Hi Laila,
Your study area is small and that mainly the reason why you want to set the patch_number to 0, i.e. one patch. As it is small it does not really allow to estimate a spatial variable powerlaw and this is likely the reason why the ridge approach does not work well.
The filter bands (1000-1100) is typically determined by contamination of the deformation, in this case you landslides (up to 1.5 km x 0.7 km as you indicated). Based on this you probably want to have a band either smaller or larger than the spatial scale of your landslide. The stamps merge-resample size determines the shortest wavelength you can apply. So I would recommend not to go smaller than 2/3* merge_resample size. The bandfitering happens in the frequency domain, but requires the full image to be interpolated. For the shorter wavelengths you might have some issues there as the data is not uniformly distributed over your study area. so you could try to also use a bigger band filter, i.e. 1200-4000km or so. The maximum bandwidth is given by the extend of your study area, so would not go above 8km.
The discrepancy between the weather model and the powerlaw can be due to few reasons. Incorrect estimate of the powerlaw as you indicate is one of them as the powerlaw would only solve for a topography-correlated component. Also care should be given to the estimated weather model correction. The weather model typically comes at coarse resolution 75 km (ERA-I) to 50 km (MERRA-2). Therefore one would not really expect to see any turbulence in the model either at the scale of your study area, so would only see a smooth version with topography superimposed.
You will want to see that the uncertainties decrease (vs option).
Some of the interferograms have a strong signal.
One option would be to leave them out of the inversion and see if this makes a difference too.
The ionosphere is typically a longer-wavelength signal.
It has appeared in S1 for longer swath processing, or when having issues in aligning a stack in the burst overlap regions.
I would not expect it to have an impact over your study area.
I am not sure if the filtering 's' step in stamps is actually removing the APS estimates first and then doing the filtering.
Best to verify that. If this is not the case then atmosphere might be removed twice.
Note that 's' will smooth and clean the time-series as it it filters in time.
Thanks for the tip on MERRA2: A fix is included in the git version of TRAIN.