Abstract. We consider the problem of reconstructing the number size distribution (or particle size distribution) in the atmosphere from lidar measurements of the extinction and backscattering coefficients. We assume that the number size distribution can be modelled as a superposition of log–normal distributions, each one defined by three parameters: mode, width and height. We use a Bayesian model and a Monte Carlo algorithm to estimate these parameters. We test the developed method on synthetic data generated by distributions containing one or two modes, and perturbed by Gaussian noise, and on three real datasets obtained from AERONET. We show that the proposed algorithm provides satisfactory results even when the assumed number of modes is different from the true number of modes, and substantially excellent results when the right number of modes is selected. In general, an over-estimate of the number of modes provides better results than an under-estimate. In all cases, the PM1, PM2.5 and PM10 concentrations are reconstructed with tolerable deviations.

中文翻译：

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从激光雷达数据中检索大气层数大小分布

摘要。我们考虑了根据消光和背向散射系数的激光雷达测量重建大气中的数量大小分布（或粒子大小分布）的问题。 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 我们假设数字大小分布可以建模为对数正态分布的叠加，每个正态分布由三个参数定义：众数、宽度和高度。我们使用贝叶斯模型和蒙特卡罗算法来估计这些参数。我们在由包含一种或两种模式的分布生成并受高斯噪声干扰的合成数据上以及从 AERONET 获得的三个真实数据集上测试开发的方法。我们表明，即使假设的模式数与真实的模式数不同，所提出的算法也能提供令人满意的结果，and substantially excellent results when the right number of modes is selected. 一般而言，高估模态数比低估模态数提供更好的结果。在所有情况下，PM1、PM2.5 和 PM10 浓度都以可容忍的偏差重建。