A Linear Radar Reflectivity–Rainrate Relationship for Steady Tropical Rain

Roland List Department of Physics, University of Toronto, Toronto, Ontario, Canada

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Abstract

Modeling by Gillesple and List established the evolution to equilibrium of raindrop number distributions in one-dimensional shaft models. Donaldson and List et al. (LDS) then demonstrated mathematically that equilibrium distributionsƒ for raindrop number concentration N consist of a product of the rainfall rate R and a shape function Δ (which is independent of Donaldson et al. and LDS) showed that such spectra contain three at diameters of ∼0.3, 0.8 and 1.8 mm, whereas Brown obtained only the two smaller ones.

For equilibrium distributions, the present shows that the mass concentration M and the radar reflectivity Z are also proportional to the rainfall rate R, with Z=CzR and that N,M, R and Z are mutually proportional. Calculation provided Cz=742μm3 (mm h−1)−1, which is suggested to be a universal constant for steady tropical rain.

Data from a tropical rain experiment, carried out jointly by the Malaysian Meteorological Service and the University of Toronto, confirmed the equilibrium peaks at diameters of ∼0.3 (estimate), 0.9 and 1.9 mm. Due to basic deficiencies of the disdrometer only study state events could be used to assess radar reflectivities. The four available cases of steady rain consist of 112 one-minute spectra with different types and origins of MID (warm clouds, clouds containing ice particles, convective or stratiform clouds). As in the model, the radar reflectivity Z as calculated from measured drop spectra, was found to be proportional to rainfall rate.

Abstract

Modeling by Gillesple and List established the evolution to equilibrium of raindrop number distributions in one-dimensional shaft models. Donaldson and List et al. (LDS) then demonstrated mathematically that equilibrium distributionsƒ for raindrop number concentration N consist of a product of the rainfall rate R and a shape function Δ (which is independent of Donaldson et al. and LDS) showed that such spectra contain three at diameters of ∼0.3, 0.8 and 1.8 mm, whereas Brown obtained only the two smaller ones.

For equilibrium distributions, the present shows that the mass concentration M and the radar reflectivity Z are also proportional to the rainfall rate R, with Z=CzR and that N,M, R and Z are mutually proportional. Calculation provided Cz=742μm3 (mm h−1)−1, which is suggested to be a universal constant for steady tropical rain.

Data from a tropical rain experiment, carried out jointly by the Malaysian Meteorological Service and the University of Toronto, confirmed the equilibrium peaks at diameters of ∼0.3 (estimate), 0.9 and 1.9 mm. Due to basic deficiencies of the disdrometer only study state events could be used to assess radar reflectivities. The four available cases of steady rain consist of 112 one-minute spectra with different types and origins of MID (warm clouds, clouds containing ice particles, convective or stratiform clouds). As in the model, the radar reflectivity Z as calculated from measured drop spectra, was found to be proportional to rainfall rate.

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