3. Sensitivity analysis
To identify the critical species controlling the tropospheric budgets of O3 and CH4, we calculate the sensitivity of the weighted mean reactivity for the Pacific or Atlantic oceanic flights of ATom (54°S to 60°N) with respect to the species measured by ATom. Sensitivity analyses are often calculated with CCMs, for example, to assess the factors controlling trends and variability in CH4 lifetime (Holmes et al., 2013). In that case the species abundances as well as the chemistry module calculating the reactivities (e.g., L-CH4) are based on the emissions, transport and chemistry in the CCM. Here, we use the ATom observations to initialize the species needed for the chemistry module and then calculate the reactivities (see P2018). Our goal is also different: to recognize the errors in modeled budgets caused by errors in initial values of the species.
The sensitivity S of reactivity R to species X is calculated from the fractional change in R per fractional change in X (dimensionless, e.g., %/%). We use Δ = 10%.
S ≡ ∂ln(R) / ∂ln(X) = ln(R[X(1+Δ)] / R[X]) / ln(1+Δ) (4)
Results from 13 species for the 3 reactivities, the Pacific and Atlantic basins, and 4 ATom deployments are given in Table S1. The variability across basins and deployments is small, and we summarize the mean and standard deviation of the 8 S values in Table 1. Surprisingly, the initial value of many species (HCHO, H2O2, PAN, HNO3, HNO4, CH3OOH, C2H6, C3+-alkanes) has little impact on the reactivities, and these are not shown in Table 1. The only one of these species that breaks the |S| > 0.10 barrier is CH3OOH for P-O3 in the Pacific.
The lessons from Table 1 are quite interesting: (i) as expected, NOx is important for P-O3 but not much more so than O3, CH4, and H2O; (ii) NOx is the least important for L-CH4 of the 5 species in Table 1; (iii) H2O is important across all reactivities; (iv) the sensitivity of L-CH4 to CH4 (0.71) shows that the OH-driven loss of CH4 decreases with a sensitivity of -0.29; and surprisingly, (v) the increase in net loss of O3 (P-O3 minus L-O3) with increasing O3concentrations is driven primarily by reduced P-O3 rather than increase L-O3. In detail, if O3 increases by 10%, then L-O3 increases by 2.5% but P-O3 decreases by 5.4%, and thus net loss increases by 7.9% (i.e., net L-P sensitivity = 0.79). Our analysis presents quite a different picture for the decay of O3than is assumed in many modeling studies where the decay of stratospheric ozone entering the troposphere assumes the sensitivity of L-O3 with respect to O3 is exactly 1.0 (Roelofs and Lelieveld, 1997; Abalos et al., 2020). The CH4 feedback factor derived here from the sensitivities (-0.29) is well within the range calculated by global models (Holms et al., 2013; Holmes, 2018), but it is only a 24-hour feedback and does not include the impact of increasing CH4 on CO and O3concentrations that would only appear in a few months. Our sensitivity of L-CH4 to NOx (0.09) is similar to Holmes et al. (2013), but theirs is larger (0.16) because they only considered lightning NOx, which generally has a larger impact on photochemistry than other sources of NOx. Their sensitivity to H2O (0.32) is close to ours (0.38). So there is nothing new here, except for the O3sensitivities, but we have shown that these sensitivities can be derived from an observational data set.
We examined the second-order quadratic nature of our S values by re-calculating with Δ = 20%, but the results hardly changed (Table S2). Thus, quadratic terms are not important for perturbations <20%. The second-order cross-species terms are far more interesting. We calculate these from a coupled 10% perturbation of 2 different variables
SXY = S(X+10% & Y+10%) – S(X+10%) – S(Y+10%) (5)
and define 2nd-order term SXY as the additional change in sensitivity due to the combined perturbation. We examine SXY using only 4 species (NOx, O3, CH4, CO) and highlight L-CH4 in the ATom-1 Pacific basin in Table 2, while the other reactivities and Atlantic basin (also only for ATom-1) are shown in Table S3. The diagonal elements in the 4x4 array of Table 2 are simply the 1st-order sensitivities, S(X+10%), shown also in Table S1. The off-diagonal elements in each array are SXY, and these are doubly signed (i.e., ++ or –) for emphasis. If SXY ~ 0, then the coupled perturbation is just the sum of the 1st-order terms.
Surprisingly, we find strong co-effects for combined perturbations that are similar in magnitude to the 1st-order sensitivities. For example, for L-CH4 in the Pacific (Table 2), the total sensitivity for NOx (+0.09) plus O3 (+0.39) is reduced by 27%, 0.09+0.39–0.13 = +0.35. Likewise, the combined NOx plus CO sensitivity is also reduced in absolute magnitude by about 50%, 0.09–0.34+0.12 = –0.13. For P-O3, the SXY are also large compared to the 1st-order sensitivities; but for L-O3, the only major 1st-order sensitivity among these 4 species is to O3 itself, and the 2nd-order SXY terms are much smaller (Table S3). L-O3 does have large 1st-order terms for H2O (Table 1), but we did not calculate 2nd-order SXY for these. In terms of net P–L for O3, the SXY terms partly cancel each other (i.e., enhancing both P and L) except for the NOx-CO pair: the combined NOx plus CO perturbation has a net P–L sensitivity of +0.16+0.06+0.11 = +0.33, 50% larger than the sum of 1st-order terms.
When modelers explore factors driving changes in the lifetime of CH4 (e.g., Holmes et al., 2013), it is essential to recognize that coupled perturbations cannot be derived simply from the 1st-order sensitivities. We note that although this study used ATom MDS data to represent the remote troposphere, it could have been done anytime over the past several decades using the distribution of species in 3D global models. An interesting result here is that when we use the UCI CTM distribution of chemical species, we calculate similar sensitivities even though the modeled species distributions are different from the observed ATom distributions (see Fig. 4 of G2021). Possibly, the sensitivities depend more on the chemistry module than on the distribution of species. Thus, we urge a multi-model comparisons of tropospheric chemistry sensitivities to use the ATom data as the observational basis.
This result is not surprising if one recognizes that most reactions are of the form R = kXY rather than R = kX2, and thus the 2nd-order cross terms ∂2R/∂X∂Y are more important than the quadratic terms ∂2R/∂X2. In addition, the rate coefficient k is usually a function of temperature, adding another 2nd-order term ∂2R/∂X∂T (not evaluated here); and thus we can expect that correlated errors between temperature and a critical species will also cause notable error in the budgets.