SEARCH

SEARCH BY CITATION

Keywords:

  • snow temperature;
  • vertical snow temperature gradient;
  • Western Tianshan Mountains;
  • China

ABSTRACT

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Materials and method
  5. 3. Results and discussion
  6. 4. Conclusion
  7. References

The temperature of snow at 10 discrete vertical levels in the snow pack was measured using automatic temperature recorders at 10 min intervals following 5 snowfalls between January and March 2009 at the Tianshan Station for Snow Cover and Avalanche Research. The amplitude of the diurnal fluctuation in the temperature during the measurement run of 10 March 2009, when the snow was melting, was 1.85 times greater than during the measurement run of 15 February, when snow was accumulating. Analysis of the vertical temperature gradient for all five measurement runs shows that the temperature gradient of the snow was at a maximum value at the snow surface. The maximum snow temperature gradient was measured during the run of 21 January and was 4.46 times greater than during the run of 15 February. The temperature gradient was approximately zero 30 cm below the snow surface. Analysis of the characteristics of the snow temperature and the daily mean volumetric moisture content of the snow leads to the conclusion that the snow cover in the western Tianshan Mountains can be divided into stable, interim, and melting stages. A critical snow volumetric moisture content of 0.1% separates the stable and interim stages, while a volumetric moisture content of 0.3% separates the interim and melting stages.


1. Introduction

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Materials and method
  5. 3. Results and discussion
  6. 4. Conclusion
  7. References

Snow temperature is a basic physical property of snow (Sokratov, 2001). Changes in snow temperature influence the position of snow crystal particles in the crystal lattice during metamorphism (Dexter, 1986). The uneven temperature distribution in snow results in a temperature gradient, which is one of the important variables that determine the processes of heat and mass transfer (Armstrong, 1977; Birkeland, 1998) and metamorphism (Colbeck, 1982; Bartelt and Lehning, 2002; Miller, 2002). It also determines water vapour migration and snow crystal growth in the snow layers (Sokratov, 2001). Dry snow metamorphism is often divided into two types, depending on the value of the temperature gradient. When the temperature gradient is low, differences in curvature between adjacent snow grains have a role in vapour transport and the term ‘equi-temperature’ (ET) metamorphism is used. When most of the water vapour transport is caused by the temperature gradient in the snow pack, the term ‘temperature-gradient’ (TG) metamorphism is used (Sommerfeld and Lachapelle, 1970). Domine et al. (2008) specify the value of the temperature gradient that is the limit between the two metamorphic regimes. Research on crystal types and temperature gradient shows that depth hoar is formed under a high temperature gradient (>0.2 °C cm−1, Marbouty, 1980) that generates strong water vapour fluxes and rapid growth, resulting in crystals with hollow facets and sharp angles. Arons et al. (1998) also concluded that depth hoar is somehow controlled by temperature gradient. Rounded grains are produced by low temperature gradient (<0.1 °C cm−1) metamorphism of precipitating snow (Albert and Shultz, 2002; Domine et al., 2003). Faceted crystals are produced under conditions of moderate temperature gradient (0.1–0.2 °C cm−1, Domine and Shepson, 2002; Domine et al., 2003). With respect to model parameterization (Slater et al., 1998), Kondo and Yamazaki (1990) propose a simple model based on the thermal balance equation of the snow layer but assume a linear temperature fluctuation from the base to the surface of the snow layers. This assumption leads to significant error when predicting the snow surface temperature. Luce and Tarboton (2009) suggest a formula for the parameterization of snow surface temperature in a full snow pack energy-balance model using Fourier frequency analysis to improve simulation accuracy.

Although many recent studies have focused on the mechanisms and influential factors of heat and mass migration during snow accumulation and melting periods, as well as on the micro-crystal change in snow cover (Katoh et al., 1997; Jiang et al., 1998), there is still insufficient comprehensive research on the quantitative variation in snow temperature because snow is a particularly porous medium. Simulation of the temperature field in snow cover is advancing slowly. There has as yet been no clear demonstration of the temperature fluctuation pattern in snow layers. Depending on the effect of air temperature (Birkeland, 2001), snow exhibits significantly different physical characteristics from accumulation to melting stages. It is important to be able to determine the exact stage of the snow cover so as to be able to identify different types of depth hoar growth (Akitaya, 1974), forecast avalanches (Armstrong, 1977; McClung and Schaerer, 1993; McClung, 2002), and predict the arrival of snow runoff and flood. This paper examines the real-time temperature data collected at 10 min intervals from 10 vertical levels in the snow cover of Tianshan Station for Snow-cover and Avalanche Research, and attempts to describe the temperature fluctuation in the snow layers. A quantitative indicator for determining the snow stage is defined based on the evolution of snow temperature and the volumetric moisture content of the snow. These will provide a basis for further research on thermal physics and the energy balance of the snow cover.

2. Materials and method

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Materials and method
  5. 3. Results and discussion
  6. 4. Conclusion
  7. References

2.1. Study area

The study was conducted at the Tianshan Station for Snow-cover and Avalanche Research, Chinese Academy of Sciences (TS), which is located at 43°16′N, 84°24′E, at an elevation of 1776 m above sea level. It lies in the upper reaches of the Künes River in the central zone of western Tianshan Mountains in China (Figure 1). TS is covered with spruce forest all year round and its dominant species is Picea schrenkiana. In TS the mean annual temperature is 1.3 °C and mean annual precipitation is 867.3 mm, of which more than 30% is solid precipitation. Seasonal snow in TS lasts from late October to early April, with a mean depth in the accumulation period of 0.78 m. The maximum depth has not exceeded 1.6 m since 1967. Both lower air temperature (the mean monthly temperature in winter was − 14.0 °C from 1965 to 2009) and thin snow cover give rise to a very large temperature gradient, with a maximum value of 2 °C cm−1 in early January in TS (Wang, 1982). Snow in this region is a dry-cold type, with low density and low volumetric moisture content, and depth hoar develops to a much greater extent than in other places in China (Wei et al., 2001).

image

Figure 1. Location of Tainshan Station for Snow-cover and Avalanche Research (TS) in Xinjiang, China

Download figure to PowerPoint

2.2. Measurement method

2.2.1. Temperature measurement

A 25 m × 25 m observation site situated on flat grassland in TS was selected for snow measurement from 20 January to 3 April 2009 (Figure 2). Temperature was measured using both a single-channel RC-30 automatic recorder and a double-channel RC-500 automatic recorder (both supplied by Jing Chuang electronics manufacturing Co., Ltd., Shanghai). Both recorders have a stated precision of ± 0.1 °C. During the observation period, the air temperature was measured by a probe mounted in an instrument shelter 1.5 m above the ground (Tair in Figure 2). After the data were checked and averaged on an hourly basis, the characteristics of the temperature profiles and temperature gradients were analysed.

image

Figure 2. Relative positions of temperature probes and snow profiles in TS

Download figure to PowerPoint

The position of the buried probe of the automatic recorder becomes unstable after two or more days owing to gravity effects in the snow layer. Therefore, in order to measure the temperature variation in the snow layers accurately, the observation data were collected when the probe positions were stable, the depth records were precise and visibility exceeded 25 km under a clear sky (Central Meteorological Bureau of China, 2003) following each of the snowfalls.

Solar radiation consistently provides a basic energy for snow layers and it is transmitted through the layers according to Lambert's Law (Thomas, 1963; Xie and Zhang, 1988). Research on the absorption co-efficient in snow layers in TS showed that temperature varies rapidly in the snow layers no more than 30 cm beneath the snow surface (Liu and Sun, 1987). Thus, the temperature probes in the upper seven snow layers were positioned at depths of 0, 2, 5, 10, 15, 20 and 30 cm from the snow surface. A probe was placed permanently at the base of the snow layer. The other two probe positions were chosen according to the actual snow depth. In the observation period five measurement runs were conducted, as follows

  • Run 1 (Run 21-Jan) was after the snowfall that began at 1524 on 18 January and ended at 1624 on 19 January 2009, local time. Probes were buried at 1354 on 20 January at depths of 0, 2, 5, 10, 15, 20, 30, 40, 45 and 51 cm below the surface. Data recorded from 1524 on 20 January to 1424 on 21 January were selected for processing. During this period, the mean, maximum and minimum air temperatures were − 13.3, − 2.4 and − 17.6 °C, respectively.

  • Run 2 (Run 15-Feb) was after the snowfall that began at 0454 on 11 February and ended at 1624 on 12 February 2009. Probes were buried at 1154 on 15 February at depths of 0, 2, 5, 10, 15, 20, 30, 40, 50 and 61 cm below the surface. Data recorded from 1524 on 15 February to 1424 on 16 February were selected for processing. During this period, the mean, maximum and minimum air temperatures were − 6.9, 1.6 and − 11.5 °C, respectively.

  • Run 3 (Run 18-Feb) was after the snowfall that began at 0000 on 17 February and ended at 1624 on 17 February 2009. Probes were buried at 1124 on 18 February at depths of 0, 2, 5, 10, 15, 20, 30, 45, 60 and 75 cm below the surface. Data recorded from 1624 on 18 February to 1524 on 19 February were selected for processing. During this period, the mean, maximum and minimum air temperatures were − 10.1, 1.6 and − 16.4 °C, respectively.

  • Run 4 (Run 23-Feb) was after the snowfall that began at 0524 on 21 February and ended at 0834 on 22 February 2009. Probes were buried at 1424 on 23 February at depths of 0, 2, 5, 10, 15, 20, 30, 45, 60 and 75 cm below the surface. Data recorded from 1624 on 23 February to 1524 on 24 February were selected for processing. During this period, the mean, maximum and minimum air temperatures were − 7.5, 2.5 and − 14.5 °C, respectively.

  • Run 5 (Run 10-Mar) was after the snowfall that began at 1524 on 9 March and ended at 0524 on 10 March 2009. Probes were buried at 1356 on 10 March at depths of 0, 2, 5, 10, 15, 20, 30, 45, 60 and 84 cm below the surface. Data recorded from 1524 on 10 March to 1424 on 11 March were selected for processing. During this period, the mean, maximum and minimum air temperatures were − 13.1, − 2.2 and − 19.7 °C, respectively.

2.2.2. Snow-cover parameters measurement

A column of snow was dug out in order to allow vertical snow profile measurements to be carried out. In order to avoid lateral impact by solar radiation on subsequent vertical snow profiles, the position of each succeeding snow column was at least 0.3 m from the previous one. Measurements were made with a Finnish Snow Fork gauge (model LK) at every 2 cm depth. Seven parameters (attenuation rate, resonance frequency, 3 dB band width, relative dielectric constant, volumetric moisture, density and weighted water content) were obtained from the Snow Fork gauge (Hao et al., 2009). Snow density was measured in two different profiles (Figure 2): a north-facing profile (profile 1) and an east-facing profile (profile 2). Attenuation rate was used to determine the time of measurements and each profile was measured three times on average. Each time the Snow Fork was activated, the probe was left stationary in the air for 15 min to ensure sufficient atmospheric correction. Selected valid data have standard attenuation values in the range of 1200–1800 and 3 dB bandwidth values of 19–21 MHz. During the observation period, snow density measurements were conducted at 0732 and 1532 each day.

2.3. Calculation method

2.3.1. Diurnal temperature simulation

Based on the reference point selected for when the snow temperature was lowest, i.e., 0624 on 21 January, 16 February, 19 February and 24 February, and 0524 on 11 March, the amplitude, angular frequency and phase that characterize the diurnal fluctuation of hourly temperature were obtained. The diurnal cycle that dominates snow energy fluxes can be simulated using a sinusoidal temperature fluctuation (Luce and Tarboton, 2009), given by:

  • equation image(1)
  • equation image(2)
  • equation image(3)
  • equation image(4)

where is daily average temperature in a snow layer ( °C); A is the amplitude of the temperature fluctuation in a snow layer ( °C); ω is angular frequency over time (0.2618 radians h−1 for a diurnal forcing); z is depth (cm) measured downwards from the surface, d is the damping depth (cm), which is related to the diffusivity (α) and frequency (ω), z/d is calculated based on the difference in phase between the surface and the temperature probes, α is the thermal diffusivity (m2 s−1), λ is the thermal conductivity (J m−1 °C−1 S−1), C is the specific heat (J Kg−1 °C−1), and ρ is the snow density (kg m−3) (Berg and McGregor, 1966). When z = 0, the surface temperature fluctuation is simplified to Equation (4), where ε is the phase whereby the peak temperature on snow surface lags behind the peak of solar radiation—initial phase.

2.3.2. Vertical temperature simulation

The snow temperature field is one-dimensional with distribution of internal heat following a non-steady state (Ma et al., 1992). The distribution of the internal heat source, which is formed by penetrating solar radiation in the snow layer (Thomas, 1963), follows Equation (6). Changes in snow layer temperature caused by the impact of periodically occurring external factors follow specific equations and defined conditions:

  • equation image(5)
  • equation image(6)
  • equation image(7)
  • equation image(8)
  • equation image(9)
  • equation image(10)
  • equation image(11)

where I0 is a constant of solar radiation (1353 W m−2); I(Z) is the penetrating radiation at z depth (MJ m−2), and µ is the absorption co-efficient for the snow 13 m−1, Liu et al. (1988); T(x, t) is the snow temperature at × depth below the snow surface at t time ( °C); α thermal diffusivity m2 s−1 calculated by Equation (3); I(t) is the penetrating radiation at t time (MJ m−2), respectively; x0 is the total depth of snow (cm); T0 is the temperature of snow bottom; f(t) is the upper boundary condition; g(x) is the initial distribution of snow temperature.

The linear specific equation divides certain solutions into a linear combination of several equations and boundary condition formulae that satisfy the solution conditions on the basis of the superimposition principle (Ma and Liu, 1991). They can be solved by Infinite Fourier series. Using Equation (10) to calculate the temperature at a given depth below the snow surface, the temperature gradient at any depth below the snow surface can be obtained from Equation (11). The distribution of temperature in the snow layers obtained by the real-time measurements can thus be used to calculate the temperature at any depth below snow surface. Using the recorded data and the theoretically deduced Equations (5)(11), it was possible to simulate the snow temperature gradient in the five measurement runs conducted after snowfalls in TS.

3. Results and discussion

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Materials and method
  5. 3. Results and discussion
  6. 4. Conclusion
  7. References

3.1. Diurnal fluctuation of snow temperature

3.1.1. Distribution of snow temperature

Continuous, smooth curved surfaces were created from measured data using the precise V4-interpolation in MATLAB. The contours of temperature distribution in the snow layers over the 24 h period were plotted (Figure 3). This plot shows that isotherms in the snow layers are well spaced at more than 30 cm below the snow surface during the five measurement runs. From Run 21-Jan to Run 10-Mar, the position of the horizontal isothermal layer gradually drops from 32 to 72 cm below the snow surface, i.e., the magnitude of advection strength in the upper layer is larger than in the lower one so that higher temperature extends to greater depths as time passes. Both the cold and warm centres appear on the snow surface from Run 21-Jan to Run 18-Feb, but gradually drop to 2 cm below the snow surface during Runs 23-Feb and 10-Mar. Although the locus of maximum temperature appears between 1124 and 1324 in all five runs, the locus of minimum temperature was recorded at 2124 from Run 21-Jan to Run 15-Feb, and at the local pre-sunrise time of 0624 in other three runs. This means that the transmission direction of vapour is towards the loci of maximum temperature, from 1124 to 1324. The diurnal range of snow temperature was at a maximum value of 31.9 °C during Run 10-Mar (maximum and minimum values of is 4.2 and − 27.7 °C, respectively) and at a minimum value of 23.4 °C during Run 18-Feb (maximum and minimum values of 3.7 and − 19.7 °C, respectively).

image

Figure 3. Contours of snow depth overlaid with surfaces of (a) hourly average temperature during Run 21-Jan, (b) hourly average temperature during Run 15-Feb, (c) hourly average temperature during Run 18-Feb, (d) Run average temperature during Run 23-Feb and (e) hourly average temperature during Run 10-Mar (contour interval 1.5 °C). Colour bar beside each panel represents that blue is the lowest and red is the highest values of entire snow layer. This figure is available in colour online at wileyonlinelibrary.com/journal/met

Download figure to PowerPoint

Solar radiation varied greatly during the five runs (Figure 4). Daily cumulative solar radiation during Runs 23-Feb and 10-Mar was 2.9 and 2.0 times higher, respectively, than during Run 21-Jan. Also mean increases in solar radiation during both runs were 2.7 and 2.1 times higher than during run 21-Jan from 0724 to 1224. This may be the reason that the locus of maximum temperature occurs 2 cm below the snow surface in Runs 23-Feb and 10-Mar, rather than at the surface. These two temperature highs are synchronous with the peak of solar radiation. However, the temperature highs lag behind the solar radiation peak by about 1 h in the earlier measurement runs from 21 January to 18 February. This means there are the other energy sources taking effect on temperature of snow except solar radiation before 23 February, as ground temperature, temperature gradient, and so on.

image

Figure 4. Hourly solar radiation during five runs, column filling with dense grid represents hourly solar radiation during Run 21-Jan, column filling with black represents hourly solar radiation during Run 15-Feb, column filling with slash represents hourly solar radiation during Run 18-Feb, column filling with white represents hourly solar radiation during Run 23-Feb, column filling with triangle represents hourly solar radiation during Run 10-Mar, respectively

Download figure to PowerPoint

3.1.2. Amplitude of temperature fluctuations

Snow layers were compared in terms of the range of their diurnal temperature fluctuation (Figure 5). The range of diurnal temperature amplitude is largest during Run 10-Mar, 1.82 times greater than the smallest during Run 15-Feb. The maximum amplitude was observed on the snow surface in Run 21-Jan, Run 15-Feb, Run 18-Feb and Run 10-Mar, but at 2 cm below the snow surface in Run 23-Feb. The mean snow density 2 cm below the snow surface during Run 23-Feb was the lowest recorded (0.08 g cm−3), equivalent to 3/4 of the density observed at 2 cm depth in the other three runs (Runs 15-Feb, 18-Feb, 10-Mar, Figure 6). Moreover, the maximum recorded air temperature during Run 23-Feb was the highest of all five runs. The combination of the lowest density and the highest temperature in Run 23-Feb 2 cm below snow surface probably causes rapid transfer of energy at this level, giving rise to the observed maximum amplitude. Although the higher temperature during Run 23-Feb had a moderate temperature gradient, it received much more heat flux, both of which caused higher thermal conductivity (K). Lower density (ρ) caused lower heat capacity (c). Thermal diffusion co-efficient (a) can be indicated as equation image in theory, thus, lower density caused higher a, which means the more rapid spread of temperature change. The diurnal fluctuation of snow temperature diminishes deeper in the snow column during all five runs, and tends towards zero 30 cm below the snow surface from Run 15-Feb to Run 10-Mar. However, the fluctuation increases at depths of 30 and 40 cm below the snow surface during Run 21-Jan. Except for new-fallen snow (top 15 cm), the snow density varies little throughout the snow column during Run 21-Jan (Figure 6) but there was much greater permittivity 30 and 40 cm below snow surface. The permittivity parameter records the ratios of air, vapour and liquid water in snow (see volumetric moisture in Figure 6). Therefore, the increase in permittivity, e.g. volumetric moisture content, may be a major cause of the increase in temperature fluctuation between 30 and 40 cm in Run 21-Jan.

image

Figure 5. Temperature amplitude calculated by fitting diurnal variation of temperature in different levels Equations (1)(4) There are 14 levels in panel and 10 levels in snow during each run (represented in Section '2.2. Measurement method'). Starting from the top, it corresponds to atmosphere, the depth of 0, 2, 5, 10, 15, 20, 30, 40, 45, 50, 60, 75 and 84 cm below the snow surface. Line with circle represents temperature amplitude during Run 21-Jan, dotted line represents temperature amplitude during Run 15-Feb, solid line represents temperature amplitude during Run 18-Feb, dot-dashed line represents temperature amplitude during Run 23-Feb, and densely dotted line represents temperature amplitude during Run 10-Mar, respectively

Download figure to PowerPoint

image

Figure 6. Snow density and volumetric moisture content profiles in selected period during five Runs averagely, line with circle represents Run 21-Jan, dotted line represents Run 15-Feb, solid line represents Run 18-Feb, dot-dashed line represents Run 23-Feb, and densely dotted line represents Run 10-Mar, respectively

Download figure to PowerPoint

3.2. Vertical profile of snow temperature

3.2.1. Distribution of temperature gradient in snow layers

The temperature gradient at different depths was obtained by differentiating Equation (10) (Figure 7). The maximum value in the five runs was 7.57 °C cm−1 at the snow surface in Run 21-Jan, much higher than the value of 1.98 °C cm−1 measured at the beginning of the snow season in the Alaska field study of Taillandier et al. (2007). The main reason for the lower gradient in Alaska was the larger porosity of Alaskan snow compared to TS snow. The larger porosity accelerates the exchange between atmosphere and snow layer to reduce the temperature gradient. The lower porosity in TS reflects the larger snow density (0.05 in TS v. 0.01 g cm−3 in Alaska) and different snow crystal composition (rimed dendritic crystals, capped columns in Alaska v. depth hoar in TS). The minimum recorded peak value in the snow layer was 1.03 °C cm−1 during Run 15-Feb at the snow surface. The peak of the temperature gradient was recorded at the snow surface from 1524 onwards in Run 21-Jan, Run 15-Feb and Run 18-Feb. However, in the other two runs, the peak of the temperature gradient was recorded at depths below the snow surface of 2 cm (23-Feb) and 9 cm (10-Mar) and at the earlier times of 1124 and 0024, respectively. During Runs 23-Feb and 10-Mar, the snow volumetric moisture content was significantly higher than in the other runs (Figure 6), giving rise to a radiative envelope on the snow surface (less than 1 cm depth). This envelope prevents solar radiation from penetrating into the snow and prevents water vapour from passing upwards to the snow surface. Thus, the maximum positive temperature gradient forms near the snow surface during Runs 23-Feb and 10-Mar.

image

Figure 7. Contours of snow depth overlaid with surfaces of (a) hourly average temperature gradient during Run 21-Jan, (b) hourly average temperature gradient during Run 15-Feb, (c) hourly average temperature gradient during Run 18-Feb, (d) hourly average temperature gradient during Run 23-Feb and (e) hourly average temperature gradient during Run 10-Mar (contour interval 0.4 °C cm−1). Colour bar beside each panel represents that blue is the lowest and red is the highest values of entire snow layer. This figure is available in colour online at wileyonlinelibrary.com/journal/met

Download figure to PowerPoint

The locus of negative temperature gradient was recorded at 9 cm below the snow surface in Run 15-Feb and on the snow surface in all other four runs, from 1024 to 1124 (Run 21-Jan and Run 18-Feb) and at 1624 (Runs 23-Feb and 10-Mar). During Run 15-Feb, the mean and minimum air temperatures (−6.9, − 11.5 °C, respectively) were the highest of the five runs. Higher air temperature increases the rate of snow densification. The top 10 cm of the snow consists of new-fallen snow type with the highest compaction rate. Figure 6 shows that the mean density of snow between 2 and 10 cm in Run 15-Feb was 2.05 times greater than in the other four runs. The thermal conductivity of denser snow with 0.21 W (m k)−1 is 2.1 times that of the loose snow, which caused the maximum changes in snow temperature which were not on the snow surface. Thus, both higher air temperature and denser snow cause the locus of the maximum negative temperature gradient to shift to a position 9 cm below the snow surface.

The range of variation of the diurnal temperature gradient is highest in Run 21-Jan (19.3 °C cm−1) and lowest in Run 15-Feb (1.7 °C cm−1). Knowledge of the temperature gradients can provide a basis for understanding how differently snow crystal types form and why avalanches occur frequently in the western Tianshan Mountains.

3.2.2. Diurnal fluctuation of average temperature gradient in snow layers

Using the results of the differentiation of the measured temperature in the 10 measured levels, the hourly temperature gradient was averaged for each snow layer. From this the diurnal fluctuation of the mean temperature gradient was obtained (Figure 8). The analysis shows that as the temperature progressively changes from the snow surface to the base of the snow layer during the five measurement runs, the temperature gradients for Run 21-Jan, Run 15-Feb and Run 18-Feb are negative between 1124 and 1424 when the solar radiation is strong and positive for the remainder of the measurement period. For Run 23-Feb and Run 10-Mar the temperature gradient is positive for a longer period, between 0924 and 1424 or 1524, and negative for the remainder of the time.

image

Figure 8. Diurnal variation of temperature gradient in different Runs, column filling with dense grid represents hourly average temperature gradient during Run 21-Jan, column filling with black represents hourly average temperature gradient during Run 15-Feb, column filling with slash represents hourly average temperature gradient during Run 18-Feb, column filling with white represents hourly average temperature gradient during Run 23-Feb, column filling with triangle represents hourly average temperature gradient during Run 10-Mar, respectively

Download figure to PowerPoint

3.2.3. Temperature gradient profile in snow layers

Complex temperature fluctuation can be expected at the snow surface, where the atmosphere interfaces with fresh snow, and a melt-freeze process is caused by evaporation and condensation. Temperature gradients at different depths in the snow layer were averaged throughout a 24 h period to obtain the daily mean temperature gradient profile in the snow layers (Figure 9). The daily mean temperature gradient is highest at the snow surface in each of the five runs and then decreases with increasing depth in the snow layer. The range of the daily mean temperature gradient is a maximum value in Run 21-Jan, 4.70 times as great as the minimum value (in Run 15-Feb). The second largest mean temperature gradient value occurs in Run 10-Mar and is 4.28 times as great as in Run 15-Feb. In all five runs, the value of the temperature gradient is less than 0.1 °C cm−1 at a depth of 30 cm or more from the snow surface. The mean temperature gradient is positive in Run 21-Jan, Run 15-Feb and Run 18-Feb and negative in Run 23-Feb and Run 10-Mar throughout the entire snow layer. This suggests that the snow layer absorbs heat from the ground surface and releases it to the atmosphere in Run 21-Jan, Run 15-Feb and Run 18-Feb. Snow metamorphism in midwinter mainly depends on ground temperature and the soil is an exothermic body (Wang, 1982). However, in Runs 23-Feb and 10-Mar, the heat is transferred in the opposite direction: the snow layer absorbs heat from the atmosphere and transfers it to the ground. With the increase in the number of hours of sunlight and increase in the solar intensity, solar energy begins to accumulate strongly from Run 23-Feb onwards (Figure 4), resulting in an increase in the maximum value of the volumetric moisture content upward in the snow layer (Figure 6). This results in an increase in the depth of penetration of solar energy. As the snow melts, the solar energy is conducted by melt water down to ground at the base of the snow layer.

image

Figure 9. Daily average of temperature gradient in different Runs, line with circle represents vertical temperature gradient during Run 21-Jan, dotted line represents vertical temperature gradient during Run 15-Feb, solid line represents vertical temperature gradient during Run 18-Feb, dot-dashed line represents vertical temperature gradient during Run 23-Feb, and densely dotted line represents vertical temperature gradient during Run 10-Mar, respectively

Download figure to PowerPoint

The differences of snow crystal growth during the five runs were modelled assuming control by the temperature gradient (Marbouty, 1980). Wang suggested a minimum critical temperature gradient value for depth hoar development of 0.2 °C cm−1 in TS (Wang, 1988). Run 21-Jan began with a slow temperature gradient increase until a positive value of around 0.5 °C cm−1 was attained between 0024 and 0824 (Figure 8). The temperature gradient was not only higher than 0.25, but also remained stable (Figure 9), causing depth hoar to grow rapidly (Akitaya, 1974; Wang, 1982). In theory, depth hoar growth in Run 21-Jan was mainly at a depth of 20–30 cm below the snow surface; rapid depth hoar growth occurred between 15 and 20 cm below the snow surface between 1624 and 0724 during Run 15-Feb; at 30 cm depth between 2024 and 0724 during Run 18-Feb; at 40–50 cm depth between 2324 and 0224 in Run 23-Feb and at 20–30 cm depth between 2324 and 0524 during Run 10-Mar. During Run 21-Jan, a maximum negative temperature gradient of − 1.19 °C cm−1 occurred at 1124; a sharp decline in the gradient resulted in gradient variation reaching a maximum value of 0.66 °C cm−1 h−1 at 1324, suppressing the growth in crystal grain size (Wang, 1982). Grain size in the snow profile was observed after a snowfall during Run 23-Feb (Figure 10). When the temperature gradient was less than 0.1 °C cm−1, the main crystal type found in the bottom 25 cm of the snow layer was congealed depth hoar caused by water vapour upwards from the ground. Depth hoar was found 40–50 cm below the snow surface. Faceted and rounded crystals of granular snow, formed under a temperature gradient of less than 0.2 °C cm−1 (Albert and Shultz, 2002; Domine et al., 2003), were observed 15–20 cm below snow surface.

image

Figure 10. Vertical snow types after a snowfall during Run 23-Feb, column filling with white represents fresh snow (L1), column filling with right slash represents fine-grain snow (L2), column filling with dense grid represents medium-grain snow (L3), column filling with sparse grid presents coarse-grain snow (L4), column filling with vertical grid represents depth hoar (L5), column filling with left slash represents congealed depth hoar (L6), respectively

Download figure to PowerPoint

3.3. Application

Daily mean volumetric moisture content was measured in the two profiles each day at TS from 21 January to 31 March 2009. When snow contains more than approximately 0.1% of volumetric moisture, wet snow metamorphism occurs (Domine et al., 2008). Therefore, 0.1% of volumetric moisture content is a critical threshold in snow. In TS, the daily mean volumetric moisture content of the entire layer did not exceed 0.1% before Run 23-Feb. When snow runoff was observed on 7 March 2009, the volumetric moisture content exceeded 0.3% and there followed a sharp increase (Figure 11). Although volumetric moisture content corresponds closely to daily average air temperature (correlation co-efficient of 0.80 at the 99% confidence level), daily snow moisture observation in mountains is not feasible in conventional meteorological observation and pentad averages can smooth the impact of extreme values. So, an exponential function relationship was created between the pentad average (the mean of observations taken on the 5, 10, 15, 20, 25 days and the last day of each month in meteorological specification) air temperature and the volumetric moisture content of whole snow layer, with a resulting determinant co-efficient of 0.97 (R2) and a residual deviation of 0.168 (Equation in Figure 11). Combined with the snow temperature variation, the daily mean volumetric moisture content was used as an indicator to divide the stable stage and melting stage of seasonal snow in the western Tianshan Mountains. The results show that the stable stage of the snow layer was before 22 February 2009, with volumetric moisture content of less than 0.1% and pentad average air temperature of less than − 6.46 °C. The interim stage of snow layer was between 23 February and 7 March 2009, with volumetric moisture content of 0.1–0.3% and pentad average air temperature of − 6.46 to − 3.74 °C. The melting stage of the snow layer was after 8 March, with volumetric moisture content exceeding 0.3% and pentad average air temperature exceeding − 3.74 °C. This result is consistent with previous observation results at TS, which indicated a development process involving formation of a depth hoar-type covering an embryonic depth hoar in mid December, a cemented depth hoar from mid January to February, and frozen and melting depth hoar at the end of March (Liu et al., 1989). Likewise the result is consistent with the typical temperature curves of snow profiles in midwinter, end winter, and snow melting stages provided by Hu et al. (1985).

image

Figure 11. Pentad average (the mean of observations taken on the 5, 10, 15, 20, 25 day and the last day of each month in meteorological specification) volumetric moisture content (VOL%) of entire snow layer changes with the air temperature, from 21 January to 31 March 2009

Download figure to PowerPoint

4. Conclusion

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Materials and method
  5. 3. Results and discussion
  6. 4. Conclusion
  7. References

Snow temperature in Tianshan correlates with the atmospheric temperature. The snow temperature gradient varied significantly according to the different stages of snow-cover. When pentad average air temperature was less than − 6.46 °C, with volumetric moisture content of less than 0.1%, and the daily average temperature gradient of the whole snow layer was positive, the snow cover was at stable accumulation period. When pentad average air temperature was more than − 3.74 °C, with volumetric moisture content exceeding 0.3%, and the daily average temperature gradient of the whole snow layer was negative, the snow cover was at melting period. When pentad average air temperature is between − 6.46 and − 3.74 °C, with volumetric moisture content between 0.1 and 0.3%, and the daily average temperature gradient of the whole snow layer was negative, the snow cover was at interim period. Thus, based on the characteristic variation of snow temperature function, as well as on the daily average volumetric moisture in the snow layers, the snow-cover in western Tianshan Mountains can be quantitatively divided into three different stages using a the volumetric moisture content of 0.1 and 0.3%.

References

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Materials and method
  5. 3. Results and discussion
  6. 4. Conclusion
  7. References
  • Akitaya E. 1974. Studies on depth hoar. Contrib. Inst. Low Temp. Sci. 26A: 167.
  • Albert MR, Shultz EF. 2002. Snow and firn properties and transport processes at Summit, Greenland. Atmos. Environ. 36: 27892797.
  • Armstrong RL. 1977. Continuous monitoring of metamorphic changes of internal snow structure as a tool in avalanche studies. J. Glaciol. 19(81): 325334.
  • Arons EM, Colbeck SC, Gray JMNT. 1998. Depth hoar growth rates near a rocky outcrop. J. Glaciol. 44(148): 477484.
  • Bartelt P, Lehning M. 2002. A physical snow pack model for the Swiss avalanche warning, part I: numerical model. Cold Reg. Sci. Technol. 35: 123145.
  • Berg PW, McGregor JL. 1966. Elementary Partial Differential Equations, Series in Mathematics. Holden-Day: San Francisco, Oakland, CA; 421 p.
  • Birkeland KW. 1998. Terminology and predominant processes associated with the formation of weak layers of near-surface faceted crystals in the mountain snow pack. Arct. Alp. Res. 30(2): 193199.
  • Birkeland KW. 2001. Spatial patterns of snow stability throughout a small mountain range. J. Glaciol. 47(157): 176186.
  • Central Meteorological Bureau of China. 2003. Surface Meteorological Observing Rules and Regulations. China Meteorological Press: Beijing (in Chinese).
  • Colbeck SC. 1982. An overview of seasonal snow metamorphism. Rev. Geophys. Space Phys. 20(1): 4561.
  • Dexter LR. 1986. Aspect and elevation effects on the structure of the seasonal snow cover in Colorado, PhD Dissertation, Department of Geography, University of Colorado, Boulder, CO.
  • Domine F, Albert M, Huthwelker T, Jacobi HW, Kokhanovsky AA, Lehning M, Picard G, Simpson WR. 2008. Snow physics as relevant to snow photochemistry. Atmos. Chem. Phys. 8: 171208.
  • Domine F, Lauzier T, Cabanes A, Legagneux L, Kuhs WF, Techmer K, Heinrichs T. 2003. Snow metamorphism as revealed by scanning electron microscopy. Microsc. Res. Tech. 62: 3348.
  • Domine F, Shepson PB. 2002. Air-snow interactions and atmospheric chemistry. Science 297: 15061510.
  • Hao XH, Wang J, Che T, Zhang P, Liang J, Li HY, Bai YJ, Bai YF. 2009. The spatial distribution and properties of snow cover in Binggou Watershed, Qilian Mountains, measurement and analysis. J. Glaciol. Geocryology 31(2): 284292 (in Chinese).
  • Hu RJ, Ma WL, Wei WS, Wang CN. 1985. Physical characteristics of snowfall and seasonal avalanche in TianShan Mountains. Arid Land Geogr. 8(1): 5357 (in Chinese).
  • Jiang FQ, Wei WS, Liu MZ, Liu WH, Wang XJ. 1998. A snow chemical survey in the middle and upper reaches of the Kunnes River, Xinjiang, China. J. Glaciol. Geocryology 20(1): 7478 (in Chinese).
  • Katoh K, Taguchi Y, Aoyama K, Endo J. 1997. A few consideration concerning acid snow and acid rain on the Japan Sea coast. Snow Eng.: Recent Adv. 1: 147150.
  • Kondo J, Yamazaki T. 1990. A prediction model for snowmelt, snow surface temperature and freezing depth using a heat balance method. J. Appl. Meteorol. 29(5): 375384.
  • Liu ZC, Cai GT, Sun L. 1988. Some characteristics of Snow cover radiation in the western hill area of Tianshan China. Arid Land Geogr. 11(2): 7380 (in Chinese).
  • Liu ZC, Sun L. 1987. Conspectus about snow physics. Physics 16(1): 1316(in Chinese).
  • Liu ZC, Sun L, Cai GT. 1989. Research results of snow cover radiation equilibrium in the western hill area of TianShan, China. Arid Land Geogr. 12(4): 3742 (in Chinese).
  • Luce CH, Tarboton DG. 2009. Evaluation of alternative formulae for calculation of surface temperature in snowmelt models using frequency analysis of temperature observations. Hydrol. Earth Syst. Sci. Discuss. 6: 38633890.
  • McClung DM. 2002. The elements of applied avalanche forecasting part II: the physical issues and the rules of applied avalanche forecasting. Nat. Hazards 26: 131146.
  • McClung D, Schaerer P. 1993. The Avalanche Handbook. The Mountaineers: Seattle, WA; 271.
  • Ma H, Liu ZC. 1991. One dimensional simulation of temperature field in dry-cold snow. Arid Land Geogr. 14(4): 4855 (in Chinese).
  • Ma H, Liu ZC, Liu YF, Hu RJ. 1992. Energy balance and snow melting simulation of seasonal snow in tianshan China. Chin. Bull. 21: 19781981 (in Chinese).
  • Marbouty D. 1980. An experimental study of temperature gradient metamorphism. J. Glaciol. 26: 303312.
  • Miller DA. 2002. An integrated microstructural study of dry snow metamorphism under generalized thermal conditions, PhD Dissertation, Department of Civil Engineering, Montana State University, Bozeman, MT.
  • Slater AG, Pitman AJ, Desborough CE. 1998. The validation of a snow parameterization designed for use in general circulation models. Int. J. Climatol. 18: 595617.
  • Sokratov SA. 2001. Parameters influencing the recrystallization rate of snow. Cold Reg. Sci. Technol. 33(2–3): 263274.
  • Sommerfeld RA, Lachapelle E. 1970. The classification of snow metamorphism. J. Glaciol. 9: 317.
  • Taillandier AS, Domine F, Simpson WR, Sturm M, Douglas TA. 2007. Rate of decrease of the specific surface area of dry snow: isothermal and temperature gradient conditions. J. Geophys. Res. 112: F03003F000514.
  • Thomas CW. 1963. On the transfer of visible radiation through sea ice and snow. J. Glaciol. 4(34): 481484.
  • Wang YL. 1982. Metamorphism of seasonal snow cover in the upper reaches of YiLiHe in TianShan. J. Glaciol. Geocryology 4(2): 6372 (in Chinese).
  • Wang YL. 1988. The relation between the growth of seasonal depth Hoar and the avalanches in China. J. Glaciol. Geocryology 10(2): 173180 (in Chinese).
  • Wei WS, Qin DH, Liu MZ. 2001. Properties and structures of the seasonal snow cover in the continental regions of China. Ann. Glaciol. 32: 93101.
  • Xie YQ, Zhang JS. 1988. Solar penetration radiation in snow layers. J. Glaciol. Geocryology 10(2): 135142 (in Chinese).