1) Temperature excursion 



a. at surface 

 272°K to 292.5°K. 



b. at -4 cm 

 274.8°K to 278°K. 



c. at -16 cm 

 275.2°K' to 276°K. 



2) Time lags of temperature minima from surface minimum: 



a. at -4 cm 



80 minutes or 16 time steps. 



b. at -16 cm 



5 hours or 60 time st^ps. 



From Tables XIa and Xlb it is clear that the simulated results on temperature extremes indicate 

 wider excursions throughout the ranges of albedo and thermal conductivities covered. At the surface, 

 the maxima and minima decline with increasing albedo while with increasing conductivity the max- 

 ima decline and the minima increase. Roughly extrapolating, the model would behave like the 

 observations for an albedo of 0.5 and a thermal conductivity of 0.003. At the 4-cm depth the model 

 temperature extremes behave somewliat differently and it is clear that to agree with observations, 

 we would have to go much further outside the albedo-thermal conductivity range. 



On the other hand. Tables XIc and Xld show substantial agreement for thermal conductivity 

 between 0.0026 and 0.0034 and appropriately no dependence of the time lag upon the albedo. 



The principal driving force of the physical variations is the diurnal variation of solar radiation 

 intensity incident upon the ground surface. However, both in reality and in the model there are two 

 additional driving forces of different spectral content. First, there is the wind vector which rotates 

 with an inertial period of 12 hours. Second, there is a nonlinear relation between turbulent thermal 

 transport in the atmosphere and the local vertical temperature gradient which generates high harmonics 

 of the diurnal frequency. Finally, there is the problem of real random cloud cover variation which is 

 not represented by the constant cloud cover assumption in the model and which may introduce into 

 observations a strong stochastic spectral contribution. 



In an effort to eliminate diurnal harmonic spectral contribution, the temperature minima were 

 followed. Below the ground surface thennal conductivity may not vary with depth to judge simply 

 by the fact that the -16 cm lag is 4 times the -4 cm lag. The reference level later may be chosen 

 more rigorously according to the thaw depth which is diurnally invariant during July and the tempera- 

 ture gradient at the -16 cm depth. 



Disagreement of the model results in surface temperature excursion is probably due to greater 

 cloud cover prevalent for the specific day of the 1966 observations. More cloud cover can easily 

 be introduced into the model to try to bring temperature excursion at both surface and 4-cm depth 

 into agreement for overall thermal conductivity between 0.0026 and 0.0034. Next, the 1966 data 

 and the model data can be processed so as to extract a nearly pure diurnal component and with this 

 information to solve the thermal conductivity as depth-dependent in two layers (0-8 cm and 8-16 cm 

 depths). At that point, an approximate representation of the physical parameters required by the 

 numerical model will have been constructed. 



Using the 1970 summer data, it will be possible to solve more closely the depth-dependent ther- 

 mal conductivity parameter. There are also better atmospheric data available for input data and more 

 comprehensive comparisons including those for wind and moisture. For both 1970 and 1966 seasons, 

 we will then have a model that works well enough to calculate the downward energy flux at the thaw 

 level. As further comparison data become available, the model will be applied to thaw lakes in 

 summer and winter, and lowland polygonal ground in other summer months and under snow during the 

 winter. 



27 



