A Microphysical Interpretation of Radar Reflectivity–Rain Rate Relationships

Abstract

The microphysical aspects of the relationship between radar reflectivity Z and rainfall rate R are examined. Various concepts discussed in the literature are integrated into a coherent analytical framework and discussed with a focus on the interpretability of Z?R relations from a microphysical point of view. The forward problem of analytically characterizing the Z?R relationship based on exponential, gamma, and monodisperse raindrop size distributions is highlighted as well as the inverse problem of a microphysical interpretation of empirically obtained Z?R relation coefficients. Three special modes that a Z?R relationship may attain are revealed, depending on whether the variability of the raindrop size distribution is governed by variations of drop number density, drop size, or a coordinated combination thereof with constant ratio of mean drop size and number density. A rain parameter diagram is presented that assists in diagnosing these microphysical modes. The number-controlled case results in linear Z?R relations that have been observed for steady and statistically homogeneous or equilibrium rainfall conditions. Most rainfall situations, however, exhibit a variability of drop spectra that is facilitated by a mix of variations of drop size and number density, which results in the well-known power-law Z?R relationships. Significant uncertainties are found to be associated with the retrieval of microphysical information from the Z?R relation coefficients, but even more so with shortcomings of the measurement of rainfall information and the subsequent processing of that data to obtain a Z?R relation. Given a proper consideration of the uncertainties, however, valuable microphysical information may be obtained, particularly as a result of long- term monitoring of rainfall for fixed observational settings but also through comparisons among different climatic rainfall regimes.