Evaluation of the Stratospheric Contribution to the Inter‐Annual Variabilities of Tropospheric Methane Growth Rates

Tropospheric methane (CH4) shows large inter‐annual variability in its growth rates on top of decadal trends, which is usually interpreted as changes in sources or sinks. The contribution of the stratosphere‐troposphere exchange (STE) is often omitted in such analyses. Here, we quantify annual anomalies of stratosphere‐troposphere CH4 fluxes using varied model‐ or observation‐based methods. Globally, the inter‐annual variability (standard deviation) of this flux during 2000–2020 is 2.0 Tg a−1, producing a variability of ∼0.6 ppb a−1 at the surface, which is only ∼20% of observed surface CH4 growth rate variability. Compared to global averages, high latitudes experience a larger STE‐induced surface variability, which is 80% of the observed surface anomalies in the Antarctic and 44% in the Arctic. Our results suggest that although the STE process is a minor contributor globally, it has a considerable impact over polar regions on the inter‐annual variability of surface CH4 growth rates.

Previous studies have demonstrated that the → term has a considerable impact on the tropospheric concentrations of N 2 O, another well-mixed greenhouse gas, at seasonal and inter-annual scales (Lickley et al., 2021;Nevison et al., 2004Nevison et al., , 2011Ray et al., 2020;Ruiz et al., 2021;Ruiz & Prather, 2022; Thompson et al., 2013). Driven by the global-scale Brewer-Dobson circulation, N 2 O-rich tropospheric air enters the stratosphere (where N 2 O is destroyed by photochemistry) in the tropics, and N 2 O-depleted stratospheric air returns to the troposphere in the extra-tropics, leading to a net troposphere-to-stratosphere N 2 O flux ( → < 0) (Ruiz et al., 2021). The variability of → is modulated by the Quasi-Biennial Oscillation (QBO) (Baldwin et al., 2001;Ruiz et al., 2021), that is, the westerly QBO phase is associated with a weaker circulation and subsequently a positive → anomaly, while the easterly QBO phase is associated with the opposite. The effect can propagate from the tropopause down to the surface with a lag of a few months, producing a periodic signal in surface observations of N 2 O growth rates with a cycle of ∼28-month and a relative magnitude of 0.1%-0.2% a −1 (Ray et al., 2020).
The same transport process should also affect CH 4 fluxes between the troposphere and the stratosphere. Meanwhile, chemical loss processes differ greatly between CH 4 and N 2 O. While N 2 O is primarily removed in the stratosphere (Tian et al., 2020), CH 4 is primarily destroyed in the troposphere through oxidation by the OH radical (∼90% of the total sink) with a minor chemical loss in the stratosphere (Saunois et al., 2020).As a result, → is on average a minor term in the tropospheric CH 4 budget, compared to or . However, this does not necessarily rule out that the inter-annual variability of → can be an appreciable contributor to the inter-annual variability of for CH 4 . If so, interpreting observed surface CH 4 growth without accounting for it may lead to biased attribution to the changes in CH 4 emissions or global OH concentrations. We will quantitively examine the contribution of → to surface CH 4 growth rate anomalies in this study.

Inter-Annual Variability of Greenhouse Gas Growth Rates
We derive the inter-annual variability of atmospheric growth of N 2 O and CH 4 from monthly marine boundary layer observations of their mole fractions from the National Oceanic and Atmospheric Administration (NOAA) Earth System Research Laboratories (ESRL) (Lan et al., 2023). We first compute annual growth rates by taking 1-year differences for each month from the 1-year running averaged monthly time series. To derive the inter-annual variability of growth rates, we then subtract 5-year running averages of the annual growth rates from their 1-year running averages. This operation preserves inter-annual signals on the time scales of 1-5 years and removes short-term seasonality and long-term trends (Ray et al., 2020). Figures 1a and 1b illustrate our computation of 1-year and 5-year running averages of growth rates for N 2 O and CH 4 . We also apply the same procedure to other simulated or derived time series in this study to obtain inter-annual variability of growth rates.

Diagnostics of Stratosphere-Troposphere CH 4 fluxes
We use three methods (i.e., fixed-budget simulation, tracer scaling, and residual circulation velocity) to estimate CH 4 fluxes between the stratosphere and troposphere ( → ). The fixed-budget simulation method is based on a chemical transport simulation of CH 4 mole fractions driven by a uniform surface CH 4 emission field (∼518 Tg a −1 ) invariant in time and space. The annually invariant monthly 3-D tropospheric OH field (a global CH 4 lifetime against tropospheric OH oxidation: ∼11.0 a) is taken from a GEOS-Chem full chemistry simulation (Wecht et al., 2014) and the monthly stratospheric loss frequency field (the stratospheric CH 4 lifetime: ∼35 a) from the NASA Global Modeling Initiative model (Murray et al., 2012). The resulting inter-annual variability of surface CH 4 mole fractions can then be attributed to the stratosphere-troposphere exchange. A similarly configured simulation was used by Prather (2022) to investigate the effect of STE on surface CO 2 variability. The simulation is conducted for 1996-2020 with the GEOS-Chem (12.9.3) model (CH 4 -only mode) where the first 4 years are for spin-up and the remaining 20 years are used for the analysis. We check after the spin-up that the global atmospheric burden and the stratosphere-troposphere gradient are established (close to the steady state; do not increase or decrease monotonically) to ensure that the CH 4 anomaly derived from the simulation is free from artifacts caused by relaxation to the steady state. The simulation has a horizontal resolution of 4° × 5° and 47 vertical layers (30 layers in the troposphere) and is driven by meteorological fields from the MERRA-2 reanalysis (Gelaro et al., 2017).
The second method is the tracer scaling method. We scale the inter-annual variability of observed surface N 2 O growth rates (as derived in Section 2.1) with the observed tracer ratio of CH 4 to N 2 O near the tropopause (Ruiz & Prather, 2022;Sankey & Shepherd, 2003). The mole fraction ratio between CH 4 and N 2 O is determined to be 4.3, based on the regression slope from their ACE-FTS satellite observations (Atmospheric Chemistry Experiment -Fourier Transform Spectrometer, level 2 version 4.1 (Bernath, 2017)) in the lower stratosphere ( Figure S1). A similar slope is also found in the GEOS-Chem simulation ( Figure S1). The premise of the N 2 O-scaling method is that the stratosphere-troposphere-exchange is the dominant process controlling the inter-annual variability of surface N 2 O concentrations (Nevison et al., 2004;Ruiz et al., 2021).
where represents the mean vertical velocity and ′ ′ is the meridional eddy heat flux (overbar denotes zonal mean). and ′ ′ are computed from 3-hourly MERRA-2 reanalyzed meteorological fields. Additionally, a represents the radius of the Earth, z altitude, and latitude. The subscripts z and represent partial derivatives with respect to altitude and latitude respectively. We integrate globally advective CH 4 flux densities that are computed as the product of the vertical residual velocity ( * ; m s −1 ) and observed CH 4 concentrations (CH 4 ; g m −3 ) near the tropopause. The computation is conducted on a monthly basis. Near-tropopause CH 4 concentrations are derived from ACE-FTS observations.

Inter-Annual Variability of Atmospheric Growth Rates of CH 4 and N 2 O
Figures 1c and 1d show the inter-annual anomalies of tropospheric CH 4 and N 2 O growth rates during 2000-2020, after removing short-term seasonality and long-term trends. The inter-annual anomalies of tropospheric N 2 O growth rates show a pronounced cycle with a period of about 28 months and an amplitude of around ±0.1% (standard deviation), and are in phase with the Brewer-Dobson Circulation variability (expressed as tropical upwelling velocity anomalies) ( Figure 1e) and the QBO (Figure 1f). The deseasonalized zonal mean tropical upwelling velocities in Figure 1e are derived from either meteorological data (MERRA-2) or satellite water vapor measurements (MLS). For the latter, upwelling velocities are derived from the ascent time of satellite-observed water vapor between two pressure levels in the lower-to mid-stratosphere for 8°S-8°N (Flury et al., 2013;Neu et al., 2014;Schoeberl et al., 2008). The QBO shear index in Figure 1f is computed as the difference of the zonal wind between 50 hPa and 20 hPa in Singapore (Neu et al., 2014). Our result is consistent with previous findings that the inter-annual variability in surface N 2 O is dominated by the net flux of N 2 O between the stratosphere and the troposphere (Nevison et al., 2004(Nevison et al., , 2011Ruiz et al., 2021). The two hemispheres are well in sync, also indicating that a global-scale process is at play, as it takes time for regional signals to propagate to the globe.
In comparison, the inter-annual anomalies of the tropospheric CH 4 growth rate ( Figure 1c) have a relative magnitude of ±0.3% (standard deviation), which is larger than that of N 2 O (±0.1%). The periodicity is also less pronounced for CH 4 compared to the 28-month cycle for N 2 O (Figures 1c and 1d). The growth rate anomalies of CH 4 do not in general correspond to that of N 2 O, the Brewer-Dobson Circulation strength, and the QBO (Figures 1c-1e), implying that the variability of surface CH 4 , unlike that of N 2 O, is not controlled by the stratospheric influence ( → ). This is not unexpected as studies have shown substantial inter-annual variabilities of both tropospheric CH 4 sources and sinks Montzka et al., 2011). The above analyses, however, do not rule out the stratosphere-troposphere exchange as a potential contributor to the inter-annual variability of tropospheric CH 4 growth. Quantification of the stratosphere-troposphere flux is required to determine to what degree surface growth rate anomalies are affected by the stratospheric influence.
In contrast to the surface analyses shown above, Figure 2 shows that both CH 4 and N 2 O anomalies near the mid-latitude lower stratosphere (40°N-50°N, 150 hPa) measured by ACE-FTS are anti-correlated with the Brewer-Dobson Circulation variability (Figure 1e) with a time lag of 5 months ( = −0.50 ), implying that → for N 2 O and CH 4 are similarly affected by the stratospheric circulation. A strengthened (weakened) stratospheric circulation, often associated with El Niño (La Niña) and easterly (westerly) shear of the QBO (Domeisen et al., 2019), enhances (suppresses) downward transport of CH 4 -and N 2 O-depleted air from the higher part of the stratosphere (where chemical loss is strong), leading to negative (positive) anomalies in CH 4 and N 2 O abundance near the mid-latitude tropopause as well as in their fluxes into the troposphere. Figure 3 shows STE-induced inter-annual anomalies of CH 4 growth rates derived from the three methods described in Section 2.2. The fixed-budget simulation, N 2 O-scaling, and residual circulation methods  Figure 3a) is about 2.0 Tg a −1 (average of ∼2.3 Tg a −1 for the fixed-budget method, ∼1.4 Tg a −1 for the N 2 O-scaling method, and ∼1.7 Tg a −1 for the residual circulation method), which creates ∼0.6 ppb a −1 anomalies at the surface. In comparison, the observed anomaly of the CH 4 annual growth rates is ∼2.8 ppb a −1 (∼7.7 Tg a −1 ) (Figure 1d), the inter-annual variability of wetland CH 4 emissions is ∼8.0 ppb a −1 (∼20 Tg a −1 ) based on the ensemble average of WetCHARTs bottom-up estimation  and that of CH 4 removal by the OH radical is ∼3.6 ppb a −1 (∼10 Tg a −1 ) based on 5% inter-annual changes in the global OH concentration reported in the literature (Montzka et al., 2011). Given the dominance of surface emission ( ) and tropospheric oxidation ( ), the STE signal ( → ) is unlikely to be discerned from surface observations of CH 4 when integrated over the troposphere, which contrasts with N 2 O. Further inspection of Figure 3 shows that → is also a minor player in individual years when strong positive (e.g., 2003, 2014, 2015, and 2020) and negative (e.g., 2000 and 2005) methane growth rate anomalies are observed at the surface.

Quantify the Contribution of Stratosphere-Troposphere Exchange to Surface CH 4 Variability
Given the small magnitude of → variations, the moderate correlation between → and ( = 0.43 ) (Figure 3) also suggests some covariations of → with and/or , indicating that they are regulated by common factors, such as ENSO and QBO. For instance, ENSO modulates variabilities in wetland methane emissions (Zhu et al., 2017) and in tropospheric oxidation (Rowlinson et al., 2019;Turner et al., 2018). QBO can modulate the tropospheric oxidation of CH 4 through its effects on stratospheric ozone and subsequently downward ultraviolet flux (Hamilton & Fan, 2000). Our results also show that the correlation is stronger with CH 4 growth rates in the Southern Hemisphere than those in the Northern Hemisphere ( NH = 0.33 ; SH = 0.53 ) and is stronger in 2010-2020 than 2000-2010 ( 2000−2010 = 0.18, 2010−2020 = 0.55 ). Figure 4a shows surface CH 4 growth rates derived from the fixed-budget simulation as a function of latitude and time. Although the STE-induced surface anomalies occur roughly simultaneously across all latitudes, the magnitude of the surface impacts is not spatially uniform. The largest effect often occurs at high latitudes where the Brewer-Dobson Circulation drives the downward transport of stratospheric air. Based on the fixed-budget simulation, the STE process is responsible for the inter-annual variability (standard deviation) of 1.76 ppb a −1 in the Antarctic and 1.79 ppb a −1 in the Arctic, which are respectively 80% and 43% of the CH 4 growth rate variability observed at the Antarctic (2.22 ppb a −1 ; average of two sites in 70°S-90°S; Halley Station and South Pole) and the Arctic surface sites (4.13 ppb a −1 ; average of six sites in 70°N-90°N; Alert, Barrow, Mould Bay, Summit, Hydrometeorological Observatory of Tiksi, and Ny-Alesund) ( Figure 5). In comparison, the STE-induced surface anomalies are only 20% of observed anomalies globally (Figure 3). The stratospheric influence is also supported by concurrent anomalies in N 2 O observations at these high-altitude surface sites ( Figure 5). These results indicate that the STE-induced CH 4 flux is an important factor, in addition to tropospheric sources and sinks, for interpreting high-latitude surface observations.

Conclusions
This work analyzes the contribution of the stratosphere-troposphere exchange (STE) to the inter-annual anomalies of tropospheric CH 4 growth rates.  We examine the inter-annual growth rate anomalies of CH 4 derived from global surface observations. We find that it is at most weakly correlated with the Brewer-Dobson Circulation and the QBO indices that characterize the variations in the STE. In contrast, the inter-annual growth rate anomalies of N 2 O, which has shown in previous studies to be controlled by the STE (Lickley et al., 2021;Nevison et al., 2004Nevison et al., , 2011Ray et al., 2020), have significant correlations with these indices. This result is consistent with the fact that the tropospheric sources and sinks play an important role for CH 4 , compared to N 2 O, but does not indicate that the contribution of the stratosphere-troposphere CH 4 flux is negligible in all cases.
We then quantify the impact of STE on tropospheric CH 4 concentrations, using three methods (i.e., the fixed-budget simulation method, the N 2 O-scaling method, and the residual circulation velocity or w* method). These methods, though based on varied principles and techniques, all achieve consistent CH 4 STE-induced fluxes for 2000-2020. The results show that the standard deviation of the STE-induced CH 4 flux is 2.0 Tg a −1 , equivalent to a 0.6 ppb a −1 surface growth rate anomaly. This value is only 20% of the observed CH 4 inter-annual growth rate anomaly (2.8 ppb a −1 ), suggesting that the STE is a minor contributor to CH 4 inter-annual growth rate anomaly on a global scale.
We further use the results from the fixed-budget simulation to show the spatial-temporal distribution of the STE-induced growth rate anomalies at the surface. We find that the STE causes surface CH 4 anomalies across all latitudes but with the largest impact at high latitudes. The inter-annual variabilities of STE-induced surface CH 4 growth rates are 80% and 44% of those observed at the Antarctic and the Arctic surface sites, respectively. The STE-induced surface anomalies are particularly large in 2000-2001and 2015-2017in the Arctic and 2003-2004 in the Antarctic. For example, the simulation shows that the STE causes a positive anomaly of ∼4.0 ppb a −1 during 2015-2016 and a negative anomaly of ∼ −4.0 ppb a −1 during 2016-2017 in the polar region. This signal is significant and is clearly seen in surface observations at the Arctic sites.
Our study suggests that the STE can have considerable impacts on high-latitude observations, although its impacts are minor globally. Omitting the stratospheric influence may cause misinterpretation of surface observations in Arctic or Antarctic regions, especially when the STE is at its maximum or minimum.