Histograms of the difference between the inferred height z^† and the height in the MHD simulations z_mhd for different optical-depth levels: log τ_c = 0 (upper-left), −1 (upper-right), −2 (bottom-left), and −3 (bottom-right). Solid colored lines represent the inferences in the hydrostatic case (red for boundary condition P_hyd, 1; blue for boundary condition P_hyd, 2), and dashed colored lines display the MHS case (red for boundary condition P_mhs, 1; blue for boundary condition P_mhs, 2). See text for details.