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Relationships between the heights of moraines and lengths of former glaciers in Tibet and surrounding mountains
Geomorphology 103 (2009) 205–211
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Geomorphology j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / g e o m o r p h
Relationships between the heights of moraines and lengths of former glaciers in Tibet and surrounding mountains Ping Fu, Chaolu Yi ⁎ Laboratory of Landsurface processes and Environment Changes, Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing 100085, China
A R T I C L E
I N F O
Article history: Accepted 20 December 2007 Available online 9 May 2008 Keywords: Statistical analysis Moraine height Glacier length Tibet
A B S T R A C T Reconstructions of the extent of Quaternary glaciations provide important knowledge of landform evolution on the Tibetan Plateau. The heights of moraines and the lengths of corresponding former glaciers in Tibet and its surrounding mountains were statistically analyzed using values for 141 observations collected from the literature and field measurements. The height of a moraine is defined as the difference between the elevation of the highest point of a lateral moraine and the elevation of the nearby valley bottom. The results show that the height of a lateral moraine is more closely related to the length of the former glacier than with the height of its end moraine. The lateral moraine was preserved better and more accurately represents the original shape of the moraine. The correlation between the height of a moraine and length of a glacier from lateral moraines in arid areas is better than that in maritime areas. This results from better preservation in arid areas. The high precipitation in the maritime areas results in stronger fluvial erosion and mass movement, and consequently is very effective in modifying and/or destroying moraines. The correlation between heights and lengths of lateral moraines is much better for Holocene than for older glaciations. Therefore, the correlation of the heights of Holocene lateral moraines to the lengths of glaciers is helpful for reconstructing the extent of Quaternary glaciation when end moraines are not preserved. This in turn is a first step towards assessing the relative importance of glaciers in landscape evolution across orogens. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Many researchers have attempted to reconstruct the extent of Quaternary glaciation throughout Tibet because of the importance of glaciers for understanding the evolution of landforms and climate change (e.g., Shi et al., 1990; Kuhle, 1998; Lehmkuhl, 1998). The changes in the extent of glaciers can be characterized by the fluctuations in the equilibrium-line altitude (ELA) of glaciers. Reconstruction of the past glaciations from reconstructing former ELAs has been employed widely by many researchers (Kuhle, 1998; Lehmkuhl, 1998; Ammann et al., 2001; Porter, 2001; Stansell et al., 2007). ELAs for former glaciers are commonly calculated by combining the results of the accumulation-area ratio (AAR) and the area–altitude balance ratio (AABR) (Meierding, 1982). The outer boundaries for calculating accumulation areas are determined by the positions of lateral and terminal moraines. End moraines, however, are easily destroyed by subsequent fluvial or glacial erosion. Once the end moraines are destroyed, determination of the accumulation area can be difficult, particularly for older glacials, thus limiting the usefulness of the AAR or AABR methods for reconstructing the former extents of glaciers. Thus, using the other relationships, such as the ratio between
⁎ Corresponding author. E-mail address: [email protected] (C. Yi). 0169-555X/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2008.04.023
the heights of moraines and the lengths of glaciers, might provide a useful estimate of the former extent of glaciers. Geomorphic methods provide good results if glacial remnants are well-preserved. Geomorphic processes will erode and destroy the moraines, however, as landforms evolve with time. The preservation of glacial landforms in maritime areas is particularly poor, and the preservation becomes worse with the time. In the Tibetan–Himalayan orogen, for example, identification of pre-Lateglacial moraines is more difficult in the Himalayan areas than on the northern Plateau (Owen et al., 2005). Meierding (1982) compared several methods and described limitations. For these reasons, different researchers have arrived at different conclusions regarding the extent of Quaternary glaciations on the Tibetan Plateau (Shi et al., 1990; Kuhle, 1998; Lehmkuhl, 1998; Zheng and Rutter, 1998). This paper examines the relationship between the dimensions of moraines and extent of former glaciers through statistical correlation between heights of moraines and lengths of glaciers. Our results are important for quantifying the extent of glaciation, which in turn has important implications for evolution of the landscape. 2. Data resources and study area Data regarding the lengths of former glaciers and heights of moraines were obtained from published literature on the glaciation of Tibet and its bordering mountains (Shi and Zhang, 1978; Zheng, 1982,
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1988, 2000, 2001, 2006a,b; Liu et al., 1986; Li et al., 1986; Shiraiwa and Watanabe, 1991; Xu and Shen, 1995; Benn and Owen, 1998; Wu et al., 2002; Jiao et al., 2005; Shi, 2005, 2006; Su and Shi, 2006; Li and Zheng, 2006; Su and Li, 2006; Zheng and Shi, 2006; Jiao and Zheng, 2006; Su, 2006). We supplemented these data sets with data from differential global positioning system (DGPS), collected during our field work in the Nyainqentanglha and Qilian Mountain. The data cover almost all of Tibet and the surrounding areas (Fig. 1) and include: Mount Bogda of Tian Shan (Su and Shi, 2006); Mount Yulong of the Hengduan Mountains (Zheng, 2006a), Xuebaoding Peak of the Hengduan Mountains; Kongur Shan on the Pamir Plateau (Su and Li, 2006); and Mount Kailash (Li and Zheng, 2006). The glaciers are categorized into three types based on glacial properties: maritime temperate; sub-continental cold; and continental cold (Shi, 2005). The south slope of the eastern Himalaya, the Hengduan Mountains and the eastern Nyainqentanglha Mountains are located in a humid region of Central Asia, influenced by the Indian monsoon, which brings abundant summer precipitation (Benn and Owen, 1998). These mountains contain maritime temperate glaciers (Shi, 2005). In the Himalaya, the data sites extend around Mt. Namjagbarwa (Zheng and Shi, 2006) and the Langtang Valley of Mt. Shisha Pangma's south slope (Zheng, 1982; Shiraiwa and Watanabe, 1991). Heights of moraines were measured from ridge-shaped moraines formed since the Last Glacial Maximum (LGM). In the Langtang Valley, the highest moraine surface lies about 400 m above the valley bottom. These were determined by Zheng (1988) to have developed during the Nyanyax-
ungla Glaciation in the early Mid-Pleistocene, when glaciers reached 35 km in length. In the Hengduan Mountains, only small and mediumsized valley glaciers developed during the Late Quaternary (Liu et al., 1986; Zheng, 2000, 2001, 2006a; Shi, 2006). The best preserved moraines have relative heights of over 100 m. These formed during the LGM. Two sets of lateral moraines exist along the valley sides in the Bome and Yigong areas in the eastern Nyainqentanglha Range (Li et al., 1986). Zheng (2006b) concluded that the higher one formed in the Penultimate Glacial and the lower in the Last Glaciation. He dated the latter to 11,252 ± 200 radiocarbon years BP. The moraines from the Penultimate Glacial in the Zhuxi Valley rise 800 m above the river valley. These were formed by a glacier that was 100 km long (Zheng, 2006b). Downstream of the 6–13 km modern glacier, three sets of end moraines have been recognized. They formed during the Dana Glacial Advance (3242 ± 101 radiocarbon years BP), the Danading Glacial Advance (which corresponds to Ruoguo Glacial Advance at 1920 ± 110 and 1540 ± 85 radiocarbon years BP), and the Baitong Glacial Advance (1056 ± 115 radiocarbon years BP) (Jiao et al., 2005). In the mid-western part of the Himalaya, the high mountains block the transportation of watervapor toward the north from the southeast monsoon and so the climate on the northern slopes differs considerably from that on the southern slopes. In the eastern Himalaya, glaciers are sub-continental, such as the Xibu Glacier at Yangpachen in the western Nyainqentanglha Range (Wu et al., 2002), and the glaciers in the Tian Shan (Wang and Zhang, 1981; Su and Shi, 2006), on the north slope of the main Karakoram, Mount Amne Machin in the
Fig. 1. Sketch map of study areas (modified from Shi, 2005).
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Kunlun Mountains (Deng et al., 2004), and Mount Geladandong in the Tanggulha Range (Li and Li, 1992; Jiao and Shen, 2003). Farther to the north, the mid-latitude westerlies influence the climate more strongly. On the north slope of the Himalaya, lateral moraines higher than 200 m are present together with eroded end moraines, and large areas of hummocky moraine, which formed during the Penultimate Glacial (Shi et al., 1982; Li et al., 1986; Zheng and Shi, 2006). At the Rongbuk Valley on the north side of Mount Qomolangma (Everest), the Holocene, Neoglacial and the Little Ice Age (dated at 410 ± 110 radiocarbon years BP; Fushimi, 1978) moraines extend within 3 km of the present ice margins (Burbank and Kang, 1991). Furthermore, four sets of ridge-shaped moraines probably formed during the Last Glacial Maximum (Burbank and Kang, 1991). These stretch several kilometers beyond the younger moraines. On the southwestern flank of the Karakoram, lateral moraines are well-preserved, but few end moraines are present, in the catchments of the Keleqing River. Su (2006) considers the glacier there to have been continental since the Late Pleistocene, but that maritime temperate glaciers developed during the two earlier glaciations in the Mid-Pleistocene. These include the Batola Glaciation in this area, considered to be earlier than 139 ± 12.5 ka, and dated on lacustrine deposit by thermal luminescence (Li and Xu, 1983). In the arid climate areas, data are mainly from the south slope of the Karakoram, the Gangdise Range, and the Qangtang Plateau. These are the most arid and coldest areas of the Tibetan Plateau. On the south slope of the Karakoram, moraines of the Last Glacial (dated by thermal luminescence at 47 ± 2.35 ka; Su, 2006) are well-preserved, and always lie along low trough valleys as lateral moraines (Shi and Zhang, 1978). These rise about 10 to 300 m high and two or three stages can be recognized based on the positions and dating (Xu and Shen, 1995). Moraines of the Neoglacial and the Little Ice Age are located near the margins of modern glaciers. At Mount Kailash, three giant end moraines from the Last Glacial are present in the valley, about 100–200 m, 50–60 m and 20–30 m above the valley bottom, while the lateral moraine of the Penultimate Glacial rises to about 50 m above the valley bottom (Li and Zheng, 2006).
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3. Method We collected two types of data, heights of lateral moraines and heights of end moraines, each with the length of its corresponding former glacier. Two “heights of moraines” can be defined: a) height of the crest of the moraine above the bottom of a given glacial valley; and b) the thickness of the till at a given location from its depositional base. Here, height of the moraine refers to the elevation of a particular moraine minus the elevation of the adjacent valley floor. Some researchers list a range of heights of moraines, but most researchers provide only the highest measured value for the height of a moraine. Thus, we use the highest values for our analysis. Using available information, we examine the relationship between the length of a glacier and height of the moraine in space and time. The lateral moraine data are subdivided into two according to the physical characteristics of the glaciers, the temperate (maritime) and continental cold glacier (Shi, 2002). The continental type includes the sub-continental cold and continental cold types. The data for lateral moraines were then subdivided into three additional sub-types according to the timing of glaciation and include those formed during the Penultimate Glacial, the Last Glacial, and the Holocene (Neoglacial and the Little Ice Age). The classification provides data for evaluating seven sub-sets (Fig. 3). The researchers cited determined the heights of moraines by barometric hypsometry and/or from large-scale topographic maps with a contour interval of 20 m. They all measured the lengths of glaciers on large-scale topographic maps. To assess the accuracy of these heights gathered from the literature, we compared the heights of some of the moraines determined by barometric hypsometry and from topographic maps with our electronic measurements of the same moraines using Mobile Mapper in the West Nyainqingtanglha Mountains and the Rongbuk Valley at Mount Qomolangma (Fig. 2). Mobile Mapper is a differential global positioning system (DGPS) made by the Thales company of France. It uses a combination of an Ashtech Mobilemapper Pro™ as a roving receiver and an Ashtech Promark™ for the reference station. The software Mobile Mapper
Fig. 2. Measurements of the moraines in Rongbu Valley, north slope of Qomolangma Peak (Everest Peak). (A) Google Earth images of the moraines, (B) tracking lines of the DGPS measurements for Pleistocene moraines, (C) tracking lines of the DGPS measurements for Holocene moraines and (D) closeup of a lateral moraine.
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Table 1 Statistical parameters of moraines for estimation of relative errors of measurements for heights of moraines Parameters
Mean SD
Height of lateral 155.7 moraine (m) The length of glaciers for 17.1 lateral moraine (km) Height of end 102.6 moraine (m) The length of glaciers for 20.9 end moraine (km)
SE
Min
Max Sum
133.2 16.9 30.0 800
Median Numbers
9653 115.0
36.3 4.6
1.5
270
1062 8.3
105.6 11.9
10.0
500
8109
60.0
20.8 2.3
1.2
100
1655
16.0
62
79
11 data points and one data point of 100 km long and 800 m high, which dominates the correlation. These data describe a former piedmont glacier in the Guxiang valley, East Nyainqentanglha (Zheng, 2006a). If we disregarded this data point, it would lead to a significantly poorer relationship. The sub-types of end moraines, however, do not show similar correlations between heights of moraines and lengths of the corresponding glaciers (Fig. 3H to I). We used the following regression equations to estimate the lengths of past glaciers for different times. y ¼ 0:09x−0:5
ðbased on 40 samplesÞfor arid areas
ð1Þ
‘SD’ means standard deviation of the mean, ‘SE’ means standard error of the mean.
y ¼ 0:05x þ 0:9 Office™ was applied to post-process the data. The DGPS enables the recording of points, lines and areas with sub-meter accuracy. 4. Results The data used in this study are listed in Table 1. The comparison of the heights of moraines measured with DGPS, topographic maps and reported by other researchers on the same moraines show errors (assuming the result of the DGPS is correct) of 0–8% for the moraines over 100 m high and between 0 and 39% for those less than 100 m high (Table 2). The former glaciers are defined as the maximum length of the past glaciers based on the positions of the end moraines. The average lengths of past glaciers are between 17 km and 21 km based on the average heights of lateral and end moraines which are between 156 m and 103 m, respectively. The past glaciers formed during the Last Glaciation and Holocene were valley glaciers. Heights of end moraines are all b 500 m, while the maximum height of lateral moraine is 800 m, which corresponds with the length of a glacier of 100 km (Zheng and Shi, 2006). The linear relationships between heights of moraines and lengths of glaciers for the case studies are shown in Fig. 3. Statistical tests indicate these relationships have a significant level at 0.01 for lateral and end moraines. By comparing the square of coefficients (r2), however, we find that the heights of lateral moraines have much closer correlation with the lengths of glaciers (Fig. 3A) than the heights of end moraines (Fig. 3B). The former has a r2 value of 0.44 (62 samples), but the latter only 0.23 (79 samples). The data for several sub-types of lateral moraines show that the correlations between the heights of moraines and lengths of glaciers are closer in the arid (Fig. 3C) than that in the maritime areas (Fig. 3D). The former has a correlation coefficient of 0.67 for 40 samples, while the latter is only 0.32 for 22 samples. The correlation of the heights of lateral moraines to lengths of glaciers has a coefficient of 0.85 for the 27 moraines that formed during Holocene (Fig. 3E). This is a higher correlation than 0.38 for 24 moraines that formed during the Last Glacial (Fig. 3F). The coefficient appears high for the moraines formed during the Penultimate Glacial (Fig. 3G), but the sample contains only
ðbased on 27 samplesÞfor the Holocene Glaciation ð2Þ
where x is the height of a lateral moraine and y is the length of a glacier. To test the reliability of these relationships, we analyzed the relative errors of the regression equations. The average values for the relative error is 38% for arid areas and 30% for the Holocene glaciations. The value for Holocene glaciations are all within 100% and decrease with increasing lengths of former glaciers, but the value for arid areas are higher for end and lateral moraines and the highest one is 211% (Fig. 4). All the estimated values of the lengths of glaciers fall within the 95% confidence interval. 5. Discussion The relative errors of the heights of moraines measured from topographic maps are within 10%, in comparison with those measured using the DGPS (Table 2) for the moraines higher than 100 m. This provides an acceptable estimation of the relationship between the heights of moraines and lengths of former glaciers. But the percentage error may be greater if the height of the moraine is b100 m. The heights of moraines measured using barometric surveying are closer to those measured by the DGPS. Furthermore, most Chinese researchers measured the heights of end moraines using barometric hypsometry. These suggest that the relative errors of the heights of end moraines collected from literature are small and the data can be used for this statistical study. As we observed in the field, the elevations of lateral moraines generally lie close to the surface of a nearby modern glacier, suggesting that the height of a lateral moraine approximates the thickness of the glacier. Based on data for about 45,000 glaciers in Tibet and its surrounding mountains from the China Glacier Catalogue, the lengths of glaciers correlate very closely (r2 = 0.88) with the corresponding thickness of the ice. The heights of lateral moraines formed in the past should also correlate with the length of former glaciers. This relationship follows more closely than the height of end moraine, particularly for measurements from the Holocene moraines in arid areas (Fig. 3).
Table 2 Estimation of the relative error of the heights of moraines measured in topographic maps or barometric hypsometry in comparison with those determined by the DGPS Mountain name
West Nyainqentanglha Mountains
Site
Shaong River valley
Langma River valley
Rongbuk River valley, Everest Mountain
Himalaya Fuqu River, Xixiabangma Mountain
Geographic coordinates
30°30′26″N, 90 56′37″E
30°35′30″N, 90°53′27″E
28°10′15″N, 86 49′45″E
28°09′3N, 85°58′46″E
Moraine type
End
End
Lateral
End
End
End
Timing
LG
LIA
LIA
LG
LG
LIA
LG
LG
Neoglacial
LG
35.2 25 29.0%
41.7 30 39.0%
33.6 25 34.4%
94.7 105 10.9%
99.8 105 5.2%
30 30 0%
254.9 250 1.9%
29.4 30# 2.0%
20.6 20# 3%
320 300 8.0%
Measured height Relative error
DGPS Map/BH
Lateral
The relative error is determined by the division of the difference between the heights measured in traditional ways and by the measured heights using the DGPS. The signal # means heights measured using barometric hypsometry (BH) by Zheng and Shi (2006).
P. Fu, C. Yi / Geomorphology 103 (2009) 205–211
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Fig. 3. Relationships between the relative heights of moraines and the lengths of the corresponding former glaciers: (A) all lateral moraines; (B) all end moraines; (C) lateral moraines in the maritime area; (D) lateral moraines in the arid area; (E) lateral moraines formed during the Holocene; (F) lateral moraines formed during the Last Glaciation; (G) lateral moraines formed during the Penultimate period; (H) end moraines in the maritime area; (I) end moraines in arid area; (J) end moraines formed during the Holocene; (K) end moraines formed during the Last Glaciations; (L) end moraines formed during the Penultimate period.
Several factors may account for the difference between the degree of correlation between the heights of moraines and the lengths of former glaciers for lateral and end moraines. First, because of the location, end moraines have poorer preservation than lateral moraines, as demonstrated in the glacial morphology literature regarding the Tibetan Plateau (Zheng, 2001; Shi, 2006). The preservation of glacial landform systems is strongly reduced by intensive glaciofluvial erosion and subsequent advances of glaciers. In contrast to lateral moraines, the end moraines occupy the fluvial breach and have eroded more intensively or may have been totally
destroyed. Consequently, heights of lateral moraines can better reflect the original sizes of the glaciers. Secondly, the genesis of the different moraines and the resulting till characteristics may cause differences in the preservation potential. Well-defined end moraines can only be formed effectively at the front of active glaciers when they are advancing or maintaining a stationary terminus (Embleton and King, 1968). So glacier dynamics largely control the size of these end moraines, and the end moraine is always not high and continuous. In contrast, lateral moraines, which extend along the margins of the glaciers, predominantly consist of angular debris derived from the rock
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The average value of relative error is between 30 and 38% for the prediction of the length of a glacier through height–length equations (Fig. 4). To minimize errors, we use the linear regression equations listed above for the relationship between the heights of Holocene lateral moraines with the lengths of corresponding glaciers or the relationship between the heights of lateral moraines of all sub-types with the lengths of the corresponding glaciers. We can, therefore, estimate the lengths of former glaciers based on the largest value of relative heights of the lateral moraines formed before the Holocene to predict the extent of the Pleistocene glacier. 6. Conclusion Fig. 4. Relative error versus the length of glaciers. The circles indicate relative error of linear regression of glaciers of arid area and the crosses indicate relative error of Holocene glaciations.
walls along the valley, which is carried passively either on top or within the glacier (Benn et al., 2003). In valley glacier systems, the texture of lateral moraines is universally coarser than the end moraines (Wang and Zhang, 1981). Lateral moraines are relatively more stable because meltwater cannot transport the larger debris as effectively. The differences in correlation of the heights of moraines with the lengths of glaciers between arid and maritime regions may result from differing climate influences on geomorphic processes between monsoon-dominated environments (developing mostly maritime temperate glaciers) and westerly-dominated environments (developing mostly continental cold glaciers; Shi, 2002). The glacial thermal regime that results from the predominant climate determines the status and dynamics of glaciation, and, therefore, produces different glacial landform systems. Temperate glaciers involve significant basal sliding and sub-glacial deformation of sediment. With the lack of supra-glacial sediment, temperate glaciers tend to create extensive, low amplitude, marginal dumping, pushing and squeezing moraines (Zheng et al., 1994; Evans and Twigg, 2002). But continental cold glaciers, with cold-bases, exhibit less active basal sliding and deformation than temperate glaciers (Waller, 2001). Consequently, moraines from continental cold glaciers suffer less deformation than those from maritime temperate glaciers during development (Kleman, 1994). Furthermore, moraines from cold glaciers contain bigger and more angular boulders than do moraines from temperate glaciers. For this reason, moraines formed by cold glaciers are relatively stable compared with those formed by temperate glaciers. Also, temperate glaciers discharge more meltwater, which transports debris effectively from the glacier margins and restricts moraine development. In contrast, to the moraines in the continental glacier area, the moraines developed in maritime area are poorly preserved because of intense erosion, mainly by fluvial and mass movement processes (Owen et al., 2005). Accordingly, the moraines in arid areas have better linear correlations with the lengths of glaciers, as mentioned above. We attribute the difference in correlation of the heights of moraines with the lengths of glaciers between Holocene and older glaciations to the following factors. None of the data for heights of moraines used in this study was calibrated to the initial size because of the lack of research on the rate of erosion rate unconsolidated landforms on the Tibetan Plateau. Researchers expect that the degradation of moraines increases with time. For example, Putkonen and O'Neal (2006) estimated that for 100–200 ka old moraines in the western North America the maximum depth of erosion averages 25% of the final height. We argue that the moraines formed in the Holocene have not been eroded very much, because they have been exposed for only about 10 ka and fresh and polished facets are still present. Thus, the length to height relationship for the Holocene glaciation correlates closely, while this relationship for moraines formed during the Pleistocene do not relate as closely because the latter have been exposed for a long time and experienced much more erosion than the former.
Our study shows that the glaciers in the arid areas of the Himalayan–Tibetan orogen have a closer correlation between the height of the lateral moraine and the length of a glacier than glaciers in maritime areas. This relationship results from less weathering and fluvial erosion in arid areas after moraine formation. The heights of lateral moraines correlate with the lengths of former glaciers more closely than with the height of end moraines. This relationship occurs because lateral moraines are better preserved than end moraines which are easily destroyed by fluvial or late glacial erosion. This relationship is stronger for moraines formed during glacial advances during the Holocene than for those formed during earlier glaciations. Holocene moraines are less intensively erosion than old lateral and end moraines that have experienced a long period of erosion. Hence, Holocene lateral moraines better represent the lengths of glaciers and are more reliable when using length to height relationships to estimate the minimum length of a valley glacier for past glaciations. This method provides an easy method for calculating ELAs across large regions, which in turn allows assessments of regional variation in glaciation that can influence landscape evolution. Acknowledgments This work is supported by the NSFC grants (40671023, 40730101) and the Knowledge Innovation Program of the Chinese Academy of Sciences, Grant No kzcx2-yw-104. The authors are grateful to Arjen Stroeven, Lewis Owen, Jack Vitek and anonymous reviewer's constructive comments. References Ammann, C., Jenny, B., Kammer, K., Messerli, B., 2001. Late Quaternary Glacier response to humidity changes in the arid Andes of Chile (18–29°S). Palaeogeography, Palaeoclimatology, Palaeoecology 172, 313–326. Benn, D.I., Owen, L.A., 1998. The role of the Indian summer monsoon and the midlatitude westerlies in Himalayan glaciation: review and speculative discussion. Journal of the Geological Society 155, 353–363. Benn, D.I., Kirkbride, M.P., Owen, L.A., Brazier, V., 2003. Chapter 15. In: Evans, J.A. (Ed.), Glacial Landsystems. Arnold Publication, pp. 372–405. Burbank, K.D.W., Kang, J.C., 1991. Relative dating of the Quaternary moraines, Rongbuk Valley, Mount Everest, Tibet: implications for an ice sheet on the Tibetan Plateau. Quaternary Research 36, 1–18. Deng, X.F., Liu, S.Y., Ding, Y.J., Shen, Y.P., Zhao, L., Xie, C.W., 2004. The Quaternary glacier and environmental evolution of the Aemye Ma-chhen Range. Journal of Glaciology and Geocryology 26, 305–311. Embleton, C., King, C.A.M., 1968. Glacial and Periglacial Geomorphology. Edward Arnold (Publishers) Ltd,, pp. 344–368. Evans, D.J.A., Twigg, D.R., 2002. The active temperate glacial landsystem: a model based on Breijamerkurjokull and Fjallsjokull, Iceland. Quaternary Science Reviews 21, 2143–2177. Fushimi, H., 1978. Glaciations in the Khumbu Himal (2). Seppyo 40, 71–77. Jiao, K.Q., Shen, Y.P., 2003. The Quaternary glaciation and glacier properties in the Tanggula Range. Journal of Glaciology and Geocryology 25 (1), 34–42 [Chinese with English summary]. Jiao, K.Q., Zheng, B.X., 2006. Quaternary glaciations in the Kunlun Mountains. In: Shi, Y.F., Cui, Z.J., Su, Z. (Eds.), The Quaternary glaciations and environmental variations in China. Hebei Science and Technology Publishing House, pp. 326–358. Jiao, K.Q., Iwata, S.J., Yao, T.D., 2005. Fluctuation and environment change of Zepu glacier on the eastern of the Nianqingtanggula Mountains since 32 ka BP. Journal of Glaciology and Geocryology 27, 74–79 [Chinese with English summary].
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Geomorphology j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / g e o m o r p h
Relationships between the heights of moraines and lengths of former glaciers in Tibet and surrounding mountains Ping Fu, Chaolu Yi ⁎ Laboratory of Landsurface processes and Environment Changes, Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing 100085, China
A R T I C L E
I N F O
Article history: Accepted 20 December 2007 Available online 9 May 2008 Keywords: Statistical analysis Moraine height Glacier length Tibet
A B S T R A C T Reconstructions of the extent of Quaternary glaciations provide important knowledge of landform evolution on the Tibetan Plateau. The heights of moraines and the lengths of corresponding former glaciers in Tibet and its surrounding mountains were statistically analyzed using values for 141 observations collected from the literature and field measurements. The height of a moraine is defined as the difference between the elevation of the highest point of a lateral moraine and the elevation of the nearby valley bottom. The results show that the height of a lateral moraine is more closely related to the length of the former glacier than with the height of its end moraine. The lateral moraine was preserved better and more accurately represents the original shape of the moraine. The correlation between the height of a moraine and length of a glacier from lateral moraines in arid areas is better than that in maritime areas. This results from better preservation in arid areas. The high precipitation in the maritime areas results in stronger fluvial erosion and mass movement, and consequently is very effective in modifying and/or destroying moraines. The correlation between heights and lengths of lateral moraines is much better for Holocene than for older glaciations. Therefore, the correlation of the heights of Holocene lateral moraines to the lengths of glaciers is helpful for reconstructing the extent of Quaternary glaciation when end moraines are not preserved. This in turn is a first step towards assessing the relative importance of glaciers in landscape evolution across orogens. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Many researchers have attempted to reconstruct the extent of Quaternary glaciation throughout Tibet because of the importance of glaciers for understanding the evolution of landforms and climate change (e.g., Shi et al., 1990; Kuhle, 1998; Lehmkuhl, 1998). The changes in the extent of glaciers can be characterized by the fluctuations in the equilibrium-line altitude (ELA) of glaciers. Reconstruction of the past glaciations from reconstructing former ELAs has been employed widely by many researchers (Kuhle, 1998; Lehmkuhl, 1998; Ammann et al., 2001; Porter, 2001; Stansell et al., 2007). ELAs for former glaciers are commonly calculated by combining the results of the accumulation-area ratio (AAR) and the area–altitude balance ratio (AABR) (Meierding, 1982). The outer boundaries for calculating accumulation areas are determined by the positions of lateral and terminal moraines. End moraines, however, are easily destroyed by subsequent fluvial or glacial erosion. Once the end moraines are destroyed, determination of the accumulation area can be difficult, particularly for older glacials, thus limiting the usefulness of the AAR or AABR methods for reconstructing the former extents of glaciers. Thus, using the other relationships, such as the ratio between
⁎ Corresponding author. E-mail address: [email protected] (C. Yi). 0169-555X/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2008.04.023
the heights of moraines and the lengths of glaciers, might provide a useful estimate of the former extent of glaciers. Geomorphic methods provide good results if glacial remnants are well-preserved. Geomorphic processes will erode and destroy the moraines, however, as landforms evolve with time. The preservation of glacial landforms in maritime areas is particularly poor, and the preservation becomes worse with the time. In the Tibetan–Himalayan orogen, for example, identification of pre-Lateglacial moraines is more difficult in the Himalayan areas than on the northern Plateau (Owen et al., 2005). Meierding (1982) compared several methods and described limitations. For these reasons, different researchers have arrived at different conclusions regarding the extent of Quaternary glaciations on the Tibetan Plateau (Shi et al., 1990; Kuhle, 1998; Lehmkuhl, 1998; Zheng and Rutter, 1998). This paper examines the relationship between the dimensions of moraines and extent of former glaciers through statistical correlation between heights of moraines and lengths of glaciers. Our results are important for quantifying the extent of glaciation, which in turn has important implications for evolution of the landscape. 2. Data resources and study area Data regarding the lengths of former glaciers and heights of moraines were obtained from published literature on the glaciation of Tibet and its bordering mountains (Shi and Zhang, 1978; Zheng, 1982,
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1988, 2000, 2001, 2006a,b; Liu et al., 1986; Li et al., 1986; Shiraiwa and Watanabe, 1991; Xu and Shen, 1995; Benn and Owen, 1998; Wu et al., 2002; Jiao et al., 2005; Shi, 2005, 2006; Su and Shi, 2006; Li and Zheng, 2006; Su and Li, 2006; Zheng and Shi, 2006; Jiao and Zheng, 2006; Su, 2006). We supplemented these data sets with data from differential global positioning system (DGPS), collected during our field work in the Nyainqentanglha and Qilian Mountain. The data cover almost all of Tibet and the surrounding areas (Fig. 1) and include: Mount Bogda of Tian Shan (Su and Shi, 2006); Mount Yulong of the Hengduan Mountains (Zheng, 2006a), Xuebaoding Peak of the Hengduan Mountains; Kongur Shan on the Pamir Plateau (Su and Li, 2006); and Mount Kailash (Li and Zheng, 2006). The glaciers are categorized into three types based on glacial properties: maritime temperate; sub-continental cold; and continental cold (Shi, 2005). The south slope of the eastern Himalaya, the Hengduan Mountains and the eastern Nyainqentanglha Mountains are located in a humid region of Central Asia, influenced by the Indian monsoon, which brings abundant summer precipitation (Benn and Owen, 1998). These mountains contain maritime temperate glaciers (Shi, 2005). In the Himalaya, the data sites extend around Mt. Namjagbarwa (Zheng and Shi, 2006) and the Langtang Valley of Mt. Shisha Pangma's south slope (Zheng, 1982; Shiraiwa and Watanabe, 1991). Heights of moraines were measured from ridge-shaped moraines formed since the Last Glacial Maximum (LGM). In the Langtang Valley, the highest moraine surface lies about 400 m above the valley bottom. These were determined by Zheng (1988) to have developed during the Nyanyax-
ungla Glaciation in the early Mid-Pleistocene, when glaciers reached 35 km in length. In the Hengduan Mountains, only small and mediumsized valley glaciers developed during the Late Quaternary (Liu et al., 1986; Zheng, 2000, 2001, 2006a; Shi, 2006). The best preserved moraines have relative heights of over 100 m. These formed during the LGM. Two sets of lateral moraines exist along the valley sides in the Bome and Yigong areas in the eastern Nyainqentanglha Range (Li et al., 1986). Zheng (2006b) concluded that the higher one formed in the Penultimate Glacial and the lower in the Last Glaciation. He dated the latter to 11,252 ± 200 radiocarbon years BP. The moraines from the Penultimate Glacial in the Zhuxi Valley rise 800 m above the river valley. These were formed by a glacier that was 100 km long (Zheng, 2006b). Downstream of the 6–13 km modern glacier, three sets of end moraines have been recognized. They formed during the Dana Glacial Advance (3242 ± 101 radiocarbon years BP), the Danading Glacial Advance (which corresponds to Ruoguo Glacial Advance at 1920 ± 110 and 1540 ± 85 radiocarbon years BP), and the Baitong Glacial Advance (1056 ± 115 radiocarbon years BP) (Jiao et al., 2005). In the mid-western part of the Himalaya, the high mountains block the transportation of watervapor toward the north from the southeast monsoon and so the climate on the northern slopes differs considerably from that on the southern slopes. In the eastern Himalaya, glaciers are sub-continental, such as the Xibu Glacier at Yangpachen in the western Nyainqentanglha Range (Wu et al., 2002), and the glaciers in the Tian Shan (Wang and Zhang, 1981; Su and Shi, 2006), on the north slope of the main Karakoram, Mount Amne Machin in the
Fig. 1. Sketch map of study areas (modified from Shi, 2005).
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Kunlun Mountains (Deng et al., 2004), and Mount Geladandong in the Tanggulha Range (Li and Li, 1992; Jiao and Shen, 2003). Farther to the north, the mid-latitude westerlies influence the climate more strongly. On the north slope of the Himalaya, lateral moraines higher than 200 m are present together with eroded end moraines, and large areas of hummocky moraine, which formed during the Penultimate Glacial (Shi et al., 1982; Li et al., 1986; Zheng and Shi, 2006). At the Rongbuk Valley on the north side of Mount Qomolangma (Everest), the Holocene, Neoglacial and the Little Ice Age (dated at 410 ± 110 radiocarbon years BP; Fushimi, 1978) moraines extend within 3 km of the present ice margins (Burbank and Kang, 1991). Furthermore, four sets of ridge-shaped moraines probably formed during the Last Glacial Maximum (Burbank and Kang, 1991). These stretch several kilometers beyond the younger moraines. On the southwestern flank of the Karakoram, lateral moraines are well-preserved, but few end moraines are present, in the catchments of the Keleqing River. Su (2006) considers the glacier there to have been continental since the Late Pleistocene, but that maritime temperate glaciers developed during the two earlier glaciations in the Mid-Pleistocene. These include the Batola Glaciation in this area, considered to be earlier than 139 ± 12.5 ka, and dated on lacustrine deposit by thermal luminescence (Li and Xu, 1983). In the arid climate areas, data are mainly from the south slope of the Karakoram, the Gangdise Range, and the Qangtang Plateau. These are the most arid and coldest areas of the Tibetan Plateau. On the south slope of the Karakoram, moraines of the Last Glacial (dated by thermal luminescence at 47 ± 2.35 ka; Su, 2006) are well-preserved, and always lie along low trough valleys as lateral moraines (Shi and Zhang, 1978). These rise about 10 to 300 m high and two or three stages can be recognized based on the positions and dating (Xu and Shen, 1995). Moraines of the Neoglacial and the Little Ice Age are located near the margins of modern glaciers. At Mount Kailash, three giant end moraines from the Last Glacial are present in the valley, about 100–200 m, 50–60 m and 20–30 m above the valley bottom, while the lateral moraine of the Penultimate Glacial rises to about 50 m above the valley bottom (Li and Zheng, 2006).
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3. Method We collected two types of data, heights of lateral moraines and heights of end moraines, each with the length of its corresponding former glacier. Two “heights of moraines” can be defined: a) height of the crest of the moraine above the bottom of a given glacial valley; and b) the thickness of the till at a given location from its depositional base. Here, height of the moraine refers to the elevation of a particular moraine minus the elevation of the adjacent valley floor. Some researchers list a range of heights of moraines, but most researchers provide only the highest measured value for the height of a moraine. Thus, we use the highest values for our analysis. Using available information, we examine the relationship between the length of a glacier and height of the moraine in space and time. The lateral moraine data are subdivided into two according to the physical characteristics of the glaciers, the temperate (maritime) and continental cold glacier (Shi, 2002). The continental type includes the sub-continental cold and continental cold types. The data for lateral moraines were then subdivided into three additional sub-types according to the timing of glaciation and include those formed during the Penultimate Glacial, the Last Glacial, and the Holocene (Neoglacial and the Little Ice Age). The classification provides data for evaluating seven sub-sets (Fig. 3). The researchers cited determined the heights of moraines by barometric hypsometry and/or from large-scale topographic maps with a contour interval of 20 m. They all measured the lengths of glaciers on large-scale topographic maps. To assess the accuracy of these heights gathered from the literature, we compared the heights of some of the moraines determined by barometric hypsometry and from topographic maps with our electronic measurements of the same moraines using Mobile Mapper in the West Nyainqingtanglha Mountains and the Rongbuk Valley at Mount Qomolangma (Fig. 2). Mobile Mapper is a differential global positioning system (DGPS) made by the Thales company of France. It uses a combination of an Ashtech Mobilemapper Pro™ as a roving receiver and an Ashtech Promark™ for the reference station. The software Mobile Mapper
Fig. 2. Measurements of the moraines in Rongbu Valley, north slope of Qomolangma Peak (Everest Peak). (A) Google Earth images of the moraines, (B) tracking lines of the DGPS measurements for Pleistocene moraines, (C) tracking lines of the DGPS measurements for Holocene moraines and (D) closeup of a lateral moraine.
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Table 1 Statistical parameters of moraines for estimation of relative errors of measurements for heights of moraines Parameters
Mean SD
Height of lateral 155.7 moraine (m) The length of glaciers for 17.1 lateral moraine (km) Height of end 102.6 moraine (m) The length of glaciers for 20.9 end moraine (km)
SE
Min
Max Sum
133.2 16.9 30.0 800
Median Numbers
9653 115.0
36.3 4.6
1.5
270
1062 8.3
105.6 11.9
10.0
500
8109
60.0
20.8 2.3
1.2
100
1655
16.0
62
79
11 data points and one data point of 100 km long and 800 m high, which dominates the correlation. These data describe a former piedmont glacier in the Guxiang valley, East Nyainqentanglha (Zheng, 2006a). If we disregarded this data point, it would lead to a significantly poorer relationship. The sub-types of end moraines, however, do not show similar correlations between heights of moraines and lengths of the corresponding glaciers (Fig. 3H to I). We used the following regression equations to estimate the lengths of past glaciers for different times. y ¼ 0:09x−0:5
ðbased on 40 samplesÞfor arid areas
ð1Þ
‘SD’ means standard deviation of the mean, ‘SE’ means standard error of the mean.
y ¼ 0:05x þ 0:9 Office™ was applied to post-process the data. The DGPS enables the recording of points, lines and areas with sub-meter accuracy. 4. Results The data used in this study are listed in Table 1. The comparison of the heights of moraines measured with DGPS, topographic maps and reported by other researchers on the same moraines show errors (assuming the result of the DGPS is correct) of 0–8% for the moraines over 100 m high and between 0 and 39% for those less than 100 m high (Table 2). The former glaciers are defined as the maximum length of the past glaciers based on the positions of the end moraines. The average lengths of past glaciers are between 17 km and 21 km based on the average heights of lateral and end moraines which are between 156 m and 103 m, respectively. The past glaciers formed during the Last Glaciation and Holocene were valley glaciers. Heights of end moraines are all b 500 m, while the maximum height of lateral moraine is 800 m, which corresponds with the length of a glacier of 100 km (Zheng and Shi, 2006). The linear relationships between heights of moraines and lengths of glaciers for the case studies are shown in Fig. 3. Statistical tests indicate these relationships have a significant level at 0.01 for lateral and end moraines. By comparing the square of coefficients (r2), however, we find that the heights of lateral moraines have much closer correlation with the lengths of glaciers (Fig. 3A) than the heights of end moraines (Fig. 3B). The former has a r2 value of 0.44 (62 samples), but the latter only 0.23 (79 samples). The data for several sub-types of lateral moraines show that the correlations between the heights of moraines and lengths of glaciers are closer in the arid (Fig. 3C) than that in the maritime areas (Fig. 3D). The former has a correlation coefficient of 0.67 for 40 samples, while the latter is only 0.32 for 22 samples. The correlation of the heights of lateral moraines to lengths of glaciers has a coefficient of 0.85 for the 27 moraines that formed during Holocene (Fig. 3E). This is a higher correlation than 0.38 for 24 moraines that formed during the Last Glacial (Fig. 3F). The coefficient appears high for the moraines formed during the Penultimate Glacial (Fig. 3G), but the sample contains only
ðbased on 27 samplesÞfor the Holocene Glaciation ð2Þ
where x is the height of a lateral moraine and y is the length of a glacier. To test the reliability of these relationships, we analyzed the relative errors of the regression equations. The average values for the relative error is 38% for arid areas and 30% for the Holocene glaciations. The value for Holocene glaciations are all within 100% and decrease with increasing lengths of former glaciers, but the value for arid areas are higher for end and lateral moraines and the highest one is 211% (Fig. 4). All the estimated values of the lengths of glaciers fall within the 95% confidence interval. 5. Discussion The relative errors of the heights of moraines measured from topographic maps are within 10%, in comparison with those measured using the DGPS (Table 2) for the moraines higher than 100 m. This provides an acceptable estimation of the relationship between the heights of moraines and lengths of former glaciers. But the percentage error may be greater if the height of the moraine is b100 m. The heights of moraines measured using barometric surveying are closer to those measured by the DGPS. Furthermore, most Chinese researchers measured the heights of end moraines using barometric hypsometry. These suggest that the relative errors of the heights of end moraines collected from literature are small and the data can be used for this statistical study. As we observed in the field, the elevations of lateral moraines generally lie close to the surface of a nearby modern glacier, suggesting that the height of a lateral moraine approximates the thickness of the glacier. Based on data for about 45,000 glaciers in Tibet and its surrounding mountains from the China Glacier Catalogue, the lengths of glaciers correlate very closely (r2 = 0.88) with the corresponding thickness of the ice. The heights of lateral moraines formed in the past should also correlate with the length of former glaciers. This relationship follows more closely than the height of end moraine, particularly for measurements from the Holocene moraines in arid areas (Fig. 3).
Table 2 Estimation of the relative error of the heights of moraines measured in topographic maps or barometric hypsometry in comparison with those determined by the DGPS Mountain name
West Nyainqentanglha Mountains
Site
Shaong River valley
Langma River valley
Rongbuk River valley, Everest Mountain
Himalaya Fuqu River, Xixiabangma Mountain
Geographic coordinates
30°30′26″N, 90 56′37″E
30°35′30″N, 90°53′27″E
28°10′15″N, 86 49′45″E
28°09′3N, 85°58′46″E
Moraine type
End
End
Lateral
End
End
End
Timing
LG
LIA
LIA
LG
LG
LIA
LG
LG
Neoglacial
LG
35.2 25 29.0%
41.7 30 39.0%
33.6 25 34.4%
94.7 105 10.9%
99.8 105 5.2%
30 30 0%
254.9 250 1.9%
29.4 30# 2.0%
20.6 20# 3%
320 300 8.0%
Measured height Relative error
DGPS Map/BH
Lateral
The relative error is determined by the division of the difference between the heights measured in traditional ways and by the measured heights using the DGPS. The signal # means heights measured using barometric hypsometry (BH) by Zheng and Shi (2006).
P. Fu, C. Yi / Geomorphology 103 (2009) 205–211
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Fig. 3. Relationships between the relative heights of moraines and the lengths of the corresponding former glaciers: (A) all lateral moraines; (B) all end moraines; (C) lateral moraines in the maritime area; (D) lateral moraines in the arid area; (E) lateral moraines formed during the Holocene; (F) lateral moraines formed during the Last Glaciation; (G) lateral moraines formed during the Penultimate period; (H) end moraines in the maritime area; (I) end moraines in arid area; (J) end moraines formed during the Holocene; (K) end moraines formed during the Last Glaciations; (L) end moraines formed during the Penultimate period.
Several factors may account for the difference between the degree of correlation between the heights of moraines and the lengths of former glaciers for lateral and end moraines. First, because of the location, end moraines have poorer preservation than lateral moraines, as demonstrated in the glacial morphology literature regarding the Tibetan Plateau (Zheng, 2001; Shi, 2006). The preservation of glacial landform systems is strongly reduced by intensive glaciofluvial erosion and subsequent advances of glaciers. In contrast to lateral moraines, the end moraines occupy the fluvial breach and have eroded more intensively or may have been totally
destroyed. Consequently, heights of lateral moraines can better reflect the original sizes of the glaciers. Secondly, the genesis of the different moraines and the resulting till characteristics may cause differences in the preservation potential. Well-defined end moraines can only be formed effectively at the front of active glaciers when they are advancing or maintaining a stationary terminus (Embleton and King, 1968). So glacier dynamics largely control the size of these end moraines, and the end moraine is always not high and continuous. In contrast, lateral moraines, which extend along the margins of the glaciers, predominantly consist of angular debris derived from the rock
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The average value of relative error is between 30 and 38% for the prediction of the length of a glacier through height–length equations (Fig. 4). To minimize errors, we use the linear regression equations listed above for the relationship between the heights of Holocene lateral moraines with the lengths of corresponding glaciers or the relationship between the heights of lateral moraines of all sub-types with the lengths of the corresponding glaciers. We can, therefore, estimate the lengths of former glaciers based on the largest value of relative heights of the lateral moraines formed before the Holocene to predict the extent of the Pleistocene glacier. 6. Conclusion Fig. 4. Relative error versus the length of glaciers. The circles indicate relative error of linear regression of glaciers of arid area and the crosses indicate relative error of Holocene glaciations.
walls along the valley, which is carried passively either on top or within the glacier (Benn et al., 2003). In valley glacier systems, the texture of lateral moraines is universally coarser than the end moraines (Wang and Zhang, 1981). Lateral moraines are relatively more stable because meltwater cannot transport the larger debris as effectively. The differences in correlation of the heights of moraines with the lengths of glaciers between arid and maritime regions may result from differing climate influences on geomorphic processes between monsoon-dominated environments (developing mostly maritime temperate glaciers) and westerly-dominated environments (developing mostly continental cold glaciers; Shi, 2002). The glacial thermal regime that results from the predominant climate determines the status and dynamics of glaciation, and, therefore, produces different glacial landform systems. Temperate glaciers involve significant basal sliding and sub-glacial deformation of sediment. With the lack of supra-glacial sediment, temperate glaciers tend to create extensive, low amplitude, marginal dumping, pushing and squeezing moraines (Zheng et al., 1994; Evans and Twigg, 2002). But continental cold glaciers, with cold-bases, exhibit less active basal sliding and deformation than temperate glaciers (Waller, 2001). Consequently, moraines from continental cold glaciers suffer less deformation than those from maritime temperate glaciers during development (Kleman, 1994). Furthermore, moraines from cold glaciers contain bigger and more angular boulders than do moraines from temperate glaciers. For this reason, moraines formed by cold glaciers are relatively stable compared with those formed by temperate glaciers. Also, temperate glaciers discharge more meltwater, which transports debris effectively from the glacier margins and restricts moraine development. In contrast, to the moraines in the continental glacier area, the moraines developed in maritime area are poorly preserved because of intense erosion, mainly by fluvial and mass movement processes (Owen et al., 2005). Accordingly, the moraines in arid areas have better linear correlations with the lengths of glaciers, as mentioned above. We attribute the difference in correlation of the heights of moraines with the lengths of glaciers between Holocene and older glaciations to the following factors. None of the data for heights of moraines used in this study was calibrated to the initial size because of the lack of research on the rate of erosion rate unconsolidated landforms on the Tibetan Plateau. Researchers expect that the degradation of moraines increases with time. For example, Putkonen and O'Neal (2006) estimated that for 100–200 ka old moraines in the western North America the maximum depth of erosion averages 25% of the final height. We argue that the moraines formed in the Holocene have not been eroded very much, because they have been exposed for only about 10 ka and fresh and polished facets are still present. Thus, the length to height relationship for the Holocene glaciation correlates closely, while this relationship for moraines formed during the Pleistocene do not relate as closely because the latter have been exposed for a long time and experienced much more erosion than the former.
Our study shows that the glaciers in the arid areas of the Himalayan–Tibetan orogen have a closer correlation between the height of the lateral moraine and the length of a glacier than glaciers in maritime areas. This relationship results from less weathering and fluvial erosion in arid areas after moraine formation. The heights of lateral moraines correlate with the lengths of former glaciers more closely than with the height of end moraines. This relationship occurs because lateral moraines are better preserved than end moraines which are easily destroyed by fluvial or late glacial erosion. This relationship is stronger for moraines formed during glacial advances during the Holocene than for those formed during earlier glaciations. Holocene moraines are less intensively erosion than old lateral and end moraines that have experienced a long period of erosion. Hence, Holocene lateral moraines better represent the lengths of glaciers and are more reliable when using length to height relationships to estimate the minimum length of a valley glacier for past glaciations. This method provides an easy method for calculating ELAs across large regions, which in turn allows assessments of regional variation in glaciation that can influence landscape evolution. Acknowledgments This work is supported by the NSFC grants (40671023, 40730101) and the Knowledge Innovation Program of the Chinese Academy of Sciences, Grant No kzcx2-yw-104. The authors are grateful to Arjen Stroeven, Lewis Owen, Jack Vitek and anonymous reviewer's constructive comments. References Ammann, C., Jenny, B., Kammer, K., Messerli, B., 2001. Late Quaternary Glacier response to humidity changes in the arid Andes of Chile (18–29°S). Palaeogeography, Palaeoclimatology, Palaeoecology 172, 313–326. Benn, D.I., Owen, L.A., 1998. The role of the Indian summer monsoon and the midlatitude westerlies in Himalayan glaciation: review and speculative discussion. Journal of the Geological Society 155, 353–363. Benn, D.I., Kirkbride, M.P., Owen, L.A., Brazier, V., 2003. Chapter 15. In: Evans, J.A. (Ed.), Glacial Landsystems. Arnold Publication, pp. 372–405. Burbank, K.D.W., Kang, J.C., 1991. Relative dating of the Quaternary moraines, Rongbuk Valley, Mount Everest, Tibet: implications for an ice sheet on the Tibetan Plateau. Quaternary Research 36, 1–18. Deng, X.F., Liu, S.Y., Ding, Y.J., Shen, Y.P., Zhao, L., Xie, C.W., 2004. The Quaternary glacier and environmental evolution of the Aemye Ma-chhen Range. Journal of Glaciology and Geocryology 26, 305–311. Embleton, C., King, C.A.M., 1968. Glacial and Periglacial Geomorphology. Edward Arnold (Publishers) Ltd,, pp. 344–368. Evans, D.J.A., Twigg, D.R., 2002. The active temperate glacial landsystem: a model based on Breijamerkurjokull and Fjallsjokull, Iceland. Quaternary Science Reviews 21, 2143–2177. Fushimi, H., 1978. Glaciations in the Khumbu Himal (2). Seppyo 40, 71–77. Jiao, K.Q., Shen, Y.P., 2003. The Quaternary glaciation and glacier properties in the Tanggula Range. Journal of Glaciology and Geocryology 25 (1), 34–42 [Chinese with English summary]. Jiao, K.Q., Zheng, B.X., 2006. Quaternary glaciations in the Kunlun Mountains. In: Shi, Y.F., Cui, Z.J., Su, Z. (Eds.), The Quaternary glaciations and environmental variations in China. Hebei Science and Technology Publishing House, pp. 326–358. Jiao, K.Q., Iwata, S.J., Yao, T.D., 2005. Fluctuation and environment change of Zepu glacier on the eastern of the Nianqingtanggula Mountains since 32 ka BP. Journal of Glaciology and Geocryology 27, 74–79 [Chinese with English summary].
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