12.4). The data obtained show that the permafrost thickness being formed on account of 100 000-year fluctuations under the values of thermal physical coefficients and moisture content given comprise from 180-210m. It takes approximately 33 thousand years to freeze these thicknesses entirely. The rate of freezing, i.e. the rate of advance of the permafrost base, is a few centimetres per year at the beginning of the process, while at the end of freezing it is fractions of

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