多普勒天气雷达波束水平距离的计算方法

摘要

Based on the spherical coordinate system, triangle cosine theorem and atmospheric refraction, with the consideration of the influence of earth curvature and atmospheric refraction, the formula of radar beam horizontal distance was derived.In addition, this paper also comparatively analyzed several calculation formulas of radar beam horizontal distance.The results indicate that: in the standard atmosphere, the difference between the true horizontal distance and the slope distance of radar beam is more than 2.5 km at high elevation angle (slope distance is larger), and reaches 3.5 km between their maximum distances;the difference between the distances calculated by surface plane approximation formula and the true horizontal distance is more than 0.5 km at low elevation angle (the distance calculated by surface plane approximation formula is larger);the difference between the distance calculated by surface spherical approximation formula and the true horizontal distance is less than 0.5 km at low elevation angle (the true horizontal distance is larger).Result also show that the influence of atmospheric refraction on electromagnetic wave propagation over Nanchang is the greatest in summer, while the smallest in winter.Furthermore, the correction relationships between standard atmosphere and the equivalent earth`s radius as well as earth curvature for all seasons in Nanchang are provided in this paper.%从球坐标系出发,利用三角形余弦定理和大气折射理论,推导了不作任何近似的、包含地球曲率和大气折射影响的多普勒天气雷达波束水平距离Dm的计算公式,并与斜距投影Dr、地表平面近似的计算公式(不考虑地球曲率和大气折射,记为Dd)和地表球面近似的计算公式(不考虑大气折射,记为Ds)进行了对比分析.结果发现,在标准大气状态下,Dm与Dr在高仰角相差2.5 km以上(Dr大),最高距离差达3.5 km(19.5°仰角最大斜距处);与Dd在低仰角相差0.5 km以上(Dd大),与Dr相差在0.5 km以下(Dm大).并利用2011-2015年南昌站的探空资料,分析了南昌地区各个季节大气折射的变化情况及其与标准大气的区别.结果显示,夏季南昌上空电磁波的传播受大气折射的影响最大,冬季电磁波受大气折射的影响最小.最后,给出了南昌地区各个季节地球曲率K及等效地球半径Rm与标准大气的订正关系.