1 Introduction

Soil freeze-thaw (FT) erosion is the gravity-induced migration and accumulation process of soil or rocks undergoing mechanical destruction resulting from the expansion and contraction of minerals, induced by volume changes of water at different phases due to the changes in surface soil temperature (Tang 2003; Eigenbrod 1996). During the freezing period, frost heaving occurs when the surface soil moisture migrates to a freezing front under subzero temperatures (Shan et al. 2009; Qi et al. 2008). The mechanical properties of the soil are destroyed by the re-arrangement of the soil particles caused by the frost heave (Niu et al. 2004; Liu et al. 2009). With rising temperature and increased precipitation during the spring melt period, the melting process is significantly exacerbated (Yan et al. 2004; Wang et al. 2001). The melt water, hampered by the unfrozen layers, accumulates during downward infiltration; this significantly increases the water content between the melt layer and the frozen layer. Part or the whole of the shallow slope slides down along the water saturation layer under gravity due to the decreasing stress within the soil particles when the water content reaches saturation or super saturation (Bai et al. 2007; Kok and McCool 1990). In autumn and winter, a portion of the shallow soil water turns into ice as the soil temperature gradually drops below freezing. The adsorbed films, composed of frozen and unfrozen water, become progressively thinner because of the continually falling temperature, which results in more residual liquid water in the pores and crevices of the soil particles (Formanek et al. 1984; Sharratt et al.2002). In addition, a small portion of the soil water may remain in a liquid state at temperatures well below the freezing point of water. Consequently, an upward migration of soil water takes place as frost penetrates the shallow surface soil. Finally, part of or the whole of the shallow slope slides down along the “water saturation layer” under gravity.

During recent decades, global warming has exerted a significant impact on terrestrial ecosystems and these impacts are projected to be even greater in the future (IPCC 2007; Fu et al. 2007).The process of FT erosion has been significantly exacerbated due to the continuously rising temperature and increased precipitation. Unfortunately, in recent decades, this phenomenon is greater than in other regions of the world (Duan et al. 2006; Li and Kang 2006). According to the second national soil erosion data by remote sensing survey, the Qinghai–Tibet Plateau, the main source of the Yangtze, Lancang and Yellow Rivers, suffers severe FT erosion. This disastrous situation has seriously affected production and thereby development of the regional economy (Li et al. 2005). In the Qinghai–Tibet Plateau, the annual freeze-thaw cycle of soils is so significant that it has impacted on the agricultural and ecological environments (Kang et al. 2010; Liu and Chen 2000). Thus, accurate evaluation of FT erosion on the Qinghai–Tibet Plateau is urgent and necessary for protection of the eco-environment.

A critical limitation to the study of the quantity of FT erosion in the Qinghai–Tibet Plateau is the lack of accurate data, including metrological data, on soil moisture because of its alpine climate and high latitude (Mao et al. 2007; Liu et al. 2009). FT erosion in this region has not attracted enough attention in China and abroad (Bai et al. 2010; Sharratt et al. 2002). Previous studies mainly focused on the soil bulk density, permeability and moisture content (Mostaghimi et al. 1988; Bai et al. 2012; Lee and Lee 2002). The process of soil FT erosion significantly impacts the stability of soil on slopes and their resistance to flowing water (Edwards et al.1995). A thaw-weakened soil is susceptible to water erosion or other exogenic forces (Demidov et al.1995). The resilience modulus is decreased by even a small number of FT cycles (Simonsen and Isacsson 2001). Numerous laboratory studies have been conducted to clarify the impacts of the FT cycles on soil nutrient cycling (Grogan et al. 2004; Reinmann et al. 2012). Caviezel et al. (2014) reveal that shrub encroachment changes soil and vegetation properties, resulting in an increase in resistance to runoff-related erosion processes, but a decrease in slope stability resulting in shallow landslides. Liu et al. (2009) found that the relationships between precipitation, temperature and FT erosion were significant in the FT region of Sichuan Province. The distribution of FT erosion in Tibet was tentatively confirmed by Zhang and Gao (2006). Some studies also suggest that the process of FT erosion greatly affects the physical properties of the soil (Li et al. 2007; Williams and Robinson. 2001).

Assessment of the state of the environment is critical to environmental prediction, management and planning. Thus, we urgently need detailed information on the FT erosion processes in the Qinghai–Tibet Plateau since it is an ecologically vulnerable zone and also an important nature reserve. In this paper, based on the traditional estimation model, we introduce and adopt the indices of microwave remote sensing (annual FT cycle days and average diurnal phase-changed water content) to establish an evaluation model of FT erosion. This is then used to determine the state of the FT erosion and monitor the FT process.

2 Data and methods

2.1 Study area

The Qinghai–Tibet Plateau is located in western China (26°00′12″N–39°46′50″N, 73°18′52″E–104°46′59″E) and has a typical arid and semiarid alpine climate (Chen et al. 2011) (Fig. 1) .It covers an area of 257.24 (104) km2 with the average altitude being about 4000 m above sea level. The temperature ranges from 12 °C in the south to −5 °C in the north, decreasing from higher to lower altitudes (Mao et al. 2007). Precipitation shows great spatial variation from more than 1500 mm in the southeast to 200 mm in the northwest, with 70–80% of total precipitation occurring between May and mid-August. The spatial heterogeneity patterns of precipitation and temperature result in high aridity in most regions with relatively low precipitation and low vegetation coverage. Climate in this region varies from warm-dry in the southeast to warm-wet in the northwest.

Fig. 1
figure 1

The location of the Qinghai–Tibet Plateau and the average NDVI in growing season for 2000–2012

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2.2 Index variable calculation

It is hard to estimate the quantities of FT erosion for this large-scale region. Currently, few methods are available for measuring the quantities of FT erosion that have been found in China and abroad. Considering the unique impact factors of the FT process in the Qinghai–Tibet Plateau, we chose the seven most critical indices to comprehensively evaluate the quantity of soil FT erosion. These were as follows: the annual FT cycle days, the average diurnal FT phase-changed water content, average annual precipitation, topographic relief, aspect, annual temperature range and average annual vegetation coverage. The spatial resolution of all the datasets (images of the seven indices) was 1 km by 1 km.

2.2.1 Annual FT cycle days

The annual FT cycle day is the number of days that the processes of FT cycles occur in a year. It is a good variable in the FT process and reflects the effects of temperature on the erosion intensity of FT. In this paper, a factor obtained by the images from the microwave remote sensing was introduced to evaluate the intensity of the FT erosion. The Advanced Microwave Scanning Radiometer-EOS (AMSR-E) datasets (available from the National Snow and Ice Data Center, USA) from satellite-borne passive microwave radiometers were used to obtain the land surface brightness temperatures day and night. The changes in the land surface temperature and emissivity were then observed using the inverse of the brightness temperature (Zuerndorfer et al. 1990). In this paper, discriminant analysis algorithms (Eqs. 1, 2) were applied to determine the FT state of the land surface, define the regions experiencing FT cycles and finally calculate the annual FT cycle days (Fig. 2).

Fig. 2
figure 2

The calculation process of annual FT cycle days

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$$F = 1.47{\text{TB}}_{36.5\;V} + 91.69\frac{{{\text{TB}}_{18.7\;H} }}{{{\text{TB}}_{36.5\;V} }} - 226.77$$
(1)
$$T = 1.55{\text{TB}}_{36.5\;V} + 86.33\frac{{{\text{TB}}_{18.7\;H} }}{{{\text{TB}}_{36.5\;V} }} - 242.41$$
(2)

where TB36.5 V is the V-polarized brightness temperature of channel 36.5 GHz and TB18.7 H represents the H-polarized brightness temperature of channel 18.7 GHz.

2.2.2 Average diurnal phase-changed water content

The phase-changed water content reflects the difference in soil liquid water content during the process of FT cycles (Li et al. 2011; Jackson and Schmugge 1989). The volume expands when liquid water turns into solid ice and this can destroy the structure of soil or rock. The destruction or failure of soil and rock is exacerbated by the increased phase-changed water content. Furthermore, the relationship of microwave emission and soil liquid water content is significant mainly because of the large difference in the dielectric constant between liquid water and dry soil and ice. Thus, soil freeze-thaw processes and the accompanying water phase change can be detected by microwave remote sensing. Therefore, AMSR-E data were used here to estimate the phase-changed water content at the land surface (Fig. 3).

Fig. 3
figure 3

The calculation process of average diurnal phase-changed water content

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$$M_{\text{pcv}} = A \cdot \left( {\frac{{{\text{TB}}_{d,10.65\;H} }}{{{\text{TB}}_{d,36.5\;V} }} - \frac{{{\text{TB}}_{a,10.65\;H} }}{{{\text{TB}}_{a,36.5\;V} }}} \right) + B$$
(3)

where M pcv refers to the phase-changed water content, subscript d indicates the descending orbit and subscript a indicates the ascending orbit. A and B are regression coefficients.

2.2.3 Annual average precipitation

Precipitation is a main contributor to soil erosion especially in arid and semiarid regions (Okin et al. 2001).The water content of soil is influenced by precipitation and shows a significant relationship with the intensity of FT erosion. Also, precipitation and melt water are the important driving forces in the movement of FT erosion materials. The meteorological data used here were obtained from the Climatic Information Center of Tibet Autonomous Region, China (http://cdc.cma.gov.cn/home.do). However, the distribution of meteorological stations was uneven. Therefore, interpolated stations were constructed using the Tropical Rainfall Measuring Mission(TRMM)with Eq. 4 (Jia et al. 2011). This equation was used to calibrate the TRMM 3B42 precipitation.

$$T_{R} = 2.048 \cdot V^{0.823}$$
(4)

where V (mm year−1) represents TRMM3B42-derived annual precipitation and T R  (mm year−1) is the annual rainfall observed by the meteorological stations during 2000–2012.

2.2.4 Aspect

Aspect can greatly influence the amount of solar radiation received on the ground. There is a large amount of solar radiation incident on sunny slopes leading to large soil temperature differences between day and night; this significantly exacerbates the intensity of FT erosion. However, the change of solar radiation on a shady slope is small so the soil temperature difference between day and night is not noticeable. Therefore, the intensity of FT erosion in these zones is small. Aspect here is calculated using the Spatial Analyst Tools of ArcGIS 10.1 based on a 90-m digital elevation model (DEM) (http://datamirror.csdb.cn), obtained from the National Geospatial-Intelligence Agency (NGA) and the National Aeronautics and Space Administration (NASA).

2.2.5 Topographic relief

Topographic relief can be defined as the difference in altitude between the highest and lowest point within certain region. It can affect the velocity and transport distance of the FT erosion materials and can contribute significantly to FT erosion.

$${\text{TR}} = H_{\hbox{max} } - H_{\hbox{min} }$$
(5)

where TR represents the value of topographic relief within an n × n average sliding window, H max is the maximum value of the sliding window, and H min is the minimum value of the sliding window. Topographic relief is here calculated via Eq. 5 based on a 90-m digital elevation model (DEM).

2.2.6 Vegetation coverage

Vegetation (canopy, understory and plant roots) is of great importance for regulating surface hydrological processes (Zhang and Gao 2006; Chen et al. 2007). The above-ground parts of the plants can mitigate the erosion forces of rainfall, while the below-ground parts increase the soil stability and reduce destructive effects on soil (Chen et al. 2007). In addition, vegetation can reduce the soil temperature difference between day and night, so it plays an important role in the FT erosion process.

The Normalized Difference Vegetation Index (NDVI, Huete and Tucker 1991) is a measure of vegetation activity and biomass. In this paper, the Spot-Vegetation NDVI data with 1 km by 1-km resolution for every 10 days from April 2000 to December 2012 were adopted. The 10-day periods were defined as the 1st to the 10th, 11th to the 20th and 21st to the end of each month. The monthly NDVI was obtained by the maximum value composite method, which minimizes cloud contamination, atmospheric effects and solar zenith angle effects (Hope et al. 2003; Stow et al. 2004). Thus, the average annual vegetation coverage was obtained based on the monthly NDVIs. Here, the following equation was employed to invert the vegetation fraction:

$${\text{FVC}} = \left( {\frac{{{\text{NDVI}} - {\text{NDVIsoil}}}}{{{\text{NDVIveg}} - {\text{NDVIsoil}}}}} \right)^{L}$$
(6)

where FVC is the fractional vegetation coverage, NDVIveg is the maximum value of pure vegetation at a confidential level (CL) of 0.95, NDVIsoil refers to the minimum value of pure bare soil (CL = 0.95), and L is an experience factor, its value is 1.1 in this paper.

2.2.7 Annual temperature range

Soil temperature is a crucial factor influencing the FT erosion process, and it determines the frozen-thawed depth of the surface soil layer (Li et al. 2005). The larger the soil temperature range, the more severe the FT erosion. Moreover, the change range and intensity of the soil temperature around 0 °C exhibit a negative relationship with the stability of physical properties and the erosion resistance of soil (Lee and Lee 2002). The larger the change in soil temperature, the more severe the FT erosion. However, soil temperatures could not be obtained on a large scale in the Qinghai–Tibet Plateau due to the lack of long-term observations. In this study, we used the data from 126 meteorological stations around the study region and found that the annual temperature range, latitude, longitude and attitude showed significant multiple linear relationships.

$$T_{\text{atr}} = 3.2103 + 1.2571X_{1} - 0.2099X_{2} - 0.0003887X_{3}$$
(7)

where the T atr is the annual temperature range, X1 represents latitude, X 2 is longitude, and X 3 refers to the altitude. These three factors were obtained based on the DEM.

2.3 Evaluation model of FT erosion

The evaluation of FT erosion requires the integration of multiple factors to obtain a comprehensive evaluation index. However, most previous studies used only the analytic hierarchy process (AHP) or an entropy method to calculate the weight of each index. The results of the AHP are mostly influenced by subjectivity, while those of the entropy method often ignore the experience and knowledge of experts (Pinzon et al. 2005). In this paper, we combined the two methods to obtain a weighting of indices so that the experience and knowledge of experts and the objective information quantity of each index could be considered. Then, we adapted the improved AHP and applied a weighted summation method to obtain the comprehensive evaluation index using the following equations:

$$W_{{{\text{AHP}} - {\text{EM}},i}} = \frac{{{\text{EM}}_{i} {\text{AHP}}_{i} }}{{\sum\nolimits_{i = 1}^{n} {{\text{EM}}_{i} {\text{AHP}}_{i} } }}$$
(8)
$$I = \frac{{\sum\nolimits_{i = 1}^{n} {W_{{{\text{AHP}} - {\text{EM}},i}} I_{i} } }}{{\sum\nolimits_{i = 1}^{n} {W_{{{\text{AHP}} - {\text{EM}},i}} } }}$$
(9)

where W AHP-EM,i is the modified weight of each index, EM i is the weight obtained by entropy method, AHP i is the weight obtained by AHP, I i is the dimensionless value of each index, n refers to the number of impact factors, and I is the comprehensive evaluation index.

Firstly, the EM i was obtained by the entropy method; then, it was taken into the calculation of WAHP-EM, i with AHP i . The values of the weightings are listed in Table 1, and some typical classification factors are shown in Fig. 4.

Table 1 Classification assignments of evaluation indices and their weights of AHP, entropy method, and the improved AHP
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Fig. 4
figure 4

Distribution maps of typically classified indices. a Aspect; b annual precipitation annual FT cycle days; c annual precipitation; d vegetation coverage; e annual temperature range; f topographic relief

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3 Results

3.1 Classification map of FT erosion and accuracy assessment

Based on Eqs. ( 8, 9) and Table 1, the evaluation of FT erosion was obtained using seven indices: the annual FT cycle days, the average diurnal phase-changed water content, average annual precipitation, average vegetation coverage, topographic relief, aspect and the annual temperature range.

The FT erosion was then divided into six categories: No-FT erosion (I < 3.4), slight erosion (3.4 < I < 4.9), mild erosion (4.9 < I < 5.5), moderate erosion (5.5 < I <6.2), intensive erosion (6.2 < I < 7.0) and severe erosion (7.0 < I < 8.4). The spatial patterns of the FT erosion are shown in Fig. 5.

Fig. 5
figure 5

Classification map of the quantity of freeze-thaw erosion in the Qinghai–Tibet Plateau

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A basic error matrix and precision index were applied to test the accuracy of the results. In order to confirm the validity of the sampling points, we chose a total of 268 sites (Table 2) from regions with different landforms, aspect, plant types, land-use types and so on. The error matrix of the calculated erosion category and the field survey is shown in Table 3.

Table 2 Error matrix of FT erosion categories
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Table 3 Precision index of FT erosion categories
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As shown in Table 3, the cartographic precision of all categories ranged from 0.68 to 0.93, which demonstrates the validity of the classification. Slight erosion showed the best precision, while the accuracies of mild and intensive erosion were much lower. However, the overall precision was 84.7 %, confirming the high efficiency and accuracy of this freeze-thaw erosion model for the Qinghai–Tibet Plateau.

3.2 Spatial differentiation of FT erosion

Figure 5 shows that FT erosion is widely distributed in the Qinghai–Tibet Plateau .It covers about 63.46 %, an area of 163.96 (104) km2 . FT erosion was discontinuously distributed in the mid-western region (30°–40°N, 80°–100°E). The No-FT region was mainly concentrated in the southern and southeastern regions and in Ulam County. The average intensity of FT erosion for the whole region was 5.77, placing it in the category of moderate erosion. Among the grades of FT erosion, mild erosion covered the largest region with an area of 48.25 (104) km2, accounting for 29.44 % of the erosion area. In addition, the zones of slight, moderate, intensive and severe erosion were 22.79 (104), 45.72 (104), 31.87 (104) and 15.28 (104) km2 with percentages of 13.90, 27.89, 19.44 and 9.32 % of the total erosion area, respectively (Table 4).

Table 4 Area and area ratios of different categories of FT erosion intensity
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The spatial disparities of different FT erosion zones differed significantly.

The zone of slight erosion was mainly concentrated in northern part of the region, in southern Hortan City, mid-southern Korla City and northern Nagqu County. Of all the FT erosion zones, the mild erosion zone was the most widely distributed and covered almost the whole erosion region of the Qinghai–Tibet Plateau. The zone of moderate erosion was discontinuously distributed in the southern and northern mountain regions, occupying the western Car County, northern Hotan City and southern Maqin County. Similar to the moderate erosion, the intensive erosion zone was also widely distributed and included Shigatse City, northern Changdu County and western Gar County. The zone of severe erosion was mainly concentrated in the southern mountains and the plateau of western Sichuan.

4 Discussion

4.1 Improvement of the model for FT erosion

The Qinghai–Tibet Plateau, the highest and largest plateau on the earth, is the major region of FT erosion in China. However, enough attention has not been paid to this issue either in China or abroad. Compared with wind and water erosion, the studies on FT erosion are few.

The traditional models of FT erosion are not very accurate and largely inadequate because of the lack of reliable data on factors such as temperature, land use, soil types, vegetation cover and annual precipitation (Kok and McCool 1990; Zhang et al. 2007). In this paper, microwave remote sensing techniques were introduced to determine the state of and detect the processes of FT erosion. Based on the images from microwave remote sensing (AMSR-E), we monitored the soil sensitivity due to the changes in moisture and calculated the annual FT cycle days and average diurnal phase-changed water content. These indices better reflect the whole process of the FT cycle (Li et al. 2005). The results of the accuracy assessment indicated that the improved model of FT erosion was efficient and was applicable to the Qinghai–Tibet Plateau.

4.2 The relationship between FT erosion, climate and terrain

Our results suggested that the spatial distribution of FT erosion intensity increased from slight erosion in the northwest of the region to severe erosion in southern part, but the determining factors were different. The slight erosion zone was mainly concentrated in the northern region, northern Gar County and northern Nagqu County, as here precipitation is scarce and the slopes much smaller. The zone of mild erosion was distributed between slight and moderate erosion. In the middle of the Qinghai–Tibet Plateau, the topographic relief and slope are much smaller and the dominant impact factors are temperature, annual FT cycle days and aspect. In the southern foot of the Himalayas and downstream of the Brahmaputra basin, warm, moist air from the Indian Ocean often brings abundant rainfall (Yu et al. 2003). In addition, high mountains are widely distributed in the southern and southeastern regions (30°–34°N, 93°–100°E), which results in larger slope and topographic relief. Thus, intensive erosion and severe erosion were concentrated in these regions. Most of Ulam County belongs to the No-FT erosion category due to the low altitude and flat terrain. In addition in the southern Qinghai–Tibet Plateau regions (28°–30°N, 87°–105°E and 30°–38°N, 101°–105°E), the process of FT erosion does not exist because of the high temperatures and vegetation cover.

The plateau has experienced significant warming during the past decades (Liu and Chen 2000), and this warming is predicted to continue in the twenty-first century (IPCC 2007). In addition, the environmental fragility created by the unique geographical conditions of the Qinghai–Tibet Plateau tends to be sensitive to climate change (Niu et al. 2004). Increasing rainfall and rising temperatures will increase the intensity of FT erosion, especially in the mid-western region with its sparse vegetation cover and large annual FT cycle days. In addition, the eco-environment has been significantly affected by human activities, including deforestation, overgrazing and construction (Zhang et al. 2007). These activities decrease the vegetation coverage and destroy the physical and chemical structure of the soil. Both natural and anthropogenic factors aggravate the process of FT erosion. Thus, it is urgent for us to pay more attention to the prevention and treatment of FT erosion.

4.3 Relationship between FT erosion and plant types

To explore the relationship between plants and FT erosion, six typical types of plant (subalpine coniferous forest (SCF), broadleaf forest (BF), alpine shrubs (AS), meadow (MD), sparse cushion vegetation (SCV) and desert (DS)) were chosen to examine how plants influence the process of FT erosion (Fig. 6). The region dominated by AS showed the largest intensity of FT erosion with an average of 6.96, i.e., severe erosion. This phenomenon resulted from the fact that the AS is mainly distributed in the mountains of the southeastern region that exhibit larger topographic relief and precipitation. The mean intensities of FT erosion for BF and SCV were 6.57, 6.23, respectively, i.e., intensive erosion. The fluctuation range of SVC was the largest due to its wide distribution and low vegetation fraction, followed by MD. The SCF had the smallest fluctuation range of FT erosion intensity because the plant types were concentrated in the mid-low mountains of the southeastern region where the erosion intensity was mainly intensive. The desert represented a zone with no or sparse vegetation, and it was mainly distributed in the northwestern plateau where precipitation was scare and the landforms much lower. Thus, the mean intensity in this zone belonged to mild erosion. By comparing the mean and fluctuation range of FT erosion intensity for each plant type, it was found that during the study period, regions which dominated by alpine shrubs were the most severely affected by FT erosion, followed by SCF and SCV. In addition, zones with sparse cushion vegetation were potentially the worst-hit area by FT erosion, exhibiting the largest fluctuation range.

Fig. 6
figure 6

Change intensity of FT erosion for each plant type. The top of box represents mean value of FT erosion intensity for each plant type; the bottom of box refers to minimum value; the top of line represents the maximum value; the bottom of line refers to the fluctuation range of FT erosion intensity. SCF, subalpine coniferous forest; BF, broadleaf forest; AS, alpine shrubs; DS, desert; MD, meadow; SCV, sparse cushion vegetation

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5 Conclusions

In this study, we introduced the microwave remote sensing technique to establish an estimation model of FT erosion. The estimated results were proved to be accurate by precision testing with the field sampling data.

The region of FT erosion was widely distributed in the Qinghai–Tibet Plateau, covering 163.96 (104) km2 and accounting for 63.46 % of the area. The average intensity of FT erosion over the whole region was moderate erosion category. The erosion intensity increased from slight erosion in northwestern regions to severe erosion in the southeastern part. Due to the great environmental heterogeneity, the dominant impacting factors for the FT cycle were different across the region. The mid-western plateau was mainly influenced by the annual FT cycle days, average diurnal phase-changed water content and temperature. The southern and southeastern zones were influenced by precipitation, topographic relief and aspect. However, further studies need to be conducted to clarify the mechanisms underlying the process of FT erosion and strengthen the precision of the evaluation process.