NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document. The ice streams in the West Antarctica Ice Sheet flow at several hundred metres per year. The lateral increase in speed from typical inland ice sheet speeds of a few metres per year to ice stream speeds of several hundred metres per year occurs over a short distance (~ 2 km) in the outer part of the ice stream known as the marginal shear zone (MSZ). The ice in this zone is highly crevassed and chaotically jumbled. This thesis is an effort to understand the dynamics of the MSZ and to find out whether the velocity of the ice stream is controlled primarily by the stresses in its MSZs or by stresses at the base. This is done by determining the marginal shear stress in one of the marginal shear zones using the ice itself as a stress meter. The observed marginal shear strain rate of 0.14 a(-1) is used to calculate the marginal shear stress from the flow law of ice determined by creep tests on ice cores from a MSZ. The test specimen orientation relative to the stress axes in the tests is chosen on the basis of c-axis fabrics so that horizontal shear across vertical planes parallel to the margin is applied to the ice specimens in the test. The resulting marginal shear stress is (2.2 ± 0.3) x 10(5) Pa. This implies that 63 to 100% of the ice stream’s support against gravitational loading comes from the margins and only 37 to 0% from the base, so that the margins play an important role in controlling the ice stream motion. The marginal shear stress value is twice that given by the ice-stream model of Echelmeyer et al. (1994), and the corresponding strain-rate enhancement factors differ greatly (E […] 1 - 2 from the creep tests vs. E […] 10 - 12.5 from the model of Echelmeyer et al. (1994)). This large discrepancy may possibly be explained by recrystallization of the ice during or shortly after coring. Estimates of the expected recrystallization time scale range widely but include the ~ 1-hour time scale of coring and leave the likelihood of recrystallization uncertain. However, the observed two-maximum fabric type is not what is expected for annealing recrystallization from the sharp single-maximum fabric that would be expected in situ at the high shear strains involved ([gamma] ~ 20). Experimental data from Wilson (1982) suggest that if the core did recrystallize, the prior fabric was a two-maximum fabric not substantially different from the observed one, which implies that the measured flow law and derived marginal shear stress are applicable to the in-situ situation. An ice-stream flow model was developed to explore the discrepancy in enhancement factors. Using this model, which is similar to the model of Echelmeyer et al. (1994), it is possible to match the observed surface velocity profile across the ice stream using a strain rate enhancement factor of 5. This is more than four times the value found in the experimental work but half the value from the modelling results of Echelmeyer et al. The flow model suggests that the lateral shear stress integrated over the margins is larger than the basal shear stress integrated over the base, so that the ice stream is controlled at the sides rather than at the base. It was thus not possible to reconcile fully the results from the experimental work and from modelling, since the modelling still suggests that there is substantial flow enhancement in the MSZ. There may be variation of the enhancement factor with depth, so that at 300 m depth the enhancement factor is close to 1, but increases at greater depths. c-axis measurements in ice from the middle of the MSZ reveal that there is an asymmetrical two-maxima fabric, as expected for ice under simple shear. 600 m away, between the middle of the MSZ margin and its outer edge, there is still a two-maxima fabric but the secondary maximum is much smaller and the primary maximum is much bigger. 500 m further, right at the boundary between the shear margin and the ice stream, there is only a single maximum. Outside the ice stream the fabrics show a single, very diffuse maximum.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Kamb, W. Barclay and Clayton, Robert W.}, } @phdthesis{10.7907/41WM-7B96, author = {Fahnestock, Mark Allen}, title = {Hydrologic control of sliding velocity in two Alaskan glaciers : observation and theory}, school = {California Institute of Technology}, year = {1991}, doi = {10.7907/41WM-7B96}, url = {https://resolver.caltech.edu/CaltechETD:etd-07182006-134101}, abstract = {Short term variations in the velocities of glaciers reflect changes in the processes which determine sliding velocity. The role of water in these processes is considered for certain types of variable behavior observed on two glaciers in Alaska. Pulses of increased velocity on Variegated Glacier (mini-surges) prior to its 1982-83 surge have been attributed to pulses of water at the glacier bed. Our field program in 1986 demonstrated that mini-surges still occurred following the surge; the propagation of two such disturbances over part of the upper reach of the glacier was documented. The mini-surges of 1986 had substantially lower peak velocities but only slightly lower propagation velocities than the pre-surge mini-surges. The first of the mini-surges observed in 1986 originated in the tributary, the second originated in the upper reach of the main glacier. A model of the basal water system with pressure dependent conductivity and storage is developed to investigate the conditions necessary for propagation of a pulse of water. The response of this system to the introduction of a localized increase in input is followed with a finite difference formulation. The extra input of water produces a downglacier propagating front, which, for reasonable values of porosity and pre-event conditions, moves at speeds similar to those observed for mini-surges. The relation between the non-linearity of the pressure dependence in this model and the shape and history of the propagating disturbances is investigated using conductivity relations which have linear, quadratic, and cubic dependence on pressure, and one with an inverse dependence on the effective pressure. The modeling indicates that a system with a non-linear change of conductivity in response to a change in water pressure (suggestive of a cavity system) is required to match the field observations. The shapes of waves which propagate with unchanging form in this system can be found theoretically; the numerical model generates these waves when the input rate is held constant. The constant form shapes are calculated for the conductivity relations mentioned above; for conductivities with higher-than-linear dependence on pressure the waves reach a plateau upglacier; the linear case increases without bound. Modeling of a Rothlisberger tunnel system with the addition of a storage term indicates that such a system will propagate a disturbance, but will not match the abrupt rise times seen in boreholes as a mini-surge wave passes. The pressure dependent conductivity model does a better job of matching observations. Columbia Glacier, a large tidewater glacier in southern Alaska, experiences noteworthy velocity fluctuations during the melt season in response to storms and increased ablation, and also displays a well developed diurnal cycle in velocity. A 1987 field project involving the University of Colorado, tbe USGS, and Caltech collected detailed time series of surface velocity, water input and discharge, and basal water pressure. These data show a complex pattern of behavior which is highly correlated with variations in hydrologic parameters. Basal water pressures near the floatation level are related to the rapid surface motion (4-8 m/d) of this glacier. A series of at least four velocity events accompanied elevated inputs of water to the glacier. These speed-ups did not have a strong coincident peak in basal water pressure, but were followed by an increase in outflow discharge from the glacier. An estimate of the change in the volume of water stored in the glacier is made by relating input to the glacier (estimated from the filling rate of an ice-marginal lake and also from meteorological records) to discharge. This calculation shows that variations in velocity on time scales longer than one day can be explained by changes in the volume of water stored in or under the ice. The first velocity event was followed by a slowdown of the glacier which was coincident with a drop in stored water volume of about 0.1 m3/m2 averaged over the ice surface. The peak in velocity for the largest velocity event is accompanied by a large peak in stored water volume. A model of the basal water system which consists of co-existing linked cavity and tunnel components is proposed to explain the melt season behavior of Columbia Glacier. In this hybrid cavity/tunnel system the distributed input of water reaches the bed and flows through the cavities to reach large tunnels which are responsible for the downglacier transport of water. The cavity part of this system is responsible for the correlation between stored water volume and velocity, while the tunnel system is responsible for the seasonal variation of velocity and the localized upwelling of water discharged from the terminus of the glacier. A model based on a simple sliding law, an effective pressure distribution at the bed which is determined by the discharge through a tunnel system, and continuity for the ice is used to look at the role of effective pressure in the difference between winter and summer glacier-flow behavior. This model produces the late-melt-season pulse in velocity at the terminus which is related to an annual increase in calving rate. This may explain the previously discovered correlation between calving rate and outflow discharge, as well as the connection between the location of calving activity and the location of upwelling at the terminus. The results of this work suggest that the complicated behavior of these glaciers can be understood at a simple level from the variations in hydrologic systems.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Kamb, W. Barclay}, } @phdthesis{10.7907/VSHG-G674, author = {Brugman, Melinda Mary}, title = {Water Flow at the Base of a Surging Glacier}, school = {California Institute of Technology}, year = {1987}, doi = {10.7907/VSHG-G674}, url = {https://resolver.caltech.edu/CaltechETD:etd-07192006-093757}, abstract = {Water tracing experiments were successfully conducted over a distance of ten kilometers along the base of Variegated Glacier for the purpose of characterizing the water drainage system of the glacier in the surging as compared to the non-surging state. Three tracing experiments were conducted, and fluorescent dyes, Rhodamine WT and Tinopal AMS, were injected into boreholes at separate locations. The two Rhodamine WT experiments were conducted over a 10 km distance, both during the most rapid surging motion of the glacier, and after its cessation.
In each experiment, the terminus streams were monitored for stream discharge, sediment content and tracer concentration. Rhodamine WT tracer was significantly adsorbed on the suspended sediment, particularly during the surge. The adsorption behavior followed the Langmuir model, and calculated distribution coefficients of Kd = 100 to 1000 ml/g were measured for during the glacier surge. The Kd values measured after the surge were lower than during the surge by a factor of 10 to 1000. The much higher Kd values in the surging as compared to non-surging glacier states can be best explained by a factor of 10 to 1000 decrease in the modal and/or mean grain-size of the suspended sediment. The abundance of fine-grained sediment during the surge is probably due to increased grinding of rock material at the glacier bed.
Theoretical models of tracer dispersion in a single tunnel, were compared to models of dispersion in linked-cavity systems to infer the details of water flow at the glacier bed. The broad, roughly symmetrical, dye-return curve measured during the glacier surge conforms to diffusive dispersion theory, and differs sharply from the highly asymmetrical dispersion curve measured after the surge. Results indicate the dispersion behavior, and calculated Manning roughness, of the post-surge Variegated Glacier is similar to those of glaciers that do not surge. The drainage system of the Variegated Glacier in the surging state is consistent with a model of tracer dispersion in an interconnecting network of conduits and cavities, and is strikingly different from the tunnel system indicated for the non-surging state.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Kamb, W. Barclay}, } @phdthesis{10.7907/5R3G-8281, author = {Jungels, Pierre Henri}, title = {Modeling of tectonic processes associated with earthquakes}, school = {California Institute of Technology}, year = {1973}, doi = {10.7907/5R3G-8281}, url = {https://resolver.caltech.edu/CaltechETD:etd-09202005-112510}, abstract = {
A finite element variational method is described and applied to the analysis of zero frequency seismic data. This technique presents a suitable tool for the analysis of permanent displacements, tilts and strains caused by seismic events, since it can model variable fault offsets in heterogeneous media.
The accuracy of the technique is demonstrated by detailed static field computations for vertical and dipping dislocations acting in plane strain, corresponding to an infinite-length fault in a homogeneous half space, by comparison with closed form analytic solutions. A parametric study of material inhomogeneities and variable fault offsets reveals that order of magnitude changes in the solutions can occur for both near and far field displacements and strains.
The technique was applied to the San Fernando earthquake using a two-dimensional (plane strain) model. The best solution was obtained by separating the fault into two distinct parts, both having offsets near the surface a factor of five larger than the average slip. Both stress drop and displacements vary by more than an order of magnitude along the fault plane, the maximum occurring at 1 km depth. Several solutions are investigated for the hypocentral region, one of them giving as much as 5 m offset.
The Alaskan earthquake of 1964 is also studied in plane strain, and the observed vertical movements are inverted numerically to yield a “best fit” offset on the fault surface. This solution gives good results for the observed horizontal movement. It is characterized by large variations of the slip with a maximum of 33 m below Montague Island.
Then, a relationship is derived, giving energy released as a function of prestress, fault area, change in the local gravitational potential energy and fault offset, neglecting nonlinear behavior outside the fault zone. The finite element method is shown to allow direct calculation of the terms of the resulting equation from static consideration of failure in a prestress medium.
This is applied to the last solution for the San Fernando earthquake, the best fit offset of the Alaska earthquake and a simple model of the Montana earthquake, 1959. In all three cases, the results indicate that a spatially variable prestress field gives the best representation of the tectonic processes involved. The force of gravity is found to be a significant factor in the energy balance of each event, increasing the estimate of prestress for the thrust faults and the apparent stress drop for the Montana normal fault.
For the San Fernando earthquake, the prestress field in the hypocentral region is shown to exceed critical stress levels corresponding to granite strength as measured in the laboratory, while the average stress drop for the entire fault is below 200 bars. This is a possible answer to the apparent discrepancy between laboratory and average field measurements.
The Wilmington oil field subsidence is modeled by using a finite element code which solves numerically Biot’s consolidation theory. The best fit is obtained for a very small interaction constant. The models result in significant stress concentrations which could have triggered the small magnitude events known as the Long Beach subsidence earthquakes.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Kamb, W. Barclay}, } @phdthesis{10.7907/E6A2-B010, author = {Raymond, Charles Forest}, title = {Flow in a transverse section of Athabasca Glacier, Alberta, Canada}, school = {California Institute of Technology}, year = {1969}, doi = {10.7907/E6A2-B010}, url = {https://resolver.caltech.edu/CaltechETD:etd-07182006-094012}, abstract = {Measurements of ice deformation at the surface and at depth in the Athabasca Glacier, Canada, reveal for the first time the pattern of flow in a nearly complete cross section of a valley glacier, and make it possible to test the applicability of experimental and theoretical concepts in the analysis of glacier flow. Tilting in nine boreholes (depth about 300 m, eight holes essentially to the bottom) was measured with a newly developed electrical inclinometer, which allows a great increase in the speed and accuracy with which borehole configurations can be determined, in comparison with earlier methods. The measurements define the distribution of the velocity vector and the strain-rate tensor over 70% of the area of the glacier cross section.
The main longitudinal component of flow has the following general features: (1) basal sliding velocity which exceeds 70% of the surface velocity over half of the width of the glacier, (2) marginal sliding velocity (not more than a few meters per year) much less than basal sliding velocity at the centerline (about 40 m yr(-1)), (3) marginal shear strain rate near the valley walls two to three times larger than the basal shear strain rate near the centerline (0.1 yr(-1)).
The observed longitudinal flow is significantly different from that expected from theoretical analysis of flow in cylindrical channels (Nye, 1965). The relative strength of marginal and basal shear strain rate is opposite to that expected from theory. In addition, the longitudinal flow velocity averaged over the glacier cross section (which determines the flux of ice transported) is larger by 11% than the average flow velocity seen at the glacier surface, whereas it would be 2% smaller if the theoretical prediction were correct. These differences are caused to a large extent by the constant sliding velocity assumed in the theoretical analysis, which contrasts strongly with the actual distribution of sliding. The observed relation between marginal and basal sliding velocity is probably a general flow feature in valley glaciers, and may be caused by lateral variation of water pressure at the ice-rock contact. The observed pattern of longitudinal velocity over the section also shows in detail certain additional features incompatible with the theoretical treatment, even after the difference in boundary conditions (distribution of sliding velocity) is taken into account.
Longitudinal strain rate (a compression of about 0.02 yr(-1) at the surface) decreases with depth, becoming nearly 0 at the bed in the center of the glacier. The depth variation cannot be explained completely by overall bending of the ice mass as a result of a longitudinal gradient in the curvature of the bed, and is at variance with existing theories, which require the longitudinal strain rate to be constant with depth.
Motion transverse to the longitudinal flow occurs in a roughly symmetric pattern of diverging marginward flow, with most of the lateral transport occurring at depth in a fashion reminiscent of extrusion flow. The observed lateral velocities averaged over depth (up to 1.9 m yr(-1)) are compatible with the lateral flux required to maintain equilibrium of the marginal portions of the glacier surface under ablation (3.7 m yr(-1)) and are driven by the convex transverse profile of the ice surface.
When the measured strain-rate field is analyzed on the basis of the standard assumption that the shear stress parallel to the glacier surface varies linearly with depth, the rheological behavior in the lower one-half to two-thirds of the glacier is found compatible with a power-type flow law with n = 5.3. However, the upper one-third to one-half of the glacier constitutes an anomalous zone in which this treatment gives physically unreasonable rheological behavior. In a new method of analysis, rheological parameters are chosen so as to minimize the fictitious body forces that appear as residuals in the equilibirum equations when evaluated for the measured strain-rate field. This new method requires no a priori assumptions about the stress distribution, although for simplicity in application, the mean stress is assumed constant longitudinally. This treatment shows that the anomalies in the near-surface zone are due to significant departures from linear dependence of shear stress on depth, and gives a flow-law exponent of n = 3.6, which is closer than n = 5.3 to values determined by laboratory experiments on ice.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Kamb, W. Barclay}, } @phdthesis{10.7907/BHED-BJ17, author = {Kieffer, Hugh H.}, title = {Near infrared spectral reflectance of simulated Martian frosts}, school = {California Institute of Technology}, year = {1968}, doi = {10.7907/BHED-BJ17}, url = {https://resolver.caltech.edu/CaltechETD:etd-07172006-093716}, abstract = {In view of the apparent conflict between spectral observations and recent theories of the Martian polar caps, comparison spectra were obtained for frosts of relevant composition and grain size. The spectral reflectances of frosts formed from pure CO2, and pure H2O and mixtures of these gases have been measured from 0.8 to 3.2 [microns]. Low-weight fractions or small surface concentrations of H2O resulted in spectra similar to pure H2O frost spectra. The concentration of the condensable gas and the radiation balance effect the frost textural scale and the contrast of the reflection spectrum. The emissivity of the polar caps may be small, in contrast to previous assumptions. Probable processes of frost formation and sublimation on Mars and seasonal variations of frost composition suggest that reflection spectra obtained in the Martian spring may be misleading. In light of the laboratory results and probable Martian conditions, previous suggestions that the Martian polar caps are H2O are not valid. Future diagnostic observations in the near and thermal infrared are suggested. Figures 10, 11 and 12 are photographs of frost samples and will not reproduce well. Photographic copies may be ordered.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Ingersoll, Andrew P. and Kamb, W. Barclay and Murray, Bruce C.}, } @phdthesis{10.7907/FCVB-NS79, author = {Chapple, William Massee}, title = {A mathematical study of finite-amplitude rock-folding}, school = {California Institute of Technology}, year = {1964}, doi = {10.7907/FCVB-NS79}, url = {https://resolver.caltech.edu/CaltechTHESIS:05152013-140445759}, abstract = {The problem of the finite-amplitude folding of an isolated, linearly viscous layer under compression and imbedded in a medium of lower viscosity is treated theoretically by using a variational method to derive finite difference equations which are solved on a digital computer. The problem depends on a single physical parameter, the ratio of the fold wavelength, L, to the “dominant wavelength” of the infinitesimal-amplitude treatment, L_d. Therefore, the natural range of physical parameters is covered by the computation of three folds, with L/L_d = 0, 1, and 4.6, up to a maximum dip of 90°.
Significant differences in fold shape are found among the three folds; folds with higher L/L_d have sharper crests. Folds with L/L_d = 0 and L/L_d = 1 become fan folds at high amplitude. A description of the shape in terms of a harmonic analysis of inclination as a function of arc length shows this systematic variation with L/L_d and is relatively insensitive to the initial shape of the layer. This method of shape description is proposed as a convenient way of measuring the shape of natural folds.
The infinitesimal-amplitude treatment does not predict fold-shape development satisfactorily beyond a limb-dip of 5°. A proposed extension of the treatment continues the wavelength-selection mechanism of the infinitesimal treatment up to a limb-dip of 15°; after this stage the wavelength-selection mechanism no longer operates and fold shape is mainly determined by L/L_d and limb-dip.
Strain-rates and finite strains in the medium are calculated f or all stages of the L/L_d = 1 and L/L_d = 4.6 folds. At limb-dips greater than 45° the planes of maximum flattening and maximum flattening rat e show the characteristic orientation and fanning of axial-plane cleavage.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Kamb, W. Barclay}, } @phdthesis{10.7907/G7V2-0T57, author = {Benson, Carl S.}, title = {Stratigraphic Studies in the Snow and Firn of the Greenland Ice Sheet}, school = {California Institute of Technology}, year = {1960}, doi = {10.7907/G7V2-0T57}, url = {https://resolver.caltech.edu/CaltechETD:etd-03232006-104828}, abstract = {
NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document. The Greenland ice sheet is treated as a monomineralic rock formation, primarily metamorphic, but with a sedimentary veneer of snow and firn. This sedimentary member is perennial above the firn line, and the classical methods of stratigraphy and sedimentation can be profitably applied to it. During a 4-year period 146 pit studies and 288 supplementary Rammsonde profiles were made along 1100 miles of over-snow traverse (Fig.1). Temperature, density, ram hardness, and grain size were measured in the strata exposed in each pit. Stratification of snow results from variations in the conditions of deposition and is emphasized by subsequent diagenesis. Summer layers are coarser-grained and have generally lower density and hardness values than winter layers; they may also show evidence of surface melt. The onset of fall is usually identified by an abrupt increase in density and hardness accompanied by a decrease in grain size. This stratigraphic discontinuity is used as the annual reference plane. Strata in the upper 10 to 20 meters compose a succession of annual sequences which are preserved in recognizable form for at least several decades. Correlation of annual layers between pits, spaced 10 to 25 miles apart along the traverse of Figure 1, gives a picture of annual accumulation during the past 5 to 20 years for western Greenland between 69 and 77°N. The control established by these data, together with information from earlier expeditions (primarily those of Koch-Wegener and DeQuervain) and from permanent coastal meteorological stations, have been used to make a map showing the distribution of gross annual accumulation, essentially the equivalent of annual precipitation, for the entire ice sheet (Fig. 30). In general, the accumulation contours follow the north-south trend of the coast lines, with extremes of less than 10 cm H2O in the northeast and more than 90 cm H2O per year in the south; the average for the ice sheet is 34 cm H2O per year. The zone of maximum precipitation lies close to the coast in two regions, one on the east coast between Angmagssalik and Scoresbysund, the other on the west coast between Upernavik and Thule. In addition to the existence of a useful stratigraphic record four diagenetic facies are recognized on the ice sheet. (1) The ablation facies extends from the outer edge, or terminus, of the glacier to the firn line. The firn line is the highest elevation to which the annual snow cover recedes during the melt season. (2) The soaked facies becomes wet throughout during the melting season and extents from the firn line to the saturation line, i.e., the uppermost limit of complete wetting. The saturation line is the highest altitude at which the 0°C isothermal surface penetrates to the melt surface of the previous summer. (3) The percolation facies is subjected to localized percolation of melt water from the surface without becoming wet throughout. Percolation can occur in snow and firn of sub-freezing temperatures with only the pipe-like percolation channels being at the melting point. A network of ice glands, lenses, and layers forms when refreezing occurs. This facies extends from the saturation line to the upper limit of surface melting, the dry-snow line. Negligible soaking and percolation occur above the dry-snow line. (4) The dry-snow facies includes all of the glacier lying above the dry-snow line, and negligible melting occurs in it. The saturation line can be identified by discontinuities in temperature, density, and ram hardness data, and it may also be located by examination of melt evidence in strata exposed on pit walls. It is as sharply defined as the firn line; but the dry-snow line, although determined by the same methods, is an ill-defined transition zone 10- to 20-miles wide. The facies represent a response to climate, therefore changes in the location of facies boundaries may be used as indicators of secular climatic change. Since facies are not restricted to the Greenland ice sheet, they provide the basis for a general classification of glaciers. This “facies classification” is areal in nature and gives a greater resolution of characteristics than Ahlmann’s “geophysical classification.” In particular, the “facies classification” permits subdivision of large glaciers which span the entire range of environments from temperate to polar. Ahlmann’s useful distinction between temperate and polar glaciers takes on new meaning in the light of glacier facies. Thus, a temperate glacier exhibits only the two facies below the saturation line whereas one or both of the facies above the saturation line are present on polar glaciers. An attempt has been made to map the distribution of facies on the Greenland ice sheet (Fig. 48). The distribution of mean annual temperature on the ice sheet may be approximated by gradients with respect to altitude and latitude of 1°C/100m and 1°C per degree latitude respectively. The altitude gradient is controlled by strong outgoing radiation, producing deep inversions and katabatic winds. The katabatic winds are warmed adiabatically as they descend along the surface of the ice sheets and this is the primary control determining the temperature gradient along the snow surface. The latitude gradient is based on temperature measurements made above 2000 m on the ice sheets and on average values from meteorological stations spanning 20° of latitude on the west coast. A contour map of isotherms based on these gradients compares well with temperature values obtained from pits on the ice sheet. (Fig. 40). The densification of snow and firn is discussed for the case where melting is negligible. The assumption is that accumulation remains constant at a given location and, under this assumption, the depth-density curve is invariant with time as stated by Sorge’s law. As a layer is buried it moves through a pressure gradient under steady-state conditions, and it is assumed that the decrease in pore space with increasing load is simply proportional to the pore spaces, i.e., […] where […] = specific volume of firn ([…] = firn density), […] = specific volume of ice = 1.09 cm3/g, […] = load at depth z below the snow surface and m = a constant which depends on the mechanism of densification. The depth-density equation obtained from equation 8 is […] where K = […], […] = void ratio for snow of density […], and […] = void ratio for snow of density […], […] = density of snow when […] = 0. The consequences of the assumption in equation 8 compare favorably with observation. A fundamental change in the mechanism of densification is recognized within 10 m of the snow surface. The concept of a “critical density” is introduced. Before the density of snow attains the critical value it is compacted primarily by packing of the grains. The critical density represents the maximum value obtainable by packing and further compaction must proceed by other mechanisms. The rate of change of volume with increasing load decreases by a factor of 4 when the critical density is exceeded. The same equations hold in the case where melt is not negligible but the rates of densification are higher. Bauer’s (1955) estimate for the balance of the ice sheet is revised. Two corrections are applied: (1) the average annual accumulation value of 31 cm H2O originally estimated by Loewe (1936) is revised to 34 cm H2O as a result of this study; (2) the relative areas of ablation and accumulation zones in Greenland north of 76°N are more accurately defined. The net result is a slightly positive balance which is interpreted to mean that the Greenland ice sheet is essentially in equilibrium with present day climate.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Kamb, W. Barclay and Sharp, Robert P.}, }