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.     

Map Comparison or Traditional Mass-balance Measurements: Which Method is Better?

A number of Norwegian glaciers were selected in the 1960s for long-term mass-balance measurements, to produce necessary hydrological information for hydropower exploitation. Special large-scale glacier maps were produced for field work and data processing, and some glaciers have been mapped more than once. Thus, comparison of glacier maps can be used to calculate changes in glacier volume for some of the glaciers, provided they are of sufficient accuracy.
Conventional mass-balance measurements were carried out on all the selected glaciers. A cumulative calculation of net balances for a series of years is used to indicate the change in a glacier's volume during that period. However, various errors originate in the field, some of which are systematic, particularly on glaciers with large winter accumulation.
The present study indicates that certain errors are difficult to define and determine, For the maritime glacier Ålfotbreen, a cumulative mass-balance calculation gives a positive total balance (+3.4 m water equivalent in the period 1968–88), whereas the map comparison indicates a total negative balance (−5.8 m water equivalent). This indicates a discrepancy between the methods, which must be accounted for.
Determination of errors in mass-balance measurements is difficult. Sinking of stakes in the accumulation area and the use of sounding sticks (steel probes) in heavy snowlayers cause problems.     

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.     

Mass Balance of Vernagtferner, Austria, From 1964/65 to 1996/97: Results for Three Sections and the Entire Glacier

In the centre of the highly glacierized Oetztal valley, mass balance is determined for the three neighbouring glaciers Hintereisferner, Kesselwandferner and Vernagtferner, applying the direct glaciological method, related to the 'fixed date' system. The diverging behaviour of the three glaciers due to slightly varying local climatic conditions as well as to different topoclimatological and physiographic features gave reason to analyse the Vernagtferner mass balance separately for three easily discernible sections, i.e. Schwarzwand, Taschachjoch and Brochkogel, each showing characteristic aspect and elevational distributions of area respectively.
The cumulative mass balance of the Vernagtferner for the period 1968/69, when separate mass balance computations for the three sections were started, until 1996/97 amounted to −8.7 m water equivalent (w.e.). The mass loss of the western Schwarzwand section as the part with the largest share of low elevation area was −13.3 m w.e., in contrast to the central Taschachjoch section which lost only −6.6 m w.e. The remaining eastern Brochkogel section with a loss of −8.5 m w.e. fits best the mass balance of the total Vernagtferner although its physiographic characteristics differ markedly from those of the entire glacier. The equilibrium line altitude (ELA) dependence on specific net mass balance ( b ) is slightly different for the three sections, whereas the dependence of the accumulation area–total area ratio (AAR) on b is characterized by nearly identical sensitivities. Moreover, AAR correlates better with b than ELA, therefore AAR is regarded as a more representative parameter for the Vernagtferner than ELA.     

Applicability of an ultra-long-range terrestrial laser scanner to monitor the mass balance of Muz Taw Glacier, Sawir Mountains, China

Glacier mass balance is a key component of glacier monitoring programs. Information on the mass balance of Sawir Mountains is poor due to a dearth of in-situ measurements. This paper introduces the applicability of an ultra-long-range terrestrial laser scanner(TLS) to monitor the mass balance of Muz Taw Glacier, Sawir Mountains, China. The Riegl VZ?-6000 TLS is exceptionally well-suited for measuring snowy and icy terrain. Here, we use TLS to create repeated high spatiotemporal resolution DEMs, focusing on the annual mass balance(June 2, 2015 to July 25, 2016). According to TLS-derived high spatial resolution point clouds, the front variation(glacier retreat) of Muz Taw Glacier was 9.3 m. The mean geodetic elevation change was 4.55 m at the ablation area. By comparing with glaciological measurements, the glaciological elevation change of individual stakes and the TLS-derived geodetic elevation change of corresponding points matched closely, and the calculated balance was-3.864±0.378 m w.e.. This data indicates that TLS provides accurate results and is therefore suitable to monitor mass balance evolution of Muz Taw Glacier.     

How many Stakes are Required to Measure the Mass Balance of a Glacier?

Glacier mass balance is estimated for South Cascade Glacier and Maclure Glacier using a one-dimensional regression of mass balance with altitude as an alternative to the traditional approach of contouring mass balance values. One attractive feature of regression is that it can be applied to sparse data sets where contouring is not possible and can provide an objective error of the resulting estimate. Regression methods yielded mass balance values equivalent to contouring methods. The effect of the number of mass balance measurements on the final value for the glacier showed that sample sizes as small as five stakes provided reasonable estimates, although the error estimates were greater than for larger sample sizes. Different spatial patterns of measurement locations showed no appreciable influence on the final value as long as different surface altitudes were intermittently sampled over the altitude range of the glacier. Two different regression equations were examined, a quadratic, and a piecewise linear spline, and comparison of results showed little sensitivity to the type of equation. These results point to the dominant effect of the gradient of mass balance with altitude of alpine glaciers compared to transverse variations. The number of mass balance measurements required to determine the glacier balance appears to be scale invariant for small glaciers and five to ten stakes are sufficient.     

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.     

Comparing Traditional Mass Balance Measurements with Long-term Volume Change Extracted from Topographical Maps: A Case Study of Storbreen Glacier in Jotunheimen, Norway, for the Period 1940–1997

Storbreen glacier is situated in the western part of Jotunheimen, a mountain area in central southern Norway. Annual mass balance data have been recorded since 1949. In addition, detailed topographical maps at the scale 1:10,000 exist from the years 1940, 1951, 1968, 1984 and 1997. In this paper, volume change calculated from maps is compared with annual mass balance data. The volume change was in reasonable agreement with the measured cumulative mass balance for the periods 1940–1951 and 1968–1984; however, for the periods 1951–1968 and 1984–1997, the mass balance measurements showed larger negative values than obtained from map comparisons. One obvious reason for this is the inaccuracy of the contour lines in the upper areas of the glacier on maps from 1940 and 1951. Other factors influencing the result are tested, and also suggestions are given for improving the techniques for mapping glacier volume changes.     

The Tarfala Mass Balance Programme

The Tarfala mass balance programme currently comprises seven glaciers distributed in two, one southerly and one northerly, east-west trending profiles. Of the studied glaciers, Storglaciären has the longest record spanning 1945 to present. The purpose of the programme is to study gradients in mass balance parameters across the northern Scandinavian mountains. The measurements of both winter and summer balance are carried out with significant redundancy each year. In order to maintain such a large programme with limited personnel, different measurement techniques and strategies are applied to the different glaciers according to a priority scale. Storglaciären is the most important glacier in the network and is measured with high accuracy and measurement density. Storglaciren is also used as a reference for all other glaciers in the programme. The other glaciers have sparser measurement systems and are sometimes measured using alternative methods such as snow radar. In general, Swedish glaciers are still responding to the major climatic warming around 1910–1920 by retreat, and the effect of very long response times. However, measured volume change indicates that most glaciers are close to or varying around a quasi-steady state.     

Using Vertical Aerial Photography to Estimate Mass Balance at a Point

The mass balance distribution over a 0.5 km² area of the lower part of South Cascade Glacier is obtained from remotely sensed measurements of its geometry and velocity field over two periods, 1992–93 and 1993–94. Vertical aerial photography from late summer 1992, 1993, and 1994 is analyzed photogrammetrically to get surface topography of South Cascade Glacier on a 100-meter square grid. The known bed topography is subtracted from the surface topography to get the ice thickness, and the surface topographies are subtracted from each other to get the thickness change. Annual displacement vectors, determined at points where natural features could be tracked from one year to the next, are contoured by hand and interpolated to the grid. Assuming that the ice follows Glen's flow law with exponent n = 3, and that 10% of the ice flow is due to sliding at the bed, the surface velocity is scaled by 0.82 to get the average velocity in the vertical ice column. The average velocities are combined with the thicknesses to calculate the flux divergence at each of 46 gridpoints on a 100-m square grid, where it is subtracted from the thickness change to get the mass balance.
Use of the same control points from year to year makes any systematic error in photogrammetric coordinates temporally constant, so such error has no effect on the mass balance estimate. Random error in coordinates is assumed to be uncorrelated from coordinate to coordinate, from point to point, from year to year; the standard error is estimated to be 1 m, resulting in a standard error in coordinate differences of about 1.5 m. A 1 m error in a vertical coordinate has nearly twice the effect on the estimated balance that one in a horizontal coordinate has and more than ten times the effect that one in ice thickness has. Compared with measurements at a stake, the estimated balances are about 1 m too negative.     

Ablation Rate Estimates over the Greenland Ice Sheet from Microwave Radiometric Data

Scanning Multichannel Microwave Radiometer (SMMR) data are used to estimate the annual melt duration (number of days with melt) for elevation transects over the Greenland ice sheet during the period from 1979-1986. The annual melt duration is used to estimate the number of positive degree days (PDDs), which are used in a degree-day mass balance model to determine ablation rates and the equilibrium line altitude (ELA). The annual melt duration along two transects estimated with SMMR data compares favorably, particularly above the ELA, to melt duration calculated from surface temperature data for the same locations. The mass balance estimates and ELA locations along eight transects agree reasonably well with measurements reported in previous studies using surface temperature data. ELAs were within 10m of published values along two transects, and the root mean square error of SMMR-derived versus surface mass balance measurements was 43mm yr^?1. The estimated error in SMMR-derived ablation is between ±15% and ±50%, but could be reduced substantially by using daily microwave data available from the Special Sensor Microwave/Imager (SSM/I). This research shows the feasibility of using passive microwave data to estimate the ablation rate in order to determine ELA, which can be used to monitor the mass balance of the ice sheet.     

Ablation Rate Estimates over the Greenland Ice Sheet from Microwave Radiometric Data

Scanning Multichannel Microwave Radiometer (SMMR) data are used to estimate the annual melt duration (number of days with melt) for elevation transects over the Greenland ice sheet during the period from 1979‐1986. The annual melt duration is used to estimate the number of positive degree days (PDDs), which are used in a degree‐day mass balance model to determine ablation rates and the equilibrium line altitude (ELA). The annual melt duration along two transects estimated with SMMR data compares favorably, particularly above the ELA, to melt duration calculated from surface temperature data for the same locations. The mass balance estimates and ELA locations along eight transects agree reasonably well with measurements reported in previous studies using surface temperature data. ELAs were within 10m of published values along two transects, and the root mean square error of SMMR‐derived versus surface mass balance measurements was 43mm yr^?1. The estimated error in SMMR‐derived ablation is between ±15% and ±50%, but could be reduced substantially by using daily microwave data available from the Special Sensor Microwave/Imager (SSM/I). This research shows the feasibility of using passive microwave data to estimate the ablation rate in order to determine ELA, which can be used to monitor the mass balance of the ice sheet.     

COMPARISON OF MEASUREMENT METHODS BASED ON A MODEL FOR THE ERROR STRUCTURE

Comparison of methods is a technique often used for investigation of systematic errors of measurementmethods.As concerns the design and analysis of such comparisons,much variety of opinion and practiceexists.In one approach a few specimens are measured several times by different operators in differentlaboratories(reproducibility conditions)and in another approach several specimens are measured on oneor a few occasions by one operator in the same laboratory(repeatability conditions).In this paper amodel for the error structure of measurements is formulated and it is emphasized that one has todistinguish between two types of systematic errors:the first type depends only on the level of themeasured quantity and the second type is specific for the separate specimens.On the basis of this modelthe information which can be obtained from the different designs of method comparisons is discussed.A new approach for the analysis of method comparisons with many specimens is also proposed.     

Evaluating Volumetric Glacier Change Methods Using Airborne Laser Scanning Data

Assessments of geodetic volume change are widely used in glaciology and have a long tradition dating back to the nineteenth century. Over time, the geodetic method and corresponding data storage have been developed further, but the resulting methodological heterogeneity can lead to errors that are difficult to separate from other survey uncertainties. In this study we used high‐resolution airborne laser scanning data from the Findelengletscher in the Swiss Alps to evaluate state‐of‐the‐art volumetric glacier change methods. For the first time we have been able to simulate errors arising from different geodetic methods and spatial resolutions. The evaluation showed that, although the digital elevation models were perfectly co‐registered, systematic and random method‐ and scale‐dependent errors still occurred. These errors have an impact on the resulting volume changes at lower spatial resolutions and may lead to exponentially larger uncertainties. Volume changes from contour methods provided reasonably accurate results, while volumetric change assessments from central profile lines were especially prone to biases at any scale.     

Effects of mechanical layering on volcano deformation

The migration and accumulation of magma beneath volcanoes often causes surface displacements that can be measured by geodetic techniques. Usually, deformation signals are explained using models with uniform mechanical properties. In this paper, we study surface displacements due to magma chamber inflation, using heterogeneous finite element models. We first present a systematic analysis of the influence of mechanical layering, showing that the stiffness contrast significantly affects the entity and the pattern of vertical and radial displacements. Second, as an example we apply the models to interpret ground displacements at Darwin volcano (Galápagos Islands) as revealed by InSAR data in the period 1992–1998. The considered models suggest that geodetic data interpreted using homogeneous models leads to underestimation of the source depth and volume change. Thus, we propose correction factors for the source parameters estimated by homogeneous models, in order to consider a range of variation due to mechanical layering as analysed in this study. The effect of the mechanical heterogeneities affects the correct understanding of geodetic data and also influences the evaluation of a volcanic hazard potential.     

Mass Balance Methods on Kongsvegen, Svalbard

On the glacier Kongsvegen (102 km²) in northwest Spitsbergen, Svalbard, traditional mass balance measurements by stake readings and snow surveying have been conducted annually since 1987. In addition, repeated global positioning system (GPS) profiling, shallow core analysis and ground-penetrating radar (GPR) surveying have been applied. The purpose of this paper is to evaluate the input from the different methods, especially the GPS profiling, using the results from the traditional direct method as a reference. The annual flow rate on Kongsvegen is low (2 ? 3 m a^?1), and the emergence velocity is almost negligible. Thus the geometry changes of the glacier, i.e. the change in altitude per distance from the head of the glacier, should reflect the change in net balance of the glacier. The mean annual altitude change from the longitudinal, centreline GPS profiles was compared to the direct stake readings and showed a very good agreement. On Kongsvegen the measured actual ice flux is so low that the mass transfer down-glacier at the mean equlibrium line altitude is less than 10% of what is needed to maintain steady-state geometry. This is clearly shown in the changing altitude profiles. GPS profiling can be used on large glaciers in remote areas to monitor geometry changes, ice flow and net mass balance changes. However, it requires that the centreline profile changes are representative for the area/altitude intervals, i.e. that the accumulation and ablation pattern is evenly distributed. For this purpose the GPR surveying quickly gave the snow distribution variability over long distances. Shallow cores drilled in different altitudes in the accumulation area were analysed to detect radioactive reference layers from the fallout after the Chernobyl accident in 1986, and showed very good agreement to the direct measured net balance. Thus older reference horizons from bomb tests in 1962 could be used to extend the net balance series backwards.     

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.     

An analysis of short-term albedo variations at Haut Glacier d'Arolla, Switzerland

Abstract An analysis of ten‐minute albedo variations, recorded on Haut Glacier d'Arolla, Switzerland, over an 11 day period in the 1999 ablation season is presented. Most of the short‐term (<1 day) albedo variability is caused by variations in cloud cover, while solar zenith angle variations in the range 25° to 75° are of minor importance, probably due to the predominantly cloudy conditions during the measurement period. A new method to calculate albedo variation as a function of cloud cover is developed. Short‐term albedo variations are expressed by the ratio of the measured albedo to the daily albedo ‘minimum’, defined as the albedo under cloud‐free conditions when the solar zenith angle is <50°. Variations in cloud cover are quantified by the ratio of the measured incoming shortwave radiation flux to the theoretical direct‐beam shortwave radiation flux. The resulting relationships are successful, explaining 83% and 87–90% of short‐term albedo variation on snow and ice respectively, and may be incorporated into albedo parameterizations already used in numerical energy balance melt models, without the need for additional data. Simulations with a glacier energy balance model suggest that melt rates are overestimated by between 1 and 3 mm water equivalent per day if a correction is not made for the increase in albedo under cloudy conditions. Other causes of albedo variation are identified and evidence is found for the removal of fine debris from the glacier surface by intense rainfall, leading to an albedo increase. The implications for energy balance models and satellite‐derived albedo measurements are discussed.     

High-resolution mean sea surface computed with altimeter data of Ers-1 (geodetic mission) and topex-poseidon

The remote-sensing satellite ERS-1, launched in 1991 to study the Earth's environment, was placed on a geodetic (168-day repeat) orbit between 1994 April and 1995 March to map, through altimetric measurements, the gravity field over the whole oceanic domain with a resolution of 8 km at the equator in both along-track and cross-track directions. We have analysed the precise altimeter data of the geodetic mission, and, by also using one year of Topex-Poseidon altimeter data, we have computed a global high-resolution mean sea surface. The various steps involved in pre-processing the ERS-1 data consisted of correcting the data for environmental factors, editing, and reducing, through crossover analyses, the radial orbit error, which directly affects sea-surface height measurements. For this purpose, we adjusted sinusoids at 1 and 2 cycle rev⁻¹ along the ERS-1 profiles in order to minimize crossover differences between ERS-1 and yearly averaged Topex-Poseidon profiles. In effect, the orbit of Topex-Poseidon is very accurately determined (within 2–3 cm for the radial component), so Topex-Poseidon altimeter profiles can serve as a reference to reduce the ERS-1 radial orbit error. The ERS-1 residual orbit error was further reduced through a second crossover analysis between all ascending and descending profiles of the geodetic mission. The along-track ERS-1 and Topex-Poseidon data were then interpolated over the whole oceanic domain on a regular grid of 1/16°× 1/16° size. The mapping of the gridded sea-surface heights reveals the very fine structure of the marine geoid, up until now unknown at a global scale. This new data set will be most useful for marine geophysical and tectonic investigations.