It is important to measure rainfall accurately with high spatial and temporal resolution in meteorology, hydrology, agriculture industry, environment conservation, flood warning and weather forecasting. The use of attenuated information about microwave propagation in rainfall areas to acquire surface precipitation intensity has been shown to be a practical approach to measuring rainfall in recent years. However, the inversion of a single-frequency link is based on the assumption of rainfall attenuation under a certain frequency condition. Further, obtaining parameters that comply with all rainfall events for the rainfall attenuation model is a challenge, often leading to an overestimation of the rainfall intensity. Therefore, based on extended boundary condition method and Gamma raindrop size distribution, an inversion method of the path rainfall intensity by using a microwave link rain-induced attenuation is proposed in order to improve the accuracy of rainfall measurement by microwave rain-induced attenuation. In this paper, we use the characteristics of an atmospheric attenuation model to eliminate the influence of non-rainfall-caused attenuation on the process of rainfall inversion. On the basis of scattering theory and by utilizing the Gamma raindrop size drop, we use the extended boundary condition method to calculate the characteristics of microwave attenuation for Pruppacher-Beard raindrop shape model. The correction model of rainfall effective attenuation and rainfall inversion model of line-of-sight microwave links are proposed, based on the microwave rain attenuation characteristics and raindrop size distribution statistics. In this paper, we propose 15-20 GHz inversion model of path-average rainfall intensity based on nonspherical rain-induced model by using Levenberg-Marquardt optimization algorithm. Meanwhile, we analyze the variations of parameters of rain-induced model under the condition of different temperatures. Besides, we design a line-of-sight microwave experimental system for measuring the rainfall, and the path average rain rate is inversed by rainfall inversion model, which is compared with an OTT disdrometer. The results show that the correlation coefficient of rain rate inversed by microwave link and that of disdrometer are both higher than 0.6 mostly, and the maximum value is 0.96; the error of accumulated rain amount is less than 2.47 mm, the minimum value is 0.28 mm; the relative error of accumulated rain amount is less than 1.84%, the minimum value is 0.44%. The experimental results validate the feasibility and accuracy of rainfall inversion method proposed in this paper. In addition, the experimental result reflects that rainfall intensity retrieved method based on nonspherical raindrop model has advantages over the method based on spherical raindrop model.
The accurate measurement of rain intensity and its distribution in vertical direction can not only help to understand the process of rainfall development, but also play an important role in human life such as agriculture, weather forecasting, water resources management, and natural disaster warning. According to the analysis of the geometric structure of earth-space link and propagation model of electromagnetic wave in atmosphere, in this paper we propose a method to reconstruct two-dimensional(2D) vertical rainfall field by using earth-space links. Firstly, the measured data of micro rain radar (MRR) from Nanjing are used to generate three real vertical rainfall fields which are marked as I, II and III respectively. Secondly, based on the analysis of the earth-space link’s geometry and the effect of signal attenuation from other factors such as scintillation, atmosphere gas and cloud, the vertical rainfall field inversion model is established. According to the power-law relationship between rain intensity and rain attenuation, which is given by International Telecommunication Union (ITU), the simultaneous algebraic reconstruction technique (SART) is used to inverse the vertical rainfall field. Then, one earth station which can receive a 17 GHz signal from satellite is employed to detect the vertical rainfall field. However, the simulation results show that it is difficult for one earth station to achieve the inversion of rainfall field, and that the correlation coefficients between rainfall fields and inversed fields are 0.556, 0.504 and 0.364 respectively. Based on the result, two earth stations are jointly used. In this simulation, the result shows that after 500 iterations the correlation coefficients all increase above 0.98, and the average biases between rainfall field I, II, III and their inversed fields are 0.122, 0.159 and 0.537 mm/h, respectively. Meanwhile, the Euclidean distances decrease to 0.246, 0.235 and 0.812 mm/h, and the relative errors of entropy are both less than 2%. It can be seen from the inversion fields that the vertical distribution of rain rate is close to that of the real field, which suggests that the method proposed in this paper can basically achieve the inversion of vertical rainfall field by using earth-space links. In addition, with the combined detection of three earth stations the accuracy of the inversion results is significantly improved. The correlation coefficients are all close to 1 and the mean deviations are all on the order of 10<sup>–12</sup> mm/h, indicating that the 2D vertical rainfall fields are accurately reconstructed. In the near future, the satellite constellation system will be globally deployed, which can promote the applications of our method in areas, such as plateaus, mountains and islands, where there exist no traditional observation data, serving as a supplement to existing precipitation measurements.
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