## 1. Molecular atmosphere Comparison

### • Conditions of the comparison (6SV1, RT3, MODTRAN, & SHARM vs. Coulson's)

Table 1. Conditions of the comparison for a pure molecular atmosphere.

 Optical thickness τ= 0.1 (λ >= 530 nm) τ= 0.25 (λ >= 440 nm) τ= 0.5 (λ >= 360 nm) Ground reflectance ρ= 0.0 ρ= 0.25 ρ= 0.0 ρ= 0.25 ρ= 0.0 ρ= 0.25 SZA 23.073953.130178.4630 0.036.869966.4218 0.036.869966.4218 23.073953.130178.4630 23.073953.130178.4630 0.036.869966.4218 AZ 0.0; 90.0; 180 VZA as in Coulson-s tables (see the Excel file)

Here SZA denotes the solar zenith angle, VZA is the view zenith angle, and AZ is the relative azimuth.

The relative differences between the simulations of each code and Coulson's values are calculated as Coulson-Code|*100%/Coulson.

### • Results of the comparison (6SV1, RT3, MODTRAN, & SHARM vs. Coulson's)

Figure 1. Some results of the comparison with Coulson's tabulated values for a molecular atmosphere. Results. An Excel file with VPD results is available by request.

### • Conditions of the comparison (6SV1 & Monte Carlo)

τmol = 0.25, ρsurf = {0.0; 0.25}, SZA = {0.0-; 23.0-; 50.0-}, 1010 photons.

### • Results of the comparison (6SV1 & Monte Carlo)

Figure 2.Results of the comparison of 6SV1 and Monte Carlo or a pure molecular atmosphere. Instead of calculating an exact value of TOA reflectance for a given geometric configuration, Monte Carlo calculates the average value of all TOA reflectances confined within a given solid angle.
The hemispherical space at the top of atmosphere is divided into a number of solid angles, specified by VZA and AZ values.
In this case, the angular sampling for the relative AZ space (0- - 180-) is 22.5-. The sampling for VZA space (0- - 90-) is shown in Figure 2. The boundary VZA values are presented as angular coordinates. The relative difference varies as the radius coordinate from 0 to 0.4%.