Sorry in advance for the long post, but I’m trying to understand the basics of how the NDR model calculates nutrient loss from a given pixel to the river. I’ve been looking at the user guide but I’m struggling a bit to make sense of the equations.
Say I use the conceptual figure in the NDR manual as basis (Fig 6) and I want to estimate the nutrient load that reaches the river from the pixel marked in red. In this figure, five downstream pixels (marked in blue) are separating the red pixel from the river. The upstream contributing area to the red pixel consists of 36 pixels (green pixels).
For simplicity, we can assume no leaching to the subsurface (p=0), that all cells have the same land use (and therefore the same load and retention), that the flow path from the red cell to the river is straight (meaning the distance from the red cell to the river is 5 x pixel length) and that the slope of the downstream pixels is constant.
Can I based on this calculate the NDR for the red pixel? I’ve tried to do some simple calculations below:
Pixel size: dx=50 m
Mean upstream slope: Sup=0.05 m/m
Downstream slope: Sdn=0.1 m/m
Upstream area: Aup=90000 m2
Distance to stream: dist=300 m
Effective (max) retention: E=0.48
Dup = Sup*sqrt(Aup) = 15
Ddn = dist/Sdn = 3000
IC = log(Dup/Ddn) = -2.30
NDR = (1-E)/(1+exp((IC0-IC)/k))
(note: I think there is an error in Eq 34 in the user guide; I think IC and IC0 should be swapped around?). NDR is quite dependent on the calibration parameters IC0 and k. If I set IC0= -1 and k=1, I get NDR=0.11
Am I getting this right? In the above, I have assumed the effective retention for the red pixel is the equal to the maximum. I’m not sure I quite understand how the effective retention is calculated using the step factor (Eq 37). I think the step factor is supposed to depend on a “critical length” but I find it unclear where it fits in in Eq 37.
Any help appreciated.