Flow velocity profiles and accumulation rates from mechanical tests on ice core samples

The Physical Basis of Ice Sheet Modelling (Proceedings of the Vancouver Symposium, August 198). IAHS Publ. no. 10. Flow velocity profiles and accumulation rates from mechanical tests on ice core samples H. Shoji & C.C. Langway, Jr. Ice Core Laboratory Department of Geology State University of New York at Buffalo 0 Ridge Lea Road Buffalo, New York 1, USA ABSTRACT Both the horizontal and vertical velocity profiles at Dye, Greenland are calculated by using a strain rate enhancement factor profile obtained by making uniaxial compression tests on samples of the Dye deep ice core. A -dimensional steady state laminar flow model is used to calculate the horizontal velocity profile. The vertical velocity profile is obtained from the horizontal velocity profile by applying the Dansgaard-Johnsen model. The depth-age relationship is calculated and compared with time-scales determined from 8 0, conductivity and dust measurements. The results indicate that the snow accumulation rate during late Wisconsin age was between 1/ and 1/ of the present day value. Profils de vitesse et taux d'accumulation déduits d'essais mécaniques sur des carottes de glace RESUME Les profiles de vitesse horizontale et verticale à Dye, Groenland, ont été calculés en utilisant les facteurs d'amplification obtenus à l'aide d'essais en compression uniaxiale de carottes de glace profonde. Un modèle d'écoulement laminaire bi-dimensionnel a été employé pour calculer le profil des vitesses horizontales. Le profil des vitesses verticales en a été déduit en utilisant le modèle de Dansgaard-Johnsen. L'âge en fonction de la profondeur a été calculé, et comparé aux âges déduits de ^80, de la conductivité et de la teneur en poussières. Les résultats indiquent qu'à la fin du Wisconsin l'accumulation était entre 1/ et 1/ de sa valeur actuelle. INTRODUCTION AND PREVIOUS WORK To understand the differential flow behavior of existing large polar ice masses, it is necessary to investigate the variations in the mechanical properties of the entire ice body. The 0 m long vertical ice core recovered continuously from the surface to the bed at Dye, Greenland ( 11'N, 9'W) during the summers of 199, 1980 and 1981 permitted an extensive study to be made on the recovered core samples. Initial mechanical tests were made in the field immediately after core recovery during the 1980 and 1981 field seasons to evaluate the volume relaxation effect as a function of time after core recovery (Shoji & Langway, 198a). Follow-

8 H. Shoji & C.C. Langway, Jr. up laboratory tests were made later on samples stratigraphically adjacent to the samples measured in the field (Shoji & Langway, 198b). The effect of aging (volume relaxation) on the mechanical property testing of ice core samples has not yet been established for the four year time-span represented in this study. Dansgaard & Johnsen (199) calculated the depth-age relationship for large ice sheets by estimating the effect of horizontal shear deformation near the bottom and the conditions existing at Camp Century, Greenland. They considered the horizontal velocity profile to be divided into two zones: the upper zone where the horizontal velocity is constant with depth, and the lower zone where the velocity decreases proportionally to the depth. The complete vertical velocity profile was then calculated by using this simple two-zone model and the incompressibility of ice. The resultant vertical velocity profile is equivalent to the annual layer thickness profile under steady state ice flow conditions. However, by using this approach a different vertical velocity profile occurs when different value is assumed for the accumulation rate, which produces a different age for ice at the same depth level. The accepted time-scale developed for the Dye deep ice core was determined by different methods. The Holocene age ice is dated by a combination of ô 18 0, solid conductivity and dust measurements (Reeh et al., 198; Hammer et al, 198). The Wisconsin age ice is dated by detailed 18 0 measurements on the ice core and a correlation of these results with sea sediment records (Dansgaard et al, 198) and lake sediment records (Oeschger, 198). The careful multiple dating of the Dye ice core combined with the mechanical measurements made on ice core samples to obtain the vertical velocity profile provides us with the unusual opportunity to estimate the accumulation rate changes that took place during the Wisconsin Ice Age. CORE SAMPLES In addition to the Dye samples measured in the field (Shoji & Langway, 198a) and later in the laboratory (Shoji & Langway, 198b), new samples from the 19 m and the 190 m depths were prepared for this study. Specimens for uniaxial compression tests were prepared by rough-cutting with a bandsaw and microtome finishing. Each specimen was covered with silicone oil to minimize sublimation. Test temperatures were held constant (±0. C) and monitored by a copper-constantan thermocouple. Uniaxial compression stress was applied to the specimens (. x. x 9.cm), which were cut inclined to the original long-core axis in order to position the maximum resolved shear stress plane parallel to the horizontal plane of the ice sheet. The specimen was deformed to about % strain under a constant crosshead speed using an Instron Model 111 testing apparatus. Specimen length was monitored during testing by a Pickering LVDT displacement detector. EXPERIMENTAL RESULTS The uniaxial strain rate, è, adopted for the tests ranged from 1CT to 1CT 8 s _1. The stress-strain curves obtained were of stress saturation type in which stress levels remain approximately constant after a 1% strain. The maximum value of the uniaxial stress, a is used in the analysis that follows. The experimental results which include the data obtained previously (Shoji & Langway, 198a, 198b) are given in Table 1. The enhancement factor E s for shear deformation along the horizontal plane in the ice sheet is defined by taking the temperature dependency of strain rate into consideration as.-, ^measured.,. E s = (1) [Ao n exp(-q/rt)]

Flow velocity profiles 9 where the flow law parameters A, n and Q are taken from Barnes et al. (191) as. x 8 s -1 (MPa) - ",.98 and 8.8 kj/mol, respectively, for the -1 to - C temperature ranges; and as.0 x 8 s _1 (MPa)~ n,.01 and 8. kj/mol, respectively, for the -8 to -1 C temperature range. R is the gas constant and T is the absolute temperature. The calculated enhancement factor profile is shown in Fig. 1. All depth scales used in Figs. 1 through were converted to true vertical depth after the calculations were made. TABLE 1 Experimental results of uniaxial compression tests. Specimen number started with F denotes the result obtained on fresh ice core specimens Specimen Number F1-1 1-1 8 F-1-1 -1 F-1 F88-1 F9-1 F18-1 Core Depth m 0 0 0 0 0 0 0 0 0 0 99 99 99 99 19 19 Temp - C 1. 1. 1.8 1. 1. 11. 11. 11. 11. 1.1 1. 1*1 '"1.1 1.0 1.8 1.8 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.0 1.8 1. 1. 1.8 1. Stress bar 18. 11. 1.. 1.8 19.1 9.0 1.1 11. 1. 1. 8.8 1.0 1..9. 1. 9.. 1.8 9..9 8.1 8. 8.8 8.. 11.0 8.9. 9.0 8.0.. 8.1 Strain Rate xlo" s~ l 0.1 0.9. 1.0.0 0. 1. 0.8 0.. 0. 1.0 1. 0.0 0.1 1. 0.9 0.9 0.9 0. 0. 0.1 0.1 1. 0.1 0.8 0. 0.9 0. 1.1 0. 0. 0. 1.1 0.8 Enhancement Factor 0. 0.0 0. 0.8 0.1 0. 0.0 0.9 0.0 0.9 0.80 0. 0. 0.1 0.9.0 0. 0.9 0. 1. 0. 0. 0.1 0.9 0.8 0. 1. 0.1 0.8 1. 1. 1. 8...

0 H. Shoji & C.C. Langway, Jr. TABLE 1 (cont.) Specimen Number 1-1 8 8-1 109-1 8 9 1-1 F1-1 1-1 1-1 1801-1 8 9 Core Depth m 18 18 18 18 18 18 18 18 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 180 180 180 180 180 180 180 181 181 181 181 181 181 181 181 181 181 181 181 181 181 181 181 181 181 Temp - C 1 1.0 1.1 1.0 1 1. 1.1 1.0 1. 1. 1. 1. 1. 1.0 1.8 1. 1. 1. 1. 1.8 1.8 1.8 1.8 1.1 1.0 1.0 1 1.1 1.0 1.0 1. 1. 1.1 1 11. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. Stress bar.....8...9 8..8.8 8.1.1. 8...1.... 11. 9.1.....1.8.0 9.......0....9..9...8..1 Strain Rate xl(t s~ l 0. 0.9 0.91 0.8 0.88 0.0 0. 1.. 0.90 1.1 0.81 0. 0.8 0.9 0.1 0. 0. 0.91 0. 0.8 0.9 0. 0.8 1..0.0 0.89 0. 0. 0.0 0.8.1 1. 1. 1. Enhancement Factor..... 9.1.1.9.....1. 1.. 1 0. 1. 0.8 1. 1 1 1 1 1..9 8.9 1. 8. 8.8 9. 8. 11 1.8 9.9 11 8.1 9..8

Flow velocity profiles 1 TABLE 1 (cont.) Specimen Number 180-1 8 1880-1 189-1 19-1 19-191-1 Core Depth m 190 190 190 190 19 19 19 19 19 19 19 19 00 00 01 01 01 01 01 01 Temp - C 1. 1. 1.8 1.8 1.8 1. 1. 1. 1.0 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 11. Stress bar..1.1.......8.1.9......9..8.0..0..8... Strain Rate xlo - s~ l 1. 0.9 0. 0. 0.8 0.8 0. 0. 0. 0. 0.8.0 1. 0. 0.8 0.8 0.89 0.0 0.1..1 Enhancement Factor.9.0..0.8......1. 9..0. 9. 9.0.0.1 8.1 1 1 1 11 1 1 8. HORIZONTAL VELOCITY The Dye drilling site is located 1. km from the ice divide measured along the flow line (Reeh et al., 198). This distance is about 0 times the ice thickness and ensures the applicability of a -dimensional laminar flow model for the horizontal velocity calculation (Raymond, 198). The horizontal velocity at height y from the bottom, u(y), is obtained by integrating the shear strain rate è converted from unixial strain rate (Nye, 19), as follows: y u(y) ={e s dy () y = f (n+1)/ i A(p^sina)''(iï - y) n exp(-q/rt)dy where p is ice density (0.91 g/cm ), a is surface slope (. x ~ rad) and H is the true ice thickness (009 meter of ice equivalent). The relationships between core depth, true vertical depth, ice equivalent depth, and height are shown in Table. The gravitational acceleration is given by g. The integration in Equation () was made by summing each velocity increment in

H. Shoji & C.C. Langway, Jr. p.*: Depth 0 0. Sb 0. 0. -awo 0.8 1 1 a> Depth (km) 0 0. 0. 0. 0.8 lu 1 1 1 18.0 o o o a a» o Holocene o-œ ca>o-oo go n Wisconsin,1,1 1, 1, 1, 1, 1, 1, 8 TO ( 1 18 Enhancement Factor 1 18.0 8 TO 1 1 1 18 Enhancement Factor FIG. 1 (left) Enhancement factor profile obtained from uniaxial compression tests of ice core specimen. FIG. (right) Enhancement factor profile obtained by averaging test results in order to calculate horizontal velocity profile. TABLE Relationship between depths and height (Gundestrup & Hansen, 198) Core Depth (m) 0 0 00 00 0 18 0 (Wisconsin/Holocene transition) (bottom) True Vertical Depth (m) 0 0 00 00 198 18 0 Ice Equivalent Depth, y' (m) 0 9 1 19 009 Ice Equivalent Height, y (m) 009 19 1 0 0 0 m depth increments above 800 m depth, 0 m increments between 800 and 0 m depth, and m increments below 0 m depth. The depth and temperature data are from Gundestrup & Hansen (198). The surface topography map of Gundestrup et al. (198) was used for obtaining the regional surface slope value. In some cases, the enhancement factor values shown in Fig. are averages from closely spaced samples from a specific depth interval. A surface velocity value of 1. m a -1 is obtained from the horizontal velocity profile shown in Fig.. The comparison of this entire profile with the results of borehole tilting measurements made by Gundestrup & Hansen (198) showed that the difference between them is smaller than % at each depth level in the ice sheet.

Flow velocity profiles VERTICAL VELOCITY The horizontal velocity u(y) is generally assumed to be proportional to the distance x from the ice divide (Dansgaard & Johnsen, 199), as follows: u(x,y) = kxfiy) () where k is a constant and fly) is a function of y. The vertical velocity v at height y fom the bottom is calculated by using the incompressibility condition of the ice: Therefore, Ufi=0 () ay ox v(y) = -k \fly)dy H k = v(h) () () The vertical velocity at the Dye surface, v(h), is taken as a 0. m a -1 (Reeh et al., 198). The absolute value is equal to the accumulation rate in meter of ice equivalent under steady state conditions. Equation () is a boundary condition which makes u(y) depend not on the absolute value but on the shape of the u(y) profile curve. The horizontal velocity u(y) (in Equation ()) for the Dye location is shown in Fig.. The integration shown in Equation () was made by summing the incremental velocity values from the same increments used for the horizontal velocity calculations. The calculated vertical velocity profile is shown in Fig.. o 0. 0. 0. 0.8 0. 0. 0. 0.8 1,0 Depth 1. - - - - 8 1 1 Horizontal Velocity (m/year) 1..0 1 Holocene Wisconsin i i i 0.1 0. 0. 0. 0. Vertical Velocity (m/year) FIG. (left) Horizontal velocity profile at Dye, Greenland. FIG. (right) Vertical velocity profile at Dye, Greenland.

H. Shoji & C.C. Langway, Jr. DEPTH-AGE RELATIONSHIP The age t of an ice layer at an ice equivalent depth y'(y' = H-y) from the surface is calculated by the following equation: H ' y AS The vertical velocity profile obtained is shown in Fig.. The integration shown in Equation () was made by summing the incremental age values from the same increments used for the velocity profile calculations. The depth-age relationship obtained for Holocene period ice (above the 18 m core depth) is shown in Fig.. These calculations are in good agreement with the Holocene ô 18 0, solid conductivity and dust measurements (Reeh et al., 198; Hammer et al, 198). The age of ice at the Holocene/Wisconsin transition depth (18 m) is shown to be about 11 kabp. For the Wisconsin ice (below 18 m), our depth-age curve (A = 1 in Fig. ) differs appreciably from the depth-age curves determined by Dansgaard et al. (198) and Oeschger (198), as shown by open and closed circles and crosses. Assuming the ô 18 0 age determinations are correct, the difference is most probably caused by a substantial decrease in the snow accumulation rate during the Wisconsin period relative to the Holocene accumulation values. SNOW ACCUMULATION DURING THE WISCONSIN The procedures we used for calculating the depth-age curves for Wisconsin ice assumes that ice thickness for the Dye location was the same during the Wisconsin age as it is at present It was also assumed that the shape of the horizontal velocity profile during the Wisconsin was the same as it is today. For this analysis the accumulation rate A for the Wisconsin age ice was chosen to be /, 1/, 1/, 1/ or 1/ of the present day value of 0. m a -1, which was taken as unity. First, the depth-age curve was calculated for the Wisconsin period with one unique value used for the accumulation rate, assuming steady state conditions. The entire ice profile was then deformed by computer modelling from the surface to the bottom. The vertical velocity profile shown in Fig. and an accumulation rate of 0. m ice equivalent a -1 were used to deform the entire ice profile for an 11 000 year period under present day steady state ice flow conditions. The results provide a unique depth-age curve for each chosen accumulation-rate value. Six depth-age curves are shown in Fig.. The 8 18 0 based results of Dansgaard et al. (198) fits our results best when À = 1/. Dansgaard et al. (198) pointed out the possibility of disturbed strata existing in the bottom 8 m of the ice core profile. Here a simple flow model would not apply. The. 18 0 results, of Oeschger (198) from between 0 m and 0 m height fits best between our A = 1/ and A = 1/ curves, although this data range is limited. The preceding comparative analysis of our data with others suggests that the snow accumulation rate which occurred during the Wisconsin period was between 1/ and 1/ of the present day value. To date the direct measurement of annual layer thicknesses for the Wisconsin ice has been limited. Among the few results available are the dust measurements of Hammer et al. (198), which give an accumulation rate for the Late Wisconsin of about half the present-day value; and the ionic chemistry measurements of Herron & Langway (198) and the Be measurements of Beer et al. (198), both of which give the Wisconsin snow accumulation rate as between 0% to 0% of the present day value. Using a temperature profile analysis of the Dye borehole, Dahl-Jensen & Johnsen (198) recently obtained a mean accumulation rate for Wisconsin period of 0% ± % of the present day value.

Flow velocity profiles Age (kabp) Age (kabp) FIG. (left) Depth-age relationship of the Dye Holocene ice. The open circles indicate the time-scale determined by 18 0, solid conductivity and dust measurements (Reeh et al, 198; Hammer et al., 198). FIG. (right) A family of depth-age curves for the Dye Wisconsin ice. Accumulation rate, A was changed from A = 1 (Holocene value) to /, 1/, 1/, 1/ and 1/ for each curve calculated. The data of Dansgaard et al. (198) are shown as dots (above 8 m height) or open circles (below 8 m height). Uncertainty exists in Dansgaard et al. data below 8 m. The data of Oeschger (198) are shown as crosses located between 0 m and 0 m height. DISCUSSION When calculating depth agerelationshipsusing simple laminar flow and the Dansgaard-Johnsen model, the uniformity of the accumulation rate and the ice thickness upstream from the drill site must be considered. The present day accumulation-rate changes from 0. m a" 1 at the ice divide to 0. m a -1 at Dye. This approximately 18% increase in annual snow accumulation found along the flow line results in making the annual layers found at deeper depths to be relatively thinner. Conversely, this thinning is nearly counterbalanced by the approximately 1% difference in the ice thickness which exists between the thinner ice divide and the downstream Dye location (Reeh et al., 198), which causes an increase in the thickness of an annual layer. The depth-age relationship calculated for Holocene ice agrees quite well with the results of S 18 0, solid conductivity and dust measurements, as is shown in Fig.. For the age calculation of the Wisconsin ice, ice thickness and the shape of the u(y) profile curve were assumed to be constant. If these assumptions were not applicable, the time scales calculated in this study would not be reliable under each accumulation rate value. However, it is revealed from the total air volume measurements (S. Herron & Langway, unpublished data) that south central Greenland experienced little or no elevation change during the last glaciation. The change of horizontal velocity profile does not affect the results of age calculations as long as the shape of the u(y) profile curve stays the same. The general shape of the horizontal velocity profile with depth should stay the same due to the increase of horizontal shear stress and temperature from the surface toward the bottom. The strain rate enhancement factor profile could vary between the Holocene and Wisconsin periods depending upon the controlling parameter. This subject

H. Shoji & C.C. Langway, Jr. needs further investigation. In a study of the Dye borehole, Gundestrup & Hansen (198) reported that the horizontal shear strain rate is strongly correlated with dust concentration levels. This suggests the possibility that the dust and/or other chemical species which vary simultaneously with the dust concentrations could be responsible for variations in the strain rate enhancement factors. On the other hand, our preliminary results from crystal orientation measurements on the Dye Wisconsin period ice, using an ultrasonic wave velocity technique, show a strong correlation between the crystal orientation distributions and the enhancement factors obtained by mechanical tests performed on the core. These results support the conclusion that fabric, or c-axes orientation, is a very dominant parameter in influencing the enhancement factor. It is reasonable to deduce that some combination of the fabric and the embedded impurities is a major factor controlling ice flow behavior. ACKNOWLEDGEMENT This research was supported by the U.S. National Science Foundation, Division of Polar Programs, Grant No. DPP80911. REFERENCES Barnes, P., Tabor, D. & Walker, J.C.F. (191) The friction and creep of polycrystalline ice. Proc. Roy. Soc. London A, 1-1. Beer, J., Andrée, M., Oeschger, H., Stauffer, B., Balzer, R., Bonani, G., Stoller, Ch., Suter, M., Wolfli, W. & Finkel, R.C. (198) Be variations in polar ice cores. In: Greenland Ice Core: Geophysics, Geochemistry, and the Environment (ed. by C.C. Langway, Jr., H. Oeschger, & W. Dansgaard), -0. Geophysical Monograph No., American Geophysical Union, Washington, D.C., USA. Dahl-Jensen, D. & Johnsen, S.J. (198) Palaeotemperatures still exist in the Greenland ice sheet. Nature 0(09), 0-. Dansgaard, W. & Johnsen, S.J. (199) A flow model and a time scale for the ice core from Camp Century, Greenland. /. Glaciol. 8(), 1-. Dansgaard, W., Clausen, H.B., Gundestrup, N., Hammer, C.U., Johnsen, S.J., Kristinsdottir, P.M., & Reeh, N. (198) A new Greenland deep ice core. Science 18, 1-1. Gundestrup, N.S. & Hansen, B.L. (198) Bore-hole survey at Dye, south Greenland. /. Glaciol. 0(), 8-88. Gundestrup, N.S., Bindschadler, R.A. & Zwally, H.J. (198) Seasat range measurements verified on a -D ice sheet Ann. Glaciol. 8, 9-. Hammer, C.U., Clausen, H.B. & Tauber, H. (198) Ice-core dating of the Pleistocene/Holocene boundary applied to a calibration of the 1 C time scale. Radiocarbon 8(A), 8-91. Herron, M.M. & Langway, C.C. Jr. (198) Chloride, nitrate, and sulfate in the Dye and Camp Century, Greenland ice cores. In: Greenland Ice Core: Geophysics, Geochemistry, and the Environment (ed. by C.C. Langway, Jr., H. Oeschger & W. Dansgaard), -8. Geophysical Monograph No., American Geophysical Union, Washington, D.C., USA. Nye, J.F. (19) The distribution of stress and velocity in glaciers and ice sheets. Proc. Roy. Soc. London A9, 11-1. Oeschger, H. (198) The contribution of ice core studies to the understanding of environmental processes. In: Greenland Ice Core: Geophysics, Geochemistry, and the Environment (ed. by C.C. Langway, Jr., H. Oeschger, & W. Dansgaard), 9-1. Geophysical Monograph No., American Geophysical Union, Washington, D.C., USA. Raymond, CF. (198) Deformation in the vicinity of ice divides. J. Glaciol. 9(), -. Reeh, N., Johnsen, S.J. & Dahl-Jensen, D. (198) Dating the Dye deep ice core by flow

Flow velocity profiles model calculations. In: Greenland Ice Core: Geophysics, Geochemistry, and the Environment (ed. by C.C. Langway, Jr., H. Oeschger, & W. Dansgaard), -. Geophysical Monograph No., American Geophysical Union. Shoji, H. & Langway, C.C. Jr. (198a) Mechanical properties of fresh ice core from Dye, Greenland. In: Greenland Ice Core: Geophysics, Geochemistry, and the Environment (ed. by C.C. Langway, Jr., H. Oeschger, & W. Dansgaard), 9-8. Geophysical Monograph No., American Geophysical Union, Washington, D.C., USA. Shoji, H. & Langway, C.C. Jr. (198b) The ice flow velocity profile for Dye-, Greenland. Geophys. Res. Lett. 1(1), 9-800.