# Precipitation Estimation Using FY-4B/AGRI Satellite Data Based on Random Forest
## 2 Materials and Methods
### Methods
#### 2.3.3 Selection of Feature Variables
Taking the satellite pixel (i,j) as the centre, the cloud top brightness temperature gradient modulus (\(Gm(IR_{10.8})\)) of this point is shown in Formula (1). \[Gm(IR_{10.8})=\sqrt{\left(IR_{10.8}(i-1,j-1)-IR_{10.8}(i+1,j+1)\right)^{2}+ \left(IR_{10.8}(i+1,j-1)-IR_{10.8}(i-1,j+1)\right)^{2}} \tag{1}\]The brightness temperature differences (\(\Delta T_{6,25-10.8}\) and \(\Delta T_{7,42-12}\)) between the water vapor channel and the long-wave infrared channel are sensitive to changes in CTH [40] and can be used to distinguish convective clouds from non-precipitation cirrus clouds. CP information such as ice or water clouds above clouds can be obtained by the difference between (\(\Delta T_{8,55-10.8}\) and \(\Delta T_{10.8-12}\)). At these two wavelengths, the radiation absorption characteristics of ice particles and water particles in the upper clouds are different [41]. Water particles absorb more between 10.8 \(\upmu\)m and 12 \(\upmu\)m than between 8.55 \(\upmu\)m and 10.8 \(\upmu\)m, while ice particles absorb more between 8.55 \(\upmu\)m and 10.8 \(\upmu\)m than between 10.8 \(\upmu\)m and 12 \(\upmu\)m, so the cloud phase can be distinguished by the difference in absorption. When the cloud top brightness temperature is low, cirrus clouds may exist, which are generally non-precipitation clouds [38]. The brightness temperature at 1.379 \(\upmu\)m and 13.3 \(\upmu\)m can be used to identify cirrus clouds [42]. Visible and near-infrared channels can provide information about CWP, and the larger the reflectivity of the channel, the larger CWP. During day, the visible reflection of sunlight is closely related to the optical thickness, while the near-infrared reflection is closely related to the effective particle radius of the cloud. At night, because the channels of visible and near-infrared wavelengths are not available, the difference (\(\Delta T_{3.75-7.42}\) and \(\Delta T_{3.75-10.8}\)) is chosen to indirectly reflect the information of the cloud water path [36]. With the increase in the particle radius, the scattering effect of particles in the 3.75 \(\upmu\)m channel is stronger than that in the 7.42 \(\upmu\)m and 10.8 \(\upmu\)m channels, and thinner clouds have stronger penetration. At the same time, the infrared radiation of a cloud with a larger optical thickness at 3.75 \(\upmu\)m is greater than that at 7.42 \(\upmu\)m and 10.8 \(\upmu\)m channels. WV channels can be used to represent different sensitivity characteristics of cloud water vapor. Although most of these channels have similar components, due to differences in sensitivity, they also have independent components for the characteristics of cloud top surface to a certain extent. Therefore, the similar characteristics of water vapor channels are represented by the sum of WV channels, while the difference between 6.25 \(\upmu\)m and 7.42 \(\upmu\)m represents the wavelength-dependent effects on emissivity difference in the cloud tops at WV channels [19]. Since satellites detect cloud top information in both visible and infrared channels, ground information related to precipitation should also be considered. Precipitation has local characteristics. Studies have shown that for annual precipitation, topographic elevation and topographic relief are the main topographic factors that affect the spatial heterogeneity of precipitation [43]. Increases and changes in topographic height will slow down the horizontal wind speed and affect the vertical wind speed at the bottom. Mountain fluctuations can force the air flow to rise or divert from both sides. Thus, digital elevation model (DEM) and orographic variation (OV) are added to the precipitation retrieval. At the same time, considering that the energy received by the satellite detection instrument is related to the observation zenith angle of the satellite, the satellite zenith angle (SAZ) is added to the retrieval as additional information. Table 3 shows the physical-related features and their specific expressions that need to be used in the model during day and at night.