Microphysical and dynamical controls on cirrus cloud optical depth distributions

We assess microphysical and dynamical controls on cirrus cloud optical depth distributions [P(sigma)] along idealized air parcel trajectories. We find P(sigma) shape depends primarily on the ratio of the ice crystal fallout timescale to timescales of other microphysical and dynamical processes. With homogeneous freezing only, two P(sigma) regimes emerged. In the limited fallout regime, relatively slow fallout allows complete depletion of the ice supersaturation, and P(sigma) has a peak at large optical depth values (sigma > 1). In contrast, in the fallout-dominated regime, relatively rapid fallout results in persistent high-ice supersaturation and multiple freezing events, and P(sigma) has a monotonically decreasing shape dominated by small optical depth values. The addition of heterogeneous freezing alters the homogeneous- freezing P(sigma) shape only in the limited fallout regime. Here glaciated ice nuclei (IN) do not inhibit homogeneous freezing but can change P(sigma) by reducing the optical depth of the P(sigma) peak and adding a monotonically decreasing tail at low optical depth values. Surprisingly, glaciated IN do not significantly change P(sigma) values or shape in the fallout-dominated regime. Fluctuations in vertical velocity and accompanying temperature changes have relatively little impact on P(sigma) unless the fluctuation timescales are shorter than fallout timescales, but longer than ice crystal growth timescales. As temperature fluctuations increase in amplitude, new freezing events affect P(sigma) as long as fluctuation timescales approach or exceed freezing timescales. Our modeled P(sigma) qualitatively resemble observed P(sigma), indicating these results could aid in GCM cirrus P(sigma) parameterization and help diagnose the controls on cirrus P(sigma).