Dr. Michael L. Larsen – Research Overview

Radiative Transfer Through Statistically Correlated Random Media (Cloudy Atmospheres)

Basic Background

We know that light from the sun makes its way through the atmosphere to the surface of the earth. The path of a single photon might be complicated – the atmosphere has matter that can interact with the photon and absorb or scatter it – but eventually some solar radiation makes its way to the surface.

An important question to address is how much of this solar radiation can propogate through the layer of “stuff” in the way (cloud droplets, aerosol particles, gas molecules).

Traditionally, the amount transmitted through a layer is computed via use of the “Beer-Lambert” law. You can get a better feel for the idea by following the link, but the upshot is that if you assume that the “stuff” is distributed perfectly randomly in space, the amount of radiation surviving after propagating a distance “z” through the layer is given by the relation:

I(z)=I(0)*exp(-csz)

Where I(z) is the intensity of the light at distance “z”, I(0) is the intensity before entering the layer, “c” is the number concentration of “stuff” and “s” is a variable associated with how much light each particle or item removes from the beam of incident light due to absorbance or scattering (called its cross-section).

So what’s the Problem?

The key assumption in the above development that is of interest is that the “stuff” is supposedly distributed perfectly randomly. We can adjust the Beer-Lambert relation (by allowing a z-dependent cross-section and/or concentration) to account for some types of variability, but not all variability. If the “stuff” isn’t perfectly random, the Beer-Lambert relationship no longer holds and I(z) does not follow the relationship noted above.

It turns out, some of the “stuff” (cloud particles and – likely to a much lesser extent – aerosol particles) does not appear to be distributed perfectly randomly in space. This is covered in more detail in some of the other research pages, but essentially particles appear to clump or cluster in space. This means that using the above relationship for I(z) (usually) under-estimates the amount of radiation present at a distance z into the layer.

How much of an underestimate is this? That depends on how the particles are distributed and how the radiation interacts with the particles (what are the particles made of, how big are they, what orientation do they take). The fact that the Beer-Lambert law is not followed may not always be particularly important. We are still working to find how big the error is in a realistic environment.

What is Dr. Larsen doing to try and Solve the Problem?

This is a complicated problem that many other investigators are working on as well (including several of Dr. Larsen’s collaborators). Dr. Larsen has decided to try a multi-pronged approach.

1. Find out how much the “stuff” in the atmosphere clusters.

2. Develop some way to quantify this clustering in terms of a quantity with as few inherent assumptions as possible.

3. Try to find how I(z) behaves as a function of z and the above quantity.

4. Attempt to simulate or model the “stuff” to determine if the amount of clustering needed to observe the true I(z) matches the amount of clustering observed in environmental measurements.

This project is closely related to several of Dr. Larsen’s other projects.

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Send a comment to: larsenml@unk.edu

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 This web site courtesy of the Department
 of Physics and Physical Science
In cooperation with the University of Nebraska at Kearney

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