Temperature profiles of different order numerical schemes for varying heat-conduction coefficients, χ, and grid resolutions, Δz, at the same physical time, t = 300 s, in the simulation. The horizontal axes indicate the atmospheric height, z. The solid blue line represents the run with the second-order numerical scheme, the dashed green and orange lines the fourth- and the eighth-order runs, respectively, and the dotted black lines the tenth-order runs. The solid red line represents the sixth-order derivative numerical scheme, which was the chosen numerical scheme for our simulation. Panels c and d show the results for a heat conduction of χ = 30 − 108 m²/s, and panels a and d the results for a heat conduction of χ = 0.5 − 108 m²/s.