Crop height effects

[sashahafner]

What is the best approach for adding this effect? What data should be used for parameter estimation.

[sashahafner]

I am working on adding a crop height effect and am thinking of a new approach to do this. @ChHaeni, any feedback would be appreciated.

Currently all predictor variables have multiplicative effects on r1 and r3 (because of transformation). For pH, wind, and broadcast, I think this makes sense.

• pH: fixed pH change means fixed relative change in free NH3 as long as pH is not so high most TAN is NH3.
• Wind: in general correlations for mass transfer coefficients are proportional to Re^n where n < 1 (e.g., 0.5 for laminar). This falls apart if there is a switch from laminar to turbulent but I still think having log(r1) proportional to log(wind speed) is a reasonable and flexible approach.
• Temperature. Relationship between log(Henry's law constant) and temperature is nearly linear (see following comment).
• Broadcast application. Here the emitting area is larger, and emission rate is expected to be proportional to area.

[sashahafner]

But for open slot injection and incorporation, along with crop height (not yet included) we are dealing with resistance elements in series, and something like this makes more sense to me:

r1 = 1/(1/r1a + 1/r1b + 1/r1c . . .)

This is not multiplicative. So for example 20 cm of grass may reduce trailing shoe emission but probably not have much of an effect on injected slurry, since resistance is already so high.

[sashahafner]

Here is Henry's law constant:

from this:

temp.k <- 0:40 + 273.15
kh.NH3<- 10^(-3.51645 -0.0013637*temp.k + 1701.35/temp.k)
plot(log10(kh.NH3) ~ temp.k)

[sashahafner]

If we add this resistance-like approach, what is the best way to fit it into our current approach for specifying secondary parameters? One simple approach (probably confusing to users) is to define a new "pseudo-primary parameter" r5, so that:

r1 = 1 / (1/r1[including effects of e.g., pH, temperature. . .] + 1/r5)

Here r5 = 1 by default and can include effects of crop height etc.

[sashahafner]

But for open slot injection and incorporation, along with crop height (not yet included) we are dealing with resistance elements in series,

Also probably manure dry matter.

[ChHaeni]

Dear Sasha, you spent so much time on the modelling (in total) and have a much better idea on the effects than I have. So forgive me, if I can't provide a better feedback and may have overlooked some things. Here are my thoughts on this. I hope I don't regret posting it on GitHub afterwards...

I find it hard to see through the complexity. Generally, I would tend to make the model not more complex than it already is. From my point of view (based on a rather quick 'thinking about' the issue), it is ok to have the crop height added as multiplicative effect. If I understand it correctly, multiplicative effects reflect some kind of interaction, so e.g. at low temperatures, the effect of a change in wind speed is "smaller" and at high temperatures the effect of a change in wind speed is "higher". This makes sense, because the emission potential is correspondingly "lower" or "higher". Same with crop height - higher sensitivity on temperature with low crop, and vice verca - seems ok to me as a rough approach. Now, for the issue of application technique and crop height, I guess that the two pools kind of address this already? With possibly a lesser response on crop height for slow pool r3 than for fast pool r1?

I hope that provides some useful input, but maybe we should talk about it 1 on 1 and you can explain better your thoughts about the issue to me?

[GilmourR]

Dear Sasha & ChHaeni. Fillery, Misselbrook and Thorman have considered the effect of crop height. Fillery includes a brief review and implements an emission factor for height in his model. I hope you might find this material useful. Fillery 2016 Soil Research.pdf.

[sashahafner]

Thanks for the input @ChHaeni and @GilmourR !

@ChHaeni , yes, this seems right about multiplicative effects:

If I understand it correctly, multiplicative effects reflect some kind of interaction, so e.g. at low temperatures, the effect of a change in wind speed is "smaller" and at high temperatures the effect of a change in wind speed is "higher".

But I am still not sure this (the current approach) is the best approach here. The relative effect (I mean the effect on, say, r1, not emission per se) is always the same size with this multiplicative response. In reality when emission rate is very low (resistance very high) addition of some more resistance will not have much of an effect because resistance in series (e.g., through films at interface, then through crop canopy, then through boundary layer above crop) is additive.

You are right the model would be more complicated with the proposed approach. In one way it would be simpler though. It would reduce the number of parameters because some of the same secondary parameters would be used for both r1 and r3. This would make parameter estimation simpler!

I will try to write down some equations to better compare the two approaches before deciding what to do.

[sashahafner]

Thanks for the suggestion @GilmourR.

Fillery, Misselbrook and Thorman have considered the effect of crop height. Fillery includes a brief review and implements an emission factor for height in his model.

I've now taken a look and see some good ideas in that paper. I often forget to check the literature on fertilizers, so I appreciate the tip.

A week or two ago I used the results from Thorman et al. (2008) to add new secondary parameters for crop height effects on r1 and r3. Results seem plausible but I am still thinking about whether this different additive resistance approach is simpler and more accurate.