Several empirical equations having firn densification were gotten,given firn porosity due to the fact a purpose of overburden tension. In the step onest picture, thereduction proportion of porosity from inside the firn is believed to get proportional to your broadening ratioof overload tension together with mth strength off this new porosity. The porosity exponent meters is near to -dos, in order to features a just-fit with fourteen depth-density pages fromGreenland and you may Antarctica. About second picture, the prevention proportion out-of porosity wasassumed to boost proportionally with the increment away from overburden tension and you may thenth stamina of porosity. The most high enough values of your exponent start from -step one to just one. This has been advised one firn thickness, calculated mostly from the overburdenpressure and you may firn temperature, subscribe a lower degree.
1 Inclusion
The latest conversion means of firn so you’re able to ice is one of the really simple sufferers during the polar ice-piece knowledge. Plenty of concepts regarding the dead densification from firn provides been recommended ( Source Robin Robin, 1958 Resource Schytt Schytt, 1958 Reference Bader Bader, 1960, 1962 Site Benson Benson, 1962 Anderson and you can Resource Benson Benson, 1963 Source Kojima Kojima, 1964 Resource Gow Gow, 1975). Although not, a thorough design also cereals-settling, sublimation/condensation, volume/ facial skin diffusion, ice deformation and recrystallization procedure was not securely established. The fresh densification processes have also read empirically ( Reference Robin Robin, 1958 Resource Schytt Schytt, 1958 Source Herron and you can Langway Herron and Langway, 1980 Site Ling Ling, 1985 Source Langway, Shoji, Mitani and you may sugar babies website Clausen Langway although some, 1993). Resource Schytt Schytt (1958) found a keen empirical family members anywhere between firn thickness plus the pounds away from overlying accumulated snow. Site Herron and you may Langway Herron and you will Langway (1980) examined this new validity from Schytt,s picture having fun with 17 breadth-thickness users off Greenland and you can Antarctica. Source Langway, Shoji, Mitani and you may Clausen Langway and others (1993) shown an easy relation between overload tension and firn occurrence
So it paper is targeted on getting a straightforward equation fora relationship anywhere between excess pressure and you may firndensity about surface on the breadth off pore personal-from considering the tests by Reference Schytt Schytt (1958) and you may Langwayand anyone else (1993).
dos Analytical Processes
As opposed to making use of the snow densification legislation ( Reference Bader Bader, 1960,1962), a presumption was developed you to snow acts such as for instance aperfectly vinyl. Which is, porosity, s(= (?i – ?)/ ?i) is determined just from the excess tension, P, at each depth top. ?is the brand new firn occurrence and you may ?i is the bubble-totally free ice density on -20°C (0.919.Mgm-3). If the pressure P expands so you can P +dP, s decrease to help you s-ds. Thereduction ratio of porosity, -ds/s are thought toincrease proportionally into the increasing ratio regarding pressure, dP/P as well as the mth away from stamina out of s below:
Several other picture is actually acquired because of the if brand new reduction proportion away from porosity, -ds/s expands proportionallytothe increment off pressure, dP, and also the nth electricity regarding s the following:
Recently, Resource Langway, Shoji, Mitani and you may Clausen Langway although some (1993) shown a linearrelation ranging from (?i-?) dos as well as in(P) on the skin in order to.the latest depth regarding pare romantic-away from for three websites into the Greenland andAntarctica. Whenever we write the term(?i-?)2of Langway although some (1993) to help you ((?i-?)/?i) 2 , the newest family members are conveyed below:
While doing so, Resource Schytt Schytt (1958) advised next loved ones between firn thickness (?) and you may breadth from the surface (h) much the Maudheim Ice key,Antarctica:
step 3 Abilities
Depth-density pointers is actually taken from 14 internet within the Greenland and Antarctica just like the found when you look at the Desk step 1. The latest 10m depth firn heat of your borehole start from-54.3° to help you -sixteen.4°C and annual buildup pricing rangefrom 0.034 to help you 0.39 yards 12 months 1 in liquids comparable. Thedata scatters in large quantities-occurrence philosophy are ±0.005 Mgm -step 3 for those from Summit, S25, H15, S25, G15, G6,Byrd surface go camping and you may Dome C. Likewise, thedata scatters having siteJ, website 2, site A good, G2, Mizuho, LittleAmerica V and Old Byrd Channel are in this ±0.003 Mgm -step three , since the densities was indeed calculated a whole lot more precisely from the a good volumetric strategy. The brand new reliabilityof 10 m breadth temperature tends to be ±0.1°C otherwise better.
A trial was developed to obtain the most complete valuesfor meters and you will letter inside Equations (1) and you may (4) by using the a lot more than depth-thickness profiles. Depth-thickness philosophy off thesurface into the breadth where the newest density are 0.80 Mg meters 3 are used for brand new correlation-coefficient analysis.
Profile la suggests the outcomes of your linearity decide to try forEquation (1) having fun with more values out-of meters. It is clear you to correlation coefficients take the highest viewpoints as much as meters = -2 (roentgen = 0.98). Figure 2b shows the outcome to own Picture (4) playing with other thinking out-of letter. It was found that the new correlation coefficients do the high worth out-of n = -1 so you can + step one (r = 0.97 at n = 1; roentgen = 0.98 al n = 0;r = 0.95 within n = 1). Thus, we get the new followingequations, which happen to be the same with Equations (7) and you may (8):
Fig.step one . The family members ranging from opinions out of energies and you may correlation coefficients through its practical deviations. Profile 1a reveals the outcome to own yards into the Formula (1) and you can Contour 1b for letter within the Picture (4).
Fig.dos . Interactions between ln(P) and you will s dos to have 14 internet sites within the Greenland and you will Antarctica. P are an excess pressure and you can s ‘s the porosity away from firn, where s =(?i-?)/?i.?i ‘s the ripple-100 % free frost occurrence and you can ? is the firn density.
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.
Shape step 3 suggests the fresh loved ones anywhere between P and also in(s) forthe fourteen freeze cores. Evidently all of the overburdenpressurecurves enjoys a bend around a density off 0.50–0.60 Mg m -step 3 . The latest linear-correlation studies is summarizedin Dining table step three. The newest imply correlation coefficient forEquation (10), due to the fact shown for the Contour step three(roentgen = 0.98), are thesame while the suggest correlation coefficients obtained getting Equation (9) because the shown inside the Contour 2 (roentgen = 0.98).
