Glacier Length Research Articles

Characteristic mass-balance scaling with valley glacier size

AbstractPrevious work on the relation between glacier volume and area and on accumulation area ratios suggests that balance rates measured at the glacier terminus are not constant or random from glacier to glacier but instead scale with glacier length. Using mass-balance data from a collection of 68 valley and cirque glaciers, we show that the terminus mass-balance rate scales roughly linearly with surface area and scales with length raised to an exponent constrained to fall roughly between 0.5 and 2 with 1.7 preferred if a glacier’s length is dependent on the mass-balance conditions (rather than balance being dependent on length). When these exponents are used to predict valley-glacier volume–area scaling, the results are very close to empirical volume–area observations. Although the data are noisy and the proposed fits could be modified by improved observations, the scaling trend for terminus balance vs length remains clear. Although the exact value of the scaling exponent is not well determined, establishing the existence of this scaling relation will be important for studies of climate change and the impact of glacier recession on sea level.

Characteristic mass-balance scaling with valley glacier size

AbstractPrevious work on the relation between glacier volume and area and on accumulation area ratios suggests that balance rates measured at the glacier terminus are not constant or random from glacier to glacier but instead scale with glacier length. Using mass-balance data from a collection of 68 valley and cirque glaciers, we show that the terminus mass-balance rate scales roughly linearly with surface area and scales with length raised to an exponent constrained to fall roughly between 0.5 and 2 with 1.7 preferred if a glacier’s length is dependent on the mass-balance conditions (rather than balance being dependent on length). When these exponents are used to predict valley-glacier volume–area scaling, the results are very close to empirical volume–area observations. Although the data are noisy and the proposed fits could be modified by improved observations, the scaling trend for terminus balance vs length remains clear. Although the exact value of the scaling exponent is not well determined, establishing the existence of this scaling relation will be important for studies of climate change and the impact of glacier recession on sea level.

Decadal and millennial velocities of rock glaciers, selwyn mountains, canada

We compare surface velocities of nine rock glaciers over decadal and millennial time scales using independently derived velocities. We surveyed 15 rock glaciers in the Selwyn Mountains in 1983 and again in 1995, thereby obtaining 12‐year average velocities. We also determined millennial scale velocities using lichenometric ages and rock glacier length on nine of the 15 rock glaciers for which lichenometric ages were available. The mean surveyed velocity of the nine rock glaciers was 0.20 ± 0.11 m/yr, and the mean age—length velocity was 0.20 ± 0.13 m/yr. A paired t‐test of the two independently derived data sets shows no difference at the 0.01 level of significance. Given that both measures have inherent errors, the decadal and millennial velocities should be considered as being the same order of magnitude. The similarity of results of these two independent methods suggests that (1) decadal scale velocities of rock glaciers are comparable to millennial scale velocities in this area, and (2) either method can resolve long‐term velocities.We examined surveyed velocities in relation to rock glacier characteristics in order to identify controls on velocities. Surface velocity is expected to vary with density, the sine of surface slope, thickness and temperature. Rock glaciers facing NE were significantly longer and moved faster than rock glaciers facing other directions. This may be due to greater snow, ice and debris accumulation causing increased mass. Maximum surveyed velocity was significantly correlated with rock glacier thickness (r2= 0.88) and with the sine of surface slope (r2= 0.50), when one and two outliers were excluded from analyses, respectively. Future work focusing on the systematic measurement of the dimensions, age, and velocities of rock glaciers should help to improve our understanding of controls on velocities of rock glaciers.

The incidence of glacier surging in Svalbard: evidence from multivariate statistics

Surge-type glaciers switch between long periods of slow flow and short periods of fast flow. The spatial distribution of surge-type glaciers is markedly non-random. The clustering of surge-type glaciers in certain glaciated regions and their complete absence from other regions, suggests that environmental factors control surging. To identify factors that control surging, the relationship between surging, glacial variables and geological environment was tested using logit regression models. In the analysis we used 132 surge-type and 372 normal glaciers identified from the literature and aerial photographs in the High Arctic archipelago of Svalbard. We calculated that approximately 13% of the glaciers of Svalbard are of surge-type. In the analysis we used 13 variables collected from glacier inventories and geology maps. Variables that are significantly associated with surging in Svalbard are glacier length, surface slope and the lithology of the underlying bedrock. Multivariate analyses show that long glaciers overlying shale or mudstone with steep surface slopes have the highest probabilities of surging. Surge-type glaciers are significantly less likely to overlie rocks older than Devonian. These findings do not support Kamb's linked cavity theory of surging but lend some support to soft-bed surge theories.

Modelling the response of glaciers to climate warming

Dynamic ice-flow models for 12 glaciers and ice caps have been forced with various climate change scenarios. The volume of this sample spans three orders of magnitude. Six climate scenarios were considered: from 1990 onwards linear warming rates of 0.01, 0.02 and 0.04 K a-1, with and without concurrent changes in precipitation. The models, calibrated against the historic record of glacier length where possible, were integrated until 2100. The differences in individual glacier responses are very large. No straightforward relationship between glacier size and fractional change of ice volume emerges for any given climate scenario. The hypsometry of individual glaciers and ice caps plays an important role in their response, thus making it difficult to generalize results. For a warming rate of 0.04 K a-1, without increase in precipitation, results indicate that few glaciers would survive until 2100. On the other hand, if the warming rate were to be limited to 0.01 K a-1 with an increase in precipitation of 10% per degree warming, we predict that overall loss would be restricted to 10 to 20% of the 1990 volume.

Sensitivity of Rhonegletscher, Switzerland, to climate change: experiments with a one-dimensional flowline model

AbstractA one-dimensional time-dependent flowline model of Rhonegletscher, Switzerland, has been used to test the glacier’s response to climatic warming. Mass-balance variations over the last 100 years are obtained from observations of the equilibrium-line altitude (ELA) and a reconstruction of the ELA based on a statistical correlation between temperature and ELA. For the period prior to AD 1882, for which no reliable climate data exist, we chose equilibrium-line altitudes that enabled us to simulate accurately the glacier length from AD 1602.The model simulates the historical glacier length almost perfectly and glacier geometry very well. It underestimates glacier-surface velocities by 1-18%. Following these reference experiments, we investigated the response of Rhonegletscher to a number of climate-change scenarios for the period AD 1990-2100. For a constant climate equal to the 1961-90 mean, the model predicts a 6% decrease in glacier volume by AD 2100. Rhonegletscher will retreat by almost 1 km over the next 100 years at this scenario. At a warming rate of 0.04 K a-1, only 4% of the glacier volume will be left by AD 2100.

Sensitivity of Rhonegletscher, Switzerland, to climate change: experiments with a one-dimensional flowline model

AbstractA one-dimensional time-dependent flowline model of Rhonegletscher, Switzerland, has been used to test the glacier’s response to climatic warming. Mass-balance variations over the last 100 years are obtained from observations of the equilibrium-line altitude (ELA) and a reconstruction of the ELA based on a statistical correlation between temperature and ELA. For the period prior to AD 1882, for which no reliable climate data exist, we chose equilibrium-line altitudes that enabled us to simulate accurately the glacier length from AD 1602.The model simulates the historical glacier length almost perfectly and glacier geometry very well. It underestimates glacier-surface velocities by 1-18%. Following these reference experiments, we investigated the response of Rhonegletscher to a number of climate-change scenarios for the period AD 1990-2100. For a constant climate equal to the 1961-90 mean, the model predicts a 6% decrease in glacier volume by AD 2100. Rhonegletscher will retreat by almost 1 km over the next 100 years at this scenario. At a warming rate of 0.04 K a-1, only 4% of the glacier volume will be left by AD 2100.

Holocene Glacier Advances in the Topolovaya Valley, Bystrinskiy Range, Kamchatka, Russia, Dated by Tephrochronology ana Lichenometry

Two moraine sequences in one of the ice-free cirques in Topolovaya valley located above the cirque threshold at altitudes of about 700–800 m are dated by tephrochronology and lichenometry. Prominent advances of the glaciers occurred twice prior to 7600–7700 yr BP; and at approximately 2200–2600, 1900–2300(?), and 800–1100(?) lichenometric (L) years ago. The glacier fluctuations over the Holocene were of small magnitude (length of glaciers did not exceed 1 km, equilibrium-line altitude [ELA] varied between 850 and 1100 m) as compared with those of the Last Glacial Maximum (8 km long glacier, ELA at approximately 600 m). Early Holocene advances were more extensive than Neoglacial advances. Because of the great variability of modern ELAs in Kamchatka (from 2700–2900 to 600–700 m), the reconstructed ELAs in Topolovaya valley should be considered as representative only for southern Kamchatka. A hypothesis for formation of rock glaciers from lateral moraines is considered in the paper. A new Rhizocarpon geographicum (L.) DC growth curve is established, which may be applied to dating other glacial deposits in Kamchatka.

Climate Sensitivity of Franz Josef Glacier, New Zealand, as Revealed by Numerical Modeling

The sensitivity of Franz Josef Glacier is studied with a numerical ice-flow model. The model calculates ice mass flux along a central flow line and deals with the three-dimensional geometry in a parameterized way. Forcing is provided through a mass balance model that generates specific balance from climatological input data. Because of the very large mass turnover, e-folding response times are short: about 15 yr for ice volume and about 25 yr for glacier length. The sensitivity of glacier length to uniform warming is about 1.5 km K−1. The sensitivity to uniform changes in precipitation is about 0.05 km %—1, implying that a 30% increase in precipitation would be needed to compensate for a 1 K warming.

Climate Sensitivity of Franz Josef Glacier, New Zealand, as Revealed by Numerical Modeling

The sensitivity of Franz Josef Glacier is studied with a numerical ice-flow model. The model calculates ice mass flux along a central flow line and deals with the three-dimensional geometry in a parameterized way. Forcing is provided through a mass balance model that generates specific balance from climatological input data. Because of the very large mass turnover, e-folding response times are short: about 15 yr for ice volume and about 25 yr for glacier length. The sensitivity of glacier length to uniform warming is about 1.5 km K-1. The sensitivity to uniform changes in precipitation is about 0.05 km %-1 , implying that a 30% increase in precipitation would be needed to compensate for a 1 K warming.

A flowline model for Nigardsbreen, Norway: projection of future glacier length based on dynamic calibration with the historic record

Historic glacier-length variations are used to constrain a computer model for Nigardsbreen, Norway. A mass-balance history is derived that, when imposed on the flow model, gives an almost perfect match between observed and simulated glacier length since AD 1748. Being calibrated with past changes, the model predicts an 800 m advance of the glacier snout if mass-balance conditions remain as they were for the period 1962–93. Several greenhouse-warming scenarios are imposed to project the glacier’s behaviour into the next century. For a uniform heating rate of 0.02 K a–1, Nigardsbreen would advance slightly until AD 2020, but then a very rapid retreat would start: in AD 2100 glacier volume would be only 10% of the 1950 volume.

A flowline model for Nigardsbreen, Norway: projection of future glacier length based on dynamic calibration with the historic record

Historic glacier-length variations are used to constrain a computer model for Nigardsbreen, Norway. A mass-balance history is derived that, when imposed on the flow model, gives an almost perfect match between observed and simulated glacier length since AD 1748. Being calibrated with past changes, the model predicts an 800 m advance of the glacier snout if mass-balance conditions remain as they were for the period 1962–93. Several greenhouse-warming scenarios are imposed to project the glacier’s behaviour into the next century. For a uniform heating rate of 0.02 K a–1, Nigardsbreen would advance slightly until AD 2020, but then a very rapid retreat would start: in AD 2100 glacier volume would be only 10% of the 1950 volume.

Modern and Little Ice Age glaciers in “humid” and “arid” areas of the Tien Shan, Central Asia: two different patterns of fluctuation

Patterns of retreat from maximum Little Ice Age (LIA) to present limits are studied at 20 glaciers in the relatively humid northwestern front ranges and arid inner areas of the Tien Shan, Central Asia. The depression of equilibrium-line altitudes has been calculated using several approaches. Data on changes of elevation ranges, glacier length and area are used to compare the patterns of glacier fluctuation. It is found that the large LIA glaciers in the warm and humid northwestern frontal ranges were 1.5–1.9 times larger in area than the modern glaciers; and the LIA glaciers in cold and arid inner parts of the Tien Shan were only 1.03–1.07 times larger. The changes in terminus-to-headwall elevation ranges are about 1.3–1.6 and 1.02–1.10, respectively. The largest LIA glaciers were 1.4–1.9 times longer than modern glaciers in “humid” ranges and only 1.02–1.12 times longer in “arid” areas. The maximum equilibrium-line depressions are approximately 100–200 m in “humid”areas and 20–50 m in “arid”areas. These results suggest that the glaciers in the “humid” areas are likely to be more variable than those in “arid” areas. The differences may be explained either by differences in the sensitivity of glaciers to climate change or by variability of climate signals from one area to another.

Modern and Little Ice Age glaciers in “humid” and “arid” areas of the Tien Shan, Central Asia: two different patterns of fluctuation

Patterns of retreat from maximum Little Ice Age (LIA) to present limits are studied at 20 glaciers in the relatively humid northwestern front ranges and arid inner areas of the Tien Shan, Central Asia. The depression of equilibrium-line altitudes has been calculated using several approaches. Data on changes of elevation ranges, glacier length and area are used to compare the patterns of glacier fluctuation. It is found that the large LIA glaciers in the warm and humid northwestern frontal ranges were 1.5–1.9 times larger in area than the modern glaciers; and the LIA glaciers in cold and arid inner parts of the Tien Shan were only 1.03–1.07 times larger. The changes in terminus-to-headwall elevation ranges are about 1.3–1.6 and 1.02–1.10, respectively. The largest LIA glaciers were 1.4–1.9 times longer than modern glaciers in “humid” ranges and only 1.02–1.12 times longer in “arid” areas. The maximum equilibrium-line depressions are approximately 100–200 m in “humid”areas and 20–50 m in “arid”areas. These results suggest that the glaciers in the “humid” areas are likely to be more variable than those in “arid” areas. The differences may be explained either by differences in the sensitivity of glaciers to climate change or by variability of climate signals from one area to another.

Width and length scaling of glaciers

AbstractAn analysis of hundreds of mountain and valley glaciers in the former Soviet Union and the Alps shows that characteristic glacier widths scale as characteristic glacier lengths raised to an exponent of 0.6. This is in contrast to most previous analyses which implicitly of explicitly assumed scaling exponents of either 0 or 1. The exponent 0.6 implies that average glacier widths are proportional to average glacier thicknesses. Although this seems to suggest V-shaped glacier valleys, the linear width-thickness relationship is not inconsistent with parabolic valley cross-sections, because the characteristic (or average) width of a glacier depends on many other aspects of channel and glacier morphology, including variations in the channel width with distance up- and downstream.

Width and length scaling of glaciers

AbstractAn analysis of hundreds of mountain and valley glaciers in the former Soviet Union and the Alps shows that characteristic glacier widths scale as characteristic glacier lengths raised to an exponent of 0.6. This is in contrast to most previous analyses which implicitly of explicitly assumed scaling exponents of either 0 or 1. The exponent 0.6 implies that average glacier widths are proportional to average glacier thicknesses. Although this seems to suggest V-shaped glacier valleys, the linear width-thickness relationship is not inconsistent with parabolic valley cross-sections, because the characteristic (or average) width of a glacier depends on many other aspects of channel and glacier morphology, including variations in the channel width with distance up- and downstream.

Controls on glacier surging in Svalbard

AbstractThe geographical distribution of surge-type glaciers worldwide displays a remarkably non-random pattern. Surge-type glaciers tend to be concentrated in certain glacierized areas and to be completely absent in others. This observation suggests that special conditions are required for surges to occur. However, the factors controlling the spatial occurrence of surge-type behaviour are not known. To investigate this problem we performed probability statistical analysis on a sample population of 615 glaciers in Svalbard. The probability that a glacier in the sample population is surge-type is 36.4%. Within the sampled area there is a spatial variation in the concentration of surge-type glaciers. Several geometric and environmental factors associated with glaciers in the sample population were measured and tested to determine if they are related to the probability of surging. Of the geometric factors tested (length, slope, elevation, orientation and presence or absence of tributaries), only glacier length is related to surging, with surge probability increasing with increasing length. Elevated probabilities of surging were also found for glaciers associated with sedimentary subglacial rocks and sub-polar thermal regimes. The distributions of related factors were used to predict the spatial distribution of surge-type glaciers. However, in each case the individual factors were unable to reproduce the observed pattern of surge-type glacier distribution.

Controls on glacier surging in Svalbard

Abstract The geographical distribution of surge-type glaciers worldwide displays a remarkably non-random pattern. Surge-type glaciers tend to be concentrated in certain glacierized areas and to be completely absent in others. This observation suggests that special conditions are required for surges to occur. However, the factors controlling the spatial occurrence of surge-type behaviour are not known. To investigate this problem we performed probability statistical analysis on a sample population of 615 glaciers in Svalbard. The probability that a glacier in the sample population is surge-type is 36.4%. Within the sampled area there is a spatial variation in the concentration of surge-type glaciers. Several geometric and environmental factors associated with glaciers in the sample population were measured and tested to determine if they are related to the probability of surging. Of the geometric factors tested (length, slope, elevation, orientation and presence or absence of tributaries), only glacier length is related to surging, with surge probability increasing with increasing length. Elevated probabilities of surging were also found for glaciers associated with sedimentary subglacial rocks and sub-polar thermal regimes. The distributions of related factors were used to predict the spatial distribution of surge-type glaciers. However, in each case the individual factors were unable to reproduce the observed pattern of surge-type glacier distribution.

Simulating the effects of mean annual air-temperature changes on permafrost distribution and glacier size: an example from the Upper Engadin, Swiss Alps

Models are developed to simulate changes in permafrost distribution and glacier size in mountain areas. The models exclusively consider equilibrium conditions. As a first application, the simplified assumption is used that one single parameter (mean annual air temperature) is changing. Permafrost distribution patterns are estimated for a test area (Corvatsch-Furtschellas) and for the whole Upper Engadin region (eastern Swiss Alps) using a relation between permafrost occurrence as indicated by BTS (bottom temperature of the winter snow cover) measurements, potential direct solar radiation and mean annual air temperature. Glacier sizes were assessed in the same region with data from the World Glacier Inventory database. The simulations for the glaciers are based on the assumption that an increase or decrease in equilibrium-line altitude (ELA) would lead to a mass-balance change. Model calculations for potential future changes in ELA and mass balance include estimated developments of area, length and volume. Mass changes were also calculated for the time period 1850–1973 on the basis of measured cumulative length change, glacier length and estimated ablation at the glacier terminus. For the time period since 1850, permafrost became inactive or disappeared in about 15% of the area originally underlain by permafrost in the whole Upper Engadin region, and mean annual glacier mass balance was calculated as −0.26 to −0.46 m w.e.a−1 for the larger glaciers in the same area. The estimated loss in glacier volume since 1850 lies between 55% and 66% of the original value. With an assumed increase in mean annual air temperature of +3°C, the area of supposed permafrost occurrence would possibly be reduced by about 65% with respect to present-day conditions and only three glaciers would continue to partially exist.

Simulating the effects of mean annual air-temperature changes on permafrost distribution and glacier size: an example from the Upper Engadin, Swiss Alps

Models are developed to simulate changes in permafrost distribution and glacier size in mountain areas. The models exclusively consider equilibrium conditions. As a first application, the simplified assumption is used that one single parameter (mean annual air temperature) is changing.Permafrost distribution patterns are estimated for a test area (Corvatsch-Furtschellas) and for the whole Upper Engadin region (eastern Swiss Alps) using a relation between permafrost occurrence as indicated by BTS (bottom temperature of the winter snow cover) measurements, potential direct solar radiation and mean annual air temperature. Glacier sizes were assessed in the same region with data from the World Glacier Inventory database. The simulations for the glaciers are based on the assumption that an increase or decrease in equilibrium-line altitude (ELA) would lead to a mass-balance change. Model calculations for potential future changes in ELA and mass balance include estimated developments of area, length and volume. Mass changes were also calculated for the time period 1850–1973 on the basis of measured cumulative length change, glacier length and estimated ablation at the glacier terminus.For the time period since 1850, permafrost became inactive or disappeared in about 15% of the area originally underlain by permafrost in the whole Upper Engadin region, and mean annual glacier mass balance was calculated as −0.26 to −0.46 m w.e.a−1 for the larger glaciers in the same area. The estimated loss in glacier volume since 1850 lies between 55% and 66% of the original value. With an assumed increase in mean annual air temperature of +3°C, the area of supposed permafrost occurrence would possibly be reduced by about 65% with respect to present-day conditions and only three glaciers would continue to partially exist.