Difference between beta0+TF and gamma0

Hello, I have some questions about radiometric calibration.

As I know, Gamma0 is Terrain Flattened Beta0.

Using S-1, the calibration output to gamma0 is exactly same as the result that calibration to beta0 + Terrain Flattening.

However using CSK, the two results became different. (using SRTM 1Sec HGT DEM)
Why did they become different?
Also, which one is more correct for normalized backscattering coefficient between directly calibrated gamma0 and beta0+TF?

Additionally, how about the sigma0 and gamma0(or beta0+TF)?
As I know, sigma0 is suitable for less topo area, gamma0 is for much topo area.
What happens if I applied gamma0 to the ocean area or sigma0 to the mountain area?
Because I want to make some big-data for deep learning, so I think one fixed processing is better for me.

If you want one-size-fits-all preprocessing my hunch is that Gamma0 is the way to go. However there is the issue of the DEM - often DEMs do not have height-values over the sea so some workaround would be needed. @ABraun would you have ideas?

to me this sounds like the terrain flattening did not work at all, because the Gamma0 from the calibration operator is less effective and correct than the terrain flattening operator, because it is only based on geometric integration of the incidence angle while terrain flatteming estimates the area illuminated by the sensor per pixel and uses this for radiometric normalization.

However, Terrain Flattening can produce weird patterns in cases of extreme slopes so it depends a bit on the aim of your deep learning approach if this makes sense or only introduces uncertainty to the model.
Also, it depends if you use both ascending and desending data which are indeed very different in mountainous areas.

Ascending and descending are comparable on terrain flattened imagery. This should be a bonus for deep learning as the NN does not need to be taught how local incidence-angle affects the unflattened sigma0 imagery.

I agree in principle, but the information on steep slopes may still not be identical, when line-like structures are introduced by Range Doppler Terrain Correction which could suggest “false” patterns. I’ll look for an example and share it once I found it.

not quite what I meant but this shows that Terrain Flattening has its limits (example from Mt. Fuji, Japan). The first is Sigma0, the second Terrain Flattened Gamma0.

In the example below Terrain Flattening worked very well (left Sigma0, right Terrain Flattened Gamma0), but the artefacts from range doppler terrain correction at slopes remain. So ascending and descending backscatter can be different in such areas.

Yes, it is not perfect but the best that is currently possible. I wonder how well things would work with a “perfect” DEM.

I fully agree. Just wanted to point out that terrain flattening will not solve all terrain induced problems, especially in cases of foreshortening.

I’ll see if I find a good example for comparison with a fine resolution DEM.