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.
The reconstruction of an image distorted by a linear transformation is a problem that is unstable with respect to the perturbation of the mathematical model of the image formation. This instability is overcome by using a priori information about the class of original images. Among the ways to use such information, there is an assumption that the original image belongs to the class of piecewise constant images. The class of piecewise constant functions can provide a good approximation for signals encountered in practice since such functions can approximate any square-integrable signal with arbitrary accuracy. On the other hand, the assumption that the brightness value of the image takes a finite set of values is plausible for some applied studies. Such a proposal, in particular, is made in the tomography, where studied samples can consist of a small number of fractions. In this paper, we propose an algorithm for reconstruction of piecewise constant signals blurred by a linear transformation and investigate the possibility of its application to the original unblurred signal estimation. For ease of implementation, the case of one-dimensional signals is considered.
Proc. SPIE. 11152, Remote Sensing of Clouds and the Atmosphere XXIV
KEYWORDS: Aerosols, Error analysis, Clouds, Monte Carlo methods, Neural networks, Solar radiation, Scatter measurement, Atmospheric particles, Atmospheric modeling, 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.
For the reconstruction of some geometrical characteristics of clouds a method was developed based on taking pictures of the sky by a pair of digital photo cameras and subsequent processing of the obtained sequence of stereo frames to obtain the height of the cloud base. 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). We developed procedure of simultaneous camera position calibration and estimation of parameters of lens distortion in Seidel approximation.
Errors of the retrieval of the atmospheric composition using optical methods (DOAS et al.) are under the determining influence of the cloudiness during the measurements. Information on cloud characteristics helps to adjust the optical model of the atmosphere used to interpret the measurements and to reduce the retrieval errors are.
For the reconstruction of some geometrical characteristics of clouds a method was developed based on taking pictures of the sky by a pair of digital photo cameras and subsequent processing of the obtained sequence of stereo frames to obtain the height of the cloud base.
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 report describes a mathematical model of stereophotography measurement, poses and solves the problem of adjusting of optical axes of the cameras, describes method of searching of cloud fragments at another frame by the morphological image analysis; the problem of estimating the cloud base height is formulated and solved. Theoretical investigation shows that for the stereo base of 60 m and shooting with a resolution of 1600x1200 pixels in field of view of 60° the errors do not exceed 10% for the cloud base height up to 4 km. Optimization of camera settings can farther improve the accuracy. Available for authors experimental setup with the stereo base of 17 m and a resolution of 640x480 pixels preliminary confirmed theoretical estimations of the accuracy in comparison with laser rangefinder.
Retrieval errors of the atmospheric composition using optical methods (DOAS et al.) are under the determining influence
of the cloudiness during the measurements. If there is information about the clouds, the optical model of the atmosphere
used to interpret the measurements can be adjusted, and the retrieval errors are reduced.
For the reconstruction of the parameters of clouds a method was developed based on taking pictures of the sky by a pair
of digital photocameras and subsequent processing of the obtained sequence of stereo frames by a method of
morphological analysis of images.
Since the directions of the optical axes of the cameras are not exactly known, the calibration of the direction of sight of
the cameras was conducted at the first stage using the photographs of the stars in the night sky. At the second stage, the
relative shift of the image of the cloud fragment on the second frame of the pair was calculated. Stereo pairs obtained by
simultaneous photography, allowed us to estimate the height of cloud.
The report describes a mathematical model of measurement, pose and solve the problem of calibration of direction of
sight of the cameras, describes methods of combining of image fragments by morphological method, the problem of
estimating cloud height and speed of their movement is formulated and solved. The examples of evaluations in a real
photo are analyzed and validated by the way of comparing with the results of measurement by laser rangefinder.
Retrieval errors of the atmospheric composition using optical methods (DOAS et al.) are under the determining influence of the cloudiness during the measurements. If there is information about the clouds, the optical model of the atmosphere used to interpret the measurements can be adjusted, and the retrieval errors are reduced. For the reconstruction of the parameters of clouds a method was developed based on taking pictures of the sky by a pair of cameras and subsequent processing of the obtained sequence of stereo of frames by a method of morphological analysis of images. Since the directions of the optical axes of the cameras are not exactly known, the graduation of the direction of sight of the cameras was conducted at the first stage using the photographs of the stars in the night sky. As a result, the coefficients of the affine transformation relating own coordinate systems of the cameras were determined. The authors have confined themselves to affine transformations, as the angle between the optical axes was small enough, and the corresponding points on the stereo pair were chosen near the optical axis. At the second stage, the relative shift of the image of the cloud fragment on the second frame of the pair was calculated. Stereo pairs obtained by simultaneous photography, allowed us to estimate the height of cloud. The paper poses and solves the problem of graduation of direction of sight of the cameras, shortly describes the main features of other steps of the method of estimating the height of cloud base. The examples of first evaluations in a real photo are analyzed.
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