Лёд и Снег • 2013 • № 4 (124)
УДК 551.578
Modeling the variation trends of glacier systems
© 2013 г. Z. Xie1, X. Wang2, Q. Li3, S. Liao1, Y. Dai1
College of Resources and Environment, Hunan Normal University, Changsha 410081, China; department of Geography, Hunan University of Science & Technology, Xiangtan 411201, China);
3Hunan Meteorological Observatory, Changsha, Hunan Province 410118, China xinwang__hn@163.com
Статья принята к печати 16 июля 2013 г.
Climate warming, functional model, glacier system, variation trend.
Ледниковая система, потепление климата, функциональная модель, тренд колебаний.
The basic principles and methods for a functional glacier systems model are introduced and applied for glaciers of Northwest China. When running the model we assume that a glacier system is under steady state conditions in the initial year. The median size of a glacier system is used as representative for the system. The curve of glacier area distribution against elevation is used to compute the increase in equilibrium line altitude (ELA), and the annual glacier ablation is calculated using a global formula a = 1.33(9.66 + fs)2-85 [4, p. 96]. The net mass balance near the ELA under steady state conditions represents the net mass balance of the whole glacier system, and the time required for glacier runoff to return to the initial year level is calculated according to the law of glacier runoff variation, and used to calculate the variation of glacier area. The variation of glacier runoff is modeled according to ablation at the ELA, and the variation of glacier volume is modeled according to the absolute value of the mass balance. The observed changes in surveyed glaciers in China over recent decades were broadly consistent with predictions of the glacier system model. The model therefore offers a reliable method for the prediction of changes in glacier systems in response to changing climate.
Introduction
As a result of continued global warming, many glaciers are retreating, with important effects on the natural environment. Therefore, studies on glacier variation, and the prediction of trends in glacier variation, have been a focus of research in the field of glaciology. Many methods have been developed to predict trends in glacier variation in response to climate warming, including models of response to climate change, dynamical models, and hydrological models. Models based on glacier energy balance can be applied to single glaciers that have been surveyed in detail [19]. However, other approaches are required for the prediction of glacial variation across large spatial scales without detailed field observation. The World Glacier Inventory provides data on many glaciers globally, and the application of satellite remote sensing technology enables the detection of large-scale glacier variation. Recently, several models simulating large-scale glacier variation have been developed. Paul et al. [20] used data on glacier accumulation area to predict glacier variation in several areas of Switzerland. Glazyrin and Kodama [12] used three phases of glacier inventory data for four basins in the Pamir Mountains of Central Asia, and developed a method to simulate changes in glacier
area. Kuzmichenok [8] developed a statistical method to simulate the runoff and evolution process for glaciers in Kyrgyzstan. According to the theory of glacier systems, a functional model was developed [5, 31] and applied to glacier systems in China [27, 36]. The modeled results of trends in glacier variation were close to observational results of glacier variation over recent decades [33]. In this paper we present a general introduction to a new functional model for glacier systems.
Principles of the glacier system functional model
Median size of the glacier system. A glacier system is a group of glaciers in the same region, influenced by similar climate patterns and intrinsic physical laws. A system can be divided and subdivided based on features including physical characteristics, mountain ranges, and watershed boundaries [13]. The concept of glacier systems has been widely applied in analyzing glacier distribution laws from glacier inventory data [1, 2]. The median size (Smed) of a glacier system is defined as the size when the cumulative glacier area reaches 50% of the glacier system as a whole. Median size was used to study the structure of glacier systems in Southern Tibet, and results confirmed that the median size of the glacier
system could appropriately represent the typical glacier area of the whole glacier system [17].
Glacier area distribution with elevation. Changes in glacier equilibrium-line altitude (ELA) have been calculated based on the curve of glacier area distribution against elevation. Kuzmichenok [7] developed a formula for calculating the glacier area distribution against elevation, which has been widely applied in China [16, 27, 32]. Recently, characteristics of Himalayan glacier systems were studied using ArcGIS software to obtain information on glacier area distribution against elevation [38].
Equilibrium-line altitude. The net mass balance close to the elevation of the ELA in steady state conditions, bn(ELA0), is equal to the mean net mass balance of the glacier, Tm:
bn(ELA0) = Tm.
(1)
This relation has been explained in detail in a previous paper [30]. When the climate fluctuates normally, changes in ELA0 are relatively small and stable, though the ELA in any one year (ELAa) is variable as a result of annual climate fluctuations. The amplitude of the fluctuation in ELA0 is smaller than that of ELAa. Consequently, the net mass balance at ELA0 was used to represent the mean net mass balance of the whole glacier in the model. ELA0 is essentially an abstract concept obtained through computer analysis. For a glacier with a long time series of mass balance observations, the formula devised by Braithwaite [10] can be used to estimate ELA0:
bn = a(ELA0 — ELAa),
(2)
ELAk = aHme + b,
(3)
where ELAk is the computed ELA; Hme is the average of the highest and the lowest elevation of the glacier, and a and b are empirical constants.
Statistical analysis was conducted on exterior drainage data from the glacier inventory of Southern Tibet, and the correlation coefficients for ELAk and
Hme (formula (3)) ranged from 0.8-0.88 for the glacier systems of the Indus, Ganges and Yarlung Zangbo Rivers [31]. For the Chinese Glacier Inventory, ELA was measured using the method devised by Hess (ELAh), determined according to changes of contour lines in the central glacier. In fact, ELAh is close to the dynamic ELA, ELAd, which is related to the period of the glacier cycle. A.N. Krenke [6] reported that the average cycle time of glacier water is approximately 100 years in mountain glaciers. Therefore, ELAh is relatively stable, and close to the concept of ELA0. However, ELAh was only recorded for about 10-12% of glaciers in the Chinese Glacier Inventory. Formula (3) was used to calculate the ELAd of all glaciers in the system, and the average value was denoted as the mean ELA, ELAk for the glacier system. The ELAk can therefore approximate the mean ELA0 of glacier systems, namely:
(4)
ELAb. ~ ELAn
Ablation at ELA0. Currently, many models are available to describe and compute the process of glacial ablation. Models based on energy balance can be used for single glaciers if enough observational parameters exist. Degree-day models based on temperature can also be applied to single glaciers [11], and degree-day factors can be changed for large scale regions [38]. We therefore selected the Krenke-Khodakov model [5, p. 96; 14] based on the mean summer temperature:
a = 1.33(9.66 + t)
,2.85
(5)
where a is the gradient of effective mass balance.
We can also obtain the elevation of ELA0 using the curve of net mass balance changes against altitude [30]. For glacier systems, the mean of ELA0, ELA0, can theoretically be derived from the ELA0 of each glacier in a glacier system. The concept of the reduced snowline presented by Seversky [21], is similar to the concept of the ELA0. Analysis of ELA data from the Chinese Glacier Inventory showed that an empirical formula could be used to calculate the mean snowline altitude for a basin or a mountainous region:
where a is the ablation (mm w. eq.) at ELA0; ts is the mean summer temperature (June-August) at ELA0 (°C).
This model has been widely used in the former Soviet Union [3, 5] and China [16, 37], with some modifications to its empirical constants. Recently, Kotlyakov and Lebedeva [5] demonstrated that under various climatic conditions the ablation curve could be different even if the value of ts is the same. However, computing ablation using mean summer temperature had common implications, and formula (5) was designated as a global formula, suitable for application in large glaciated regions. We therefore used Formula (5) in this paper.
Mean summer temperature at ELA0. To calculate the mean summer temperature at ELA0, the temperature from June to August at 600 MPa was obtained from the Meteorological Atlas for the Qinghai-Xizang Plateau [10]. The Meteorological Atlas was compiled on the basis of meteorological survey data recorded between the 1960s and 1970s (Lanzhou Institute of
Plateau Atmospheric Physics, Chinese Academy of Sciences, unpublished data). Using the mean summer temperature at 600 MPa, tpa, according to the vertical lapse rate and taking in to account jumps in temperature of the glaciers, At), the mean summer temperature at ELA0 was calculated:
ts = tpa + AhY + At), (6)
where Ah = hpa - ELA0; y is the vertical lapse rate of temperature, ranging from 0.55-0.75 K/100 m.
The corrected temperature of the glaciers At) was arbitrarily assumed to be -0.5, -1.0 and -1.5 K according to the Smed of the glacier systems. Most of the original aerial photos used for the Chinese Glacier Inventory were taken in the 1960s and 1970s, which was coincident with the time th
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