Measurements and Models of the Mass Balance of Hintereisferner

This paper summarizes the methods applied to determine the mass balance of Hintereisferner and several other glaciers in the Tyrolean Alps since 1952. On an annual basis the direct glaciological method was applied with fixed date measurements on 10–15 accumulation pits and 30–90 ablation stakes on 9 km².
Indirect mass balance determination from equilibrium line altitude, accumulation area ratios or representative stakes, yield fair results and some exceptions could be related to anomalous meteorological conditions.
Monthly or more frequent stake readings supplied time series of ablation at various altitudes and slope aspects that served as basis for the calibration of energy and mass balance models. Of various models developed, two are presented in this paper. Both are based on degree days, one using daily values from a valley station to predict the mean annual balance of the entire glacier, while the other calculates day-to-day changes at 50-m grid points on the glacier.
The geodetic method has been applied for longer periods and yields results consistent with those of the glaciological method. The balance velocity calculated from recent ice thickness soundings and accumulation measurements is significantly less than observed velocity.     

Mass Balance Reconstruction Since 1963 and Mass Balance Model for East Rathong Glacier,Eastern Himalaya,Using Remote Sensing Methods

In this study mass balance, accumulation, ablation, runoff and temperature lapse rate for the East Rathong glacier are estimated for the time period 1963–2011 using remote sensing methods and climate data. A mass balance model is proposed for the glacier that computes mass balance as difference of volumes of consecutive years. Volume estimates of glacier are based on application of volume–area scaling law to glacier area computed from satellite images. It is observed that the glacier is summer‐accumulation type. Time series analysis is applied to the annual mass balance series. The annual mass balance of the glacier is showing a statistically significant negative trend. It is also showing a statistically significant shift in the year 1985. Change in the mean of mass balance before and after the shift year is 0.19 m w.e. Cumulative mass balance suggests that the glacier has lost ～11 m w.e. or 0.047 km³ during the last 48 years.     

Analysis of Difference Between Direct and Geodetic Mass Balance Measurements at South Cascade Glacier, Washington

Net mass balance has been measured since 1958 at South Cascade Glacier using the 'direct method,' e.g. area averages of snow gain and firn and ice loss at stakes. Analysis of cartographic vertical photography has allowed measurement of mass balance using the 'geodetic method' in 1970, 1975, 1977, 1979–80, and 1985–97. Water equivalent change as measured by these nearly independent methods should give similar results. During 1970–97, the direct method shows a cumulative balance of about −15 m, and the geodetic method shows a cumulative balance of about −22 m. The deviation between the two methods is fairly consistent, suggesting no gross errors in either, but rather a cumulative systematic error. It is suspected that the cumulative error is in the direct method because the geodetic method is based on a non-changing reference, the bedrock control, whereas the direct method is measured with reference to only the previous year's summer surface. Possible sources of mass loss that are missing from the direct method are basal melt, internal melt, and ablation on crevasse walls. Possible systematic measurement errors include under-estimation of the density of lost material, sinking stakes, or poorly represented areas.     

A Mass Balance Model that Uses Low-altitude Meteorological Observations and the Area–Altitude Distribution of a Glacier

A glacier mass balance model that requires only low-altitude precipitation and temperature observations and the glacier's areaaltitude distribution is presented as an alternative to direct field measurements. Input to the model for South Cascade Glacier are daily weather observations at stations 30–60 km from the glacier and at altitudes 1300 to 1500 m lower than the glacier. The model relies on the internal consistency of mass balance variables that are generated by simulation using the low-altitude weather data. The daily values of such balance variables as snowline altitude, zero balance altitude, glacier balance, balance flux and the accumulation area ratio are correlated throughout the ablation season using two-degree polynomial regressions to obtain the lowest fitting error. When the minimum average error (or maximum R ²) is attained, the generated balances and other variables are considered to be real. A simplex optimization technique is used to determine the optimal coefficient values that are used in algorithms to convert meteorological observations to snow accumulation and snow and ice ablation. The independently produced simulation results for the 1959–1996 period are compared with balances measured at the glacier. The agreement between annual balances for individual years is fair and between long-term volume changes measured by the geodetic method is excellent.     

A Small Glacier as an Index of Regional Mass Balance: Baby Glacier, Axel Heiberg Island, 1959–1992

Baby Glacier, Axel Heiberg Island, N.W.T., Canada is a small (0.6 km²), high-latitude (79°N), high-altitude (700–1200 m) glacier with a mass balance record extending from 1959–60 to the present. The record demonstrates shrinkage of the glacier, but a statistically significant trend is not evident. Correlations are strong between the mass balance of Baby Glacier and that of the nearby and much larger White Glacier, and also those of even larger, more distant glaciers. Thus programmes of measurement on small, simple ice bodies such as Baby Glacier can be representative of a large region. However, inter-annual changes are more accentuated for Baby Glacier. Baby Glacier does not meet all of the usual criteria for a representative glacier, but it straddles the regional equilibrium zone, a fact which helps to offset the disadvantages of its small size and limited altitudinal range. The equilibrium zone deserves to be an important focus for studies of high-arctic mass balance, with the aim of facilitating future measurement programmes which will rely on satellite remote sensing.     

Effective Sample Size for Glacier Mass Balance

Correlograms from multiple time series of point mass balance, measured on White Glacier (Axel Heiberg Island, Canada) and Abramov Glacier (Alai Range, Kirgizia), show that the correlation decreases with the difference in elevation between the points. The correlogram is used to calculate an integral spatial scale or effective sample area which, when divided into the area of the glacier, yields an estimate of the number of degrees of freedom in a stake-based estimate of the whole-glacier balance. This number – the 'effective sample size'– is a small fraction of the number of point measurements; indeed, it is independent of the number of measurements. Estimates of average balance for elevation bands are at one remove from raw stake measurements, but they are amenable to a principal component analysis which confirms that the effective sample size is very small. The small effective sample size means that uncertainty in a typical measurement of whole-glacier mass balance cannot be much less than the large value implied by the conservative assumption that stakes are perfectly correlated. One way around this difficulty would be to increase the role of prior physical understanding by seeking to model the spatial variability of mass balance. A successful model would need only a few parameters, and would allow for the joint estimation of both magnitude and uncertainty; the uncertainty in mass balance could be derived objectively from the uncertainty in the parameters. This, however, would require good estimates of the variability of mass balance at the elevation-band scale, which might in turn require that many measurement networks be redesigned.     

Mass Balance Measurements on the Lemon Creek Glacier, Juneau Icefield, Alaska 1953–1998

Annual balance measurements on the Lemon Creek Glacier, Alaska conducted by the Juneau Icefield Research Program (JIRP) from 1953 through 1998 provide a continuous 46 year record. This is one of the nine American glaciers selected in a global monitoring network during the International Geophysical year, 1957/58. These data have been acquired primarily by employing consistent ground methods, conducted on similar annual dates and calculated using comparable methodology. The results have been until now fairly precise, but of uncertain accuracy. An adjunct comparison of topographic surface maps of the glacier made in 1957 and 32 years later in 1989 provides a rough determination of glacier surface elevation changes which are clearly of less precision than the compilation of annual ground data. Airborne surface profiling in 1995, and global positioning system leveling transects in 1996–1998 update the record of surface elevation changes over the past decade. The mean glacier ice thickness reductions suggested by these methods from 1957–1989, from 1957–1995 and from 1957–1998 are ?13.2 m, ?16.4 m, and ?21.7 m, respectively. It is of interest that the geodetic interpretations agree fairly well with the trend of sequential balances from ground-level stratigraphic measurements. To date, however, the infrequent mapping methods in this study have yielded specific balances averaging between 5 and 11% less than those resulting from our annual on-site glaciological monitoring. For future studies this can be an important factor. The ground data are, therefore, the ones in which we have most confidence. These show cumulative ice losses of ?13.9 m (12.7 m water equivalent w.e.) from 1957–1989, of ?19.0 m (?17.1 m w.e.) from 1957–1995, of ?24.4 m (22 m w.e.) from 1957–1998, and ?24.7 m (22.2 m w.e.) for the total cumulative loss over the full 46 years between 1953 and 1998. Although the balance trend has been increasingly negative it averages ?0.48 m/a in w.e. or 0.52 m of ice loss per year. To refine the reliability of density determinations in this data set the effects of internal accumulation from refrozen meltwater producing diagenetic ice structures in the annual firnpack have been taken into account. An unusual dearth of such structures within the 1997/98 firnpack provided a unique opportunity to facilitate application of the probing technique over broad areas of the nv. This added to our ground truth and verified accuracy of the test-pit measurements used in these long-term mass balance computations. The glacier's continuing negative mass balance has fueled a terminal retreat of 800 m during the 1953–1998 period. The annual balance trend indicates that despite a higher mean elevation and a higher elevation terminus from thinning and retreat, mean annual balance has been strongly negative since 1977 (?0.78 m/a w.e.). Dramatically increased negative mass balances have occurred in the 1990s, with 1996 and 1997 being the only years on record with no retained accumulation since field observations were initiated in the glacier source areas in 1948.     

Inferring Glacier Mass Balance Using Radarsat: Results From Peyto Glacier, Canada

The capability of RADARSAT synthetic aperture radar (SAR) for the purpose of snow-line/accumulation area mapping for a temperate alpine glacier is examined. In agreement with other orbital C-band SAR studies, RADARSAT can discriminate between firn and bare ice facies. Limited observations are reported with respect to the electromagnetic variability of the ice facies in the ablation area, but they are inconclusive. Operational considerations are discussed with respect to reconciling the uncertainties of late-summer weather and their possible impact on the dielectric and scattering properties of the glacier surface. Vagaries associated with other glacier settings, mass balance states and their associated facies configurations are discussed including the difficulty of using the transient snow-line to define the equilibrium line and the lower extent of the accumulation area for glaciers where superimposed ice may form.
The radar remote-sensing reconnaissance of equilibrium line altitude (ELA) and accumulation area ratio (AAR) for estimating glacier mass balance requires serious consideration in those instances where traditional ground measurements used in the direct glaciological method are absent. However, with respect to the ELA, such estimates can vary depending on the accuracy of the reference digital elevation information. Moreover, for many glacier configurations, where mass balance variations due to altitude are influenced or in some cases completely masked by local balance variations, defining the ELA may be an irreconcilable problem. Using the AAR may be more robust in this regard. It is further determined that the total error inherent in the reconnaissance method would have serious implications for the confident estimation of mass balance normals and climate-related trends if the method were to be utilized over the longer term.     

过去44年乌鲁木齐河源一号冰川物质平衡结果及其过程研究

通过1997—2003年度天山乌鲁木齐河源一号冰川物质平衡的观测结果,分析比较了过去44年间一号冰川物质平衡、累积物质平衡的变化过程,以及反映气候一地形要素和冰川发育条件要素的平衡线高度和冰川积累区比率,认为一号冰川负平衡波动期随时间推移而递增,目前处于其观测历史上物质平衡亏损最为强烈的时期。     

Mass balance and near-surface ice temperature structure of Baishui Glacier No.1 in Mt. Yulong

The accumulation and ablation of a glacier directly reflect its mass income and wastage, and ice temperature indicates glacier＇s climatic and dynamic conditions. Glaciological studies at Baishui Glacier No.1 in Mt. Yulong are important for estimating recent changes of the cryosphere in Hengduan Mountains. Increased glacier ablation and higher ice temperatures can cause the incidents of icefall. Therefore, it is important to conduct the study of glacier mass balance and ice temperature, but there are few studies in relation to glacier＇s mass balance and active-layer temperature in China＇s monsoonal temperate glacier region. Based on the field observations of mass balance and glacier temperature at Baishui Glacier No.1, its accumulation, ablation, net balance and near-surface ice temperature structure were analyzed and studied in this paper. Results showed that the accumulation period was ranged from October to the following mid-May, and the ablation period occurred from mid-May to October, suggesting that the ablation period of temperate glacier began about 15 days earlier than that of continental glaciers, while the accumulation period began about 15 days later. The glacier ablation rate was 6.47 cm d 1 at an elevation of 4600 m between June 23 and August 30, and it was 7.4 cm d 1 at 4800 m between June 26 and July 11 in 1982, moreover, they respectively increased to 9.2 cm d 1 and 10.8 cm d 1 in the corresponding period and altitude in 2009, indicating that glacier ablation has greatly intensified in the past years. The temperature of the main glacier body was close to melting point in summer, and it dropped from the glacier surface and reached a minimum value at a depth of 4-6 m in the ablation zone. The temperature then rose to around melting point with the depth increment. In winter, the ice temperature rose gradually with the increasing depth, and close to melting point at the depth of 10 m. Compared with the data from 1982, the glacier temperature has risen in the ablation zone in recent decades.     

Annual Mass Balance of Blue Glacier, USA: 1955–97

Mass changes of Blue Glacier, USA are calculated from topographic maps made from vertical aerial photography in late summer of 1939, 1952, 1957, and 1987, along with laser altimetry flown in June 1996. Changes in elevation between maps were adjusted for seasonal variations in the snow cover, and to account for the ablation between the date of photography and 1 October. Topography obtained from the laser altimetry was adjusted for snow thickness and glacier motion to estimate topography of 1 October 1995. The mass of Blue Glacier has changed less than 7 m (water equivalent) during this 56 year period which is minor compared with other glaciers in the region and elsewhere in the world. Glacier-average annual mass balances, beginning in 1956, have been calculated either from stake measurements and probing of late-season snow, or from a regression analysis using late-season measurements of the equilibrium line altitude. A comparison with the changes derived from surface maps shows values obtained from field measurements are too positive by about 0.4 m a^?1 , indicating that considerable caution is needed when interpreting time series of mass balance. Two alternative time series of mass balance consistent with the long-term mass changes are created by making simple adjustments: (1) a single constant is subtracted from each value so that the series is consistent with the 1957–95 mass change; (2) one constant is subtracted from each value over 1957–87 and another is subtracted from each value over 1987-95 so that the series is consistent with both the 1957–87 and 1987–95 mass changes. The mass balance of Blue Glacier was generally positive until the mid-1970s and negative since. The fluctuations of mass balance closely resemble those of snowfall on the glacier as estimated from the joint distribution of temperature and precipitation. The climate in western Washington was cooler and wetter during the decade before the mid-1970s, but the trend since has been towards warmer and drier conditions.     

The mass-balance characteristics and sensitivities to climate variables of Laohugou Glacier No. 12, western Qilian Mountains, China

Due to global warming, glaciers on the Tibetan Plateau(TP) are experiencing widespread shrinkage; however, the mechanisms controlling glacier variations across the TP are still rather unclear, especially on the northeastern TP. In this study, a physically based, distributed surface-energy and mass-balance model was used to simulate glacier mass balance forced by meteorological data. The model was applied to Laohugou No. 12 Glacier, western Qilian Mountains, China, during2010~2012. The simulated albedo and mass balance were validated and calibrated by in situ measurements. The simulated annual glacier-wide mass balances were-385 mm water equivalent(w.e.) in 2010/2011 and-232 mm w.e. in 2011/2012,respectively. The mean equilibrium-line altitude(ELA) was 5,015 m a.s.l., during 2010~2012, which ascended by 215 m compared to that in the 1970 s. The mean accumulation area ratio(AAR) was 39% during the two years. Climatic-sensitivity experiments indicated that the change of glacier mass balance resulting from a 1.5 °C increase in air temperature could be offset by a 30% increase in annual precipitation. The glacier mass balance varied linearly with precipitation, at a rate of130 mm w.e. per 10% change in total precipitation.     

Application of Kriging Interpolation for Glacier Mass Balance Computations

In order to compute the specific mass balance of a glacier, point measurements of mass balance need to be integrated and thus interpolated over the entire glacier. In this study kriging was applied as interpolation technique to mass balance data of Storglaciren, a 3 km² valley glacier, focusing on the sensitivity of results to the choice of some kriging parameters. Although the spatial means varied only little in most cases, the spatial distribution of the mass balance quantities was sensitive to the assumption on kriging parameters, suggesting that the kriging parameters need to be carefully optimized for each case if the spatial distribution is of interest.     

水文气象学方法计算喜马拉雅山北坡冰川流域物质平衡

卡鲁雄曲是喜马拉雅that坡唯一具有长期常规水文气象观测资料的冰川流域.根据中国冰川水文和气候的分布特征,可推导出一组以水文、气象观测数据计算流域冰川平均物质平衡的公式.据此恢复了1983-2006年卡鲁雄曲流域冰川平均物质平衡各分量的逐年值序列,并用SPSS软件对计算结果进行r统计分析.结果表明:1983-2006年的24 a里,卡鲁雄曲流域的冰川消融逐步加剧:多年平均值为-136.3 mm/a,前12 a(1983-1994年)多年平均值为-83.61 mm/a,后12 a(1995-2006年)多年平均值为-188.98 mm/a,且1986、1998和2005年出现较大的波动,冰川物质平衡值分别为:149.19mm、-654.36 mm和-316.43 mm.通过对影响冰川物质平衡动态变化的影响因素进行分析,发现冰川物质平衡变化主要由强烈消融期(5-9月)的平均温度决定,二者的相关系数达到-0.786,并具有很好的线性关系:MB=-331.8T_(5-9)+2683.5.     

On the Mass Balance of Low Latitude Glaciers with Particular Consideration of the Peruvian Cordillera Blanca

Glacier mass balance studies in the low latitudes are rare and glaciological methods and terminology are basically adapted from mid- and high latitude conditions. The low latitudes are considered to be the tropics and, to some extent, the adjoining dry subtropics. The outer tropics are proposed as an intermediate zone with tropical character during the humid season and subtropical character during the dry season. Delimitations as well as respective climate and glacier regimes are discussed in order to distinguish them from each other and from the mid-latitudes. Different sensitivities of the glaciers can be expected and promise, in turn, a complex climatological interpretation of glacier fluctuations. For this, detailed mass balance studies on low latitude glaciers are required. The respective discussion is concentrated on the Peruvian Cordillera Blanca whose topographical setting provides both spatial and temporal subdivisions in humid and dry regimes in one region. However, theoretical considerations and field experience show problems for the determination of mass balance variables in the Cordillera Blanca and the low latitudes in general. The absence of annual temperature variations hinders the development of impermeable layers which can be identified as annual reference layers and which prevent meltwater from percolating into the firn body. Thus, a combination of ablation measurements and the application of the flux divergence method for the determination of accumulation is proposed.     

Changes of Snow Cover Thickness Measured by Conventional Mass Balance Methods and by Global Positioning System Surveying

The most labour-intensive and time-consuming part of many mass balance programmes is the acquisition of snow depth data. The standard technique, which involves probing the snow cover at intervals along a series of profiles, generally by an individual on skis, may involve more than 300 discrete measurements along a total of more than 20 km of profiling at a single glacier. Kinematic surveying with a global positioning system (GPS) in differential mode provides much more information about changes of glacier surface level and snow thickness between surveys. The positions of a large number of points can be fixed in a relatively short time by GPS surveying, and the technique is usable in adverse weather conditions. With real-time kinematic GPS surveying, it is possible to return to the same positions (longitude, latitude) during successive field programmes, and a previously followed route can be retraced precisely. GPS surveying facilitates the production of accurate glacier maps for mass balance programmes. Data obtained by snow depth probing and GPS surveying in 1995 at Austre Okstindbreen, the largest glacier of the Okstindan area, Norway (66°N), indicate that repeated GPS surveys are likely to provide a large amount of information on withinyear and between-year changes of surface topography and are not subject to the errors in mass balance calculations which arise from probing snow depths along selected profiles. Kinematic GPS surveying of several glaciers within an area would overcome the difficulties arising when mass balance studies are confined to a single glacier within a particular area.     

Accumulation Rate Measurements at Taylor Dome, East Antarctica: Techniques and Strategies for Mass Balance Measurements in Polar Environments

Accumulation rate measurements on the East Antarctic plateau are challenging due to both spatial and temporal variability. Annual stratigraphy is often not reliably or consistently preserved in the firn, and so accumulation cannot be determined from snow pit stratigraphy. We present a suite of accumulation rate measurements collected over several seasons at Taylor Dome, East Antarctica. We compare net accumulation results from direct burial rate measurements and β -activity firn cores along a 35 km traverse. The two methods are consistent and show that the net accumulation varies from greater than 10 cm a⁻¹ to about 1 cm a⁻¹ (ice equivalent) southwest to northeast across the dome. We map the depth of shallow radar layering to interpolate and extrapolate these point-location measurements and show that considerable variations occur over kilometer scales resulting from subtle surface topography. We also present accumulation rates estimated from concentration of the cosmogenic isotope ¹⁰Be and from activity profiles of ²¹⁰Pb. Finally, satellite passive microwave data are used to estimate spatially averaged accumulation rates on the regional to continental scale to provide a context for these local observations. We show that robust mass balance measurements in this environment must rely on spatial and/or temporal averaging.     

Analysis of Winter and Summer Glacier Mass Balances

Seasonal mass balance components b_w (winter balance) and b_s (summer balance) as well as c_t (total accumulation) and a_t (total ablation), can be used directly to infer climate variables. In contrast, a_c (net balance of the accumulation area) and a_a (net balance of the ablation area), and b_a or b_n (annual or net balance) can not. The traditional Alpine system of observations of a_c and a_a , however, can be converted to true seasonal values b_w and b_s if both pairs of components are simultaneously observed for some years, because a correlation between the two pairs of components exists. We analyzed b_w and b_s data and their mean, standard deviations and ratios of these to the corresponding net or annual balances for 50 glaciers with relatively long records representing different regions in the northern hemisphere. We also investigated correlations between seasonal components. A negative correlation between b_w and b_s exists at many glaciers. About two-thirds of the glaciers show insignificant correlations (?0.3 < r < 0.3), implying independence of summer and winter balances. In a few unusual cases the correlations are positive. These different correlations, or lack thereof, may offer insight into feedback conditions that must exist in this climate-related system. The correspondence of the b_w and c_t , and b_s and a_t , appears to depend largely on the relative amounts of summer snowfall, a function of their climatic environment expressed as [α = (b_w+b_s)/2]. The contribution of variability of b_s to the net balance increases markedly with decreasing values of α. The variability of b_w and b_s , and therefore the net balance, has been increasing with time; whether this is due to an increase in climate variability or to other causes is not clear. It appears that b_w has been increasing with time at the highest altitudes, but b_s has been increasing more rapidly especially at low altitudes; the many-glacier average net balance is becoming more negative.     

中国西部大陆性冰川与海洋性冰川物质平衡变化及其对气候响应——以乌源1号冰川和帕隆94号冰川为例

为认识全球变暖背景下中国西部大陆性冰川与海洋性冰川物质平衡变化及其对气候响应,本研究以天山乌鲁木齐河源1号冰川和藏东南帕隆94号冰川为例,结合大西沟与察隅站气象资料,对1980 — 2015年两条冰川的物质平衡变化特征及差异进行了分析。结果表明：36 a来乌源1号冰川与帕隆94号冰川物质平衡总体上均呈下降趋势,累积物质平衡达-17102与-8159 mm w.e.,相当于冰川厚度减薄19与9.01 m,且分别于1996、2004年左右发生突变。同期两条冰川所处区域年均温呈显著上升趋势,而降水量却表现出不同的变化态势;二者年内气温分配相仿,但降水分配差异较大。初步分析认为气温上升是导致乌源1号冰川与帕隆94号冰川物质亏损的主要原因,冰川区气温和降水变化幅度的差异和地性因子（坡度、冰川面积）的不同使得乌源1号冰川对气候变化响应的敏感性高于帕隆94号冰川,由于目前海洋性冰川物质平衡监测时段相对较短,为深入研究中国西部冰川物质平衡变化及过程仍需加强对冰川的持续观测。     

Study on mass balance and sensitivity to climate change in summer on the Qiyi Glacier, Qilian Mountains

Based on the glacier mass balance and meteorological data of air temperature and precipitation on the Qiyi Glacier from June 30 to September 5, 2010, we used a degree-day mass balance model to simulate the change of mass balance during this period. Our results indicate that the current value of the mass balance is ?856.2 mm w.e. Subjected to the strong influences of air temperature and precipitation, the mass balance process can be divided into three stages: accumulating exiguously → melting intensively → melting exiguously. The variation trends of the mass balance according to the degree-day mass balance model and the observed values are similar and wholly reflect the spatial distribution characteristics of the glacier mass balance, which increases with the increase of altitude. Our experiment on climate sensitivity of the mass balance showed that mass balance was very sensitive to the change of temperature; air temperature is the key factor which influences mass balance; and a slight increase in precipitation will have a negligible effect on mass balance when the air temperature increases continuously.