Comparison of the Lyman-α upward radiative rate coefficient (R₁₂) computed with and without the Doppler effect. Panels (a) and (b) present the simulation outputs for temperature and vertical velocity, respectively. Panels (c) and (d) show the rate coefficients calculated with and without accounting for the Doppler effect. Panel (e) compares the rate coefficients along the dashed line indicated in panels (c) and (d), while panel (f) presents the point-to-point comparison, with the evaluation formula provided above the panel. The rate coefficients at high temperatures (T > 0.2 MK) were manually set to zero to emphasize the results in the lower atmosphere.