Joint Application of Concentration and Δ O to Investigate the Global Atmospheric Co Budget

Most previous top-down global carbon monoxide (CO) budget estimates have used only concentration information and shown large differences in individual source estimates. Since CO from certain sources has a specific isotopic signature, coupling the concentration and isotope fraction information can provide a better constraint on CO source strength estimates. We simulate both CO concentration and its oxygen isotopologue C 18 O in the 3-D global chemical transport model MOZART-4 and compare the results with observations. We then used a Bayesian inversion to calculate the most probable global CO budget. In the analysis, δ 18 O information is jointly applied with concentration. The joint inversion results should provide more accurate and precise inversion results in comparison with CO-only inversion. Various methods combining the concentration and isotope ratios were tested to maximize the benefit of including isotope information. The joint inversion of CO and δ 18 O estimated total global CO production at 2951 Tg-CO/yr in 1997, 3084 Tg-CO/yr in 1998, and 2583 Tg-CO/yr in 2004. The updated CO budget improved both the modeled CO and δ 18 O. The clear improvement shown in the δ 18 O implies that more accurate source strengths are estimated. Thus, we confirmed that the observation of CO isotopes provide further substantial information for estimating a global CO budget.


Introduction
Carbon monoxide (CO) is closely coupled to the hydroxyl radical (OH), which produces CO through the oxidation of methane (CH4) and other hydrocarbons while also being the predominant removal agent for CO as well [1,2].Thus CO-and OH-related chemistry directly and indirectly affects the abundance of other atmospheric gases including methane and halocarbons [3].In conjunction with NOx, CO also plays a central role in determining the abundance of tropospheric ozone [4,5].Carbon monoxide has also been useful as a tracer of transport for pollutants [6,7] and fire emissions [8] and as an additional constraint for CO2 fluxes [9].
It is known that methane oxidation, fossil fuel and biofuel combustion, non-methane hydrocarbon (NMHC) oxidation, and the burning of biomass are the major sources of CO (Table S1).The complex distribution of these various sources of CO, together with the short lifetimes and large temporal variations of some of its chemical precursors, make it very difficult to estimate a reliable global CO budget [1,10].Reaction with OH is the primary sink, removing approximately 90% of CO from the atmosphere [11][12][13][14], with surface deposition accounting for the remainder [15].
The inverse modeling technique estimates the source strength of atmospheric components by constraining a priori source inventories using observational data of chemical species and an atmospheric chemical transport model.Most previous CO source strength estimates have used only concentration information [14,[16][17][18][19][20][21][22][23].Regardless of the origin of concentration data sets (satellite, aircraft, or surface measurement), there were discrepancies of up to 30% in total CO inventory estimates as well as large variations among the source types of 15%-100% (Figure 1).
Since fractionation of isotopes occurs in most biological, physical and chemical processes, the different source types of CO have different isotope ratios.Thus, isotope measurements provide strongly complementary source information for finding more realistic estimates [24][25][26].
The isotope ratio of a sample is generally referenced to the isotope ratio in a standard material and expressed as: ( 1) 1000 where R is the ratio of the minor isotope to the major isotope, and the standard used for oxygen isotope ratio (δ 18 O) of CO is Vienna Standard Mean Ocean Water (VSMOW).
There have been several δ 18 O and δ 13 C values reported for the main sources of CO (Figure 2 and Table S2).Since δ 13 C and δ 18 O signatures of each CO source are uncorrelated, each carbon and oxygen isotope contains its own isotopic source signature and can be independently applied in the budget optimization [24,27].For some sources, the C or O isotope composition is clearly different from the other sources and this enables us to separate it from the others.For instance, the oxygen isotopic signature of CO from the combustion process such as fossil fuel combustion and biofuel use is distinctively different to non-combustion sources (Figure 2).S2.The size of each circle represents the relative source strengths estimated in IPCC 2001 report.
Including isotope information in an inversion study can lead to more accurate and precise source strength estimates [28], since isotope measurements provide significant additional information on the sources by enabling separate analyses of C 16 O and C 18 O, instead of CO alone.There have been several concentration-isotope ratio inversion schemes that were applied to find the best source strength estimates of atmospheric CO2 and CH4 [24,26,[29][30][31][32].For carbon monoxide, Bergamaschi et al. [24] analogously adopted the methane isotope inversion technique [33] and showed isotope information can constrain the CO sources more reliably.Along with a posteriori concentration, a posteriori isotope ratio also provides additional information to confirm the inversion results and this adds more reliability to the inversion results.
The goal of the work presented here is to improve and develop a new joint inversion method of CO and its isotopes for accurate CO budget estimation.Thus, optimization methods that maximize the benefit of including isotope information are investigated.The availability of an enhanced 3-D global chemical transport model and updated isotope ratio measurements enables more robust CO inversion results.Here we use MOZART-4 (Model for OZone And Related chemical Tracers) [34] to simulate CO and δ 18 O in ways which agree fairly well with observations.Although, we ran the model for CO concentration and δ 18 O from 1996 through 2004, the availability of isotope measurements allows us to constrain CO budgets for 1997, 1998, and 2004.For constraining the sources of CO, although the δ 13 C signature from the methane oxidation is clearly different from the other sources, this source is relatively well known.In addition, δ 13 C signatures are close to each other for some major sources (e.g., NMHC oxidation and fossil fuel use) while the oxygen isotopic source signatures are distinctly different for those sources.Therefore, this study focuses on the oxygen isotopes of CO and shows these have a greater potential to separate the CO sources [1,35,36].
The outline of the paper is as follows.The measurements of carbon monoxide concentration and its isotope ratios measurements used in this study are described in Section 2. In Section 3, detailed descriptions of the forward model simulation including inventories of a priori sources, methods of C 18 O incorporation, and evaluations of model performance are presented.Next, the development of various joint inversion schemes combining concentration and isotope ratio information are presented (Section 4).In Section 5, the results of inversion analyses including the source strength estimates are discussed.

Observation of Atmospheric Carbon Monoxide and Its Isotopes
The concentration and isotope ratios of CO used here have been measured from eight stations and most air samples were collected weekly or biweekly.The location of each station is shown in Figure S1.Table S3 shows the periods of model simulation, CO, δ 13 C and δ 18 O observations at each sampling location.Monthly averaged concentration and isotope ratios were used in the inversion analyses.A subset of the NOAA (National Oceanic and Atmospheric Administration) GMD (Global Monitoring division) network CO mixing ratios [37,38] was also used to get inversion results for comparison.Each concentration and isotope ratio data set was inverted individually or together to update CO source strengths.
Because the average lifetime of tropospheric CO is approximately two to three months [39], the background CO can be considered zonally well-mixed in the atmosphere and its inter-hemispheric mixing is quite limited [16,40].Thus, sampling locations were carefully selected to represent the background state of the atmosphere at specific latitude zones.
The methodologies of the sampling and measurement techniques are well described in [41][42][43].A brief description of the isotope analysis method is given here.The collected air samples are processed through a cryogenic vacuum extraction line.Water vapor and most trace gases are trapped in the first two cryogenic traps and CO is then oxidized to CO2 by Schütze reagent [44].The produced CO2 is collected in the last cryogenic trap.Concentrations are determined by measuring the total pressure of the oxidized CO in a calibrated volume, and isotopes are measured in an isotope ratio mass spectrometer.The manometrically measured CO mixing ratios are consistent with the NOAA GMD CO measurements (Figure 3).Additionally, the National Institute of Water and Atmospheric Research (NIWA) data sets used gas chromatography method as well for quality control.The δ 18 O of CO2 is converted to the δ 18 O of CO and the precision of measurement is ±2 ppbv for concentration, ±0.2‰ for δ 13 C and ±0.8‰ for δ 18 O [36,41].
A tracer version of MOZART-4 [34,39,51] was developed and applied in this study.Chemical reactions directly related to CO are included in the model along with prescribed mixing ratios and other parameters such as OH concentration and chemical production rates.This information is pre-calculated and saved from the simulation of a full-chemistry version of MOZART-4.Due to its simplified chemistry, the tracer version is much faster than the regular version of MOZART-4, yet still allows for analyzing the relationships between sources and concentrations or isotope ratios.In the tracer version of MOZART-4, we tagged CO for each source, isotopologue, and geographic regions of origin, which enables tracking the CO and its isotopes.Fossil fuel use, biofuel use, and biomass burning sources were divided into nine emission regions: North America, Central America, South America, North Asia, South Asia, Australia, Europe, North Africa, and South Africa.Hence, 62 tagged tracers are included in the model.
The MOZART-4 simulation used in this study has a horizontal resolution of 2.8° × 2.8°.There are 28 levels from the surface to the top of the stratosphere (2hPa).The model was driven by the NCAR reanalysis of the National Centers for Environmental Prediction forecasts (NCEP/NCAR reanalysis) [52,53].The chemical species react and are transported in the model every 20 min.The time period of model simulation was from April 1996 to December 2004, and the first six months' simulations were discarded since those months were considered as spin-up months.

Sources and Sinks of Atmospheric CO
The global budget of a priori CO sources used in this study is shown in Table 1.Carbon monoxide emissions from fossil fuel and biofuel use are taken from [17].They derived CO source strengths from April 2000 to March 2001 using MOPITT (Measurement of the Pollution in the Troposphere) satellite observations and updated the inventory monthly for 15 regions.In Figure 1, some previous fossil fuel and biofuel CO inventories are shown and a priori fossil fuel and biofuel used in this study (679 TgCO/year) is a little lower than the average (799 TgCO/year).
The Global Fire Emissions Database (GFED) version 2 [54] inventory is used for the biomass burning source of CO.Annual CO emissions estimated by the GFED-v2 are shown in Table 1.
Carbon monoxide is also directly emitted from other natural sources: vegetation and the ocean.Carbon monoxide emissions from live or dead plant matter are from the photodegradation or photooxidation of cellular material [55] and oceanic CO is mainly produced by the photochemical oxidation of dissolved organic matter [56,57].The inventories of these natural sources are taken from the POET atmospheric gas inventory [58] (Table 1).
Methane-derived CO is the most accurately constrained CO source because of the long lifetime of CH4 (~10 years) [34,36,59,60], known atmospheric concentration, and well-known oxidation rate.Carbon monoxide from methane oxidation is calculated on-line using methane distributions specified by the zonal average of the monthly mean NOAA GMD surface CH4 measurements.
In the tracer version of MOZART-4, NMHC-derived CO is calculated by subtracting on-line calculated methane-derived CO from the CO from total hydrocarbon oxidation taken from the full chemistry MOZART-4 runs.Reaction with the hydroxyl radical is the dominant sink of tropospheric CO.The calculated lifetime of methane from the MOZART-4 run is 10.5 years [34] and previous estimates of 9.4 years [59] indicate that the model may slightly underestimate globally averaged OH.Another minor CO sink is its surface deposition, which is controlled by the activity of microorganisms in the soil.The soil uptake velocity is a function of soil moisture content of different ecosystems and is implemented in MOZART-4 [34,61].

Incorporation of Oxygen Isotopes
To analyze the oxygen isotopes of CO in the model, each source of CO was determined for C 16 O and C 18 O and specific chemical reaction rates and deposition velocities were assigned to each isotopologue.To build inventories of CO isotopes, for the direct emission sources, the total CO inventory is divided based on δ 18 O source signatures.
Both isotopologues of carbon monoxide are produced from the CH4 + OH reaction in the model:  16 O + OH and C 18 O + OH respectively.When CO is oxidized by the hydroxyl radical, the behavior of C 18 O shows an inverse mass dependence.Thus, C 18 O is preferentially removed from the atmosphere (KIE = 0.990) and this is weakly dependent on pressure.The rate constant for CO + OH itself is strongly dependent on pressure [62,63].The reaction rate (k) of the CO + OH reaction and the reaction rate ratio (η) between C 16 O and C 18 O are as follows: 11.6 0.0042 1.9 10 Carbon monoxide removal from soil uptake is similar to the normal KIE and the fractionation has been measured as η(δ 18 O)soil sink = 12‰ [64].
The isotopic source signature from fossil fuel combustion applied in this study is 23.5‰ [42,65].Based on Brenninkmeijer [42] and Brenninkmeijer and Röckmann [10], 0‰ is used for δ 18 O in CO from methane and NMHC oxidation sources.Since two globally averaged estimates of δ 18 O in CO from biomass burning have been reported (16.3‰ [42] and 18‰ ± 1‰ [62]), a rough average of the estimates (17.5‰) is applied in the forward model.For the ocean source of CO, 15‰ is used in the model [66].
Since there is no previous study on the δ 18 O of biogenic CO and biofuel CO (Table S2), δ 18 O values from those sources are estimated in this study.δ 18 O of CO from the direct biogenic emission was estimated to be 0‰.While the factors controlling this source are not well known [67], it is a minor source of CO (60-160 TgCO/year) [1].Thus, uncertainties originated from this assumption should not largely affect the modeled results.The isotopic source signature from biofuel use is assumed to be the same as δ 18 O of CO from biomass burning.

Simulated Atmospheric [CO] and δ 18 O: Model Evaluation
Because an inverse modeling method relies on the assumption that the physical-chemical connection between the parameters (e.g., source strengths and reaction constants) and the observed properties (e.g., concentration and isotope ratio) are known, if a chemical transport model does not simulate the real measurement accurately, its source estimates would lose reliability even though all of the mathematical assumptions are correct.To get more confidence in our forward modeling results, NOAA GMD CO concentrations are shown together in Figure S2.
Three different measures are used here to assess the model performance: chi-squared (goodness of fit) test, model-observation difference and correlation.Usually the "correlation" represents dissimilarity of the trend or patterns between the modeled property and measured property and the "distance" shows the offset between the model and measurements.If a model accurately reproduces observational data, the distance (d) will be close to '0' and correlation (ρ) will be close to "1".The goodness of fit of a model statistically describes how well a simulated result fits the measured data set.The reduced chi-square (χred 2 ) is chi-square divided by the number of degrees of freedom and this estimates the ratio of the variance of modeled data set to the variance of measured data set.If the observed data are well explained by the model, the χred 2 value will be close to 1.
The results of the evaluation at each station are shown in Table S5.For the overall data sets, the modeled and measured concentration showed a strong correlation (ρ = 0.94) which implies the model captures the seasonal and interannual variation of the CO sufficiently and the mean model-observation difference was 10.5 ppbv.Figure 4 shows Southern Hemispheric (SH) CO concentrations are slightly overestimated by the model (SCO: 6.2 ppbv, BHD: 6.4 ppbv).This possibly results from the underestimation of OH or overestimation of some sources.However, if OH is increased, the modeled δ 18 O will be smaller and therefore further removed from the 1:1 correlation line (Figure 4).Hence, to fit both δ 18 O and CO, the strength of sources having a light δ 18 O signature (oxidation sources) should be reduced.Since the NMHC oxidation source has a strong seasonality (Figure S3), even if the source strengths are decreased, it is not applicable to explain the year-round overestimation of the modeled CO concentration.In Manning et al. [35], they estimated CO yield from the CH4 oxidation is less than 0.7 based on δ 13 C measurements while 1 is used for the yield in this study which is also assumed in Duncan et al. [68].This suggests the presented CH4 oxidation source might be overestimated in the SH.In the NH, especially during the winter, modeled concentrations are generally lower than measured concentrations (Figure 4).For δ 18 O, the model accurately reproduced observations at high latitude stations (ICE, ZEP, ALT) while the modeled δ 18 O were lighter than the observations at mid-and low latitude stations.In high latitudes, the dominant sources (fossil fuel and biofuel combustion) have isotope ratios that are similar to the mean isotope ratios of total CO.Thus, the isotopic data is not sensitive to their source strength change, particularly during winter.For example, the wintertime oxygen isotope ratio from the biofuel source in high latitude is approximately 12‰ and total δ 18 O‰ (shown in Figures S3 and S4 respectively), so variations in this source have a minimal effect on δ 18 O but can improve the concentration fit.In the mid-and low latitude NH, the underestimations of the modeled [CO] and δ 18 O implies that the 18 O enriched sources (fossil fuel, biofuel and biomass burning) are underestimated in the model.
The χred 2 of the forward model run for CO concentration was 0.65 and of δ 18 O was 2.29.The modeled δ 18 O shows good agreement to measurements, however, the simulation results of CO concentration were even more reliable; ρ[CO] = 0.94 > ρδ18O = 0.86 and χred 2 [CO] = 0.65 < χred 2 δ18O = 2.29.This supports the discrepancies of global CO source distributions of previous studies shown in Figure 1; the current estimation of total CO emission is relatively well defined, whereas the strength of each source is less certain.The δ 18 O signatures of natural sources such as biomass burning and NMHC oxidation have more variability and uncertainty which might lead to additional errors in the isotope simulation.

Bayesian Synthesis Inversion
The Bayesian inversion method was used to find the best estimates of source strengths of CO.Assuming a Gaussian distribution for all probability distributions and a linear relationship between sources and concentrations [14,16,18,20,21,24], the measured concentration of CO can be expressed as: where y is the observed concentrations of CO, x is the vector of each CO source strength, K is the Jacobian matrix that links concentration and source strength calculated from the forward chemical transport model and e is the total error of measurement and model.Since K describes the sensitivity of CO concentration to the source change, Kx represents a modeled concentration of CO that expressed itself as a sum of the concentration of each source category.The maximum a posteriori (MAP) probability solution of the inverse problem is finding an x ( ˆ( | ) x xP x y dx =  ) where the posteriori probability distribution is a maximum, i.e., X a denotes a matrix of a priori source strength estimates, S e is the error covariance matrix of the model, S a is the error covariance matrix of prior information and x is a matrix of optimized source strengths.The covariance matrix of x is expressed as:

Assigning Uncertainties in the Analyses
Two error covariance matrices are involved in the inversion calculation using the Bayesian method.Properly specifying and assigning those uncertainty terms is a particularly important part of the analysis since both inversion results and the a posteriori error covariance matrix (Ŝ) can be sensitive to the error covariance matrices [28,69].

Uncertainties in Measurements: S e
The total observations error (S e ) is a diagonal covariance matrix comprised of the following uncertainties: measurement error, representation error, and forward model error.The measurement error is the sum of all factors affecting the accuracy of the measurement including instrumentation error, CO extraction system error, and inter-calibration error.Brenninkmeijer estimated the maximum absolute uncertainty (m.a.u.) of CO concentration as 2% and of δ 18 O as 1‰ [42].The same extraction system design for analyzing CO concentration and measuring isotope ratios are used in this study.The errors of measurements presented here (1 σ) are calculated to be 1.3% and 0.27‰, respectively, through the more than 300 calibration runs.Therefore, the m.a.u. of our data sets is also conservatively estimated as 2% for concentration.Since, for δ 18 O measurements, the systematic error produced from the Schütze oxidant is dominant and is less than 1‰, the m.a.u. is estimated at 1‰ (Table 2) [41,42].To apply the errors to the inversion analysis, the estimated error of CO and δ 18 O are converted to the error of C 16 O and C 18 O.The error of C 16 O is considered to be the same as that for CO.The δ 18 O error is converted for C 18 O error using both C 16 O error and δ 18 O error because, by the definition of the δ-value, δ 18 O is the ratio of C 16 O to the C 18 O.Thus, the total measurement error is propagated to 5.4%.Typically, in CO inversion studies, the measurement error has been evaluated as less than 2% [20,69].However, 5.5% for the measurement error was applied here since the uncertainty of the isotope ratio is commonly higher than the uncertainty of the concentration due to the trace amount of the minor isotopes.
Because, practically, there is no 'true' model to measure the uncertainties of the chemical transport model, errors in forward models are very hard to quantify.Sometimes the uncertainties of the forward model are neglected and the model is assumed to be perfect [16].In this study, the errors related to the forward model (e 2 representation and e 2 forward model) are treated as described below.
Representation error is an aggregated error of the mismatch of the spatial and temporal scale between the model and observation.Usually, for analyzing both concentration and isotope ratios of CO, air samples are collected for a couple of hours at a surface station while, in the model, the size of the corresponding grid box is 2.8° × 2.8° and the concentration is averaged for a day.Since the CO monitoring sites used for this inversion analysis are located in remote locations, local sources minimally affect the CO measurements.It is also assumed that CO is blended well in the atmosphere on the scale of each model grid box because the average lifetime of CO is several months.Therefore, the contribution of representation error to the uncertainty analysis is considered to be minimal.In [69], aircraft measurements in each model grid box were used to define the representation error.The variability of the direct measurements was approximately 5%-10% in each 2° × 2.5° grid.The representation error is analyzed by calculating the percentage of mean variance of monthly modeled concentration from the overall mean concentration and 8% of the concentration is obtained in this study [19,70,71].
Another uncertainty related to the model is the forward modeling error.It consists of errors raised from inaccurate or incomplete chemical reactions, transport, and model parameters (e.g., reaction rates and kinetic isotope effects).Error estimation is performed following [69], which assumed the residual of the relative error (i.e., the standard deviation of (Ka − y)/y where Ka denotes modeled concentration and y is observed concentration) represents the uncertainties of the chemical transport model.In this study, the forward modeling error was calculated to be 8.5% of the concentration.
The observation error covariance matrix S e is derived from the sum of the measurement error and representation error and forward chemical model error.The total observation error is approximately 13%.Considering unknown and unevaluated possible error factors, 15% is used in this study for the total observation error in the inversion analyses [9,16,18,20,69,72,73].

Uncertainties in a Priori Source Estimates: S a
The bottom-up estimates of CO source strengths still have large error ranges and the top-down estimates cover a wide range (Figure 1).Thus, to start with, large uncertainties are assigned to the a priori emissions, which weakly constrains the sources.In [74], the uncertainty of global annual emissions of biomass burning CO was estimated at 30%; however, they also indicated that the regional variations are often much higher (factor of 2-5).Duncan et al. [68] showed a 25% uncertainty remains for fossil fuel CO despite rigorous and extensive bottom-up estimates.The inconsistency of source estimates from the previous inversion analyses shown in Figure 1 also indicates that the uncertainty of each source is at least 20% for anthropogenic, 50% for biomass burning, 100% for biogenic hydrocarbon oxidation, and 15% for CH4 oxidation [14,[16][17][18][19][20][21].Previous studies also carefully started inversion analyses using weak constraints: 50% of a priori source strength estimates [20,21,68,69,75].In this study, to find the best estimate of the a priori source error covariance matrix (S a ), a sensitivity test was performed to analyze the response of inverse modeling results with varying S a .
In Figures 5 and 6, smaller optimized model-observation differences were found with higher a priori source uncertainties (S a ).However, the inversions with larger uncertainties frequently failed to constrain the sources.Not only a posteriori errors are increased after inversion for some cases but also unrealistic large source changes or negative sources are obtained.Assigning more than 100% of the uncertainties of each CO source tends to ignore the a priori information too much during the inversion process.In contrast, the inversion analyses fail to improve the a priori inventories with small uncertainties, e.g., 10% or 20%, because they significantly rely on the a priori source information rather than the observations.The distance between the measured concentration and the a posteriori concentration converged to a specific value after assigning higher than 50% of source uncertainties in the all three cases (97NH, 04SH, and 04NH in Figure 5); the inversion results are insensitive to larger than 50% error covariance matrices.Hence 50% of the current source estimates are determined to be within the most proper uncertainty range, based on our sensitivity test results and prior investigations.In addition, instead of assigning the same errors for all of the sources, additional constraints were given to the methane oxidation sources and fossil fuel sources.Because atmospheric methane has a long lifetime, its reservoir is relatively well known and only a 7% interannual variability was observed during 1978-1998 [76].Moreover, in these model studies, the CH4 oxidation source is directly scaled to the NOAA GMD surface measurements.Therefore, 10% is assigned for the a priori error of methane-derived CO.For the fossil fuel source, many inversion studies have been updating the fossil fuel source inventory (Figure 1) and this is relatively well known, compared to the natural sources.The a posteriori error of the fossil fuel emission inventory in [17] was evaluated as 13% for the global average, and the variability of anthropogenic source strength estimates shown in Figure 1 was 18%.Thus, 18% was defined as the maximum uncertainty and we choose 20% for the uncertainty (Sa) of fossil fuel sources, which arbitrarily added 2% to loosen the constraint (Sa).Thus, the a priori source estimation errors (Sa) are set to 10% for methane oxidation sources, 20% for fossil fuel sources, and 50% for all other sources.

Inversion Schemes; Incorporation of Isotope Information to the Source Optimization
Since the units of concentration (ppbv) and isotope ratio (‰) are different, the meanings of unity for the model-observation difference are very different and are not comparable.The impact of the different units should be correctly accounted for the inversion [77].Previous studies [24,26,33] have solved the inverse problems through minimizing the model-observation difference without balancing the two properties.
Furthermore, for carbon monoxide, in contrast to carbon dioxide or methane, its lifetime is short and, therefore, its temporal variation is relatively large.This is especially important for C 18 O.For example, in the NH mid-latitude, the typical inter-seasonal variation of δ 13 C of CO is 5‰ and δ 18 O of CO is 8‰, while δ 13 C of CO2 is 0.4‰ and CH4 is 0.5‰ [36,43,78,79].Thus, if the long-lived species' isotope-inverting methodologies are analogously applied to the CO isotope inversion, nonlinearity problems develop and can affect the inversion results [33].
In this study, a two stage isotope inversion scheme is devised that is able to avoid the shortcomings of the previous isotope inversion methods as well as more effectively constrain the sources of CO.

Decoupled Inversion
The scheme of the decoupled inversion is basically an extension of the CO-only inversion that has been performed by the previous Bayesian synthesis inversion studies.While the CO-only inversion uses the concentration of CO, the decoupled inversion uses C 16 O and C 18 O separately.Since the measurement errors and model uncertainties in C 16 O and C 18 O are assumed to be uncorrelated, the sources of C 16 O and C 18 O can be individually optimized by using the C 16 O and C 18 O information: where, 16 O and 18 O indicate the C 16 O and C 18 O data sets.
The two independent inversion results allow for the estimation of both a posteriori C 16 O and C 18 O source strengths.The ratio of 16O x to 8 1 O x also provides a posteriori δ 18 O signature of the CO sources.This approach can be applied to evaluate potential correlations among isotopologues in isotope inversions.

Coupled (Simultaneous) Inversion
Two different joint inversion approaches that combine concentration and isotope ratio data sets were tested in this study.One is a simultaneous inversion technique, where the concentration and isotope information constrain the sources in one inversion process.The other is a sequential inversion technique: each of the measured properties constrains the sources in two consecutive inversion processes.
In the simultaneous inversion, both modeled and observed concentration and isotope ratio are coupled in the solution matrices for the inverse problem: Since the two measurement data sets (major and minor isotopes; C 16 O and C 18 O) are used to optimize the sources at the same time, the isotope information plays like an additional observational data set in the inversion system and, in comparison with the [CO]-only inversion, this renders more robust inversion results.

Coupled (Sequential) Inversion
When simultaneously inverting different data sets that have a large difference in their magnitude (e.g., C 16 O and C 18 O), a weighting issue arises because the inversion results can be dominantly constrained by the larger magnitude measurement data.One of the methods to balance the contribution of two data sets is sequential use of each observation, where the solution inverts one measurement data set first and the result provides the input for the inversion of the second observational information [77,80].
In this study, the sequential use of concentration and isotope information is formulated as follows: x = x +( K S K +S ) K S ( y -Kx ) (10) where x * is an intermediate estimated source strength vector that is acquired from the first step of the inversion process.
The joint inversion results of the simultaneous use of concentration and isotope ratios and the sequential use of them are compared and discussed in detail in Section 5.3.

Optimization of Source Strengths and δ 18 O Signature in These Inversion Methods
Estimating the fluxes of each CO source by jointly inverting C 16 O and C 18 O is the primary purpose of this study.In addition to this, C 18 O source strength estimates are derived from the optimized CO source strengths and a posteriori isotope ratio (rj) of each source obtained from the decoupled inversion (Figure 7).Although the same prescribed isotopic source signatures can be applied to calculate a posteriori isotope ratios, Bergamaschi et al. [24] showed that applying a posteriori carbon isotopic source signatures, instead of using fixed isotopic source signatures, provides more robust inversion results.Our comparison of the inversion results with fixed and updated oxygen isotopic source signatures confirm their result for the oxygen isotopic source signatures (Section 5).Thus, the δ 18 O source signature optimization process is implemented in the joint inversion system, in lieu of assuming fixed isotope ratios of the sources.Optimized δ 18 O source signatures calculated from the a posteriori CO and C 18 O source strengths provide an additional benefit of including isotopic signatures in inverse modeling.It allows for the verification of the joint inversion results by showing the fit of the optimized δ 18 O values to the observations, while the CO-only inversions can confirm the results only by comparing measurements with a posteriori CO concentrations.To optimize the isotopic source signature, the C 16 O-C 18 O ratio is iteratively optimized from the decoupled run since it has been known that the isotope ratio is a nonlinear function of the source strengths [24].Therefore, an iterative method that updates the Jacobian matrix (K, Equation ( 4)) in each iteration was used to solve the inverse problem (Figure 7).Iterations were performed for each source and continued until the solution converged: During the iterations, the isotope ratios were allowed to vary within a certain range (ε).The threshold is assigned for each source based on current understanding of the isotopic source signature.
For the fossil fuel source, 2‰ is assigned for the threshold since the previous estimates of the isotope signatures are reported in between 22‰ and 24‰ [10,42,62,65] and the direct measurements of the exhaust from numerous automobiles indicate the variations of δ 18 O of CO as ±1.0‰ [81].The previous global estimates of δ 18 O from biomass burning were 16.3‰ and 18‰ [42,65] and the uncertainties reported for biomass burning source signature were ±1‰ [62,82].However, 5‰ is allocated for the threshold of the biomass burning source because [83] indicated a very wide range (3‰-26‰) for δ 18 O from their chamber experiment.For the ε of the other sources, since there is one number reported for δ 18 O of the sources, ±5‰ is estimated for ε, analogous to that for the biomass burning source.
The role of isotope information is expanded in the inverse modeling analysis with the optimized source signatures.This enables the separation of the a posteriori source estimates to the inventories of major and minor isotopes while the joint inversion gives updated information of the CO source strengths.

Optimized Atmospheric CO Sources for 1997, 1998, and 2004
The global atmospheric CO budget is estimated for 1997, 1998 and 2004.The sources are constrained by both CO concentration and oxygen isotope ratio information.Concentration and δ 18 O are either simultaneously or sequentially applied to constrain the a priori CO sources and the former method is used to discuss the inversion results, unless otherwise noted.The results of applying different inversion techniques will be explained in detail later in this section.
Frequently, the result of inversion analysis is expressed as a correction or optimization factor (f) that is the ratio of a posteriori estimates to the prescribed a priori source fluxes., ˆi where xa and x is a priori and a posteriori source strength of source i.Thus, if an optimization factor is greater than 1, then this means the current estimate of source strength is underestimated.While fossil fuel and biofuel are both anthropogenic sources of CO, the inversion analysis showed very different results (Table 3).In the SH, the optimization factors of fossil fuel and biofuel sources are close to unity.This implies that the anthropogenic sources of CO in the SH were accurately estimated.The fossil fuel source changed less than 2% after inversion and biofuel estimates changed less than 5% except in 1997, during which the a posteriori biofuel source decreased 15%.Since the anthropogenic sources play a minor role in the SH, the measurements did not constrain the sources tightly.The reductions of their uncertainties are relatively small compared to those in the NH where the sources are major components of total CO concentration.
In the NH, the optimized fossil fuel emission inventory was adjusted less than approximately ±15% for the three years.This indicates the a priori fossil fuel source strength [17] is close to the actual fossil fuel CO emission in both hemispheres.A slight decreasing trend of the optimization factor is also found suggesting CO emissions from fossil fuel combustion decreased from +10% (1997) to −13% (2004), albeit a 20% increase in annual global fossil fuel consumption from 1990 to 2005 [World Resources Institute, http://earthtrends.wri.org].This may reflect advancement of fossil fuel use efficiency and stricter regulations for vehicle emissions.The NH biofuel emission changed significantly after the inversion.It increased 79% in 1997, 64% in 1998, and 31% in 2004.In comparison with the fossil fuel source, the biofuel source showed a larger source adjustment with a larger a posteriori error covariance.This indicates that there are large uncertainties in biofuel source estimate.The biofuel source also demonstrated a downward tendency of the optimization factor, which indicates the use of biofuel decreased from 1997 to 2004.

Optimized Biomass Burning Source Strength
There was only a small difference between the a priori and a posteriori source strengths for biomass burning in 1998 and 2004; however, for 1997, which was a high fire year, the inversion results suggest an increase of 33% for the NH biomass burning CO indicating GFED-v2 missed some sources of the biomass burning CO.The inventory was also not adjusted much for the SH biomass burning CO.In general, the joint inversion analyses estimated ca. 10% less CO than the GFED-v2 inventory on average.

Optimized Chemical Oxidation Source Strengths
The methane oxidation source is the biggest source of CO.However, because the methane lifetime is long (~10 years) and its reservoir is large, this source is already relatively well-constrained compared to the other sources of CO.The joint inversion analysis confirmed this.For all three years, the optimization factors are relatively constant in each hemisphere; 1.10-1.12 in the NH and 0.97-0.98 in the SH.
Biogenic NMHC emission is the largest component of the NMHC oxidation source of CO (>80% of total NMHC-derived CO; [14,68]).Isoprene emissions are estimated to be ~75% of the total natural NMHC emissions [39].Therefore, this source is expected to be sensitive to environmental factors such as temperature and precipitation patterns.The strong El Niño event in 1997 was followed by a strong La Niña in 1998-1999 and the effect of this on the NMHC-derived CO source is seen very clearly in the inversion analysis for each hemisphere.NMHC-derived CO also responded more sensitively to the ENSO index change in the NH [84].

Optimized Ocean and Biogenic Source Strengths
The optimization factors of the ocean source were close to 1 and a posteriori uncertainty was not reduced much.Thus, this source was hardly constrained because of the small influence of the ocean on the atmospheric CO.
The inversion results of direct biogenic CO emission sources suggest a reduction of the emission by up to 50%.However, due to the small contribution of the biogenic source, it has limited influence to the global CO.Similar to the ocean source, this also was not tightly constrained as evidenced by a small reduction in the uncertainty of the source.

Comparison to the Previous CO Sources Strength Estimates Derived from Inversion Analyses
The global CO budget estimated in this study is compared to previous CO budget estimates (Table 4).Although direct comparison between this study and earlier studies is difficult due to the different years of data sets and source categories, most of the a posteriori emissions fall within the range of the previous estimates.
The total direct CO emission was 1210-1651 TgCO/year and the total chemical production of CO was 1300-1579 TgCO/year.Those show large ranges because of the large interannual variability of biomass burning CO (direct emission) and biogenic NMHC-derived CO (chemical production).Both of the improved CO inventories are also placed within the previously reported estimated value ranges; 1091-1663 TgCO/year for direct emission and 1461-1644 TgCO/year for chemical production.The total CO emission and the individual a priori sources are mostly updated by the inversion analysis (this study) within the range of previous source estimates.Hence, isotope information adjusts each source strength more precisely and accurately while keeping consistency with the total inventory estimates.

A Posteriori CO and δ 18 O
In order to see the effect of updated source inventories on the CO concentration and δ 18 O, the difference between a posteriori CO and δ 18 O and observations are analyzed.A detailed derivation of a posteriori CO and δ 18 O is described in the auxiliary material (Doc.S1).The new source inventory is more reliable if, in comparison with the model-observation difference, which is based on the a priori source information, the difference between a posteriori source strengths derived CO and δ 18 O is reduced.
The model-observation differences of δ 18 O are apparently reduced by more than 50% when the a posteriori source strengths are applied (Figures 8 and 9, Table S6).The modeled concentration also showed a better fit to the measurements with the updated source inventory (Figure 8).Although, since the forward concentration simulation already reproduced the observations quite well (Figure 4), the improvement of a posteriori CO concentration is not as clear as a posteriori δ 18 O (Figures S4 and S5), the modeled concentrations are about 45% closer to the observations (Figure 8). Figure S4 shows that the a posteriori inventory especially improves wintertime modeled CO.While the a posteriori source emissions are estimated for each year and do not contain seasonality, this implies certain sources are significantly underestimated during the winter.The a posteriori δ 18 O decreased the overall offset of model-observation difference (Figure 9) and the improvement was more noticeable in the SH (Figure 8).These results indicate that each updated source contributed to improving both the modeled CO and δ 18 O while there was relatively small adjustment of the total CO inventory (Table 4).Thus, this suggests that an accurate estimation of source strength distribution is more important than the optimization of total CO emission in CO inversion analyses.Due to the advantages of including isotope information to the inversion analysis, more realistic source distributions were derived which sufficiently satisfy both measured CO and δ 18 O.Moreover, the improved δ 18 O fits provide additional confidence to the results that are obtained from CO-only inversions.S7.

Inversion Results by Different Inversion Schemes: CO-only, Sequential, and Simultaneous Inversion
Various inversion schemes are tested and discussed in this section to elucidate the influence of different isotope information combining methods on the a posteriori source strength estimates.
Joint application of isotope ratio and concentration measurements generally gives more robust inversion results since the isotope ratios provide additional constraint.In Figure 10, a posteriori uncertainties of the three different inversion methods are presented.The sequential inversion provided the smallest uncertainties and always the biggest uncertainty was found in the CO-only inversion.The impact of different inversion methods on biomass burning, NMHC oxidation and the NH biofuel source is larger than that on other sources.Due to the small concentration of the minor source, biogenic and ocean sources are loosely constrained.The smaller a priori source uncertainties of fossil fuel and methane oxidation limit the influence of each inversion method.In the sequential inversion, the inverted data sets and the obtained uncertainties from the first inversion step are used as initial values for the second inversion (Equation ( 10)).The final uncertainties (error covariance, Ŝ; Equation ( 6)) of each source strength from the sequential inversion is obtained from the intermediate a posteriori source uncertainty term which is already once reduced using C 16 O information while the joint simultaneous inversion constrains the source only once.A basic underlying assumption of the Bayesian synthesis inversion is the linear relation between the source strengths and measurements.If the relation is nonlinear, as applies in the case of δ 18 O, the inversion should be iterated until converging.The linearity can be verified by comparing the results of the sequential and simultaneous inversions.If the results are different, this implies at least one of the measurement data sets is not linear with source change.Since the a posteriori source strengths from the two different methods are very similar in this study (approximately ±2% on average; Table 5), [C 16 O] and [C 18 O] appear to be linearly related to a change in source strength.
While the sequential and simultaneous inversions clearly improve the modeled δ 18 O and estimate similar a posteriori source strengths, the simultaneous inversion shows a significantly better fit to the observed δ 18 O (Figure 9).The averaged differences from the observation were derived to be 1.3‰ and 1.9‰ for the simultaneous inversion and sequential inversion, respectively.
In summary, insignificant a posteriori source inventory differences, especially between the joint sequential and joint simultaneous inversions, were found in the results of the three inversion schemes: CO-only, sequential and simultaneous inversions (Table 5).However, when [CO] and δ 18 O are jointly used in the inversion analyses, the optimized source strengths and δ 18 O were more reliable than the CO-only inversion results.The sequential use of the concentration and isotope information tends to reduce the a posteriori uncertainties more effectively (precision) and the simultaneous use of them shows smaller model-observation differences (accuracy).

The Influence of the Number of Observation Stations in the Inversion Results
In order to see the influence of the number of observation stations and the consistency of the inversion results with using different observational data sets, the sources of NH CO are constrained with 11 NOAA GMD surface station measurements (CONOAA).Table 5.The ratios of optimization factors.seq/sim is ratio of optimization factor of sequential inversion to that of simultaneous inversion and CO/sim is ratio of optimization factor of CO-only inversion to that of simultaneous inversion.Mean deviation from the unity (identical result) is ±1.7% for seq/sim and ±4.6% for CO/sim.CONOAA inversion results are very similar to the results of the joint inversion (Figure S5).For the biofuel and biogenic sources, although each method estimated notably different optimization factors, the discrepancies are within the uncertainty ranges.The difference between a posteriori concentrations of each inversion result and measured concentrations are compared in Figure 11.A similar degree of improvement from the a priori model-observation differences is found.Therefore, consistency of a posteriori source strengths and model-observation differences between the CONOAA inversion and joint inversion results indicate that inversion results are sufficiently constrained despite the limited number of observations.

Summary and Conclusions
The simulation results from the tracer version of MOZART-4 reproduced observations of CO and δ 18 O fairly well in both hemispheres.The modeled and measured concentration showed a strong correlation (ρ = 0.94) and a small averaged model-observation difference (10.5 ppbv).In general, the model underestimated the concentration measurements in the NH and overestimated them in the SH.For δ 18 O, the correlation between the model and observation was 0.86 and the mean model-observation difference was 3‰.The model accurately reproduced observed δ 18 O at high latitude stations while modeled δ 18 O was lighter than observations at mid-and low latitude stations.
The joint inversion of CO and δ 18 O estimated total global CO production at 2951 TgCO/yr, 3084 TgCO/yr and 2583 TgCO/yr for 1997, 1998, and 2004 respectively.The a posteriori fossil fuel combustion source changed less than 5% in the SH and adjusted ±15% in the NH.The inversion result showed that the a priori biofuel inventory is significantly underestimated in the NH (up to 80%).For the biomass burning source, the a posteriori source did not change much.However, in 1997, the inversion analysis increased 33% compared to the a priori biomass burning source in the NH.The inversion result indicated a significant current overestimation of direct biogenic emission source (up to 50% in the NH).The methane oxidation source is considered to be a well-known source and its a posteriori source strength is similar to the a priori source strength.However, in the NH, ~10% more methane-derived CO was estimated, whereas ~3% less methane-derived CO was estimated in the SH.
The updated CO budget has improved agreement between data and model estimates of CO and δ 18 O, and this is seen more clearly in the oxygen isotope ratio, which can distinguish between different sources and so provide more accurate a posteriori source estimates.Moreover, this indicates the correct estimation of CO source distribution that can be obtained when isotope information is combined with concentration.
The joint inversion result was compared to the inversion result using CO measured from 11 NOAA GMD stations in the NH.While the two observational data sets are independent, the inversion results estimate similar a posteriori source strengths and interannual trends.Thus, the joint inversion reliably constrains the CO sources albeit a small number of observational stations.Also, CO concentration and δ 18 O were simultaneously and sequentially applied in the inversion analysis to find a more effective way for combining the two observations.While the sequential inversion provided more precise results (smaller a posteriori uncertainties), the simultaneous inversion more accurately constrained the CO sources, resulting in smaller model-observation differences.

Figure 1 .
Figure 1.Carbon monoxide (CO) sources and total amount of CO emissions derived from inversion analyses.

Figure 2 .
Figure 2. Isotopic source signatures of CO based on data in Table S2.The size of each circle represents the relative source strengths estimated in IPCC 2001 report.

Figure 3 .
Figure 3. Global zonal distribution of CO concentration.The blue squares are National Oceanic and Atmospheric Administration Global Monitoring Division (NOAA GMD) CO and the red dots are CO used in this study, showing they are comparable.All available monthly mean concentrations during 1996-2004 are used for plotting.The error bar is the range of mean seasonal variation of the multi-year CO observations.

Figure 4 .
Figure 4.A scatter plot of measured versus modeled concentration of CO (upper panel) and measured versus modeled δ 18 O of CO (lower panel).The black solid line depicts 1:1 correspondence and the red line is a regression line of all measurements.The dotted lines are regression lines of the NH (dark gray) and the SH (light gray) data sets.

Figure 5 .
Figure 5. Averaged distance between the measurements and a posteriori CO concentrations.

Figure 6 .
Figure 6.Inversion results (optimization factors and a posteriori errors) of each source with different a priori source uncertainties.A logarithmic scale is used for optimization factors.

Figure 7 .
Figure 7. Schematic diagram for the two-stage Bayesian synthesis isotope inversion for atmospheric carbon monoxide.

Figure 8 .
Figure 8.The ratio of a posteriori model-observation difference (simultaneous inversion) to a priori model-observation difference for concentration simulation (dark gray) and δ 18 O simulation (light gray).

Figure 9 .
Figure 9.Comparison of a priori (brown line) and a posteriori modeled surface δ 18 O with measurements (blue dots).Green and purple lines denote a posteriori δ 18 O from simultaneous inversion and sequential inversion, respectively.Orange line is a posteriori δ 18 O with fixed isotope source signature.A posteriori isotope source signatures obtained from the simultaneous inversion are presented in the TableS7.

Figure 10 .
Figure 10.Comparison of a posteriori uncertainty of three different inversion schemes: CO-only, sequential and simultaneous inversion.

Figure 11 .
Figure 11.Comparison of model (a priori (orange) and a posteriori (green))-observation difference of the Northern Hemisphere.

Table 1 .
Annual mean of a priori source strengths used in this study (TgCO/year).Global Fire Emissions Database version 2 (GFED-v2) inventory is used for biomass burning carbon monoxide (CO).

Table 2 .
Estimated and measured uncertainties in isotopic and concentration measurements.
* e.m.a.u denotes estimated maximum absolute uncertainty, i.e., sum of systematic and random errors.

Table 3 .
Optimization factors (f) and a posteriori uncertainty (e, %) of each CO source.

Table 4 .
The results of global CO budget estimation (this work) in comparison to previous global CO budget estimates.