**3. Comparison with Traditional Method**

In order to determine the type of data that can provide information regarding the haze concentration and the type of input data of the convolutional neural network, it is necessary to study the data used in the traditional inversion method. Then, from the data processing process used in the traditional method, the data type and processing method required by the convolutional neural network are analyzed and obtained. This section presents the traditional method selected to set up the convolutional neural network in order to obtain the required information. The method will also be used to examine the performance of the proposed neural network method.

The data processing process in the traditional method is as follows:


**Figure 2.** Corrected remote sensing images. Here, (**a**,**b**) are two remote sensing images with different haze levels on different dates. The corrected results show that the size and range of the images are the same.

(4) The processing of angle data: First, we used the ground control point file to correct the angle dataset geometrically and used the shape-file cutting angle data of the Beijing area, and then synthesized the angle data according to the order of the solar zenith angle, the solar azimuth angle, the satellite zenith angle, and the satellite azimuth angle. Finally, the time sequence stored the processed data for subsequent inversion processing.

(5) AOD inversion: The inversion method was the lookup table method (LUT): the lookup table file is a general-purpose file. Its content is a table of the relationship between radiation reflection, emissivity, angle data, and AOD. This paper used the aerosol inversion tool in ENVI to read the data results processed in steps (3) and (4). Then, it combined the relationship between the corresponding emissivity, reflectivity, angle, and AOD in the lookup table file to perform the aerosol inversion.

Through the operation of the above five parts, the inversion of the AOD was realized. We can learn from previous researchers that there is a functional mapping between the optical depth of aerosol and the sun's radiation. Holben et al. [29] proposed a radiation transfer formula that combines AOD with radiation. The relationship between them is described as Equation (1).

$$R(\mathbf{x}\_{a\prime}\mu\_{\rm s\prime}\mu\_{\rm v\prime}\boldsymbol{\phi}) = R\_0(\mathbf{x}\_{a\prime}\mu\_{\rm s\prime}\mu\_{\rm v\prime}\boldsymbol{\phi}) + \frac{F\_d(\mathbf{x}\_{a\prime}\mu\_{\rm s})T(\mathbf{x}\_{a\prime}\mu\_{\rm v})\rho}{1 + s(\mathbf{x}\_a)\rho} \tag{1}$$

*R*(*xa*, *μs*, *μv*, *φ*) in the above formula denotes a comprehensive signal of all reflected signals received by satellite, where *xa* denotes AOD. *μ<sup>s</sup>* and *μ<sup>v</sup>* denote the solar zenith angle and satellite zenith angle when the satellite passes through the region of interest, respectively. *φ* denotes the corresponding sun azimuth angle and satellite azimuth. *R*0(*xa*, *μs*, *μv*, *φ*) denotes the reflected solar radiation by the atmosphere. *Fd*(*xa*, *μs*) denotes the solar radiation that is not reflected and injected into the atmosphere, and *T*(*xa*, *μv*) denotes the satellite emission signal that passes through the atmosphere. *ρ* is the reflectivity of the ground to solar radiation. *s*(*xa*) denotes the reflectivity of the atmosphere to the sun's radiation.
