Table IX. Space increments for mesh points. 



Table X. Thermal properties of soils. 



In order to include the effect of moisture transpcHrt, thermal properties of soils are considered to be 

 a function of location as well as time. The upper boundary is the surface of the soil at the base of 

 the plant canopy. The measured surface temperatures are used in terms of specified mean values, 

 such as mean daily temperatures, 6-hourly mean temperatures, etc. The lower boundary is a hori- 

 zontal surface located 20 m below the surface where the temperature is presumably constant. The 

 space between these two boundaries is dissected into about 300 mesh points with variable space 

 increments as shown in Table IX. 



The initial condition is introduced into the program in such a way that the measured temperature 

 profile available down to 70 cm below the ground surface is directly fed into the program by the use 

 of polynomial interpolation. The temperatures at the rest of the mesh points are extrapolated by the 

 use of polynomial approximation. The time increment is chosen according to the temperature dif- 

 ference between two successive surface temperatures, so that a sudden large change of surface tem- 

 perature does not introduce error in the finite difference scheme. The criterion of selecting proper 

 time increment was made through error analysis of the present scheme for the Neumann type of 

 problem for which an exact solution is known. 



As an example, the results of computation for temperature cae 7 on control plot 106 will be 

 presented. This core has a 4-cm-thick organic layer and we assumed the two-layered system for 

 which estimated thermal properties are tabulated in Table X. The predicted mean daily temperature 

 profiles as well as observed profiles are shown in Figure 12 and the thaw depths are plotted in 

 Figure 13. The accuracy of prediction ds quite satisfactory. It is obvious from these graphs that 

 soil temperature can be accurately predicted any time during the summer based upon known surface 

 temperatures and soil physical properties. Thermal properties of soils, especially in the organic 

 layer, and the moisture contents in frozen soils are two major factors influencing the thaw depth. 

 The moisture contents of frozen soils were measured gravimetrically on samples adjacent to this core, 

 but the thermal properties were estimated based on available literature. Therefore, the ultimate 

 validation of the model still requires the accurate determination of thermal properties of the soils. 



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