scholarly journals A computer scheme for rapid calculations of balance-flux distributions

1996 ◽  
Vol 23 ◽  
pp. 21-27 ◽  
Author(s):  
W. F. Budd ◽  
R. C. Warner
Keyword(s):  
Steady State ◽  
Flow Direction ◽  
Grid Point ◽  
The State ◽  
Surface Velocity ◽  
Ice Flow ◽  
Direct Observations ◽  
Flow Through ◽  
Net Flux ◽  
Steady State Balance

A simple computer scheme developed by Budd and Smith (1985) and modified by D. Jenssen has been further developed to provide a rapid computation of steady-state balance fluxes over arbitrary ice masses, given the surface elevations and net accumulation distribution. The scheme provides a powerful diagnostic tool to examine the flux and state of balance over whole ice masses or limited regions to interpret field observations for dynamics or the state of balance. In many cases the uncertainty in the state of balance may be much less than the uncertainty in the deformation and sliding properties of the ice and so the flux and velocities derived from balance could provide a useful guide for the dynamics where direct observations are sparse. The scheme assumes that, on a horizontal scale of many ice thicknesses, the ice-flow direction is approximately down the steepest surface slope. The continuity equation is used to compute steady-state implied downslope fluxes at each grid point from integrations of the net accumulation over the area from the summits to the edges. The algorithm ensures the exact integral balance of the surface net flux over the area with flow through boundaries. Applications are demonstrated for the whole of Antarctica and for regional areas. Comparisons are made between fluxes computed from observed ice thicknesses and velocities and those computed from balance. The observed ice thicknesses can also be used to compute surface velocities from assumed column-to-surface velocity ratios. The combined fluxes from observations and balance can be used to compute rates of change of elevation with time.

scholarly journals A computer scheme for rapid calculations of balance-flux distributions

1996 ◽  
Vol 23 ◽  
pp. 21-27 ◽  
Author(s):  
W. F. Budd ◽  
R. C. Warner
Keyword(s):  
Steady State ◽  
Flow Direction ◽  
Grid Point ◽  
The State ◽  
Surface Velocity ◽  
Ice Flow ◽  
Direct Observations ◽  
Flow Through ◽  
Net Flux ◽  
Steady State Balance

A simple computer scheme developed by Budd and Smith (1985) and modified by D. Jenssen has been further developed to provide a rapid computation of steady-state balance fluxes over arbitrary ice masses, given the surface elevations and net accumulation distribution. The scheme provides a powerful diagnostic tool to examine the flux and state of balance over whole ice masses or limited regions to interpret field observations for dynamics or the state of balance.In many cases the uncertainty in the state of balance may be much less than the uncertainty in the deformation and sliding properties of the ice and so the flux and velocities derived from balance could provide a useful guide for the dynamics where direct observations are sparse.The scheme assumes that, on a horizontal scale of many ice thicknesses, the ice-flow direction is approximately down the steepest surface slope. The continuity equation is used to compute steady-state implied downslope fluxes at each grid point from integrations of the net accumulation over the area from the summits to the edges. The algorithm ensures the exact integral balance of the surface net flux over the area with flow through boundaries.Applications are demonstrated for the whole of Antarctica and for regional areas. Comparisons are made between fluxes computed from observed ice thicknesses and velocities and those computed from balance. The observed ice thicknesses can also be used to compute surface velocities from assumed column-to-surface velocity ratios. The combined fluxes from observations and balance can be used to compute rates of change of elevation with time.

scholarly journals Assessment of Recent Flow, and Calving Rate of the Perito Moreno Glacier Using LANDSAT and SENTINEL2 Images

2021 ◽  
Vol 14 (1) ◽  
pp. 52
Author(s):  
Daniele Bocchiola ◽  
Francesco Chirico ◽  
Andrea Soncini ◽  
Roberto Sergio Azzoni ◽  
Guglielmina Adele Diolaiuti ◽  
...  
Keyword(s):  
Flow Velocity ◽  
Landsat Imagery ◽  
Surface Velocity ◽  
Dam Failure ◽  
Correlation Technique ◽  
Ice Flow ◽  
Overall Stability ◽  
Glacier Front ◽  
Flow Through ◽  
Calving Rate

We mapped flow velocity and calving rates of the iconic Perito Moreno Glacier (PMG), belonging to the Southern Patagonian Icefield (SPI) in the Argentinian Patagonia. We tracked PMG from 2001 to 2017, focusing mostly upon the latest images from 2016–2017. PMG delivers about ca. 106 m3 day−1 of ice in the Lago Argentino, and its front periodically reaches the Peninsula Magallanes. Therein, the PMG causes an ice-dam, clogging Brazo Rico channel, and lifting water level by about 10 m, until ice-dam failure, normally occurring in March. Here, we used 36 pairs of satellite images with a resolution of 10 m (SENTINEL2, visible, 9 pairs of images) and 15 m (LANDSAT imagery, panchromatic, 27 pairs of images) to calculate surface velocity (VS). We used Orientation Correlation technique, implemented via the ImGRAFT® TemplateMatch tool. Calving rates were then calculated with two methods, namely, (i) M1, by ice flow through the glacier front, and (ii) M2, by ice flow at 7.5 km upstream of the front minus ablation losses. Surface velocity ranged from about 4 m day−1 in the accumulation area to about 2 m day−1 in the calving front, but it is variable seasonally with maxima in the summer (December–January–February). Calving rate (CRM) ranges from 7.72 × 105 ± 32% to 8.76 × 105 ± 31% m3 day−1, in line with recent studies, also with maxima in the summer. We found slightly lower flow velocity and calving rates than previously published values, but our estimates cover a different period, and a generally large uncertainty in flow assessment suggests a recent overall stability of the glacier.

scholarly journals The Causes of Debris-Covered Glacier Thinning: Evidence for the Importance of Ice Dynamics From Kennicott Glacier, Alaska

2021 ◽  
Vol 9 ◽  
Author(s):  
Leif S. Anderson ◽  
William H. Armstrong ◽  
Robert S. Anderson ◽  
Dirk Scherler ◽  
Eric Petersen
Keyword(s):  
Mass Balance ◽  
Flow Direction ◽  
Surface Velocity ◽  
Glacier Surface ◽  
Ice Dynamics ◽  
Ice Flow ◽  
Thickness Change ◽  
Air Temperatures ◽  
Compressive Flow ◽  
Wide Range

The cause of debris-covered glacier thinning remains controversial. One hypothesis asserts that melt hotspots (ice cliffs, ponds, or thin debris) increase thinning, while the other posits that declining ice flow leads to dynamic thinning under thick debris. Alaska’s Kennicott Glacier is ideal for testing these hypotheses, as ice cliffs within the debris-covered tongue are abundant and surface velocities decline rapidly downglacier. To explore the cause of patterns in melt hotspots, ice flow, and thinning, we consider their evolution over several decades. We compile a wide range of ice dynamical and mass balance datasets which we cross-correlate and analyze in a step-by-step fashion. We show that an undulating bed that deepens upglacier controls ice flow in the lower 8.5 km of Kennicott Glacier. The imposed velocity pattern strongly affects debris thickness, which in turn leads to annual melt rates that decline towards the terminus. Ice cliff abundance correlates highly with the rate of surface compression, while pond occurrence is strongly negatively correlated with driving stress. A new positive feedback is identified between ice cliffs, streams and surface topography that leads to chaotic topography. As the glacier thinned between 1991 and 2015, surface melt in the study area decreased, despite generally rising air temperatures. Four additional feedbacks relating glacier thinning to melt changes are evident: the debris feedback (negative), the ice cliff feedback (negative), the pond feedback (positive), and the relief feedback (positive). The debris and ice cliff feedbacks, which are tied to the change in surface velocity in time, likely reduced melt rates in time. We show this using a new method to invert for debris thickness change and englacial debris content (∼0.017% by volume) while also revealing that declining speeds and compressive flow led to debris thickening. The expansion of debris on the glacier surface follows changes in flow direction. Ultimately, glacier thinning upvalley from the continuously debris-covered portion of Kennicott Glacier, caused by mass balance changes, led to the reduction of flow into the study area. This caused ice emergence rates to decline rapidly leading to the occurrence of maximum, glacier-wide thinning under thick, insulating debris.

scholarly journals Subglacial roughness of the Greenland Ice Sheet: relationship with contemporary ice velocity and geology

2019 ◽  
Vol 13 (11) ◽  
pp. 3093-3115 ◽  
Author(s):  
Michael A. Cooper ◽  
Thomas M. Jordan ◽  
Dustin M. Schroeder ◽  
Martin J. Siegert ◽  
Christopher N. Williams ◽  
...  
Keyword(s):  
Flow Direction ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Flow Speed ◽  
Surface Velocity ◽  
Ice Flow ◽  
Systematic Analysis ◽  
Subglacial Environment ◽  
Topographic Roughness ◽  
Ice Surface

Abstract. The subglacial environment of the Greenland Ice Sheet (GrIS) is poorly constrained both in its bulk properties, for example geology, the presence of sediment, and the presence of water, and interfacial conditions, such as roughness and bed rheology. There is, therefore, limited understanding of how spatially heterogeneous subglacial properties relate to ice-sheet motion. Here, via analysis of 2 decades of radio-echo sounding data, we present a new systematic analysis of subglacial roughness beneath the GrIS. We use two independent methods to quantify subglacial roughness: first, the variability in along-track topography – enabling an assessment of roughness anisotropy from pairs of orthogonal transects aligned perpendicular and parallel to ice flow and, second, from bed-echo scattering – enabling assessment of fine-scale bed characteristics. We establish the spatial distribution of subglacial roughness and quantify its relationship with ice flow speed and direction. Overall, the beds of fast-flowing regions are observed to be rougher than the slow-flowing interior. Topographic roughness exhibits an exponential scaling relationship with ice surface velocity parallel, but not perpendicular, to flow direction in fast-flowing regions, and the degree of anisotropy is correlated with ice surface speed. In many slow-flowing regions both roughness methods indicate spatially coherent regions of smooth beds, which, through combination with analyses of underlying geology, we conclude is likely due to the presence of a hard flat bed. Consequently, the study provides scope for a spatially variable hard- or soft-bed boundary constraint for ice-sheet models.

scholarly journals Subglacial roughness of the Greenland Ice Sheet: relationship with contemporary ice velocity and geology

2019 ◽  
Author(s):  
Michael A. Cooper ◽  
Thomas M. Jordan ◽  
Dustin M. Schroeder ◽  
Martin J. Siegert ◽  
Christopher N. Williams ◽  
...  
Keyword(s):  
Flow Direction ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Flow Speed ◽  
Surface Velocity ◽  
Ice Flow ◽  
Systematic Analysis ◽  
Subglacial Environment ◽  
Topographic Roughness ◽  
Ice Surface

Abstract. The subglacial environment of the Greenland Ice Sheet (GrIS) is poorly constrained, both in its bulk properties, for example geology, presence of sediment, and of water, and interfacial conditions, such as roughness and bed rheology. There is, therefore, limited understanding of how spatially heterogeneous subglacial properties relate to ice-sheet motion. Here, via analysis of two decades worth of radio-echo sounding data, we present a new systematic analysis of subglacial roughness beneath the GrIS. We use two independent methods to quantify subglacial roughness: first, the variability of along- track topography—enabling an assessment of roughness anisotropy from pairs of orthogonal transects aligned perpendicular and parallel to ice flow; and second, from bed-echo scattering—enabling assessment of fine-scale bed characteristics. We establish the spatial distribution of subglacial roughness and quantify its relationship with ice flow speed and direction. Overall, the beds of fast-flowing regions are observed to be rougher than the slow-flowing interior. Topographic roughness exhibits an exponential scaling relationship with ice surface velocity parallel, but not perpendicular, to flow direction in fast-flowing regions, and the degree of anisotropy is correlated with ice surface speed. In many slow-flowing regions both roughness methods indicate spatially coherent regions of smooth bed, which, through combination with analyses of underlying geology, we conclude is likely due to the presence of a hard flat bed. Consequently, the study provides scope for a spatially variable hard bed/soft bed boundary constraint for ice-sheet models.

Combining SAR interferometry and the equation of continuity to estimate the three-dimensional glacier surface-velocity vector

1999 ◽  
Vol 45 (151) ◽  
pp. 533-538 ◽  
Author(s):  
Niels Reeh ◽  
Søren Nørvang Madsen ◽  
Johan Jakob Mohr
Keyword(s):  
Steady State ◽  
Mass Balance ◽  
Vertical Velocity ◽  
Velocity Vector ◽  
Thickness Distribution ◽  
Vertical Surface ◽  
Horizontal Velocity ◽  
Sar Interferometry ◽  
Surface Velocity ◽  
Ice Thickness

AbstractUntil now, an assumption of surface-parallel glacier flow has been used to express the vertical velocity component in terms of the horizontal velocity vector, permitting all three velocity components to be determined from synthetic aperture radar interferometry. We discuss this assumption, which neglects the influence of the local mass balance and a possible contribution to the vertical velocity arising if the glacier is not in steady state. We find that the mass-balance contribution to the vertical surface velocity is not always negligible as compared to the surface-slope contribution. Moreover, the vertical velocity contribution arising if the ice sheet is not in steady state can be significant. We apply the principle of mass conservation to derive an equation relating the vertical surface velocity to the horizontal velocity vector. This equation, valid for both steady-state and non-steady-state conditions, depends on the ice-thickness distribution. Replacing the surface-parallel-flow assumption with a correct relationship between the surface velocity components requires knowledge of additional quantities such as surface mass balance or ice thickness.

scholarly journals Advanced Constitutive Modeling of the Thixotropic Elasto-Visco-Plastic Behavior of Blood: Steady-State Blood Flow in Microtubes

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 367
Author(s):  
Konstantinos Giannokostas ◽  
Yannis Dimakopoulos ◽  
Andreas Anayiotos ◽  
John Tsamopoulos
Keyword(s):  
Blood Flow ◽  
Steady State ◽  
Constitutive Model ◽  
Blood Plasma ◽  
Constitutive Modeling ◽  
Flow Direction ◽  
Momentum Balance ◽  
Plastic Behavior ◽  
Flow Investigation ◽  
The Impact

The present work focuses on the in-silico investigation of the steady-state blood flow in straight microtubes, incorporating advanced constitutive modeling for human blood and blood plasma. The blood constitutive model accounts for the interplay between thixotropy and elasto-visco-plasticity via a scalar variable that describes the level of the local blood structure at any instance. The constitutive model is enhanced by the non-Newtonian modeling of the plasma phase, which features bulk viscoelasticity. Incorporating microcirculation phenomena such as the cell-free layer (CFL) formation or the Fåhraeus and the Fåhraeus-Lindqvist effects is an indispensable part of the blood flow investigation. The coupling between them and the momentum balance is achieved through correlations based on experimental observations. Notably, we propose a new simplified form for the dependence of the apparent viscosity on the hematocrit that predicts the CFL thickness correctly. Our investigation focuses on the impact of the microtube diameter and the pressure-gradient on velocity profiles, normal and shear viscoelastic stresses, and thixotropic properties. We demonstrate the microstructural configuration of blood in steady-state conditions, revealing that blood is highly aggregated in narrow tubes, promoting a flat velocity profile. Additionally, the proper accounting of the CFL thickness shows that for narrow microtubes, the reduction of discharged hematocrit is significant, which in some cases is up to 70%. At high pressure-gradients, the plasmatic proteins in both regions are extended in the flow direction, developing large axial normal stresses, which are more significant in the core region. We also provide normal stress predictions at both the blood/plasma interface (INS) and the tube wall (WNS), which are difficult to measure experimentally. Both decrease with the tube radius; however, they exhibit significant differences in magnitude and type of variation. INS varies linearly from 4.5 to 2 Pa, while WNS exhibits an exponential decrease taking values from 50 mPa to zero.

scholarly journals Steady State Response of Linear Time Invariant Systems Modeledby Multibond Graphs

2021 ◽  
Vol 11 (4) ◽  
pp. 1717
Author(s):  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Direct Determination ◽  
The State ◽  
Steady State Response ◽  
State Variables ◽  
Linear Time Invariant ◽  
State Response ◽  
Time Invariant

The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure of a multibond graph in an integral causality assignment (MBGI) to get the state space of the system is introduced. By assigning a derivative causality to the multiport storage elements, the multibond graph in a derivative causality (MBGD) is proposed. Based on this MBGD, a theorem to obtain the steady state response is presented. Two case studies to get the steady state of the state variables are applied. Both cases are modeled by multibond graphs, and the symbolic determination of the steady state is obtained. The simulation results using the 20-SIM software are numerically verified.

Approximating the stationary distribution of an infinite stochastic matrix

1991 ◽  
Vol 28 (1) ◽  
pp. 96-103 ◽  
Author(s):  
Daniel P. Heyman
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Stationary Distribution ◽  
Numerical Approximation ◽  
Stochastic Matrix ◽  
Sufficient Conditions ◽  
Finite System ◽  
Balance Equations ◽  
The Given ◽  
Steady State Balance

We are given a Markov chain with states 0, 1, 2, ···. We want to get a numerical approximation of the steady-state balance equations. To do this, we truncate the chain, keeping the first n states, make the resulting matrix stochastic in some convenient way, and solve the finite system. The purpose of this paper is to provide some sufficient conditions that imply that as n tends to infinity, the stationary distributions of the truncated chains converge to the stationary distribution of the given chain. Our approach is completely probabilistic, and our conditions are given in probabilistic terms. We illustrate how to verify these conditions with five examples.

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