Interpreting the n_load parameter

Science, Research & Data
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Hi Stacie et al.,
I’d like to follow up on this thread by better understanding how nutrient loads for a given pixel are calculated. From my understanding of the documentation and the above discussion,

  1. the load for a given land use type can be calculated from the sum of the inputs (say, fert + manure + deposition).
  2. The modified load to a given pixel is the load x RPI to account for higher transport potential with higher precipitation (eq. 42 in the on-line documentation).
  3. NDR then estimates how much of that modified load reaches the stream by calculating the retention efficiency of that pixel and all downslope pixels on the flowpath to the stream. NDRo,i = 1 - eff’i (eq. 47). The NDRo,i is then modified by Borselli’s k and the topographic index IC, to account for hydrological connectivity, to get the NDRi for a given pixel (eq. 46.
  4. So, a given pixel’s export to the stream = LOADi x NDRi (Equation in Fig. 5).

What I’ve had difficulty understanding is that I don’t see anywhere that the LOADi to a given pixel is augmented by nutrients carried to it from upslope pixels. That is, say you have a forest pixel that is part of a riparian buffer, with an eff_N of 0.8, and a LOAD of 5 kg N/ha/yr from deposition. NDR would estimate that pixel’s export to be 5 * (1-0.8) = 1 kg N/ha/yr (for simplicity, here I’m not accounting for conversions of pixel sizes to ha, IC, k, and critical lengths longer than a pixel size, etc.). But say that forest buffer pixel has a crop pixel just upslope of it. The crop pixel has a LOAD of 100 kg N/ha/yr and eff_N = 0.5.

  1. NDR calculates the N export of the crop pixel as 100 (1 - eff_Nforest) = 20 kg N/ha/yr (from eq. 48, where the eff,down,i > eff,i), and the export from the forest pixel as 1 kg N/ha/yr, for a total of 21 kg N/ha/yr.

  2. But with the cropland only retaining 50% of the applied N, that means that 50 kg N/ha/yr are leaving the crop pixel and going to the forest pixel (assuming that all the N leaves in runoff and none in gaseous form). So, the true load to the forest pixel is 50 from runoff + 5 from deposition = 55 kg N/ha/yr. Assuming, as NDR does, that the forest pixel has a constant eff_N no matter how much N comes in (more on that later), export = 55 * (1 - 0.8) = 11 kg N/ha/yr. So, of the N load to the crop pixel, the total making it to the stream is LOADcrop*(1-EFFcrop)*(1-EFFforest) = 100 * 0.5 * 0.2 = 10 kg N/ha/yr, rather than 20.

  3. And, if we want to know the ecosystem service of N retention by the forest buffer, NDR tells us that the buffer has just absorbed 4 kg N/ha/yr [LOADforest * (1 - EFFforest)], but really it has absorbed 44 kg N/ha/yr.

  4. This gets more complicated if one assumes multiple crop pixels upslope of the single pixel of forest buffer. In that case, the first crop pixel would retain 50 kg N/ha/yr and export 50 to the downslope crop pixel, which would now have a load of 150 kg N/ha/yr, of which it would retain 75 and pass on 75 to the forest, whose load now becomes 80, of which it would retain 64 and pass on 16 to the stream. But NDR would calculate the exported N as 100 * (1 - 0.8) from the first crop pixel + 100*(1-0.8) from the second crop pixel + 5 * (1 - 0.8) from the forest pixel = 41 kg N/ha/yr, with the forest still only retaining 4, rather than 64.

  5. These discrepancies are important for our application, since we’re trying to estimate the ecosystem service provided by the forest buffer and test different buffer scenarios. Can we just not use NDR for this application?
    a. It has led to some counter-intuitive results, as @atershy pointed out in a recent post. We added more forested riparian buffer to predominantly agricultural watersheds, but ended up with less total N retention by forested buffers.
    b. How could this be - even with NDR’s formulation? More land area of forest should lead to more total N retention by forest, no matter what, correct?

  6. As an aside, it seems contrary to the idea of N saturation to allow a forest or cropland to have a constant eff_N, no matter what the load to it is. So, we’re trying to figure out if there is a way to decrement eff_N for a pixel if LOADi for that pixel exceeds a certain threshold (e.g., whatever the maximum absolute retention capacity of that LULC type is, in kg N/ha/yr). But maybe this can’t work in NDR, if NDR never augments loads to a pixel based on upslope runoff. Thoughts?

Sorry for the long post! Just trying to work through the nuts and bolts to better interpret our results and make sure the model is capable of doing what we’re asking of it.
Thanks,
Dave

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