Inversion algorithm of vertical visibility based on lidar and its error evaluation
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摘要: 针对大气垂直方向上消光系数分布不均匀难以用传统方法直接测量垂直能见度的问题，提出了一种基于激光雷达探测垂直能见度的计算方法。根据大气辐射传输基本原理，借助于辐射传输方程，推导出了垂直能见度的计算公式；然后利用激光雷达原理方程和Klett算法反演出大气垂直方向上的消光系数分布，基于此提出了垂直能见度的迭代算法。最后，利用灰色模型GM(1,1)和批统计算法，对激光雷达反演得到的后向散射系数进行了评估，给出了误差置信区间为（0.760±0.339）×10−4（srad·km）−1。结果表明，该方法是一种特别有效的计算垂直能见度的方法，符合探测的基本需求，且误差小精度高。Abstract: To solve the problem that the non-uniform distribution of extinction coefficients in the vertical direction of the atmosphere makes it difficult to directly measure the vertical visibility by traditional methods, this paper presents a method for calculating the vertical visibility based on lidar detection. Firstly, according to the basic principle of atmospheric radiation transmission and radiation transfer equation, it deduces the calculation formula of vertical visibility, which solves the problem that there is no specific formula for calculating vertical visibility. Secondly, it inverts the extinction coefficient distribution in the vertical direction of the atmosphere by using the lidar equation and Klett algorithm. On this basis, it proposes an iterative algorithm for vertical visibility. Finally, it uses the gray model GM(1,1) and batch statistics algorithm to evaluate the backscattering coefficient obtained by laser radar inversion, and gives the error confidence interval (0.760±0.339)×10−4(srad·km)−1. The results show that the method is a particularly effective one for calculating vertical visibility, which meets the basic requirements of detection, with small error and high precision.
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Key words:
- lidar /
- vertical visibility /
- extinction coefficient /
- radiative transfer equation /
- GM(1,1) model /
- batch statistics
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图 2 2019年5月2日00时00分大气的消光系数廓线
Figure 2. Atmospheric extinction coefficient profile at 00:00 on May 2, 2019
表 1 CL51型激光雷达主要技术指标
Table 1. The main technical indicators of CL51 lidar
laser wavelength/nm operating mode pulse energy/μWs repetition rate/kHz optics focus/mm effective lens diameter/mm measurement range/km range resolution/m measurement interval/s field-of-view divergence/mrad 910 pulsed 3.0 6.5 450 148 0~15.4 10 6 0.56 
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表 2 后向散射系数的批统计结果分析表
Table 2. Backscattering coefficient deviation result analysis by batch statistics
date altitude/m mean of error/10−4（srad·km）−1 standard deviation of error/10−4（srad·km）−1 confidence interval/10−4（srad·km）−1 2019-05-02 0 0.726 0.225 0.726±0.318 10 0.721 0.223 0.721±0.316 20 0.743 0.231 0.743±0.327 30 0.741 0.230 0.741±0.326 40 0.760 0.240 0.760±0.339 50 0.746 0.235 0.746±0.332 60 0.708 0.223 0.708±0.223 70 0.726 0.228 0.726±0.322 80 0.683 0.215 0.683±0.304 90 0.639 0.201 0.639±0.284 100 0.609 0.192 0.609±0.192 2019-05-03 0 0.604 0.203 0.604±0.287 10 0.593 0.200 0.593±0.282 20 0.608 0.206 0.608±0.292 30 0.608 0.207 0.608±0.292 40 0.632 0.213 0.632±0.302 50 0.628 0.211 0.628±0.298 60 0.619 0.207 0.619±0.293 70 0.618 0.207 0.617±0.292 80 0.615 0.207 0.615±0.292 90 0.590 0.197 0.590±0.279 100 0.571 0.190 0.571±0.269
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