SDR sensitivity analysis -- unexpected result for C factor

This question is probably best suited for Perrine Hamel, my favorite NatCap hydrologist -- 

I've completed a "One at a Time" sensitivity analysis of the various SDR input parameters for the total export values and the results turned out as expected with the exception of the C factor. 

Note: the DEM and advanced calibration constants, ICo and Kb, were not included in the analysis.

I quickly noticed that adjusting the K, P, and R inputs would produce linear increases and decreases, which is logical and kind of a "no duh" given the equation for the USLE component of the total export.

Upon first glance, it appeared that the C factor simply resulted in a near-linear results (e.g. +15% C = +20% export, or -15% C = -20% export). I figured this was a function of the C factor and its role in the IC value and eventually the SDR component.

However, when the watershed results were aggregated by sub-basins I found that a 15% decrease in C led to a few non-linear outcomes.

The sub-basins are 7 unequal sized reservoir catchments along the river course within the larger study basin. The model used 92 total HUC12 catchments as the watershed input, and the sub-basins ranged from 2 to about 50 HUCs. So vastly different sub-basin catchment areas.

Out of the 16 C factor sensitivity results (+/- and including the full basin) 12 of them had the nearly-linear +/- 20% outcome, with only 4 of the sub-basins producing non-linear results. Also, all of the non-linear results were from a 15% decrease in C. Specifically they were -4%, -16%, -35%, and -44%. All of the other outcomes, both for the increase and decrease of C, were between 20 and 22%.

I double checked the inputs for the sensitivity runs and even inspected the SDR intermediate raster output and didn't see anything that would explain the 4 non-linear results. At least nothing that jumped out to me. I even inspected the C factor summary stats for each sub-basin for clues and correlations but I didn't find anything that might explain these results.

Ultimately, my question is: are my C factor sensitivity results out of the ordinary? Is there something in the full SDR model function that would explain them? Or is it just a coincidence that 12 of the 16 C factor sensitivity results fall into that near-linear range?

I've attached a spreadsheet of all the sensitivity results needed to follow the content of this thread including the baseline scenario and the +/- C factor outcomes.

Many thanks to Perrine or whoever else can provide some feedback!
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Comments

  • PerrinePerrine Moderator, NatCap Staff
    Hi SPardo, 

    Thanks for sharing these analyses!

    In our work in a different watershed (Cape Fear, NC) we also found a difference in sensitivity to the C factor between subwatersheds. If you haven't checked it out yet, you'll find further details in the article presenting these analyses (Hamel et al. 2015, see ref. below)

    In Fig. 5 of this paper, you'll see that a change from 0.15 to 0.10 in the C factor had a distinct effect for different subwatersheds.
    Also, in Section 5.2, we discuss the results of the sensitivity analysis. These results may differ if you've changed the C factors homogeneously (i.e. the same % change for all LULC types, or if you've changed them one at a time).

    Two related points that can explain these results:

    - the % LULC in each subwatershed: e.g. if you have changed the C factor for Forests, and your subwatershed only comprises <10% of forest, the effect may be smaller;
    - the range of values for the index of connectivity (IC): in Figure 3 of the User's guide you'll see that the function relating IC and SDR, for each pixel, is highly non linear, which may explain why a change in IC (resulting from a change in C values) may have a different effect for different subwatersheds.

    I hope this helps with your results interpretation.
    Feel free to share your work on this forum if it's publicly available!

    Best,

    Perrine


  • SPardoSPardo Member
    Perrine,

    Those are excellent theories and sincerely appreciate the feedback. 

    Alas, I have wasted everyone's time because the real issue was that my sub-basins were incorrectly copied/pasted for the non-linear results. It was just a coincidence that 3 of the sub-basins still resulted in - 20%. When that was fixed all of the sub-basin results were +/- 20%. 

    I failed to mention above that calibrating (and therefore investigating) absolute results was beyond the scope of this project so only relative changes in watershed ranks are considered significant.

    As such the only parameter that produced non-linear results amongst individual watersheds was the flow accumulation threshold. In fact, results varied  in unpredictable and, in some cases, even counterintuitive ways. Consequently, my final results are reported with a low (200) and high (700) scenario for flow acc with a baseline of 500.

    ... apparently my flawed table never attached from the first post. Sorry about that. I'm almost positive I uploaded it. I must not have done something correctly or in the right order.

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