1a
(5 points possible)
A schematic of a two layer model of the Earth-atmosphere energy balance is shown in the image below. The atmosphere is assumed to be transparent to solar radiation, and the total solar radiation absorbed by the surface is written in terms of the emission temperature defined,
There are two atmospheric layers, with temperatures T1 and T2 respectively, while the surface temperature is denoted Ts.
Assuming the surface and each atmospheric layer have long-wave emissivities of 1, fill in the values of the long-wave fluxes represented by each of the red arrows by dragging and dropping the appropriate values into the boxes.
To fill in the values of the long-wave fluxes represented by each of the red arrows, we need to understand the energy balance between the different layers of the atmosphere and the Earth's surface.
The red arrows represent the long-wave radiation fluxes between different layers of the atmosphere and the surface. To determine these fluxes, we need to consider the Stefan-Boltzmann law, which states that the power radiated by an object is proportional to the fourth power of its temperature.
In this two-layer model, we assume that the surface and each atmospheric layer have long-wave emissivities of 1. This means that they are perfect emitters and absorbers of long-wave radiation.
To calculate the long-wave fluxes, we can use the Stefan-Boltzmann law:
Radiative Flux = σ * ε * T^4
Where:
- σ is the Stefan-Boltzmann constant (approximately 5.67 x 10^-8 W/m^2K^4)
- ε is the emissivity of the object
- T is the temperature of the object in Kelvin
Let's fill in the values of the long-wave fluxes step by step:
1. The long-wave flux from the surface to atmospheric layer 1:
- The emissivity (ε) is 1, as mentioned in the question.
- The temperature (T) of the surface (Ts) is given in the diagram.
- Use the Stefan-Boltzmann law to calculate the flux.
2. The long-wave flux from atmospheric layer 1 to atmospheric layer 2:
- The emissivity (ε) is 1 for both layers, as mentioned in the question.
- The temperatures (T1 and T2) of each layer are given in the diagram.
- Use the Stefan-Boltzmann law to calculate the flux.
3. The long-wave flux from atmospheric layer 2 back to atmospheric layer 1:
- The emissivity (ε) is 1 for both layers, as mentioned in the question.
- The temperatures (T1 and T2) of each layer are given in the diagram.
- Use the Stefan-Boltzmann law to calculate the flux.
4. The long-wave flux from atmospheric layer 1 to space:
- The emissivity (ε) is 1 for the atmospheric layer, as mentioned in the question.
- The temperature (T1) of the atmospheric layer is given in the diagram.
- Use the Stefan-Boltzmann law to calculate the flux.
Remember to convert temperatures to Kelvin before using the Stefan-Boltzmann law (Kelvin = Celsius + 273.15).
By following these steps, you can calculate the values of the long-wave fluxes represented by each of the red arrows in the diagram.