Solution to Exercise 4
Part 1: The volumetric heat capacity for each constituent is the product of specific heat and mass density, calculated using the following equation.
The first phase in the thawing process is a saturated and frozen soil column. The volumetric heat capacity for this phase is derived from the following equation using a theta of zero because the total porosity is ice and the liquid water content is zero.
The second phase is characterized by saturation of the soil and in the absence of ice and is estimated from the following equation.
The final phase is characterized unfrozen, unsaturated soil with a drained water content θd of 0.5, thus volumetric heat capacity is estimated from the following equation.
The following table presents the computed values of volumetric heat capacity for the three soil conditions using kilojoules
Part 2: First divide the peat profile into a number of computational layers, and conclude that the uppermost layer will be the layer that thaws first, thus would be the first to transition from an ice-water-soil mixture to one of water and soil only, and finally to an unsaturated mixture of water-soil-air. Assuming that each layer below also thaws and drains, they too would follow this same transition, although the initiation of the transition would be delayed with increasing depth below the ground surface. Peat layers composed of an ice-water-soil mixture warm relatively quickly. For layers near the ground surface, this condition is relatively short-lived since such layers are the first to thaw. Deeper layers can remain in this condition for extended periods. With the transition to the next composition stage of water and soil only, the rate of warming reduces considerably due to the increase in specific heat that accompanies the phase change of ice to water. Layers that transition to the final compositional stage of water-soil-air, can warm readily given the much lower specific heat of air than water. The rate and pattern of warming of the peat profile therefore depends on the rate that its individual layers thaw and drain. Precipitation inputs including the amount of snow water equivalent present at the end of winter, the slope of the ground surface, and the hydraulic properties of the peat in each computational layer each effect the rate of thaw and drainage and therefore indirectly affect the rate and pattern of peat profile warming.
Part 3: Given the high porosity of peat, this soil type is susceptible to large variations in thermal conductivity with variations in soil moisture content and phase changes. When frozen and saturated, peat is a highly effective thermal transmitter. During winter, this enables the peat profile to conduct energy toward the atmosphere at high rates in response to the upward directed thermal gradient. As the soil thaws, it becomes saturated with liquid water. In this condition it is still a highly effective thermal conductor and conducts energy from the ground surface into the peat profile at high rates in response to the downward directed thermal gradient. For this condition, ground thaw proceeds at a high rate. With continued thaw and drainage, layers in the upper part of the peat profile become unsaturated and as a result, their thermal conductivity decreases. For this condition, the near-surface layers become effective thermal insulators, and the rate of ground thaw therefore decreases.