Allow tau OH H2 coefficient to vary with CO coefficient

[kdorheim]

Since #758 $H_2$ emissions have indirect effects on CH4 lifetime with respect to OH. However, this implementation is independent of the other coefficients in the $\tau_{OH}$ equation. See these old dynamics in Figure 1, even when the CO parameter is doubled, there is no change in $\tau_{OH}$ and $RF_{CH_4}$.

Since we were expecting changes in some of the coefficients of the $\tau_{OH}$ equation with #786 @ssmithClimate and I discussed an adjustment to the implementation so that the $H_2$ effect on $\tau_{OH}$ varies when the CO coefficient varies. See in Figure 2 how, when the CO parameter is doubled, there is a change in $\tau_{OH}$ and $RF_{CH_4}$. Since the CO emissions are held constant during the Hector runs, the changes in $\tau_{OH}$ and $RF_{CH_4}$ can be attributed solely to $H_2$.

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Materials: PR_787.zip

[kdorheim]

Previously, $\tau_{OH}$

New Implementation of $\tau_{OH}$

From this PR equation 5 is now

Where $c_{H2_{C_{CO}}}= 4.25$ was derived by collaborator B.M. based on the mass balance model from Bertagni et al. 2022, equations 1-4 (henceforth Bertagni equations will be denoted with BX).

Let $X$ be an emission species, with $R_x$ being the reaction rate, $[X]$ being the concentration, and $\tau_X$ being the lifetime.

With $R_{x} = \frac{[X]}{\tau_x}$

Using (B1) solve for $\tau_{CO}$

$R_{CO} = \frac{[CO]}{\tau_{CO}} = k_3 [OH][CO] \rightarrow \tau_{CO} = \frac{1}{k_3 [CO]}$

similarly solve for $\tau_{H_2}$

$\tau_{H_2} = \frac{1}{k_2 [H2]}$

Suppose that $\tau_{CO} = \tau_{H_2}$ solve for $[H_2]$

$\tau_{CO} = \tau_{H_2} \rightarrow \frac{1}{k_3[CO]} = \frac{1}{k_2[H_2]} \rightarrow [H_2] = \frac{k_3}{k_2}[CO]$

When in steady state $\frac{d[X]}{dt} = 0$ with $[X] = E_x \tau_{x}$, use this to relate $\tau_{CO}$, $\tau_{H_2}$, $E_{H_2}$ and $E_{CO}$ with one another.

$[H_2] = E_{H_2} \tau_{H_2} \rightarrow E_{H_2} \tau_{H_2} = \frac{k_3}{k_2} [CO] \rightarrow ... \rightarrow$
$E_{H_2} = \frac{k_3}{k_2} \frac{\tau_{CO}}{\tau_{H_2}} E_{CO}$

Let $c_{H2_{C_{CO}}} = \frac{k_3}{k_2} \frac{\tau_{CO}}{\tau_{H_2}}$, where $\alpha$ quantifies the effect of $H_2$ emissions on OH lifetime to the effect of CO emissions on OH lifetime

Using the values from Bertagni et al. Table 1 evaluate $\alpha$

$c_{H2_{C_{CO}}} = \frac{k_3}{k_2} \frac{\tau_{CO}}{\tau_{H_2}} = \frac{1.9 \times 10^{-13}}{3.8 \times 10^{-15}} \times \frac{0.17}{2} = 4.25$

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Bertagni, M. B., Pacala, S. W., Paulot, F., & Porporato, A. (2022). Risk of the hydrogen economy for atmospheric methane. Nature Communications, 13(1), 7706. https://doi.org/10.1038/s41467-022-35419-7

[kdorheim]

Feedback on the name of H2_CCO would be helpful & do we think that the comment "PR 787" is sufficient documentation for how the value of 4.25 was derived?

[bpbond]

Yes, I think PR787 is unambiguous.

Nice job here @kdorheim --thank you! See a few comments below.

[kdorheim]

@ssmithClimate anythoughts?