Deep convective cloud has high, stable, and reliable reflectivity in the visible-near infrared (VIS/NIR) band, which is suitable for radiometric calibration. In addition, the development of deep convective clouds is deeply located at the top of the troposphere and is less affected by water vapor absorption and aerosols. The deep convective cloud is mainly distributed in the equatorial region, which is suitable for the calibration of polar orbit and geostationary satellites. However, the deep convective cloud is not a real Lambertian target. When the satellite detects from different observation angles, the anisotropy characteristics of the deep convective cloud make the satellite observation biased, which leads to calibration errors. Therefore, it is necessary to analyze the directional reflectance characteristics of deep convective clouds and establish an effective bidirectional reflectance distribution function (BRDF) to correct the directional reflectance and improve the calibration accuracy. The operational Hu model is not only inapplicable to the shortwave infrared channel but also has a slight influence on the data stability in the VIS/NIR channel when the eigenvalue is selected as the mean reflectivity. Since the previously constructed model has been relatively long compared with the current one and may be affected by human activities, the anisotropic reflection factors of deep convective clouds will change to some extent. The operational Hu model and CERES thick ice cloud model are broadband models. Therefore, we use the latest data to model the BRDF characteristics of deep convective clouds, which can better characterize the directional characteristics of deep convective cloud reflectivity. Modeling each channel separately can make up for the deficiency that the Hu model and CERES thick ice cloud model are broadband models. For the modeling of the shortwave infrared channel, it can fill the gap that the Hu model used by the current business is not applicable to the shortwave infrared channel, and it is of great significance to improve the calibration accuracy of the deep convective cloud target.

The BRDF modeling of each channel of deep convective clouds in this paper classifies the deep convective cloud reflectivity data into angle intervals and establishes a look-up table method. In view of the low attenuation of the instrument itself and in order to maintain sufficient data to make the interval of the look-up table established more smoothly, the data from 2016 to 2020 are used. With regard to the selection of normalized objects, it does not affect the relative value of the BRDF factor but only the absolute value of the BRDF factor. It affects the absolute rather than relative quantity of corrected reflectivity value and does not affect the relative calibration and attenuation analysis. The BRDF modeling normalization object in this paper selects a solar zenith angle of 35°, observation zenith angle of 0°, and relative azimuth direction reflectivity of 0° as standard observation geometry. The reasons why they are used as the normalized objects are as follows: 1) for BRDF measurement of objects, since the albedo requires directional integration of data from all angles, which is too complex, the reflectivity in the vertical direction corresponding to the zenith angle is often used as a substitute; 2) the data volume of the interval deep convective cloud corresponding to this angle is the largest. As a normalized object, it can make the BRDF model more evenly distributed. Theoretically, as the interval division gets detailed, the anisotropy of the deep convective cloud target can be explained better. However, according to the principle of statistical model, in order to ensure that each angle interval has a certain amount of data distribution, for each channel, the zenith angle is classified as interval data of 5°, and an interval look-up table of 5° is constructed based on the existing data. In other words, the solar zenith angle is taken as 0°-5°, 5°-10°,…, and 45°-50°, and the observation zenith angle is taken as 0°-5°, 5°-10°,…, and 45°-50°. The data of every interval of 10° of the relative azimuth angle are classified into one category, that is, 5°-15°,…, 165°-175°, which is divided into intervals of 10×10×17=1700 in total, and the mean value, standard deviation, and number of pixel points within each interval are calculated and counted.

The results show that the BRDF characteristics of the VIS/NIR channels are almost the same. The lowest reflectivity appears at the larger observation zenith angle, and the highest reflectivity appears in the perigee direction. On the contrary, the lowest reflectivity of the shortwave infrared channel appears near the perigee, and the highest reflectivity appears at the location where the zenith angle of the forward scattering observation is large (Fig. 1). Hu BRDF model chooses 17.5° between 15°–20° of solar zenith angle to normalize the anisotropy factor corresponding to different observation zenith angle and relative azimuth, with solar zenith angle of 35°, observation zenith angle of 30°, and relative azimuth of 135°. The results are plotted as a polar image (Fig. 2) and compared with the modeling results. Compared with that of the Hu model, in the VIS/NIR band, the overall anisotropy of the proposed model shows a high consistency, which proves the reliability of the model. In the shortwave infrared channel, the Hu model shows a great difference, which is related to the inapplicability of the Hu model to the shortwave infrared channel. For the VIS/NIR band, the reflectivity of deep convective clouds is related to the cloud optical thickness, while the shortwave infrared channel is related to the absorption characteristics of particles, which is the fundamental reason for the large difference in anisotropy between the shortwave infrared channel and the VIS/NIR channel.

In this paper, BRDF feature modeling of deep convective clouds is realized. The extracted data of deep convective clouds during 2016-2020 are divided into intervals by angles, and the BRDF characteristics are characterized by calculating the mean reflectivity of each interval. The experimental results show that the BRDF characteristics of the VIS/NIR band are basically the same. The lowest reflectivity appears at the location of the larger observation zenith angle, and the highest reflectivity appears in the perigee direction. For the shortwave infrared channel, the situation is the opposite. The lowest reflectivity appears near the perigee, and the highest reflectivity appears at the location of the larger forward scattering observation zenith angle. The BRDF characteristics of different bands in the shortwave infrared channel are quite different. When the model and Hu model are normalized to the same angle, the difference is compared. The results of the Hu model in the VIS/NIR band are similar to those of modeling, and the shortwave infrared channel is quite different. The effect of the BRDF model on reducing the standard error of deep convective cloud responses is further analyzed. Compared with the model without BRDF correction, the Hu model and the proposed model both reduce the standard error of the response in the VIS/NIR band. For the shortwave infrared channel, the Hu model is not applicable, and the standard error of this model can be reduced by 31% at most. Compared with the Hu model, except for the poor correction effect of the model in the band of 460 nm, other bands show a better correction effect. Finally, the model in this paper is used to correct the direction of deep convective cloud reflectivity data based on Himawari-8 from 2016 to 2022, calculate its attenuation, and compare it with the attenuation results of the calibration coefficient method. It is found that it has a high consistency in the VIS/NIR band, and there are differences in the shortwave infrared band, which is related to the low attenuation rate of deep convective clouds in the shortwave infrared channel and its large fluctuations. This thus proves the reliability of the model in this paper.