Typical values for r and k factors? r's seem too high.

I'm working with the sediment delivery ratio model in the Orinoquia region of Colombia and am looking for the right r factor layer to use. There are quite a few of these that have been generated, but they have very different values. For instance, we have data from:

1. A TNC-led InVEST study in Colombia in 2011 (http://www.unep.org/pdf/IWR_2012.pdf); r factor ranges from 0-92 with 250 m spatial resolution. I'd feel confident using this but Table 5 of the Foster et al. 1981 reference below suggests that SI r-factors should go as high as 8000, while metric k factors should range from 0-0.06. Both the r and k factors are much more in line with what we expect from English unit r and k values, according to Foster (further, most k factor datasets I've seen range from e.g., 0-0.5 - more in line with what Foster et al. suggest are typical English system values). It of course seems inconceivable that English system units were mistakenly used in this study, so are Foster et al.'s guidelines incorrect and are those lower r factors and higher k factors credible?

2. We also have global r factor data at coarser resolution from Yang et al. 2003 (http://www.hydroyang.com/sites/default/files/hpv17-2.pdf) at 0.5 degree resolution and r-factor values as high as 42,500, and a more recent study from Naipal et al. 2015 (http://pubman.mpdl.mpg.de/pubman/item/escidoc:2213606/component/escidoc:2213605/gmd-8-2893-2015.pdf) at 10 km resolution and r-factor values as high as 242,000. These values are obviously orders of magnitude greater than either the TNC study or Foster et al.'s guidelines. I assume this is part of the reason why RUSLE overestimates erosion in mountainous areas, but are such large values credible?

I'd greatly appreciate any recommendations on what credible SI-unit r and k factor values should be when using the RUSLE/SDR models, to help guide selection of which dataset to use in our study.


Reference: Foster, GR, et al. 1981. Conversion of the universal soil loss equaiton to SI metric units. Journal of Soil and Water Conservation 36(6):355-359.

835 x 354 - 45K


  • PerrinePerrine Moderator, NatCap Staff
    Hi Ken, 

    There's often some confusion around the erosivity R values. As you point out, two systems of units are typically used. As long as you are sticking to the same system for R and K, it does not affect the results (except that if you use the US customary units, soil loss A will be expressed in ton/acre instead of ton/ha.) 

    To answer your questions:
    1) I couldn't find the technical details in the report you linked, but the values you cite suggest that they've used US customary units. The values in Foster's table are in line with what I see in the literature, i.e. R is typically between 200 and 10,000 MJ.mm /(ha.h.y); and K doesn't go beyond 0.06 t.ha.h/ (ha.MJ.mm)

    2) The other pair of values (42,000 and 240,000) seem VERY high/ impossible. I think there's a problem with units or something else. Two things to note: 
    - the values shouldn't vary too much with raster resolution since they represent normalized values (the spatial variability will be somehow attenuated with coarser resolution but not show a dramatic increase).
    - the issue with applying USLE in mountainous area is in my view broader than an problem with erosivity. Erosivity has a straightforward definition (a function of the rain intensity over 30min interval) and is a function of precipitation patterns only. The empirical equation A=R*K*LS*CP tends to break down for higher slopes but it's due to a combination of all the factors (and in particular the LS factor that can take very high values on high slopes).

    So basically, the values from the TNC study seem ok if they are in US customary units, and otherwise you can get other estimates with precipitation time series (but takes some pre-processing) or the empirical equations with annual or monthly precipitation we have in the User's guide.



  • Thanks Perrine - it's extremely helpful to have my suspicions confirmed. I'll use the TNC values and also be in touch with Naipal et al. to better understand their values. If I hear anything back I'll repost here so others can use that information.

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