# Sigma Nought Uncertainty S1-GDRH

Hi everyone. I’m a physicist, and I’m currently working on S1 data to study soil moisture over bare agricultural soils. My question is: how much uncertainty do I have on my backscattering coefficient (sigma nought)? How much the processing of the data affects the natural uncertainty of the initial digital number? What is the uncertainty on the calibration constant?

I worked on GDR-H images from S1, and this is the processing algorithm I used to retrieve the backscattering values:
definitivo_singolo_subset_thermal_inizio_nocsv_source-target.xml (5.7 KB)
Notes: I didn’t make this from scratch, I used the GraphBuilder in SNAP. The subset node is necessary because of memory usage issues.

It is unclear to me how much the initial DN is affected by such a processing, and what is its initial uncertainty. I really just need to know if it falls on the 5-10% or 0.1-1% side, and which are the ways to calculate it.

I would be very glad to start a conversation about this topic, given that I found no mention of uncertainties on any paper I’ve read so far. Is there a specific paper from the official documentation that could help me?

Thank you very much.

P.S. Any comment or suggestion on the way I am processing the data is highly appreciated.

The answer depends on at what level you want to look at the subject. One part is coming from the target itself and the deterministic (but random) speckle noise, which can be mitigated by filtering, and the second part depends on the instrument calibration, the scene properties etc.

Thank you very much. I was looking for a way to address the uncertainty introduced by the instrument calibration and processing of the images. I am studying a 15x15 pixel area by its mean backscattering coefficient, therefore I am using standard deviation (st.dev.) for the “statistical” part of the uncertainty. St.dev. is roughly 30-40% of the mean value in most of the data I am using, and I wondered if the “instrument” uncertainty was about 10% (not negligible with respect to st.dev.) or 1% (negligible).

Then you should look for reports on S-1 radiometric calibration, as it is an empirical measure on the stability of the instrument. Are you sure that your 15x15 pixel area is really homogeneous in the sense that the underlying backscattering-coefficient (without spekcle) should be the same for each pixel? You probably want to allocate some part of the observed st.dev for inhomogenities of the target, as few natural things are completely homogeneous.

edit: here is one relevant doc: https://sentinel.esa.int/documents/247904/685163/S1-Radiometric-Calibration-V1.0.pdf

Thanks a lot. I followed that same document for the radiometric calibration, to understand the maths involved, even though I let SNAP do all the work. Should I look for the error associated with the calibration costants (the values in the LUTs)? Or maybe I could use the measurements reported on the Cyclic Reports to get an accurate uncertainty?
I am referring to, for example: https://sentinel.esa.int/documents/247904/4074738/Sentinel-1B-N-Cyclic-Performance-Report-01-2020.pdf
There I found an average error associated with the measurements of the relative radar cross section of the corner reflectors. But what is the “relative” RCS? Relative to the maximum value? If I have something as (x+dx) dB for a certain swath and a certain angle, should I consider the error (±dx) an average error for measurement taken in the same swath and angle?

Regarding the area, it is mostly homogeneous. It covers small agricultural fields with no vegetation and no irrigation, but the tillage practices and probably the soil texture differ from field to field so I’m aware of roughness inhomogenities. I tried to apply a Lee Sigma once on a set of data, but i didn’t check the effect on st.dev. (it wasn’t my biggest concern at the time): should it improve it? I never wanted to use it because I couldn’t estimate its effect on the spatial resolution.
You’re right, I should put part of the blame on natural variations of the surface: is there any method to do it quantitatively, to try to reduce the st.dev. itself? I’ve read papers that use both S1 and S2 data to account for vegetation or anthropic features, but at the level of the study I am working on, it is a little too much. Maybe masking the high-reflectance parts with a threshold mask? As an example, there’s an electricity pole that falls in the study area (other than that there are no buildings or roads).

Thank you very much again for your time.