Grain growth theories and the isothermal evolution of the specific surface area of snow

Abstract

Quantifying the specific surface area (SSA) of snow and its variation during metamorphism is essential to understand and model the exchange of reactive gases between the snowpack and the atmosphere. Isothermal experiments were conducted in a cold room to measure the decay rate of the SSA of four snow samples kept in closed systems at −15 °C. In all cases, a logarithmic law of the form SSA=B−A ln(t+Δt) fits the SSA decrease very well, where A, B and Δt are adjustable parameters. B is closely related to the initial SSA of the snow and A describes the SSA decay rate. These and previous data suggest the existence of a linear relationship between A and B so that it may be possible to predict the decay rate of snow SSA from its initial value. The possibility that grain coarsening theories could explain these observations was investigated. The logarithmic equation was shown to be an approximation of a more general equation, that describes the time evolution of the mean grain radius R in most grain coarsening theories, such as Ostwald ripening: R̄n−R̄0n=Kt. R0¯ is the initial mean grain radius, R̄ is the mean grain radius, n and K are the growth exponent and the growth rate, respectively. Values of n between 2.8 and 5.0 are found. It is concluded that snow metamorphism and Ostwald ripening processes are governed by similar rules. Ostwald ripening theories predict that a steady-state regime is reached after a transient stage, but our results suggest that the steady-state regime is not reached after a few months of isothermal snow metamorphism. This last feature makes is difficult to predict the rate of decrease of snow SSA using the theory of Ostwald ripening.