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\begin{document}

\title{Deconstruction of tropospheric chemical reactivity using aircraft
measurements: the ATom data}



\author[1]{Hao Guo}%
\author[1]{Michael J. Prather}%
\affil[1]{University of California, Irvine}%


\vspace{-1em}



  
  \date{June 14, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
From NASA's Atmospheric Tomography (ATom) mission, we calculate the
average production/loss of O\textsubscript{3} and CH\textsubscript{4}
for 10s air parcels along profiling transects through the
Pacific/Atlantic Oceans for four seasons. We find photochemically hot
air masses on all scales from 2 to 2000 km. Tropical production of
O\textsubscript{3} is high (\textasciitilde{}2 ppb/day) throughout the
ATom profiles (0--12 km). In the Eastern Pacific we find large coherent
air masses of extremely high reactivities in August (monsoonal) and May
(biomass burning). The tropics dominate the O\textsubscript{3} and
CH\textsubscript{4} budgets. Sensitivity analysis identifies only five
critical species (NOx, O\textsubscript{3}, CH\textsubscript{4}, CO, and
H\textsubscript{2}O) responsible for driving the budgets. Sensitivity
analysis shows large 2\textsuperscript{nd}-order effects for coupled
perturbations, indicating that 1\textsuperscript{st}-order sensitivities
cannot simply be added. Feedback analysis indicates a
slower-than-expected timescale for decay of O\textsubscript{3}
perturbations. ATom data shows how global tropospheric chemistry is
constructed from a myriad of fine and large scales.%
\end{abstract}%



\sloppy


\textbf{Deconstruction of tropospheric chemical reactivity using
aircraft measurements: the ATom data}

Hao Guo* and Michael J. Prather*

Department of Earth System Science, University of California, Irvine, CA
92697 USA

* \emph{Correspondence to:} Hao Guo (haog2@uci.edu) and Michael J.
Prather (mprather@uci.edu).

Abstract.

From NASA's Atmospheric Tomography (ATom) mission, we calculate the
average production/loss of O\textsubscript{3} and CH\textsubscript{4}for
10s air parcels along profiling transects through the Pacific/Atlantic
Oceans for four seasons. We find photochemically hot air masses on all
scales from 2 to 2000 km. Tropical production of O\textsubscript{3} is
high (\textasciitilde{}2 ppb/day) throughout the ATom profiles (0--12
km). In the Eastern Pacific we find large coherent air masses of
extremely high reactivities in August (monsoonal) and May (biomass
burning). The tropics dominate the O\textsubscript{3} and
CH\textsubscript{4} budgets. Sensitivity analysis identifies only five
critical species (NOx, O\textsubscript{3}, CH\textsubscript{4}, CO, and
H\textsubscript{2}O) responsible for driving the budgets. Sensitivity
analysis shows large 2\textsuperscript{nd}-order effects for coupled
perturbations, indicating that 1\textsuperscript{st}-order sensitivities
cannot simply be added. Feedback analysis indicates a
slower-than-expected timescale for decay of O\textsubscript{3}
perturbations. ATom data shows how global tropospheric chemistry is
constructed from a myriad of fine and large scales.

1. Introduction

The environmental damage caused by chemically reactive greenhouse gases
and air pollutants is controlled by a balance between sources and sinks,
with the major sink usually being atmospheric photochemistry. The net
chemical loss is a key budget term, and it comprises a highly
heterogeneous mixture of air parcels, each with its own mix of species,
and each with its own chemical production and/or loss rates designated
here as the reactivities: P-O3, L-O3, and L-CH4 (see Prather et al.,
2017; 2018, hence P2017 and P2018). Reactivity here is simply the
24-hour integration of a reaction rate, or the sum of several reaction
rates, that describe budgets of species in units of ppb per day. In this
paper we continue our efforts to understand how tropospheric chemistry
is constructed by examining reactivities starting at the finest spatial
scales.

A recent observation-based study of the chemical reactivity of
individual air parcels used the 10 s in situ aircraft measurements from
the NASA Atmospheric Tomography (ATom) mission's first deployment
(ATom-1; Guo et al., 2021, hence G2021). Recent publications have
identified new scientific opportunities coming from ATom with its
intensive, chemically comprehensive measure of composition combined with
an extensive, semi-global profiling through the remote troposphere
(Wofsy et al., 2018; Thompson et al., 2021). Topics include scales of
variability (Schill et al., 2020; G2021), global CO forecasting (Strode
et al., 2018), and OH oxidative capacity (Wolfe et al., 2019; Brune et
al., 2020; Travis et al., 2020; Anderson et al., 2021; G2021), as well
as areas unrelated to this work, such as aerosol distribution,
formation, and precursors (Brock et al., 2021; Williamson et al., 2021;
Veres et al., 2020).

Here we extend G2021 to report reactivities for all four seasonal
deployments (ATom-1234, see Figure S1) and examine how their statistical
patterns change with each deployment. Second, we perform sensitivity
analyses to identify which of the ATom-measured species drives the
reactivities, and thus which are critical for the chemistry-climate
models (CCMs) to simulate accurately. Third, probability densities for
these critical species from ATom are presented as possible performance
metrics for CCMs.

Our interests in the reactivity of air parcels or model grid cells began
with P2017, continuing with P2018 and G2021. We focused on the budgets
of O\textsubscript{3} and CH\textsubscript{4}, and reactivities were
defined by some key reaction rates:

loss of CH\textsubscript{4} (L-CH4),

CH\textsubscript{4} + OH CH\textsubscript{3} + H\textsubscript{2}O (1)

production of O\textsubscript{3} (P-O3),

HO\textsubscript{2} + NO NO\textsubscript{2} + RO (2a)

RO\textsubscript{2} + NO NO\textsubscript{2} + RO (2b)

O\textsubscript{2} +\selectlanguage{greek}\emph{hν} \selectlanguage{english}O + O (x 2) (2c)

and loss of O\textsubscript{3} (L-O3),

O\textsubscript{3} + OH O\textsubscript{2} + HO\textsubscript{2} (3a)

O\textsubscript{3} + HO\textsubscript{2} HO +
O\textsubscript{2}+O\textsubscript{2} (3b)

O(\textsuperscript{1}D) + H\textsubscript{2}O OH + OH (3c)

These rates are readily calculated in most CCMs, and we found that the
net P-O3 minus L-O3 accurately described the 24 h
O\textsubscript{3}tendencies over the ocean basins but not in highly
polluted boundary layers. Reaction 2c is important in the upper tropical
troposphere (Prather, 2009), but only above ATom flight levels. The
calculation of reactivities here use the UCI model and the RDS*-2
protocol described in G2021.

We mainly consider the Pacific and Atlantic oceanic flights of ATom,
which we constrain to be 54\selectlanguage{ngerman}°S to 60°N (see the included flights in
Figure S2), but also include a focus on the tropical flights (30°S to
30°N), splitting the Pacific flights into Central and Eastern Pacific
(0°-30°N only). Reactivities at latitudes poleward of 60° are smaller
than over the oceans, and we present a less extensive analysis for the
Arctic and Antarctic.

Latitude-by-altitude curtain plots of the reactivities along flight
tracks are presented in Section 2, along with altitude profiles of the
mean reactivities and probability densities over the ocean basins. In
Section 3 we present our analysis of the sensitivity of the reactivities
to ATom MDS species, identifying those critical species where a model
bias will introduce large errors in the O\textsubscript{3} and
CH\textsubscript{4} budgets. Critical species probability densities from
ATom are introduced in Section 4 as a possible model metric, and Section
5 concludes this analysis.

2. Variation of photochemical reactivities across the four ATom
deployments

\emph{2.a. Curtain plots}

The spatial structures and variability of P-O3 as sampled by the ATom
transects over the Pacific Ocean are presented in Figure 1a. The full
set of plots covering all three reactivities and also the Atlantic Ocean
are shown in Supplementary Figures S3-S8. For these curtain plots, the
10 s reactivities (2 km by 80 m thick parcels) are averaged and plotted
in 1° latitude by 200 m thick cells. In August (ATom-1), the highly
reactive (hot) P-O3 parcels (3.5 to 6+ ppb/day) are common throughout
most of the lower troposphere (0-5 km) from 20°S to 60°N, and there is
also a region of very high P-O3 in the upper northern tropics (8-12 km,
15°N-30°N). In February (ATom-2), P-O3 shifts to the southern
mid-latitude and tropics following the overhead sun as expected, but the
tropical production lacks the intensity seen in ATom-1 in the 20°N-30°N
region. In October (ATom-3) the high P-O3 parcels are primarily
tropical, but favor the southern latitudes. Finishing in May (ATom-4) we
find the northern dominance returns although not as strongly as in
ATom-1 and find some regions of P-O3 \textgreater{} 5 ppb/day as also in
ATom-1. Overall, this shows the dominance of the tropics for production
of O\textsubscript{3} over the oceans. The northern summer mid-latitudes
almost contribute a fifth tropical season, and all of the highly
reactive regions probably show the importance of deep convection over
northern continents influencing the tropical Pacific in August and May.
The loss of O\textsubscript{3}shows similar seasonal shifts as P-O3,
following the sun especially in the tropics, and moving into the
northern mid-latitudes in August and May, but high reactivities are
limited to below 8 km. The loss of CH\textsubscript{4} parallels that of
O\textsubscript{3}.

In the Atlantic P-O3 also follows the sun, with high reactivity south of
the equator for February (ATom-2) and October (ATom-3). In August
(ATom-1), a substantial number of air parcels show high P-O3 (2-6
ppb/day) from 10°S to 45°N. There is a cluster of hot parcels in the
lower troposphere (1-5 km) but also a clustering in the upper
troposphere (6-12 km), including about 20°S in May (ATom-4). We know
that the tropical Atlantic O\textsubscript{3} is influenced by
continental outflow of biomass burning from South America and Africa
(Fishman et al., 1990), and here we see that outflow is actively
producing O\textsubscript{3}. L-O3 occurs in a more tightly constrained
region than P-O3, both in latitude and altitude (0-6 km). L-O3 is
centered on the tropics for all Atom-1234 but, like in the Pacific, it
includes a highly reactive region in northern summer mid-latitudes
(30°N-50°N, ATom-1). The Atlantic pattern of L-CH4 is almost identical
to that of L-O3, but peaks about 1 km lower in altitude.

Given the importance of the tropics in the global reactivity of the
atmosphere, we create expanded 30°S-30°N curtain profiles and separate
the Pacific into Central (about 180°E-210°E) and Eastern (about 240°E,
the first flight of each deployment from Palmdale CA south to the
equator and back) (Figures S9-S17). The expanded plots clearly show the
patchy nature of P-O3 hot spots in the Central Pacific and the Atlantic
(except for 15°S-25°S, 7-9 km), while emphasizing the large coherent hot
spots in L-O3 and L-CH4 in the Atlantic. The Eastern Pacific stands out:
there are large coherent regions (20° by 2-3 km) associated with well
mixed convective outflow from North America having extreme reactivities
in August (monsoonal) and May (possibly biomass burning).

Curtain profiles for the Arctic (Figure S18) are presented only for
ATom-1 and ATom-4 when there was enough sunlight to generate
non-negligible reactivities. The stratospheric air parcels are excluded.
Reactivities appear moderately high, but the color scale here is 3 times
smaller than in Figures S3-S17. In the Arctic, much of the P-O3 occurs
above 6 km, and L-CH4 is suppressed relative to L-O3 because of the
colder temperatures. Only one of the two Antarctic flights had enough
sunlight to produce much reactivity (ATom-3, Figures S19). Like the
Arctic, P-O3 is in the upper troposphere, while L-O3 and L-CH4 are in
the lower. Note that the color scale is 6-to-12 times smaller than in
Figures S3-17.

\emph{2.b. Mean altitude profiles}

Altitude profiles of the mean P-O3 for the three tropical basins and the
4 deployments are compared in Figure 1b (for other regions and
reactivities, see Figures S20-S27). For Central Pacific and Tropic
Atlantic, the variation across deployments is not so large with values
\textasciitilde{}2 ppb/day throughout. ATom-1, however, shows slightly
higher P-O3 (\textasciitilde{}3 ppb/day) below 4 km in both regions and
also in the upper troposphere but only in the Atlantic.

In the Eastern Pacific, however, each deployment seems unique: ATom-2 is
almost uniform at 2 ppb/day; ATom-134 show enhanced upper troposphere
P-O3 probably from deep convection and lightning NOx over North America;
ATom-13 show large mid-tropospheric production of \textasciitilde{}3
ppb/day not seen in ATom-24; and ATom-4 finds a thick atmospheric layer,
1-3 km, with an astounding rate of P-O3, averaging \textasciitilde{}10
ppb/day. The end of the biomass burning season in Central America
(15°N-20°N) is probably the cause of the peak P-O3 in ATom-4 (May);
while the start of the North American Monsoon season is probably the
cause of the extensive deep-convection layer (8-12+ km) with high P-O3
in ATom-1 (August). With this high level of variability, it will be
important to re-examine the time period of the ATom flights with a
chemistry-transport model to assess the spatio-temporal scales of these
incredible events. As expected from Figure 1a, the lowest P-O3 in all 3
tropical basins occurs in northern winter (ATom-2, February). For L-O3
and L-CH4, the Central Pacific and Tropical Atlantic show little
variability across ATom-1234, but the Eastern Pacific shows the
extremely high reactivities for ATom-14 as found in P-O3 (Figures
S23-S25).

In the Arctic (Figure S26) ATom-14 show nearly identical and constant
profiles for all 3 reactivities; while ATom-23 have negligible
reactivities. P-O3 peaks at 8-12 km with values from 1-2 ppb/day. The
reactivities in the Arctic, even in summer are less than the average
over the Pacific and Atlantic oceans and thus have little impact on the
global O\textsubscript{3} or CH\textsubscript{4} budgets. In the
Antarctic (Figure S27), reactivities are much less than the Arctic and
only reported for ATom-3.

2.c. Probability densities of photochemical reactivities

The probability densities (PDs) of the ATom reactivities have proven
useful in testing model climatologies (see G2021). Here, we plot the PDs
for the 4 deployments in the major oceanic regions for all 3
reactivities (Figures S28-S33). Overall, we find ATom-1 has more
frequent high reactivities, and the East Pacific has the least
conformity across ATom-1234. The Central Pacific and Tropical Atlantic
provide a repeatable pattern that should provide an excellent test for
CCM climatologies.

3. Sensitivity analysis

To identify the critical species controlling the tropospheric budgets of
O\textsubscript{3} and CH\textsubscript{4}, 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
CH\textsubscript{4} 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 \selectlanguage{greek}Δ \selectlanguage{english}= 10\%.

S [?] [?]ln(R) / [?]ln(X) = ln(R{[}X(1+\selectlanguage{greek}Δ\selectlanguage{english}){]} / R{[}X{]}) / ln(1+\selectlanguage{greek}Δ\selectlanguage{english}) (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,
H\textsubscript{2}O\textsubscript{2}, PAN, HNO\textsubscript{3},
HNO\textsubscript{4}, CH\textsubscript{3}OOH,
C\textsubscript{2}H\textsubscript{6}, C\textsubscript{3+}-alkanes) has
little impact on the reactivities, and these are not shown in Table 1.
The only one of these species that breaks the \textbar{}S\textbar{}
\textgreater{} 0.10 barrier is CH\textsubscript{3}OOH 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 O\textsubscript{3},
CH\textsubscript{4}, and H\textsubscript{2}O; (ii) NOx is the least
important for L-CH4 of the 5 species in Table 1; (iii)
H\textsubscript{2}O is important across all reactivities; (iv) the
sensitivity of L-CH4 to CH\textsubscript{4} (0.71) shows that the
OH-driven loss of CH\textsubscript{4} decreases with a sensitivity of
-0.29; and surprisingly, (v) the increase in net loss of
O\textsubscript{3} (P-O3 minus L-O3) with increasing
O\textsubscript{3}concentrations is driven primarily by reduced P-O3
rather than increase L-O3. In detail, if O\textsubscript{3} 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
O\textsubscript{3}than is assumed in many modeling studies where the
decay of stratospheric ozone entering the troposphere assumes the
sensitivity of L-O3 with respect to O\textsubscript{3} is exactly 1.0
(Roelofs and Lelieveld, 1997; Abalos et al., 2020). The
CH\textsubscript{4} 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 CH\textsubscript{4} on CO and
O\textsubscript{3}concentrations 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 H\textsubscript{2}O
(0.32) is close to ours (0.38). So there is nothing new here, except for
the O\textsubscript{3}sensitivities, 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 \selectlanguage{greek}Δ \selectlanguage{english}= 20\%, but the results hardly changed (Table S2).
Thus, quadratic terms are not important for perturbations
\textless{}20\%. The second-order cross-species terms are far more
interesting. We calculate these from a coupled 10\% perturbation of 2
different variables

S\textsubscript{XY} = S(X+10\% \& Y+10\%) -- S(X+10\%) -- S(Y+10\%) (5)

and define 2\textsuperscript{nd}-order term S\textsubscript{XY} as the
additional change in sensitivity due to the combined perturbation. We
examine S\textsubscript{XY} using only 4 species (NOx,
O\textsubscript{3}, CH\textsubscript{4}, 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
1\textsuperscript{st}-order sensitivities, S(X+10\%), shown also in
Table S1. The off-diagonal elements in each array are
S\textsubscript{XY}, and these are doubly signed (i.e., ++ or --) for
emphasis. If S\textsubscript{XY} \textasciitilde{} 0, then the coupled
perturbation is just the sum of the 1\textsuperscript{st}-order terms.

Surprisingly, we find strong co-effects for combined perturbations that
are similar in magnitude to the 1\textsuperscript{st}-order
sensitivities. For example, for L-CH4 in the Pacific (Table 2), the
total sensitivity for NOx (+0.09) plus O\textsubscript{3} (+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 S\textsubscript{XY} are also
large compared to the 1\textsuperscript{st}-order sensitivities; but for
L-O3, the only major 1\textsuperscript{st}-order sensitivity among these
4 species is to O\textsubscript{3} itself, and the
2\textsuperscript{nd}-order S\textsubscript{XY} terms are much smaller
(Table S3). L-O3 does have large 1\textsuperscript{st}-order terms for
H\textsubscript{2}O (Table 1), but we did not calculate
2\textsuperscript{nd}-order S\textsubscript{XY} for these. In terms of
net P--L for O\textsubscript{3}, the S\textsubscript{XY} 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
1\textsuperscript{st}-order terms.

When modelers explore factors driving changes in the lifetime of
CH\textsubscript{4} (e.g., Holmes et al., 2013), it is essential to
recognize that coupled perturbations cannot be derived simply from the
1\textsuperscript{st}-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 = kX\textsuperscript{2}, and thus the
2\textsuperscript{nd}-order cross terms [?]\textsuperscript{2}R/[?]X[?]Y are
more important than the quadratic terms
[?]\textsuperscript{2}R/[?]X\textsuperscript{2}. In addition, the rate
coefficient k is usually a function of temperature, adding another
2\textsuperscript{nd}-order term [?]\textsuperscript{2}R/[?]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.

4. Probability densities of critical species

The sensitivity analysis here helps us identify the critical species
where a bias in the modeled distribution will produce a large bias in
the budgets of O\textsubscript{3} and CH\textsubscript{4}. The main
species singled out here (NOx, O\textsubscript{3}, CO,
CH\textsubscript{4}) are well known and CCMs often use these as standard
measurement metrics. A surprise was the emergence of
CH\textsubscript{3}OOH as being important for P-O3, and a global
climatology of this species should be a priority measurement. Although
we have long known that H\textsubscript{2}O and T are important factors
(e.g., Table 2 of Holmes et al., 2013), these quantities have often been
relegated to the physical climate system and not often though of a major
source of model error in chemical system. Thus, when we are diagnosing
the future tropospheric O\textsubscript{3} or CH\textsubscript{4} from
the multi-model comparisons (Stevenson et al., 2013; Voulgarakis et al.,
2013; Young et al., 2013, 2018; Griffiths et al., 2021), we need to
document biases in T and H\textsubscript{2}O.

Comparing T with mean profiles is straightforward, but
H\textsubscript{2}O is more difficult, even with profiles, because of
the 3 orders of magnitude change over the troposphere. Thus, we
recommend that relative humidity over liquid water (RHw, \%) be used to
detect bias. We show histograms of probability densities (PDs) of RHw
from ATom-1234 in Figure 1c\textbf{.} We select the three tropical basin
(C. Pacific, E. Pacific, Atlantic) and lower troposphere (0-6 km)
because this is where most of the reactivity occurs (see Figure 1b). The
ATom data for RHw show a clear bimodal distribution with extensive
tropic regions having narrow PD with RHw \textless{} 10\% and the bulk
showing a broad PD about 80\%. The E. Pacific has high seasonality with
ATom-14 (the more reactive periods) lacking air with RHw \textless{}
20\%, consistent with the high reactivities noted above. PDs and for
O\textsubscript{3}, NOx and CO, as well as the 0-12 km PD for RHw, are
shown in Figures S34-S37. These gases show a wide range of seasonality,
especially in the Pacific and provide a challenge for the models.

5. Conclusions

In terms of reactivities, by extending the ATom-1 (G2021) to the four
seasons of ATom-1234, we find:

\begin{itemize}
\tightlist
\item
  The tropics dominate production of O\textsubscript{3}, over at least
  the Pacific and Atlantic Ocean basins, with average P-O3 greater than
  2 ppb/day throughout 0-12 km. Loss of O\textsubscript{3} and
  CH\textsubscript{4} are also tropical, but primarily at lower
  altitudes (0-6 km), and show similar seasonal shifts as P-O3,
  following the overhead sun. The northern mid-latitudes add a hot
  reactive season in the summer that is comparable to the tropics, but
  high reactivities are limited to below 8 km. There is no corresponding
  hot season for the southern mid-latitudes.
\item
  Elevated levels of O\textsubscript{3} in the tropical Atlantic
  O\textsubscript{3} are known to be influenced by continental outflow
  of biomass burning from primarily Africa and also South America
  (Fishman et al., 1990), and here we find that the outflow is still
  actively producing O\textsubscript{3}. High levels of L-O3 occur in a
  more tightly constrained region than P-O3, both in latitude and
  altitude (0-6 km), indicating a different process.
\item
  The Eastern Pacific stands out: there are large, coherent reactive
  regions (20\selectlanguage{ngerman}° in latitude by 2-3 km thick) associated with well mixed
  convective outflow from North America having extreme reactivities in
  both August (monsoonal) and May (biomass burning).
\item
  The Arctic and Antarctic have much lower overall reactivity; and,
  given their small area, they play little role in the global
  O\textsubscript{3} and CH\textsubscript{4} budgets.
\end{itemize}

Our sensitivity analyses using ATom measurements has identified some
clear direction and pitfalls, as well as providing a more robust view of
chemical feedbacks:

\begin{itemize}
\tightlist
\item
  The critical species (S \textgreater{} 0.1) are NOx,
  O\textsubscript{3}, CH\textsubscript{4}, CO, and H\textsubscript{2}O.
\item
  While the sensitivities are linear for 0-20\% perturbations, there are
  large 2\textsuperscript{nd}-order effects for coupled perturbations,
  comparable to 1\textsuperscript{st}-order sensitivities. Thus, coupled
  perturbations cannot be calculated simply from the sum of the linear
  sensitivities.
\item
  Our 24-hour CH\textsubscript{4} feedback factor derived from ATom
  flights is similar to the global, steady-state feedback factors
  derived from global models over the past two decades.
\item
  Our analysis presents quite a different picture of the lifetime of
  O\textsubscript{3} than is often assumed: if
  O\textsubscript{3}increases by 10\%, then L-O3 increases by only 2.5\%
  but P-O3 decreases by 5.4\% and thus net loss increases by 7.9\%. This
  lengthens the effective timescale of a O\textsubscript{3}perturbation,
  especially since the regions of high P-O3 and L-O3 do not often
  coincide.
\end{itemize}

Probability densities for these critical species from ATom are presented
as possible performance metrics for CCMs.

Comparing H\textsubscript{2}O with mean profiles is difficult because of
the 3 orders of magnitude change over the troposphere, and thus, we
recommend that relative humidity over liquid water (RHw) be used to
detect model bias. Here we present a clear bimodal distribution of RHw
in the tropics as measured by ATom.

The full ATom data set, including reactive species and the derived
reactivities along with other atmospheric components describing the
origins and processing of the air masses, provides the most extensive
sampling of tropospheric chemistry over the remote ocean basins to date.
The objective flight planning and near-continuous climb/descent
profiling provided full sampling of the 0-12 km troposphere over the
oceans. The statistics, including the co-variations of critical species
(2D probability densities, in G2021), provide an excellent measurement
metric for CCMs. The model-derived reactivities provide a testbed for
the chemistry modules used in CCMs and also for independent analyses of
the origins and chemical evolution of the air that matters, those
chemically hot air masses clearly seen in the ATom flights. The
sensitivity analysis of the 24-hour reactivities provides some core data
that we feel should become a standard part of CCM evaluations and
inter-comparisons. With this analysis, based on 10 s (2 km) air parcels,
we believe we have partially deconstructed the spatial scales and
variability that defines tropospheric chemistry.

Acknowledgements. The authors are indebted to the entire ATom Science
Team including the managers, pilots and crew, who made this mission
possible. We thank the instrument teams (co-authors on the first paper,
Guo et al., 2021) for this valuable data set. Primary funding of the
preparation of this paper at UC Irvine was through NASA grants
NNX15AG57A and 80NSSC21K1454.

Data Availability. The full ATom data set as well as the derived MDS-2
and RDS*-2 data for ATom 1, 2, 3 and 4 are posted on the NASA ESPO ATom
website (https://espo.nasa.gov/atom/content/ATom). The final archive for
ATom data will be at Oak Ridge National Laboratory (ORNL), see
https://daac.ornl.gov/ATOM/guides/ATom\_merge.html. The MATLAB codes and
data sets used in the analysis here are posted on Dryad
(https://doi.org/10.7280/D1Q699), which has been expanded from Guo et
al., 2021 to include this paper's data and codes.

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\textbf{Table 1.} First-order sensitivities of the reactivities (R) with
respect to the dominant species (X), S \selectlanguage{english}[?] \selectlanguage{english}[?]{[}ln(R){]}/\selectlanguage{english}[?]{[}ln(X){]}
(\%/\%) are calculated with a perturbation of 10\%. Results are averaged
over ATom-1234 for Pacific and Atlantic basins (54degS to 60degN), and the
standard deviation is shown. The H\textsubscript{2}O results include
only ATom-1. The CTM results are calculated using the chemical species
from the UCI CTM on 16 August 2016 as the initial conditions, and
separate large Pacific and Atlantic blocks are used (see Figure S1 of
G2021) and air-mass weighted, with the average of the 2 basins shown
here. For the expanded ATom table showing Pacific and Atlantic, and the
4 deployments separately, plus the other species (HCHO,
H\textsubscript{2}O\textsubscript{2}, PAN, HNO\textsubscript{3},
HNO\textsubscript{4}, CH\textsubscript{3}OOH,
C\textsubscript{2}H\textsubscript{6}, C\textsubscript{3+}-alkanes) see
Supplemental Table S1.\selectlanguage{english}
\begin{longtable}[]{@{}llllllllll@{}}
\toprule
\textbf{X} & \textbf{P-O3} & \textbf{P-O3} & \textbf{P-O3} &
\textbf{L-O3} & \textbf{L-O3} & \textbf{L-O3} & \textbf{L-CH4} &
\textbf{L-CH4} & \textbf{L-CH4}\tabularnewline
\midrule
\endhead
& \emph{ATom} & \emph{s.d.} & \emph{CTM} & \emph{ATom} & \emph{s.d.} &
\emph{CTM} & \emph{ATom} & \emph{s.d.} & \emph{CTM}\tabularnewline
\textbf{NOx} & \textbf{0.21} & \emph{0.02} & \textbf{0.19} & 0.04 &
\emph{0.01} & 0.03 & \textbf{0.09} & \emph{0.01} &
\textbf{0.11}\tabularnewline
\textbf{O\textsubscript{3}} & \textbf{-0.54} & \emph{0.04} &
\textbf{-0.53} & \textbf{0.25} & \emph{0.03} & \textbf{0.23} &
\textbf{0.36} & \emph{0.03} & \textbf{0.40}\tabularnewline
\textbf{CH\textsubscript{4}} & \textbf{0.15} & \emph{0.01} &
\textbf{0.16} & -0.02 & \emph{0.01} & -0.02 & \textbf{0.71} &
\emph{0.02} & \textbf{0.69}\tabularnewline
\textbf{CO} & 0.07 & \emph{0.01} & 0.07 & 0.00 & \emph{0.00} & 0.00 &
\textbf{-0.38} & \emph{0.02} & \textbf{-0.35}\tabularnewline
\textbf{H\textsubscript{2}O} & \textbf{0.14} & \emph{0.00} &
\textbf{0.14} & \textbf{0.48} & \emph{0.01} & \textbf{0.47} &
\textbf{0.38} & \emph{0.01} & \textbf{0.37}\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 2.} Second-order, cross-term sensitivities of the
reactivity L-CH4 relative to critical species (NOx, O\textsubscript{3},
CH\textsubscript{4}, CO) calculated in pair combinations. Results here
are from ATom-1 and the Pacific basin (54\selectlanguage{ngerman}°S-60°N). The single +10\%
sensitivities calculated for individual species, S(X+10\%), are shown in
italics along the diagonal. The doubly signed (i.e., ++ or --)
off-diagonal values represent the additional change in sensitivity due
to the coupling of the two species: S(X+10\% \& Y+10\%) -- S(X+10\%) --
S(Y+10\%). When the 2\textsuperscript{nd}-order is small (only the
O\textsubscript{3} x CO term here), the coupled perturbation is simply
the sum of the two individual ones. Atom-1 results for other
reactivities (P-O3, L-O3) and the Atlantic basin are given in
Supplemental Table S3.\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
& \textbf{Pacific} & \textbf{Pacific} & \textbf{Pacific} &
\textbf{Pacific}\tabularnewline
\midrule
\endhead
\textbf{L-CH4} & NOx & O\textsubscript{3} & CH\textsubscript{4} &
CO\tabularnewline
NOx & \emph{+0.09} & \textbf{--0.13} & \textbf{--0.18} &
\textbf{++0.12}\tabularnewline
O\textsubscript{3} & & \emph{+0.39} & \textbf{--0.19} &
\textbf{--0.01}\tabularnewline
CH\textsubscript{4} & & & \emph{+0.69} & \textbf{--0.12}\tabularnewline
CO & & & & \emph{-0.34}\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{longtable}[]{@{}l@{}}
\toprule
\textbf{(a)}\tabularnewline
\midrule
\endhead
\textbf{(b)}\tabularnewline
\textbf{(c)}\tabularnewline
\textbf{Figure 1}. \textbf{(a)} Curtain plots for P-O3 (0-6 ppb/d)
showing the profiling of the 4 ATom deployments over the Pacific Ocean
(54\selectlanguage{ngerman}°S-60°N). \textbf{(b)} Mean altitude profile of P-O3 over the 3
tropical ocean basins (30°S-30°N) for the 4 ATom's. \textbf{(c)}
Probability densities of relative humidity over liquid water (RHw,
0-110\%) in the lower troposphere (0-6 km) in the 3 tropical basins for
the 4 ATom's. Color coding in the legend identifies the 4 ATom
deployments. The numbers in the legend of panel (c) are, successively,
the mean value, standard deviation, and skewness.\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{ngerman}

\selectlanguage{english}
\FloatBarrier
\end{document}

