scholarly journals Using Sequential Photography to Estimate Ice Velocity at the Terminus of Columbia Glacier, Alaska

1986 ◽  
Vol 8 ◽  
pp. 117-123 ◽  
Author(s):  
R.M. Krimmel ◽  
L.A. Rasmussen
Keyword(s):  
Time Resolution ◽  
Principal Direction ◽  
Film Plane ◽  
Time Sequence ◽  
Line Of Sight ◽  
Glacier Surface ◽  
Ice Flow ◽  
Straight Line ◽  
Camera Orientation ◽  
Ice Velocity

The terminus of Columbia Glacier, Alaska, was observed with a single automatic 35 mm camera to determine velocity with a time resolution in the order of a day. The photographic coordinates of the image of a target were then transformed linearly into the direction numbers of the line of sight from the camera to the target. The camera orientation was determined from the film-plane locations of known landmark points by using an adaption of vertical photogrammetry techniques. The line of sight, when intersected with some mathematically-defined glacier surface, defines the true space coordinates of a target, The time sequence of a target’s position was smoothed, first in horizontal x, y space to a straight line, then in y (the principal direction of ice flow) and time with a smoothing cubic spline, and then the x-component was computed from the y-component by considering the inclination of the straight line. This allows daily velocities (about 8 m/day) to be measured at a distance of 5 km, using a 105 mm lens. Errors in daily displacements were estimated to be 1 m. The terminus configuration was also measured using the same photo set.

scholarly journals Using Sequential Photography to Estimate Ice Velocity at the Terminus of Columbia Glacier, Alaska

1986 ◽  
Vol 8 ◽  
pp. 117-123 ◽  
Author(s):  
R.M. Krimmel ◽  
L.A. Rasmussen
Keyword(s):  
Time Resolution ◽  
Principal Direction ◽  
Film Plane ◽  
Time Sequence ◽  
Line Of Sight ◽  
Glacier Surface ◽  
Ice Flow ◽  
Straight Line ◽  
Camera Orientation ◽  
Ice Velocity

The terminus of Columbia Glacier, Alaska, was observed with a single automatic 35 mm camera to determine velocity with a time resolution in the order of a day. The photographic coordinates of the image of a target were then transformed linearly into the direction numbers of the line of sight from the camera to the target. The camera orientation was determined from the film-plane locations of known landmark points by using an adaption of vertical photogrammetry techniques. The line of sight, when intersected with some mathematically-defined glacier surface, defines the true space coordinates of a target, The time sequence of a target’s position was smoothed, first in horizontal x, y space to a straight line, then in y (the principal direction of ice flow) and time with a smoothing cubic spline, and then the x-component was computed from the y-component by considering the inclination of the straight line. This allows daily velocities (about 8 m/day) to be measured at a distance of 5 km, using a 105 mm lens. Errors in daily displacements were estimated to be 1 m. The terminus configuration was also measured using the same photo set.

scholarly journals On the Role of Mechanical Energy in Maintaining Subglacial Water Conduits at Atmospheric Pressure

1984 ◽  
Vol 30 (105) ◽  
pp. 180-187 ◽  
Author(s):  
Roger Leb. Hooke
Keyword(s):  
Atmospheric Pressure ◽  
Flow Direction ◽  
Mechanical Energy ◽  
Glacier Surface ◽  
Ice Flow ◽  
Small Perturbations ◽  
Point Pressure ◽  
Ice Velocity ◽  
Glacial Landforms

AbstractRecent theoretical studies of glacier hydrology have assumed that subglacial conduits are completely filled with water under steady-state conditions. This, however, is not necessarily the case. Where discharges are larger than a few tens of liters per second and the down-glacier slope of the bed is more than a few degrees, the potential energy released by water descending this slope may be capable of melting the walls of a subglacial conduit many times faster than the conduit can close by plastic flow of the ice. As a result, the pressure in such tunnels may normally be atmospheric, or possibly even at the triple-point pressure if there is no open connection to the glacier surface. Simple calculations suggest that such pressures in subglacial conduits may be more common than heretofore anticipated.The positions of such “open” conduits may be unstable to small perturbations in discharge or ice velocity. This is because the mechanical energy available in excess of that needed to balance closure can instead offset the general flow of the ice. Conduits can thus trend diagonally across the direction of ice flow. If an increase in the angle which such a conduit makes with the ice flow direction also results in an increase in slope of the conduit, more mechanical energy will become available, resulting in a positive feedback process.Subglacial channels at atmospheric pressure may influence the origin and morphology of certain glacial landforms, such as eskers and “plastically-molded” features.

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

1999 ◽  
Vol 45 (151) ◽  
pp. 575-583 ◽  
Author(s):  
Andreas Kääb ◽  
Martin Funk
Keyword(s):  
Pilot Study ◽  
Mass Balance ◽  
Surface Strain ◽  
Swiss Alps ◽  
Surface Velocity ◽  
Glacier Mass Balance ◽  
Glacier Surface ◽  
Ice Flow ◽  
Applied Model ◽  
Ice Velocity

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.

Glacier movement, ice structures, and medial moraine form at a glacier confluence, Berendon Glacier, British Columbia, Canada

1977 ◽  
Vol 14 (12) ◽  
pp. 2807-2816 ◽  
Author(s):  
N. Eyles ◽  
R. J. Rogerson
Keyword(s):  
British Columbia ◽  
Strain Rate ◽  
Lateral Compression ◽  
Ice Streams ◽  
Glacier Surface ◽  
Ice Flow ◽  
Contact Plane ◽  
Confluence Zone ◽  
Ice Velocity ◽  
Surface Ice

On Berendon Glacier, Canada, at the asymmetric Y junction of two large valley glaciers, observations of ice velocity, strain rate, and ice structures indicate that the form of a medial moraine is determined by severe lateral compression between the two ice streams. Debris of the moraine is recycled along complex transport paths determined by ice structures. For example, supraglacial debris is precipitated into the confluence zone between the two glaciers forming a subglacial debris reservoir. Debris is evacuated from the reservoir by shearing between the two glaciers and is revealed on the glacier surface as debris dykes and melt-out tills along the contact plane. Important implications regarding the sedimentology of the moraine can be stated. Elsewhere debris is precipitated into transverse crevasses subsequently resulting in transverse till ridges at the glacier surface.Annually-formed wave ogives, bulges in surface ice, and overriding along the glacier contacts result from severe lateral compresssion, and add further diversity to the moraine.Downglacier, confluence ice structures are destroyed by ablation, the pattern of ice flow becomes less complex, unified flow between the two glaciers is established, and a distinct structurally-determined moraine morphology is replaced by one dependent upon the differential ablation of debris covered and clean ice.

scholarly journals Changes in ice thickness and flow velocity of Yala Glacier, Langtang Himal, Nepal, from 1982 to 2009

2013 ◽  
Vol 54 (64) ◽  
pp. 157-162 ◽  
Author(s):  
Shin Sugiyama ◽  
Kotaro Fukui ◽  
Koji Fujita ◽  
Kenta Tone ◽  
Satoru Yamaguchi
Keyword(s):  
Flow Velocity ◽  
Surface Elevation ◽  
Ice Thickness ◽  
Glacier Surface ◽  
Ice Flow ◽  
Ice Volume ◽  
Glacier Changes ◽  
Ice Velocity ◽  
Ground Penetrating ◽  
Thinning Rate

Abstract To investigate recent glacier changes in the Himalayan region, we carried out GPS and ground-penetrating radar (GPR) measurements at Yala Glacier, a benchmark glacier in Nepal. Glacier surface elevation and ice thickness were surveyed along a 1.5 km profile from the glacier top to the terminus. Ice flow velocity was measured at five locations by surveying stakes for either 1 year or 4 day periods. Obtained surface elevation and ice velocity were compared with those measured in 1982 and 1996. The mean ice thickness along the radar profile was 36 m in 2009 and the ice has been thinning at rates of-0.69 ±0.25 and -0.75 ± 0.24 m a-1 during the periods 1982-96 and 1996-2009, respectively. The thinning rate increases down-glacier, reaching a magnitude up to -1.8 m a-1 near the terminus from 1996 to 2009. The ice velocity has reduced by >70% from 1982 to 2009 in the lower half of the glacier. By assuming a constant driving stress over the glacier, the total ice volume in 2009 was estimated as 0.061 km3. Our results indicate that Yala Glacier has lost ∼40% of its ice volume over the last 27 years and that the rate of the mass loss has accelerated over the last decade.

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

1999 ◽  
Vol 45 (151) ◽  
pp. 575-583 ◽  
Author(s):  
Andreas Kääb ◽  
Martin Funk
Keyword(s):  
Pilot Study ◽  
Mass Balance ◽  
Surface Strain ◽  
Swiss Alps ◽  
Surface Velocity ◽  
Glacier Mass Balance ◽  
Glacier Surface ◽  
Ice Flow ◽  
Applied Model ◽  
Ice Velocity

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.

scholarly journals On the Role of Mechanical Energy in Maintaining Subglacial Water Conduits at Atmospheric Pressure

1984 ◽  
Vol 30 (105) ◽  
pp. 180-187 ◽  
Author(s):  
Roger Leb. Hooke
Keyword(s):  
Atmospheric Pressure ◽  
Flow Direction ◽  
Mechanical Energy ◽  
Glacier Surface ◽  
Ice Flow ◽  
Small Perturbations ◽  
Point Pressure ◽  
Ice Velocity ◽  
Glacial Landforms

AbstractRecent theoretical studies of glacier hydrology have assumed that subglacial conduits are completely filled with water under steady-state conditions. This, however, is not necessarily the case. Where discharges are larger than a few tens of liters per second and the down-glacier slope of the bed is more than a few degrees, the potential energy released by water descending this slope may be capable of melting the walls of a subglacial conduit many times faster than the conduit can close by plastic flow of the ice. As a result, the pressure in such tunnels may normally be atmospheric, or possibly even at the triple-point pressure if there is no open connection to the glacier surface. Simple calculations suggest that such pressures in subglacial conduits may be more common than heretofore anticipated.The positions of such “open” conduits may be unstable to small perturbations in discharge or ice velocity. This is because the mechanical energy available in excess of that needed to balance closure can instead offset the general flow of the ice. Conduits can thus trend diagonally across the direction of ice flow. If an increase in the angle which such a conduit makes with the ice flow direction also results in an increase in slope of the conduit, more mechanical energy will become available, resulting in a positive feedback process.Subglacial channels at atmospheric pressure may influence the origin and morphology of certain glacial landforms, such as eskers and “plastically-molded” features.

scholarly journals Pupillary axis of a heterocentric astigmatic eye

2013 ◽  
Vol 72 (1) ◽  
Author(s):  
W. F. Harris
Keyword(s):  
Anterior Chamber ◽  
Contact Lens ◽  
Line Of Sight ◽  
Compound System ◽  
Linear Optics ◽  
Optical Instrument ◽  
Entrance Pupil ◽  
Naked Eye ◽  
Straight Line

The pupillary axis of the eye is a clinically useful concept usually defined as the line through the centre of the entrance pupil that is perpendicular to the cornea. However if the cornea is astigmaticthen, strictly speaking, the entrance pupil is blurred and the pupillary axis is not well defined.  A modified definition is offered in this paper: the pupillary axis is the infinite straight line containing the incident segment of the ray that passes through the centre of the (actual) pupil and is perpendicular to the first surface of the eye.  The definition holds for the naked eye and for an eye with an implant in the anterior chamber.  It also holds for the com-pound system of eye and optical instrument such as a contact lens in front of it if the first surface is interpreted as the first surface of the compound system and the pupil as the limiting aperture of the compound system.  Linear optics is applied to obtain a formula for the position and inclination of the pupillary axis at incidence onto the system; the refracting surfaces may be heterocentric and astigmatic.  The formula allows one to examine the sensitivity of the pupillary axis to displacement of the pupil and any other changes in the anterior eye.  Strictly the pupillary axis depends on the frequency of light but examples show that the dependence is probably negligible.  The vectorized generalization of what is sometimes called angle lambda is easily calculated from the inclination of the pupillary axis and the line of sight. (S Afr Optom 2013 72(1) 3-10)

RADISHCHEV PLOT IN MULTIVARIATE ANALYSIS OF THE PROBLEM OF MULTIPLE TARGETS GROUP PURSUIT

2021 ◽  
pp. 22-31
Author(s):  
A. A. Dubanov
Keyword(s):  
Multivariate Analysis ◽  
Line Segment ◽  
Iterative Process ◽  
Straight Line Segment ◽  
Line Of Sight ◽  
Radius Of Curvature ◽  
Time Step ◽  
Minimum Radius ◽  
Group Pursuit ◽  
Straight Line

This article discusses a kinematic model of the problem of group pursuit of a set of goals. The article discusses a variant of the model when all goals are achieved simultaneously. And also the possibility is considered when the achievement of goals occurs at the appointed time. In this model, the direction of the speeds by the pursuer can be arbitrary, in contrast to the method of parallel approach. In the method of parallel approach, the velocity vectors of the pursuer and the target are directed to a point on the Apollonius circle. The proposed pursuit model is based on the fact that the pursuer tries to follow the predicted trajectory of movement. The predicted trajectory of movement is built at each moment of time. This path is a compound curve that respects curvature constraints. A compound curve consists of a circular arc and a straight line segment. The pursuer's velocity vector applied to the point where the pursuer is located touches the given circle. The straight line segment passes through the target point and touches the specified circle. The radius of the circle in the model is taken equal to the minimum radius of curvature of the trajectory. The resulting compound line serves as an analogue of the line of sight in the parallel approach method. The iterative process of calculating the points of the pursuer’s trajectory is that the next point of position is the point of intersection of the circle centered at the current point of the pursuer’s position, with the line of sight corresponding to the point of the next position of the target. The radius of such a circle is equal to the product of the speed of the pursuer and the time interval corresponding to the time step of the iterative process. The time to reach the goal of each pursuer is a dependence on the speed of movement and the minimum radius of curvature of the trajectory. Multivariate analysis of the moduli of velocities and minimum radii of curvature of the trajectories of each of the pursuers for the simultaneous achievement of their goals i based on the methods of multidimensional descriptive geometry. To do this, the projection planes are entered on the Radishchev diagram: the radius of curvature of the trajectory and speed, the radius of curvature of the trajectory and the time to reach the goal. On the first plane, the projection builds a one-parameter set of level lines corresponding to the range of velocities. In the second graph, corresponding to a given range of speeds, functions of the dependence of the time to reach the target on the radius of curvature. The preset time for reaching the target and the preset value of the speed of the pursuer are the optimizing factors. This method of constructing the trajectories of pursuers to achieve a variety of goals at given time values may be in demand by the developers of autonomous unmanned aerial vehicles.

scholarly journals Short-term surface ice motion variations measured with a ground-based portable real aperture radar interferometer

2011 ◽  
Vol 57 (201) ◽  
pp. 53-60 ◽  
Author(s):  
Patrick Riesen ◽  
Tazio Strozzi ◽  
Andreas Bauder ◽  
Andreas Wiesmann ◽  
Martin Funk
Keyword(s):  
Line Of Sight ◽  
Interferometric Imaging ◽  
Short Term ◽  
Glacier Surface ◽  
Fast Acquisition ◽  
Surface Ice ◽  
The Impact ◽  
Real Aperture Radar ◽  
Aperture Radar

AbstractWe report measurements using a portable real aperture radar (Gamma Portable Radar Interferometer (GPRI)) for interferometric imaging of the surface ice motion on Gornergletscher, Switzerland, during the drainage of the adjacent ice-marginal lake Gornersee. The GPRI tracked the surface ice motion in line of sight over an area of ∼3 km2 down-glacier of Gornersee almost continuously during the drainage event. The displacement maps derived from the acquired interferograms capture the spatial distribution of the surface ice motion. Due to fast acquisition times of the microwave images, the GPRI was able to record sub-daily variations of the ice displacements, most likely caused by the impact of the Gornersee drainage on the ice motion of Gornergletscher. In situ point measurements of the ice displacement agree reasonably well with the results obtained by the GPRI and highlight the use of the GPRI for high-resolution measurements of glacier surface ice motion.

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