is the normalized solar flux received by the Earth 1360 Wm 2 In radiative

# Is the normalized solar flux received by the earth

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is the normalized solar flux received by the Earth (~1360 W/m 2 ). In radiative equilibrium, F IR must equal F S and S EFF is equal to 1. Thus, values of S EFF that differ from unity measure how far a planetary atmosphere deviates from radiative equilibrium, which is also equivalent to deviations in the normalized flux ( S/S o ). Radiative equilibrium is imposed for the Earth located at 1 AU, but not for the inner and outer edges of the HZ. However, for HZ calculations, it suffices only to know how much more (or less) stellar energy a planet receives with respect to Earth, after also accounting for the changes in planetary albedo ( A p ) through energy balance (Equation (2)): S o 4 ( 1 - A p ) = σ T 4 = F s (2) Here, T is surface temperature. Thus, S EFF values greater than 1 also represent smaller semi-major axis distances, corresponding to distances of increased stellar (or solar) flux, whereas small values correspond to farther distances of reduced stellar (or solar) flux. The inverse-square law can be rearranged to solve for the distance required to support a given value of S EFF (Equation (3)): d = s L / L sun S EFF (3) where L/L sun is the stellar luminosity in solar units and d is the orbital distance (in AU). Thus, assigning L/L sun = S EFF = 1 yields a value of d = 1 AU for the Earth. Equation (3) can also be used to compute the effective flux minus the albedo effect. The flux received by the Earth before the energy enters the atmosphere is ~1360 W/m 2 [ 1 ]. At Mars’ distance of 1.52 AU, Equation (3) predicts that S EFF is ~0.43, which is equal to a flux of (0.43 × 1360) ~585 W/m 2 . 2.3. The Inner Edges of the Classical Habitable Zone At distances that are close enough to the star, planetary temperatures rise, and photolysis is enhanced, which is a process in which upper atmospheric H 2 O vapor molecules dissociate into H + and OH - ions. Although often misrepresented in the literature, the inner edge boundaries are not calculated using the boiling point of water. Indeed, the inner edge has nothing to do with the boiling point of water. On a planet with an Earth-like non-condensable inventory (~300–400 ppm CO 2 ), a moist greenhouse (a pessimistic inner edge distance) can be triggered when the upper atmospheric water vapor mixing ratio above the cold trap exceeds ~2 × 10 - 3 , which corresponds to a computed mean surface temperature of 340 K [ 1 ]. Above the cold trap, the air is too cold for water vapor to convect to even higher levels. However, at this surface temperature, water vapor photolysis above the cold trap
Geosciences 2018 , 8 , 280 4 of 48 becomes efficient enough to remove an Earth-like surface water inventory via escape to space within the age of the solar system (or 4.5 billion years) (Figure 1 ). An example calculation is shown below. Geosciences 2018 , 8 , x FOR PEER REVIEW 4 of 48 space within the age of the solar system (or 4.5 billion years) (Figure 1). An example calculation is shown below.

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