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Physical Modeling of the Densification of Snow/Firn and Ice in the Upper Part of Polar Ice Sheets

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Physical Modeling of the Densification of Snow/Firn and Ice in the Upper Part of Polar Ice Sheets Title Physical modeling of the densification of snow/firn and ice in the upper part of polar ice sheets Author(s) Arnaud, Laurent; Barnola, Jean M.; Duval, Paul Citation Physics of Ice Core Records, 285-305 Issue Date 2000 Doc URL http://hdl.handle.net/2115/32472 Type proceedings Note International Symposium on Physics of Ice Core Records. Shikotsukohan, Hokkaido, Japan, September 14-17, 1998. File Information P285-305.pdf Instructions for use Hokkaido University Collection of Scholarly and Academic Papers : HUSCAP Physical modeling of the densification of snow/firn and ice III the upper part of polar ice sheets Laurent Arnaud, Jean M. Barnola and Paul Duval Laboratoire de Glaciologie et de Geophysique de l'Environnement, CNRS, B.P. 96, 38402 St. Martin d'Heres Cedex, FRANCE x o 20 40 60 I .r:: CL -OJ so o 100 Age at .84 density SAE t5 data 2850 yrs Herron·Langway 2850 yrs '... ' ", Pimienta 2950 yrs , II 120 Alley-Arzt 2800 yrs , II , 1\ ----- Herron·Langway 7400 yrs ', \ ----- Pimienta 6750 yrs , 140 ----- Alley-Arzt 6450 yrs , 0.3 0.4 0.5 0.6 0.7 o.s 0_9 density Plalc 8. L. Arnaud el al. , Figure 3. X l Close-off Age 3000 4000 "'" .'!l'" 0; 0 5000 6000 a) Vc=I(T), OO=I(T) ---- b) Vc=I(Gas Cont.), OO=I(T) ---- c) Vc=I(Gas Cont.), OO=I(Gas Cont. ---- d Pimienta, VC=f(T) Close-Off depth 90 100 5 .<:: a.OJ 110 "C 120 130 o 500 1000 1500 2000 2500 Depth (m) Plate 9. L. A rn aud et al.. Figure 7. 285 Physical modeling of the densification of snow/firn and ice in the upper part of polar ice sheets Laurent Arnaud, Jean M. Barnola and Paul Duval Laboratoire de Glaciologie et de Geophysique de l'Environnement, CNRS, B.P. 96, 38402 St. Martin d'Heres Cedex, FRANCE Abstract: We propose a model for the densification of snow, fim, and ice that includes the following: the densification of isothermal snow by grain boundary sliding [Alley, 1987], the microscopic approach of Arzt [1982] for the geometrical description of porous materials during densification, and plastic deformation with a power law creep for fim and ice densification. Current density profiles are well reproduced by this physical model assuming variations of the relative density at the snow-fim transition. This density, Do, corresponds to the change from densification by deformationless restacking to densification by power law creep. Do is always lower than the theoretical packing density for mono-sized spheres (Do = 0.64) and decreases with temperature; its low values are unlikely to be an effect of the particle size distribution, but instead arise from nonuniform densification. Variations of Do with temperature are correlated with variations of the load between sites for a given density. Do could also be modified by differences in porosity structure during snow metamorphism due to different surface conditions (for instance, wind, surface temperatures, and temperature gradients). Applied to past climatic conditions of Vostok, Antarctica, the densification model predicts close-off ages and depths during the last climatic cycles. Through variations of Do parameters, uncertainties in these predictions were estimated. 1. Introduction information in the air to that in the ice it is crucial to know precisely the conditions Environmental information preserved that snow transforms into ice. The in polar ice is associated either with the ice following are needed: (a) the close-off matrix, for instance the temperature which density, (b) the age of the gas at this density, depends on the isotopic content of the ice; (c) the age of the ice, and (d) the close-off or it is associated with the air trapped in the depth. ice, as is the atmospheric composition. (a) The close-off density can be estimated Because the air is trapped at the fim-ice from measurements of the evolution of transition (the close-off depth, approxi­ closed porosity on fim samples mately 80 m below the surface), to link the [Schwander et aI., 1984, 1993; Kameda Physics alIce Core Records Edited by T. Hondoh Hokkaido University Press, 2000, Sapporo 286 Physical modeling ofthe densification ofsnowlfirn and ice and Naruse, 1994]. However, these and their age range can smooth the measurements were from small samples concentration of the trapped gas over a that need corrections to get the effective few centuries when the accumulation close-off density. Another way is to rate is very low (as it is at Vostok). measure the total gas content of the ice; (c) The age of the ice at the close-off is the then, when the atmospheric pressure main parameter to link the ice and gas and the temperature are known, it records. When no density measure­ allows to estimate the density at which ments are available, densification the air is isolated from the atmosphere models have to be used as discussed (in terms of pressure) [Martinerie et aI., below. 1992]. This method has been applied to (d) The close-off depth can be estimated by a large number of different firns, and an measuring the gravitational enrichment empirical relationship between the firn of 15N of N2 trapped in air inclusions temperature (present-day climate) and [Sowers et aI., 1992], or it can be the pore volume Vi when the air is estimated usmg firn-densification isolated has been found: models. When no data are available, the precision of the last two parameters depends on quality of the firn-densification However, gas content profiles of the model. Furthermore, recent studies use Vostok core suggests that this empirical independent information to determine the relationship might not be valid for all air dating or trapping depths, and then use a the past climatic conditions, and also densification model to get climatic that wind could affect the pore volume information. For instance, Schwander et ai. at the isolation depth [Martinerie et aI., [1997], working on the GRIP core, used 1994]. CH4 to get a gas chronology for GRIP and (b) The age of the air in the firn, and thus at 15N to get close-off depths, and then ran a the close-off depth, has been studied by densification model with different climatic diffusion models validated by measure­ parameters to fit the data and thus calibrate ments of the composition of interstitial the glacial to interglacial temperature firn air. The gravitational separation of change m Greenland. Similarly, the different elements that causes an Greenland CH4 records of GISP or GRIP, enrichment of the heavier compounds which are of global significance, are now as a function of firn depth were widely used to synchronize Antarctic and included. This allows one to reproduce Greenland ice cores through densification the concentrations of atmospheric models [Blunier et aI., 1998; Steig et aI., compounds measured in the fim air 1998]. These examples show that firn­ [Schwander et aI., 1993; Trudinger et densification models should both reproduce aI., 1997], and also to reconstruct their the present- day situations and predict firn atmospheric history using an inverse profiles under climatic conditions having no method [Rommelaere et aI., 1997]. present-time analogues. The Vostok total These models showed that the air is few gas content profile [Martinerie et aI., 1994] tens of years old at the base of the firn, shows that an empirical relationship based L. Arnaud et al. 287 on present-day data might not be valid for and the depth at which this density is the past. This stresses the need for a reached increases as the temperature physical model instead of an empirical one. decreases [Anderson and Benson, 1963; We present a physical model based on Gow, 1975; Herron and Langway, 1980]: at pressure sintering and apply it to past -57°C it is approximately 30 m [Alley, Vostok climatic conditions. 1980] and at -23°C it is approximately 12 m [Herron and Langway, 1980]. In addition to the dependence on temperature, the 2. Densification model accumulation rate for a given temperature can also affect the depth of the critical The formation of ice in polar ice sheets density [Herron and Langway, 1980; results from the densification of dry snow Nishimura et aI., 1983] and firn. This densification is similar to the The second stage is firn (consolidated hot pressing procedure in ceramics and snow). Because seasonal variations of metals in which pressure is applied during surface temperature disappear, the trans­ sintering at high temperature, except that on formation of firn into ice can be considered ice sheets the pressure is due to the as isothermal. The end of this stage is accumulation of snow at the surface. characterized by the growth of the Three stages of densification are impermeable pore space fraction under the generally distinguished. During the first increasing overburden pressure. The stage, the densification of snow is mainly a average number of bonds per grain structural rearrangement of grains by grain­ (coordination number) increases with boundary sliding. Sintering is driven by the density from approximately 6 at the start of temperature gradient in the first few meters this stage to 16 for ice [Gow, 1969, this and by surface tension. Transport work]. Plastic deformation increases this mechanisms such as evaporation- coordination number and causes neck condensation and surface diffusion growth; particle motion is negligible. contribute to rounding of the grains and to During the final stage, atmospheric air intergranular bonding [Benson, 1962; Gow, is trapped in cylindrical or spherical pores; 1975]. The rearrangement of unbounded further densification of this bubbly ice is grains dominates the densification of highly driven by the pressure lag between the ice porous snow. Alley [1987] proposed a first matrix and the air in bubbles [Maeno and model for densification by grain boundary Ebinuma, 1983; Pimienta, 1987; Alley and sliding for snow below 2-m depth where Bentley, 1988; Salamatin et aI., 1997].
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