Determination of the content of trace gases (such as, for example, NO2, formaldehyde) by DOAS (differential optical absorption spectroscopy) method in the lower troposphere can be difficult with significant scattering of light on clouds and aerosol. Often, the parameters of cloudiness and aerosol are unknown for specific DOAS measurements, and, therefore, the estimation of these parameters directly from the DOAS analysis data is an approach that could increase the final measurement accuracy of trace gases. In this work, we consider the problems of retrieving such characteristics as: cloud bottom height, cloud optical depth, aerosol optical depth, F-factor (a factor reciprocal to air mass factor) from the input data obtained during DOAS analysis. To do this, we trained and compared two machine learning (ML) models - neural network and random forest. Both ML algorithms solve the regression problem; data obtained by numerical computation by linearized radiative transfer model were used as a learning dataset. The dependence of the error on the test dataset depending on the regularizing parameters was investigated for the neural network. Retrieval errors of aerosol and cloud characteristics were preliminary estimated.
KEYWORDS: Clouds, Neural networks, Error analysis, Aerosols, Atmospheric particles, Atmospheric modeling, Monte Carlo methods, Scatter measurement, Solar radiation, Radiative transfer
Light scattering by cloudiness and aerosol have a significant impact on the possibility of quantitative estimation of the content of NO2, H2CO and other trace gases in the lower troposphere using the MAX-DOAS and ZDOAS techniques. Since there is a large volume of optical observations of trace gases by these techniques that are not accompanied by measurements of their characteristics, solving the problem of determining the properties of clouds and aerosol from the spectral measurements themselves could increase the accuracy of measuring trace gases. The paper considers the tasks of determining the characteristics of clouds (the bottom height, the optical depth, etc.) and aerosol (the optical depth, the vertical distribution parameters, etc.) from quantitates obtained from ZDOAS measurements (the O4 slant column, the color index, the absolute intensity, etc.). We performed numerical experiments for retrieving clouds and aerosol characteristics basing on radiative transfer simulations in cloudy atmosphere. A neural network is used as a method for solving emerging nonlinear estimation problems, the accuracy of the evaluation is determined on the training set, and a control set is used to characterize the agreement of the evaluation results (i.e., how much confidence can be given to the parameter estimation and its error).
Earlier, we developed a method for estimating the height and speed of clouds from cloud images obtained by a pair of digital cameras. The shift of a fragment of the cloud in the right frame relative to its position in the left frame is used to estimate the height of the cloud and its velocity. This shift is estimated by the method of the morphological analysis of images. However, this method requires that the axes of the cameras are parallel. Instead of real adjustment of the axes, we use virtual camera adjustment, namely, a transformation of a real frame, the result of which could be obtained if all the axes were perfectly adjusted. For such adjustment, images of stars as infinitely distant objects were used: on perfectly aligned cameras, images on both the right and left frames should be identical. In this paper, we investigate in more detail possible mathematical models of cloud image deformations caused by the misalignment of the axes of two cameras, as well as their lens aberration. The simplest model follows the paraxial approximation of lens (without lens aberrations) and reduces to an affine transformation of the coordinates of one of the frames. The other two models take into account the lens distortion of the 3rd and 3rd and 5th orders respectively. It is shown that the models differ significantly when converting coordinates near the edges of the frame. Strict statistical criteria allow choosing the most reliable model, which is as much as possible consistent with the measurement data. Further, each of these three models was used to determine parameters of the image deformations. These parameters are used to provide cloud images to mean what they would have when measured using an ideal setup, and then the distance to cloud is calculated. The results were compared with data of a laser range finder.
For the reconstruction of the cloud base height a method was developed based on taking pictures of the sky by a pair of digital photo cameras from the ground and subsequent processing of the obtained sequence of stereo frames. Since the directions of the optical axes of the stereo cameras are not exactly known, a procedure of adjusting of obtained frames was developed which use photographs of the night starry sky. In the second step, the method of the morphological analysis of images is used to determine the relative shift of the coordinates of some fragment of cloud. The shift is used to estimate the searched cloud base height. The proposed method can be used for automatic processing of stereo data and getting the cloud base height. The earlier paper described a mathematical model of stereophotography measurement, poses and solves the problem of adjusting of optical axes of the cameras in paraxial (first-order geometric optics) approximation and was applied for the central part of the sky frames. This paper describes the model of experiment which takes into account lens distortion in Seidel approximation (depending on the third order of the distance from optical axis). Based on this model a procedure of simultaneous camera position adjusting and estimation of parameters of lens distortion in Seidel approximation was developed. The first experimental results of its application are shown.
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