# How many scattering events happen in the atmosphere over 1 km?

In Vector Monte Carlo Atmospheric Radiative Transfer Simulations, they take a Stokes vector, let's say [1,1,0,0] and multiply it with a matrix, with elements close to 1. But if there are much scattering events, then the continuus multiplication with a number less then one should cause the Stokes vector to decrease to zero. Does it mean there are very few scattering events in the model, or matrix elements can take a greater value than 1? If they are greater then one, how is it that the Stokes-vector elements don't go over 1? How does it work?

• Is the matrix you're referring a Müller matrix, and are the (norm of the) values <1 because you account for extinction? If I understand correctly, you're right that it means that too many scattering events make the Stokes' vector vanish, i.e. light is absorbed. But the abs. cross section is λ-dependent, and in the atmosphere there aren't many scattering events in the optical (or else it would be opaque), whereas there are in, say, the UV (or else we would get sunburnt). The number of scatterings depend on λ, and can be calculated looking at a transmission curve of the atmosphere. – pela May 22 at 11:33
• Thank you! Yes, sorry, I didn't clarify it, I was thinking in IR, somewhere about 800 nm-s. – Gregonymus May 22 at 11:48
• It depends on the exact wavelength. In the IR window, the transmitted fraction of light goes from ~0% at 6-7 μm to 80-90% at both smaller and larger wavelengths. But I think the answer is given in this earlier post. – pela May 23 at 11:42