Abstract
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 parametrized by a surprisingly small (at most three) independent “degrees of freedom”: the self-similar density, and auxiliary information about two moments of the rainfall distribution. 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.
Highlights
The indirect effects of aerosols on precipitation influence the Earth’s hydrological, energy and geochemical cycles on a range of timescales
The parameters that we identify are related to the dependencies of the first and second moments of the rainfall rate distribution on cloud-droplet number concentration (CDNC) and aerosol number concentration (AC); information that is readily available from simulations and satellite retrievals
In this paper will we show that the rainfall rate distributions simulated by our cloud-aerosol interacting mesoscale model have a common, underlying ‘shape’ that is independent of cloud-droplet number concentration (CDNC) and independent of aerosol concentration
Summary
The indirect effects of aerosols on precipitation influence the Earth’s hydrological, energy and geochemical cycles on a range of timescales. If we restrict attention to large enough volumes, and short enough timescales, the total mass of water (including accumulated surface precipitation) and the total energy are obvious atmospheric quantities that are approximately conserved when the aerosol amount changes These quantities are of limited use for aerosol-cloud interactions because we are interested in the partitioning of mass between the condensed and gaseous phases and 95 the effect that this partitioning has on the precipitation rate. We will show that these stretches amount to transforming how frequently rainfall occurs and 110 how much rainfall occurs for a given number of cloud droplets It is because an invariant distribution exists that a succinct specification of cloud-aerosol interactions in terms of the CDNC-dependencies of only two moments of the rainfall rate distribution is possible. This 115 implies that systems with the same power-law exponents and the same invariant distribution will have the same sensitivities to aerosols
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