Atmosphere visibility is an important and popular indicator for evaluating the atmosphere quality and is of great significance for our daily life and traffic safety. According to the observation paths, visibility can be defined as horizontal visibility and slant-range visibility. In some cases, slant-range visibility may be different from horizontal visibility to some degree. In civil aviation, horizontal visibility or ground visibility is normally measured by ground-based equipment called transmissometer. Reported horizontal visibility is employed for air traffic management. However, slant-range visibility is more important for pilots during flights. Thus, far slant-range visibility has not been applied in air traffic management, which is due to the absence of feasible methods for deriving or measuring slant-range visibility. The space-borne lidar CALIOP carried by the sun-synchronous satellite CALIPSO is capable of obtaining the atmosphere properties along the vertical direction, and therefore, it is a good candidate for deriving the slant-range visibility. We aim to develop a sufficient method of deriving slant-range visibility with high accuracy based on the aerosol data provided by CALIPSO and the theory of atmosphere radiative transfer.

We successfully derive the slant-range visibility for North China through the aerosol data provided by the CALIPSO satellite and the atmosphere radiation transfer model of SBDART. Firstly, the aerosol optical properties are characterized by optical depth, single scattering albedo, and scattering phase function provide by the CALIPSO aerosol products. They are leveraged in solving the atmosphere radiative transfer equation using the SBDART model. As the result, the spatial sky background radiance is obtained. The target-background brightness contrast is hence obtained, which is adopted to determine the slant-range visibility based on the visibility definition. Consequently, the atmosphere layer is determined for the desired brightness contrast. Finally, the δ-two-stream approximation is utilized to estimate the sky background radiation with high spatial resolution within the specific atmosphere layer. The slant-range visibility is hence derived with high accuracy.

The radiance on the ground obtained by the proposed method is shown to have a relative difference of 12.3% from that obtained by the MARRA-2 dataset (Fig. 7). The results show that the sky background radiance obtained by the proposed method is accurate and can be applied for deriving the slant-range visibility. The slant-range visibility obtained with and without the help of δ-two-stream approximation is compared (Table 1). The results show that the invisibility under the two conditions is significantly different for low-visibility weather and small observation pitch angle, while it tends to be consistent with each other as the atmosphere visibility and pitch angle increase. When the slant-range visibility is less than 1 km, the average relative error of slant-range visibility with and without the help of δ-two-stream approximation is about 15.0%, while the average relative error is about 6.2% with the slant-range visibility of less than 10 km. For low-visibility weather and small pitch angle, the slant-range visibility obtained by the proposed method is expected to have higher accuracy because the sky-background radiance is derived with higher spatial resolution. On the other hand, slant-range visibility is obtained through the empirical expression for slant-range visibility. The results of slant-range visibility for low-visibility weather are shown to have a good correlation with the correlation coefficient of 0.928 (Fig. 10). Meanwhile, under the assumption that the slant-range visibility is less than 1 km, the average relative error of slant-range visibility retrieved by this method is about 7.1% compared with that of the empirical expression. Nevertheless, the empirical expression is valid only for air-to-ground observation angles smaller than 15° (Table 2). The proposed method is sufficient for deriving slant-range visibility with high accuracy under a wide range of observation angle.

We propose a new method of deriving slant-range visibility based on the aerosol products provided by the CALIPSO satellite and the atmosphere radiative transfer model SBDART. The δ-two-stream approximation is first introduced in solving the atmosphere radiative transfer equation using the SBDART model. As a result, the sky-background radiance is obtained with high spatial resolution, which enables us to derive the slant-range visibility with high accuracy. We successfully derive the slant-range visibility of North China. The results show that in certain circumstances the derived slant-range visibility obtained by the proposed method has good consistency with that obtained without employing δ-two-stream approximation, and the average relative error between them is about 15.0%. It is also the case when the derived slant-range visibility using the proposed method is compared with the slant-range visibility obtained by the empirical expression. When the slant-range visibility is less than 1 km, the average relative error of slant-range visibility is about 7.1%, which verifies the reliability of the slant-range visibility calculation results. This indicates that the proposed method also has excellent performance and solves the problems of the standard SBDART model under small pitch angles. Additionally, the proposed method exhibits higher accuracy of slant-range visibility and may be applied for extensive weather and observation conditions.