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SDR - extreme values of RKLS for steep, high rainfall areas


I wondered if anyone on the InVEST team has any thoughts on the
extreme values for the model's RUSLE results that can be encountered in steep,
high rainfall areas, for example from their experiences in Central or South
America, Myanmar or China? I haven't found (but may have missed) a discussion
of these extremes or their impacts on overall watershed sediment yields, and
any thoughts would be greatly appreciated.

The LS factor varies over a huge range for the landscape I am
working on (plains and extremely steep and dissected mountain ranges of East
Kalimantan), from 0 to 5320. (Based on a 30 m SRTM DEM)

When LS factors of up to 5320 are combined with rainfall
erosivities in the range 6,000 - 17,000, and moderate to highly erodible soils
(k in SI units 0.018 -.045), many of the RKLS values become incredibly high,
far beyond any values for erosion of bare soil I've been able to find in the

For example, 8% of pixels have RKLS values equivalent to more than
20,000 tonnes per hectare per year, with a maximum of 2,721,000 t ha-1 yr-1
(i.e. when converted from values per pixel to per hectare for comparison),
whereas the highest literature values I've found for bare soils on steep plots
in the tropics have maxima of 3,000 to 10,000 t ha-1 yr-1.

The input values for R and LS are far beyond the ranges used for
development of RUSLE, and the multiplicative structure of the equation leads
naturally to extreme values.

Given the approximately log-normal distribution of values, one
option is to log-linearly rescale the resulting RKLS values to a plausible range
(e.g. max 4,000 t ha-1 yr-1, where the log-linear scaling means that only the
extremely high values are altered by a large amount), then multiply the
back-transformed rescaled RKLS values by (untransformed) C and P values to give
a new usle.tif, then multiply by SDR to give a revised sediment export map.

If I do this, then the resulting watershed sediment export totals
are surprisingly close to the few observations of sediment yield that I have
for two of the major river basins within the study area (when calibrated with
Borselli's kb = 1.8). The rescaling therefore seems to preserve RUSLE's
estimates of erosion potential over most of the landscape, while moderating the
extreme values, and the SDR seems to translate this well into sediment export
to streams.

If I don't perform any rescaling, then the highest 2% of pixels
(with RKLS and export values several orders of magnitude larger than the
majority of pixels) completely dominate the watershed totals, and the export
totals are far beyond the observed sediment loads, even for very low values of
Borselli's k parameter, e.g. 1.2, lower than the calibrated values for any of
the studies in Hamel et al. (2017 Sci. Tot. Env. 580: 1381-1388) which were in
the range 1.8 to 3.5. 

Does this sound like a reasonable approach to take? It was the
only one I could think of that would conserve the shape of the distribution of
potential erosion values while reducing the disproportionate impact of extreme
values, but perhaps there are theoretical justifications for accepting extreme
values of RKLS that mean rescaling is not advised?

On a related technical question, the User Guide states below
Equation 2 for the length slope factor:

"To avoid overestimation of the LS factor in heterogeneous
landscapes, long slope lengths are capped to a value of 333m (Desmet and
Govers, 1996; Renard et al., 1997)"

 Could you please explain how this affects the values entered into
Equation 2 ?
- I think it means the values of Ai-in (upslope contributing
areas) are capped at a maximum flow path distance of 333 m, but I'm not sure.

Thanks very much for your time,

- Jessie


  • RichRich Administrator, NatCap Staff
    Hi Jessie, I can comment on your very last question.  The "overestimation of LS factor" cap at 333m affects only the "L" part of the "LS" equation. In the case of Eq. 2 in the user's guide, that's the fraction to the right of S_i.  It doesn't otherwise affect the slope. You can see how the increasing slope will then approximately linearly increase the USLE factor in that case since it essentially becomes a function of sin(theta) (the part described right under Eq. 2).

    I am not a hydrologist, but your log-linear rescale sound brilliant. To the point if I wonder if we should be using that as our LS factor directly. I'll see if I can get one of our 3 hydrologists to comment. More soon!

  • Thanks very much Rich.

    I'm currently working through a few different options for log-linear rescaling the upper ranges of LS factor, R factor, and/or the product RKLS, based on possible alternative min and max values for rescaling (based on the datasets used for RUSLE's development, and everything I can find on upper plausible limits to potential erosion).
    - so I'll let you know how that goes in the next few days.

    One extra, and possibly daft, question:
    When calculating SDR, the equations incorporate C factor values for upslope and downslope cells, but not the P factor.
    Would the P factor values (support practices to reduce erosion e.g. terracing) also influence sediment connectivity? 

    - Jessie
  • RafaelRafael Member, NatCap Staff

    Dear Jessie,

    Thank you for starting that very relevant discussion. As you point
    out, it is not astonishing that RUSLE results in extreme values if applied to
    conditions that are far out of the range for which the equation was originally developed.

    Regarding the physical justification of very high erosion values
    and the appropriateness of your approach: 
    in such a diverse landscape, a wide spread of erosion values can be
    expected with a small part of the landscape producing most of the basin’s
    sediment budget. Hence, the statistical distribution of sediment yields are
    commonly right skewed [1]. However, the maximum magnitude of values needs to be credible,
    which is not the case for the values that the model produces for your case study. For example, converting 20,000
    t/ha/yr into length units (assuming a sediment density of 1.5 t/m3) would result
    in several meters of soil eroded per year. Even if instantaneous erosion rates
    of few decimeters to meters per year might occur after a massive disturbance of
    a landscape or via mass wasting, such erosion rates over longer time-spans
    (years) would quickly deplete the soil layer. Then, erosion rates would
    decrease as more resistant underlying bedrock is exposed. Especially in steep,
    upslope areas where the top soil is likely thin [2].

    The approach you describe for rescaling seems practical but imposes
    some strong assumptions (do you have a reference for the procedure and how and
    in which software did you implement it?). Are you rescaling
     all values, as indicated by your original question, or only values above a threshold? Results are likely very sensitive to the assumed distribution in the rescaling procedure and the upper boundary for
    erosion rates. In a setting with diverse topographic and climatic conditions I
    would expect that the distribution of pixel-scale erosion rates should still be
    strongly skewed even after the rescaling procedure.

    I hope that this can answer some of your points.  We are currently working on case studies in
    the high Himalayas and are running into similar problems. Hence, your
    experiences might be very useful also to implement some ex-post scaling
    procedure in a future version of INVEST. If you are interested, we can discuss
    in more detail looking at some numerical results from your case study.





    [1] Panagos, P.,
    Borrelli, P., Poesen, J., Ballabio, C., Lugato, E., Meusburger, K.,
    Montanarella, L., Alewell, C., 2015.
    The new assessment of soil loss by water erosion in Europe.
    Environmental Science & Policy 54, 438–447.

    [2] Tesfa, T.K., Tarboton, D.G., Chandler, D.G., McNamara, J.P.,
    2009. Modeling soil depth from topographic and land cover attributes. Water
    Resour. Res. 45, W10438.

  • RichRich Administrator, NatCap Staff
    Hi @JessieWells, I see what you mean about the P-factor. I could only guess. And I'm going to guess that the "C" factor in the SDR model is really a proxy for potential for erosion and maybe should use the P factor? In all my work here I haven't seen that we've otherwise used P for anything other than 1.0. So more soon!
  • RafaelRafael Member, NatCap Staff
    Hi Jessie, 

    the P factor might indeed have a great importance for landscape sediment connectivity. The P factor is not integrated in the model yet, because it was not considered in the original paper of Borselli et al. [1]. I can only speculate on why that is, but probably because Borselli et al. worked on a less agriculturally dominated catchment in Europe, a setting in which the impact of the P-factor on sediment yield is rather low (around 3% as average over the continent [2]). 

    However, in a setting where agricultural practices with high impact on sediment routing, e.g., terracing, which can result in a P as low as 0.2, the P factor can be very relevant. Please also note the proposed double effect of terracing by (1) reducing sediment yield, and (2) the slope length - for a discussion see Wischmeier and Smith, (1979), p. 37 [3].

    For now, we are experimenting with implementing the P factor explicitly for our projects in Nepal and Pakistan. 

    Meanwhile, an easy work around would be to multiple your C values with an appropriate value of P and use the Product CxP instead of the original C value. 

    I hope that can be a first hint. How did your re-scaling experiments go? 


    (for the NatCap hydrology team) 

    [1] Borselli, L., Cassi, P., Torri, D., 2008. Prolegomena to sediment and flow connectivity in the landscape: A GIS and field numerical assessment. CATENA 75, 268–277.
    [2] Panagos, P., Borrelli, P., Meusburger, K., van der Zanden, E.H., Poesen, J., Alewell, C., 2015. Modelling the effect of support practices (P-factor) on the reduction of soil erosion by water at European scale. Environmental Science & Policy 51, 23–34.

    [3] Wischmeier, W.H., Smith, D.D., 1978. Predicting rainfall erosion losses - a guide to conservation planning. Predicting rainfall erosion losses - a guide to conservation planning.

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