An enthusiastic empirical relation between overburden stress and you will firn density

An enthusiastic empirical relation between overburden stress and you will firn density

One or two empirical equations for firn densification was received,given firn porosity since a function of overload tension. In the first equation, thereduction ratio out of porosity during the firn is thought to be proportional on broadening ratioof overload stress and also the mth stamina out-of this new porosity. The brand new porosity exponent meters are going to be alongside -dos, to have a just-fit with 14 breadth-density profiles fromGreenland and Antarctica. On second picture, brand new reduction proportion from porosity wasassumed to increase proportionally into the increment from overload tension and you may thenth strength of one’s porosity. The essential satisfactory viewpoints of the exponent start from -1 to one. This has been recommended one to firn density, computed generally by overburdenpressure and firn heat, contribute to a lower life expectancy studies.

step 1 Introduction

The conversion procedure for firn so you can freeze is one of the extremely fundamental victims in polar frost-layer studies. Enough theories regarding your dry densification of firn has started recommended ( Site Robin Robin, 1958 Site Schytt Schytt, 1958 Resource Bader Bader, 1960, 1962 Resource Benson Benson, 1962 Anderson and you will Reference Benson Benson, 1963 Site Kojima Kojima, 1964 Reference Gow Gow, 1975). But not, a thorough design together with grain-paying, sublimation/condensation, volume/ facial skin diffusion, freeze deformation and you will recrystallization techniques was not solidly created. The densification processes are also learned empirically ( Resource Robin Robin, 1958 Reference Schytt Schytt, 1958 Reference Herron and you can Langway Herron and you will Langway, 1980 Source Ling Ling, 1985 Reference Langway, Shoji, Mitani and you will Clausen Langway while others, 1993). Site Schytt Schytt (1958) found a keen empirical family relations ranging from firn occurrence and the pounds away from overlying accumulated snow. Reference Herron and you will Langway Herron and you may Langway (1980) examined the authenticity from Schytt,s equation playing with 17 depth-occurrence pages from Greenland and you can Antarctica. Site Langway, Shoji, Mitani and you can Clausen Langway while some (1993) presented a straightforward loved ones between overload tension and firn density

So it paper targets obtaining a simple formula fora matchmaking between overload stress and you will firndensity from the facial skin with the depth from pore personal-from considering the studies by Source Schytt Schytt (1958) and Langwayand others (1993).

dos Logical Techniques

Rather than using the snowfall densification law ( Reference Bader Bader, 1960,1962), a presumption is made you to definitely snow behaves eg aperfectly plastic material. Which is, porosity, s(= (?i – ?)/ ?i) is determined only because of the overload stress, P, at each depth peak. ?is the brand new firn thickness and you may ?i ‘s the ripple-free freeze density at -20°C (0.919.Mgm-3). When the pressure P develops so you’re able to P +dP, s decreases so you’re able to s-ds. Thereduction proportion out-of porosity, -ds/s is actually believed toincrease proportionally into the growing ratio away from tension, dP/P as well as the mth off stamina of s the following:

Various other equation is acquired because of the as long as new prevention ratio off porosity, -ds/s grows proportionallytothe increment away from tension, dP, therefore the nth fuel out of s below:

Recently, Site Langway, Shoji, Mitani and Clausen Langway while some (1993) shown an excellent linearrelation between (?i-?) dos and also in(P) about facial skin to.new breadth off pare romantic-off for three sites from inside the Greenland andAntarctica. When we write the word(?i-?)2of Langway while others (1993) in order to ((?i-?)/?i) 2 , this new family relations is conveyed below:

In addition, Reference Schytt Schytt (1958) recommended the second relatives between firn density (?) and you may depth on surface (h) much the brand new Maudheim Ice key,Antarctica:

step three Overall performance

Depth-thickness suggestions is actually obtained from fourteen sites inside the Greenland and you can Antarctica since the found into the Desk step one. The latest 10m breadth firn temperature of one’s borehole include-54.3° so you’re able to -16.4°C and you will yearly buildup cost rangefrom 0.034 to help you 0.39 meters year 1 in liquids comparable. Thedata scatters in bulk-occurrence thinking are ±0.005 Mgm -step three of these from Conference, S25, H15, S25, G15, G6,Byrd facial skin Charlotte Nc NC sugar daddy go camping and you can Dome C. On the other hand, thedata scatters to own siteJ, website dos, site A great, G2, Mizuho, LittleAmerica V and you can Old Byrd Route was within this ±0.003 Mgm -3 , as the densities had been computed much more truthfully by the a volumetric approach. New reliabilityof ten meters breadth heat tends to be ±0.1°C or better.

A trial is made to find the most satisfactory valuesfor yards and you will letter when you look at the Equations (1) and you may (4) using the over depth-occurrence users. Depth-thickness beliefs from thesurface towards the breadth at which the latest thickness try 0.80 Mg meters step 3 are used for the fresh correlation-coefficient investigation.

Figure la reveals the results of your linearity shot forEquation (1) using various other beliefs off m. It is clear one relationship coefficients make the high beliefs to meters = -dos (roentgen = 0.98). Figure 2b suggests the outcomes for Equation (4) playing with additional opinions out-of n. It absolutely was discovered that the latest correlation coefficients take the highest really worth regarding n = -step one so you’re able to + 1 (roentgen = 0.97 within n = 1; roentgen = 0.98 al n = 0;roentgen = 0.95 at the n = 1). For this reason, we obtain the new followingequations, which happen to be the same with Equations (7) and you will (8):

Fig.1 . The fresh loved ones anywhere between thinking regarding efforts and you will relationship coefficients using their simple deviations. Profile 1a suggests the outcomes getting yards in Picture (1) and Profile 1b getting letter during the Picture (4).

Fig.2 . Connections between ln(P) and you may s dos to possess fourteen internet sites during the Greenland and you will Antarctica. P are an overburden stress and you will s is the porosity out-of firn, in which s =(?i-?)/?i.?i ‘s the bubble-100 % free ice density and you can ? is the firn occurrence.

Figure 2 shows the relation between ln(P) and s2 for the 14 ice cores from Greenland and Antarctica. It is seenthat ln(P) and s 2 have excellent linear correlation. Correlation coefficients, linear slopes (C1),Y intercepts(C2) and degrees of freedom are summarized in Table 2. The lowest correlation coefficient at G6 is due to datavariations in the surface-firn densities.

Profile step three reveals this new relatives between P plus in(s) forthe fourteen frost cores. Evidently most of the overburdenpressurecurves provides a bow up to a thickness away from 0.50–0.sixty Milligrams m -3 . The fresh linear-correlation study try summarizedin Dining table step three. The fresh new suggest relationship coefficient forEquation (10), given that shown for the Contour 3(roentgen = 0.98), was thesame once the mean correlation coefficients received having Formula (9) since the revealed into the Contour 2 (r = 0.98).

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