Several additional factors influence the composition of air in the firn. Gravitational fractionation is one ( 8 , 9 , 10 ). The pressure of gases increases with depth below the surface of the firn according to the barometric equation:
m = mass in units of g mol-1, g is the gravitational acceleration constant, z is depth, R is the ideal gas constant, and T is Kelvin temperature.
As Craig et al. ( 8 ) and Schwander ( 10 ) recognized, this equation applies not only to bulk air but to each individual constituent of air in that (dominant) depth interval of the firn where transport is essentially entirely by diffusion (the stagnant air column). The rate at which the enrichment-per-mass unit increases with depth, expressed in the d notation, is (?mg/RT -1)·1,000, or about 0.005‰/amu per meter at typical firn air temperatures. The relative enrichment with depth for different species is directly proportional to the mass difference. The firn air data for the GISP2 site, central Greenland, demonstrate the expected enrichment for the d15N of N2 ( Fig. 2 ). The enrichment or depletion is significant for nearly all species, corresponding to 3 ppmv of CO2 at the base of deep firn profiles, for example.
Seasonal changes in the concentrations of gases in air cause seasonal variations in firn air chemistry. The magnitude of these variations relative to their secular trends depends on location and property. The effect is perhaps largest for O2, CO2, and d13C of CO2 in Greenland. Seasonal variations are damped out with depth and become very small below 30–50 m.
Thermal fractionation also affects the isotopic and elemental composition of firn air. Severinghaus ( 11 ) and Severinghaus et al. ( 12 ) first recognized the importance of thermal fractionation in porous environmental media in their studies of the composition of air in sand dunes. Temperature gradients cause fractionation, with heavier gases or isotopes being enriched in colder regions. For 15N, the fractionation is about 0.025‰/°C. Thermal fractionation is large in firn because gases diffuse faster than heat. In consequence, steep seasonal temperature gradients occur in the upper ˜5 m of the firn and gases nearly equilibrate with these temperature gradients. This effect produces large seasonal variations in isotopic compositions and in the O2/N2 ratio in the top few meters of the firn. The seasonal anomalies decrease with depth, and for most species are insignificant below 30 m. O2 is an exception; the concentration of this gas in air is changing so slowly (on a percentage basis) that seasonal thermal gradients are significant down to 60-m depth.
These processes combine to influence the composition of gas throughout the firn, and at its base where gases are trapped as bubbles in impermeable ice. Here, two modes of trapping are possible. First, seasonal layering may be absent and air may be trapped throughout the bubble closeoff zone. In this case, the composition of the bulk trapped gases in ice cores will be further convoluted because of the finite closeoff interval. At Vostok, for example, the bubble closeoff zone is about 8 m