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An enthusiastic empirical relation between overburden tension and you can firn thickness

An enthusiastic empirical relation between overburden tension and you can firn thickness

One or two empirical equations to own firn densification was indeed obtained,given firn porosity while the a purpose of overburden tension. In the first formula, thereduction proportion away from porosity inside the firn is assumed to-be proportional to your growing ratioof overburden stress while the mth strength off this new porosity. The latest porosity exponent meters are going to be alongside -dos, to be able to keeps a sole-fit with fourteen breadth-density pages fromGreenland and you can Antarctica. Regarding the second formula, the new protection proportion away from porosity wasassumed to increase proportionally on the increment away from overburden tension and you can thenth fuel of your own porosity. Many high enough beliefs of exponent range between -step one to a single. This has been suggested that firn thickness, computed mainly by overburdenpressure and you may firn heat, contribute to less education.

step 1 Inclusion

The brand new conversion process procedure of firn so you can frost is one of the very fundamental subjects during the polar frost-layer education. Many ideas about your dead densification away from firn keeps started recommended ( Resource Robin Robin, 1958 Resource Schytt Schytt, 1958 Resource Bader Bader, 1960, 1962 Site Benson Benson, 1962 Anderson and you will Site Benson Benson, 1963 Reference Kojima Kojima, 1964 Reference Gow Gow, 1975). However, a thorough model including grains-paying down, sublimation/condensation, volume/ body diffusion, frost distortion and recrystallization process wasn’t solidly established. The fresh densification process have also been studied empirically ( Resource Robin Robin, 1958 Resource Schytt Schytt, 1958 Site Herron and Langway Herron and Langway, 1980 Reference Ling Ling, 1985 Site Langway, Shoji, Mitani and Clausen Langway while others, 1993). Reference Schytt Schytt (1958) located a keen empirical family relations ranging from firn thickness additionally the pounds away from overlying snow. Resource Herron and you may Langway Herron and you will Langway (1980) investigated the new legitimacy away from Schytt,s formula playing with 17 depth-thickness pages out-of Greenland and you may Antarctica. Reference Langway, Shoji, Mitani and you will Clausen Langway while some (1993) presented a straightforward relation ranging from overload stress and you can firn density

It report focuses on acquiring a straightforward picture fora dating ranging from overload tension and you will firndensity throughout the facial skin with the depth of pore personal-away from as sugar daddies in New Jersey a result of the studies by Site Schytt Schytt (1958) and Langwayand anybody else (1993).

2 Analytical Process

As opposed to utilizing the snow densification law ( Source Bader Bader, 1960,1962), an assumption was created that accumulated snow acts including aperfectly plastic. That’s, porosity, s(= (?i – ?)/ ?i) is determined simply by excess stress, P, at each depth peak. ?is the brand new firn density and you may ?i ‘s the ripple-totally free freeze thickness from the -20°C (0.919.Mgm-3). In the event that stress P grows in order to P +dP, s minimizes in order to s-ds. Thereduction proportion out-of porosity, -ds/s is actually assumed toincrease proportionally with the broadening proportion out-of tension, dP/P additionally the mth from stamina out-of s below:

Some other equation try received by if the newest reduction proportion out of porosity, -ds/s increases proportionallytothe increment of stress, dP, and nth stamina regarding s below:

Has just, Reference Langway, Shoji, Mitani and Clausen Langway while others (1993) showed an excellent linearrelation ranging from (?i-?) 2 along with(P) from the surface in order to.the fresh new breadth regarding pare personal-regarding for three internet sites when you look at the Greenland andAntarctica. Whenever we rewrite the phrase(?i-?)2of Langway while some (1993) to ((?i-?)/?i) 2 , the brand new family members is conveyed the following:

Simultaneously, Reference Schytt Schytt (1958) proposed the second family members anywhere between firn occurrence (?) and you will depth on facial skin (h) far this new Maudheim Frost key,Antarctica:

step three Results

Depth-occurrence pointers try taken from fourteen internet during the Greenland and you will Antarctica as revealed into the Dining table step 1. The fresh new 10m depth firn heat of borehole vary from-54.3° to -sixteen.4°C and you may annual accumulation prices rangefrom 0.034 so you’re able to 0.39 meters year 1 in liquids comparable. Thedata scatters in bulk-thickness thinking are often ±0.005 Mgm -step three for these out of Meeting, S25, H15, S25, G15, G6,Byrd skin go camping and you will Dome C. In addition, thedata scatters having siteJ, web site 2, web site A, G2, Mizuho, LittleAmerica V and you can Dated Byrd Channel was contained in this ±0.003 Mgm -step three , as the densities was indeed determined far more precisely by the a beneficial volumetric strategy. The new reliabilityof 10 m breadth temperatures is generally ±0.1°C otherwise most readily useful.

A trial is made to get the most satisfactory valuesfor yards and you can n in Equations (1) and you can (4) using the a lot more than depth-occurrence users. Depth-thickness values of thesurface toward breadth of which the density try 0.80 Mg meters step three are used for brand new correlation-coefficient research.

Figure los angeles reveals the results of the linearity sample forEquation (1) playing with more philosophy out-of yards. It is obvious you to definitely relationship coefficients use the large philosophy up to m = -2 (roentgen = 0.98). Shape 2b suggests the results to own Equation (4) having fun with different values regarding n. It absolutely was found that this new relationship coefficients do the large worthy of out of n = -step one to + step one (roentgen = 0.97 within n = 1; r = 0.98 al n = 0;roentgen = 0.95 on letter = 1). Ergo, we have the newest followingequations, being similar with Equations (7) and you can (8):

Fig.1 . The brand new family anywhere between values out of powers and you will relationship coefficients and their practical deviations. Figure 1a reveals the outcomes to have meters inside Formula (1) and you may Profile 1b for n within the Equation (4).

Fig.2 . Interactions anywhere between ln(P) and you will s 2 having fourteen internet in the Greenland and you may Antarctica. P is an excess stress and you will s is the porosity of firn, where s =(?i-?)/?i.?i ‘s the bubble-totally free freeze density and ? ‘s 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 3 shows the brand new relation ranging from P along with(s) forthe 14 freeze cores. Seemingly every overburdenpressurecurves has actually a bow as much as an occurrence out of 0.50–0.60 Milligrams m -step three . The newest linear-relationship research try summarizedin Table step three. The mean relationship coefficient forEquation (10), due to the fact found during the Shape step three(roentgen = 0.98), was thesame while the imply relationship coefficients received to own Picture (9) once the found within the Profile 2 (r = 0.98).

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