激光掩星探测大气水汽的阿贝尔变换

对流层顶-平流层下区域(UTLS)的水汽分子密度对于研究全球变化、大气物质能量交换具有十分重要的意义,激光掩星技术可能是 一种探测该区域水汽的有效手段。掩星对于大气探测的核心思想源于阿贝尔(Abel)变换。GPS掩星的阿贝尔积分变换表达的是 连线的折射角与切点处折射率之间的关系,而与GPS掩星的阿贝尔积分变换不同的是,激光掩星的阿贝尔积分变换建立的是全路 径大气光学厚度与切点处大气消光系数之间的关系。从光线的程函方程出发,通过变量替换、坐标置换,从而建立起 大气光学厚度与大气消光系数之间的关系。由于光在切点处大气的消光系数和该处大气的水汽浓度成正比,因此分别在微 卫星和微卫星之间发射、接收0.935 $\mu$m掩星激光脉冲,连接两者之间的光束穿过大气层,计算积分路径上其水汽双波长 差分光学厚度,由阿贝尔积分变换反演即可获得光束路径切点处水汽浓度。随着掩星连线的上下移动,连线切点高度随着卫星 相向或背向而行而变化形成水汽浓度廓线。由于激光束发散角小,因此由激光掩星方法获得的水汽廓线高程精度高, 水汽的吸收消光可以直接得到水汽的分子密度,优于GPS掩星的相位延迟间接方法,可以更直接精确地探测大气对流层顶-平 流层下区域的水汽分子密度。此外,研究表明激光掩星方法的光谱分辨率优于太阳掩星方法的光谱分辨率。

Abel Transformation of Laser Occultation for Profiling Water Vapor in UTLS

The molecular density of water vapor in upper troposphere-lower stratosphere (UTLS) is of great significance for studying global change and exchange of atmospheric matter and energy. Laser occultation technique may be an effective means to detect water vapor in this area. The core idea of occultation for atmosphere detection stems from the Abel transformation. Unlike the Abel integral transformation of the GPS occultation, which expresses the relationship between the refraction angle of the ray and the refractive index at tangent point, the Abel integral transformation of laser occultation establishes the relationship between the atmospheric optical depth and the atmospheric extinction coefficient at tangent point. Starting from the eikonal equation of the light, the relationship between the atmospheric optical depth and the atmospheric extinction coefficient is re-established through variable substitution and coordinate replacement. The extinction coefficient of the atmosphere at the tangent point is proportional to the concentration of water vapor at the site. A 0.935 $\mu$m occultation laser pulse is transmitted and received between the two microsatellites and the beam between the two microsatellites passes through the atmosphere. The water vapor dual-wavelength differential optical depth on the integrated path is calculated, and then the water vapor concentration at the tangent point of the beam path can be obtained through the inversion of Abel integral transform. Furthermore, as the occultation ray moves up and down, the height of the ray tangent point forms a water vapor concentration profile as the height of the satellite changes with satellite moving front to front or back to back. Because of the small divergence angle of the laser beam, the obtained water vapor profile has high elevation accuracy with the laser occultation method, and the molecular density of water vapor can be directly obtained from the water vapor absorption and extinction, which is superior to that obtained by the phase delay indirect method of GPS occultation, so the concentration of water vapor molecules in the upper troposphere-lower the stratosphere can be detected more directly and accurately. In addition, the spectral resolution of laser occultation is higher than that of the sun occultation.