Advanced Search



ISSN  2096-3955

CN  10-1502/P

Citation: Hao Chen, JinHu Wang, Ming Wei, HongBin Chen, 2018: Accuracy of radar-based precipitation measurement: An analysis of the influence of multiple scattering and non-spherical particle shape, Earth and Planetary Physics, 2, 40-51. doi: 10.26464/epp2018004

2018, 2(1): 40-51. doi: 10.26464/epp2018004


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


Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Key Laboratory for Aerosol-Cloud-Precipitation of China Meteorological Administration, Nanjing University of Information Science and Technology, Nanjing 210044, China


State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China


National Demonstration Center for Experimental Atmospheric Science and Environmental Meteorology Education, Nanjing University of Information Science & Technology, Nanjing 210044, China


Key Laboratory of Middle Atmosphere and Global Environment Observation, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China

Corresponding author: JinHu Wang,

Received Date: 2017-09-13
Web Publishing Date: 2018-01-01

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.

Key words: Finite difference time domain (FDTD), generalized Lorenz Mie theory, raindrops, RCS, multiple scattering, oblate ellipsoid particle

Atlas, D., Kerker, M., and Hitschfeld, W. (1953). Scattering and attenuation by non-spherical atmospheric particles. J. Atmos. Terr. Phys., 3(2), 108–119. doi: 10.1016/0021-9169(53)90093-2

Atlas, D., Srivastava, R. C., and Sekhon, R. S. (1973). Doppler radar characteristics of precipitation at vertical incidence. Rev. Geophys., 11(1), 1–35. doi: 10.1029/RG011i001p00001

Bai, J. J., Li, Y., and Zhao, B. (2017). Directional light scattering from individual Au nanocup. Opt. Commun., 387, 208–213. doi: 10.1016/j.optcom.2016.11.062

Bruscaglioni, P., Ismaelli, A. and Zaccanti, G. (1995). Monte-Carlo calculations of LIDAR returns: Procedure and results. Appl. Phys. B, 60(4), 325–329. doi: 10.1007/BF01082266

Chen, M. X., Yu, X. D., Tan, X. G., and Wang, Y. C. (2004). A brief review on the development of nowcasting for convective storms. J. Appl. Meteor. Sci. (in Chinese), 15(6), 754–766.

Draine, B. T., and Flatau, P. J. (1994). Discrete-dipole approximation for scattering calculations. J. Opt. Soc. Am. A, 11(4), 1491–1499. doi: 10.1364/JOSAA.11.001491

Eremin, J. A., Orlov, N. V., and Rozenberg, V. I. (1995). Multiple electromagnetic scattering by a linear array of electrified raindrops. J. Atmos. Terr. Phys., 57(3), 311–319. doi: 10.1016/0021-9169(94)P4361-2

Konoshonkin, A. V., Kustova, N. V. Shishko, V. A., and Borovoi, A. G. (2016). The technique for solving the problem of light backscattering by ice crystals of cirrus clouds by the physical optics method for a Lidar with zenith scanning. Atmos. Oceanic Opt., 29(3), 252–262. doi: 10.1134/S1024856016030088

Kunkel, K. E., and Weinman, J. A. (1976). Monte Carlo analysis of multiply scattered Lidar returns. J. Atmos. Sci., 33(9), 1772–1781.<1772:MCAOMS>2.0.CO;2 doi: 10.1175/1520-0469(1976)033<1772:MCAOMS>2.0.CO;2

Li, S. H., Sun, X. M, Wang, H. H., and Lei, C. X. (2014). Study on electromagnetic wave scattering by raindrops. J. Light Scattering (in Chinese), 26(1), 1–7. (请核对刊名缩写是否正确)

Li, Y. Y., Sun, D. S., Wang, Z. Z., Shen, F. H., Zhou, X. L., and Dong, J. J. (2008). Study of clouds multiple-scattering influence on Lidar measurement. Laser Technol. (in Chinese), 32(6), 611–613, 638.

Liu C., Bi, L., Lee Panetta, R., Yang, P., and Yurkin, M. A. (2012a). Comparison between the pseudo-spectral time domain method and the discrete dipole approximation for light scattering simulations. Opt. Express, 20(15), 16763–16776. doi: 10.1364/OE.20.016763

Liu, C., Lee Panetta, R., and Yang, P. (2012b). Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200. J. Quant. Spectrosc. Radiat. Transfer, 113(13), 1728–1740. doi: 10.1016/j.jqsrt.2012.04.021

Liu, L. P., and Xu, B. X. (1991). A study of scattering and attenuation properties of model hail with different phase at 5.6 cm wavelength. Plateau Meteor. (in Chinese), 10(1), 26–33.

Liu, X. C., Gao, T. C., Qin, J., and Liu, L. (2010). Effects analysis of rainfall on microwave transmission characteristics. Acta Phys. Sin. (in Chinese), 59(3), 2156–2162.

Liu, X. C., Gao, T. C., Liu, L., and Hu, S. (2013). Advances in microphysical features and measurement techniques of raindrops. Adv. Earth Sci. (in Chinese), 28(11), 1217–1226.

Loiko, V. A., Konkolovich, A. V., Zyryanov, V. Y., and Miskevich, A. A. (2017). Small-angle light scattering symmetry breaking in polymer-dispersed liquid crystal films with inhomogeneous electrically controlled interface anchoring. J. Exp. Theor. Phys., 124(3), 388–405. doi: 10.1134/S1063776117020133

Mason, B. J. (1979). The Physics of Clouds (in Chinese) (pp. 343–345). The Institute of Atmospheric Physics, Chinese Academy of Sciences, trans. Beijing: Science Press.222

Mätzler, C. (2002). Drop-size distributions and Mie computations for rain. Research Report No.16. Switzerland: Institute of Applied Physics, University of Bern.222

Mishchenko, M. I. (1993). Light scattering by size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength. Appl. Opt., 32(24), 4652–4666. doi: 10.1364/AO.32.004652

Mishchenko, M. I., Travis, L. D. and Mackowski, D. W. (1996). T-matrix computations of light scattering by nonspherical particles: A review. J. Quant. Spectrosc. Radiant. Transfer, 55(5), 535–575. doi: 10.1016/0022-4073(96)00002-7

Mishchenko, M. I., Hovenier, J. W., and Travis, L. D. (2000). Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications. New York: Academic Press.222

Mooradian, G. C., Geller, M., Levine, P. H., Stotts, L. B., and Stephens, D. H. (1980). Over-the-horizon optical propagation in a maritime environment. Appl. Opt., 19(1), 11–30. doi: 10.1364/AO.19.000011

Platt, C. M. R., and Dilley, A. C. (1984). Determination of the cirrus particle single-scattering phase function from Lidar and solar radiometric data. Appl. Opt., 23(3), 380–386. doi: 10.1364/AO.23.000380

Pruppacher, H. R., and Beard, K. V. (1970). A wind tunnel investigation of the internal circulation and shape of water drops falling at terminal velocity in air. Quart. J. Roy. Meteor. Soc., 96(408), 247–256. doi: 10.1002/(ISSN)1477-870X

Pruppacher, H. R., and Pitter, R. L. (1971). A semi-empirical determination of the shape of cloud and rain drops. J. Atmos. Sci., 28(1), 86–94.<0086:ASEDOT>2.0.CO;2 doi: 10.1175/1520-0469(1971)028<0086:ASEDOT>2.0.CO;2

Seliga, T. A., and Bringi, V. N. (1978). Differential reflectivity and differential phase shift: Applications in radar meteorology. Radio Sci., 13(2), 271–275. doi: 10.1029/RS013i002p00271

Spinhirne, J. D. (1982). Lidar clear atmosphere multiple scattering dependence on receiver range. Appl. Opt., 21(14), 2467–2468. doi: 10.1364/AO.21.002467

Taflove, A. (1998). Advances in Computational Electrodynamics. Boston, MA: Artech House.222

Taflove, A., and Hagness, S. C. (2000). Computational Electrodynamics. Boston, MA: Artech House.222

Wang, G. L., Liu, L. P., and Ruan, Z. (2007). Application of Doppler radar data to nowcasting of heavy rainfall. J. Appl. Meteor. Sci. (in Chinese), 18(3), 388–395.

Wang, J. H., Ge, J. X., Wei, M., and Yu, W. W. (2013). Influence of scattering properties due to complex refractive index of ice. In Proceedings of the 3rd International Conference on Information Science and Technology (pp. 997–999). Yangzhou, Jiangsu, China: IEEE.

Wang, J. H., Ge, J. X., and Wei, M. (2014). Theoretical study on single-scattering properties of ice particles of different orientation at 94 GHz. Prog. Electromagn. Res. M, 36, 39–46. doi: 10.2528/PIERM14033106

Wang, J. H., Ge, J. X., Zhang, Q. L., Li, X. C., Wei, M., Yang, Z. X., and Liu, Y. A. (2016a). Radar cross-section measurements of ice particles using vector network analyzer. AIP Adv., 6(9), 095310. doi: 10.1063/1.4963080

Wang, J. H., Ge, J. X., Zhu, X., Wei, M., Yang, Z. X., and Li, J. Q. (2016b). Effect of orientation and air content of ice particles on radar reflectivity factor. J. Infrared Millim. Waves (in Chinese), 35(1), 78–86.

Wang, J. H., Ge, J. X., Wei, M., Gu, S. S., and Yang, Z. X. (2016c). Study of the relationship between IWC and Z for nonspherical ice particles at millimeter wavelength. J. Trop. Meteor., 22(S1), 78–88.

Wang, K., Do, K. D., and Cui, L. (2017). Underwater active electrosense: A scattering formulation and its application. IEEE Trans. Rob., 33(5), 1233–1241. doi: 10.1109/TRO.2017.2694829

Wang, Z. H., (2002). Study on backscattering experiment and DDA calculation of spherical cone ellipsoid. Journal of Nanjing Institute of Meteorology, 25 (3): 307-313.

Wang, Z. H., Xu, X. Y., Wang, Q. A., and Chao, Z. M. (2003). Comparison between the lab observations and DDA computations on the backscattering features of sphere-cone-oblate ice particles. J. Quant. Spectrosc. Radiat. Transfer, 77(4), 455–462. doi: 10.1016/S0022-4073(02)00165-6

Xiong, X. L., Li, M., Jiang, L. H., Feng, S., and Zhuang, Z. B. (2014). The study of the Lidar ratio retrieval method with multiple scattering cirrus cloud. J. Optoelectron. Laser (in Chinese), 25(6), 1158–1164.

Wu, J. X., Wei, M., Zhou, J., and Wang, J. H. (2012). Effects of temperature and orientation on 3.2 mm radar backscattering from ice crystals. In Proceedings of the 5th International Conference on Advanced Computational Intelligence (pp. 742–746). Nanjing, China: IEEE.

Xu, L. S., Chen, H. B., Ding, J. L., and Xia, Z. Y. (2014). An overview of the advances in computational studies on light scattering by nonspherical particles. Adv. Earth Sci. (in Chinese), 29(8), 903–912.

Xu, X. Y. (2002). Scattering of microwaves by non-spherical raindrops and hails (in Chinese). Nanjing: Nanjing University of Information Engineering, [Master’s thesis].222

Xu, Y. L. (1995). Electromagnetic scattering by an aggregate of spheres. Appl. Opt., 34(21), 4573–4588. doi: 10.1364/AO.34.004573

Xu, Y. L., and Gustafson, B. Å. S. (1997). Experimental and theoretical results of light scattering by aggregates of spheres. Appl. Opt., 36(30), 8026–8030. doi: 10.1364/AO.36.008026

Yang, P., and Liou, K. N., (1996). Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space. J. Opt. Soc. Am. A, 13(10), 2072–2085. doi: 10.1364/JOSAA.13.002072

Yee, S. (1996). Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag., 14(3), 302–307.

Zhang, P. C., and Wang, Z. H. (1995). Analysis of Atmospheric Microwave Remote Sensing (in Chinese). Beijing: Meteorological Press,16–19.222

Zhong, L. Z., Liu, L. P., and Ge, R. S. (2009). Characteristics about the millimeter-wavelength radar and its status and prospect in and abroad. Adv. Earth Sci. (in Chinese), 24(4), 383–391.


Chao Wei, Lei Dai, SuPing Duan, Chi Wang, YuXian Wang, 2019: Multiple satellites observation evidence: High-m Poloidal ULF waves with time-varying polarization states, Earth and Planetary Physics, 3, 190-203. doi: 10.26464/epp2019021


Md Moklesur Rahman, Ling Bai, 2018: Probabilistic seismic hazard assessment of Nepal using multiple seismic source models, Earth and Planetary Physics, 2, 327-341. doi: 10.26464/epp2018030


Jiang Yu, Jing Wang, Jun Cui, 2019: Ring current proton scattering by low-frequency magnetosonic waves, Earth and Planetary Physics, 3, 365-372. doi: 10.26464/epp2019037


BinBin Ni, Jing Huang, YaSong Ge, Jun Cui, Yong Wei, XuDong Gu, Song Fu, Zheng Xiang, ZhengYu Zhao, 2018: Radiation belt electron scattering by whistler-mode chorus in the Jovian magnetosphere: Importance of ambient and wave parameters, Earth and Planetary Physics, 2, 1-14. doi: 10.26464/epp2018001


ShuWen Tang, Yi Wang, HongYun Zhao, Fang Fang, Yi Qian, YongJie Zhang, HaiBo Yang, CunHui Li, Qiang Fu, Jie Kong, XiangYu Hu, Hong Su, ZhiYu Sun, YuHong Yu, BaoMing Zhang, Yu Sun, ZhiPeng Sun, 2020: Calibration of Mars Energetic Particle Analyzer (MEPA), Earth and Planetary Physics, 4, 355-363. doi: 10.26464/epp2020055


Wei Chu, JianPing Huang, XuHui Shen, Ping Wang, XinQiao Li, ZhengHua An, YanBing Xu, XiaoHua Liang, 2018: Preliminary results of the High Energetic Particle Package on-board the China Seismo-Electromagnetic Satellite, Earth and Planetary Physics, 2, 489-498. doi: 10.26464/epp2018047


LingGao Kong, AiBing Zhang, Zhen Tian, XiangZhi Zheng, WenJing Wang, Bin Liu, Peter Wurz, Daniele Piazza, Adrian Etter, Bin Su, YaYa An, JianJing Ding, WenYa Li, Yong Liu, Lei Li, YiRen Li, Xu Tan, YueQiang Sun, 2020: Mars Ion and Neutral Particle Analyzer (MINPA) for Chinese Mars Exploration Mission (Tianwen-1): Design and ground calibration, Earth and Planetary Physics, 4, 333-344. doi: 10.26464/epp2020053


Konrad Sauer, Klaus Baumgärtel, Richard Sydora, 2020: Gap formation around Ωe/2 and generation of low-band whistler waves by Landau-resonant electrons in the magnetosphere: Predictions from dispersion theory, Earth and Planetary Physics, 4, 138-150. doi: 10.26464/epp2020020


YanZhe Zhao, YanBin Wang, 2019: Comparison of deterministic and stochastic approaches to crosshole seismic travel-time inversions, Earth and Planetary Physics, 3, 547-559. doi: 10.26464/epp2019056


KeDeng Zhang, Hui Wang, WenBin Wang, Jing Liu, ShunRong Zhang, Cheng Sheng, 2021: Nighttime meridional neutral wind responses to SAPS simulated by the TIEGCM: a universal time effect, Earth and Planetary Physics. doi: 10.26464/epp2021004

Article Metrics
  • PDF Downloads()
  • Abstract views()
  • HTML views()
  • Cited by(0)

Figures And Tables

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

Hao Chen, JinHu Wang, Ming Wei, HongBin Chen