A 3D-model inversion of methyl chloroform to constrain the atmospheric oxidative capacity

Variations in the atmospheric oxidative capacity, largely determined by variations in the hydroxyl radical (OH), form a key uncertainty in many greenhouse and other pollutant budgets, such as that of methane (CH4). Methyl chloroform (MCF) is an often-adopted tracer to indirectly put observational constraints on :::::::: large-scale : variations in OH. We investigated the budget of MCF in a 4DVAR inversion using the atmospheric transport model TM5, for the period 1998-2018, with the objective to derive information on ::::::::: large-scale, interannual variations in OH and in its spatial distribution ::::::::: atmospheric :::: OH :::::::::::: concentrations. 5 We derived interannual variations in the global oxidation of MCF that bring simulated mole fractions of MCF within 1-2% of the assimilated observations from the NOAA-GMD surface network at most sites. Additionally, the posterior simulations better reproduce aircraft observations used for independent validation, :::::::: compared :: to ::: the ::::: prior ::::::::: simulations. The derived OH variations showed robustness with respect to the prior MCF emissions and the prior OH distribution. The interannual variations were typically small (<3%/year), with no significant longterm trend in OH ::::: global :::: mean :::: OH :::::::::::: concentrations. 10 The inverse system found strong adjustments of the latitudinal distribution of OH, with systematic increases in tropical OH and decreases in extra-tropical OH :::::::::::: concentrations (both up to 30%). These spatial adjustments were driven by intrahemispheric biases in simulated MCF mole fractions, which have not been identified in previous studies. Given the unexpectedly large amplitude of these adjustments and a residual bias in intrahemispheric gradients, we suggest a reversal in the extratropical ocean sink of MCF in response to declining atmospheric MCF abundance (as hypothesized in Wennberg et al. (2004)). This 15 reversal ::::: ocean ::::: source : provides a more realistic explanation for the biases, possibly complimentary to adjustments in the OH distribution. While we identified significant added value in the use of a 3D transport model over simpler box models, we also found a trade-off in computational expense and convergence problems. However, although the signals are smallcompared to assuming interannually repeating OH, ::::: While ::: the :::::: effect :: of ::: the ::::::: derived ::::::: temporal :::: OH ::::::::: variations :: on ::::: MCF ::::: mole ::::::: fractions :: is :::::: small, ::::: these 20 :::::::: variations :: do ::::: result :: in :: an :::::::: improved :::::: match :::: with :::: MCF ::::::::::: observations :::::: relative :: to :: an ::::::::::: interannually :::::::: repeating :::: prior ::: for :::: OH. ::::::::: Therefore, :: we :::::::: consider the derived variations better match the global MCF observations and are relevant for studying the budget of e.g. CH4.

possibility for an important contribution from OH to CH 4 growth rate variations. However, the looseness of derived constraints on OH variations also allowed for a solution with no variations in OH. In an extension of these studies, we investigated in previous work how the use of a relatively simple box model, rather than a more sophisticated 3D transport model, could have affected these conclusions (Naus et al., 2019). We found that large changes in the MCF budget over time (i.e. the sudden drop in its emissions) resulted in significant changes in, for example, interhemispheric transport of MCF and the stratospheric MCF sink. However, accounting for these changes in our two-box model did not alter the conclusion that MCF-derived constraints on 60 multi-annual variations of OH are too uncertain to determine the exact contribution of OH to the relatively small but important CH 4 growth rate variations.
In this study, we present an inversion of MCF in the 3D chemistry-transport model TM5 aimed at constraining OH. The advantage of approaching the problem in a 3D transport model, instead of in a box model, is two-fold. Firstly, by explicitly resolving transport, we avoid the transport biases that hamper simple box models. Secondly, we can fully exploit the available to investigate the Indonesian wildfires (Nechita-Banda et al., 2018). The objective of our set-up of the TM5-4DVAR inverse system is to find the optimal configuration of MCF emissions and OH variations that best reproduce atmospheric observations of MCF. Formally, this objective is quantified as minimization of the cost function J (Equation 1).
(1) 90 J is a function of the state x, which contains all the parameters to be optimized, such as OH. The cost consists of two terms.
First is the deviation from the first guess x prior , weighted by the prior error covariance matrix B. Second is the difference between simulated MCF mole fractions, calculated in the forward version of TM5 (denoted as H), and the real-world observations y, weighted by the observational covariance matrix R. Additionally, in the 4DVAR optimization, the gradient of the cost function ∇J is calculated and used (Equation 2).

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∇J with H T the adjoint of the forward model H. The adjoint of TM5 is extensively described in Meirink et al. (2008) andKrol et al. (2008). Since OH chemistry is non-linear and since we optimized emissions non-linearly (see Section 2.1.2), H T is actually the adjoint of the forward tangent linear model. The derivation of the adjoint OH chemistry is described in Supplement S5.

Inversion set-up
In this section we discuss the set-up of the three inversions we performed. First we describe the set-up of the standard inversion (hereafter referred to as REF); next we describe the corresponding B matrix; finally we describe the two variations of the standard inversion which we performed. Note that the R matrix is discussed in Section 2.2.
In the standard inversion, we used the MCF source and sink fields from the TransCom-CH4 project (Patra et al., 2011).

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Loss fields for OH, stratospheric photolysis and ocean uptake are described in the TransCom-CH 4 protocol. Briefly, the OH fields are a combination of tropospheric OH fields from Spivakovsky et al. (2000), scaled by a factor 0.92, and stratospheric OH fields derived with the 2D MPIC chemistry model (Brühl and Crutzen, 1993). The ocean flux is a first-order sink proportional to MCF mole fractions in the lowest model layer and a spatially variable uptake rate, which maximizes in the tropics. Stratospheric photolysis fields were generated with simulations of the ACTM model (Patra et al., 2009 grid box with an assumed grid-box error of 50%, and with a horizontal correlation length of 500 kilometres and a temporal this choice is that we cannot retrieve the posterior covariance matrix. We instead tested the robustness of derived solutions with respect to the OH and the emission distribution, two very likely sources of uncertainty, in two additional inversions.
In our second inversion, referred to as POP, we redistributed the same annual total MCF emissions as in the REF inversion proportional to population density (as retrieved from CIESIN, Columbia University (2018)). In the third inversion (referred to as TM5OH), we used the same emissions as in the REF inversion, but adopted a tropospheric OH distribution based on a 130 simulation of the year 2006 performed with the full-chemistry version of TM5 (Huijnen et al., 2010), combined with the same stratospheric distribution as in the standard inversion. Differences between the two OH distributions are typically 10-15%, depending on the latitude. The TM5OH distribution has relatively higher OH concentrations in the Northern hemisphere.
On a final note, while we optimized scaling factors for OH per latitudinal band, we prefer to discuss the change in global mean oxidation in further sections, rather than the change in global mean OH. We quantified the change in oxidation as the 135 atmospheric mass-weighted average of k(T )·OH, with k(T ) the temperature-dependent reaction rate between OH and MCF (Burkholder et al., 2015). This is necessary, because we allowed for adjustments in the latitudinal distribution of OH. Since latitude and temperature are strongly correlated, a latitudinal redistribution of OH that conserves global total oxidation often implies a change in global mean OH. In that case, we consider the conservation of global total oxidation the relevant quantity, rather than a change in global mean OH (similar to the recommendation in Lawrence et al. (2001)). We calculate the variations 140 in oxidation relative to the prior, so that for example interannual variations of temperature will not affect these variations in oxidation, since temperature variations remain the same between prior and posterior simulations. Where relevant, we make note of this distinction. We also present results for the latitudinal adjustments in OH.

Observations
2.2.1 Surface observations 145 We used MCF observations from the surface network of the National Oceanic and Atmospheric Administration (NOAA) Global Monitoring Laboratory (GML) as the only observational constraints in the inversion. The network consists of a core set of 7 surface sites that have monitored MCF since 1992, and additional sites have been added since: data from a total of 12 sites are available since 1998. The sites we used, including site abbreviations, are described in Table S1. At each site, paired flask samples are collected at weekly to monthly frequency, following a sampling protocol that typically favors sampling under meteorological conditions that correspond to clean background air. Flask samples are then collected and measured on one central measurement system against the NOAA calibration scale for MCF. The measurement uncertainties we used are those reported by NOAA, which are based on the difference between the mole fractions measured for each flask in a flask pair.
Up to 2018, short-term measurement repeatability remained consistently around 0.5% of the measured mole fraction. On top of the measurement error, we also included a model error that was proportional to the 3D spatial gradients simulated in the 155 atmosphere around the surface sites. Typically, the model error was up to 1% at Northern midlatitude sites (e.g. LEF), and as low as 0.1% at e.g. SPO or ALT. The addition of these two error sources, with no correlations in between, constitute the R matrix (see Section 2.1).

Aircraft campaigns
For validation of the inversion results, we used two sets of aircraft campaigns: the HIAPER Pole-to-Pole Observations (HIPPO, NOAA's surface network results (i.e., in methodology, precision, and calibration consistency). ATom results from deployments A-2 and A-3 were also included in this work, as those flask samples were analyzed on the same NOAA instrument as the surface network flasks. We exclude from our analysis a subset of results from HIPPO-1, as well as all of HIPPO-2 and the ATom-1 missions, since samples from these deployments suffered from a deployment-specific measurement interference (a 170 portion of H-1 and all of H-2) or were analyzed on a different instrument in NOAA that exhibited poorer precision (A-1).

Variations in the atmospheric oxidative capacity and in MCF emissions
In Figure 1, we show the monthly anomalies in global oxidation (different from global mean OH: see Section 2.1.2), as derived in the three inversion set-ups. We have shown the entire twenty-year inversion period, which will include a spin-up and spin-175 down period of 1-2 years. For example, even though our initial MCF mole fraction fields are realistic, the strong positive oxidation anomaly in 1998 might be linked to errors in the initial field.
Interannual variations in global oxidation are typically small (∼ 2%). In this, there is consistency between the different in-  two, as it shares its emission distribution with the TM5OH inversion, and its OH distribution with the POP inversion. Contrastingly, the POP and TM5OH inversion share neither. This indicates convergence problems, rather than a significant influence from prior distributions. For reasons outlined in Section 3.5, we attribute differences in variations mostly to differences in the degree of convergence. Because the REF inversion resulted in the best match with observations (see Section 3.2), and because the REF inversion is most consistent with a set of ten-year inversions (see Supplement S4), we consider it to be the solution 185 that converged best.
As outlined in Section 2, we optimized OH in 45 latitude bands of 4 • each. Figure 2 shows the adjustments in OH per latitude band through time, for the standard inversion. Clearly, adjustments to zonal mean OH can be much larger (up to 30%) than adjustments to annual global mean OH (up to 5%). Moreover, there is a strong systematic tendency to increase tropical OH, and decrease extra-tropical OH, especially in the SH. This tendency was observed in each of the three inversion set-ups, 190 i.e. also when a different OH field was used. We further investigate this tendency in Sections 3.2 and 3.4.   However, the inversion cannot reproduce some of the observed gradients between stations, especially gradients within hemispheres. In Figure 5, gradients between three pairs of NOAA surface sites are shown. Firstly, the interhemispheric gradient between ALT and CGO is captured well in all inversions. This interhemispheric gradient is strongly affected by emissions and therefore the inversion framework can adjust it with relative ease.  Table S1. Bottom two panels: Timeseries of the posterior measurement-model mismatch at MHD (top) and SMO (bottom) from individual observations, from monthly means and from twelve-month running averages, with the average total error shaded in gray.
In contrast, intrahemispheric gradients are less well captured. In Figure 5 it can be seen that both the gradient within the Northern Hemisphere, between ALT and MLO, and the gradient within the Southern Hemisphere, between SMO and CGO, are underestimated. More precisely, MCF mole fractions simulated at tropical sites are systematically too high (1-2 σ, with σ the total error), with a smaller, opposite bias at high-latitude sites (0.5-1 σ). The large latitudinal adjustments of OH (see Figure 2) are an attempt by the inversion to reduce this bias, but the adjustments only reduce the bias partly ( Figure 5). As an example, 220 the SMO-CGO gradient is, in the REF inversion, increased from -1.5% to -2%, i.e. an increase of 30%, which corresponds well with a 30% latitudinal adjustment in OH. However, the observed gradient is larger still at -3%. We investigate this residual bias in more detail in Section 3.4.

We have quantified the skill of a simulation that uses optimized OH and MCF emission fields from the REF inversion to
reproduce observed MCF mole fraction in a root-mean-squared error (RMSE) per site, averaged over the 1998-2018 period 225 (top panel in Figure 6). We distinguish between the RMSE of individual observations (as used in the optimization, in red), the RMSE of the monthly mean values (cyan), and the RMSE of twelve-month running averages (green). This helps to disentangle the contribution of short-term versus long-term variations to the model-measurement mismatch. Also shown is the pre-defined total observational error (gray), which we used in all inversions. The total error consists of a model error based on modelled At all sites, the posterior RMSE of individual observations exceeds the total error. However, at most sites, the RMSE comes more in line with the total error for monthly means, and especially for twelve-month running averages. This implies that, largely, the RMSE is related to short-term variations. Our inverse system, which employs relatively smooth and stiff OH and 235 emission fields, has limited capability to fit short-term variations of MCF. Short-term variations in MCF are likely related to errors in the emission distribution and in small-scale transport, since OH has an integrated, slow effect on MCF mole fractions.
Therefore, we do not expect these residuals to affect our OH estimate significantly. Importantly, we point out that our initial error estimate might have been overly conservative (mostly < 1%, see Figure 6), which is supported by error estimates used in previous MCF inversions (1-2% for individual observations (Bousquet et al., 2005); 5% for monthly, hemispheric averages 240 (Turner et al., 2017;Rigby et al., 2017)). We conclude that, as long as we capture long-term variations of MCF at each site, the unresolved residuals on a sample-to-sample basis are unlikely to impact our conclusions. At some sites (notably SMO, MLO and PSA), we have identified systematic biases which are of more concern, and these result in relatively large RMSE even in twelve-month running averages. We further discuss systematic offsets in Section 3.4.

HIPPO and ATom aircraft campaigns 245
As the inversions were driven by observations from the NOAA surface network, we used the HIPPO and the ATom aircraft campaigns as independent data sources for validation. The main added value of the aircraft over surface observations is that the former provide snapshots of vertical gradients. When observed MCF mole fractions from all campaigns are compared to model-sampled mole fractions (Figure 7), a few features emerge.
Firstly, we find that the optimized REF simulation overestimates MCF mole fractions in the lower stratosphere at high 250 latitudes (> 50 • ) in both hemispheres (left panel in Figure 7). This bias points to limited ability of TM5 to capture vertical gradients in the downward branch of the Brewer-Dobson circulation. A similar bias was identified in TM5 simulations of CH 4 , which has a stratospheric sink similar to MCF (Houweling et al., 2014).
In addition to the large overestimation at high altitudes, we also find a weak but significant positive correlation between altitude and model-measurement mismatch (R 2 =0.12; p<0.001). Close to the surface, the average model-measurement mismatch 255 is close to 0%, which increases to 1.5% at 10km. In other words, TM5 increasingly overestimates MCF mole fractions at higher altitudes, resulting in an underestimate of vertical gradients in TM5.
Positively, we find that the inversion improves the agreement between simulations and aircraft observations (right panel in In conclusion, assimilation of surface observations improves agreement of our simulations with aircraft observations. However, modelled vertical gradients of MCF remain slightly smaller than those observed, although the maximum model bias 265 is 1.5%, which is small compared to the 5% random error. Moreover, since these biases are consistent between the aircraft campaigns, we deem the impact of the biases on derived interannual and multi-annual variability of OH or MCF emissions small. Estimates of the total atmospheric oxidizing capacity are more likely to be affected by incorrect vertical transport. While TM5 typically compares well to other transport models in terms of large-scale transport features, for example in the Age of Air experiment (Krol et al., 2018), this comparison does highlight the crucial role of aircraft campaigns in helping to identify 270 remaining transport model biases.

Physical drivers of OH variations
The El Niño Southern Oscillation (ENSO), a dominant mode of natural atmospheric variability, has previously been suggested to influence interannual variations in OH (Prinn et al., 2001;Turner et al., 2018). ENSO affects many processes that are linked to OH, such as temperature, atmospheric moisture, lightning, wildfires and atmospheric transport. The correlation improves if we leave out 1998 as a spin-up year, since in 1998 we derive a positive OH anomaly coinciding with the an El Niño event, counter to the negative correlation we find over the rest of the timeseries. We note that the correlation is not driven by only a few outliers. Namely, if the outliers are removed (2010 and 2015), we still find correlations of -0.60, in 280 that case even without a time lag. In general, we deem the negative correlation a robust property of the whole timeseries.
That variability in OH correlates with a dominant driver of atmospheric variability seems logical. However, attribution of the negative correlation to specific processes is difficult, given the large number of processes that are affected by ENSO and that in turn could affect OH. Nonetheless, we can hypothesize. For example, El Niño years (high MEI) are associated with more wildfires, resulting in higher CO emissions which could suppress OH concentrations (e.g., Nechita-Banda et al., 2018). La Niña years (low MEI) are associated with increased convection over the Pacific, increased lightning NO x production and by extent increased OH recycling (Turner et al., 2018).
The correlation between MEI and the OH variations derived in a two-box model (Naus et al., 2019) is -0.01 if we do not tune the box model with a 3D transport model, and -0.34 if we do. This increase after accounting for some of the box model biases, and the even higher correlation if we move the inversion completely to a 3D transport model, shows that the correlation 290 becomes apparent only when realistic transport of a 3D transport model is included. For example, transport variations related to ENSO have been shown to strongly affect interhemispheric differences of CO 2 (Francey and Frederiksen, 2016) and of CH 4 , as well as mole fractions of MCF at SMO (Prinn et al., 1992).

Explaining the underestimated intrahemispheric gradients of MCF
The systematic underestimation of intrahemispheric gradients in both hemispheres deserves further elaboration, since the in-295 version framework has difficulties to adjust OH and emissions in such a way that intrahemispheric gradients are reproduced.
MCF mole fractions are overestimated in the tropics and underestimated at high latitudes ( Figure 5). To resolve these biases, the inversion introduces large adjustments in the latitudinal distribution of OH (up to 30%, see Figure 2). A set of inversions that only covered the 1998-2008 period were run to higher convergence (see Supplement S4). These inversions show that more extreme adjustments in the latitudinal OH distribution (up to 60%) better reproduce intrahemispheric gradients. However, in-300 trahemispheric gradients were still not quite captured, and substantially higher MCF emissions were required to reproduce the gradients. The amplitude of these adjustments seem physically unlikely and in none of the inversions the biases were fully resolved. Therefore, we consider here alternative, or complimentary explanations for the biases, that were not explored in the inverse framework. We emphasize that the biases are quite constant over the twenty-year period, and while especially pronounced in the Southern Hemisphere, also present in the Northern Hemisphere. These aspects make anthropogenic emissions 305 as a sole explanation unlikely.