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.