Hi @marye_belete, and welcome to the forum!
Looking at the paper, the caption for Figure 4 says this: “Correlation between observed and modeled (uncalibrated) exports and specific exports (i.e. standardized by catchment area).” And the units for sediment export are Mtons/year, while the units for specific export are tons/year/km2. So it appears that they took the sediment export model results, summed by catchment, and divided by catchment area. This is done in post-processing, the model does not do this.
sdr_factor is the sediment delivery ratio calculated by equation 6 in the User Guide based on the land cover map you provide as input. sdr_bare_soil is the ratio calculated for a hypothetical landscape that has been turned to bare soil. The model takes the difference in sediment between these to create an index of retention, as described here. The paper also says this: “For quantitative
assessment of the service, the model uses a hypothetical scenario as a benchmark, where all land is cleared to bare soil: the value of the retention service is calculated as the difference between the sediment export from this bare soil catchment and that of the scenario of interest.”
One thing to note is that this paper uses a somewhat older version of the SDR model. The current version is very similar, but now also includes a sediment deposition output, which provides a quantitative value for sediment deposition, along with the index of retention described in the paper.