Exoplanet Climate Modeling

Y-axis (Optical Depth, τ): On a log scale, ranging from the top of the atmosphere (low τ) to deeper layers (high τ). The plot is inverted to reflect increasing depth downward (similar to atmospheric cross-sections)

X-axis (Temperature, K): Temperature profile from cold upper atmosphere to warmer lower atmosphere.

Blue Curve (Earth-like atmosphere): Earth’s temperature structure assuming moderate greenhouse effect (τ ≈ 1), producing surface temperatures around ~288 K. 

Orange Curve (CO₂-rich atmosphere): Simulates a planet with much thicker atmosphere (τ ≈ 6), leading to enhanced greenhouse warming and a higher surface temperature.

Red Vertical Lines: Mark where CO₂ absorbs strongly in the infrared. 4.3 μm and 15 μm bands, with corresponding Wien temperatures around 674 K and 193 K.

Green Vertical Lines: Show H₂O IR absorption features. 2.7 μm (~1073 K) and 6.3 μm (~460 K).

I chose to use a simplified gray atmosphere:

In order to determine what the value is for the Earth's predicted atmosphere using this tactic, I used the following variables to determine:

A τ of 1 is fairly appropriate for simulating an Earth-like atmosphere (with an optically thin / moderately thin atmosphere). Therefore, my simulation of an Earth-like atmosphere resulted in:

The actual surface temperature of Earth is approximately 288K, so 263K is an alright approximation for such a simplified model. Some of the factors I considered that may be contributing to the temperature being low could be:

• The model only accounts for radiative equilibrium, not convection (which warms the lower atmosphere)

• No internal heat flux or cloud effects are accounted for in this model

• The albedo may be too high

• This is a simplified greenhouse, so the actual Earth's atmosphere has IR windows and non-gray opacity that shape the profile