C. Details of the Model

The dependency of the structure of the three-dimensional gray atmosphere on the solar constant and the runaway greenhouse states C.e. Moist Convective Adjustment Scheme C.g. Vertical Filter

f. Upper Damping Layers

In order to thoroughly eliminate noise in the upper layers, Rayleigh friction and Newtonian cooling type smoothing are included in the top seven layers. Specifically, the terms displaymath6896 and displaymath6897 are added to the x- and y-components of the equations of motion, respectively, and the term displaymath6898 is added to the equation of temperature. Here, tex2html_wrap_inline6906 and tex2html_wrap_inline6908 represent the relaxation time for damping and smoothing, respectively, and are functions of height. tex2html_wrap_inline6910 represents zonal mean temperature. The values of tex2html_wrap_inline6906 andtex2html_wrap_inline6908in Table 1 are used for calculations. The values of tex2html_wrap_inline6906 andtex2html_wrap_inline6908 adopted for the upper-most layer, which is 3 hours, are based on the SKYHI general circulation model of Geophysical Fluid Dynamics Laboratory (Manzini and Hamilton, 1993). Furthermore, the choice of the number of layers into which the Rayleigh friction and Newtonian cooling type smoothing are incorporated is based on the results from a number of test experiments. If the upper damping layer consists of only five layers, integration over a long time period becomes infeasible for the case of S = 1800 W/m2.
verical level τm, τH
k = 32   10800
k = 31   21600
k = 30   32400
k = 29   43200
k = 28   54000
k = 27   64800
k = 26   75600
Table 1: Relaxation time for the upper damping layer. k = 32 indicates the upper-most layer. The relaxation time for this layer is 3 hours.

C.f. Upper Damping Layers The dependency of the structure of the three-dimensional gray atmosphere on the solar constant and the runaway greenhouse states C.e. Moist Convective Adjustment Scheme C.g. Vertical Filter