A few empirical equations to own firn densification were obtained,provided firn porosity while the a function of excess stress. In the first picture, thereduction proportion of porosity inside the firn is thought as proportional with the broadening ratioof overburden stress plus the mth electricity out-of the brand new porosity. The newest porosity exponent m is alongside -dos, in order to keeps an only-fit with 14 depth-thickness pages fromGreenland and you will Antarctica. About 2nd equation, the brand new protection ratio off porosity wasassumed to increase proportionally on the increment off overload pressure and thenth stamina of porosity. The quintessential sufficient beliefs of your own exponent vary from -1 to a single. It has been ideal one to firn density, computed mostly because of the overburdenpressure and you can firn temperatures, donate to a reduced training.
step 1 Inclusion
The brand new conversion means of firn in order to freeze is one of the really fundamental sufferers during the polar freeze-sheet education. A good amount of concepts concerning your deceased densification off firn features already been suggested ( Reference Robin Robin, 1958 Site Schytt Schytt, 1958 Site Bader Bader, 1960, 1962 Site Benson Benson, 1962 Anderson and you can Site Benson Benson, 1963 Resource Kojima Kojima, 1964 Resource Gow Gow, 1975). Although not, an intensive design and additionally cereals-repaying, sublimation/condensation, volume/ skin diffusion, freeze distortion and you may recrystallization processes was not firmly centered. Brand new densification processes have also analyzed empirically ( Source Robin Robin, 1958 Resource Schytt Schytt, 1958 Site Herron and you can Langway Herron and Langway, 1980 Source Ling Ling, 1985 Source Langway, Shoji, Mitani and Clausen Langway although some, 1993). Reference Schytt Schytt (1958) found a keen empirical family members between firn density and the pounds out-of overlying accumulated snow. Reference Herron and you will Langway Herron and Langway (1980) examined the fresh validity out-of Schytt,s formula using 17 depth-density pages regarding Greenland and Antarctica. Site Langway, Shoji, Mitani and Clausen Langway and others (1993) demonstrated an easy loved ones ranging from excess pressure and firn thickness
It papers concentrates on acquiring an easy equation fora relationship ranging from overload stress and you can firndensity about surface on the breadth out-of pore close-out-of because of the studies by Site Schytt Schytt (1958) and you will Langwayand anyone else (1993).
2 Logical Procedure
Instead of making use of the snow densification law ( Reference Bader Bader, 1960,1962), a presumption is made you to accumulated snow acts instance aperfectly plastic. That is, porosity, s(= (?i – ?)/ ?i) is decided only by excess stress, P, at each and every depth top. ?is the fresh new firn occurrence and ?i ‘s the ripple-100 % free freeze occurrence at the -20°C (0.919.Mgm-3). In the event that stress P increases so you’re able to P +dP, s decrease to help you s-ds. Thereduction proportion out-of porosity, -ds/s is thought toincrease proportionally towards the expanding ratio of tension, dP/P and also the mth away from electricity off s below:
Various other formula is received by if brand new reduction proportion from porosity, -ds/s expands proportionallytothe increment off tension, dP, together with nth energy out of s the following:
Recently, Source Langway, Shoji, Mitani and you will Clausen Langway while others (1993) presented an excellent linearrelation anywhere between (?i-?) 2 along with(P) in the surface to help you.the newest depth away from pare personal-out-of for three websites inside Greenland andAntarctica. When we rewrite the expression(?i-?)2of Langway while some (1993) to ((?i-?)/?i) dos , the loved ones is actually shown as browse around here follows:
In addition, Resource Schytt Schytt (1958) advised another family anywhere between firn occurrence (?) and breadth on the facial skin (h) far new Maudheim Freeze key,Antarctica:
step three Results
Depth-thickness pointers is actually obtained from fourteen internet for the Greenland and you may Antarctica just like the found from inside the Desk step one. The fresh 10m depth firn temperatures of borehole start around-54.3° to help you -sixteen.4°C and you can yearly buildup prices rangefrom 0.034 to help you 0.39 meters year 1 in liquids comparable. Thedata scatters in large quantities-density viewpoints are generally ±0.005 Mgm -step three of these of Discussion, S25, H15, S25, G15, G6,Byrd epidermis go camping and you can Dome C. Likewise, thedata scatters having siteJ, web site dos, website Good, G2, Mizuho, LittleAmerica V and Dated Byrd Route are inside ±0.003 Mgm -step three , just like the densities have been computed way more precisely by the good volumetric strategy. The latest reliabilityof 10 m breadth temperatures is generally ±0.1°C or most readily useful.
A shot was created to find the most complete valuesfor meters and you will n from inside the Equations (1) and you can (4) utilising the significantly more than depth-thickness pages. Depth-thickness thinking out of thesurface on breadth of which this new occurrence is actually 0.80 Milligrams meters 3 can be used for the newest correlation-coefficient investigation.
Figure la suggests the outcome of your linearity sample forEquation (1) having fun with different values away from meters. It is clear you to definitely correlation coefficients take the high opinions as much as meters = -2 (roentgen = 0.98). Profile 2b shows the outcomes to possess Picture (4) having fun with more philosophy regarding letter. It absolutely was unearthed that the fresh relationship coefficients make large really worth out-of letter = -step one to help you + step one (r = 0.97 within n = 1; roentgen = 0.98 al letter = 0;r = 0.95 during the letter = 1). Ergo, we become the newest followingequations, being the same with Equations (7) and you will (8):
Fig.1 . This new relation ranging from opinions of vitality and you can correlation coefficients with their fundamental deviations. Contour 1a shows the results to possess m for the Equation (1) and Shape 1b to own letter when you look at the Picture (4).
Fig.2 . Affairs anywhere between ln(P) and you can s 2 having 14 sites in Greenland and you will Antarctica. P are an overload stress and you may s is the porosity out of firn, where s =(?i-?)/?i.?i is the bubble-100 % free freeze density and you can ? 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 three reveals the family members ranging from P plus in(s) forthe fourteen freeze cores. It seems that most of the overburdenpressurecurves enjoys a bow as much as a thickness off 0.50–0.60 Mg meters -step three . The new linear-relationship data is actually summarizedin Dining table step 3. Brand new indicate correlation coefficient forEquation (10), because found when you look at the Figure step three(r = 0.98), is thesame as suggest correlation coefficients gotten having Formula (9) once the found in the Figure 2 (r = 0.98).