Reconciling Contrasting Relationships Between Relative Dispersion and Volume-Mean Radius of Cloud Droplet Size Distributions

Cloud droplet spectral relative dispersion is critical to parameterizations of cloud radiative properties, warm-rain initiation, and aerosol-cloud interactions in models; however, there is no consistent relationship between relative dispersion and volume-mean radius in literature, which hinders improving relative dispersion parameterization and calls for physical explanation. Here we show, by analyzing aircraft observations of cumulus clouds during Routine AAF [Atmospheric Radiation Measurement (ARM) Aerial Facility] Clouds with Low Optical Water Depths (CLOWD) Optical Radiative Observations, that the correlation between relative dispersion and volume-mean radius changes from positive to negative as volume-mean radius increases. With the new observation, we postulate that the sign of the correlation is determined by whether or not condensation (evaporation) occurs simultaneously with significant new activation (deactivation). The hypothesis is validated by simulations of both an adiabatic cloud parcel model and a parcel model accounting for entrainment-mixing. A new quantity, first bin strength, is introduced to quantify this new observation. Theoretical analysis of truncated gamma and modified gamma size distributions further supports the hypothesis and reconciles the contrasting relationships between relative dispersion and volume-mean radius, including the results in polluted fog observations. The results could shed new light on the so-called “twilight zone” between cloudy and cloud-free air, which in turn affects evaluation of aerosol-cloud interactions and retrieval of aerosol optical depth.