Modeling the densification of polar firn including heat diffusion: Application to close-off characteristics and gas isotopic fractionation for Antarctica and Greenland sites

Modeling the densification of polar firn is essential to estimate variations of close-off characteristics (density, close-off depth, delta age) in relation with past climate parameters (temperature and accumulation rates). Furthermore, the air composition in the firn is modified by gravitational and thermal fractionation, and stable isotope measurements of permanent gases like nitrogen or argon can provide information on the amplitude of these fractionations. In this work, we propose a new model coupling firn densification and heat diffusion. In addition to the determination of the firn thickness and gas-ice age differences, the model allows a reconstruction of the time evolution of the temperature for different sites in Antarctica (Vostok) and Greenland (GISP2) and therefore the evolution of gravitational and thermal isotopic fractionations in firn. Under present-day conditions, the modeled profiles are in good agreement with the available temperature measurements in firn. For sites with low accumulation rates such as Vostok, the results show the existence of temperature gradients in the firn column even when no rapid climatic changes occur. The comparison of the modeled delta(15)N results to measurements allows to better constrain the delta(18)O-temperature relationship, used to infer the surface temperature history, and for GISP2, the model validates the long-term borehole-based temperature.