## Perennially frozen ground

As noted above, the particular value of surface temperature is formed in the process of interrelated and mutually conditioned variation of the individual components of the radiation-thermal balance in the 'ground-atmosphere' system. There are several methods of determining the functional relationship between the temperature regime of the Earth's surface and certain components of the radiation-thermal balance. One of them is associated, for example, with determination of the difference of mean annual temperature of surface and air Aip using the value of the turbulent component p of the radiation-thermal balance. It is assumed that the temperature field of the soil and air is a result not only of radiation-thermal exchange over the surface of the given site, but also a result of inflow and outflow of heat in the course of air circulation. With the known coefficient of convec-tive heat transfer k from the surface the above relationship can be expressed by the equation:

then

Another method of determining dependence of soil temperature on components of the radiation-thermal balance is based on solution of the balance equation as to Iet:

where a is Stefan-Boltsmann's constant (2.08 x 10" 7); s is radiating power of the surface as compared with that of an absolutely black body (0.85-1.0); rsurf is the absolute temperature of the radiating surface; e is absolute air humidity; n is cloud cover in fractions of a unit; c is coefficient of variation of cloud cover by latitude.

By simple transformations and using the values of all parameters included in the equation (10.6) mean annual temperature T of the radiating surface can be obtained from the summer (index 'S') and winter (index 'w') periods (17):

1 ( JiQäir + 9dif)(l - <4 - LEs -Ps- -.78Bs year 2V^W (1 - cn*)(0.4 - 0.06^)

, </(Qdir + gdif)w(l ~ «)w ~ LEw - Pw + 0.7Bw Q (1-^(0.4-0.067^)

If the right-hand side of this equation is equal to or less than 273.1K, then perennially frozen ground can be formed. Condition Tyeà[ < 273.1 K shows that mean annual temperature of the layer that underlies the ground surface is below 0°C, i.e. water will freeze and the ground will pass into the frozen state. In truth, that will be valid for a bare surface without snow cover and vegetation and in the absence of infiltrating water and of a temperature offset in the layer of seasonal freezing.

Finally, dependence of ground temperature on components of the radiation-thermal balance can be determined from the balance equation solved against annual heat cycles in the ground B. Indeed, since the heat cycles in soil and rocks depend on the temperature regime of the ground, and the thermal conductivity, heat capacity and phase transformations of moisture are known (17), then:

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