Theoretical Analysis and Meteorological Interpretation of the Role of Raindrop Shape on Microwave Attenuation and Propagation Phase Shifts: Implication for the Radar Measurement of Rain

Abstract

In rain radars can measure various powers of the drop diameter averaged over the drop size distribution. These averages can then be used to infer rain water content (W) or the rainfall rate in still air (R0). Besides being sensitive to drop sizes however, radar parameters are also functions of the shapes of raindrops. In particular raindrop shape is known to affect both attenuation and propagation phase shift at vertical and horizontal linear polarizations. While the effect of raindrop shape on these quantities is understood qualitatively, its role has not previously been investigated analytically. In this work raindrops are assumed to be oblate spheroids with shapes specified by an axis ratio of the smallest to largest dimension. The impact of raindrop shape is evident in analytic expressions derived from detailed numerical scattering computations for drops from 0.01 to 0.6 cm diameter and over a range of axis ratios. These expressions reveal how the axis ratio can produce significant differences in attenuation and phase shift between measurements at horizontal and vertical polarization while simultaneously inducing only minor perturbations in these quantities at each polarization separately. These expressions also suggest that the effect of raindrop shape on attenuation and propagation phase shift can be removed by summing the rates at both vertical and horizontal linear polarizations. For wavelengths greater than a few centimeters, radars do not directly measure W or R0. Instead these quantities can only be inferred after invoking assumptions about the shapes and size distribution of the raindrops. In this study it is shown, however, that the rate of change with distance of sum of propagation phase shifts at vertical and horizontal linear polarization (ΣΦ) is directly proportional to the liquid water content (W) for radar wavelengths greater than 2.2 cm. Unfortunately, white the relation between ΣΦ and W is independent of the drop size distribution and raindrop shapes, ΣΦ can not be measured. For wavelengths greater than two centimeters, radars can not directly measure rainfall. Hence, W and R0 must be inferred from interpolations among radar observables. The best estimates of rainfall are most likely to be derived using a combination of many different polarization and attenuation techniques.