Data collection

The 15 glaciers used in our study are located in western China (Fig. 1) and were investigated or monitored during different periods in the past (Reference Zhang and BaiZhang and Bai, 1980; Reference SuSu and others, 1985; LIGG, 1986–93; Reference Zhang and ZhouZhang and Zhou, 1991; Reference Liu, Xie and YangLiu and others, 1992; Reference Yao and AgetaYao and Ageta, 1993; Reference Li and SuLi and Su, 1996; Reference Su, Wang and XieSu and others, 1998). The terminus elevations of these glaciers range from 2640 to 5450 m a.s.l.

Fig. 1. Map of the study area, with locations of the 15 monitored glaciers in western China: 1. Urumqi No. 1; 2. Qiongtailan; 3. Keqicar Baqi; 4. Qirbulake; 5. Yangbulake; 6. Teram Kangri; 7. Meikuang; 8. Qiyi; 9. Halong; 10. Xiaodongkemadi; 11. Kangwure; 12. Hailuogou; 13. Dagongba; 14. Xiaogongba; 15. Baishuihe No. 1.

In this study, the ablation data were measured using ablation stakes. Most of the ablation records span >1month (Table 1), and fortunately, on most glaciers, the meteorological data were recorded over the entire period. The longest combined ablation–climate dataset is for Ürümqi glacier No. 1 (UG1; 8years, 1986–93).

Table 1. DDFs on different monitored glaciers in western China

However, on four glaciers, namely Meikuang, Halong, Qirbulake and Yangbulake glaciers, there are no meteorological data. Hence, daily temperature on these glaciers was extrapolated from the closest national meteorological station using the vertical lapse rate (VLR). The distance between the glacier and the national meteorological station varied considerably, from several kilometers to a few hundred kilometers. The VLR of the different latitude and altitude zones over the Tibetan Plateau and surrounding regions can be taken from Reference Li, Cheng and LuLi and others (2003) and ranges from –0.0054 to–0.0068C m⁻¹. The equilibrium-line altitude (ELA) for each of the 15 glaciers was taken from the China Glacier Inventory (CGI) and ranges from 4000 to 7000 m a.s.l. (Reference Shi, Liu, Wang, Liu and YeShi and others, 2005).

Method

The DDF is an important parameter for the degree-day model, which is based on a linear correlation between snow or ice melt and the sum of daily mean temperatures above the melting point during a period. Commonly, the DDF is computed either from direct measurements, using ablation stakes (e.g. Reference Liu, Ding, Ye and ChengLiu and others, 1996; Reference Braithwaite, Konzelmann, Marty and OlesenBraithwaite and others, 1998) or snow lysimeter outflow (e.g. Reference Kustas, Rango and UijlenhoetKustas and others, 1994), or from melt obtained by energy-balance computations (e.g. Reference BraithwaiteBraithwaite, 1995; Reference Arendt and SharpArendt and Sharp, 1999; Reference ZhangZhang, 2005).

In our study, DDFs are computed from direct measurements using ablation stakes distributed on different monitored glaciers. In general, the DDF is given by

(1)

where DDF is the degree-day factor, different for snow and ice, M is the depth of meltwater in an Nday period, and PDD is the sum of daily mean air temperatures above the melting point in the same Nday period. Commonly, PDD is given by (Reference Braithwaite and OlesenBraithwaite and Olesen, 1993)

(2)

where T_t is the daily mean air temperature on day t, and H_t is a logical variable, which can be defined such that H_t = 1:0 for T_t > 0°C and H_t = 0:0 for T_t < 0°C Strictly speaking, it might be better to define T_t as a function of a daily degree-day total, because daily mean temperatures can sometime be negative while temperatures are actually above freezing for part of the day. However, the familiar daily mean air temperature is used here for convenience in using conventional climatological data.

Based on the monitoring data of the 15 glaciers in different periods (Reference Zhang and BaiZhang and Bai, 1980; Reference SuSu and others, 1985, Reference Su, Wang and Xie1998; LIGG, 1986–93; Reference Zhang and ZhouZhang and Zhou, 1991; Reference Liu, Xie and YangLiu and others, 1992; Reference Yao and AgetaYao and Ageta, 1993; Reference Li and SuLi and Su, 1996), the DDFs for ice and snow in western China can be obtained by Equations (1) and (2) (Table 1). The results reveal a large variability from site to site. The values of the factors are derived from different integration periods ranging from a few days (e.g. Dagongba glacier) to several years (e.g. UG1), which limits their direct comparison. In addition, the computed processes of DDFs involve two main sources of error:

Degree-day factors

Table 1 shows that there is a large variation in DDFs, which can be attributed to the difference in relative importance of individual energy components providing energy for melt. It is generally accepted that DDFs for snow are considerably lower than those for ice, due to the higher albedo of snow compared to ice. In western China, the mean value of DDFs for ice on the monitored glaciers is 7.1 mmd⁻¹ ˚C⁻¹, whereas for snow it is 4.1 mmd⁻¹ ˚C⁻¹. So the DDF for snow reaches about 58% of that for ice in western China, while the corresponding percentage is about 40% and 70% on two Greenland glaciers and four Scandinavian glaciers (Reference HockHock, 2003).

Since the energy balance of the glacier surface varies considerably in space and time, the DDF can be expected to vary seasonally and spatially. Some studies suggest that seasonal variations in DDFs for ice tend to be less pronounced because of low seasonal variations in surface albedo (Reference Braithwaite and OlesenBraithwaite and Olesen, 1993). In western China, monthly variations of DDFs on Keqicar Baqi glacier, southwestern Tien Shan, given by Table 2, clearly show that monthly variations of the factor are less distinct. Similarly, seasonal variations during two summers are less pronounced over the ice on Qiongtailan glacier, which only varies from –8% to 12% (Table 3). This finding is in agreement with that of Reference Braithwaite and OlesenBraithwaite and Olesen (1993), who detected no evidence of distinct seasonal variation in DDFs in their analysis of 6 years of summer data over ice on Qamanârssûp sermia, Greenland. Over snow, the seasonal variation in surface albedo is more pronounced due to metamorphic evolution, so DDFs also tend to be more pronounced (Reference KuusistoKuusisto, 1980). In this study, however, we cannot discuss the variation in DDFs for snow due to lack of the long-term monitoring data for snow in western China.

Table 2. Monthly variation of DDFs on Keqicar Baqi glacier (2003)

Table 3. Seasonal variation ofDDFson Qiongtailan glacier, 1977–78

Spatial variation of degree-day factors

With different elevations, solar radiation and surfaces (albedo), DDFs will vary considerably in space. In addition, the DDF is considerably affected by the topographic effects, such as slope, aspect and shape in mountain regions. Since temporal variations of DDFs on the observed glaciers of western China tend to be less pronounced, the spatial variation of the factors is discussed below.

For a single glacier, spatial variation is reflected by the relationship between the DDF and the distance between the observed site of the factor and the ELA (Figs 2 and 3). Figure 2 clearly shows that the DDFs for ice increase with decreasing distance to the ELA. It is concluded that on these monitored glaciers (Fig. 2) the larger DDFs converge at a range of 500m which is the distance below the ELA. It is evident from Figure 2 that the DDF at higher altitude is larger than at lower altitude on these monitored glaciers where the ELA is very high (>4000 m). This characteristic can be attributed primarily to ablation due to absorbed global radiation near the ELA where the positive degree-day (PDD) is low due to low air temperature (Reference Kayastha, Ageta, Nakawo, Fujita, Sakai and MatsudaKayastha and others, 2003). This means that glacier melt near the ELA (with small PDD) is mainly attributed to the absorbed global radiation, which results in a larger DDF at higher altitudes than at lower altitudes, called ‘the low-temperature effect’ (Reference BraithwaiteBraithwaite, 1995). Nevertheless, an opposite trend of the DDF is given by Figure 3, which clearly indicates that the DDFs for ice decrease with distance to the ELA on the glaciers in the central Tibetan Plateau and the Himalaya. On these glaciers, evaporation from ice, especially sublimation, plays a major role in the heat budget. Due to the high energy consumption involved, evaporation from ice reduces considerably the energy available for melt, and thus reduces DDFs. In brief, the DDFs for a single glacier are subject to significant small-scale variations.

Fig. 2. Increasing variations of the DDFs with decreasing distance to the ELA in western China.

Fig. 3. Decreasing variations of DDFs with decreasing distance to the ELA in western China.

In western China the glaciers can be split into three types: extremely continental, subcontinental and maritime (Reference Shi and LiuShi and Liu, 1999). For different glacier types, maritime glaciers are likely to have higher DDFs than subcontinental and extremely continental glaciers. The average values of DDFs for maritime, subcontinental and extremely continental glaciers are 10.9, 7.2 and 4.3 mm d ⁻¹ ˚C⁻¹, respectively. This finding is not in agreement with Reference HockHock (2003), who suggested that glaciers in maritime environments are likely to have lower DDFs than those in more continental climate regions due to relatively large turbulent fluxes, including condensation. Although the turbulent fluxes on maritime glaciers in western China account for >50% of the heat budget in the melt season (Reference Xie, Xie and KotlyakovXie, 1994), DDFs of maritime glaciers are higher than those of subcontinental and extremely continental glaciers. Besides the influence of different regional climate conditions, the fact that the ablation area of maritime glaciers in western China is generally covered with a thin debris layer that accelerates glacier melt (Reference ØstremØstrem, 1959; Reference Rana, Nakawo, Fukushima and AgetaRana and others, 1997; Reference Zhang, Liu, Shangguan, Han, Xie and WangZhang and others, 2005) should be emphasized among the most important reasons for this phenomenon. This debris layer has a strong influence on the surface energy balance and melting of the underlying ice, and the thermal conductivity and albedo are the main physical characteristics of a debris layer that control heat conduction to the ice-debris interface.

For the total glacier system of western China, regional patterns of DDFs are clearly detectable (Fig. 4). Figure 4 is a map of isolines for the DDFs for ice, which clearly shows that the factors increase gradually from northwest to southeast in western China. According to the DDF values, we can split the observed glaciers in western China into three categories: a high-value region (>9.0mmd⁻¹ °C⁻¹), a mid-value region (6.0−9.0 mm d⁻¹ °C⁻¹) and a low-value region (<6.0mmd⁻¹ °C⁻¹) (Fig. 4). It is evident that the high-value region is located in the southeast of western China, whereas the low-value region lies in the northwest of western China. This distinct spatial variation of DDFs can mainly be attributed to the unique climatic environment and heat budget of the Tibetan Plateau and the surrounding regions.

Fig. 4. Map of DDF isolines for ice in western China.

Like the variation of DDFs, from northwest to southeast in western China, the climatic environment varies gradually from cold-dry to warm-wet, while the type of heat budget varies from evaporation type to condensation-evaporation type (Reference Shi, Huang, Yao and DengShi and others, 2000). This shows that regional climate conditions greatly affect the spatial variation of DDFs in western China. Generally speaking, low DDFs can be expected for cold-dry areas where available ablation energy may be mainly consumed by evaporation, especially sublimation; whereas high DDFs can be expected for warm-wet areas where the available ablation energy is mainly consumed by melting.