scholarly journals Bed Topography and Mass-Balance Distribution of Columbia Glacier, Alaska, U.S.A., Determined from Sequential Aerial Photography

1988 ◽  
Vol 34 (117) ◽  
pp. 208-216 ◽  
Author(s):  
L. A. Rasmussen
Keyword(s):  
Mass Balance ◽  
Aerial Photography ◽  
Continuity Equation ◽  
The Other ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Bed Topography ◽  
Displacement Vectors ◽  
Grid Nodes

AbstractAn internally consistent data set of geometry and flow variables for the lower part of Columbia Glacier, south-central Alaska, is derived entirely from vertical aerial photography. The principle of mass conservation is imposed on the data in the form of a centered finite-difference approximation of the continuity equation. It is applied on a 120-node section of a square grid covering the 15 km long, high-velocity stretch ending at the grounded, heavily calving terminus of this large glacier.Photography was obtained 22 times between June 1977 and September 1981. Surface altitudes on the dates of the flights and the displacement vectors between pairs of flights were determined photogrammetrically. Natural features on the glacier surface were sufficiently prominent and enduring to be followed from the date of one flight to the next.Because both the altitude points and displacement vectors were irregularly positioned spatially, interpolation was necessary to get values on the grid nodes. The points had already been subjected to the method of optimum interpolation to get surface altitudes on the grid nodes. The displacement vectors are subjected here to a constrained–interpolation method to get velocity vectors at the grid nodes that are consistent, through the continuity equation, with the other variables.The other variables needed to achieve closure of the variable set are bed topography and mass-balance distribution. The latter was taken to be a separate linear function of altitude for each time interval. Values for bed altitudes at 120 nodes and two coefficients of each 21 balance functions were inferred as the 162 model parameters in a non-linear minimization problem having 4305 observed velocity components as its data.

scholarly journals Bed Topography and Mass-Balance Distribution of Columbia Glacier, Alaska, U.S.A., Determined from Sequential Aerial Photography

1988 ◽  
Vol 34 (117) ◽  
pp. 208-216 ◽  
Author(s):  
L. A. Rasmussen
Keyword(s):  
Mass Balance ◽  
Aerial Photography ◽  
Continuity Equation ◽  
The Other ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Bed Topography ◽  
Displacement Vectors ◽  
Grid Nodes

Abstract An internally consistent data set of geometry and flow variables for the lower part of Columbia Glacier, south-central Alaska, is derived entirely from vertical aerial photography. The principle of mass conservation is imposed on the data in the form of a centered finite-difference approximation of the continuity equation. It is applied on a 120-node section of a square grid covering the 15 km long, high-velocity stretch ending at the grounded, heavily calving terminus of this large glacier. Photography was obtained 22 times between June 1977 and September 1981. Surface altitudes on the dates of the flights and the displacement vectors between pairs of flights were determined photogrammetrically. Natural features on the glacier surface were sufficiently prominent and enduring to be followed from the date of one flight to the next. Because both the altitude points and displacement vectors were irregularly positioned spatially, interpolation was necessary to get values on the grid nodes. The points had already been subjected to the method of optimum interpolation to get surface altitudes on the grid nodes. The displacement vectors are subjected here to a constrained–interpolation method to get velocity vectors at the grid nodes that are consistent, through the continuity equation, with the other variables. The other variables needed to achieve closure of the variable set are bed topography and mass-balance distribution. The latter was taken to be a separate linear function of altitude for each time interval. Values for bed altitudes at 120 nodes and two coefficients of each 21 balance functions were inferred as the 162 model parameters in a non-linear minimization problem having 4305 observed velocity components as its data.

scholarly journals A Numerical Model of Temperate Glacier Flow Applied to the Quiescent Phase of a Surge-Type Glacier

1982 ◽  
Vol 28 (99) ◽  
pp. 239-265 ◽  
Author(s):  
Robert Bindschadler
Keyword(s):  
Shear Stress ◽  
Numerical Model ◽  
Stress Gradient ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Small Contribution ◽  
Base Shear ◽  
Quiescent Phase ◽  
Glacier Flow

AbstractA time-dependent numerical model of temperate glacier flow without sliding is developed and applied to the quiescent phase of surge-type Variegated Glacier, Alaska. The model is based on a one-dimensional continuity equation but the transverse channel shape is explicitly included allowing the complex geometries of real glaciers to be modelled. Velocities and volume fluxes are calculated from the glacier geometry. Transverse stress is taken into account by shape factors which are fitted to measurements of geometry and velocity and are chosen to be insensitive to changes in geometry. Longitudinal stress gradients are taken into account by use of a large-scale surface slope. A Crank-Nicholson finite-difference approximation is used and it is unconditionally stable when a small contribution from the local slope is added to the average slope.Model parameters are fitted to extensive data collected on Variegated Glacier in 1973 and 1974. Predictions of the model over a four year interval agree well with field measurements. Predictions of the current quiescent phase (1965–84) indicate depth increases in the upper glacier of more than 75 m with a twenty-fold increase in the volume flux. During this interval the base shear stress increases 40% in the upper glacier and decreases 20% in the lower glacier. During the mid to late quiescent phase, ice motion becomes more important than mass balance in the redistribution of mass over the central region of the glacier. If normal flow were to persist, the predicted steady-state profile would be an average of 100 m deeper and 41% more voluminous than in 1973.The predicted base shear-stress gradient is never negative enough to satisfy Robin and Weertman’s (1973) condition for blockage of subglacial water flow. The annual rate of water production by dissipation of mechanical straining at the bed remains two orders of magnitude below that produced by summer surface melt. The predicted fractional increase in base stress during the quiescent phase is a maximum in the region believed to be the trigger zone of the surges.

Properties of signature partner superdeformed bands in mercury nuclei

2015 ◽  
Vol 11 (1) ◽  
pp. 2918-2926 ◽  
Author(s):  
Mahmoud Abokilla ◽  
Hayam Yassin ◽  
Eman R. Abo Elyazeed
Keyword(s):  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Transition Energies ◽  
Fitting Procedure ◽  
Higher Order Terms ◽  
Fourth Derivative ◽  
The Difference ◽  
Experimental Transition ◽  
Search Program

The properties of superdeformed (SD) bands of five pairs signature partners in mercury nuclei have been systematically analyzed in framework of four parameters formula including higher order terms of Bohr-Mottelson collective rotational energies. The level spins and the model parameters are determined by fitting procedure using a computer simulated search program in order to obtain minimum root mean square deviations between the calculated and the experimental transition energies.The best fitted parameters have been used to calculate the transition energies Eγ, the rotational frequencies , the kinematic J(1) and dynamic J(2) moments of inertia. The calculated results agree excellently with the experimental data. J(2) is significantly larger than J(1) for all values of  . Also J(2) show a smooth increase with increasing . The appearance of ΔI = 1 and ΔI = 2 staggering in γ-ray transition energies have been examined by using the five-points formula representing the finite difference approximation to the fourth derivative of the γ-ray transition energies at a given spin. The signature partners in Hg nuclei show large amplitude staggering. Also to appear the ΔI = 1 staggering, the transition energies relative to a rigid rotor with a moment of inertia J = 128.219 are plotted against spins for each signature partner pairs. The difference in transition energies between transitions in the two SD bands 191Hg(SD3)and 193Hg(SD3) are small, therefore, these two bands have been considered as identical bands.

scholarly journals Mass-balance model parameter transferability on a tropical glacier

2013 ◽  
Vol 59 (217) ◽  
pp. 845-858 ◽  
Author(s):  
Wolfgang Gurgiser ◽  
Thomas Mölg ◽  
Lindsey Nicholson ◽  
Georg Kaser
Keyword(s):  
Mass Balance ◽  
The Other ◽  
Balance Model ◽  
Small Scale ◽  
Model Parameters ◽  
Glacier Mass Balance ◽  
Ablation Zone ◽  
Model Errors ◽  
Mass Balance Model ◽  
Cumulative Mass

AbstractWe explore the small-scale spatial and temporal transferability of model parameters between two points in the ablation zone of tropical Glaciar Shallap, Cordillera Blanca, Peru (9°S, −77° W; ∼4800 m a.s.l.) in order to provide a robust assessment of the performance of a process-based glacier mass-balance model. Relative surface height change is calculated at hourly time-steps, and cumulative values are compared to surface height measurements made at irregular intervals (14–64 days) over the course of two continuous hydrological years (August 2006–August 2008). Best-performing parameter combinations were determined for each point from the outcome of 1000 model simulations for which parameters were varied randomly within a defined range. With these parameter combinations measurements for a specific location and time-span are well reproduced. Transferring the parameter combination as optimized for one location to the other location in the ablation zone increases the errors of modeled cumulative mass balance by 5–1326 mm ice eq.a−1. Transferring the parameter combinations as optimized for one year to the other year increases the modeled errors in cumulative mass balance by 18–3179 mm ice eq.a−1. Model errors generally increase during periods with frequent snowfall and snow cover. This could reflect either the inherent difficulty of modeling complex snow processes, or the inability of the model to correctly capture the pattern of albedo evolution at this site. The magnitude of errors associated with parameter transfer in space and time highlights the need for improving model performance for robust climatological and/or hydrological analyses on tropical glaciers.

scholarly journals Three-dimensional modeling of hydrodynamic problems taking into account elastic processes

2021 ◽  
pp. 1-15
Author(s):  
Yuri Andreevich Poveschenko ◽  
Alexander Yur’evich Krukovskiy ◽  
Dmitri Sergeevich Boykov ◽  
Victoria Olegovna Podryga ◽  
Parvin Ilgar gizi Rahimly
Keyword(s):  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Difference Schemes ◽  
Finite Difference Approximation ◽  
Vector Analysis ◽  
Difference Approximation ◽  
Sound Waves ◽  
Displacement Vectors ◽  
The Difference ◽  
Elastic Processes

A finite-difference approximation of elastic forces on spaced Lagrangian grids is constructed, based on the method of support operators. For displacement vectors on irregular grids, on the topological and geometric structure of which minimal reasonable restrictions are imposed, the approximations of vector analysis operations are constructed in relation to difference schemes for problems of elasticity theory. Taking into account the energy balance of the medium, the constructed families of integrally consistent approximations of vector analysis operations are sufficient for discrete modeling of these processes. The schemes are considered, both using the stress tensor in an explicit form, and dividing it into spherical and shear components (pressure and deviator). The latter is used to construct homogeneous algorithms applicable to both the solid and the vaporized phase. The linear theory of elasticity is used for constructing approximations. The resulting forces in spatial geometry are obtained explicitly. Calculations of the sound waves propagation in a three-dimensional orthogonal aluminum plate due to end impact are presented. These calculations confirm the good quality of the difference schemes constructed in work.

Efficient inversion of 2.5D electrical resistivity data using the discrete adjoint method

Geophysics ◽  
2021 ◽  
pp. 1-54
Author(s):  
Diego Domenzain ◽  
John Bradford ◽  
Jodi Mead
Keyword(s):  
Electrical Resistivity ◽  
Gradient Descent ◽  
Adjoint Method ◽  
Sparse Matrices ◽  
Joint Inversion ◽  
Geophysical Data ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Inversion Algorithm

We present a memory and operation-count efficient 2.5D inversion algorithm of electrical resistivity (ER) data that can handle fine discretization domains imposed by other geophysical (e.g, ground penetrating radar or seismic) data. Due to numerical stability criteria and available computational memory, joint inversion of different types of geophysical data can impose different grid discretization constraints on the model parameters. Our algorithm enables the ER data sensitivities to be directly joined with other geophysical data without the need of interpolating or coarsening the discretization. We employ the adjoint method directly in the discretized Maxwell's steady state equation in order to compute the data sensitivity to the conductivity. In doing so, we make no finite difference approximation on the Jacobian of the data and avoid the need to store large and dense matrices. Rather, we exploit matrix-vector multiplication of sparse matrices and find successful convergence using gradient descent for our inversion routine without having to resort to the Hessian of the objective function. By assuming a 2.5D subsurface, we are able to linearly reduce memory requirements when compared to a 3D gradient descent inversion, and by a power of two when compared to storing a 2D Hessian. Moreover, our method linearly outperforms operation counts when compared to 3D Gauss-Newton conjugate-gradient schemes, which scales cubically in our favor with respect to the thickness of the 3D domain. We physically appraise the domain of the recovered conductivity using a cut-off of the electric current density present in our survey. We present two case studies in order to assess the validity of our algorithm. First, on a 2.5D synthetic example, and then on field data acquired in a controlled alluvial aquifer, where we were able match the recovered conductivity to borehole observations.

scholarly journals A Numerical Model of Temperate Glacier Flow Applied to the Quiescent Phase of a Surge-Type Glacier

1982 ◽  
Vol 28 (99) ◽  
pp. 239-265 ◽  
Author(s):  
Robert Bindschadler
Keyword(s):  
Shear Stress ◽  
Numerical Model ◽  
Stress Gradient ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Small Contribution ◽  
Base Shear ◽  
Quiescent Phase ◽  
Glacier Flow

AbstractA time-dependent numerical model of temperate glacier flow without sliding is developed and applied to the quiescent phase of surge-type Variegated Glacier, Alaska. The model is based on a one-dimensional continuity equation but the transverse channel shape is explicitly included allowing the complex geometries of real glaciers to be modelled. Velocities and volume fluxes are calculated from the glacier geometry. Transverse stress is taken into account by shape factors which are fitted to measurements of geometry and velocity and are chosen to be insensitive to changes in geometry. Longitudinal stress gradients are taken into account by use of a large-scale surface slope. A Crank-Nicholson finite-difference approximation is used and it is unconditionally stable when a small contribution from the local slope is added to the average slope.Model parameters are fitted to extensive data collected on Variegated Glacier in 1973 and 1974. Predictions of the model over a four year interval agree well with field measurements. Predictions of the current quiescent phase (1965–84) indicate depth increases in the upper glacier of more than 75 m with a twenty-fold increase in the volume flux. During this interval the base shear stress increases 40% in the upper glacier and decreases 20% in the lower glacier. During the mid to late quiescent phase, ice motion becomes more important than mass balance in the redistribution of mass over the central region of the glacier. If normal flow were to persist, the predicted steady-state profile would be an average of 100 m deeper and 41% more voluminous than in 1973.The predicted base shear-stress gradient is never negative enough to satisfy Robin and Weertman’s (1973) condition for blockage of subglacial water flow. The annual rate of water production by dissipation of mechanical straining at the bed remains two orders of magnitude below that produced by summer surface melt. The predicted fractional increase in base stress during the quiescent phase is a maximum in the region believed to be the trigger zone of the surges.

Development and validation of mathematical model of hydrotropic-reactive extraction of lignin

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Indah Hartati ◽  
Wahyudi Budi Sediawan ◽  
Hary Sulistyo ◽  
Muhammad Mufti Azis ◽  
Moh Fahrurrozi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Effective Diffusivity ◽  
Reaction Rate Constant ◽  
Reactive Extraction ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Explicit Finite Difference ◽  
The Mathematical Model

AbstractHydrotropes have been largely explored as reactive extraction agent for lignin separation. In this paper, a mathematical model of hydrotropic-reactive extraction of sugarcane bagasse lignin was proposed and validated by experimental data from literature. The mathematical model was developed by assuming the particle is in slab shape, and by considering simultaneous processes of hydrotrope intra particle diffusion, second order reaction of lignin-hydrotrope, and intra-particle soluble delignification product diffusion. The proposed model results in a set of partial differential equations which were then solved by explicit finite difference approximation method. The mathematical model parameters were determined by fitting the model to the hydrotropic reactive extraction experimental data reported by Ansari and Gaikar (2014). Simulations show that the mathematical model of the hydrotropic-reactive extraction were well fitted to the experimental data with the obtained hydrotrope effective diffusivity (DeA) of 5.0 × 10−11 m2/s, effective diffusivity of soluble lignin product (DeC) of 9.0 × 10−12 m2/s and reaction rate constant (kr) of 1.78 × 10−10 m3/(g.s). It was also observed that the reaction was first order to the hydrotrope (n = 1), and one half order to the lignin (m = 0.5). Meanwhile the pseudo-stoichiometric mass ratio of hydrotrope to lignin was 6.4 g hydrotrope/g lignin.

Determination of Main-Term and Cross-Term Gas Diffusivities in Heavy Oil Systems Considering Local Oil Swelling Effect

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Hyun Woong Jang ◽  
Daoyong Yang
Keyword(s):  
Liquid Phase ◽  
Heavy Oil ◽  
Molecular Diffusion ◽  
Numerical Solutions ◽  
The Other ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Dissolved Gas ◽  
Cross Term ◽  
The Individual

Abstract To inject gas into a heavy oil reservoir, molecular diffusion of the dissolved gas into heavy oil is one of the crucial mechanisms to lower its viscosity while swelling the diluted oil. Various efforts have been made to predict the diffusivity of such gas dissolved in heavy oil with or without considering the oil swelling. Practically, the oil swelling is always considered in an excessively simplified manner so that such swelling is not able to exhibit its true effect on the estimated diffusivity. In most studies where the oil swelling is considered, the liquid-phase hydrocarbon is assumed to swell equally at every location because the height of liquid-phase in a diffusion vessel is simply extended proportionally to the oil swelling direction. Such a proportional swell is often realized during numerical solutions by uniformly extending the numerical cells, regardless of the amount of dissolved gas contained in each of them. In addition, no studies have been made to examine the contribution of one gas over the other for a gas mixture-liquid system. In this study, a pragmatic approach is proposed to determine the main- and cross-term diffusivities of gas–liquid systems considering local swelling effect. More specifically, diffusivities of CO2 and a CO2–C3H8 mixture in a Lloydminster heavy oil are respectively estimated by implementing the finite difference approximation (FDA) with the face-centered explicit scheme. For the CO2–C3H8 mixture, the individual diffusivity of each gas in the mixture is firstly computed independent of the other gas in the mixture. Then, the cross-term diffusivity is included to verify the effect of the other gas in heavy oil for the diffusion of one gas, while the local oil swelling is implemented during the estimation of the individual gas diffusivities. It is found that the obtained diffusivities of pure CO2 and each individual component of the CO2–C3H8 mixture in the Lloydminster heavy oil are reasonable and accurate to reproduce the measured oil swelling factors obtained from the dynamic volume analysis (DVA) tests.

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