scholarly journals Volume-area scaling for debris-covered glaciers

2020 ◽  
Vol 66 (259) ◽  
pp. 880-886
Author(s):  
Argha Banerjee

AbstractA volume-area scaling relation is commonly used to estimate glacier volume or its future changes on a global scale. The presence of an insulating supraglacial debris cover alters the mass-balance profile of a glacier, potentially modifying the scaling relation. Here, the nature of scaling relations for extensively debris-covered glaciers is investigated. Theoretical arguments suggest that the volume-area scaling exponent for these glaciers is ~7% smaller than that for clean glaciers. This is consistent with the results from flowline-model simulations of idealised glaciers, and the available data from the Himalaya. The best-fit scale factor for debris-covered Himalayan glaciers is ~60% larger compared to that for the clean ones, implying a significantly larger stored ice volume in a debris-covered glacier compared to a clean one having the same area. These results may help improve scaling-based estimates of glacier volume and future glacier changes in regions where debris-covered glaciers are abundant.

2013 ◽  
Vol 9 (6) ◽  
pp. 6161-6178 ◽  
Author(s):  
L. Zhao ◽  
J. Xu ◽  
A. M. Powell Jr.

Abstract. Using the fifth Coupled Model Intercomparison Project (CMIP5) model simulations and two observational datasets, the surface temperature trends and their discrepancies have been examined. The temporal-spatial characteristics for the surface temperature trends are discussed. Different from a constant estimated linear trend for the entire simulation period of 1850–2012, a dynamical trend using running linear least squares fitting with the moving 10 yr time windows are calculated. The results show that the CMIP5 model simulations are generally in good agreement with the observational measurements for the global scale warming, but the temperature trends depend on the temporal change and the regional differences. Generally, contrary to the small discrepancies on the global scale, the large discrepancies are observed in the south- and north-polar regions and other sub-regions.


2010 ◽  
Vol 4 (4) ◽  
pp. 2593-2613 ◽  
Author(s):  
T. Bolch ◽  
T. Pieczonka ◽  
D. I. Benn

Abstract. Mass loss of Himalayan glaciers has wide-ranging consequences such as declining water resources, sea level rise and an increasing risk of glacial lake outburst floods (GLOFs). The assessment of the regional and global impact of glacier changes in the Himalaya is, however, hampered by a lack of mass balance data for most of the range. Multi-temporal digital terrain models (DTMs) allow glacier mass balance to be calculated since the availability of stereo imagery. Here we present the longest time series of mass changes in the Himalaya and show the high value of early stereo spy imagery such as Corona (years 1962 and 1970) aerial images and recent high resolution satellite data (Cartosat-1) to calculate a time series of glacier changes south of Mt. Everest, Nepal. We reveal that the glaciers are significantly losing mass with an increasing rate since at least ~1970, despite thick debris cover. The specific mass loss is 0.32 ± 0.08 m w.e. a−1, however, not higher than the global average. The spatial patterns of surface lowering can be explained by variations in debris-cover thickness, glacier velocity, and ice melt due to exposed ice cliffs and ponds.


2016 ◽  
Vol 9 (1) ◽  
pp. 283-305 ◽  
Author(s):  
M. F. McCabe ◽  
A. Ershadi ◽  
C. Jimenez ◽  
D. G. Miralles ◽  
D. Michel ◽  
...  

Abstract. Determining the spatial distribution and temporal development of evaporation at regional and global scales is required to improve our understanding of the coupled water and energy cycles and to better monitor any changes in observed trends and variability of linked hydrological processes. With recent international efforts guiding the development of long-term and globally distributed flux estimates, continued product assessments are required to inform upon the selection of suitable model structures and also to establish the appropriateness of these multi-model simulations for global application. In support of the objectives of the Global Energy and Water Cycle Exchanges (GEWEX) LandFlux project, four commonly used evaporation models are evaluated against data from tower-based eddy-covariance observations, distributed across a range of biomes and climate zones. The selected schemes include the Surface Energy Balance System (SEBS) approach, the Priestley–Taylor Jet Propulsion Laboratory (PT-JPL) model, the Penman–Monteith-based Mu model (PM-Mu) and the Global Land Evaporation Amsterdam Model (GLEAM). Here we seek to examine the fidelity of global evaporation simulations by examining the multi-model response to varying sources of forcing data. To do this, we perform parallel and collocated model simulations using tower-based data together with a global-scale grid-based forcing product. Through quantifying the multi-model response to high-quality tower data, a better understanding of the subsequent model response to the coarse-scale globally gridded data that underlies the LandFlux product can be obtained, while also providing a relative evaluation and assessment of model performance. Using surface flux observations from 45 globally distributed eddy-covariance stations as independent metrics of performance, the tower-based analysis indicated that PT-JPL provided the highest overall statistical performance (0.72; 61 W m−2; 0.65), followed closely by GLEAM (0.68; 64 W m−2; 0.62), with values in parentheses representing the R2, RMSD and Nash–Sutcliffe efficiency (NSE), respectively. PM-Mu (0.51; 78 W m−2; 0.45) tended to underestimate fluxes, while SEBS (0.72; 101 W m−2; 0.24) overestimated values relative to observations. A focused analysis across specific biome types and climate zones showed considerable variability in the performance of all models, with no single model consistently able to outperform any other. Results also indicated that the global gridded data tended to reduce the performance for all of the studied models when compared to the tower data, likely a response to scale mismatch and issues related to forcing quality. Rather than relying on any single model simulation, the spatial and temporal variability at both the tower- and grid-scale highlighted the potential benefits of developing an ensemble or blended evaporation product for global-scale LandFlux applications. Challenges related to the robust assessment of the LandFlux product are also discussed.


1999 ◽  
Vol 45 (149) ◽  
pp. 17-21 ◽  
Author(s):  
David B. Bahr ◽  
Mark Dyurgerov

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.


The Holocene ◽  
2016 ◽  
Vol 27 (1) ◽  
pp. 164-171 ◽  
Author(s):  
Tron Laumann ◽  
Atle Nesje

Over the recent decades, glaciers have in general continued to lose mass, causing surface lowering, volume reduction and frontal retreat, thus contributing to global sea-level rise. When making assessments of present and future sea-level change and management of water resources in glaciated catchments, precise estimates of glacier volume are important. The glacier volume cannot be measured on every single glacier. Therefore, the global glacier volume must be estimated from models or scaling approaches. Volume–area scaling is mostly applied for estimating volumes of glaciers and ice caps on a regional and global scale by using a statistical–theoretical relationship between glacier volume ( V) and area ( A) ( V =  cAγ) (for explanation of the parameters c and γ, see Eq. 1). In this paper, a two-dimensional (2D) glacier model has been applied on four Norwegian ice caps (Hardangerjøkulen, Nordre Folgefonna, Spørteggbreen and Vestre Svartisen) in order to obtain values for the volume–area relationship on ice caps. The curve obtained for valley glaciers gives the best fit to the smallest plateau glaciers when c = 0.027 km3−2 γ and γ = 1.375, and a slightly poorer fit when the glacier increases in size. For ice caps, c = 0.056 km3−2 γ and γ = 1.25 fit reasonably well for the largest, but yield less fit to the smaller.


2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Tingting Sun ◽  
Yunxin Gen ◽  
Hujun Xie ◽  
Zhouting Jiang ◽  
Zhiyong Yang

The translocation of a polymer chain through a crowded cylindrical channel is studied using the Langevin dynamics simulations. The influences of the field strength F, the chain length N, and the crowding extent ρ on the translocation time are evaluated, respectively. Scaling relation τ~F-α is observed. With the crowding extent ρ increasing, the scaling exponent α becomes large. It is found that, for noncrowded channel, translocation probability drops when the field strength becomes large. However, for high-crowded channel, it is the opposite. Moreover, the translocation time and the average translocation time for all segments both have exponential growth with the crowding extent. The investigation of shape factor δ shows maximum value with increasing of the number of segments outside s. At last, the number of segments inside channel Nin in the process of translocation is calculated and a peak is observed. All the information from the study may benefit protein translocation.


2012 ◽  
Vol 57 (9) ◽  
pp. 964
Author(s):  
A.I. Ivanitskyi ◽  
K.A. Bugaev

The critical exponents α, α', β, γ', and δ of the model of quark-gluon bags with surface tension are found as functions of the most general model parameters. Two versions of the model that generate the phase diagram of the strongly interacting matter with critical or tricritical endpoint, respectively, are considered. The analysis of the relations between the critical exponents (scaling laws) shows that the scaling can be violated in a general case. The question whether it is possible to restore the scaling laws with the help of the Fisher definition of the α's exponent and its generalizations α'c and α'm is studied. It is shown that the Fisher scaling relation can be recovered with the help of the generalizations α'c and α'm, whereas no definition of the α' index is able to recover the Griffiths scaling relation in its traditional form. It is explicitly demonstrated that the additional condition α = α' is not sufficient to restore the Griffiths scaling relation in the traditional form. A generalization of this scaling relation which is valid for all known models is suggested. The obtained results allow us to conclude on the possible existence of the non-Fisher universality classes, for which the traditional scaling relations can be violated, whereas the generalized scaling laws can be established.


1999 ◽  
Vol 45 (149) ◽  
pp. 17-21
Author(s):  
David B. Bahr ◽  
Mark Dyurgerov

Abstract Previous 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.


Water ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 623 ◽  
Author(s):  
Jing He ◽  
Ninglian Wang ◽  
An’an Chen ◽  
Xuewen Yang ◽  
Ting Hua

Glaciers in the Qilian Mountains are important sources of fresh-water for sustainable development in the Hexi Corridor in the arid northwest China. Over the last few decades, glaciers have generally shrunk across the globe due to climate warming. In order to understand the current state of glaciers in the Qilian Mountains, we compiled a new inventory of glaciers in the region using Landsat Operational Land Imager (OLI) images acquired in 2015, and identified 2748 glaciers that covered an area of 1539.30 ± 49.50 km2 with an ice volume of 81.69 ± 7.40 km3, among which the Shule River basin occupied the largest portion of glaciers (24.8% in number, 32.3% in area, and 35.6% in ice volume). In comparison to previous inventories, glacier area was found to shrink by 396.89 km2 (20.5%) in total, and 446 glaciers with an area of 44.79 km2 disappeared over the period from the 1960s to 2015. This situation was primarily caused by the increase in air temperature, and also related with the size of glacier and some local topographic parameters. In addition, the change of glaciers in the Qilian Mountains showed a distinct spatial pattern, i.e., their shrinking rate was large in the east and small in the west.


2015 ◽  
Vol 26 (03) ◽  
pp. 1550029 ◽  
Author(s):  
Semra Gündüç

A model of opinion dynamics with two types of agents as social actors are presented, using the Ising thermodynamic model as the dynamics template. The agents are considered as opportunists which live at sites and interact with the neighbors, or fanatics/missionaries which move from site to site randomly in persuasion of converting agents of opposite opinion with the help of opportunists. Here, the moving agents act as an external influence on the opportunists to convert them to the opposite opinion. It is shown by numerical simulations that such dynamics of opinion formation may explain some details of consensus formation even when one of the opinions are held by a minority. Regardless the distribution of the opinion, different size societies exhibit different opinion formation behavior and time scales. In order to understand general behavior, the scaling relations obtained by comparing opinion formation processes observed in societies with varying population and number of randomly moving agents are studied. For the proposed model two types of scaling relations are observed. In fixed size societies, increasing the number of randomly moving agents give a scaling relation for the time scale of the opinion formation process. The second type of scaling relation is due to the size dependent information propagation in finite but large systems, namely finite-size scaling.


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