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

Hi,

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

literature.

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

## Comments

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.

Best

Rafael

[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.

https://doi.org/10.1016/j.envsci.2015.08.012

[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. https://doi.org/10.1029/2008WR007474