Clarifying definition of NDR terms

[emlys]

There's been recent discussion about making enhancements to NDR, and I think there is some confusing terminology that would be helpful to clear up first.

First I'd like to make a better distinction between the $\text{eff}$ and $\text{eff}'$ terms. Having both “efficiency” and “effective” shortened to “eff” creates some confusion, and implies a similarity between the terms that I don’t think is accurate. I'd suggest we come up with a different variable and definition for one or both of them.

$\text{eff}_i$

also known as

• $\text{eff}_{LULC_i}$ in the user's guide
• eff_n and eff_p, retention_eff_lulc_path, and retention_efficiency_path in the code
• eff_n.tif and eff_p.tif in the model results
• "the maximum retention value that LULC types along the flow path can provide" NOTE I think we should avoid saying "value", this is a ratio.
• "the maximum retention efficiency that LULC type i can reach"

The model calculates this by simply mapping the eff_n and eff_p values from the biophysical table onto the LULC raster.

$\text{eff}'_{i}$

• $\text{eff}'_{down_i}$ is the same thing, just on the downslope pixel from i
• effective_retention_path, retention_path in the code
• effective_retention_n.tif and effective_retention_p.tif in the model results
• "the maximum retention efficiency of the land between a pixel and the stream"
• "the effective downslope retention"

The model calculates this recursively upslope using $\text{eff}_i$, $\text{eff}'_i$ of downslope pixels, and the "step factor" $s_i$.

[emlys]

I think that in phrasing "effective downslope retention", the word "effective" is not adding anything useful, and we could choose different terminology that is not so easily confused with "efficiency".

[emlys]

Maybe "cumulative downslope retention" to capture the idea that it's accumulated across the slope?

[phawthorne]

I think "retention fraction" is more clear than "efficiency". So we could have "downslope retention fraction" and "LULC max retention fraction". I like adding "fraction" to clarify your point that this is a ratio, not a physical unit.

[emlys]

I like "LULC max retention fraction". What would be suitable variables to use for these in the math, maybe $f$ and $g$? For translating the user's guide into other languages, it's clearer if we can use single-letter variable names and avoid shortened English words.

[emlys]

Additionally we should clarify the meaning and purpose of the "step factor" $s_i$. All the users guide has to say is:

$$ s_i=\exp\left(\frac{-5 \ell_{i_{down}}}{\ell_{LULC_i}}\right) $$

where

• $\ell_{i_{down}}$ is the length of the flow path from pixel to its downslope neighbor. This is the euclidean distance between the centroids of the two pixels.
• $\ell_{LULC_i}$ is the LULC retention length (“Critical Length”) of the landcover type on pixel i

"the factor 5 is based on the assumption that maximum efficiency is reached when 99% of its value is reached (assumption due to the exponential form of the efficiency function, which implies that the maximum value cannot be reached with a finite flow path length)."

In the Gura sample data, the critical length is 150m for all LULC types, and pixel size is 15m. So $s_i = exp(-0.5) = 0.6$ for adjacent pixels and $exp(-0.5\sqrt{2}) = 0.49$ for diagonal pixels.

From the conversation on Monday, I got the impression that the purpose of this factor was to solve an issue in the older nutrient model where retention would compound and approach 100% too quickly - is that correct? Can we develop a clear statement of what $s_i$ represents and what purpose it serves?