A dry snow pack model

A dry snow pack is viewed as an interacting mixture of rigid ice grains and air occupying the pore space in the matrix. The three-dimensional mass, momentum and energy balances are formulated within the framework of interacting continua theory. The assumption of a common ice and air temperature is made to reflect the very slow relative motion between the air and ice. Focusing on a one-dimensional vertical snow pack, five constitutive postulates and two external prescriptions are made to obtain a closed system of partial differential equations. We consider the response of the snow pack to surface forcing by annual variations of heat flux and pressure. Non-dimensional analysis of the differential equations and surface conditions determines the major balances and leads to a reduced model. The equations are solved numerically for the temperature, air velocity, density and pressure through the snow pack resulting from both thermal forcing and pressure forcing at the surface.