Study Area

This research was carried out in the Heihe River Basin, the second-largest inland river basin in northwest arid region of China (97°42′E–102°04′E and 37°45′–42°40′N; ∼128,000 km2) (Ma et al., 2002) (Fig. 1). The Heihe River flows northward through a piedmont diluvial-alluvial plain, an alluvial-lacustrine plain, and a desert. It also flows through three different climate zones: cold and humid or semiarid mountain zone, midstream temperate zone, and a downstream warm temperate zone (Zhang et al., 2003).Overall, climate in the Heihe River Basin is dry, with scarce, concentrated precipitation, strong winds, strong solar radiation, and large temperature differences between day and night (Lu et al., 2002; Pan and Li, 2011).

In field investigations, boreholes were drilled with depths ranging from 20 to 150 m and elevation spanning from 3600 m to 4132 m, then permafrost temperatures were measured about once a month after borehole drilling was completed. Permafrost temperatures were measured using a thermistor string with accuracy of 0.05 °C in the laboratory calibration. Mean annual ground temperature varies from ∼0 to –1.5 °C with increasing elevation. The lower limit of permafrost distribution in the basin is at ∼3650 m a.s.l. (above sea level). Based on the lower limit, the result indicates that approximately 14,100 km2, or 10.3%, of the Heihe River Basin consists of permafrost (Fig. 2) (Wang and Zhang, 2013).

Data Collection

Data collected in this study include daily air temperature, daily ground surface temperature, and daily soil temperature at different depths; a digital elevation model (DEM); mean monthly grid air temperature; and land use data. The in situ temperature data were from China Meteorological Administration (CMA). Data from 24 meteorological stations (12 stations in the research region, and the other 12 stations nearby) were included (Table 1). The soil temperature data records (STT) ended in 2006, except Jihe De and Wutong Gou stations. The air and ground temperature records (AGTT) ended in 2013 also except Jihe De and Wutong Gou stations. The daily air temperature was used to estimate mean annual air temperature, air freezing/thawing index, and lapse rate. The daily ground surface temperature was used to calculate the surface freezing/thawing index, and the daily soil temperature was used to estimate the freeze depth in each station.

FIGURE 1.

Geographic location of the Heihe River Basin in western China. CMA stations represent meteorological stations within the Heihe River Basin, while the nearby CMA stations are meteorological stations outside the Heihe River Basin.

In addition, a 30-m-resolution DEM (Fig. 1) from the Environmental and Ecological Science Data Center for West China ( http://westdc.westgis.ac.cn/) (Li et al., 2011), was used to adjust the monthly grid air temperature data for the complex terrain (from Fig. 1, we knew that the elevation varied from 500 m to more than 5000 m).

The mean monthly grid air temperatures on a 5-km-resolution grid from 2000 to 2009 was acquired from the Environmental and Ecological Science Data Center for West China ( http://westdc.westgis.ac.cn/) (Pan and Li, 2011). It was simulated by the Weather Research and Forecasting Model. Testing of the observational data revealed that the mean bias error of temperature was –0.19 °C and that the average correlation coefficient was 0.99 (Pan and Li, 2011). These data were used to calculate the air freezing/thawing index and freeze depth.

We obtained the land-use data from the GLC2000 project, which was coordinated by the Global Vegetation Monitoring Unit of the European Commission Joint Research Centre. This data set was derived from remote sensing platforms: the Advanced Very High Resolution Radiometer (AVHRR) (resolution 2.3–4.2 km) and the SPOT4 VGT sensor (vegetation; resolution 1.7 km). The Heihe River Basin is comprised of 11 types of land cover (Fig. 3) (Ran et al., 2010). The land-use data were incorporated into the calculation of freeze depth (the method is listed in the Freezing Depth section).

TABLE 1

Geographical information for meteorological stations in the Heihe River Basin, China.

FIGURE 2.

Map of frozen ground distribution in the Heihe River Basin in western China.

Methods

Temperature Data

The daily soil temperature data were used to calculate the maximum soil freeze depth; therefore, we first considered the data from winter and spring because related research indicated that the maximum soil freeze depth occurred in winter and spring based on soil temperature data and field work in the area (Wang et al., 2013). There were several missing data situations, and we used the appropriate methods to make up for missing data. The first situation was that there were less than three missing data in one month. Here we used the mean soil temperature of the previous day and the following day to interpolate the daily soil temperature. The second situation was that there were more than three but less than five missing data in one month, in which case, we chose the nearest station (it was calculated by the distance and combined with higher coefficient R2) and used that data to build the linear dependence relation (it should be guaranteed the coefficient R² is over 0.95 and the confidence level is 95%) and interpolated the missing data. The third situation was that there were more than five missing data in one month, in which case, we would delete the data for that year.

For the daily air temperatures and ground surface temperatures, we used the same method to make up for missing data. Based on the IPCC climatological baseline period from 1971 to 2000, we calculated the mean annual temperature departure with time period from 1960 to 2013.

Based on the 5-km-resolution mean monthly grid air temperature, we obtained the 30-m grid temperature data using the topographical correction with the 30-m-resolution DEM. There were several steps, the first of which was to obtain the lapse rate. We used the mean monthly air temperature at the12 meteorological stations in the Heihe River Basin to establish the relationship between mean monthly air temperature and elevation. Then, we determined the mean lapse rate (Table 2) for every month. Second, based on the 5-km mean monthly grid air temperature, we obtained grid latitude and longitude information, and the grid elevation value can be obtained using the DEM. Third, we set the 5-km mean monthly grid temperature down to sea level with the lapse rate. Fourth, we interpolated the grid data with ArcGIS software, using the Kriging method on the raster data. Fifth, using the lapse rate and 30 m DEM, we recalculated the mean monthly air temperature at the actual elevation with ArcGIS software. This way, we obtained the 30-m mean monthly grid air temperature over the study area. This method is widely used, namely the topography adjustment method for the complicated terrain, especially mountainous areas (Willmott and Robeson, 1995).

FIGURE 3.

Land cover types of the Heihe River Basin in western China.

TABLE 2

The lapse rate of air temperature at 12 meteorological stations in the Heihe River Basin, China.

Annual Freezing/Thawing Index and the n Factor

We used mean daily air and ground surface temperatures at the meteorological stations to calculate the air and surface freezing and thawing indices (FI_a, TI_a, FI_s, and TI_s) at the point scale and used the 30-m-grid temperature data to calculate the air freezing and thawing indices (FI_a and TI_a) at the basin scale.

We calculated the annual air and surface freezing (thawing) index as the sum of the daily temperature for all days with temperatures below (above) 0 °C during the freezing (thawing) period. We defined the annual freezing period from 1 July through 30 June of the next year, and the thawing period from 1 January through 31 December (Steurer and Crandell, 1995; Zhang et al., 2005; Frauenfeld et al., 2007; Wu et al., 2011).The FI and TI could be estimated using the following:

where N_F is the number of days with temperature below 0 °C; i = 1, 2 … N_F; N_T is the number of days with temperatures above 0 °C; and T_i represents the temperature on a specific day.

Based on the freeze-thaw index, we calculated the n factor, which reflects the relationship between the air and surface freezing/thawing index:

Freezing Depth

There were many methods to estimate soil freezing depth, such as soil temperature measurements, numerical models, and the Stefan formula. We used the Stefan formula to estimate soil freezing depth:

where MFP is frozen depth (m), K_f represents the thermal conductivity of frozen soils (W m^-1 °C^-1), nf is n factor for the freezing season, DDFa is the annual air freezing index (°C d), P_b is the soil bulk density (kg m^-3), w is the soil water content by weight, and L is the latent heat of fusion (J kg^-1) (Zhang et al., 2005). From this, we can see that there are many factors in estimating soil freezing depth and that it was difficult to obtain these data sets for large regions. Figure 4 indicates the relationship between DDFa and MFP, the linear relation correlated well by slope at 0.11, with an R² greater than 0.5 and statistical significances as high as p < 0.05. Thus, we can simplify Equation 4 to Equation 5 (Harlan and Nixon, 1978):

where E was defined in Equation 6 (Nelson and Outcalt, 1987):

FIGURE 4.

Linear relationship between the maximum freeze depth and the annual freezing index of air temperature (DDFa). Data used are from all meteorological stations within and outside the Heihe River Basin in western China as shown in Figure 1.

To obtain E, we used soil temperature data from the 12 meteorological stations in the Heihe River Basin and 12 other stations near the river basin. We interpolated the depth of the 0 °C isotherm throughout the 0.0–3.2 m soil temperature profiles by linear method (Frauenfeld et al., 2004). Therefore, we estimated E value base on MFP and DDFa at every station using Equation 6. Past research has indicated that the E factor was mainly affected by land use (Zhang et al., 2005).

Thus, based on land use type from the 24 stations, the E value can be divided into 11 groups. For each group, we obtain an average E value as summarized in Table 3. Table 3 represents the mean and standard deviation of E with different land cover types. The average E value varied from 0.028 to 0.053. The gravels were highest at 0.053, followed by bare rocks at 0.049. The minimum was desert at 0.028. The standard deviation of alpine and subalpine meadow was the largest at 0.023. The smallest was for plain grassland at 0.003 and bare rocks at 0.004. Because there were no stations with land cover types of needle-leaved deciduous forest in the study area, no E value was obtained, thus we could not estimate the freeze depth for regions with needle-leaved deciduous forest.

TABLE 3

Mean values of E and their standard deviation across different land cover types in the Heihe River Basin, China.

Air Temperature Change

Figure 5 represents the variation trend of mean annual air temperature anomaly from 1960 to 2013 for the 12 sites with daily air temperature observations. The trend exhibited a statistically significant (p < 0.01) increase over the 1960–2013 period of 0.35 °C decade^-1, or approximate change of 1.9 °C for the 54-year period. From late 1987 onward, air temperature has been above the long-term (1971–2000) average. In addition to this long-term increase, the time series also indicated some large interdecadal variability. Mean annual air temperature increased slightly from 1962 to 1965, and this was followed by a sharp decrease until 1970. From 1970 to 1998, however, mean annual air temperature increased dramatically. After 1998, a slight decrease occurred. The overall 1960–2013 change was therefore largely driven by the increase during the 1970–1998 periods.

Based on monthly grid air temperature from 2000 to 2009, the spatial variation of mean annual air temperature (Fig. 6) showed that mean annual air temperature of less than -2 °C appeared in the upper reaches of Heihe River Basin. The highest temperature, ranging from 7.5 to 10.3 °C, occurred in the mid- and downstream regions with low altitude and sparse vegetation. The overall spatial variation of mean annual air temperature was that it was colder in the south and warmer in the north.

FIGURE 5.

Anomalies of mean annual air temperature from its long-term (1971–2000) mean in the Heihe River Basin from 1960 to 2013. The thick black dashed line is the linear trend during the study period. The thick black line is the smoothing average.

FIGURE 6.

The mean annual air temperature from 2000 to 2009 in the Heihe River Basin.

Changes in Freezing/Thawing Indices

Of the total 12 stations with daily air and surface temperature, the FI_a, FI_s, TI_a, and TI_s were estimated. Linear trend and moving average methods were used to analyze their variability (Figs. 7 and 8).

Figure 7 presents a time series of FI_a and FI_s. They clearly exhibited decreasing trends over the period of the station data with p < 0.05. The trend of FI_a in Shandan station, and trend of FI_s in Ejina Qi station were slightly larger than other stations, with statistical significances p < 0.05. FI_a and FI_s varied between 300 °C d and 2400 °C d during the period. In general, FI_s was smaller than FI_a in the same period, indicating winter ground surface temperature is higher than air temperature. Furthermore, the difference between FI_a and FI_s was larger with altitude increase. The probable reason was that the differences between air temperature and ground surface temperature were larger in the high altitude regions. FI_a and FI_s increase with elevation, indicating winter air temperature decreases with elevation increase.

Figure 8 indicated the linear trends of the thawing index, including TI_a and TI_s for observational stations. It clearly exhibited increasing trends over the period of the station data with p < 0.05. The resulting changes in TI_a and TI_s ranged between 886 and 4641 °C d, and between 1664 and 6036 °C d, respectively. The fastest increase of TI_a was by Ejina Qi station at 9.70 °C d yr^-1, and followed by Zhangye station at 8.44 °C d yr^-1. The slowest increase of TI_a was by Gaotai station at 4.52 °C d yr^-1. For TI_s, the fastest increase was also by Ejina Qi at 15.76 °C d yr^-1, followed by Zhangye at 13.12 °C d yr^-1, respectively. However, the slowest increase was by Tuole station at 3.75 °C d yr^-1.

FIGURE 7.

Linear trends of freezing index for 8 meteorological stations within the Heihe River Basin. The thick black line is the linear trend of air freezing index, and the gray line is the trend of ground surface freezing index.

FIGURE 8.

Linear trends of thawing index for 10 meteorological stations within the Heihe River Basin. The thick black line is the linear trend of air thawing index, and the gray line is the trend of ground surface thawing index.

FIGURE 9.

Spatial variation of annual air freezing index (FI) and thawing index (TI) in the Heihe River Basin, China.

Except for FI and TI at the point scale, we also used the 30-m grid mean monthly air temperature to calculate the FI_a and TI_a from 2000 to 2008 (Fig. 9). The time series trend of FI_a and TI_a were also estimated by the linear trend method, but with statistical significances as high as p > 0.1. Thus, the variation trends are not discussed in this paper.

Figure 9 exhibits the distribution of FI_a ranging from 624–5646 °C d. Spatially, FI_a in the lower and middle reaches of Heihe River Basin was less than 1000 °C d, and in the upper reaches, it was 1000–5600 °C d. FI_a in the eastern part of the river basin was larger than in the west. Figure 9 shows that TI_a varied from 0 to 4558 °C d from 2000 to 2009. TI_a was greater than 3000 °C d in the downstream and midstream regions, and in the upstream region it was less than 3000 °C d. TI_a was larger in the north and east, and smaller in the south and west. In general, the spatial distribution of TI_a was opposite to FI_a.

n_f and n_t

To compare with FI and TI at 12 observational stations, n_f and n_t were introduced in this paper. Table 4 presents the character of these parameters. The n_f ranged from 0.78 to 1.09. Jiuquan station ranked first at 1.09, and the last was Yeniu Gou station at 0.78. As for n_t, the range was between 1.26 and 1.82. Yeniu Gou station ranked first, followed by Tuole station, while n_t was lowest at Ejina Qi and Dingxin stations. The mean n_f was less than 1.0, and the n_t was more than 1.0. It can be clearly seen that n_t was larger than n_f.

TABLE 4

n_f and n_t at the 12 meteorological stations in the Heihe River Basin, China.

These results indicated that the FI was less than TI. Furthermore, the change of these parameters correlated with elevation. Thus, we estimated the relationship between FI, TI, these parameters, and elevation (Table 5). It was clear that FI and n_t were positively correlated with elevation with statistical significances as high as p < 0.05. This means that these two parameters increased as elevation increased. However, TI and n_f were negatively correlated with elevation. The reason was that elevation affected the air temperature more than the ground surface temperature, because air temperature was controlled by the atmospheric state and related with air pressure. However, the ground surface temperature was controlled by the surface energy balance, and had no direct relation with elevation. Thus, the changes in ground surface temperature may be slower (Zhao et al., 2008).

TABLE 5

Linear relationship between factors and elevation.

Spatial and Temporal Variability of the Freezing Depth

Using the air freezing index and E values, we estimated the soil freezing depth over the period 2000 to 2008. In the permafrost regions, the freezing depth was the potential seasonal freezing depth, while in SFG, the freezing depth was the maximum freezing depth.

Table 6 and 7 show the total area and area fraction of the maximum freezing depth from 2000 to 2008 with six ranges of <1 m, 1–1.5 m, 1.5–2.5 m, 2.5–3.5 m, >3.5 m, and no value. With freezing depths of <1 m and 1–1.5 m, the maximum and the minimum area occurred in 2008 and 2004, respectively. The maximum area was 3.221 × 10⁴ km² or 28.2% of the SFG region in 2008, and 7.584 × 10⁴ km² or 66.4% in 2004. The minimum area was 0 and 2.655 × 10⁴ km², respectively. On the other hand, with freezing depth ranges of 1.5–2.5 m and 2.5–3.5 m, the areas ranking first and last occurred in 2004 and 2008, respectively. Overall, it was approximately 58.1% and 0.04% of SFG regions where soil maximum freeze depth ranged between1.5 m and 2.5 m, and between2.5 m and 3.5 m, respectively. Meanwhile, approximately 0.0302 × 10⁴ km² at 0.26% of the SFG region area had no value.

Tables 8 and 9 indicate the potential seasonal freezing depth in the permafrost region from 2000 to 2008. It is clear that there was no place with a potential seasonal freezing depth less than 1 m in this region. Meanwhile, with a potential seasonal freezing depth range of 1–1.5, 2.5–3.5, and >3.5 m, the largest area was less than 0.20 × 10⁴, 0.360 × 10⁴, and 0.0020 × 10⁴ km², respectively. Additionally, the percentage of area covered by these three ranges was less than 26%. Meanwhile, the area with a potential seasonal freezing depth range of 1.5–2.5 m was more than 0.935 × 104 km², and the percentage more than 67.9%. There were also some permafrost places with no value at 0.0655 × 10⁴ km² or 4.8% of this study region.

Figure 10 shows the mean freezing depth in the Heihe River Basin. The region in which the freezing depth was <1 m was mainly in the midstream portion of the basin and in a part of the downstream portion. The region with freezing depth between 1 and 1.5 m occupied most of the midstream region, between 1.5 and 2.5 m was in the upstream and downstream regions, while the freezing depth was deeper than 2.5 m in the entire upstream region.

It can be clearly seen that a potential seasonal freezing depth of 1.5–2.5 m was observed in most of the permafrost regions, and maximum freezing depth below 2.5 m was in most of the SFG regions.