Continuous Grey Atmosphere Model

In summary, the grey atmosphere radiative energy balance model uses a continuous atmosphere with varying temperature, which is a function of optical depth. In order to find the total optical thickness of the atmosphere of Venus, the same emission and ground temperatures are assumed. Additionally, the temperature difference between the ground temperature and the atmospheric temperature at ground level can be calculated using equations for optical depth and emission temperature. There are two equations for optical depth, but it is unclear which one is correct. The emission temperature can be calculated using the third equation, but finding the ground temperature remains a challenge.
  • #1
il27

Homework Statement


In the grey atmosphere radiative energy balance model, we replace the multi-layer approximation used above with still simplified but significantly more realistic model involving a continuous atmosphere with a continuously varying temperature. The variation with temperature is a function of optical depth.

a) Find the total optical thickness of the atmosphere of Venus using the gray atmosphere model. Assume the same emission and ground temperatures as in the previous question.

b) Find the temperature difference between the ground temperature Tg and the atmospheric temperature at ground level.

Homework Equations



$$ T_g ^4 = T_e ^4(1 + \frac{3}{4} \tau) $$

There is another equation for optical depth, but I am not sure how to derive this:

$$ \tau = \frac{T_g ^4}{T_e ^4} - 1 $$

$$ T_e = (\frac{(1-\alpha)}{4 \sigma} F_0)^.25 $$

The Attempt at a Solution



I am thinking I can calculate the emission temperature with the 3rd equation, but I am stuck on finding the ground temperature.
Also which optical depth equation is correct?
 
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  • #2
help please!
 

1. What is the Continuous Grey Atmosphere Model?

The Continuous Grey Atmosphere Model is a simplified model used to study the behavior of energy transfer in the Earth's atmosphere. It assumes that the atmosphere is a continuous medium that absorbs and emits radiation at all wavelengths and that the atmosphere is in thermal equilibrium.

2. How is the Continuous Grey Atmosphere Model different from other atmospheric models?

The Continuous Grey Atmosphere Model is simpler than other atmospheric models, such as the two-stream model or the radiative-convective model, as it does not take into account the spatial variations of temperature, pressure, and other atmospheric parameters. It also assumes that the atmosphere is a perfect absorber and emitter of radiation, which is not the case in reality.

3. What are the limitations of the Continuous Grey Atmosphere Model?

The Continuous Grey Atmosphere Model has several limitations. Firstly, it does not account for the effects of scattering, which is an important process in the Earth's atmosphere. Additionally, it does not consider the vertical structure of the atmosphere, which can significantly impact energy transfer. Lastly, it assumes that the atmosphere is always in thermal equilibrium, which is not always the case in reality.

4. What are some applications of the Continuous Grey Atmosphere Model?

The Continuous Grey Atmosphere Model is commonly used in climate studies to understand the overall behavior of energy transfer in the atmosphere. It is also used in remote sensing to estimate the amount of radiation absorbed and emitted by the Earth's atmosphere. Additionally, it is often used as a benchmark for more complex atmospheric models.

5. How can the Continuous Grey Atmosphere Model be improved?

While the Continuous Grey Atmosphere Model is a useful tool for studying energy transfer in the atmosphere, it has its limitations. To improve the model, researchers are working on incorporating the effects of scattering into the model and developing more accurate representations of the vertical structure of the atmosphere. Additionally, including more realistic atmospheric properties, such as variable absorption and emission coefficients, can also improve the accuracy of the model.

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