Do aerosols increase or decrease precipitation?

The observed variety of aerosol effects on precipitation at different spatial and time scales means that no simple answer to this question has so far been discovered.  However, although aerosol effects are many, it remains possible that there are universal constraints on the number of degrees of freedom needed to represent them.  We use convective-scale simulations to reveal a self-similar probability density function that underpins surface rainfall statistics. This function is independent of cloud-droplet number concentration and is unchanged by aerosol perturbations. It therefore represents an invariant property of our model with respect to cloud–aerosol interactions. For a given aerosol concentration, if at least one moment of the rainfall distribution on cloud-droplet number is a known input parameter, then this can be combined with the self-similar function to reconstruct the entire rainfall distribution to a useful degree of accuracy. We will demonstrate this using simulations from convective permitting, aerosol interacting simulations over China.