Model sensitivity and selecting parameter space

[gismat]

My workflow for model sensitivity analysis follows your excellent guide.

I am testing sensitivity to k_param, ic0_param, sdr_max, and l_max. To do this, I am interating the script over (one at a time)
[0.12,0.25,0.5,0.75,1,5,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,30,40,50,100]

My question is: what is the range I ought to be testing - here, for all 4 parameters I am testing over the parameter space: 0.12 - 100, which might be excessive (and I have done it, and it seems excessive).

As an example, for k_param, the guide encourages start at 2, and alter by 10% (I assume 0.2) per run to analyse sensitivity to k_param. In my set I have gone to 100 but it makes me wonder: what are the theoretical bounds for the 4 parameters (k_param, ic0_param, sdr_max, and l_max).

[jesseG]

Hi @gismat,

Thanks for writing in with your question. I’m not a hydrologist, but I’ll share my perspective here on recommended ranges. I do not claim to know the theoretical bounds for all but one of these four parameters.

I recommend referring to Hamel 2015 et al. (referenced in the InVEST User Guide). In addition to providing good guidance on how to perform sensitivity analysis on the InVEST SDR model, at the bottom of Table 1 there, you will see they claim to have varied k from 1 to 3 and IC0 from 0.25 to 0.75. These values should always remain low. However, to be safe, I’d recommend going with the values revealed in their Figure 5:

• k between 0.5 and 3.0,
• IC0 between 0.1 and 0.8,
• SDRmax between 0 and 1.0, and with my addition of
• Lmax bewteen 122 and 333.

Valid values for SDRmax are clamped between 0 and 1, since it’s a ratio, so certainly do not go above 1 for that parameter. Please also note that the model responds proportionally to a change in SDRmax, so it’s likely not worth analyzing that parameter.

Lmax is the parameter I’m least certain about, so it’s possible you would want to test outside the range I recommended, but those values should almost certainly all be > ~100.

I hope this helps,
Jesse

Jesse Goldstein
GIS Analyst
Natural Capital Project, Stanford University

[RafaSchmitt]

Hi @gismat I commend your approach for an in-depth sensitivity analysis. To echo what Jesse wrote below, you need to be careful about the meaning of the parameters. E.g., SDR_max is by definition from 0-1, so sampling from 0.12-100 does not make sense. You should sample this parameter between 0 and 1.
Similarly, l_max is usually set at either 122m or 333m, and this range is pretty deeply engrained in the original formulation of the USLE model. So setting it to values far outside of it will likely yield non-sensical results (very low or very very high erosion rates). For you likely very low as all values you use are below the recommended lower limit of 122m.
I’d suggest reviewing some literature for each parameter in order to find a good lower and upper bound (e.g., 0-1 for SDR max, 122 - 333 for lmax) and then sampling 10 values (x values) within that range.