Broadening of Adiabatic Droplet Spectra through Eddy Hopping: Polluted versus Pristine Environments

The observed widths of droplet spectra in adiabatic volumes of natural clouds have been a conundrum in cloud physics from the early days of in situ cloud observations. Observed spectral widths are often in the range of 1–2 mm, whereas adiabatic parcel calculations suggest widths up to only a few tenths of 1 mm. Part of the problem likely comes from artificial spectral broadening by at least some airborne measuring devices. We use a 1D Eulerian updraft model with Lagrangian particle–based microphysics (from the 2025 study by Grabowski et al.) to study the impact of cloud turbulence on droplet formation and diffusional growth. The model excludes or includes effects of cloud turbulence. The impact of turbulence is simulated using a stochastic model of updraft fluctuations that drive supersaturation fluctuations experienced separately by each superdroplet. The model setup considers shallow cumulus clouds growing from a turbulent convective boundary layer with cloud base updrafts between 1 and 4 m s^-1. The focus is on contrasting adiabatic spectral broadening in pristine and polluted environments. Adiabatic simulations without turbulence feature wider droplet spectra in highly polluted clouds. Turbulence significantly impacts CCN activation and droplet diffusional growth above cloud base and leads to an increased adiabatic spectral width aloft. The impact is moderate for polluted clouds, but spectral widths in pristine conditions are up to several times larger than those without turbulence. The difference comes from a larger magnitude of supersaturation fluctuations for the same vertical velocity fluctuations because of a larger phase relaxation time in pristine conditions.