Cloud timescales and orographic precipitation

Orographic precipitation is studied by analyzing the sensitivity of numerical simulations to variations in mountain height, width, and wind speed. The emphasis is on upslope lifting over isolated mountains in cold climates. An attempt is made to capture the essential steady-state volume-averaged cloud physics in a pair of coupled nonlinear algebraic equations. To do this, single-pathway snow formation models are analyzed with both linear and nonlinear accretion formulations. The linear model suggests that the precipitation efficiency is determined by three timescales - the advection timescale (tau(a)), fallout timescale (tau(f)), and a constant timescale for snow generation (tau(cs)). Snow generation is controlled by the ratio of tau(cs) /tau(a) and the fraction of the snow that falls to the ground is controlled by the ratio of tau(f) /tau(a). Nonlinear terms, representing accretion, reduce the utility of the timescale concept by introducing a threshold or "bifurcation'' point, that is, a critical condensation rate that separates two states: a precipitating state and a nonprecipitating state. If the condensation rate is below the threshold value, no snow is generated. As it surpasses the threshold value, the snow generation rate increases rapidly. The threshold point is a function of advection and fallout timescales, low-level water content, mountain height, and a collection factor, which is further dependent on the geometries, terminal velocity, and density of snow particles. An approximate formula for precipitation efficiency is given in closed form.