ement were sampled and examined with an oven-dry bulk density of 0.91 g∙cm−3 and soil organic carbon content of 139.09 g∙kg−1.
2.2. Measurement and Data Analysis
Soil apparent thermal properties are measured by KD2 Pro Thermal Properties Analyzer (Decagon Devices, Inc., Pullman, WA). The KD2 Pro Analyzer takes measurements using the transient line heat source method  . Briefly, every measurement cycle consists of a 30-sec equilibrium time, a 30-sec heating time and a 30-sec cooling time. Temperature measurements are made every second during heating and cooling processes, and then temperature measurements are fitted with an exponential integral function using nonlinear least-squares procedure. In general, samples are relatively thin (3 -
Moisture contents of soil columns in PVC container were adjusted and balanced for 2 days, and determined accurately by calculating the weight and volume of soil columns after every measurement, and then wrapped up tightly and carefully by transparent soft film. Wrapped soil column with a certain moisture content was incubated in a thermostatic incubator. The incubation temperature was adjusted and balanced completely before measuring the soil thermal properties. Measurements were performed by inserting the KD2 Pro probe horizontally into the middle of soil samples with different moisture contents, soil volumetric specific heat capacity and thermal conductivity were recorded during the cooling process (from 0˚C to −20˚C) and subsequently a heating process(from −20˚C to 0˚C) for each soil sample. Three repeated measurements were conducted for each sample during both heating and cooling processes.
Using SPSS statistical software to analyze data.
3. Results and Discussion
3.1. Apparent Volumetric Specific Heat Capacity (Cv) in Cooling and Heating Processes of Frozen Soil
Soil apparent volumetric specific heat capacity () is presented as a function of soil temperature in cooling and heating processes under different moisture contents (Figure 1(A) and Figure 1(B)). The results show that the Cv decreases as initial water contents decrease, and the values underthe same water content showasimilar response pattern to soil temperatureduring bothheating andcooling processes. One possible reason is that water content is one of dominating factors for under sub-zero temperature, and the frozen soil heat capacities are of attributable to the distribution of ice, voids and mineral materials, and showing a significant decreasing heat capacity with an increase in volumetric fraction of voids in soil will reduce the heat capacity significantly  .
We observed a significant change for when soil temperature near 0˚C (−20˚C - 0˚C). Similar phenomena were also observed by study for the thermal properties of permafrost soil   . Previous studies on thermal behaviors of arctic soils have suggested that vapor advection and the associated latent heat effects may contribute to the heat transfer in frozen soils significantly  , and latent heat release in phase transition of soil unfrozen water and ice may be the most important contributor to the sharp increase in heating process and the great drop in cooling process of when temperature near 0˚C (−20˚C - 0˚C).
We fitted an inverse function for the relationship between and soil temperature ranging from 0˚C to −20˚C. The regression equation was shown in Equation (1):
where A and B are constants, t is soil temperature ranging from −20 to 0˚C, and is the soil apparent volumetric specific heat capacity. The regression constants of A and B are presented in Table 1.
3.2. Prediction of Unfrozen Water and Ice Content in Soil under Sub-Zero Temperature
Ice, water and soil grain are three main phase diagrams impacting thermal properties of freezing soil  ).
Figure 1. Soil apparent volumetric specific heat capacity changes of different moisture content in cooling (A) and heating (B) processes.
Generally, the contribution of air and organic matter can be ignored  . Thus, the specific heat capacity (C) of soil can be given by the following equation:
where, and are the specific heat capacity of soil particles, soil water and soil ice with unit of MJ∙kg−1∙K−1;, and are masses in kg of soil particles, soil water and soil ice, respectively. The
Table 1. Values of constant A and B of Equation (1) for relationship between C and temperature at different water contents in cooling and heating processes beneath zero temperature.
Note: Ww is initial soil qualitywater contents, A and B are constants in Equation (1). * and ** indicate the variation explained by each model is significant at P < 0.05 level, and significant at P < 0.01 level.
Equation (2), when divided by the total mass of the soil sample, yield
where Ws, Ww and Wi are percentage quality of soil particles, water and ice, respectively.
Since the apparent volumetric specific heat capacity of moist soil with unit of MJ∙m−3∙K−1 is given by; is the bulk density in kg∙m−3, and given by
where is the total volume of the soil sample.
So, Equation (3) can be rewritten in the following equation:
Then the ice content of frozen soils can be written as
When T < −10˚C, the vast majority of the unfrozen water is frozen within a few degrees of 0˚C. The unfrozen water content changes very slightly with the initial water content within the range of 1% when the temperature is lower than −10˚C  . The mean value of unfrozen water content we determined by the pulsed nuclear magnetic resonance technique is 2.98% as soil temperature below −10˚C with different initial water contents. We use this value asunfrozen water content to calculate soil apparent specific heat capacity and ice content of frozen soils. Equation (5) can be rewritten as
Generally, the values of and are 4.2 × 10−3 MJ/(kg∙K) and 2.1 × 10−3 MJ/(kg∙K), respectively. Using Equation (7) and Equation (8) to calculate the value of. After getting those parameters, Equation (6) can be used to figure outice content in frozen soils. Regression equations between soil ice contents and soil temperature are deduced utilizing valid data below −2˚C we calculated. After an ensemble test, the following equation give the best estimation:
where is initial water content; is percentage quality of ice below 0˚C; a , b and c stand for constants; t is relative temperature measured in laboratory. Residual sum of squares is used as the sensitivity indicator.
All of soils were regressed by Equation (9) for ice content prediction and the values of constants were presented in Table 2 for each soil moisture condition. Soil ice contents of two selected moisture condition were calculated under sub-zero temperature for cooling-heating cycles (Figure 2). It showed that the changing pattern of soil ice contents was not unique between heating and cooling processes due to retention effect during a one-way process of freezing or thawing, i.e., soil ice content may be different at the same temperature in the two processes.
Soil ecosystems in high altitude and latitude are regarded as higher temperature sensitivity to climate change   , and the effect of temperature and season on soil microorganisms and enzymes has been addressed by several researchers   , and it has been suggested that season-dependent abiotic parameters, such as soil water phase transition and freeze-thaw cycle induced by temperature subzero and above-zero, could influence the microbial community structure   ), ecological function, species diversity and respiration activity  . In fact, we also found that soil temperature in 5 -
3.3. Dynamics of Apparent Thermal Conductivity (K) of Frozen Soil
Soil apparent thermal conductivity (K) decreases with the decrease of temperature and soil moisture contents below 0˚C in both cooling and heating processes (Figure 3(A) and Figure 3(B)). During soil freezing, the volumetric expansion of water as well as ice lens tends to change the soil structure and reduce the hydraulic conductivity  , and the heat transfer between soil components tends to be weakening. The transport of latent heat may exceed the contribution of heat flow by conduction at temperatures close to 0˚C  , and ice melts and soil solution conductivity enhance in heating process. In soil, water is the heat-conducting medium, and it just coats soil particles and voids between the soil particles which are not filled with soil liquid at lower water contents   , indicating that there is a strong dependence of the soil thermal conductivity on moisture in freezing soil. Similar results are also observed   .
We found that there is also a dramatic change of soil apparent thermal conductivity in the study region from −2˚C to 0˚C whether heating or cooling process (Figure 3(A) and Figure 3(B)). In our study, the thermal conductivity of alpine forest soils tends to decrease within a few degrees below 0˚C in cooling process rather than significant increase as a function of temperature within the range of −15˚C - 0˚C as observed in Ling and Zhang’ study  . However, the relationship between thermal conductivity and soil temperature we observed was different from some other studies, Overduin et al.  found similar change pattern as our result in thawing process
Table 2. Values of constant a, b and c of Equation (9) for prediction of ice and unfrozen water ratio at different water contents in cooling and heating processes beneath zero temperature.
Note: ww is initial soil quality moisture contents; a, b and c are constants in Equation (9).
Figure 2. Ice content prediction by Equation (9) in two selected soil moisture in cooling and heating processes under subzero temperature.
below 0˚C with the line heat source, but thermal conductivity data changed adversely in freezing process.
Seigo  found that thermal conductivity-temperature line was almost straight in the frozen sate and the empirical formula of temperature from 0˚C to −170˚C was presented in Equation (10).
where A and B are constant, T is absolute temperature in the study region ranging from 100 kelvin units to 270 kelvin units, K stands for apparent thermal conductivity in freezing soil. In our study, however, the relationship between K and T is presented by the following equation,
where A and B are constant, T is temperature in centigrade (˚C) in the region ranging from −20˚C to 0˚C.
Values of constant A and B with different moisture contents in our study are presented in Table 3. It is
Figure 3. Soil apparent thermal conductivity changes with different moisture contents in cooling (A) and heating (B) Processes.
considered most likely that constant A is the mean value of soil thermal conductivity when soil temperature is below −10˚C, and we also found that values of A decrease as soil initial water content decrease in cooling process.
Table 3. Values of constant A and B of Equation (11) for relationship between K and temperature at different water contents in cooling and heating processes beneath zero temperature.
Note: Ww is initial soil water contents, A and B are constants in Equation (11). * and ** indicate the variation explained by each model is significant at P < 0.05 level, and significant at P < 0.01 level.
We analyzed the relationship between the apparent volumetric specific heat capacity () and apparent thermal conductivity (K) and soil temperature for seasonally frozen soil in alpine zones of the Qinghai-Tibetan Plateau. The results indicate that the values of and K increase as temperature decreases with the same moisture content in cooling or heating processes, and both of them increase with soil water contents within subzero temperature. The asymptotic character of the apparent volumetric thermal capacity and thermal conductivity is at the vicinity of the initial temperature of phase transitions, suggesting the values of and K are particularly sensitive to changes of soil temperature within the range of −2˚C - 0˚C. Moreover, ice content of frozen soils can be well predicted by Logistic model in cooling and heating processes. Our results highlight that soil thermal properties change dramatically near subzero temperature, indicating soil ecological processes may be extremely sensitive to climate warming especially in cold season for the alpine soil in the Qinghai-Tibetan Plateau.
This study was funded by National Natural Science Foundation of China (NSFC, No. 41271094 and No. 40871124). We appreciate the anonymous reviewers for their excellent comments that benefit the improvement of this paper.