Comparison of glaciological and geodetic mass balance at Urumqi Glacier No. 1, Tian Shan, Central Asia

    Comparison of glaciological and geodetic mass balance at Urumqi Glacier No. 1, Tian Shan, Central Asia Puyu Wang, Zhongqin Li, Huilin Li, Wenbin Wang, Hongbing Yao PII: DOI: Reference:

S0921-8181(14)00008-3 doi: 10.1016/j.gloplacha.2014.01.001 GLOBAL 2076

To appear in:

Global and Planetary Change

Received date: Revised date: Accepted date:

15 May 2013 31 December 2013 2 January 2014

Please cite this article as: Wang, Puyu, Li, Zhongqin, Li, Huilin, Wang, Wenbin, Yao, Hongbing, Comparison of glaciological and geodetic mass balance at Urumqi Glacier No. 1, Tian Shan, Central Asia, Global and Planetary Change (2014), doi: 10.1016/j.gloplacha.2014.01.001

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Comparison of glaciological and geodetic mass balance at Urumqi Glacier No. 1, Tian Shan, Central Asia

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Puyu Wang 1,*, Zhongqin Li1,2, Huilin Li1, Wenbin Wang1, Hongbing Yao2 1

State Key Laboratory of Cryospheric Sciences, Cold and Arid Regions Environmental and Engineering Research

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Institute/Tianshan Glaciological Station, Chinese Academy of Sciences, Lanzhou 730000, Gansu, China 2

College of Geography and Environment Science, Northwest Normal University, Lanzhou 730070, Gansu, China

*Corresponding author: Puyu Wang

E-mail address: [email protected] Abstract. Glaciological and geodetic measurements are two

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methods to determine glacier mass balances. The mass balance of Urumqi Glacier No. 1 has been measured since 1959 by the glaciological method using ablation stakes and snowpits, except during the period 1967-1979 when the observations were interrupted. Moreover, topographic surveys have been carried out at various time intervals since the beginning of the glacier observations. Therefore, glacier volume changes are calculated by comparing topographic maps of different periods during nearly 50 years. Between 1962 and 2009, Urumqi Glacier No. 1 lost an ice volume of 29.51×106 m3, which corresponds to a cumulative ice thickness loss of 8.9 m and a mean annual loss of 0.2 m. The results are compared with glaciological mass balances over the same time intervals. The differences are 2.3%, 2.8%, 4.6%, 4.7% and 5.9% for the period 1981-86, 1986-94, 1994-2001, 2001-06 and 2006-09, respectively. For the mass balance measured with the glaciological method, the systematic errors accumulate linearly with time, whereas the errors are random for the geodetic mass balance. The geodetic balance is within the estimated error of the glaciological balance. In conclusion, the geodetic and glaciological mass balances are of high quality and therefore, there is no need to calibrate the mass balance series of Urumqi Glacier No. 1. Keywords: glaciological mass balance; geodetic mass balance; volume change; uncertainty analysis; Urumqi Glacier No. 1; Tian Shan

1. Introduction Knowledge of the glacier mass balance is crucial both for climatic sensitivity studies and for understanding the hydrological behavior (Oerlemans and Fortuin, 1992; Fountain et al., 1999; Aizen et al., 2007; Bolch, 2007; Haeberli et al., 2008; Li et al., 2010, 2011; Wang et al., 2012, 2013). However, there are only twelve mass balance programs with continuous observations dating back to 1960 (Zemp et al., 2009), and worldwide merely 33 glaciers have annual mass-balance series longer than 40 years (Dyurgerov and Meier, 1999). The mass balance can be determined

by

various

methods

including

the

glaciological,

geodetic

and

the

ACCEPTED MANUSCRIPT hydrological-meteorological method. The glaciological and geodetic measurements are two commonly used methods (Hoinkes, 1970). Over the past decades, it has become a standard procedure to compare the glaciological with the geodetic mass balance method, utilizing

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techniques such as comparing digital elevation models (DEM) generated from topographic maps (e.g. Andreassen, 1999; Conway et al., 1999; Kuhn et al., 1999; Hagg et al., 2004; Andreassen et

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al., 2012), photogrammetry (e.g. Krimmel, 1999; Cox and March, 2004; Thibert et al., 2008; Haug et al., 2009; Huss et al., 2009; Fischer, 2010; Zemp et al., 2010), global positioning systems (GPS) (e.g. Hagen et al., 1999; Miller and Pelto, 1999), or laser altimetry (e.g. Echelmeyer et al., 1996;

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Sapiano et al., 1998; Conway et al., 1999; Geist and Stötter, 2007; Fischer, 2011). However, some studies (Østrem and Haakensen, 1999) show disagreeing results of the two methods, indicating

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that there were errors in the glaciological measurements. To decide whether a mass balance series needs calibration, Zemp et al. (2013) present a conceptual framework for reanalysing glacier mass

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geodetic mass balance series.

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balance series using statistical tools to assess the accuracy and erors of the glaciological and

With the glaciological method the yearly point mass balances are obtained from ablation stakes

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and snowpits. These are then extrapolated over the glacier, based on the area-altitude distribution (AAD) (Østrem and Brugman, 1991). Systematic errors in field measurements increase linearly with the number of years and result in cumulative errors that are potentially problematic.

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For the geodetic method volume changes are used to estimate the mass balance over several years. The method is not suitable for annual change detection. As outlined by many studies the intrinsic errors are mostly random (Finsterwalder, 1954; Echelmeyer et al., 1996; Andreassen et al., 2002; Cox and March, 2004; Cogley, 2009; Thibert and Vincent, 2009). Geodetic programs provide an independent check of the traditional mass balance measurements, by comparing the cumulative glaciological balances with the geodetic balances over ten or more years. Several studies have been undertaken to calculate the glaciological and geodetic mass balance and estimate the errors in the geodetic method, which are consistently about ±1 to 2 m w.e., depending on the map quality and photographs’ condition (Andreassen, 1999; Krimmel, 1999; Cox and March, 2004). However, Krimmel (1999) reports a significant discrepancy between the two types of measurements and suggests the water-equivalent conversion and the area integration as possible sources of bias.

ACCEPTED MANUSCRIPT Urumqi Glacier No. 1, located in the eastern Tian Shan, in the middle of Central Asia, is considered as the best monitored glacier in China. The continuous record of mass balance measurements begins in 1959/60 and thus is among the longest worldwide. Since the 1950s, the

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glacier surface elevation has been surveyed eight times at intervals of several years and the glacier terminus twice every year. Due to the extensive glacier data sets available, Urumqi Glacier No. 1

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can be considered as one of the test glaciers to study the glaciological and geodetic methods to determine the mass balance. The aims of this study are therefore to quantify the ice volume changes of Urumqi Glacier No. 1 during the period 1962-2009, to determine the geodetic balance

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over five time intervals, to compare the mass balances measured with the geodetic and

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glaciological method and to evaluate if the glaciological record needs to be calibrated.

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2. Geographical setting

Fig. 1. (a) Location of Urumqi Glacier No. 1 within the eastern Tian Shan, Central Asia and (b) an overview of Urumqi Glacier No. 1 with the ablation stake network in 2008. The photo in the bottom-right corner was taken by Zhongqin Li in 2009.

Urumqi Glacier No. 1 (43°06′ N, 86°49′ E) is located on the northern slope of Tianger Peak Ⅱ (4484 m a.s.l.), eastern Tian Shan, and at the headwaters of the Urumqi River. It is a northeast facing valley glacier with two branches covering 1.646 km2 in 2009 (Fig. 1). The elevations of the East Branch and the West Branch range from 4267 m to 3743 m a.s.l. and 4484 m to 3845 m a.s.l., respectively. As described by Ageta and Fujita (1996), Urumqi Glacier No. 1 is classified as a summer-accumulation-type glacier because both accumulation and ablation occur in the summer.

ACCEPTED MANUSCRIPT For the past several decades, Urumqi Glacier No. 1 has experienced a rapid and accelerated shrinkage (e.g. Han et al., 2006; Jing et al., 2006; Li et al., 2010). Due to glacier retreat, the glacier separated into two independent branches in 1993. Observed surface velocities on Urumqi Glacier

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No. 1 indicate that it is predominantly cold-based, with basal sliding occurring only close to the snouts and in summer (Zhou et al., 2009).

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The region is dominated by the westerly circulation and the Siberian High. The precipitation originates mainly from the moisture carried by the westerlies in summer, while the winter temperature is controlled by the Siberian High (Aizen et al., 1995; Xu et al., 2009). During the

approximately 4050 m a.s.l. (Wu et al., 2011).

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past 50 years, the annual equilibrium line altitude (ELA) of the glacier was in average at

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At the Daxigou Meteorological Station (3539 m a.s.l.), 3 km southeast of Urumqi Glacier No. 1, the annual mean air temperature measured is about -5.0oC and the annual mean precipitation is

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456 mm during 1959-2010. For the study period (1981-2010), the standard deviation for the

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annual mean temperature and precipitation are 0.7oC (p<0.01) and 80.8 mm (p<0.05), respectively. The linear trend analysis in Fig. 2 indicates that the annual mean temperature increased by

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approximately 0.603°C (10a)-1 and the annual precipitation had been increasing gradually with an

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average rate of 37.87 mm (10a)-1.

Fig. 2. Variations in annual mean temperature and precipitation observed at the Daxigou Meteorological Station from 1959-2010. The shaded area indicates the study period 1981-2010.

Observations of Urumqi Glacier No. 1 were initiated in 1959, implemented by the Tianshan

ACCEPTED MANUSCRIPT Glaciological Station, Chinese Academy of Sciences (CAS) (Li et al., 2003). It is one of the reference glaciers reported to the World Glacier Monitoring Service (WGMS), representing the glaciers in the Tian Shan due to its important location, ease of access and significance to local

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water supply. It provides the longest glaciological and climatological record of a glacier monitored in China and has been a major focus for glaciological, hydrological and climatological research in

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Central Asia.

3. Data and methods

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3.1. Glaciological method

The glaciological method, or the so called direct or traditional method, is used to measure the

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mass balance based on in-situ determination of accumulation and ablation for the mass balance year (Hoinkes, 1970; Braithwaite, 2002). The glacier mass balance at Urumqi Glacier No. 1 is measured following the glaciological method as described by Østrem and Brugman (1991). The

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mass balance has been measured on a monthly basis from 1 May to 30 August since 1959 by the

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stake/snowpit method (Xie and Huang, 1965; Yang et al., 1992; Braithwaite, 2002), representing

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the longest time series in China. With the stakes accumulation is measured in the firn area and ice melt in the ablation area. The density of the snow is measured along profiles in snowpits at representative points. The stake network consists of 42 stakes across the entire glacier as shown in

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Fig. 1 for the year 2008. Few stakes are distributed in crevassed and steep areas such as the headwalls of the glacier. Although the number of stakes has varied from year to year, it has never been smaller than half the recent values (Tianshan Glaciological Station, 2011). The stakes cover nearly the whole glacier, are evenly distributed in different elevations and represent the mass balance well. Stake and snowpit measurements are then converted to water equivalent using the measured densities for snow and ice. The glaciological observation broke off during the period 1967-1979 due to the Chinese political event (Han et al., 2005; Tianshan Glaciological Station, 2011). The glaciological mass balances during this period were extrapolated from glaciological observations during the other years and the records of Daxigou Meteorological Station. Therefore, the data for this period has been excluded to substantially determine the difference of the two mass balance methods. There are several ways to calculate the specific mass balance bn of a glacier. For Urumqi

ACCEPTED MANUSCRIPT Glacier No. 1, the following two methods have been used to interpolate the glacier mass balance. One way is to interpolate from the measured data manually by drawing contour lines of equal mass balance (Paterson, 1994). Areas between adjacent contour lines are integrated using a

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1  sibi S

(1)

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bn 

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planimeter and assigning a constant balance value to each of these areas as follows:

Where, si and bi is the area between the two contour lines and the corresponding mass balance, respectively, and S is the total area of Urumqi Glacier No. 1.

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Another method is to calculate the mass balance from repeated measurements at ablation stakes at different altitudes. The point mass balance data are then extrapolated to the entire glacier as a

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linear function of altitude as follows: n

bn   si'bi' / S

(2)

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Where, si and bi is the area of the altitude band i and corresponding mass balance, respectively,

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n is the number of altitude band and S is the total area of Urumqi Glacier No. 1. Geographical Information System (GIS) were used to derive spatial information from point values by the

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commercial software ArcGIS, applying the default parameter set of ordinary kriging. With the two methods, the mean mass balance has been calculated for both the summer and winter, and the entire budget year. The observational results of the mass balance for Urumqi Glacier No. 1 have

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been submitted to the WGMS since 1981. 3.2. Geodetic method The geodetic method is an indirect method to determine the glacier mass balance. Topographic maps of a glacier made at two different times are compared and the differences in glacier surface elevation are used to determine the mass balance over the respective time period. The specific geodetic mass balance MBgeo is calculated by multiplying the volume change ΔV with the mean density ρ, and then divided by the area A, which refers to the larger glacier area of the two periods:

MBgeo  V   / A

(3)

The volume change is derived from surface elevation change, which is calculated based on the digital elevation model (DEM) differences by subtracting the earlier from the later DEM. Possible errors are estimated by evaluating the elevation differences in non-glaciated terrain. This DEM can

ACCEPTED MANUSCRIPT be obtained using topographic maps, aircraft and satellite imagery, and by airborne laser scanning. In this study topographic maps are used. The Sorge’s law is assumed, which states that the density

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conversion of volume change to water equivalent for the entire glacier.

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structure remains constant in an unchanging climate. A density of 850 kg m-3 is used for the

Repeated topographic maps of Urumqi Glacier No. 1 had been produced in the years 1962, -73,

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-81, -86, -94, 2000, -06 and -09, respectively as listed in Table 1, and form a substantial database to determine the volume change in this study. These data are from The Annual Report of Tianshan Glaciological Station (2011). For the year 2009, a high quality DEM has been generated using the

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Real Time Kinematic-Global Position System (RTK-GPS). Hagen et al. (1999) found that kinematic GPS profiling could successfully be applied to measure the mass balance, given that it

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sampled the area-altitude distribution representatively. All topographic maps are based on the same coordinate system using three ground-control points from 1962, which served as fixed points

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for coordinate transformations. The consistent use of the Universal Transverse Mercator (UTM)

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projection World Geodetic System 1984 ellipsoidal elevation (WGS84) reference system was an important precondition for precisely calculating changes in mass, volume and area. The elevation

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errors are estimated to be less than 1 m and are randomly distributed, considering the instrument settings and the network of benchmarks. The glacier boundaries are mapped and digitized manually. Based on experiences reported from previous studies and discussions, it is assumed that

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the real changes of the boundary of the accumulation area are smaller than the differences due to the interpreter. Hence, boundaries of the glacier tongue are digitized for all the survey dates, keeping the outline of the accumulation area consistent (based on the 1962 topographic map). Based on the boundaries of the different surveys, the corresponding areas and area changes are calculated. The in-situ observation of the terminus changes are based on tape measurements from five points across the glacier terminus (1962-2009) and with the use of a theodolite, GPS, and a distance meter from one single fixed point. From the topographic maps, regular DEMs with a resolution of 5 m×5 m are generated by a standard kriging method. The DEM 1962, DEM 1973, DEM 1981 and DEM 1986 and corresponding glacier extents presented in this paper have been reported in the Doctor Dissertation of Li Xin. The data is freely available at: http://wdcdgg.westgis.ac.cn/. For the geodetic method, the DEMs were compared at time intervals of a few years to a few decades and the volume differences between 1981 and 2009 were

ACCEPTED MANUSCRIPT determined. Table 1 Characteristics of topographic maps used in this study. Topographic map

Year

Survey method

1962

1 : 10 000

plane table

1973

1 : 10 000

stereophotogrammetric survey

1981

1 : 50 000

aerial photograph

1986

1 : 5 000

1994

1 : 5 000

2001

1 : 5 000

2006

1 : 5 000

2009

1 : 5 000

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stereophotogrammetric survey stereophotogrammetric survey theodolite

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total station RTK-GPS

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4. Results and discussion

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4.1. Terminus, area, thickness and volume change

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The terminus retreat and shrinkage in area, thickness and volume of Urumqi Glacier No. 1 has

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been clearly identified as shown in Table 2. Variations at the glacier terminus between 1962 and 2009 based on in-situ measurement are illustrated in Fig. 3. A glacier terminus retreat of about

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215.2 m with an average rate of 4.6 m a-1 has been observed during the investigation period from 1962 to 2009. The average retreat rates of the glacier terminus were 6.0 m a-1 in 1962-1973, 2.9 m a-1 in 1973-81, accelerating then to 4.2 m a-1 (1981-86), 4.5 m a-1 (1986-94), 4.5 m a-1 (1994-2001),

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4.7 m a-1 (2001-06), and 5.0 m a-1 in 2006-09. Because of the severe ablation, the glacier separated into two individual branches in 1993, showing different recession rates. During 1994-2009, the terminus retreat of the West Branch was accelerated with an average rate of 6.0 m a-1, while the East Branch stayed with a relatively lower retreating rate of 3.5 m a-1. This was most likely because the debris cover on the tongue of the East Branch reduced the melting intensity (Li et al., 2007a). The results from the in-situ observations and the topographic maps agree well for the seven periods between 1962 and 2009, differences of which are within 5 m. The area of Urumqi Glacier No. 1 continuously shrank over the study period as shown in Fig. 4 and Fig. 5. The area changes between 1962 and 2009 amounted to -0.304 km2 or -16% of the area in 1962. Moreover, the reduction rate from 1986 to 2009 was 36% higher than that from 1962 to 2009. As shown in Table 2, the shrinkage rates were relatively stable in the 1960s and 1970s and from 1994-2006, accelerated in the 1980s with a maximum rate of 0.012 km2 a-1 between 1986 and

ACCEPTED MANUSCRIPT 1994, and a high rate of 0.010 km2 a-1 between 2006 and 2009. Changes in the area and terminus of this glacier between 1962 and 2005, including the photos taken in 1962, 1988, 1993, 1994,

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2001 and 2005 have been published by Li et al. (2007b).

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Table 2 Terminus, area, thickness and volume changes at Urumqi Glacier No. 1 for given time periods. Note the terminus change is the average value of the two branches in the period 1986-94, 1994-2001, 2001-06 and 2006-09. Area change

Thickness change

(m a )

(km a )

1962-73

-6.0

-0.004

1973-81

-2.9

-0.003

1981-86

-4.2

-0.007

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Terminus change

1986-94

-4.5

1994-2001

Time period

2

-1

(106 m3 a-1)

0.00

-0.22

0.00

-0.25

0.16

-0.61

-0.012

0.15

-0.47

-4.5

-0.005

0.23

-1.16

2001-06

-4.7

-0.005

0.62

-1.37

2006-09

-5.0

-0.010

0.73

-1.10

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-1

Volume change

(m a )

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-1

Fig. 3. The cumulative terminus changes of Urumqi Glacier No. 1 during 1962-2009 based on in-situ measurements and derived from topographic maps. The glacier separated into an East Branch and West Branch in 1993, shown with different symbols. Stars represent the glacier position derived from topographic maps, and circles and triangles represent in-situ measurements with the glacier position given for selected years. All values are given in meters.

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Fig. 4. Terminus changes of Urumqi Glacier No. 1 over the period 1962-2009. Dashed lines represent the glacial boundaries of 1962, 1973, 1981, 1986, 1994, 2001 and 2006. The glacial boundary of 2009 is shown with a solid

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line.

Fig. 5. Shrinkage of Urumqi Glacier No. 1 over the period 1962-2009 shown by photos taken in different years. The glacier separated into two independent glaciers in 1993, followed by an accelerated terminus retreat of the West Branch. The photos taken in 1962, 1988, 1993, 1994, 2001 and 2005 have been published by Li et al. (2007b).

As shown in Table 2, thickness change rates were minimal (<0.01 m a-1) during the first two periods (1962-73, 1973-81), but there was a clear volume loss of 2.42×106 m3 (0.22×106 m3 a-1) and 1.99×106 m3 (0.25×106 m3 a-1). The intense volume loss was mainly the result of the terminus retreat and area reduction. During the following periods (1981-86, 1986-94, 1994-2001), the thinning rate was nearly constant and a volume loss of 3.07×106 m3 (0.61×106 m3 a-1), 3.79×106 m3 (0.47×106 m3 a-1) and 8.13×106 m3 (1.16×106 m3 a-1) was found. Thus, the reduction in ice volume was caused by the changes of terminus, area and ice thickness. The dominant component for the

ACCEPTED MANUSCRIPT last two periods (2001-06, 2006-09) with a volume loss of 6.83×106 m3 (1.37×106 m3 a-1) and 3.30×106 m3 (1.10×106 m3 a-1) was the accelerated thickness loss on the entire glacier with the rate of 0.62 m a-1 and 0.73 m a-1, respectively. For the entire period results a volume loss of 29.51×106

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m3 or 0.63×106 m3 a-1. Hence, according to the available DEMs, the volume changes at Urumqi Glacier No. 1 between 1962 and 2009 are negative with mainly accelerated trend.

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The spatial distribution of thickness changes at Urumqi Glacier No. 1 is shown in Fig. 6, giving the patterns for the different time steps as well as for the entire period. Graduated colors are used to show the variation range of the ice thickness changes. During the period 1962-73, 1973-81 and

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1994-2001, the thickness change was rather random over the whole glacier. Particularly in the accumulation area, the thickness loss was clearly visible. In the following years (1981-86,

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1986-94), the highest values of thickness loss were at the terminus. During the last decade (2001-06, 2006-09) again the highest values occurred at the terminus of the glacier whereas the

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accumulation area experienced a moderate thickness increase. For the entire time period

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1962-2009, the decrease in ice thickness clearly concentrated in the ablation area. Moreover, it was also obvious on the ridge and cliff area of the glacier, probably resulting from higher radiative

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exposure (Li, 2005). Changes in ice thickness of the order of -35 to 5 m were observed in the East Branch and -35 to 2 m in the West Branch, respectively. The average change in ice thickness was -8.9 m for the whole of Urumqi Glacier No. 1. The maximum values of thickness loss were

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calculated at the terminus of the glacier and at a small patch at the southeastern edge of the glacier. The only positive changes, of the order of 0-5 m for the East Branch and 0-2 m for the West Branch, were found in the upper parts, probably caused by the increase in precipitation in the recent years (Li et al., 2007a) and topographic effects. Previous studies found that there was a good correlation between the areas of largest thickness decreases and those of highest surface slopes (Evans, 2006; Hodgkins et al., 2007). Overall, before 2001 the volume loss of the glacier was the combined effects of the shrinkage of terminus, area and thickness. However, the reduction of glacier thickness accelerated after 2001. Therefore, the intense volume loss in this period was mainly the result of a thickness reduction over the entire glacier area.

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Fig. 6. Ice surface elevation changes of Urumqi Glacier No. 1. The changes are calculated based on DEM

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differences by subtracting the earlier from the later DEM.

The combined analysis of length and area changes, representing the changing shape and volume

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of the entire glacier, represents the glacier reaction to a change in climatic forcing in an integrative way (Braithwaite and Zhang, 2000; Koblet et al., 2010). Three mechanisms have been identified to be responsible for the accelerated shrinkage of Urumqi Glacier No. 1 by Li et al. (2011), including

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1) air temperature rise in the melting season. The analysis of the temperature at the Daxigou Meteorological Station showed that the average annual positive degree day (PDD) increased from 516.1oC (1959-84) to 521.4oC (1985-96) and to 642.9oC (1997-2008). Although the precipitation increased, it did not prevent the glacier from an accelerated mass loss, 2) ice temperature rise. The measured data at an elevation of 3840 m a.s.l. of the glacier showed that the ice temperature increased with a rate of 0.06oC a-1 for 1986-2001 to 0.08oC a-1 for 2001-06, which played an important role in the acceleration of shrinkage, and 3) surface albedo reduction, due to not only the continued increase of the ablation area, but also surface dust mentioned by Takeuchi and Li (2008). 4.2. Uncertainty analysis The uncertainty inherent to the glaciological and geodetic data must be assessed and accounted for

ACCEPTED MANUSCRIPT in order to accurately compare the two methods. Therefore, a sound uncertainty assessment has been conducted for the in-situ observations and geodetic measurements. Based on these assessments, the volume changes of Urumqi Glacier No. 1 presented above are considered as a

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consistent high-quality dataset which can be compared with the glaciological mass balances. 4.2.1. Glaciological mass balance

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The accuracy of the mass balance measured with the glaciological method is difficult to assess because it contains various sources of uncertainty. In most cases, the accuracy of the method is in the centimeter to decimeter range (Haeberli et al., 1998). Fountain and Vecchia (1999) and Kuhn

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et al. (1999) estimated the accuracy of the glaciological mass balance as ±0.1 m w.e. a-1. Error sources such as internal accumulation (Rabus and Echelmeyer, 1998) and calving (Arendt et al.,

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2002; Rignot et al., 2003; O’Neel et al., 2005), as well as any changes in glacier area are usually not accounted for during measurement campaigns (Elsberg et al., 2001). Other possible error

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sources are the reference areas, basal or internal melt, superimposed ice and flux divergence.

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Field measurements The accuracy of the glaciological mass balance depends on the field measurements, including the distribution of the ablation stakes and snowpits (Cogley, 1999;

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Fountain and Vecchia, 1999), the accuracy of stake readings and snow/firn density measurements (Østrem and Brugman, 1991; Jansson, 1999). Interpolation method Further, sources of errors result from the interpolation method (Kaser et al.,

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1996; Hock and Jensen, 1999), and the extrapolation method applied for unsurveyed areas such as crevassed (Karlén, 1965; Jansson, 1999) or debris-covered areas (Nakawo and Rana, 1999). Hock and Jensen (1999) demonstrated that the estimated error introduced by the kriging interpolation method is about ±0.1 m w.e. a-1 for the mean specific mass balance. Internal accumulation and ablation With the traditional glaciological method the surface mass balance is measured, and excludes measurements of the internal accumulation and internal ablation (Østrem and Brugman, 1991). This can lead to annual small but significant systematic cumulative errors. Internal ablation is due to ice motion, geothermal heat, and heat-conversion of gravitational potential energy loss from water flow through and under the glacier. Internal accumulation is due to re-freezing of water trapped by capillary action in snow and firn by the winter cold mentioned by Schneider and Jansson (2004). Systematic errors related to the field measurements, such as the sinking of stakes in the accumulation area or the false determination of

ACCEPTED MANUSCRIPT the last year’s summer surface, might be an issue for individual survey years, but cannot be quantified due to the lack of corresponding information. A bias in the methodology such as an insufficient number of stakes or neglecting meltwater percolating into the previous year’s firn

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layer are other errors (Dyurgerov, 2002).

Reference area On the one hand, the glaciological mass balance is defined in the vertical

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direction, and therefore, the projected area is taken as glacier area but not the real surface area. Thus the surface area of steep parts of the glacier is larger than the area projected on the map, which is a problem currently neglected in most mass balance calculation as described by Fischer

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(2010). On the other hand, considerable time lags exist between the date of the mass balance measurements and the survey date of the reference area. The reference area for calculating the

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glaciological mass balance of Urumqi Glacier No. 1 has not been updated for every survey year, causing large errors in the comparison of the glaciological and geodetic mass balance.

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4.2.2. Geodetic mass balance

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The error of the geodetic mass balance is determined by the accuracy of DEMs, density assumptions, and survey dates.

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Accuracy of the DEMs The uncertainty of the DEMs and derived elevation/volume changes are estimated by comparing the DEM values with an independent set of GPS points in the non-glaciated area. A T-Test is performed to test the statistical significance of the glacier changes

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versus the elevation changes in the non-glaciated area. The mean difference between two DEMs in non-glaciated terrain can be considered as the uncertainty for the volume changes σDEM of the corresponding time period as following: n

 DEM 

 (Z

DEM 1

1

n

 Z DEM 2 ) (4)

Where n is the number of non-glacierized DEM grid cells. In addition, deriving DEMs from maps instead of the original aerial photographs introduces additional errors. Moreover, the datum level and different methodologies applied by different operators cannot be ignored. This resulted in a complete and consistent dataset of DEMs. The relative error of the DEMs is more important than their absolute error when calculating the geodetic mass balance, giving encouraging results within ±0.3 m.

ACCEPTED MANUSCRIPT Density assumption Density determination is important for converting the change of a snow/firn/ice volume into a mass change. Some studies generally assume a mean density for the whole glacier not considering the differentiation of densities among snow, firn and ice (Haakensen,

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1986; Krimmel, 1999). Ice flow transports mass from the upper parts of the glacier towards the tongue and the density of the snow layer changes. For the total glacier area, a common assumption

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is that ice flow does not alter the total mass of a glacier, and therefore changes of the glacier volume are related to mass changes only. Hagg et al. (2004) used density of firn and ice separately taking account of the mean equilibrium-line altitude (ELA). However, most assumed mean

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densities are between 800 kg m-3 and 900 kg m-3, and in this study 850 kg m-3 as the average of the two density is assumed. The difference to the maximum/minimum estimated densities (50 kg m-3)

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is taken as an uncertainty measure, according to Zemp et al. (2010). So the error associated with density is assumed to be less than ±0.25 m w.e.

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Survey dates The surveys for the field measurements and topographic maps are usually not

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carried out on the same date, and therefore influencing the glaciological and geodetic mass balance. This time lag is an important factor that needs to be considered when comparing the two

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mass balance calculations. The related error corresponds to the mass balance for the time lag and, hence, depends on the time span between the surveys, the season, and the glacier mass turnover. Holmlund et al. (2005) addressed the time lag by recalculating the glaciological mass balance

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series on the basis of time periods with constant glacier extents centered on the years when the aerial photos were taken. For the mass balance correction, a classical degree-day model is used and the melt m is calculated as follows:

m  DDF  PDD

(5)

where DDF is the degree-day factor and PDD is the sum of positive degree days within time intervals. PDD is given by n

PDD   H tTt

(6)

t 1

where Tt is the mean temperature on a typical day; Ht is logic variable (when Tt≥0℃, Ht=1.0 and when Tt＜0℃, Ht=0.0). Measured daily air temperatures from the Daxigou Meteorological Station, which are available

ACCEPTED MANUSCRIPT since 1958, are used in the model. The model is then tuned by varying temperature lapse rates and snow and ice degree-day factors to model the summer balance and match to the summer balance measured at each index site. Finally, the ablation in meters of water equivalent is calculated for the

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period from the date of topographic map to the end of the balance year as a function of elevation and weather data using the tuned parameters.

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The error sources of the cumulative glaciological and geodetic mass balances were analyzed individually as described above. Furthermore, all potential sources of stochastic and systematic uncertainties are discussed below. The stochastic uncertainties of the cumulative glaciological and

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geodetic mass balance are shown in Table 3, and are calculated based on the law of standard error propagation. The systematic uncertainties are an important component of the overall uncertainties.

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For the systematic uncertainties of the cumulative glaciological mass balance the reference area, internal ablation and accumulation were considered. For the geodetic mass balance the accuracy of

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the DEM and the survey dates were included. However, there have been some problems with the

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quantitative assessment of internal ablation and accumulation. Therefore, the overall uncertainties are estimated as shown in Table 4. The overall uncertainties for the cumulative glaciological mass

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balance are estimated to be ±0.5, ±0.8, ±0.7, ±0.6 and ±0.5 m w.e. for the period 1981-86, 1986-94, 1994-2001, 2001-06 and 2006-09, respectively. For the geodetic mass balance, it is estimated to be ±0.5, ±0.6, ±0.6, ±0.5 and ±0.4 m w.e. for the same periods. By comparison, the errors mentioned

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above are much less time-dependent than the possible systematic errors in the glaciological method, making the geodetic balance more accurate than the glaciological balance over time-scales longer than a few years. Table 3 The stochastic uncertainties of the cumulative glaciological and geodetic mass balances in meters water equivalent. Glaciological mass balance Time Field

Interpolation

Reference

measurement

method

area

1981-86

±0.2

±0.3

±0.2

1986-94

±0.3

±0.3

1994-2001

±0.2

2001-06 2006-09

period

Geodetic mass balance Total

Total

Density

Accuracy of

assumption

the DEM

±0.4

±0.1

±0.4

±0.4

±0.3

±0.5

±0.1

±0.5

±0.5

±0.3

±0.2

±0.4

±0.1

±0.5

±0.5

±0.1

±0.3

±0.2

±0.4

±0.1

±0.3

±0.3

±0.1

±0.3

±0.2

±0.4

±0.1

±0.2

±0.2

stochastic uncertainties

stochastic uncertainties

ACCEPTED MANUSCRIPT 4.3. Comparison of glaciological and geodetic method The comparison between the glaciological and geodetic mass balance is shown in Table 4 and Fig. 7. Table 4 indicates the glaciological and geodetic mass balances for the given time periods with

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the respective uncertainties. The cumulative glaciological mass balance was -11.7 m w.e. and the cumulative geodetic mass balance was -12.2 m w.e. from 1981 to 2009. The difference is 2.3%,

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2.8%, 4.6%, 4.7% and 5.9% for the years 1981-86, 1986-94, 1994-2001, 2001-06 and 2006-09, respectively. The geodetic mass balances differ from the glaciological by less than 10.0% for the total period. As the Fig. 7 shows, the agreement between the geodetic and glaciological data is

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very good for all periods. The geodetic balance is within the estimated error bars of the glaciological balance. This implies that the glaciological balance record on Urumqi Glacier No. 1

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does not contain large systematic errors. However, the cumulative geodetic mass balance is more negative than the glaciological mass balance. The geodetic mass balance can be used to calibrate

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the glaciological mass balance, however, no adjustment for Urumqi Glacier No. 1 is required.

1981-86 1986-94 1994-2001

Geodetic mass balance (Mgeo)

(m w.e.)

(m w.e.)

-1.4±0.5

-1.4±0.5

2.3

-1.7±0.8

-1.7±0.6

2.8

-3.8±0.7

-4.0±0.6

4.6

-3.2±0.6

-3.4±0.5

4.7

-1.6±0.5

-1.7±0.4

5.9

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2001-06 2006-09

Comparison

Glaciological mass balance (Mgla)

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Time period

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Table 4 Glaciological and geodetic mass balances for given time periods with the uncertainties.

((Mgeo- Mgla)/ Mgla) (%)

Fig. 7. Comparison of the cumulative geodetic and glaciological mass balances. The geodetic balance is within the estimated error bars of the glaciological balance.

ACCEPTED MANUSCRIPT 5. Conclusions and outlook Based on the topographic maps, changes of Urumqi Glacier No. 1 in terminus, area, thickness and volume are computed for seven time periods. The volume loss between 1962 and 2009 showed an

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accelerating trend. The glacier lost 0.22×106 m3 a-1 and 0.25×106 m3 a-1 for 1962-73 and 1973-81,

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respectively. In the following periods (1981-86, 1986-94, 1994-2001), a volume loss of 0.61×106

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m3 a-1, 0.47×106 m3 a-1 and 1.16×106 m3 a-1 was found, resulting from the reduction of terminus, area and ice thickness. The intense volume loss with the rate of 1.37×106 m3 a-1 and 1.10×106 m3 a-1 for 2001-06 and 2006-09 coincides with an accelerated thickness reduction. Over the entire

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period of 1962-2009, Urumqi Glacier No.1 lost a volume of 29.51×106 m3 with the terminus retreat of 4.6 m a-1 and area reduction of 0.006 km2 a-1. Averaged over the glacier area, this

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corresponds to a total ice thickness loss of 8.9 m, or to a mean annual ice loss of 0.2 m. By comparison, the geodetic mass balances differ from the glaciological less than 10.0% for the

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period from 1981 to 2009, and are within the error band of the glaciological balances. The

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geodetic mass balance fits well overall with the glaciological ones and confirms the excellent quality of this data series. Therefore, there is no need to calibrate the mass balance series measured

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with the glaciological method. However, these results cannot be applied to other glaciers or even to Urumqi Glacier No. 1 in future. The glaciological mass balance provides accurate information for point measurements and yearly balance values. The geodetic mass balance is ideal for

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long-term measurements. In contrast to possible systematic errors in the glaciological mass balance, the errors of the geodetic mass balance for Urumqi Glacier No. 1 are much less time-dependent, making the geodetic balance more accurate than the glaciological balance over time-scales longer than a few years. Further investigations should address the better quantification of systematic error sources, such as internal ablation, accumulation, as well as the issue of the changing reference areas used for mass balance calculations. In order to improve the investigation of glacier change and crosschecking in-situ measurements, the spatial distribution and visibility of the ground control points around Urumqi Glacier No. 1 have to be improved to enhance the resolution and precision of the geodetic data. In addition, the date of the survey should be as close as possible to the in-situ annual mass balance measurements. Furthermore, more analyses of the comparison of geodetic and glaciological mass balance should be performed at other surveyed glaciers to make a joint

ACCEPTED MANUSCRIPT analysis to identify possible biases and update estimates of the mass balance.

Acknowledgements

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We greatly appreciate the Tianshan Glaciological Station for the help on data collection and

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Dorothea Stumm from ICIMOD for the language polishing. Thanks also to suggestions from

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anonymous referees and the editorial staff for the improvement of our paper. This research was jointly supported by the Funds for Creative Research Groups of China (41121001), the National Natural Science Foundation of China (41301069), the SKLCS founding (SKLCS-ZZ-2012-01-01),

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the West Light Program for Talent Cultivation of Chinese Academy of Sciences and the

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Postdoctoral Science Foundation of China (2013M540779).

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Highlights of this study: (1) Glaciological and geodetic are two commonly used to determine mass balance. The

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glaciological method is the direct and traditional method. The systematic errors of this method are increased linearly with the number of years. The geodetic method is using volume change to

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estimate mass balance outlined by many studies as its intrinsic errors are mostly random. Therefore, it is very important that the value of geodetic programs is providing an independent check of traditional mass balance work, by comparing the cumulative changes over ten or more

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(2) Urumqi Glacier No.1, located in the eastern Tian Shan, at the core area of central Asia, is

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considered as the best monitored glacier in China. The continuous record of mass balance measurements begins in 1959/60 and thus is amongst the longest worldwide. It is one of the

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reference glaciers in WGMS (World Glacier Monitoring Service), which represents the glaciers in

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China due to its important location, ease of access and significance to local water supply. Since the 1950s, the glacier surface elevation has been surveyed eight times at intervals of a few years

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and the glacier terminus for twice every year. Due to all kinds of glacier data are available, Urumqi Glacier No.1 can be considered as one of the test glaciers to study the comparison of

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glaciological and geodetic mass balance determination.