Changes in mountain glaciers are generally considered one of the best natural indicators of climatic change (Reference Pachauri and ReisingerPachauri and Reisinger, 2007). Glaciers and ice caps are also believed to have a significant effect on global sea levels (e.g. Reference FairbanksFairbanks, 1989;Reference Berthier, Schiefer, Clarke, Menounos and RemyBerthier and others, 2010) and thus they have been selected as one of the fundamental climate indicators in the Global Climate Observing System (GCOS, 2003). Over the past five decades, most of the world's glaciers have shown a tendency to shrink (Reference Hall, Benson and FieldHall and others, 1995a; Reference VuilleVuille and others, 2008) and, recently, numerous relatively small glaciers have even completely disappeared (e.g. Reference Delgado Granados, Julio Miranda, Higgel, Ortega del Valle and Alatorre IbarguengoitiaDelgado Granados and others, 2007; Reference Dyurgerov and MeierDyurgerov and Meier, 1997). According to previous studies, more than 80% of the glaciers in China may be retreating (e.g. Reference Liu, Sun, Shen and LiLiu and others, 2003;Reference Jin, Xin, Che, Wu and MoolJin and others, 2005;Reference ShangguanShangguan and others, 2006). Numerical simulations of the response of these glaciers have also suggested that they will probably shrink further under increasingly warm conditions in the future (Reference OerlemansOerlemans and others, 1998; Reference Shi and LiuShi and Liu, 2000).
Compared with the detailed studies of glaciers in the European Alps (e.g. Reference BerthierBerthier and others, 2005; Reference Paul, Kaab and HaeberliPaul and others, 2007) or the Greenland and Antarctic ice sheets (e.g. Reference Davis, Li, McConnell, Frey and HannaDavis and others, 2005), studies on glacier changes in the Lenglongling mountains are rare. To our knowledge, there are only two published papers concerning glacier changes in the Lenglongling mountains, both in Chinese (Reference Cao, Pan, Gao, Jing, Wen Yand and hangguanCao and others, 2010;Reference Zhang, Lu, Wang, Guo and ZhangZhang and others, 2010a), and the data accuracy described in those papers does not meet the requirements of the Global Land Ice Measurements from Space (GLIMS) project. Changes in glaciers in the northeastern margin of the Tibetan Plateau indicate a sensitive response to global climate change (Reference Liu, Sun, Shen and LiLiu and others, 2003; Reference ShangguanShangguan and others, 2010). Studies of these glacier variations will provide valuable information concerning glacier response to climate change in the Tibetan Plateau and globally. In addition, glaciers within our study area are a significant freshwater resource for hydropower generation, irrigation and domestic and animal consumption in the Gansu corridor (Reference Yang and ZengYang and Zeng, 2001). Accurate studies of glacier change and how climatic factors impact on the retreat of glaciers are therefore necessary and urgent in this area.
Over the past decade, remote-sensing satellite techniques have been widely adopted in investigations of mountain glaciers (e.g. Reference Racoviteanu, Williams and BarryRacoviteanu and others, 2008a; Reference Paul and AndreassenPaul and Andreassen, 2009). Satellite imagery that can distinguish between glacier area, seasonal snow cover and clouds can be employed to evaluate glacier change in areas that are difficult to access. The GLIMS project evaluates the extent and change of glaciers globally using satellite multispectral images (http://www.glims.org/), which are primarily obtained from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) and Landsat Enhanced Thematic Mapper Plus (ETM+) (Reference RaupRaup and others, 2007). Previous work has mainly concentrated on large-scale glaciers, whereas many small glaciers that are relatively inaccessible receive little attention, even though they are more sensitive to global climate change (Reference Delgado Granados, Julio Miranda, Higgel, Ortega del Valle and Alatorre IbarguengoitiaDelgado Granados and others, 2007). According to Reference Paul, Kaab and HaeberliPaul and others (2007), relatively small glaciers can be readily investigated repeatedly using remote-sensing techniques. A series of multi- spectral satellite data generated in the period 1995-2007 are investigated in this paper, aimed at analyzing the shrinkage mechanisms of the remote, relatively small glaciers of the northeastern Tibetan Plateau.
Aerial photographs, Landsat Thematic Mapper (TM), ETM+ and ASTER satellite data across the western Lenglongling mountains are used to reconstruct an archive of glacier change in the study area using GIS and digital imageprocessing technology as described by Reference Paul, Kaab and HaeberliPaul and others (2007) and Reference ShangguanShangguan and others (2007). These data are then integrated with glacier size and meteorological information in order to understand the shrinkage of 179 glaciers in this region during the past 35 years.
The western Lenglongling mountains are located in the northeastern part of the Tibetan Plateau and are about 250 km in length and 30-50 km in width (Fig. 1). The mean altitude is >4000 m and Gangshika peak is 5254ma.s.l. Climatically, the area exhibits arid to semi-arid conditions. Glaciers of the western Lenglongling mountains are classified as subcontinental (subpolar)-type glaciers (Reference Shi and LiuShi and Liu, 2000) and are influenced by the combined effects of the east Asian monsoon, the south Asian monsoon and westerlies (Reference Tang and XuTang and Xu, 1984).
Mean annual air temperature in the period 1957-2010 was ~1 °C at Menyuan meteorological station (2924 m a.s.l.). The mean equilibrium-line attitude (ELA) is ~-4500m in the western Lenglongling mountains (Reference Wang, Liu, You, Pu, Yang and TianWang and others, 1981) and, extrapolating with a standard atmospheric lapse rate of 0.72°C (100 m)-1 (Reference WangWang and others, 2009), mean annual air temperature at the ELA is ~-10°C.
The Chinese Glacier Inventory (CGI) (Reference Wang, Liu, You, Pu, Yang and TianWang and others, 1981; Reference Shi, Liu, Wang, Liu and YeShi and others, 2005) shows that a total of 179 continental-type glaciers occur above 4000 m a.s.l. in the western Lenglongling mountains, covering a total area of ~87.2 km2 (i.e. an average glacier area of ~-0.49km2; Fig. 1). On the southwest-facing slope of the western Lenglongling mountains, there are 103 glaciers feeding the drainage basin of the Datong River, a tributary of the Yellow River. The average glacier area is ~0.38km2. The remaining 76 glaciers dominate the northeast-facing slope and are the source of some inland drainage basins. The average area of these glaciers is ~0.63 km2.
Data and Methods
Topographical/aerial photograph map data
We obtained from the State Bureau of Surveying and Mapping a series of 1 : 50 000 topographical maps of the study area, originally generated from aerial photographs taken in 1972. We then digitized the 20 and 40 m interval contours and spot heights in order to generate a triangular irregular networks (TIN) map and to create a digital elevation model (DEM) based on Beijing54 using ArcGIS software. The center and flattening of Beijing54 are different from the World Geodetic System 1984 ellipsoidal elevation (WGS84) Universal Transverse Mercator (UTM). In order to compare with those data, the DEM was reprojected to the WGS84 UTM using a seven-parameter datum transformation model. The application of the seven-parameter datum transformation model has been discussed by Reference Guo, Bo, Ji and MaoGuo and others (2002), Reference Wang, Wang and LuWang and others (2003) and zhang and others (2010b). The error using a seven-parameter datum transformation model is <0.002 m (Reference Wang, Wang and LuWang and others, 2003).
However, taking into account the inevitable errors of glacier borderline in the process of generation from aerial photographic to topographical map (Reference Hall, Bayr, Schoner, Bindschadler and ChienHall and others, 2003), original aerial photographs were employed directly in order to identify the precise glacier outline or other surface types (e.g. Reference Van Westen and Lulie GetahunVan Westen and Lulie Getahun, 2003;Reference Andreassen, Paul, Kaab and HausbergAndreassen and others, 2008). Fortunately, a total of 552 aerial photographs taken in 1972 exactly cover the western Lenglongling mountains. They were scanned and georectified using the DEM and a set of ground-control points (GCPs) for comparison with the topographical maps. These GCPs were selected from distinguishable landmarks present in the aerial photograph, such as summits, peninsulas and geologic patterns. The aerial photographs were resampled to 5 m resolution and the rectification error was <2 pixels (10 m) root-mean-square (rms). The identified glacier outline was then digitized using GIS based on vector files.
One TM image (path 132, row 34, 11 June 1995), two ETM+ images (path 132, row 34, 1 August 1999 and path 132, row 34, 24 July 2002) and an ASTER image (16 May 2007) (Table 1) were selected to investigate the dynamic changes of the 179 glaciers in the study area during different time intervals. Some regions could not be covered by a single scene, so it was necessary to develop a mosaic of several scenes from different years (Reference Paul and AndreassenPaul and Andreassen, 2009). Apart from the ETM+ image in 1999, the remaining four satellite scenes are free of cloud and seasonal snow cover. According to image pretreatment, most of the ETM+ in 1999 can also avoid interference from snow and cloud;never- theless a small central part in this image suffered from slight interference by cloud. This section was therefore replaced by a China-Brazil Earth Resources Satellite (CBERS) image (path 15, row 58, 15 July 2000). For the western Lenglongling mountains, the glacier borderline in 1999 was estimated from the merged vector polygons, which were outlined by the two images independently. The TM, ETM+ and ASTER data were obtained from the Global Land Cover Facility (GLCF) and United States Geological Survey (USGS), while the CBERS data are from the China Center for Resources Satellite Data and Application. They were all orthorectified to the WGS84 UTM datum.
There are several fusion methods, for example principal components analysis (PCA), smoothing filter-based intensity modulation (SFIM), Brovey transform and intensity-hue- saturation (IHS), which can be used to enhance the resolution and image interpretability of ETM+ data (Reference LiuLiu, 2000;Reference Yang, Xia and ChenYang and others, 2007). However, enhancing spatial resolution and improving spectral characteristics are mutually contradictory, and, according to Reference Yang, Xia and ChenYang and others (2007), the PCA method of enhancing spatial resolution retains the greatest degree of spectral characteristics. We use band 5, 4, 3 (as red, green, blue) false-colour compositing, then fuse the image with the panchromatic band by the PCA method with 28.5 m resolution multispectral data and 14.25 m resolution panchromatic data, yielding effectively a 14.25m resolution multispectral image (Reference Lillesand and KieferLillesand and Kiefer, 1999;Reference Jiang, Strittholt, Frost and SlosserJiang and others, 2004). The resultant sensor resolutions of TM, ETM+, CBERS and ASTER are 28.50, 14.25, 19.60 and 15.00 m, respectively.
In previous work, the methods for glacier delineation with Landsat data can generally be divided into three distinct groups: supervised classification (Reference Aniya, Sato, Naruse and Skvarca Pand CasassaAniya and others, 1996; Reference Sidjak and WheateSidjak and Wheate, 1999), normalized-difference snow index (NDSI) (Reference Hall, Benson and FieldHall and others, 1995b;Reference Racoviteanu, Williams and BarryRacoviteanu and others, 2008b) and segmentation of ratio images from various TM band combinations (Reference PaulPaul, 2001). Among these algorithms, the band ratio method, which has been adopted for many glacierized areas (e.g. Reference PaulPaul, 2001;Reference BolchBolch, 2007; Reference Paul and AndreassenPaul and Andreassen, 2009), is considered the most accurate and convenient algorithm to extract glacier borderlines. We also use this method to extract glacier borderlines from satellite images across the western Lenglongling mountains.
The processing chain for extracting glacier outlines from images is composed of four steps: (1) calculation of band ratio, (2) selection of threshold value, (3) creation of binary image and (4) manual digitization.
Calculation of band ratio
The band ratio method is based on the fact that ice has a high reflectivity of visible spectrum and a low reflectivity of shortwave infrared (SWIR) spectrum. Utilizing this, we can clearly distinguish glacier from other surface types. For Landsat imagery, according to the difference in glacier size and image content (shadow, vegetation, water), there are two band ratios that can be used (Reference Paul, Kaab and HaeberliPaul and others, 2007): (1) TM3/TM5 (Reference Narama, Shimamura, Nakayama and AbdrakhmatovNarama and others, 2006;Reference Paul and AndreassenPaul and Andreassen, 2009) and (2) TM4/TM5 (Reference BolchBolch, 2007;Reference ShangguanShangguan and others, 2007). For the 179 glaciers studied in the western Lenglongling mountains, TM4/TM5 is more effective than TM3/TM5 in distinguishing glacier from other surface types. TM4/TM5 is thus adopted in this paper as the primary method to extract glacier outlines. Since the wavelengths of ASTER in bands 3 and 4 approximate those of Landsat in bands 4 and 5, TM3/TM4 was used to deal with ASTER data. The CBERS imagery has no SWIR band, so the glacier outlines were extracted based on manual digitization rather than the band ratio method.
Selection of threshold value
Thresholds appear to be different in different regions, also depending on the image content (Reference Paul, Kaab and HaeberliPaul and others, 2007). Reference ShangguanShangguan and others (2007) selected a value of 2.1 as a threshold in the western Kunlun Shan, Reference BolchBolch (2007) considered 2.0 as a threshold in the Tien Shan, while Reference Paul and AndreassenPaul and Andreassen (2009) used 2.6 as a threshold in the Svartisen region, Norway. On the basis of repeated experiments, a threshold set to 2.3 will clearly distinguish glaciers from other surface types.
Creation of binary image
If the value of the ratio image exceeds the threshold value, the study object can be identified as a glacier or vice versa. That is, a value of 0 is assigned to pixels with a ratio less than the threshold, and a value of 1 to pixels with a ratio greater than or equal to the threshold. The glaciers are thus represented as 1s in the binary image, and the binary raster is converted to a vector for more efficient data handling during post-processing (Reference Svoboda and PaulSvoboda and Paul, 2009). However, serrated vector borderlines are not suitable to depict natural glacier boundaries, and a specially designed procedure to smooth the lines is needed. The basic idea is to connect the midpoints of each line segment that has a length equal to single cell size, remove vertexes of line segments that have equal slopes, then offset the two end-points of line segments that are longer than single cell size towards the middle of the line with half cell-size distance. However, this may lead to negative errors (~1-2%) in the glacier area attribute.
Although the band ratio method is robust and the results are very accurate for debris-free ice (Reference Andreassen, Paul, Kaab and HausbergAndreassen and others, 2008;Reference Paul and AndreassenPaul and Andreassen, 2009), it is difficult to automatically distinguish debris-covered ice from its surroundings as the spectral characteristics are close (Reference Paul, Huggel and KaabPaul and others, 2004a). The best tool to extract more reliable information from satellite images for many glaciers is manual digitization (Reference RaupRaup and others, 2007). All glaciers in the western Lenglongling mountains are debris-free and the glacier borderlines only occasionally need manual modification, relying on the DEM. However, in order to reduce the impact of subjective factors on precision in the process of manual digitization, we chose three experts to perform this process independently and then ultimately integrated their results.
Uncertainties in Glacier Borderline Extraction
In order to verify the accuracy in extracting glacier borderlines from satellite images, a GPS real-time kinematic (GPS-RTK) measurement for Ningchan and Shuiguan River glaciers was performed in July 2010. The precision of the vertical and horizontal measurements by GPS was approximately 0.1 and 0.05 m, respectively. When applied to glacier area, for some unclear reason (e.g. clouds, ionosphere error) the precision may decrease. However, the accuracy will be restricted by an accuracy of 0.3 m in the vertical and 0.1 m in the horizontal (Reference Rivera, Casassa, Bamber and KaabRivera and others, 2005). ATM image (path 132, row 34, 8 September 2010) that is coincident with the GPS-RTK measurement was obtained to verify the accuracy in mapping the glacier borderline. However, it was not possible to extract the complete glacier borderline from this TM image due to interference by seasonal snow cover (Fig. 2a), so the 2010 TM was only considered as a reference for glacier borderline verification rather than a data source. Fortunately, however, some parts of the glacier in this image (e.g. Ningchan and Shuiguan River glaciers) can be distinguished clearly from other surface types (Fig. 2b). For these glaciers, the borderlines extracted from the TM image in 2010 are in good agreement with the GPS-RTK measurements in 2010 (Fig. 2c). Therefore, in the western Lenglongling mountains, we believe the band ratio method for extracting a glacier borderline from satellite images is an accurate and reliable approach. In addition, the glacier extents outlined by GPS- RTK in 2010 are inside the borderlines extracted from the ASTER image in 2007. This result indicates that the trend in glacier variation from 2007 to 2010 is retreat, similar to that of 1972-2007.
The accuracy in measuring glacier terminus positions extracted from multitemporal satellite images primarily relies on the sensor resolutions (Reference Williams, Hall and ChienWilliams and others, 1997) and the co-registration errors (Reference Hall, Bayr, Schoner, Bindschadler and ChienHall and others, 2003;Reference Silverio and JaquetSilverio and Jaquet, 2005). Therefore, an uncertainty will probably occur in this measurement. According to Reference Silverio and JaquetSilverio and Jaquet (2005) and Reference Ye, Kang, Chen and WangYe and others (2006), this uncertainty can be calculated from
where U T is the measurement uncertainty of the glacier terminus in the study area, A is the original pixel resolution of each image and e is the co-registration error of each image to the topographic map generated in 1972. For the images in 1972, 1995, 1999, 2000, 2002 and 2007, the resolutions are 5.00, 28.50, 14.25, 19.60, 14.25 and 15.00 m, respectively. As a result, according to Eqn (1), the uncertainties in our glacier tongue measurements were 57.4 m between 1972 and 1995, 63.7 m between 1995 and 1999, 40.3 m between 1999 and 2002, 41.3 m between 2002 and 2007 and 30.8 m between 1972 and 2007. The total U T among the data sources is 86.9 m.
According to Reference Ye, Kang, Chen and WangYe and others (2006) the co-registration error also plays an important role in variation measurement between datasets. Therefore, we introduce the co-registration error into the accuracy evaluation in our glacier extent calculation. The uncertainty in calculating the variation in extent of the 179 glaciers in the western Lenglongling mountains from 1972 to 2007 can be evaluated to be 0.009km2, i.e.
where U A is the uncertainty in calculating glacier extent.
Considering the small values of U T and U A, the uncertainty in mapping the glacier borderline from multitemporal satellite images is negligible.
Glacier size and distribution
From the aerial photographs, the 179 glaciers in the study area covered a total area of 86.2 km2 (average glacier area ~0.48 km2) in 1972. There is a strong asymmetry between relatively large glaciers and smaller glaciers in glacier number and area (Fig. 3). Glaciers smaller than 0.5 km2 account for 69% of the total number of glaciers in the western Lenglongling mountains, yet represent just 30% of the total glacier area in the region. In contrast, although the larger glaciers (i.e. those larger than 1 km2) constitute just 11.1% of the total number, they represent 41.4% of the total glacier area. The discrepancy with the CGI estimate of 87.2 km2 (Reference Wang, Liu, You, Pu, Yang and TianWang and others, 1981; Reference Shi, Liu, Wang, Liu and YeShi and others, 2005) can probably be attributed to the different data source and errors in manual processing of glacier borderlines.
The mean slope and aspect of each glacier have been calculated (Fig. 4). Generally, the glaciers in the study area are steep, with a mean slope of 23°, and slopes are close to normally distributed. The studied glaciers are oriented in all directions, but the two predominant aspects are south and east.
All 179 glaciers in the western Lenglongling mountains shrunk between 1972 and 2007 (Fig. 5). The total glacierized area was 86.2, 70.5, 66.9, 64.6 and 61.8 km2 in 1972, 1995, 1999, 2002 and 2007, respectively (Table 2). Total area decreased significantly, with a total area loss of 24.4km2, equivalent to 28.3% of the original area in 1972. The mean rate of area reduction was 0.70 km2 a-1, but the shrinkage rates in different time periods are inconsistent. The annual shrinkage rate of the glacier area from 1995 to 2002 was faster than in other intervals.
Based on the different size categories derived from the standard in 1972 (Fig. 3), total glacier area change with time within each category is shown in Table 3. Glaciers with an area less than 0.1 km2 in 1972 lost ~67.2% of their area between 1972 and 2007. Glaciers with an area of 0.1-0.2 km2 in 1972 decreased by 70.3%, while the larger glaciers (>1 km2) lost 14.3% of their total area. In summary, the relatively small glaciers of the western Lenglongling mountains decreased faster than the larger glaciers. This significant discrepancy in rate of decrease may arise from the fact that the small glaciers have smaller altitudinal range (Reference Racoviteanu, Williams and BarryRacoviteanu and others, 2008b). As a result, local climate fluctuations may result in the ELAs increasing to above the glacier maximum elevation, so that the entire area occupied by the glacier is within the ablation zone (Reference Kaser and OsmastonKaser and Osmaston, 2002).
By using the DEM to define drainage basins, we see that the glaciers of the western Lenglongling mountains can be separated into two categories: those with southwest-facing slopes and those with northeast-facing slopes. Between 1972 and 2007, the annual area variation rate of glaciers facing southwest was 0.41 km2, significantly greater than for those facing northeast (0.28 km2; Table 4).
Relationship Between Glacier Variation and Climate Change
The key to understanding the mechanisms of glacier variation likely lies in a thorough analysis of glacier response to climate change (Reference Dyurgerov and MeierDyurgerov and Meier, 2000;Reference Anderson, Lawson and OwensAnderson and others, 2008). Instrumental records are available from only a few meteorological stations in western China, especially in mountainous regions. Four meteorological stations have been established in the region of the western Lenglongling mountains (Fig. 1). Menyuan (37°23' N, 101°37' E;2924m a.s.l.) and Jiutiaoling (37°50' N, 102°01' E;2350 m a.s.l.) meteorological stations are closer to the glaciers in the study area than are Wushaoling (37°12' N, 102°52' E;3044m a.s.l.) and Wuwei (37°55' N, 102°40' E; 1532 m a.s.l.) stations. Menyuan and Wushaoling stations are located respectively south and east of the western Lenglongling mountains, while Jiutiaoling and Wuwei stations are to the north. Meteorological data are available from the China Meteorological Data Sharing Service System (http://cdc.cma.gov.crv).
Analyzing data from the above four meteorological stations, we find that during the past six decades the annual precipitation seems to show a stable pattern, which can be well represented by roughly parallel fitting lines (Fig. 6). The precipitation on the south-facing slope of the western Lenglongling mountains shows a negligible decrease (Menyuan station), while it appears to slightly increase on the north-facing slope (Jiutiaoling and Wuwei stations). Compared with the low precipitation trend, air temperature seems to display a dramatic increasing pattern (Fig. 7). Menyuan station is the closest of the four to the glaciers in our study area, and the pattern of air temperature reflected by the data from this station is probably consistent with the actual pattern over the glaciers. In comparison with the global average air temperature increase between 1950 and 2000, ~1°C(100a)-1 (Reference HoughtonHoughton and others, 2001), the increase in air temperature in the western Lenglongling mountains from 1957 to 2010 is ~3.7 times greater. While inevitably there is a time lag in the response of a glacier to climate change, the lag is expected to be discrepant for different glacier sizes. According to Reference Yao, Wang, Liu, Pu, Shen and LuYao and others (2004), the smaller and shorter glaciers will probably respond more rapidly to climate change. Most glaciers of the western Lenglongling mountains are relatively small, with individual areas of <1 km2, and the reaction time for most mountain glaciers is expected to be <10years (Reference PatersonPaterson, 1994;Reference Ren, Jing, Pu and QinRen and others, 2006). In summary, the glacier shrinkage in the western Lenglongling mountains from 1972 to 2007 can probably be attributed to the dramatic increase in air temperature.
The rate of glacier shrinkage in the study area was 0.90 km2 a-1 from 1995 to 1999 and 0.77 km2 a-1 from 1999 to 2002. The precipitation from 1988 to 1995 exhibits a decreasing trend at Menyuan, Wushaoling and Jiutiaoling stations (Fig. 6), while air temperature recorded by all meteorological stations exhibited a stable pattern (Fig. 7). The precipitation from 1995 to 1999 shows a decreasing trend at Menyuan, Wushaoling and Jiutiaoling stations (Fig. 6), while air temperature recorded by all stations indicates a relatively rapid increase (Fig. 7). Thus, the higher glacier shrinkage rate from 1995 to 2002 in the western Lenglongling mountains may result from the combination of decreasing precipitation and increasing air temperature from 1988 to 1999. The clear correspondence between glacier shrinkage and climate change suggests that the lag in a glacier's reaction to climate change is probably ~5-8years.
The glacier shrinkage rate on the southwest-facing slope of the western Lenglongling mountains is faster than on the northeast-facing slope, likely for three reasons. First, the precipitation shows a slight decreasing trend on the south- west-facing slope, yet a small increasing trend on the northeast-facing slope (Fig. 6). Second, the rate of increase in summer air temperature (June-August) on the south-facing slope is ~4.5°C (100 a)-1, two to three times higher than on the northeast-facing slope (~1.6°C(100a)-1), although the increase in annual air temperature on the two sides of the mountains seems to be the same (Fig. 7b). According to Reference GardnerGardner and others (2011), an increase in glacier mass loss is probably a direct response of the glacier to higher air temperature in summer. Thirdly, the average glacier size on the southwest-facing slope is 0.38km2, smaller than that (0.62 km2) on the northeast-facing slope.
During the past few decades, glacier change has been widely investigated, for example in Alaska (e.g. Reference Arendt, Echelmeyer, Harrison, Lingle and ValentineArendt and others, 2002), Patagonia (e.g. Reference Rignot, Rivera and CasassaRignot and others, 2003), the Andes (e.g. Reference Racoviteanu, Williams and BarryRacoviteanu and others, 2008b), the Himalaya (e.g. Reference KaabKääb, 2005) and central Asia (e.g. Reference BolchBolch, 2007). Results suggest that glacier retreat is now a consistent phenomenon. The degree of retreat has varied spatio-temporally by about 5-10% over the past three decades in China (Reference LiLi and others, 2008). According to Reference Liu, Sun, Shen and LiLiu and others (2003), the total glacier area loss in the western Qilian Shan from 1956 to 1990 is ~10.3%. The glaciers located further into the continental interiors and at high altitudes, for example in the eastern Pamir (Reference ShangguanShangguan and others, 2006) and the inner Tibetan Plateau (Reference Li, Sun and ZengLi and others, 1998), show lower rates of glacier shrinkage. On the basis of our analysis, the 179 glaciers in the western Lenglongling mountains have lost 28.3% of their total 1972 area or 0.81% a-1 from 1972 to 2007. Compared with other glaciers worldwide, these glaciers present a relatively higher shrinkage rate. For example, the total glacier area loss in the Alps is ~20% (Reference Kaab, Paul, Maisch, Hoelzle and HaeberliKääb and others, 2002;Reference Paul, Huggel and KaabPaul and others, 2004b) and the glaciers of the Northern Patagonia Icefield have decreased by ~3.4 ± 1.5% from 1979 to 2001 (Reference Rivera, Benham, Casassa, Bamber and DowdeswellRivera and others, 2007). According to Reference OerlemansOerlemans (1994), a temperature increase of ~0.1°C (10a)-1 can result in a variation of several hundred meters in glacier length. The higher rate of glacier shrinkage in our study area is probably attributable to a dramatic increase in air temperature and relatively small glacier size (an average area of 0.48 km2).
We have provided a comprehensive and multitemporal analysis of glacier change in the western Lenglongling mountains. The primary data sources employed included aerial photographs, satellite images, a DEM and GPS data. The band ratio method worked well to extract glacier borderlines from satellite images. The 179 glaciers in the western Lenglongling mountains have lost 28.3% of their area in the period 1972-2007. The glacier shrinkage rates seem to be discrepant over different time intervals. A higher shrinkage rate appeared in the period 1995-2002. Compared with other glaciers worldwide, those in our study area show a higher shrinkage rate, 0.81% a-1 from 1972 to 2007. We believe that this is a consequence of a dramatic increase in air temperature and the relatively small glacier size.
We thank T.H. Jacka and Tingjun Zhang for their help and structural improvements to the manuscript. This paper has benefited from valuable comments and constructive suggestions by Keith A. Brugger and an anonymous reviewer, whose efforts are gratefully acknowledged. This study is financially supported by the Investigation of Glacier Resource and its Variations in China (No. 2006FY110200), National Natural Science Foundation of China (No. 91125008), National Natural Science Foundation of China (No. 41171063) and National Science Foundation of China Innovation Team Project (No. 41021091).