The controls on the variability of raindrop size distributions in extreme rainfall and the associated radar reflectivity-rain rate relationships are studied using a scaling-law formalism for the description of raindrop size distributions and their properties. This scaling-law formalism enables a separation of the effects of changes in the scale of the raindrop size distribution from those in its shape. Parameters controlling the scale and shape of the scaled raindrop size distribution may be related to the microphysical processes generating extreme rainfall. A global scaling analysis of raindrop size distributions corresponding to rain rates exceeding 100 mm h(-1), collected during the 1950s with the Illinois State Water Survey raindrop camera in Miami, Florida, reveals that extreme rain rates tend to be associated with conditions in which the variability of the raindrop size distribution is strongly number controlled (i.e., characteristic drop sizes are roughly constant). This means that changes in properties of raindrop size distributions in extreme rainfall are largely produced by varying raindrop concentrations. As a result, rainfall integral variables (such as radar reflectivity and rain rate) are roughly proportional to each other, which is consistent with the concept of the so-called equilibrium raindrop size distribution and has profound implications for radar measurement of extreme rainfall. A time series analysis for two contrasting extreme rainfall events supports the hypothesis that the variability of raindrop size distributions for extreme rain rates is strongly number controlled. However, this analysis also reveals that the actual shapes of the (measured and scaled) spectra may differ significantly from storm to storm. This implies that the exponents of power-law radar reflectivity-rain rate relationships may be similar, and close to unity, for different extreme rainfall events, but their prefactors may differ substantially. Consequently, there is no unique radar reflectivity-rain rate relationship for extreme rain rates, but the variability is essentially reduced to one free parameter (i.e., the prefactor). It is suggested that this free parameter may be estimated on the basis of differential reflectivity measurements in extreme rainfall
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