Mass Balance Distribution Research Articles

Balance mass flux and ice velocity across the equilibrium line in drainage systems of Greenland

Estimates of balance mass flux and depth‐averaged ice velocity through the cross section aligned with the equilibrium line are produced for each of six drainage systems in Greenland. The estimates are based on a model equilibrium line fitted to field data and on a revised distribution of surface mass balance for the conterminous ice sheet. Ice drainage divides and six major drainage systems are delineated using surface topography from ERS radar altimeter data. Ice thicknesses at the equilibrium line and throughout each drainage system are based on the latest compilation of airborne radar sounding data described elsewhere. The net accumulation rate in the area bounded by the equilibrium line is 399 Gt a−1, and net ablation rate in the remaining area is 231 Gt a−1. Excluding an east central coastal ridge reduces the net accumulation rate to 397 Gt a−1, with a range from 42 to 121 Gt a−1 for the individual drainage systems. The mean balance mass flux and depth‐averaged ice velocity at the cross‐section aligned with the modeled equilibrium line are 0.1011 Gt km−2 a−1 and 0.111 km a−1, respectively, with little variation in these values from system to system. In contrast, the mean mass discharge per unit length along the equilibrium line ranges from one half to double the overall mean rate of 0.0468 Gt km−1 a−1. The ratio of the ice mass in the area bounded by the equilibrium line to the rate of mass output implies an effective exchange time of approximately 6 ka for total mass exchange. The range of exchange times, from a low of 3 ka in the SE drainage system to 14 ka in the NE, suggests a rank as to which regions of the ice sheet may respond more rapidly to climate fluctuations.

Greenland ice-sheet mass-balance distribution: a variance analysis of existing field data

AbstractA large number of mass-balance measurements have been carried out on the Greenland ice sheet, but few of the series obtained are well suited for statistical studies. Rather than looking at the global mass-balance value, this paper deals with the spatial and temporal mass-balance variability on the ice sheet. Two sorts of analysis are possible: direct comparisons of the series measured at a given site, or a broader approach involving comparisons between different sites using variance analysis. For glaciers in the southwest ablation area, a significant interannual variability (around 1.0 m w.e.) is found. This variability is spatially consistent. In the accumulation area, the results are more complex. For example, there is consistent evidence of year-to-year variations on the west–east Expéditions Glaciologiques Internationales au Groenland (EGIG) profile, but other closer sites are weakly correlated. These results emphasize the need for a better coverage of measurements over the entire ice sheet, as well as longer and more continuous measurement series.

Spatial distribution of net surface mass balance on Greenland

AbstractThe spatial distribution of surface mass balance on the Greenland ice sheet is mapped on a 50 km grid using a combination of methods depending on a zonal characterization of the diagenetic snow fades. In the zones of dry snow and upper percolation fades, the accumulation rate is calculated from microwave emissivities derived from satellite measurements using a model that is calibrated with field accumulation data. In the lower percolation zone, accumulation rates are obtained from visual interpolation of previously compiled field data, with some modification so the balance is zero at the equilibrium line In the ablation zone, ablation rates are calculated as a function of ice-surface elevation and latitude. Average values of the surface balance are 263 kg m–2a–1 in the accumulation zone, (-) 1259 kg m–2 a–1 in the ablation zone and 1286 kg m–2 a–1 overall. Compared to the findings of a previous study using practically the same approach but different models, our bulk estimate of balance (216 Gt a–1) is 57% smaller, but the differences in the estimates of net accumulation and net ablation are, respectively, 30% and 172% larger. In this and other comparisons, there is evidence that the differences in estimates are primarily due to differences in the delineation of the equilibrium line and the estimate of ablation, and secondarily to the estimate of accumulation and interpolation of field data. The differences noted with six other estimates reported in the last two decades are all of a size close to the composite variation of the difference (±50Gtσ–1) . Our surface balance is smaller than three estimates, larger than one and in agreement with two. If substituted in the latest mass-budget estimate that indicates equilibrium, our surface balance estimate would suggest a negative budget of 55 Gt a–1 and thus a positive contribution to sea-level change of 0.15 mm a–1.

Glacier mass-balance determination by remote sensing and high-resolution modelling

AbstractAn indirect methodology for determining the distribution of mass balance at high spatial resolution using remote sensing and ice-flow modelling is presented. The method, based on the mass-continuity equation, requires two datasets collected over the desired monitoring interval: (i) the spatial pattern of glacier surface-elevation change, and (ii) the mass-flux divergence field. At Haut Glacier d’Arolla, Valais, Switzerland, the mass-balance distribution between September 1992 and September 1993 is calculated at 20 m resolution from the difference between the pattern of surface-elevation change derived from analytical photogrammetry and the mass-flux divergence field determined from three-dimensional, numerical flow modelling constrained by surface-velocity measurements. The resultant pattern of mass balance is almost totally negative, showing a strong dependence on elevation, but with large localized departures. The computed distribution of mass balance compares well (R2 = 0.91) with mass-balance measurements made at stakes installed along the glacier centre line over the same period. Despite the highly optimized nature of the flow-modelling effort employed in this study, the good agreement indicates the potential this method has as a strategy for deriving high spatial and temporal-resolution estimates of mass balance.

Photogrammetric reconstruction of glacier mass balance using a kinematic ice-flow model: a 20 year time series on Grubengletscher, Swiss Alps

AbstractThe kinematic boundary condition at the glacier surface can be used to provide glacier mass balance at individual points if changes in surface elevation, horizontal and vertical surface velocities and surface slope are known. Vertical ice velocity can in turn be estimated from basal slope, basal ice velocity and surface strain. This relation is applied to reconstruct a 20 year mass-balance curve of Grubengletscher, Swiss Alps, largely using repeated aerial photogrammetry, with only a minimum of fieldwork For individual years the mass-balance distribution on the glacier tongue was modelled with an accuracy of about ±0.9 m a"1. Ice-mechanical assumptions and errors in glacier bed geometry markedly affect discrete mass-balance patterns but are largely eliminated in the calculation of year-to-year mass-balance changes The resulting 1973–92 curve for the Grubengletscher tongue shows reasonable consistency with meteorological data and other glaciologically derived mass-balance series. Large changes in measured ice speed on the glacier tongue (±50%) significantly governed the long-term variability of ice thickness over the observational period.

Sensitivity of mass balance of five Swiss glaciers to temperature changes assessed by tuning a degree-day model

AbstractA degree-day model is used to assess the sensitivity of the mass balance of five Swiss glaciers to temperature changes. The model uses temperature data extrapolated from nearby climate stations, and is tuned by varying precipitation to make the model fit the observed distribution of mass balance with altitude. Once the model is tuned, the effect of temperature change is simulated by recalculating the mass balance with the same parameters as before, but with a temperature increase of 1°C throughout the year. The largest mass-balance changes, involving increased ablation of > 1 m w.e. a−1 °C−1, occur at the snout, with a progressively smaller increase with altitude. The area-averaged sensitivities for the five glaciers are −0.7 to −0.9 m w.e. a−1 °C−1. If annual precipitation also increased by 20% it would partly offset the effect of the 1°C higher temperatures but could not compensate for it.

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.

Evaluating the potential of an airborne laser‐scanning system for measuring volume changes of glaciers

Airborne laser scanning (ALS) is well suited for the production of digital elevation models (DEM), and can, in contrast to photographic methods, be used to acquire a DEM independently of surface texture and external light sources. ALS thus serves as a tool to generate DEMs of firn areas where photogram‐ metric methods often fail.The potential of an integrated ALS system – comprising a laser scanner, precise differential global positioning system, and a gyro platform – for DEM generation of firn areas is currently being assessed. The Unteraargletscher, Bernese Alps, Switzerland, has been chosen as a test site. As part of a pilot project aimed at determining the mass balance distribution of that glacier without the use of in situ information, ALS measurements were conducted in autumn 1997. The DEM derived from laser measurements is extremely sensitive to the position and attitude of the aircraft. Currently the main work focuses on assessing and improving the system's accuracy by error modelling and by the development of error‐correction algorithms.Preliminary results from Unteraargletscher are presented, and the potential of this method for the generation of DEMs of firn areas is discussed.

Towards an indirect determination of the mass‐balance distribution of glaciers using the kinematic boundary condition

The kinematic boundary condition at the surface is utilized to arrive at an estimate of the mass‐balance distribution of the ablation region of Unteraargletscher, Bernese Alps, Switzerland. This is achieved without the use of any ground measurements. The terms of the kinematic boundary condition, involving surface‐altitude changes with time, surface slopes, and horizontal surface velocities, are determined using high precision aerial photogrammetry. Estimating the vertical velocity distribution along the surface poses a major problem. Different approaches to solving this problem are discussed, and the potential of one particular approach is evaluated. This approach is, in essence, based on the assumption that the variation of vertical strain rates with depth is simple. The accuracy of the resulting indirect estimate of the mass balance distribution is assessed by a comparison with results from stake measurements made at about 40 different points at the surface. Although calculated values of mass balance are found to be within a reasonable range, they differ, as a function of altitude, in a systematic fashion from stake values. This suggests that the vertical strain‐rate variation with depth is too complex to be parameterized in a simple manner.

Towards an Indirect Determination of the Mass-balance Distribution of Glaciers using the Kinematic Boundary Condition

Towards an Indirect Determination of the Mass-balance Distribution of Glaciers using the Kinematic Boundary Condition

Influence of Spatial Resolution and Treatment of Orography on GCM Estimates of the Surface Mass Balance of the Greenland Ice Sheet

Abstract The major ice sheets are of considerable importance in the evolution of climate, and in order to predict their future state, or understand their past history, it is necessary to understand the forcing imposed upon their evolution by the atmosphere. Ice sheet models have already been coupled to atmospheric models with some degree of success, but before such tools are used to predict the past and future evolution of the ice sheets, it is important that the atmospheric model is capable of reproducing the current mass balance distribution of the ice sheets reasonably. At first inspection, the surface mass balance of the Greenland ice sheet predicted by the United Kingdom Universities Global Atmospheric Modelling Project general circulation model (UGCM) is typical of that produced by the majority of GCMs, with a moderate overestimation of accumulation and a large overestimation of ablation. Further investigation reveals that there are a number of systematic errors involving the treatment of orography ...

Modelling mass balance using photogrammetric and geophysical data: a pilot study at Griesgletscher, Swiss Alps

AbstractThe kinematic boundary condition al the glacier surface can be used to give glacier mass balance at a point as a function of changes in the surface elevation, and of the horizontal and vertical velocities. Vertical velocity can in turn be estimated from basal slope, basal ice velocity and surface strain. In a pilot study on the tongue of Griesgletscher, Swiss Alps, the applicability of the relation for modelling area-wide ice flow and mass-balance distribution is tested. The key input of the calculations, i.e. the area-wide surface velocity field, is obtained using a newly developed photogrammetric technique. Ice thickness is derived from radar-echo soundings. Error estimates and comparisons with stake measurements show an average accuracy of approximately ±0.3 ma-1 for the calculated vertical ice velocity at the surface and ±0.7 ma-1 for the calculated mass balance. Due to photogrammetric restrictions and model-inherent sensitivities the applied model appeared to be most suitable for determining area-wide mass balance and ice flow on flat-lying ablation areas, but is so far not very well suited for steep ablation areas and most parts of accumulation areas. Nevertheless, the study on Griesgletscher opens a new and promising perspective for the monitoring of spatial and temporal glacier mass-balance variations.

Modelling mass balance using photogrammetric and geophysical data: a pilot study at Griesgletscher, Swiss Alps

AbstractThe kinematic boundary condition al the glacier surface can be used to give glacier mass balance at a point as a function of changes in the surface elevation, and of the horizontal and vertical velocities. Vertical velocity can in turn be estimated from basal slope, basal ice velocity and surface strain. In a pilot study on the tongue of Griesgletscher, Swiss Alps, the applicability of the relation for modelling area-wide ice flow and mass-balance distribution is tested. The key input of the calculations, i.e. the area-wide surface velocity field, is obtained using a newly developed photogrammetric technique. Ice thickness is derived from radar-echo soundings. Error estimates and comparisons with stake measurements show an average accuracy of approximately ±0.3 ma-1for the calculated vertical ice velocity at the surface and ±0.7 ma-1for the calculated mass balance. Due to photogrammetric restrictions and model-inherent sensitivities the applied model appeared to be most suitable for determining area-wide mass balance and ice flow on flat-lying ablation areas, but is so far not very well suited for steep ablation areas and most parts of accumulation areas. Nevertheless, the study on Griesgletscher opens a new and promising perspective for the monitoring of spatial and temporal glacier mass-balance variations.

Greenland and Antarctic Mass Balances for Present and Doubled Atmospheric CO2from the GENESIS Version-2 Global Climate Model

Abstract As anthropogenic greenhouse warming occurs in the next century, changes in the mass balances of Greenland and Antarctica will probably accelerate and may have significant effects on global sea level. Recent trends and possible future changes in these mass balances have received considerable attention in the glaciological literature, but until recently relatively few general circulation modeling (GCM) studies have focused on the problem. However, there are two significant problems in using GCMs to predict mass balance distributions on ice sheets: (i) the relatively coarse GCM horizontal resolution truncates the topography of the ice-sheet flanks and smaller ice sheets such as Greenland, and (ii) the snow and ice physics in most GCMs does not include ice-sheet-specific processes such as the refreezing of meltwater. Two techniques are described that attack these problems, involving (i) an elevation-based correction to the surface meteorology and (ii) a simple a posteriori correction for the refreezi...

Geological and geochemical evidence for discriminating anatectic and subsolidus migmatites in the Dabieshan Complex, northeastern Hubei Province

Based on the geological and geochemical information about migmatites, the following lines of evidence have been proposed for discriminating the anatectic leucosome in the Dabieshan Complex: (1) its width is larger than that derived from the subsolidus genesis, cutting across regional foliation, thus giving rise to complicated folds and wider selvages; (2) it is composed of melanic and accessory minerals in addition to quartz and feldspars; (3) the significant difference in anorthites of plagioclase between paleosome and leucosome; (4) temperature and pressure (P/T) conditions revealed by the mineral compositions and assemblages are over those for the onset of anatexis; and (5) it is enriched in the major elements (e.g. Al2O3, Fe2O3 and TiO2) and immobile and incompatible elements (e.g. LREE, Th, Hf and Zr). Finally, by combining the geological and geochemical features with the statistical data for the spatial distribution of minerals and mass-balance in the migmatites, it is concluded that anatexis is the cardinal mechanism of migmatization in the Dabieshan Complex.

Snow-accumulation distribution in the interior of the Lambert Glacier basin, Antarctica

A prime input variable to uncoupled ice-sheet models, or for estimating the mass budget of present-day ice sheets, is the distribution of net surface mass balance. In most eases this is extrapolated from relatively few direct measurements over a limited time period, and parameterised in terms of continentality, surface elevation and other broad-scale indicators. Between 1989 and 1995 a series of oversnow traverses around the interior of the Lambert Glacier basin gathered a comprehensive set of data on snow accumulation and surface properties, surface climatology, ice-sheet velocities, elevations and thicknesses. Above the 2000 m level accumulation averages were found to be 76 kg ma−2a−1(σ= 74), much lower than at similar elevations in Wilkes Land. The traverse route contains three distinct accumulation regimes: a relatively high accumulation zone along the western side despite higher average elevations, a very low accumulation zone in the south due to the effect of inereased continentality and an eastern sector that exhibits a rain-shadow effect in predominantly easterly wind fields. Inter-annual variability is high- with 1993 a colder year, recording only half the longer term average accumulation over the portion of the route that was measured.

A Distributive Mass Balance Correction in Single- and Multigrid Incompressible Flow Calculation

The pressure-velocity coupling in a finite volume method (SIMPLE-type) is enhanced using a distributed mass balance correction method. The mass imbalance generated by the momentum equations is distributed over all control volumes prior to solving the pressure-correction equation. This method considerably enhances the convergence of the SIMPLE method, whether used on either a single staggered grid or a collocated multigrid. Some simple two- and three-dimensional laminar flows are used to test the method.

Infiltration and Solute Transport Experiments in Unsaturated Sand and Gravel, Cape Cod, Massachusetts: Experimental Design and Overview of Results

A series of infiltration and tracer experiments was conducted in unsaturated sand and gravel deposits on Cape Cod, Massachusetts. A network of 112 porous cup lysimeters and 168 time domain reflectometry (TDR) probes was deployed at depths from 0.25 to 2.0 m below ground surface along the centerline of a 2‐m by 10‐m test plot. The test plot was irrigated at rates ranging from 7.9 to 37.0 cm h−1 through a sprinkler system. Transient and steady state water content distributions were monitored with the TDR probes and spatial properties of water content distributions were determined from the TDR data. The spatial variance of the water content tended to increase as the average water content increased. In addition, estimated horizontal correlation length scales for water content were significantly smaller than those estimated by previous investigators for saturated hydraulic conductivity. Under steady state flow conditions at each irrigation rate, a sodium chloride solution was released as a tracer at ground surface and tracked with both the lysimeter and TDR networks. Transect‐averaged breakthrough curves at each monitoring depth were constructed both from solute concentrations measured in the water samples and flux concentrations inferred from the TDR measurements. Transport properties, including apparent solute velocities, dispersion coefficients, and total mass balances, were determined independently from both sets of breakthrough curves. The dispersion coefficients tended to increase with depth, reaching a constant value with the lysimeter data and appearing to increase continually with the TDR data. The variations with depth of the solute transport parameters, along with observations of water and solute mass balance and spatial distributions of water content, provide evidence of significant three‐dimensional flow during the irrigation experiments. The TDR methods are shown to efficiently provide dense spatial and temporal data sets for both flow and solute transport in unsaturated sediments with minimal sediment and flow field disturbance. Combined implementation of lysimeters and TDR probes can enhance data interpretation particularly when three‐dimensional flow conditions are anticipated.

Mass-balance variability as a base for interpreting ice-core data

The spatial extrapolation of data from ice cores depends on the complexity of the glacier system where the drilling site is located. The correlation between net mass balance, b n, of a specific point and of the whole glacier is different for each point. Analysis of net mass balance of Tuyuksu glacier in the Tien Shan, central Asia, confirms that the distribution of mass balance with height is more-or-less constant from year to year except in years with extreme values b n. Two types of “similarity” are described, additive and multiplicative. The “similarity” changes gradually from additive at the peripheral parts of the Tien Shan to multiplicative in the most continental central and eastern parts. Glacier mass-balance fluctuations of the frontal ridges are connected to the oscillations of accumulation and consequently to precipitation. Where the climate is more continental the mass-balance variability depends much more on the melting conditions than on accumulation. For the spatial interpretation of ice-core drilling results, a special analysis of “similarity type” is necessary. It allows the fixing of the spatial borders of the glacier system for which the dhilling site is representative.

Mass-balance variability as a base for interpreting ice-core data

The spatial extrapolation of data from ice cores depends on the complexity of the glacier system where the drilling site is located. The correlation between net mass balance, bn, of a specific point and of the whole glacier is different for each point. Analysis of net mass balance of Tuyuksu glacier in the Tien Shan, central Asia, confirms that the distribution of mass balance with height is more-or-less constant from year to year except in years with extreme values bn. Two types of “similarity” are described, additive and multiplicative. The “similarity” changes gradually from additive at the peripheral parts of the Tien Shan to multiplicative in the most continental central and eastern parts. Glacier mass-balance fluctuations of the frontal ridges are connected to the oscillations of accumulation and consequently to precipitation. Where the climate is more continental the mass-balance variability depends much more on the melting conditions than on accumulation. For the spatial interpretation of ice-core drilling results, a special analysis of “similarity type” is necessary. It allows the fixing of the spatial borders of the glacier system for which the dhilling site is representative.