... Email conversation with DMS
From what I can see once we correct the errors in Robins spreadsheet (divide % by 100) there is not a lot of difference in not taking the sin of the slope which agrees with some old hacking I did when I could understand this stuff.
But for correctness we should all use the RUSLE method including sin(slope).
Thanks for bringing it up, Mel. For reference, Peter, we’re looking at the erosion.for code for this, maybe that is outdated?
I’ve gone back to the original Wischmeier & Smith document and have worked through their ‘table 3’ (attached as PDF), and that would indicate to me that ‘slope angle’, or ‘s’ in the calcs below, should be in radians.
Have a gander at the attached spreadsheet. Cols C, D & E replicate TABLE 3 from Wischmeier & smith, using radians (and Sine). Columns F & G then do what the PERFECT manual uses for the METRIC versions, and things line up reasonably well. Column H shows what I really hope APSIM isn’t doing – using % slope without converting to radians nor having the SINE applied. The resulting LS factors would appear to get out of hand rapidly as slope increases.
Very happy to find out that we’re just interpreting this incorrectly though!
We have a quick question for you from the apsim erosion module…
When we run apsim all our simulations are done on a single slope and single K factor. And then Rob does an adjustment when he takes the results into the catchment scale model for the slope/K factor that a DEM/soilmap says was actually there.
We just had a look at the equations using slope and were wondering if you could tell us what the parameter ‘pcnt2fract’ is (used in eqns as below)?
Does it really just convert the percent slope input to a fraction or is there more to it, like taking sine of the slope angle?
! Calculate USLE LS factor
s = p%slope * pcnt2fract
a = 0.6 * (1.0 - exp (-35.835 * s))
p%ls_factor = ((p%slope_length / 22.1) ** a)
: * (65.41*s*s + 4.56*s + 0.065)