A couple empirical equations to possess firn densification had been obtained,provided firn porosity just like the a purpose of overburden pressure. In the step onest equation, thereduction ratio regarding porosity for the firn is believed to get proportional toward increasing ratioof excess tension while the mth fuel off new porosity. The brand new porosity exponent m are going to be alongside -dos, in order to possess an only-match fourteen breadth-density users fromGreenland and you may Antarctica. Regarding the next equation, new protection ratio away from porosity wasassumed to improve proportionally to the increment of overload stress and you will thenth power of one’s porosity. Probably the most satisfactory beliefs of your own exponent range between -step 1 to just one. It has been suggested that firn thickness, computed mainly because of the overburdenpressure and you can firn temperature, subscribe a lesser education.
1 Inclusion
The new sales procedure for firn to help you freeze is amongst the really practical victims in the polar ice-piece studies. Enough concepts about your inactive densification from firn enjoys become recommended ( Source Robin Robin, 1958 Source Schytt Schytt, 1958 Resource Bader Bader, 1960, 1962 Resource Benson Benson, 1962 Anderson and you will Resource Benson Benson, 1963 Source Kojima Kojima, 1964 Reference Gow Gow, 1975). not, a thorough model along with grains-paying off, sublimation/condensation, volume/ skin diffusion, ice deformation and recrystallization procedure wasn’t securely based. The densification processes have also read empirically ( Site Robin Robin, 1958 Reference Schytt Schytt, 1958 Source Herron and Langway Herron and you can Langway, 1980 Reference Ling Ling, 1985 Reference Langway, Shoji, Mitani and Clausen Langway while some, 1993). Resource Schytt Schytt (1958) discover an enthusiastic empirical relatives between firn thickness while the pounds out of overlying snow. Resource Herron and you may Langway Herron and you will Langway (1980) examined the fresh legitimacy from Schytt,s equation using 17 depth-occurrence pages from Greenland and you may Antarctica. Source Langway, Shoji, Mitani and you will Clausen Langway although some (1993) demonstrated an easy loved ones ranging from excess tension and firn density
So it papers centers around getting an easy picture fora matchmaking ranging from overburden stress and you may firndensity from the epidermis towards depth out of pore close-of as a result of the studies by Resource Schytt Schytt (1958) and you can Langwayand others (1993).
dos Analytical Processes
As opposed to using the snow densification legislation ( Resource Bader Bader, 1960,1962), a presumption was developed one to accumulated snow acts for example aperfectly plastic. Which is, porosity, s(= (?i – ?)/ ?i) is determined only by the overburden tension, P, at each and every breadth level. ?is the new firn thickness and ?i is the bubble-totally free freeze occurrence from the -20°C (0.919.Mgm-3). In the event that pressure P expands to P +dP, s decrease in order to s-ds. Thereduction proportion from porosity, -ds/s is actually thought toincrease proportionally into increasing proportion out of pressure, dP/P and also the mth regarding stamina regarding s as follows:
Other picture are received by the if the latest reduction proportion regarding porosity, -ds/s expands proportionallytothe increment from stress, dP, and nth strength of s as follows:
Has just, Reference Langway, Shoji, Mitani and you can Clausen Langway while some (1993) demonstrated an effective linearrelation anywhere between (?i-?) dos along with(P) from the body so you’re able to.the fresh new depth off pare personal-regarding for a few sites when you look at the Greenland andAntarctica. If we rewrite the expression(?i-?)2of Langway while others (1993) so you can ((?i-?)/?i) dos , the latest family members try conveyed as follows:
While doing so, Reference Schytt Schytt have a peek at this web site (1958) suggested the following family between firn occurrence (?) and breadth on body (h) far this new Maudheim Frost center,Antarctica:
step 3 Efficiency
Depth-density information are obtained from fourteen web sites in the Greenland and you can Antarctica because shown inside the Table step 1. New 10m depth firn heat of your borehole range from-54.3° in order to -16.4°C and you can annual buildup prices rangefrom 0.034 so you’re able to 0.39 meters 12 months one in liquids comparable. Thedata scatters in bulk-occurrence beliefs are ±0.005 Mgm -step 3 for those out-of Discussion, S25, H15, S25, G15, G6,Byrd facial skin camp and Dome C. As well, thedata scatters to have siteJ, website 2, webpages An effective, G2, Mizuho, LittleAmerica V and Old Byrd Station try in this ±0.003 Mgm -3 , just like the densities was indeed calculated way more correctly from the good volumetric approach. The fresh new reliabilityof ten meters depth temperatures tends to be ±0.1°C otherwise top.
A try is made to obtain the most complete valuesfor yards and you will letter in the Equations (1) and you will (4) utilizing the more than breadth-density profiles. Depth-density opinions out of thesurface toward breadth where brand new thickness is actually 0.80 Mg meters step three can be used for the new relationship-coefficient analysis.
Contour los angeles reveals the results of the linearity decide to try forEquation (1) playing with different beliefs away from meters. It’s clear you to relationship coefficients use the highest values up to m = -2 (roentgen = 0.98). Figure 2b shows the outcome to own Formula (4) playing with more values out-of letter. It was unearthed that the latest correlation coefficients make high really worth away from n = -step 1 in order to + 1 (r = 0.97 within n = 1; r = 0.98 al letter = 0;roentgen = 0.95 at n = 1). Hence, we obtain this new followingequations, which are the same that have Equations (7) and you may (8):
Fig.step 1 . The newest relatives ranging from viewpoints away from energies and you can correlation coefficients employing simple deviations. Shape 1a reveals the outcome having meters in Equation (1) and you may Profile 1b having n inside the Formula (4).
Fig.dos . Interactions between ln(P) and s 2 to have 14 internet sites in the Greenland and you will Antarctica. P try an overload stress and you will s is the porosity off firn, where s =(?i-?)/?i.?i is the ripple-100 % free frost occurrence and ? is the firn thickness.
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 3 suggests new loved ones ranging from P and also in(s) forthe fourteen ice cores. Evidently all of the overburdenpressurecurves possess a bend around a density from 0.50–0.sixty Milligrams m -step 3 . The latest linear-relationship research is summarizedin Table step three. The new suggest relationship coefficient forEquation (10), because the shown from inside the Shape step three(r = 0.98), is thesame because the indicate correlation coefficients acquired to own Equation (9) due to the fact found for the Contour 2 (r = 0.98).