A Microphysical Interpretation of Radar Reflectivity–Rain Rate Relationships

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 longterm monitoring of rainfall for fixed observational settings but also through comparisons among different climatic rainfall regimes.