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
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,