Accuracy of radar-based precipitation measurement: An analysis of the influence of multiple scattering and non-spherical particle shape

Two assumptions are typically made when radar echo signals from precipitation are analyzed to determine the micro-physical parameters of raindrops: (1) the raindrops are assumed to be spherical; (2) multiple scattering effects are ignored. Radar cross sections (RCS) are usually calculated using Rayleigh's scattering equation with the simple addition method in the radar meteorological equation. We investigate the extent to which consideration of the effects of multiple scattering and of the non-spherical shapes within actual raindrop swarms would result in RCS values significantly different from those obtained by conventional analytical methods. First, we establish spherical and non-spherical raindrop models, with Gamma, JD, JT, and MP size distributions, respectively. We then use XFDTD software to calculate the radar cross sections of the above raindrop models at the S, C, X and Ku radar bands. Our XFDTD results are then compared to RCS values calculated by the Rayleigh approximation with simple addition methods. We find that: (1) RCS values calculated using multiple scattering XFDTD software differ significantly from those calculated by the simple addition method at the same band for the same model. In particular, for the spherical raindrop models, the relative differences in RCS values between the methods range from a maximum of 89.649% to a minimum of 43.701%; for the non-spherical raindrop models, the relative differences range from a maximum of 85.868% to a minimum of 11.875%. (2) Our multiple scattering XFDTD results, compared to those obtained from the Rayleigh formula, again differ at all four size distributions, by relative errors of 169.522%, 37.176%, 216.455%, and 63.428%, respectively. When nonspherical effects are considered, differences in RCS values between our XFDTD calculations and Rayleigh calculations are smaller; at the above four size distributions the relative errors are 0.213%, 0.171%, 7.683%, and 44.514%, respectively. RCS values computed by considering multiple scattering and non-spherical particle shapes are larger than Rayleigh RCS results, at all of the above four size distributions; the relative errors between the two methods are 220.673%, 129.320%, 387.240%, and 186.613%, respectively. After changing the arrangement of particles at four size distributions in the case of multiple scattering effect and non-spherical effect, the RCS values of Arrangement 2 are smaller than those of Arrangement 1; the relative errors for Arrangement 2, compared to Rayleigh, are 60.558%, 76.263%, 85.941%, 64.852%, respectively. We have demonstrated that multiple scattering, non-spherical particle shapes, and the arrangement within particle swarms all affect the calculation of RCS values. The largest influence appears to be that of the multiple scattering effect. Consideration of particle shapes appears to have the least influence on computed RCS values. We conclude that multiple scattering effects must be considered in practical meteorological detection.