Modelled temperatureT_F and apparent emissivity ε_F versus topographic models: (a) T(ε) (b) ε(Em). In the simulations A = 0.63, p = 0.5, R = 2 mm and the ice phase is amorphous. The thermal conductivity is constant, either k_E0 = 0 (Γ = 0 when not specified in the legend) or k_E0 = 0.001 W m⁻¹ K⁻¹ (Γ ~ 15 MKS). T_F and ε_F are calculated for five footprints (#1 to #5) regularly distributed along the emission angle Em. The observed (T_obs, ε_obs) in the 350 footprints of observation CIRS_222DI_DIONE001_PIE are plotted (+). The topographic models are: flat for the flat case assuming average hemispherical emissivity ε_h (Eq. (13)), flat+e_d for the flat case assuming directional emissivity ϵ_d (Eq. (14)), n=222 for the ellipsoidal n-ell model, q=64, 128 or 512 for the q-topo model at various spatial resolutions of the GTM. The effect of the spatial sensitivity (SS) of FP1 is shown for the GTM with q = 64 and k_E0 = 0 (q=64+SS) or for k_E0 = 0.001 W m⁻¹ K⁻¹ and p = 0.5 (q=64+SS, Γ = 15).