Atmosphere Heating

One of the effects that Universe Sandbox uses to calculate the temperature of an object is atmospheric heating, which is caused when heat from the object's atmosphere is radiated back down towards the object's surface.

## Related Properties & Settings

### Properties

* The rate at which energy is added to the object's surface from its atmosphere is shown in the Atmosphere Power property.
* The amount of heating depends on the Atmosphere Mass of the object.
* The amount of atmosphere heating will determine the object's Greenhouse Effect.
* Atmosphere heating will affect an object's Average Temperature.

## Models

In reality, light from a star (like the sun) passes through the atmosphere of a planet like Earth without being absorbed. But the energy radiated back out by the heated surface of the planet has a different wavelength, and can be absorbed by the atmosphere. This heats the atmosphere, which then also radiates energy outwards in all directions. Some of this energy will radiate upwards into space, but some will be radiated back down towards the planet's surface, adding an additional source of heat energy to the surface. This effect is known as the greenhouse effect.

Universe Sandbox simulates this effect by estimating the amount of energy radiated towards the surface from the atmosphere. The simulation assumes that the atmosphere is in thermal equilibrium with the surface, and that the atmosphere has an Infrared Emissivity,

ϵ

{\displaystyle \epsilon}

, between zero and one. Then the rate at which the atmosphere adds energy to the surface, or the Atmosphere Power, is calculated using a single-layer atmosphere approximation, given by:

P

a
t
m

=

ϵ
2

σ

T
4

4
π

R
2

,

{\displaystyle P\_{atm} = \frac{\epsilon}{2} \sigma T^4 4 \pi R^2,}

where

T

{\displaystyle T}

 is the current Average Temperature of the surface, and

R

{\displaystyle R}

 is the radius of the object. The Atmosphere Power is included in the Energy Absorption Rate, which is used to calculate the change in temperature for the object.

The single-layer atmospheric heating model can only approximate thinner atmospheres that create greenhouse effects no larger than about 19% of the object's Average Temperature. Thicker atmospheres, such as Venus' atmosphere, create a much larger greenhouse effect in reality, and must be simulated with a more complex multilayer atmospheric heating model. To simulate these thicker atmosphere, each object has a Number of Atmosphere Layers property to represent the number of opaque layers of atmosphere. The Infrared Emissivity then represents the emissivity of the topmost, non-opaque layer. The Atmosphere Power is then given by:

P

a
t
m

=
f
(
ϵ
)
σ

T
4

4
π

R
2

,

{\displaystyle P\_{atm} = f(\epsilon) \sigma T^4 4 \pi R^2,}

where the emissivity factor

f
(
ϵ
)

{\displaystyle f(\epsilon)}

 depends on the Number of Atmosphere Layers,

N

{\displaystyle N}

, by:

f
(
ϵ
# )

(
2
N
−
2
)
−
(
N
−
2
)
ϵ

(
2
N
)
−
(
N
−
1
)
ϵ

.

{\displaystyle f(\epsilon) = \frac{(2 N - 2) - (N - 2) \epsilon}{(2N) - (N - 1)\epsilon}.}

## References

1. ↑ For example, see: American Chemical Society. A Single-Layer Atmosphere Model. *ACS Climate Science Toolkit: How Atmospheric Warming Works*.
2. ↑ For example, see: American Chemical Society. A Multilayer Atmosphere Model. *ACS Climate Science Toolkit: How Atmospheric Warming Works*.