A modelling study of the impact of cirrus clouds on the moisture budget of the upper troposphere

We present a modelling study of the effect of cirrus clouds on the moisture budget of the layer wherein the cloud formed. Our framework simplifies many aspects of cloud microphysics and collapses the problem of sedimentation onto a 0-dimensional box model, but retains essential feedbacks between saturation mixing ratio, particle growth, and water removal through particle sedimentation. The water budget is described by two coupled first-order differential equations for dimensionless particle number density and saturation point temperature, where the parameters defining the system (layer depth, reference temperature, amplitude and time scale of temperature perturbation and inital particle number density, which may or may not be a function of reference temperature and cooling rate) are encapsulated in a single coefficient. This allows us to scale the results to a broad range of atmospheric conditions, and to test sensitivities. Results of the moisture budget calculations are presented for a range of atmospheric conditions (T: 238-205 K; p: 325-180 hPa) and a range of time scales τ_T of the temperature perturbation that induces the cloud formation. The cirrus clouds are found to efficiently remove water for τ_T longer than a few hours, with longer perturbations (τ_T≳10 h) required at lower temperatures (T≲210 K). Conversely, we find that temperature perturbations of duration order 1 h and less (a typical timescale for e.g., gravity waves) do not efficiently dehydrate over most of the upper troposphere. A consequence is that (for particle densities typical of current cirrus clouds) the assumption of complete dehydration to the saturation mixing ratio may yield valid predictions for upper tropospheric moisture distributions if it is based on the large scale temperature field, but this assumption is not necessarily valid if it is based on smaller scale temperature fields.