A numerical model for the brightness of polar mesospheric clouds (PMC) is described, and is compared with measurements from the Solar Mesosphere Explorer (SME) satellite. These clouds occur during the summer months at polar latitudes where temperatures are known to fall below 140 K. We calculate the optical properties of a cloud by simulating the growth and sedimentation of ice particles at the cold supersaturated mesopause. Time-dependent trajectories of ice particles are calculated from their origin at the temperature minimum region to their demise at the cloud base through evaporation. We consider the effects of the removal of atmospheric water vapor by the growing particles and its restoration by ice evaporation at the cloud base. This ''freeze-drying'' effect is crucial in limiting the maximum size of the particles and therefore the maximum brightness of the cloud. Assuming spherical particles, Mie-scattering calculations of the directional albedo of a cloud are performed using a range of possible values for the atmospheric variables (water vapor mixing ratio, temperature, upward wind speed, atmospheric pressure, and eddy diffusion coefficient). We find that for a nominal atmospheric case the model predicts a moderately weak cloud at 265 nm, the wavelength of the SME measurement. An extreme model (cold and moist with high vertical and eddy transport) is needed to account for the brightest cloud observed. We estimate an upper limit for the water vapor to be of the order of 5 parts per million by volume. Higher values would imply the existence of clouds which exceed in brightness every cloud observed by the satellite over the time period 1981--1986. SME observations of greater cloud height in the northern hemisphere, despite their greater brightness, possibly imply an excess (by a factor of 2) of northern hemisphere water vapor.

This holds if the other atmospheric variables (and cloud particle numbers) are the same in both north and south. Dependence of model cloud brightness on atmospheric pressure (~P4.4), water vapor mixing ratio (~w2.8), thickness of the cloud saturation region (~d4) and advective wind speed (~v) are determined. These scalings are shown to result from a calculated proportionality of the cloud brightness to R6 (R is the maximum particle radius), and from simple considerations of ice layer growth, particle sedimentation, and the mass budget of water. Mie scattering calculations for a wavelength of 550 nm show that SME and OGO-6 data on PMC brightnesses are consistent. ¿ American Geophysical Union 1988