A strong statistical link between aerosol indirect effects and the self-similarity of rainfall distributions

We use convective-scale simulations of monsoonal clouds to reveal a self-similar probability density function that underpins surface rainfall statistics. This density 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 the dependence of at least one moment of the rainfall distribution on cloud-droplet number is a known input parameter, then the self-similar density can be used to reconstruct the entire rainfall distribution to a useful degree of accuracy. In particular, we present both single-moment and double-moment reconstructions that are able to predict the responses of the rainfall distributions to changes in aerosol concentration. In doing so, we show that the seemingly high-dimensional space of possible aerosol-induced rainfall-distribution transformations can be parameterised by surprisingly few (at most 3) independent “degrees of freedom”: the self-similar density and auxiliary information about two moments of the rainfall distribution. Comparisons to convection-permitting forecasts of mid-latitude weather and atmosphere-only global simulations show that the self-similar density is also independent of model physics and background meteorology. A theoretical explanation for this invariance is given, based on numerical results from a stochastic rainfall simulator. This suggests that, although aerosol indirect effects on any specific hydro-meteorological system may be multifarious in terms of rainfall changes and physical mechanisms, there may, nevertheless, be a universal constraint on the number of independent degrees of freedom needed to represent the dependencies of rainfall on aerosols.