## Abstract

Mountain glaciers in China are an important water source for both China and adjoining countries, and therefore their adaptation to glacier change is crucial in relation to maintaining populations. This study aims to improve our understanding of glacial vulnerability to climate change to establish adaptation strategies. A glacial numerical model is developed using spatial principle component analysis (SPCA) supported by remote sensing (RS) and geographical information system (GIS) technologies. The model contains nine factors—slope, aspect, hillshade, elevation a.s.l., air temperature, precipitation, glacial area change percentage, glacial type and glacial area, describing topography, climate, and glacier characteristics. The vulnerability of glaciers to climate change is evaluated during the period of 1961–2007 on a regional scale, and in the 2030s and 2050s based on projections of air temperature and precipitation changes under the IPCC RCP6.0 scenario and of glacier change in the 21st century. Glacial vulnerability is graded into five levels: potential, light, medial, heavy, and very heavy, using natural breaks classification (NBC). The spatial distribution of glacial vulnerability and its temporal changes in the 21st century for the RCP6.0 scenario are analyzed, and the factors influencing vulnerability are discussed. Results show that mountain glaciers in China are very vulnerable to climate change, and 41.2% of glacial areas fall into the levels of heavy and very heavy vulnerability in the period 1961–2007. This is mainly explained by topographical exposure and the high sensitivity of glaciers to climate change. Trends of glacial vulnerability are projected to decline in the 2030s and 2050s, but a declining trend is still high in some regions. In addition to topographical factors, variation in precipitation in the 2030s and 2050s is found to be crucial.

## Keywords

Mountain glaciers; Climate change; Vulnerability; Projection

## 1. Introduction

It has been reported that since 1850, most glaciers in the world have been shrinking due to climate warming (Oerlemans, 2005, Arendt, 2011 and Bolch et al., 2012), and the shrinkage has continued over the last two decades (Ren et al., 2004, Liu et al., 2006a, Liu et al., 2006b, IPCC, 2007a, IPCC, 2013 and Arendt, 2011). Glacier melting has already made considerable impacts on both regional and global scales. For example, the contribution of glacier melting to sea level rise increased from (0.50 ± 0.18) mm per year in 1961–2004 to (0.77 ± 0.22) mm per year in 1991–2004 (IPCC, 2007a), and such a rise in sea level threatens coastal lowlands and small island countries. In high altitude regions of Asia, such as the Tibetan Plateau and high mountainous areas of central Asia, disasters including glacial lake outbursts, glacial floods, and glacial debris flow have occurred frequently in relation to rapid glacier melting (Mool et al., 2001a, Mool et al., 2001b, Che et al., 2004, Che et al., 2005, Wang, 2008 and Pradhan et al., 2012), and such occurrences have severely threatened the socio-economic development and ecological patterns in both mountainous areas and downstream regions (UNDP, 2007 and Xu et al., 2008). In the short-term, there are advantages from glacial melting, such as increases in river flow alleviating short-term water shortage in arid and semi-arid regions. However, the flow will reduce in the long-term with prolonged glacier melting, and its effects on food production and economic growth are likely to be unfavorable in the high altitude regions of Asia. In addition, it is considered that the flow reduction in the long-term would then give rise to a further demand for water and food supplies—a demand that is already increasing in this region (WB (World Bank), 2005, UNDP, 2006 and IPCC et al., 2007c). Therefore, glacial changes and associated effects have captured the attention of international politics and the academic world.

There are 48,571 glaciers covering a total area of 51.8 × 103 km2 in China (Liu et al., 2015). The glaciers are distributed mainly on the Tibetan Plateau and in the high mountains of West China: the Altai, Tianshan, Karakorum, Kunlun, Qilian, Hengduan, and Himalaya Mountains. The glaciated areas in western China represent the sources of the ten largest rivers in Asia: the Yangtze, Yellow, Tarim, Salween, Mekong, Ili, Ertix, Brahmaputra, Indus, and Ganges Rivers, and they thus have a very prominent effect on the formation and change of the water resources of these rivers. For example, glaciers in western China provide rivers with approximately 60.47 × 109 m3 of meltwater per year, which is equivalent to the average annual runoff of the Yellow River into the sea.

Glacier meltwater is of considerable importance in the inland arid area of Northwest China. In the Tarim River Basin, the largest inland river basin in China, and the most glacierised watershed in arid Northwest China, there are 11,665 glaciers covering a total area of 19,878 km2. The ratio of glacial meltwater to runoff for each tributary is above 30%, and for some this ratio rises to 80%. A number of oases are generated and maintained in the arid hinterland of China. These would not exist without glaciers, and the region would therefore no longer be able to support populations.

China implemented the West Development Project in 2000 to improve the living standard of people in western China, and to reduce differences in development between eastern and western China, with the aim of bringing the Chinese economy into a period of rapid, stable, harmonious, and sustainable development. Although the year 2011 marked the second step in the 10-year development plan, water resources are a restrictive factor for rapid development. If future changes in glacial water supply hamper the sustainable development of society, both the economy and ecological conservation will suffer in the arid area. Thus, water supplies are keys to realizing the strategic objective of western China development. It remains both a practical and strategic issue for the Chinese central government and related local governments to gain an understanding of how to adapt to a series of natural, social, and economic effects resulting from glacier variations in the near future, and how to cope with the threatening long-term effects of continuous warming and diminishing of glacier water resources.

An assessment of the vulnerability of glaciers to climate change forms the basis for scientific adaptation to glacial variations. However, studies on glacier vulnerability to climate change have been seldom reported, and thus adaptive countermeasures formulated by Chinese government departments lack a scientific basis, and fail to achieve optimal results in practice. It is thus evident that further studies relating to glacial changes and associated impacts, glacial vulnerability, and adaptation are necessary. Vulnerability is a versatile concept that is widely used in many fields, such as climate change, risk assessment, disaster management, food security, and public health, and so on. Therefore, its associated underlying concepts can differ widely. Recently the integrated vulnerability concept of the IPCC has been gradually accepted, particularly in global change and climate change researches (IPCC, 2001b). The IPCC Third Assessment Report (TAR) (IPCC, 2001a and IPCC, 2001b) defines vulnerability as the degree to which a system is susceptible to, or unable to cope with, adverse effects of climate change, including climate variability and extremes, which is a function of the character, magnitude, and rate of climate variation to which a system is exposed, its sensitivity, and its adaptive capacity. A system can be a nature, a society, an ecosystem, or in cases where one largely depends on the other, a human-environmental system.

Based on the above definition of vulnerability, Yang and Zhang (2010) defined cryospheric vulnerability as the degree to which cryosphere and its elements are susceptible to adverse effects of climate change, especially from air temperature and solid precipitation, and it is a function of the character, magnitude, and rate of climate variation, its sensitivity, and its self-adaptive capacity. The vulnerability of cryospheric change was defined as vulnerability of a system to cryospheric change, including the environment-oasis system in arid regions, ecosystems in cold regions, and other human-environmental system (Yang and Zhang, 2010). Researches on the vulnerability of both cryosphere and its change are still in initial stage. There are only a few studies addressing these issues. The composite index assessment method used widely was mainly introduced to this field. Based on the definition of vulnerability provided by the IPCC, He et al. (2012) selected seven indicators to assess the vulnerability of cryospheric change in China, from 2001 to 2020 and from 2001 to 2050 in A1 and B1 scenarios. Glacier is a very important component of the cryosphere, and it is very vulnerable to climate change, especially air temperature rise and precipitation variations.

In this paper, glaciers in China are chosen as the object of study. Based on the IPCC vulnerability definition, the authors aim to comprehensively assess the vulnerability level of glaciers to climate change, with the object of revealing temporal and spatial variations in glacier vulnerability, and to advance the understanding of glacier vulnerability in China.

The paper is organized as follows: In Section 2, we present our approach relating to a vulnerability assessment, which introduces a set of index systems for use in evaluating glacial vulnerability (Section 2.3.2). In addition, we introduce a glacial vulnerability evaluation (GVE) model developed using spatial principal component analysis (SPCA) method (Section 2.5). Section 3 presents glacial vulnerability in the period 1961–2007, and the scenario and change in vulnerability projected during the 21st century, together with its spatial pattern. In Section 4, the evaluation results, uncertainties, and factors influencing glacial vulnerability are discussed. Section 5 then concludes this paper.

## 2. Data and methods

### 2.1. Data and sources

Digital elevation models (DEM) were used in this study, in addition to the data derived from them, meteorological data, and glacier inventory data; these data sources are presented in detail in the sections below.

#### 2.1.1. DEM and derivative data

DEM data at a spatial resolution of 1 km × 1 km using the projection system Albers, were obtained from the National Administration of Surveying, Mapping and Geoinformation. Slope, aspect, and elevation data were then generated from DEM data.

#### 2.1.2. Meteorological observation and simulation data

Annual mean air temperature at 594 Chinese stations and annual total precipitation at 590 stations during the period 1961–2007 were derived from the China Meteorological Administration. The simulated results of air temperature and precipitation in the 2030s and the 2050s over China under the IPCC RCP6.0 scenario were obtained from a high resolution Regional Climate Model (RegCM4.0) one-way nested by the global model BCC_CSM1.1 (Beijing Climate Center_Climate System Model version 1.1) (Ji, 2012), which are also used for analyzing climate change on the Tibetan Plateau of China in the 21st century (Ji, 2012).

#### 2.1.3. Chinese Glacier Inventory data

Research for the first compilation of the Chinese Glacier Inventory 1978–2002 involved a thorough investigation of glacial resources during the period of the 1960s to the 1970s. The second compilation was carried out after 2006, in order to evaluate the total size and variations of Chinese glacier resources in the most recent 20–30 years. In this study, data from 2005 to 2006 are considered to be a baseline reference. Based on glacial area data of the two glacier inventories, the percentage of change in glacial areas is thus calculated as:

 ${\displaystyle (S_{2}-S_{1})/S_{1}\times 100\%\quad {\mbox{,}}}$
(1)

where S1 is an area of each glacier in the first Glacier Inventory, and S2 is glacial area of the second Glacier Inventory.

### 2.2. Data processing methods

 ${\displaystyle k_{i}=n_{i}/N_{i}\quad {\mbox{,}}}$
(2)

where ki is the hillshade within i km; ni is the grid number where the difference between sea level elevation and the height of the center point is greater than R within a square area subjected to the center point and i km of apothem; Ni is the total grid number in the square area of i km of apothem, excluding the center. In our study, i and R equal 2.5 km and 200 m, respectively. The raster data of hillshade were generated using the DEM.

#### 2.2.2. Processing methods of meteorological data

The Mann–Kendall trend test (Modarres and Silva, 2007) was used to detect possible trends in air temperature and precipitation series at each station during the period 1961–2007. Using the Kriging interpolation method, the trend magnitudes were then spatially interpolated to attain a spatial resolution matching that of DEM data. Interpolation results for the glacier distribution region were obtained through GIS clipping. Similarly, the simulated data of air temperature and precipitation changes in the 2030s and 2050s were also obtained for the glacier distribution region.

#### 2.2.3. Assignment of glacier type

Glaciers in China are classified into three types, maritime, sub-continental, and extreme continental (Shi and Liu, 2000). Maritime glaciers are mainly distributed in the Hengduan Mountains, in the southeastern part of the Tibetan Plateau (including the eastern Himalayas and the mid-east section of the Nyainqentanglha Mountains). Sub-continental glaciers are mainly located in the mountain ranges of Altai, Tianshan, mid-to-east of Qilian, eastern Kunlun and Tanggula, western Nyainqentanglha, the northern slope of the mid-to-western Himalayas, and Karakorum in China. Extreme continental glaciers are mainly located in the western part of the Tibetan Plateau (including the western Kunlun Mountains, the Qiangtang Plateau, eastern Pamir, western sections of Tanggula, Gangdise and Qilian Mountains). Previous research indicates that the three types of glaciers in China have different response patterns to global warming. For example, maritime glaciers are very sensitive to climate change, extreme continental glaciers are insensitive, and sub-continental glaciers have responses between those of maritime and extreme continental (Shi and Liu, 2000). Thus, glacier type is selected as an index of glacier vulnerability in the following text (in Section 2.3.2).

Glacier type, however, is not a quantitative value, and it cannot be used directly in glacial vulnerability assessment. Based on the results reported in Shi and Liu (2000), a sociological method was employed in this study. This firstly involved designing a questionnaire, and then in 2010 conducting a questionnaire survey for completion by experts in the field of cryospheric science. A total of 61 questionnaires were sent to experts, and 48 responses were received—the ratio of callback of valid questionnaire is 98%. Using weighted average statistical calculations, results showed the value of extreme continental glaciers to be 2.6, sub-continental glaciers 3.5, and maritime glaciers 4.2, and therefore a value of 2.6 is assigned all extreme continental-type glaciers, 3.5 all subcontinental-type glaciers, and 4.2 all maritime-type glaciers.

#### 2.2.4. Method used in estimation of future glacier changes

Estimating of glacier change in China is a prerequisite when compiling a glacier vulnerability projection of the 21st century. Shi and Liu (2000) preliminarily estimated the changes for three types of glaciers under estimated climatic warming scenarios in the 21st century, and determined empirical relations between glacier retreat and temperature rise since the Little Ice Age. Based on their research results, and glacial area data obtained from the first Glacier Inventory, in this study the projected areas of maritime, sub-continental, and extreme continental glaciers in the 2030s and 2050s are calculated.

In addition to the above-mentioned methods, all data were projected using the Albers projection system, which includes parameters of the first standard parallel of 25.0000, the second standard of 47.0000, the central meridian of 105.0000, and the Krasovsky ellipsoid. Using ArcGIS software, all data were transferred to 1 km × 1 km raster data.

### 2.3. Evaluation principles and indicators

#### 2.3.1. Principles involved in the selection of evaluation indicators

According to the definition of vulnerability, the three accepted criteria for selection of evaluation indicators in the field of climate change vulnerability research are exposure, sensitivity, and adaptive capacity (IPCC, 2001b, IPCC, 2007b and Bernard and Ostländer, 2008), and therefore these criteria are also used as basic criteria in this text. However, in addition to scientific criteria, we also consider certain specifics pertaining to mountain glaciers in China, such as their distribution, size, and type.

Numerous factors, such as geographical location, terrain, landform, climate, glacial size, and type influence glacial vulnerability. For example, responses to climate change differ depending on the size of the glaciers: a slow response for large glaciers with an area of >2 km2 and a fast response for small glaciers in China. Therefore, when selecting the indicators it is not only necessary to cover various possible factors involved in vulnerability, but also to highlight dominant factors. In addition, to adequately consider the 46,377 glaciers in China (Shi et al., 2005), it is necessary to consider the availability of related data. Furthermore, the indicators chosen should not only be representative, but also be simple and practical to enable convenient processing. Therefore, factors involved in a comprehensive analysis can be summarized by adhering to three principles: the combined principle of scientific characteristics and practical characteristics, the principle of comprehensiveness and dominancy, and the principle of representativeness and operationality.

#### 2.3.2. Construction of an evaluation index system for glacier vulnerability

Exposure is the nature and degree to which a system is exposed to significant climatic variations (IPCC, 2001b), and the exposure of a system to climate stimuli depends on the level of global climate change and on the systems location (Füssel and Klein, 2006). According to this definition, six factors are selected from topography and climate parameters: slope, aspect, hillshade, and elevation above sea level, which depict specific circumstances of glaciers, and trend magnitudes of variations in air temperature and precipitation, which represent the level of climate change. Sensitivity is the degree to which a system is affected by climate stimuli (IPCC, 2001b), and in relation to available glacier data only the percentage of glacial area change is used to reflect the sensitivity of glaciers to climate variation. In addition, adaptive capacity is determined as the ability of a glacier system to self-adjust to climate stressors within a certain range, and this is mainly determined by the internal structure, size, type, etc. of the glacier system. On the basis of these descriptions, therefore, glacial type and area are chosen for the index in this study, and an integrated evaluation system with nine factors is thus quantitatively established. This contains four layers: objective, standard, element, and indicator (Table 1).

Table 1. An index system for glacier vulnerability assessment in China.
Objective layer Standard layer Element layer Indicator layer Unit
Glacier vulnerability Exposure Topography Slope °
Aspect °
Elevation a.s.l. m
Climate parameters Air temperature variation magnitude °C per 10 years
Precipitation variation magnitude mm per 10 years
Sensitivity Glacier Glacial area change percentage  %
Glacial area km2

### 2.4. Data normalization method

There are considerable differences between the varying units of values for all the variables used, and therefore the variables cannot be used directly to evaluate glacial vulnerability; their values must therefore be standardized to reflect a uniform measurement system across all factors to enable an evaluation of glacier vulnerability. The original values of each factor were standardized using the following equation:

 ${\displaystyle Y_{ij}={\frac {x_{ij}-x_{min,j}}{x_{max,j}-x_{min,j}}}\times 10\quad {\mbox{,}}}$
(3)

where Yij is the standardized value of factor j of grid i, varying from 0 to 10; xij is the original value of factor j of grid i; and xmax,j and xmin,j are the maximum and minimum values of factor j of grid i, respectively.

### 2.5. Evaluation model

A key issue when constructing a vulnerability assessment is to determine how to convert different types of information obtained from many different sources into an integrated vulnerability index (Locantore et al., 2004). A number of methods have been suggested, such as the indices weight method (IWM) (Diakoulaki et al., 1995 and Li et al., 2001) and the analytical hierarchy process (AHP) (Tran et al., 2002 and Liu et al., 2003). However, these methods depend on experts' evaluation when weighing the importance of factors, and thus the final evaluation results depend on the capacity of the said experts. The assessment of Chinese glacier vulnerability involves many variables, and is also a vulnerability evaluation on a regional scale; therefore, issues such as the overall condition of the regions vulnerability, spatial variations, and the trend of future vulnerability change, need to be addressed. In this study, we aim to attain a method of assessment that is capable of processing many different types of data, and which is also able to generate relative objective evaluation results. As spatial principal component analysis (SPCA), which is a modified PCA approach, has advantages for use an eco-environmental vulnerability method of evaluation (Li et al., 2006 and Wang et al., 2008), it was thus used in this study to evaluate glacier vulnerability, and a glacial vulnerability evaluation (GVE) model was developed using the SPCA method. The formula for SPCA evaluation is as follows:

 ${\displaystyle E=\alpha _{1}Y_{1}+\alpha _{2}Y_{2}+\cdots +\alpha _{n}Y_{n}\quad {\mbox{,}}}$
(4)

where E is an integrated vulnerability evaluation index, Yi is the ith principal component, and αi is its corresponding contribution.

The process of glacial vulnerability evaluation using the SPCA method is explained as follows: 1) original data are standardized; 2) a covariance matrix M is established for each variable; 3) an eigenvalue λi of matrix M and its corresponding eigenvectors αi are computed; 4) to group αi by linear combination and n principal components are output. In the software environment of the Spatial Analyst module in ArcGIS, the function of Principal Components is used to transform the data in a stack from the input multivariate attribute space to a new multivariate attribute space, where the axes are rotated with respect to the original space and the axes in the new space are uncorrelated. According to the cumulative contribution of principal components, the number of components is affirmed as 4, and SPCA is accomplished; the corresponding results are shown in Table 2. An evaluation function can then be set up to compute an integrated evaluation index on the basis of selected components.

Table 2. Results of spatial principal component analysis performed in this study.
Selected principal components 1961–2007 2030s 2050s
λi Contribution (%) Cumulative contribution (%) λi Contribution (%) Cumulative contribution (%) λi Contribution (%) Cumulative contribution (%)
I 3.68 39.87 39.87 3.68 34.65 34.65 3.64 34.05 34.05
II 3.14 33.97 73.84 3.50 33.02 67.66 3.49 32.68 66.73
III 0.998 10.75 84.59 1.86 17.54 85.21 2.05 19.12 85.85
IV 0.87 9.46 94.04 0.85 8.03 93.24 0.85 7.96 93.81

According to each components weight and generated stack, the formula is calculated and evaluation indexes determining the situation of glacial vulnerability are output. In this paper this is termed the glacial vulnerability index (GVI). The higher the GVI value, the more vulnerable a glacier is to climate change.

Derived from Table 2 and Eq. (4), the linear formulas for computing GVI are created as follows:

 ${\displaystyle {\begin{array}{l}\displaystyle GVI_{1961-2007}=0.3987\times A_{1}+0.3397\times A_{2}+0.1075\times A_{3}+\\\displaystyle +0.0946\times A_{4}{\mbox{,}}\end{array}}}$
(5)
 ${\displaystyle {\begin{array}{l}\displaystyle GVI_{2030{\mbox{s}}}=0.3465\times B_{1}+0.3302\times B_{2}+0.1754\times B_{3}+\\\displaystyle +0.0803\times B_{4}{\mbox{,}}\end{array}}}$
(6)
 ${\displaystyle {\begin{array}{l}\displaystyle GVI_{2050{\mbox{s}}}=0.3405\times C_{1}+0.3268\times C_{2}+0.1912\times C_{3}+\\\displaystyle +0.0796\times C_{4}{\mbox{,}}\end{array}}}$
(7)

where GVI is the glacial vulnerability index, and A1A4 are four principal components established from nine initial spatial variables throughout the period 1961–2007; similarly, B1B4 are principal components in the 2030s, and C1C4 in the 2050s. The cumulative contribution of the four components is 94.04% (1961–2007), 93.24% (the 2030s) and 93.81% (the 2050s), respectively, each of which are within 90%–95%, which is in accord with a highly reliable convention of choosing factors by the PCA method. However, there is a loss of information of about 6.0%, when the number of selected components reaches four, which shows that the initial factors have relatively independent functions within the evaluation.

The result computed from the GVE model gives a continuous value, and it thus needs to be classified into several levels to deliver various levels of glacial vulnerability. The natural breaks classification (NBC) is a graphical tool that is used to explore the statistical distribution of classes and clusters in an attributed space. As the classes are based on natural grouping inherent within the data, NBC is able to identify break points by picking class breaks that group similar values. It is then able to maximize the differences between classes, and where there are relatively large jumps in data values it divides features into classes with set boundaries. In this study, the NBC was applied to discrete computed values by analyzing the natural properties of the computed values and determining dividing points between clusters. Glacial vulnerability was graded into five levels: potential (P), light (L), medial (M), heavy (H), and very heavy (Vh). Using the period 1961–2007 as an example, each level is characterized by a spatial pattern, as shown in Table 3.

Table 3. Results of glacial vulnerability classifications in China 1961–2007.
Vulnerability level GVI Spatial pattern description
Potential (P) <4.5 Patchy and banded pattern, mainly distributed in the southern edge of Altai, the northern edges of Qilian and Kunlun, southern and northern borders of Tianshan, and the margin of mountains in the southern Qaidam Basin
Light (L) 4.5–5.7 Patchily distributed in Altai, Tianshan, Qilian mountains, northern Tibetan Plateau, and the Hengduan Mountains area
Medial (M) 5.7–6.7 Mainly distributed in the western areas of the Qilian mountains, northern Tibetan Plateau, northern Altun Mountain, and the Tianshan and Hengduan Mountains area
Heavy (H) 6.7–7.7 Mainly distributed in Altai, Tianshan, Karakorum, middle and eastern areas of the Qilian mountains, southern Tibetan Plateau, and the Hengduan Mountains area
Very heavy (Vh) >7.7 Mainly distributed in Altai, Tianshan, Karakorum, middle and eastern areas of the Qilian mountains, southern Tibetan Plateau, and the Hengduan Mountains area

## 3. Results

According to the standard mentioned above, the integrated evaluation indexes for the periods 1961–2007, the 2030s, and the 2050s were classified to generate the results shown in Fig. 1.

 Fig. 1. Glacier vulnerability level and distribution in China in (a) 1961–2007, (b) the 2030s, and (c) 2050s.

### 3.1. Grade of vulnerability in 1961–2007

During the period 1961–2007, 91.9% of glaciated areas in western China were classified as having light vulnerability or higher (Table 4): 28.5% of areas were in the medial vulnerable zone, 25.0% in the heavy vulnerable zone, 22.2% in the slight vulnerable zone, and 16.2% in the very heavy vulnerable zone. Therefore, the percentage area classified into the heavy and very heavy vulnerable zones equals 41.2%, and if the medial vulnerable zone is also included in this calculation, the proportion would be approximately 70.0% of all glacial areas in western China. These results therefore indicate glaciers in China were very vulnerable to climate change during 1961–2007.

Table 4. Percentage levels of glacier vulnerability within specified time periods.
Glacier vulnerability level 1961–2007 2030s 2050s
Grid number Percentage (%) Grid number Percentage (%) Grid number Percentage (%)
P 235,519 8.1 552,723 19.1 600,668 20.8
L 644,046 22.2 649,520 22.5 615,888 21.3
M 826,725 28.5 686,675 23.8 691,427 24.0
H 723,556 25.0 679,480 23.5 675,621 23.4
Vh 467,521 16.2 318,875 11.1 303,654 10.5

### 3.2. Scenario and vulnerability changes in the 21st century

#### 3.2.1. Vulnerability scenario

Under the RCP6.0 scenario for the 2030s, 80.9% of glaciated areas in western China will be in the category of light vulnerability or higher. The proportion of areas relating to medial, heavy, light, potential, and very heavy vulnerable zones is 23.8%, 23.5%, 22.5%, 19.1%, and 11.1% in order (Table 4). In addition, by the 2050s, 79.2% of glaciated areas will be in the category of light vulnerability and higher, where the medial vulnerable zone covers the largest area proportionally at 24%, the heavy vulnerable zone 23.4%, the light vulnerable zone 21.3%, the potential vulnerable zone 20.8%, while the very heavy vulnerable zone accounts only for a very small proportion of 10.5% (Table 4).

#### 3.2.2. Vulnerability change

Results show that glacier vulnerability as a whole shows a declining trend (Fig. 1). Where 91.9% of glaciated areas showed a light vulnerability or higher during the period 1961–2007, the proportion then drops to 80.9% in the 2030s, and to 79.2% in the 2050s. In relation to vulnerability level, the area proportion of the very heavy vulnerable zone decreases from 16.2% during 1961–2007 to 11.1% in the 2030s; the medial vulnerable zone decreases from 28.5% to 23.8%, while the potential vulnerable zone increases largely from 8.1% during 1961–2007 to 19.1% in the 2030s (Table 4). Furthermore, relative to the results for the 2030s, there is very little change to each level in the 2050s. However, glaciers in some areas continue to show heavy and very heavy vulnerability in the 2030s and 2050s.

### 3.3. Spatial distribution pattern

The spatial distribution of glacier vulnerability was not uniform in western China in the period of 1961–2007 (Fig. 1a), but, on the whole vulnerability had a decreasing distribution pattern from the high mountains of the Tibetan Plateau periphery to the Plateau hinterland. More specifically, glaciers were mainly classified as being in the heavy and very heavy vulnerable levels to the south of ∼32°N on the Tibetan Plateau, while northward to the northern Tibetan Plateau glacial vulnerability weakened to medial, even slight levels. Vulnerability was also high, over medial level in Altai, Tianshan, middle and eastern areas of Qilian Mountains, and was low (primarily medial, light, and potential levels) in the fringes of these mountain ranges and at the northern edge of the Tibetan Plateau (Table 3).

In general, the geographical distribution pattern of glacier vulnerability in the 2030s and 2050s, is predicted to be similar to that of 1961–2007. Any differences are related to a decrease in vulnerability in the Tibetan Plateau hinterland (primarily to potential, slight and medial levels) in the two periods (Fig. 1b and c).

## 4. Discussion

### 4.1. Evaluation of results

The index system of glacial vulnerability assessment constructed in this text covers five aspects of major parameters: topography, climate change, glacier change, glacier size and type. The GVI, which was generated using the SPAC method, ingests information relating to all these variables. Results show that, in general, the levels of glacial vulnerability are medial in western China. The GVI is also able to present an apparent spatial distribution, showing that glaciated areas in western China are typically found in the plateau and high mountainous areas where there are complex changes in the sudden rise and fall of landforms. The spread of a mountain, its slope direction and degree, and changes in regional climate all contribute to the varying sizes and types of glaciers. Thus, results show that vulnerability can be strictly represented by regional feature.

The above results show that mountain glaciers are very vulnerable to climate change in China, which are consistent with previous studies. Of the 5000 glaciers studied in China over the past decades, 82.2% have retreated (Liu et al., 2006a and Liu et al., 2006b). Moreover, these glaciers have undergone rapid shrinking in recent years (Ren et al., 2004, Liu et al., 2006a, Liu et al., 2006b, Kang et al., 2007 and Li et al., 2007). In China, the effects of glacier melting on water resources are gradually becoming increasingly serious, as are glacial disasters, such as glacial meltwater floods and glacial lake outburst floods (GLOFs). Glacier No. 1 at the headwaters of Urumqi River, in eastern Tianshan, China, has been determined that the mean annual meltwater runoff of the glacier increased by 84.2% between 1986 and 2001 compared with 1958–1985 (Li et al., 2003). In addition, the flow of the Aksu River, which is the primary tributary in the Tarim River Basin, increased by 30% in relation to glacier meltwater runoff in the 1990s (Liu et al., 2006a and Liu et al., 2006b). However, some studies indicate that glacier meltwater runoff will increase over a number of decades, but this will be followed by a decrease with future predicted temperature rise (Ye et al., 2001 and Liu et al., 2006b); if this occurs, western China will be faced with even more serious water resource shortages than at present.

### 4.2. Uncertainty

There are a number of uncertainties associated with the future projection of glacial vulnerability. Firstly, air temperature and precipitation simulated by Regional Climate Model (RegCM4.0) (Ji, 2012) is uncertain in the 21st century, and secondly, the estimated glacier change is also highly uncertain (Shi and Liu, 2000).

### 4.3. Factors affecting glacier vulnerability

The vulnerability of glaciers results from the joint influence of many factors. However, it is necessary to identify the key factors involved and the minor factors. In addition, it is not clear why the degree of glacial vulnerability to climate change actually decreases in the 21st century, even when there is a rise in predicted climate warming. To discuss these issues, an Analysis of Variance (ANOVA) is used to test the vulnerability evaluation indicators, and key factors affecting glacier vulnerability and their influences on glacier vulnerability are identified.

Results show that during the period of 1961–2007, the key factors influencing glacial vulnerability were aspect, the percentage glacial area change, elevation a.s.l., and hillshade (Table 5). According to the concept of the vulnerability and evaluation index system (Table 1), aspect, elevation, and hillshade are all topographical exposure indicators, and the percentage glacial area change is one of sensitivity indicators, reflecting the sensitive degree of glaciers to climate change. This shows that under the level of climate change that occurred during 1961–2007, glaciers were very sensitive to climate change, and that their degree of vulnerability to climate change depended largely on topographical exposure and sensitivity. These results show that respective changes in air temperature and precipitation had minor effects on glacial vulnerability in this period, and the authors therefore consider that these two factors do not directly affect glacier vulnerability, but that they indirectly influence vulnerability via an integrated effect on glacier change.

Table 5. Results of variance analysis for glacial vulnerability evaluation indicators.
Indicator Variance
1961–2007 2030s 2050s
Aspect 3.1321 3.5358 3.5358
Glacial area change percentage 2.1255 0.2217 0.1674
Elevation a.s.l. 2.0468 2.3106 2.3106
Precipitation 0.3555 1.9993 2.1296
Slope 0.2216 0.2502 0.2502
Glacier type 0.1995 0.2252 0.2252
Glacier area 0.0080 0.0090 0.0095
Air temperature 0.0028 0.7943 0.7949

In the 2030s, topography will remain the principal factor affecting glacial vulnerability. However, the influence of glacial area change percentage will decrease significantly, but the impacts of air temperature and precipitation variations, in particular precipitation, will increase significantly. The results that the sensitivity of glaciers to climate change will weaken greatly with the further melting of glaciers under a climate scenario of continuous warming, and the variations in precipitation may become a key factor affecting glacial vulnerability after 2007. In addition, this condition is projected to be similar in the 2050s and the 2030s. Therefore, based on the above analyses, the authors consider that the 2030s will be a crucial period for glacier change under the RCP6.0 scenario. The reduced sensitivity of glaciers to climate change may then be the main cause of reduced glacial vulnerability in the 2030s and subsequent years.

## 5. Conclusions

This study constructs an evaluation index system for glacial vulnerability based on the concept of vulnerability. Additionally, it analyzes the characteristics of Chinese mountain glaciers, evaluates the situation of glacial vulnerability during the period 1961–2007, and projects changes in the 2030s and the 2050s under the RCP6.0 scenario in western China on a regional scale. Furthermore, a numerical evaluation model is developed to analyze glacial vulnerability using RS and GIS data, and the SPCA method is used to determine variables and their weights. The conclusions provided by this study are as follows:

• Mountain glaciers are very vulnerable to climate change in western China. During the period 1961–2007, approximately 92% of glaciated areas had a light or higher vulnerability to climate change, of which 41.2% of glacial areas were considered to be at heavy and very heavy levels of vulnerability. In general, glacial vulnerability shows a declining trend in the 2030s and the 2050s, but glaciers in Altai, Tianshan, Kunlun, middle and western areas of Qilian Mountains, middle and eastern areas of Himalayas, and southeastern Tibet will continue to be classified as being at heavy and very heavy levels of vulnerability.
• Glacial vulnerability is a product of the joint influences of multi-factors. Glaciers were relatively highly vulnerable in the period 1961–2007, and it is considered that both topography and the high sensitivity of glaciers to climate change are responsible for this situation. In addition to topographical factors, however, it is considered that variations in precipitation could become a crucial factor affecting glacial vulnerability in the 2030s and 2050s. With continuous climate warming and continuous glacier melting, the reduced sensitivity of glaciers to climate change is likely to be the major reason for a reduction in glacial vulnerability in the future.

The authors developed the evaluation index system of glacier vulnerability based on the concept of climate change vulnerability, where various factors based on existing data were taken into account. However, the mechanism of glacial vulnerability and its predicted reduced vulnerability in the future requires further studies.

## Acknowledgements

This study was supported by grants from the National Basic Research Program of China (2013CBA01808) and the National Natural Science Foundation of China (41271088). We are very grateful to Dr. Wu Li-Zong and Guo Wang-Qin for providing Chinese Glacier Inventory and glacier changes data. We thank the editor and anonymous reviewers for their valuable suggestions leading to significant improvement in the paper. We are also thankful to all persons for their help to us.

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