LS factor in Sediment Retention Model


I'm using the Sediment Retention Model of InVEST 2 and I have a question about the LS factor in USLE equation: The user's guide describes two equations which are choosen according to Slope Threshold parameter. For slopes lower then the threshold, the 1st equation is used and for higher slopes, the second equation is used.

I've made a sensibility analysis with Slope Threshold = 0 and = 1000, so that InVEST would use only equation 1 and 2, respectively. But results are so different. With equation 1, LS is more than 15 times greater than LS calculated by equation 2 (see attached file). 

So my question is, which equation is advisible to use? I believe mixing both equations would not be a good idea as that will be a a sharp fall in LS for slopes greater than Slope Threshold.
822 x 674 - 135K


  • RichRich Administrator, NatCap Staff
    Hi Sandrasaad, 

    A while back we made major core updates to sedimentation model an packaged them in a new model called the Sediment Delivery Ratio model (SDR).  SDR captures the hydrological connectivity of the landscape better than the old sediment model, does away with the slope threshold entirely, and has a host of other changes.  Here's the guide if you want to read about it:

    And here is the latest InVEST installer if you want to try it out:

  • PerrinePerrine Moderator, NatCap Staff
    Hi Sandrasaad, 

    One last point to add to Rich's response: in the new (SDR) version of the model, LS is still an intermediate model output. However, we have removed the idea of a slope threshold since there was only scarce literature to provide guidance on this parameter. 

    If you find local studies that give an estimate of the soil loss (R*K*LS) for the high slope areas, you can use these values in post-processing. You would do that by adjusting all the USLE values to the appropriate amount (e.g. capping all the values with the max value provided by the study).

  • Hi Rich and Perrine,

    I've noticed that all this improovement were made in SDR model, but I'm afraid I'll not be able to used it now since I've been working a long time with the older version and I just have a few months to end my reaserch (of my PhD thesis in University of Sao Paulo, in Brazil). Maybe in another oportunity!

    I'm aware that I can adjust the other terms of USLE in order to compensate very hight or very low values of LS. And that's what I'll do in case I have no other options.

    Other option I've been thinking of was to apply SDR formulation of LS in InVEST 2, in case it is compatible. Do you think it is a good idea? I know python and I've seen InVEST2 code, and I thing I can try, if I see the part of SDR code wich calculates LS. 

    Thanks, Sandra

  • PerrinePerrine Moderator, NatCap Staff
    Hi Sandra

    Changing the LS formulation in InVEST 2.0 is certainly an option. This means that you'd be using the revised expression of the LS factor (better suited to GIS) proposed by Desmet and Govers (1996).

    The fact that you find very different results for the slope thresholds of 1 and 1000 is not surprising. The alternative equation for high slopes is supposed to be used for... high slopes! and shouldn't be applied to the whole landscape (i.e. threshold =0). If you use this version of the code, I'd recommend using the original equation for all slopes (threshold=1000), thereby ignoring the (potential) overestimation for high slopes.

    To clarify the differences between InVEST v2 and InVEST v3, here is a short summary:

    * the LS formulation changed, from the original expression (Renard et al. 1997) to the GIS expression proposed by Desmet and Govers (1996)
    * the alternative LS equation for high slopes was removed
    * the slope-length was capped (max 333m)
    * a new routing was introduced (this is the "SDR" model in v3.1 and later, vs. what used to be called "sediment retention" model in v2)

    I hope this helps.
    Good luck with your thesis!


    Renard, K., Foster, G., Weesies, G., McCool, D., & Yoder, D. (1997). Predicting Soil Erosion by Water: A Guide to Conservation Planning with the revised soil loss equation (p. 404). doi:Agriculture Handbook No. 703
    Desmet, P. J. J., & Govers, G. (1996). A GIS procedure for automatically calculating the USLE LS factor on topographically complex landscape units. Journal of Soil, 51(5), 427–433.

  • Hi Perrine,

    I was wondering if you could send me SDR code (, or at list part of it (LS calculation). That's the only chance I have to suceed in employing it in InVEST v2, as I have not much time. And in case I succeed, I could send the code back to you as a contribution, if you are interested.

    However, if you thing the code would not be compatible, or that would be any problem, don't worry because your commentaries has already been very helpfull!


  • RichRich Administrator, NatCap Staff
    Hi Sandra,

    The code for the sdr LS calculation can be found in the calculate_ls_factor function on line 475 on this file:

    Good luck!
  • That's nice! I didn'd now this website.

    Thank you Rich!

    best, Sandra
  • Hello Perrine and Rich,

    I'm writting to give you a feed-back about this discution. The easiest way for me to employ LS equation from Invest version 3 into version 2, was to run version 3 and use its LS output as an input for version 2. I made just a few adjustments in the code and I succeded.

    However, I was surpresed to notice that the mean LS in the basin was even lower than the calculated by the 2nd eq. of version 2 (the one for higher slopes). Moreover, I ploted LS as function of slope (attached file) and I saw that LS doesn't increase with slope, differently of what I had expected (and of InVEST 2 results). 

    I'm checking if I hadn't commited any mistake. Please let me now if you have a clue, or if you had checked this issue.

    1753 x 945 - 353K
  • PerrinePerrine Moderator, NatCap Staff
    Hi Sandra, 

    Thanks for this feedback. 

    The lower LS values that you get for high slopes may be due to the slope length factor. Remember that LS is a product, and the slope length factor (the "S" of the equation - see details in the user's guide here) has very low values in the high slope areas. This can compensate the high slope steepness factors 

    FYI, I have similar results with several DEMs I've worked with. How much of this is a model artifact, I"m not sure. We are using here the popular formulation from Desmet and Govers (see user's guide).

    About your first comment: I'm not sure how you us LS as an input for InVEST v2. Do you mean you pasted that section in the code?


  • Hi Perrine,

    About the decrease of LS with the increase of slope: That's truth, the slope length factor is what certainly explains the graph pattern! Interestingly in the other two equations LS is more sensitive to slope, at least in my case.

    About your question, actually I runned InVEST3 with similar conditions that I was using in v2, wich generated this file: "prepared_data\ls.tif". Secondly, I edited v2 code, adding one more parameter: the LS, and I used this ls file as an input data. And then, I edited the code to start using this given LS instead of calculating it. I attached the script in case you are interested to see. I put my name in the modified parts.

    best, Sandra
Sign In or Register to comment.