Research On Forward Algorithm For Hail Size Distribution By Vertical Doppler Radar

Hail is a solid precipitation formed in strong convective clouds,which can cause serious damage to crops,people,livestock and buildings.It is one of the main natural disasters.Vertical Doppler radar is a powerful tool for detecting precipitation,which is mostly used for raindrop spectrum detection.In addition to the spherical shape,hail is ellipsoidal,conical and other shapes.The non-spherical characteristics have a great influence on the scattering characteristics and hydrodynamic characteristics of hail,which limits the application of Doppler radar in hail spectrum detection.Therefore,it is of great significance to study the hail spectrum forward algorithm for vertical Doppler radar,which is of great significance to the detection of hail spectrum.In view of the important influence of hail shape and grain size distribution on Doppler power spectrum,the shape and grain size distribution characteristics of hail were investigated in depth.The results show that spherical and ellipsoidal hails account for the largest proportion,accounting for about 70%of the total.The particle size of hail ranges from 5 mm to 50 mm,and most of them are concentrated within 20 mm.The hail spectrum can be approximated by an exponential function.Based on the T-matrix method,the scattering characteristics of ellipsoidal hail in X-band and C-band are studied.The results show that the complex refractive index difference of hail at 3.2 cm and 5.56 cm wavelengths is small,and the hail with a particle size difference of 1.7 times is basically consistent with Q_ext and Q_sca at 3.2 cm and 5.56 cm.When the incident wavelength is 3.2 cm,the Q_ext and Q_sca of the ellipsoidal hail with a particle size range of 5 mm-50 mm increase first and then decrease with the increase of particle size.When the scale parameter of the hail with an incident wavelength of 3.2cm is 4,the Q_ext and Q_sca of the ellipsoidal hail decrease first to the lowest values of about 2.7 and 2.6,respectively,with the increase of the axial ratio,and then increase and stabilize.The value is about 3.4.In view of the fact that the traditional theoretical analysis method does not fully consider the shape and hydrodynamic characteristics of hail,the terminal velocity of hail falling is analyzed based on computational fluid dynamics simulation.The effects of particle size and axial ratio on the terminal velocity were studied.The results show that the terminal velocity of the ellipsoid hail with the same shape increases first and then decreases with the increase of the angle between the long axis and the vertical direction.The maximum deviation of the terminal velocity of the same ellipsoid falling in different attitudes can reach 18%.For the ellipsoid hail with the same axial ratio,the terminal velocity increases with the increase of particle size.For ellipsoidal hail with the same volume,the terminal velocity increases with the increase of axial ratio.Based on the scattering characteristics and terminal velocity characteristics of hail,the Doppler power spectrum corresponding to the terminal velocity of hail is studied,and the mathematical model between the two is established.Based on this model,a hail spectrum inversion algorithm was designed and preliminarily verified.The results show that the piecewise linear fitting can better describe the Doppler power spectrum,and the linear relationship between the fitting parameters and the key parameters No and A of the hail spectrum is satisfied.According to the inversion algorithm,the hail spectrum is inverted by Doppler power spectrum,in which the relative error of parameter N0 is less than 7.3%,and the relative error of parameter Λ is less than 10.9%.The research results verify the feasibility of the model and inversion algorithm.