  Aerosol-cloud interactions (ACI) pose the largest uncertainty for climate
projections. Among many challenges of understanding ACI, the question of
whether ACI is deterministic or stochastic has not been explicitly formulated
and asked. Here we attempt to answer this question by predicting cloud droplet
number concentration Nc from aerosol number concentration Na and ambient
conditions. We use aerosol properties, vertical velocity fluctuation w', and
meteorological states (temperature T and water vapor mixing ratio q_v) from the
ACTIVATE field observations (2020 to 2022) as predictor variables to estimate
Nc. We show that the climatological Nc can be successfully predicted using a
machine learning model despite the strongly nonlinear and multi-scale nature of
ACI. However, the observation-trained machine learning model fails to predict
Nc in individual cases while it successfully predicts Nc of randomly selected
data points that cover a broad spatiotemporal scale, suggesting the stochastic
nature of ACI at fine spatiotemporal scales.
