Dear Arun,

I assume (1) that you are talking about energy balance models of the Earth, probably in the context of climate change, and (2) that you are interested mostly in global scale issues. If not, then sharpen your question and explain better the context and expected outcome of your research.

The transmissivity of the Earth atmosphere is highly dependent on the composition of the medium in which radiation travels, and on the wavelength of that radiation. The typical tool used to estimate how much radiation is transmitted, scattered (in particular reflected) or absorbed by the medium (here, the atmosphere) is called a radiation transfer model.

Given the broad range of models available, the degree of complexity you should adopt should match the sophistication of your energy balance model and the requirements of your application, including the expected accuracy of the outcomes. It is difficult to be much more specific in the absence of more precise information on the context of your question.

However, remember that different models have been developed and optimized for different wavelength ranges, because the primary physical processes that control how radiation interacts with the atmosphere are so different in each spectral range. The following points constitute only some initial items to address a very complex question, which has already been addressed in many thousands of publications:

- In the UV range, the key (but not the only) issue is the presence of ozone. In particular, the excessive destruction of ozone in the stratosphere (a problem known as the "ozone hole") reduces the absorption of solar radiation in that range, thereby increasing the transmissivity and thus the amount of UV radiation reaching the surface. This has been identified as a serious public health issue.

- In the visible and near-infrared spectral range, the key climatic factors of interest are clouds and aerosols. Clouds tend to reflect more solar light towards space (thereby contributing a cooling term, though even that depends on the altitude of the clouds, because they also have a strong impact on the transmission of thermal infrared radiation). Similarly, aerosols tend to scatter light in all directions, including back to space. However, both components (especially aerosols) feature absorption characteristics too, depending in particular on their chemical composition.

- In the thermal infrared range, water vapor, carbon dioxide and other greenhouse gases play a critical role: an increase in their concentration decreases the transmissivity and therefore blocks the radiation in the lower atmospheric layers. This is one of the main causes of the now familiar climate warming problem.

- For the purpose of assessing the energy balance of the Earth, other types of radiation (X and Gamma rays, or radio and microwaves) are of less importance because the global energy amounts are relatively smaller, but understanding atmospheric transmissivity in those spectral bands can be crucial for specific applications, including communications (radio, TV, telephony and networking), navigation (e.g., GPS), security (e.g., radars), etc.

You will find introductions to these topics on Wikipedia, and detailed reviews of the state of the art in radiation transfer modeling within the context of climate change in the IPCC assessments Report (AR-5; https://www.ipcc.ch/report/ar5/).

In summary, atmospheric transmissivity is a critical component of the problem of characterizing the energy balance of the atmosphere (or of the planet). Which model you should use will depend on the spectral range of interest, on the complexity and detail of the energy balance model, on the desired level of performance and reliability, as well as on the ultimate purpose of calculating the energy balance.

Cheers, Michel.

Thank you Professor for your detailed explanation on EMR interactions with Atmosphere in different spectral wavelengths. Thanks for sharing IPCC link as well. I'm particularly concentrating on Radiation Transfer in Shortwave and longwave region in spational format in regular basis to apply energy balance approach to track El-nino events.  

Hi Arun

I hope you can find it out using the RTM equations. But since RTM equations are very difficult and complicated to implement so you can derive some linear or non linear relationship using the empirical iterations. You can further improve your relation based on the observations if you have for your study area or you can simulate the datasets for the verification of your assumptions.

I am not sure but there might be a way to model it using AOD(Aerosol Optical Depth). You just find out because when we make corrections for the atmospheric effects in remote sensing data, this factor is very prime and it can be easily determined also.

Once you are done with this process definitely you can further use the outcome for energy balance.