Hooray?

In an attempt to find if I had some bugs on my codes, I went back to the basics and tried to reproduce the figures found in Tsang (2001), Vol I, Chapter 8, regarding the scattering from a half space of spherical particles using the radiative transfer method. I was able to get all the figures (codes are working!), and that enocuraged me to go ahead and try to model something closer to our scenario.

So I got two complex permitivities for water (fresh and salty, respectively) from the literature (Ray, 1972 and Plant, 1997), set up a range of ka values and solve the same set of equations at 10 GHz.

The results seems to be pretty interesting. The resonance region typical of Mie scatterers seems to be well recovered (e.g. Sharkov, 2007) and I take this as a confirmation that using Mie is better than Rayleigh and indeed is the regime appropiate for the particle sizes used. Aditionally, the sizes seem to be reasonable for water droplets. But perhaps more important is that it seems that the backscattered power is at least of the order of the values we have seen in the MR-SENSO data (O(-10) dB). Now that's encouraging!

I need to address if we are talking about the same variable though (backscattering coefficient versus NRCS), but I'll do that on monday. The other thing is that it seems that the result is insensitive to the volume fraction of scatterers. I think is due to the normalization of the scattering based on the extinction coefficient, which is also linearly proportional to the number of particles (remember, this is independent scattering), and the two could cancel out.

In the meantime, this simple plot has made me very, very happy.