Supersaturation Fluctuations in Cirrus Clouds Driven by Colored Noise

Fundamental properties of ice supersaturation variability in cirrus clouds are studied by means of an idealized probabilistic model. Damped supersaturation fluctuations are assumed to be exponentially correlated in time, statistically stationary, and normally distributed. The damping process is tied to the ability of the ice crystals to scavenge water vapor. The temporal evolution of supersaturation separates into an early ballistic and a late asymptotic regime. The latter allows for a stationary solution for the probability distribution of supersaturation in the presence of cloud ice and corresponds to a diffusive solution in cloud-free conditions. Low ice crystal number densities, small ice crystal sizes, short supersaturation correlation times, and large fluctuation intensities favor the spreading of cirrus ice crystal sizes, especially in conditions conducive to sublimation. Otherwise, size spreading of ice crystals is hampered by ice-induced damping of supersaturation fluctuations. The spreading of the probability distributions of ice supersaturation for very weak damping may lead to an increase of cirrus fractional coverage, as parameterized in large-scale atmospheric models, even for small mean supersaturations.