Calculation results of RADEX. First row: Correlation between RADEX input column densities and column densities of different ¹³CO transitions derived using LTE equations with T_rot and T_ex using T_R computed by RADEX for different volume densities. Second, third, and fourth rows: Column density ratios of different ¹³CO transitions derived using LTE equations with T_rot and T_ex as a function of the RADEX column density input for different volume densities. Vertical lines mark the peak values of the ¹³CO column density derived from ¹³CO J = 3−2, J = 2−1, J = 1−0 and ATLASGAL+Planck 870 µm emission (from left to right) shown in Figs. 7−9; here the abundance ratio of H₂ compared with ¹³CO ~ 7.1 × 10⁵ is used. Cyan circles mark the ratios predicted by RADEX when the input ¹³CO column density takes the peak values of the column density derived by different methods in Sect. 3.3.