Ice Movement and Temperature Distribution in Glaciers and Ice Sheets

ABSTRACT. Water is present in glaciers in the form of veins at the threegrain junctions. This water remains unfrozen even many degrees below the normal freezing point, mainly because it contains much of the soluble impurity content of a glacier, but also because of the microscopic curvature of the ice-water interfaces. As the temperature is lowered and the veins shrink, the concentration of impurities in them increases, and the curvature effect also increases. The predicted relation between vein size and temperature has now been verified by laboratory experiments.Because of the latent heat of the vein water, the ice behaves macroscopically as a continuum with an anomalous specific heat capacity that depends strongly on temperature. From this point of view, a poly thermal glacier is a single medium with continuously varying properties, rather than consisting of distinct cold and temperate phases with sharp boundaries between them. The paper sets up differential equations for heat diffusion in such a continuum. To explain the local uniformity of the vein system seen under the microscope, it is found necessary to include the effect of diffusion of solutes along the veins.Solutions are presented for a model in which two semi-infinit.e slabs, initially having different temperatures, impurity concentrations and vein sizes, are instantaneously brought into contact. In this way, transition thicknesses between cold and temperate ice are estimated, and also the velocities of various kinds of waves that are generated from the original discontinuity at the interface. INTRO DUCTIO NOne approach to the problem of a poly thermal glacier (Fowler and Larson, 1978;Hutter, 1982;Fowler, 1984; Hutter and others, 1988) is to model it as consisting of two distinct continuous phases, namely, temperate and cold (or polar) ice. Temperate ice is at the melting point and contains moisture, while cold ice is below the melting point and is dry. Appropriate differential equations are formulated for the two different phases, and jump conditions are defined for the interface between them. We adopt here the different point of view that polycrystalline ice can be modelled as a single medium, but with smoothly varying thermal properties. Of course, this is not necessarily in conflict with the two-phase model, which may still be appropriate if the transition layer between the cold and temperate phases turns out to be sufficiently thin. The view of ice as a single medium with smoothly varying properties is based on observations in the laboratory of the behaviour of single veins of water in polycrystalline ice at the three-grain junctions (Mader, 1990, in press a, b). At temperatures within the range 0° to about -1°C, change of temperature is observed to be accompanied by a change in the size of the veins. This results from two effects (Lliboutry, 1971;Harrison, 1972;Nye and Frank, 1973;Raymond and Harrison, 1975;Harrison and Raymond, 1976) . present dissolved in the vein water. Because the ice phase tends to reject impurities, the shrinking of a v...

Section: Introductionmentioning

confidence: 99%

Thermal behaviour of glacier and laboratory ice

Nye

1991

“…Observed temperature gradients to 70 m depth along th e profile are in approximate agreement with these calculations. The effect is due to advection of colder ice from further inland b en eath warmer surface layers, as suggested by Robin ( 1955). In regions with high rates of accumulation of ice, especially with considerable ice depths, horizontal advection often dominates the temperature gradients in the upper part of the ice sheet.…”

Section: Analysis An D Calcu Lation Of T E Mpe Rat Ur E Profilesmentioning

confidence: 88%

“…The results should apply near the centre of an ice sheet in a steady state, where the vertical velocity at the top of the column will b e the same as the m ean rate of accumulation of ice, so that Equation (I) can be simplified considerably. Solutions to this problem given in Robin (1955) and shown in Figure 1 show the great influence of th e rate of accumulation on the temperature distribution in the steady-state model. For conditions encountered n ear the centre of Greenland, with an ice thickness of 3 000 m and an accumulation rate of about 30 cm ice a-I, upward flow of h eat from the base of th e ice does not penetrate more than half-way to the surface, due to advection of h eat through downward and outward motion of the ice.…”

Section: Analysis An D Calcu Lation Of T E Mpe Rat Ur E Profilesmentioning

confidence: 99%

“…The basic parameters that come from this work are a figure for the vertical velocity at the ice surface, u sually taken as being equal to the accumulation rate, the rate of change of surface temperature of the ice column and the basal temperature gradient. In Robin (1955) such curve fitting was used in conjunction with the steady-state assumption to determine the accumulation rate and ice movement at Camp VI in Greenland. Budd and others ( I971[b] ) have introduced an elegant method of curve fitting using a least-squares adjustment with a uniform vertical strain-rate model.…”

Section: Fig !/ Trajectories (Arrows ) Isochrones ( I03 Years Bromentioning

confidence: 99%

See 1 more Smart Citation

Reconciliation of Temperature-Depth Profiles in Polar Ice Sheets with Past Surface Temperatures Deduced from Oxygen-Isotope Profiles

Robin

1976

Self Cite

ABSTRACT. In ves tigati ons of isotopi c a nd tempera ture pro fil es in polar ice sh ee ts were mostly carri ed out inde p endently of one a nother until 19 73 whe n a workshop d ealing with both topics was held in Ca mbridge. Studies of temperature profi les show the a pproximate validity of theoreti call y d e rived tempera ture d istributio n s for stead y-state models of ice sh eets, whi le other a na lyses h elp to determin e d e partures from the s tead y sta te . The rev iew gives some idea of the d egree of accuracy of various solution s arising from studies of the hea t Aow a nd temperature distributio n of ice sheets. Much of this knowledge is directly applicable to interpre tatio n of isotopic profi les if a direct co rrespond ence be tween m ean isotopi c (5 values and mea n a nnual te mpe ra tures can be es tablished. The paper therefor e reviews vari ous methods of comparing IJ values and te mpe ra tures, and shows tha t for cen t ra l regions of polar ice sh ee ts a reaso n a b ly consistent rel ationship b e tween these fa ctors does exist. RESUME . Compatibilite des profils tempiratures-prqfondeurs dans les calottes polaires avec les temperatures passees de la surface telles qu'on les deduit des profils de teneur en isotope de l'oxy gene.Les rech erch es sur les profils en iso topes e t e n temperatures dans les calottes po laires ont sunout ete m e n ees independem m e nt l'un e de l'autre jusqu 'en ZUSAMMENFASSUNG. ZusammenJiihnmg von T emperatur-T ie.fen-Profilen ill polaren E isdecken und JnlherellOberjlachentel7lperaturen, hergeleitet aus Sauerstoifisotopell-Profilell. Untersu chungen von l so to p en-und T emperaturpro fil e n in polaren Eisdecken wurd en m e ist unabha ngig vonein a nder durchgefuhrt, bis im J ahre 1973 e in Se minar uber beide V e rfa hren in Cambridge a bgehalten wurde. Studien d er T e mperaturprofi le zeigen di e a nge n a h erte Gultigke it theoretisch a bgele iteter T emperaturve rteilungen fur stationare Mod ell e von E isd ecken, wahrend an d ere Analysen z ur Bes timmung d e r Abweichungen vom stationa ren Zusta nd b e itragen. D ie Zusammenstellung gibt ei n e n Eindruck von d el' Genauigkeit verschied ener Ansatze fur die Verteilung des Warm e Ausses und del' T e mpe ra tur in Eisdecken. Viele dieser Einsichten sind fur die D eutung vo n I sotopen-Profilen unmittelba r a nwe ndbar, wenn ein dire kte r Zusammenhang zwischen den mittle ren iso to pisch en (5-vVerten und del' mittl e re n Jahres tempera tur fes tzustellen ist. Die Arbeit diskuti ert d a h er verschi ed ene M ethode n d es Vergleich s von (5-Werten und T empera turen und weist nach , dass im Zentralb e re ich von polare n Eisd ecken zwisch e n di esen beid en Faktoren eine a usreich e nd konsistente Bez iehung besteht.] NTROD UCTION

“…It can be made partially temperature-dependent if necessary. The ice temperature can be specified (as a function of Z , or of both X and Z) or it can be calculated at each iteration by using the steady-state temperature distribution derived by Robin (1955). Once the temperature at a point is known, it is used to adjust the parameter A in the flow law by using the Arrhenius relation (Paterson, [c 1981 D. This can only be considered a rough approximation, however, since it only represents a steady-state decoup1ed solution.…”

Section: Approximationsmentioning

confidence: 99%

Two-Dimensional, Time-dependent Modelling of an Arbitrarily Shaped Ice Mass with the Finite-Element Technique

Hodge

1985

ABSTRACT. The two-dimensional, time-dependent flow of an arbitrarily shaped ice mass can be successfully modeled with the finite-element technique on a small computer. Methods developed for automatically generating the mesh data greatly simplify the data preparation and optimize the numerical simulations. Using quadratic basis functions permits the flow to be approximated quite adequately by only two element rows (five nodes vertically). Mixed-order basis functions , however, must be used so that numerical oscillations do not set in, and the ends of the ice mass, where the thickness tends to zero, must be treated carefully. Time simulations to a steady-state condition are necessary to test such numerical models adequately.South Cascade Glacier, Washington, is currently close to equilibrium. A bedrock sill dominates the bed topography in the lower half of the glacier, rising to a height of about 20% of the ice thickness. This sill produces a maximum increase in the overall thickness of about 6-7% compared to what the thickness would have been if the sill were not present. Finally, this glacier does not appear to be sliding much, if at all, despite its maritime alpine environment. This could help explain the difficulties encountered when trying to measure sliding and basal water pressures on the same glacier (Hodge, 1979), or it could imply that drag exerted by the valley walls has a significantly greater effect than conventional shape-factor concepts imply. REsuME. Modelisation il deux dimensions en fonction du temps d'une masse de glace de forme quelconque par la technique des elements finis . L'ecoulement bidimensionnel fonction du temps d'une masse de glace de forme quelconque peut-etre modelise avec succes par la technique des elements finis it l'aide d'un petit calculateur. Une generation automatique du maillage simplifie grandement la preparation des donnees et optimise les simulations numeriques.