Estimation of fire-induced carbon emission from Equatorial Asia in 2015 by using in situ aircraft and ship observations

The inverse analysis was used to estimate the fire carbon emission in Equatorial Asia induced by the big El Niño in 2015. This inverse analysis is unique because it extensively used high-precision atmospheric mole fraction data of carbon dioxide (CO2) from the commercial aircraft observation project. By comparisons with independent shipboard observations, especially carbon monoxide (CO) data, the validity of the estimated fire-induced carbon emission was elucidated. The best estimate, which used both aircraft and shipboard CO2 observations, indicated 273 Tg C for fire emission during September– 15 October 2015. This two-month-long emission accounts for 75% of the annual total fire emission and 45% of the annual total net carbon flux within the region, indicating that fire emission is a dominant driving force of interannual variations of carbon fluxes in Equatorial Asia. Several sensitivity experiments demonstrated that aircraft observations could measure fire signals, though they showed a certain degree of sensitivity to prior fire-emission data. The inversions coherently estimated smaller fire emissions than the priors, partially because of the small contribution of peatland fires, indicated by enhancement ratios of CO 20 and CO2 observed by the ship. In the future warmer climate condition, Equatorial Asia would experience more severe droughts and have risks for releasing a large amount of carbon into the atmosphere. Therefore, the continuation of aircraft and shipboard observations is fruitful for reliable monitoring of carbon fluxes in Equatorial Asia.

In this study, we estimated carbon emissions in Equatorial Asia for 2015 using in situ atmospheric observations by 65 aircraft and ship. The observational data were obtained from the commercial aircraft observation project of Comprehensive Observation Network for TRace gases by AIrLiner (CONTRAIL: Machida et al., 2008) and the National Institute for Environmental Studies (NIES) Volunteer Observing Ship (VOS) Programme (Tohjima et al., 2005;Terao et al., 2011;Nakaoka et al., 2013;Nara et al., 2011Nara et al., , 2014Nara et al., , 2017. Because of in situ measurements, the observational data provide much higher accuracy than the satellite observations used in previous studies. The moderate distance of the observational locations from 70 the source areas (i.e., in the free troposphere or offshore) should ensure enough spatial representativeness of the observations in the inverse analysis. Given the sparse ground-based observations in Equatorial Asia, these programmes provide valuable opportunities to investigate the fire-induced emissions in the region. The long-term aircraft observation (the predecessor of CONTRAIL) observed CO2 and CO mole fraction variations associated with El Niño over the western Pacific since 1993 (Matsueda et al., 2002(Matsueda et al., , 2019. Its occasional observation flight to Singapore  and a campaign flight 75 over Australia and Indonesia (Sawa et al., 1999) captured pronounced elevations of CO from the Equatorial fires in 1997.
Furthermore, Nara et al. (2017) observed prominent CO2 and CO enhancements from the peatland fires in Equatorial Asia in 2013 by NIES VOS.
To link the atmospheric observations to surface carbon fluxes, we performed an inverse analysis of atmospheric CO2 using the NICAM-based Inverse Simulation for Monitoring CO2 (NISMON-CO2) (formerly NICAM-TM 4D-Var: Niwa et 80 al., 2017aNiwa et 80 al., , 2017b). The inversion system uses the Nonhydrostatic Icosahedral Atmospheric Model (NICAM: Tomita and Satoh, 2004;Satoh et al., 2008Satoh et al., , 2014)-based transport model (NICAM-TM: Niwa et al., 2011b). Using the same atmospheric transport model, Niwa et al. (2012) performed a CO2 inverse analysis and demonstrated a strong constraint of the CONTRAIL data for Equatorial Asia. In this study, we estimated surface fluxes at a higher resolution using a more sophisticated inversion method than that of Niwa et al. (2012), namely the four-dimensional variational (4D-Var) method (Niwa et al., 2017a). The  estimates fluxes at a model grid-resolution to address flux signals from spatially limited phenomena such as biomass burning.
We newly implemented CO into the inverse system to evaluate combustion sources. In our inverse analysis, we predominantly used atmospheric CO2 observations from CONTRAIL and evaluated the inversion results using independent CO2 and CO observations from NIES VOS. Finally, we performed an inverse analysis using both the CONTRAIL and NIES VOS CO2 observations to enhance the reliability of the inverse analysis. 90

CONTRAIL
The CONTRAIL data were obtained from in situ CO2 measurements by Continuous CO2 Measurement Equipment (CME), 100 which is installed onboard the Boeing 777-200ER and -300ER of Japan Airlines (Machida et al., 2008;Sawa et al., 2012;Umezawa et al., 2018). For the analysis period from November 2014 to January 2016, the number of CONTRAIL-CME data exceeds 1.3 million, comprising 10-s interval data from ascending/descending sections and 1-min interval data from cruising sections. In the analysis, we only used data in the free troposphere, derived by excluding data in the stratosphere and the planetary boundary layer identified by thresholds of two potential vorticity units (PVU, 1 PVU = 10 −6 m 2 s −1 K kg −1 ) and Ri = 105 0.25 (Ri is the bulk Richardson number), respectively (Sawa et al., 2008. This data filtering is needed because the signals of surface fluxes being efficiently attenuated in the stratosphere, and lower altitude data could be affected by local emissions from a neighbouring city of an airport (Umezawa et al., 2020). After filtering, the number of observations is still as large as 1.1 million. In particular, the observational coverage for Equatorial Asia is noteworthy, which is predominantly contributed by high-frequency flights between Japan and Singapore. 110 https://doi.org/10.5194/acp-2020-1239 Preprint. Discussion started: 23 December 2020 c Author(s) 2020. CC BY 4.0 License.

NIES VOS programme
The NIES VOS programme has been conducting atmospheric and surface ocean observations in the Pacific Ocean using commercial cargo vessels (Tohjima et al., 2005;Terao et al., 2011;Nakaoka et al., 2013;Nara et al., 2011Nara et al., , 2014Nara et al., , 2017. The observation network ranges from Japan to North America, Oceania (Australia and New Zealand), and Southeast and Equatorial Asia. In 2015, the motor vessel named Fujitrans World (owned by the Kagoshima Senpaku Kaisha, Ltd. Kagoshima, Japan) 115 was used for observations in Southeast and Equatorial Asia. Onboard the ship, an in situ measurement system continuously observed atmospheric mole fractions of greenhouse gases and other related atmospheric species (Nara et al., 2017). In this study, in addition to CO2, atmospheric CO data were used for the proxy of fire-induced emissions. The ship normally travels once a month, but for 2015, observational data were obtained in January and from May to November. It takes approximately two weeks to travel around Southeast and Equatorial Asia. In this study, we used 1-h interval data that passed careful quality 120 control. Using ancillary data of the cruising speed and mole fractions of related species (e.g., ozone), the quality control excluded mole fraction data of CO2 and CO that were judged as the ship's exhaust and contaminated by local ports.

Inversion system and transport model
Similar to previous inversions (e.g., Baker et al., 2006;Chevallier et al., 2010;Rödenbeck, 2005), the inverse analysis of this 125 study is based on Bayesian estimation (e.g., Rayner et al., 1996;Enting, 2002). The cost function is defined as where is the control vector, including parameters to be optimised, y represents the vector of observations, and x0 denotes the basic model state of the parameters. The matrices B and R are the prescribed error covariance for and the modelobservation mismatch, respectively. The operator M(.) describes the forward simulation, including linear spatiotemporal 130 interpolation to each observational location/time. In this inverse analysis, x0 and comprise prescribed surface CO2 flux data and deviation from them, respectively, and the operator M(.) represents the atmospheric transport. Atmospheric mole fraction observations of CO2 are input to the vector y.
In this study, we used the 4D-Var method to obtain an optimal vector that minimises the cost function. In the method, an optimal parameter vector is sought by iterative calculations using the gradient of the cost function, 135 where M T is the transpose of the tangent linear operator M (in this study, ≈ ( ) because of the linearity of the problem). The M T calculation requires an adjoint model.
The inversion system NISMON is specifically designed for the inverse analysis of an atmospheric constituent (Niwa et al., 2017a(Niwa et al., , 2017b). In the system, the forward model of NICAM-TM simulates atmospheric mole fractions from given 140 surface fluxes, and its adjoint model calculates the sensitivities of fluxes against atmospheric mole fractions (Niwa et al., https://doi.org/10.5194/acp-2020-1239 December 2020 c Author(s) 2020. CC BY 4.0 License. 2017b). Specifically, the continuous adjoint model was chosen for the adjoint calculation, assuring monotonicity of tracer concentrations and sensitivities at the expense of minor nonlinearity (Niwa et al., 2017b). The optimisation calculation uses the quasi-Newton algorithm of the Preconditioned Optimizing Utility for Large-dimensional analyses (POpULar: Fujii and Kamachi, 2003;Fujii, 2005;Niwa et al., 2017a). 145 The atmospheric transport model NICAM-TM adopts an icosahedral grid system with hexagonal or pentagon-shaped grids ( Fig. 1) that are produced by the recursive division of an icosahedron. All the model simulations were performed at a horizontal resolution of glevel-6 (n of glevel-n denotes the number of divisions of an icosahedron, representing the level of the model horizontal resolution). The averaged grid interval of glevel-6 is 112 km, sufficiently resolving the major archipelagos in Equatorial Asia (Fig. 1). For forward and adjoint simulations of atmospheric transport, archived meteorological data drive 150 NICAM-TM, which is an off-line calculation. The meteorological data were prepared in advance from the simulation of the parent model NICAM, whose wind fields are nudged towards Japanese 55-year Reanalysis data (JRA-55: Kobayashi et al., 2015;Harada et al., 2016) (see Niwa et al., 2017b for a detailed description of the archived meteorological data). Other model settings can be found in Niwa et al. (2017b).

Implementation of CO 155
In this study, we newly implemented a CO function in the above inversion system to use CO as a proxy of fire-induced emissions. It also considers oxidation from CO to CO2, which could have measurable effects on CO2 observations near fires. Figure 2 shows a schematic diagram for the forward and adjoint simulations of NICAM-TM, including CO. This CO function considers only the chemical reaction with hydroxyl radicals (OH). The OH fields are given as input data and, hence, the model does not have nonlinear chemical reactions, retaining the linearity, which is assumed in the inverse analysis theory. 160 Furthermore, the oxidation from methane (CH4) to CO with OH is also considered. For simplicity, however, the atmospheric mole fraction of CH4 was set at a globally constant value of 1844 ppb (= 10 −9 mol −1 ), which was derived from the global annual mean mole fraction for 2015, reported by the World Data Center for Greenhouse Gases (WDCGG: WMO, 2018). The atmospheric three-dimensional data of OH were derived from the TransCom-CH4 project (Patra et al., 2011). In the model, the contribution of oxidation from biogenic volatile organic compounds (BVOCs) to CO is given as emissions from the earth's 165 surface. Note that we did not input CO observations to the inverse analysis. The dominant part of the observations was from the in situ CONTRAIL measurements, which did not have simultaneous CO data available. In the inversion, the CO flux in the model was modified along with the biomass burning emission of CO2, as described in the next section.

Flux model
As described in Fig. 2, we introduced scaling factors to surface fluxes, which is another updated feature of the inversion system 170 from Niwa et al. (2017a). The surface CO2 flux input to the model, () ! , is described as +51 + ∆ /0 ( , )9 /0 ( , ) +51 + ∆ *123 ( , )9 *123 ( , ) where x and t indicate flux location and time, and f represents prescribed flux data, whose subscripts of fos, GPP, RE, fire and 175 ocn denote flux components of fossil fuel combustion and cement production, Gross Primary Production (GPP) and respiration For the surface CO flux, we considered fossil fuel, BVOCs and biomass burning emissions. For the biomass burning emissions, we imposed the common scaling factor with that of CO2. Therefore, in the inversion, the biomass burning emission of CO was modified along with that of CO2. The modification of the biomass burning emission could also be made by signals transported via atmospheric CO that should have oxidised to CO2 (Fig. 2). 190 In Eq. (3), the temporal resolution of a flux-scaling factor could be different from that of its corresponding flux and be different by regions (Table 1). In this study, we set the daily temporal resolution for the scaling factors of GPP, RE and biomass burning emissions in Equatorial Asia so that the inversion could exploit the full information of those surface fluxes from the observations. For the rest of the region, we set monthly temporal resolutions. For the scaling factor of fossil fuel emissions, we set an annual temporal resolution for Equatorial Asia, and we did not optimise the flux for the rest of the region, 195 i.e., the modification factor was set to 0. We set the monthly temporal resolution for the deviation of the ocean flux. Table 1: Temporal resolution and standard error and error correlation of each flux component, which was separately configured for Equatorial Asia and the rest of the world. Note that the ocean flux was optimised by its absolute value and the others by their scaling factors; therefore, the monthly standard deviation (SD) of the long-term data was used for the ocean flux error and ratios were used for the other flux

Error covariance matrices
As in the case of the different flux temporal resolutions, we constructed the flux error covariance matrix B for Equatorial Asia and the rest of the world separately. Table 1 summarises the standard errors and error correlations that were introduced into the diagonal and off-diagonal elements of B, respectively. For GPP and RE, we assume 40% error for daily fluxes in Equatorial 210 Asia and 10% for monthly fluxes in the rest of the world, which means 0.16 and 0.01 for the diagonal elements of B. The higher standard error for Equatorial Asia allows observations to modify surface fluxes sufficiently. Nevertheless, a 3-day scale temporal error correlation was introduced to stabilise flux estimates. The smaller standard error for the rest of the world had to constrain the surface flux to the prior because we did not use enough observations to cover the globe. Furthermore, for the stabilisation, the spatial error correlation with the 1000 km scale length was introduced. The above error correlations were 215 defined by the Gaussian function (Niwa et al., 2017a). Similarly, the errors for fossil fuel and fire emissions were introduced, but without error correlations. For the monthly ocean flux errors, we used the standard deviation of the long-term data  and introduced the spatial error correlation of 3000 km. Table 1 shows each parameter.

Prescribed flux dataset
For ffos and focn in Eq. (3), we used monthly mean data of fossil fuel and cement production emission from the Carbon Dioxide 220 Information Analysis Center (CDIAC) (Andres et al., 2016) and of air-sea CO2 flux from the Japan Meteorological Agency (Takatani et al. 2014;Iida et al., 2015), respectively. For fGPP and fRE, we used 3-hourly data for resolving distinct diurnal cycles of terrestrial biosphere flux. These fGPP and fRE were originally based on monthly mean data from the Carnegie-Ames-Stanford Approach (CASA) model (Randerson et al., 1997), but were modified according to the inversion of Niwa et al. (2012).
They were further downscaled in time to 3-hourly with 2 m temperature and downward shortwave radiation data of JRA-55 225 using Olsen and Randerson's (2004) method.
In the inversion of Niwa et al. (2012), the classical low-resolution inversion method (e.g., Enting, 2002) was used, in which the global terrestrial area was divided into 31 regions, and the scaling factors for those regions were optimised.
Furthermore, the inversion used both surface and CONTRAIL data for 2006-2008, and the mean flux data of those three years were used in this study. Therefore, such an integrated flux could produce consistent atmospheric mole factions with the 230 observations from the surface to the upper troposphere, although some discrepancies could arise because of the different analysis period. In this study, those discrepancies were modified using the consistent year data of CONTRAIL and further flux information was exploited because of using the 4D-Var high-resolution (model grid level) inversion, with a specific focus on Equatorial Asia.
For the biomass burning flux of ffire, we used four datasets and performed independent inversions to evaluate 235 sensitivities to the biomass burning data ( Table 2). The first is the mean of the GFED4s and GFAS v1.2 (noted as GG). The

Initial mole fraction field and analysis period
In addition to the flux-scaling factors, the model parameter vector includes the global offset of atmospheric mole fractions. 250 Therefore, of Eqs. (1) and (2) is constructed as where ∆ and ∆focn represent all the modification scaling factors and ocean flux deviations of Eq. (3), respectively, and ∆ denotes the modification to the global offset. Thus, its corresponding basic state vector x0 is described as % = (1, … ,1, +45 , 0) # . Note that the forward model calculation started from a reasonable spatial gradient, which was prepared in 255 advance by a spin-up calculation. At the beginning of the 4D-Var iterative calculation, all the elements of were set to zero as the initial estimates.
The target period for this study is the whole year of 2015. However, in the inverse calculation, two extra months were added before the target period to attenuate the errors in the initial mole fraction fields before the beginning of 2015, which was inevitable because of the global unique parameter described above (∆ ). Furthermore, one more month was also added after 260 the target period to well constrain fluxes at the end of 2015. Therefore, the inverse calculation period consists of 15 months from November 2014 to January 2016.

Notation of sensitivity tests
As described in 2.2.5, we performed inversion analyses with four biomass burning datasets (GG, GD, GS and NO). We only used the CONTRAIL data, but with GG, we additionally performed an inversion using the NIES VOS data and CONTRAIL 265 to leverage all available observations, denoting C_ and CV_ as prefixes, respectively. Thus, we have five inversion results (C_GG, C_GD, C_GS, C_NO and CV_GG) ( Table 2). Note that although they used different biomass burning data, prior flux errors for biomass burning (Table 1) were commonly used. It is true even in C_NO whose practical prior uncertainty in Equatorial Asia is 80% of GG.

Results 270
In this section, we first describe spatiotemporal features of the CONTRAIL and NIES VOS observational data with supplemental model analyses. Then, we show the inversion results and demonstrate their validity by comparing posterior mole fractions of CO and CO2 with the NIES VOS data.

Observational features
As shown in Fig. 3, the CONTRAIL aircraft frequently flew to Singapore 209 times during 2015. These high-frequency 275 observations manifested a small but distinct seasonal cycle of CO2 mole fractions around Equatorial Asia, with double peaks in April-May and December, and a minimum during June-October, depending on altitudes and latitudes. Furthermore, the CONTRAIL aircraft frequently observed additional highly elevated mole fractions below 3 km altitude over Singapore (Fig.  3a, lower panel), which could be attributable to local or regional emissions in Equatorial Asia. The model with the prior flux data produced similar mole fraction elevations; however, their timing and magnitudes were sometimes different from the 280 observations (Fig. 3b). A further model analysis with prior biomass burning data suggested that fire contributions to the observed mole fraction elevations were limited mostly within the latter period of the dry season from mid-August to the beginning of November (Fig. 4b). In the other seasons, the model showed almost no contributions from fire emissions (not shown). In particular, the model showed a distinct fire contribution at the end of September, which elevated mole fractions up to the upper troposphere by ~4 ppm. In the observations, although similar mole fraction elevations are found in the upper 285 troposphere, its magnitude is smaller (~2 ppm). Furthermore, the observation shows a slightly later peak that lasted until the beginning of October (Fig. 4a). After that, the observations also captured elevated mole fraction events from mid-October onward. However, the prior model estimate showed smaller fire contributions in October than in September (Fig. 4b), although the simulated total CO2 mole fractions were comparable to the observations (Fig. 3b), indicating that non-fire emissions (e.g., from terrestrial biosphere respiration and fossil fuel emission) had a certain level of contribution during this period. 290 Figure 3: CO2 mole fractions in the free troposphere around Equatorial Asia (note that data in the boundary layer and stratosphere are excluded (see the main text)) observed by CONTRAIL (a) and their corresponding model values from prior (GG) (b) and posterior (C_GG) fluxes (c). Each upper panel presents a time-latitude cross-section from cruising mode data (~11 km above sea level) within the longitude range of 90°-130°E, and the lower one shows a time-altitude cross-section from ascending/descending data over Singapore. Note that the 295 data in the upper panels are not only from the Singapore flights but from all flights within the range. For visualisation, data are all 5-day running mean. Note also that an additional offset of 1.93 ppm is added to prior mole fractions so that the resulting global offset equals the posterior one. On the right-hand side, correlation coefficients and root-mean-square difference (RMSD) (ppm) between the simulated and observed mole fractions are noted for each time-latitude and time-altitude cross-section.  in the east of the Malay Peninsula and west of Borneo. By performing a transport simulation of tagged fire-induced CO tracers (the fire emission of GG was used here), we found that the fires in Borneo and Sumatra contributed almost every notable mole fraction elevation, except for 17 September and 15-16 October, both of which might be contributed by the fossil fuel emission in Jakarta city (Fig. 6). As highlighted by the grey shades in Fig. 6, seven of those events contributed by the fires are designated by P1, P2,…, P7 in this study. These events will be used for evaluating the inverse analysis, especially for fire-emission 310 features, as described in Section 3.2.2. Note that mole fraction data during 13-15 September and 11-14 October were excluded before the analysis. During these periods, some data were not correctly obtained because the signals were too large and out of the measurable range. Furthermore, the NIES VOS ship travelled slowly or stayed around the Malacca Straits, resulting in contamination by the ship-self exhaust.     Figure 7 shows sensitivities of the CONTRAIL and NIES VOS observations against surface CO2 fluxes, i.e., 325 footprints, for September and October 2015, calculated by the adjoint model of NICAM-TM (Niwa et al., 2017b). The CONTRAIL footprints represent sensitivities of observations obtained during ascending or descending flights over Singapore (i.e., the data shown in the lower panel of Fig. 4a). For both September and October, the calculated footprints indicate that the CONTRAIL observations could provide significant constraints on flux estimates for Equatorial Asia, especially Borneo (Figs. 7a and b). These widespread footprint features are because the data were obtained in the free troposphere, which is an advantage 330 of aircraft observations in terms of representativeness. Figure 7 also suggests that the constraint is stronger during October than September because the number of data is larger in October (Fig. 3 or Fig. 4). Compared to CONTRAIL, the NIES VOS

Posterior fluxes
In this study, we investigate surface fluxes by the sum of CO2 and CO fluxes, defined as a carbon flux. We do not consider CH4 fluxes, although they could contribute some percentage of the total carbon flux (Huijnen et al., 2016). Furthermore, we evaluate the carbon flux separately for the total net flux and biomass burning emission. Note that the total net flux includes 345 terrestrial biosphere fluxes, biomass burnings emissions and fossil fuel emissions. Table 3 summarises the total net and fire carbon fluxes of Equatorial Asia estimated by the five sets of inversions.
The prior biomass burning emissions of GG, GD and GS are consistently 300 Tg C for September-October, which constitutes ~80% of the annual total fire emission and amounts to more than 80% of the total net flux we prescribed as the prior (355-360 Tg C) for September-October. By inversion, all experiments, other than C_NO, estimated smaller total net fluxes by ~10% 350 (304-324 Tg C) than the priors, and they were mostly contributed by the smaller estimates of fire emissions (256-277 Tg C).
Interestingly, even when prior fire emissions were excluded in Equatorial Asia (C_NO), a significantly large fire emission of 122 Tg C was retrieved for September-October, indicating that the CONTRAIL data have fire-emission signals. However, the estimate is half of the others, indicating some dependency of the inversion on the prior fire emissions.  In September, C_GG estimated significantly high emissions in southeast Sumatra and south of Borneo, where the fire emission dominated in the prior flux (Fig. 8), supporting prior knowledge of biomass burnings. However, the total emission estimate is smaller than the prior by 31 Tg (Fig. 8c). In October, the differences between prior and posterior fluxes of C_GG were 365 moderate, with a net difference of 2.7 Tg (Fig. 9c). This small change in October indicates that the simulated mole fractions from the prior flux were well consistent with the CONTRAIL observations.    Table 3, even when the fire emission was excluded from the prior, the inversion estimated notable fire emissions (C_NO), in both September and October (Figs. 8e and 9e). Furthermore, the locations of the estimated fire emissions are well coincident with those of prior fire emissions. They were to some extent guided by the higher prior flux errors that were derived from the fire-emission data (the uncertainty was set as 80% of GG), which was confirmed by another sensitivity test without prior uncertainty of fire emissions (not shown). Nevertheless, this result confirms that the CONTRAIL data have 380 information about biomass burning emissions. adding the NIES VOS data to the CONTRAIL data because the number of CONTRAIL data is overwhelming and the footprint of CONTRAIL covers Equatorial Asia much more extensively in space (Fig. 7). Compared to the prior flux, the posterior fluxes have a smaller peak at the beginning of September, whereas they show larger peaks from the end of September to the beginning of October. In the latter part of October, the prior and posterior fluxes are similar.  different. GFED has larger peaks than GFAS in September, whereas it has smaller ones in October (Fig.11a). Generally, the posterior fire emissions, except for C_NO, fall within the range of both prior emission estimates. In September, the posterior estimates are consistent and their magnitudes are closer to GFAS rather than GFED. In October, however, notable discrepancies occur among the posterior emissions, which is contributed by different emission estimates for Sumatra rather 400 than Borneo according to the breakdown of the posterior estimates (Figs. 11b and c). In October, GFAS has higher emissions than GFED on both islands and its degree is more prominent in Sumatra. These different prior fire-emission estimates might have contributed to the large discrepancy among posterior estimates. As shown in Fig. 7, the CONTRAIL footprint covers Borneo better than Sumatra, and its degree is larger in October 410 than in September. In practice, however, the constraint on fire emission has a different feature, as seen in the noticeable spread of fire-emission estimates in October (Fig. 11c). Note that the spread of estimates, including C_NO, is small in Sumatra at the end of September (Fig. 11b). In this period, the observational data and model analysis indicated that strong fire signals reached Singapore, although its timing, as suggested by the model, was slightly earlier (Fig. 4b). For this event, the inversion successfully optimised the fire emission in Sumatra with strong constraints by the observations, even from the no-fire prior 415 (C_NO), resulting in the later-shifted peak with the consistent magnitude of 4-5 Tg C dy −1 (Fig. 11b).

Posterior mole fractions
In this section, we evaluate the simulated atmospheric CO2 and CO mole fractions from the posterior fluxes. First, as shown in Fig. 3, the posterior mole fractions of CO2 simulated for CONTRAIL have shown much better agreement with the observations than the prior ones, demonstrating that the inverse analyses were reasonably well performed. Compared to the 420 simulation results of the prior fluxes, the posterior mole fractions have greater correlation coefficients and smaller root-meansquare differences from the observations (see the numbers at the right-hand side of Fig. 3). In the following, we will compare the model with the CO2 and CO observations of NIES VOS, which were left independent of the inversions, except for CV_GG. In the comparative analysis of CO2 observations, an additional offset of 1.93 ppm is added to the prior CO2 mole fractions so that the resulting global offset becomes equivalent to the posterior ones, i.e., ∆ of Eq. (4) is 1.93 ppm (note that there is almost no difference in the global offset among the five inversions). Because the initial global offset was arbitrarily given, the comparison analysis of CO2 should exclude the effect of the improvement in the global offset to better understand 430 the inversion effects. Figure 12 demonstrates how the posterior mole fractions of CO2 and CO were improved from the prior ones.
Comparing the posterior results with the prior ones, we found better consistency with the NIES VOS observation, which is true for both CO2 and CO. Especially, its degree is notable for September; all inversions, except CV_GG, reduced the rootmean-square difference (RMSD) of CO2 from 2.14-2.62 ppm to 2.05-2.09 ppm, whereas those of CO were reduced from 92-435 211 ppb to 80-111 ppb. These results indicate the validity of the inversions that used the CONTRAIL CO2 observations. Especially, the experiment without the prior fire emission (C_NO) remarkably improved the correlation coefficients of CO2 and CO for both September and October (in September from 0.43 to 0.56 for CO2 and from 0.34 to 0.81 for CO, whereas in October from 0.29 to 0.49 for CO2 and from −0.18 to 0.49 for CO); however, the other inversions, except for CV_GG, did not improve the correlation coefficients significantly. In both months, CV_GG showed the best scores for CO2, which is 440 reasonable because it used the CO2 observations of NIES VOS. Note, however, that CV_GG used only the CO2 observations, but not those of CO. Therefore, the RMSD reduction of CO for September by CV_GG (from 136 to 103 ppb) demonstrates some improvement in fire emissions. Therefore, it is better to use both the CONTRAIL and NIES VOS observations for flux estimations; however, the impact of NIES VOS is limited for the total carbon fluxes in Equatorial Asia (Table 3 and Fig. 10). For each elevated mole fraction event defined by Figs. 5 and 6, we calculated an enhancement ratio of ΔCO/ΔCO2 from the reduced major axis regression, as Nara et al. (2017) did. For all peaks, except P1 and P2, every correlation between CO2 and CO variations is statistically significant (p < 0.05) for both the observations and simulations. For P1 and P2, some 455 simulated results could not have significant correlations; therefore, we combined the two events so that every correlation was statistically significant (combining P1 and P2 would be reasonable because the Sumatra fires contributed to both; see Fig. 6).
The enhancement ratios for those events could provide implications for emission ratios between CO and CO2. Note that the simulated ratios are derived from the posterior fluxes, but the overall feature does not change when the prior fluxes are used because the fire-emission ratios between CO and CO2 were unchanged by the inversion. Figure 13 depicts the observed and 460 simulated enhancement ratios and the observed correlation coefficients for each event. The figure shows that the observed ratio has a significantly large variation from 0.034 ppb/ppb to 0.169 ppb/ppb. Interestingly, the higher ratios were obtained from events that were likely contributed by the Borneo fires (P3, P6 and P7; see also

Discussion
In this study, we extensively used the aircraft observations from CONTRAIL to constrain carbon fluxes in Equatorial Asia, focusing on the devastating fire event in 2015. With the help of NIES VOS observations, especially its CO data, we have demonstrated the validity of our inverse analysis. The estimates of biomass burning emissions are moderately smaller than the 480 prescribed datasets of GFED and GFAS. Our conceivably best estimate of CV_GG, which used both the CONTRAIL and NIES VOS data, amounts to 273 Tg C and 362 Tg C for fire-induced carbon emissions during September-October and all months in 2015, respectively. These numbers are in better agreement with previous top-down estimates of Huijnen et al. (2016) (227 Tg C for September-October, and 289 Tg C for the annual total) and Heymann al. (2017) (204 Tg C for July-November) than that of Yin et al. (2016) (510 Tg C for the annual total). Furthermore, the fire-induced carbon emission of 273 Tg C for 485 September-October is also consistent with an aerosol-based study of Kiely et al. (2019), the best estimate of which is 247 Tg C as the sum of CO2 and CO emissions for Equatorial Asia but not including eastern areas (e.g., Papua New Guinea).
This study used high-precision in situ observations of CO2 to estimate carbon fluxes in contrast to studies that used satellite observations of CO (Huijnen et al., 2016;Yin et al., 2016). Therefore, we obtained the total net carbon flux that included biomass burning emission, terrestrial biosphere photosynthesis and respiration, and fossil fuel emission. The 490 estimated total net carbon flux amounts to 322 Tg C for September-October (CV_GG), 85% of which is contributed by fire emissions (Table 3 climate variations, especially to El Niño, with major driving forces of terrestrial biosphere flux changes in response to temperature and precipitation changes (Yang and Wang, 2000;Zeng et al., 2005;Wang et al., 2013).
As described in Section 2.2, we used the common scaling factor for CO2 and CO fire fluxes; therefore, the ratio of the emission factors (CO/CO2) was fixed to that of prior fire-emission data (GFED and GFAS) and burned carbon mass was modified by the inverse analysis. It is likely that the spatial pattern of fire-emission ratios was reasonably represented because 500 the model reproduced the observed variation in the enhancement ratio that might be caused by the difference in their origins (Figs. 6 and 13). However, as shown in Fig. 13, the model overestimated the enhancement ratios from September to early October, irrespective of its origin (Borneo or Sumatra). Meanwhile, it was not the case for the latter period, although the simulated ranges were large, indicating that the temporal change of the fire-emission ratio, i.e., a decrease of combustion efficiency, might not be well represented in the fire-emission data. Typical fire-emission ratios of CO/CO2 are 0.2-0.3 mol/mol 505 for peatlands and 0.1 mol/mol for tropical forests, respectively (Akagi et al., 2011;Huijnen et al. 2016;Stockwell et al., 2016). Therefore, the observed smaller enhancement ratio infers that the contribution of fires (or smouldering) in dried peatlands was smaller in the early fire period than expected. This might have partially resulted in the smaller-than-prior estimates of the fireinduced carbon emission (Table 3) because peatlands have high carbon density and are dominant sources of carbon (Page et al., 2002). Nevertheless, the uncertainty is high, as demonstrated by the model large spreads, especially for the latter period, 510 and we need more observations for robust estimations of the fire-emission ratio.
We noted that the inverse analysis of this study has several limitations. First, we employed only CO2 observations in the inverse analysis, which does not allow us to distinguish biomass burnings from other terrestrial fluxes. To separate fireinduced and other terrestrial fluxes, it would be helpful to incorporate CO observations simultaneously with CO2 observations into the inverse analysis; however, the availability of in situ CO observations (Novelli et al., 2003) is limited, especially for 515 Equatorial Asia. A joint CO2-CO inversion is left for a future study.
The second limitation is the dependency of the inverse analysis results on the prior estimate. We found that our inverse calculations had a significant sensitivity to prior fire-emission data. The posterior fluxes were similar when GFED or GFAS data were used as the prior. However, when the prior fire emissions were excluded (i.e., C_NO), the posterior flux had much lower values, indicating that we cannot fully constrain the fluxes with CONTRAIL alone and that prior fire-emission data 520 should be as accurate as possible. The relatively small sensitivity to the difference between GFED and GFAS was because the original GFED and GFAS data are comparable. Nevertheless, the well-constrained flux at the end of September in Sumatra ( Fig. 11) tells us that we could obtain a sufficient constraint from CONTRAIL when the time and location of the observations coincide with the timing of airflow rich in emission signals. Such an airflow dependency could be reduced by making the observations denser in space and time. To this end, the CONTRAIL project continues effort to reduce chances of missing data. 525 Finally, model transport errors would be the third limitation. Figures 3 and 4 show that even after the inversion, the model could not sufficiently reproduce high mole fractions near the surface, suggesting some limitation of the model.
Compared to the wind data obtained from the CONTRAIL aircraft, the speed and direction of winds over Singapore were well simulated in the model (not shown). Therefore, representative errors that include both model transport and fluxes could be one cause. A higher resolution model is desirable, and is left for a future study with advanced computational resources. 530 In this study, we tried a regionally focused inversion using different flux parameter settings for Equatorial Asia and the rest of the world (Table 1), which gave a sufficient degree of freedom to fluxes in Equatorial Asia, while strongly constraining fluxes to the prior ones in the rest of the world. This inversion approach would be acceptable only when prior fluxes can produce comparable spatiotemporal variations of atmospheric CO2 with observations, which was confirmed using the previous inversion flux of Niwa et al. (2012). Furthermore, Niwa et al. (2012) found that CONTRAIL data could 535 independently constrain the fluxes in Equatorial Asia itself, supporting the validity of separating fluxes in Equatorial Asia from those in the other regions. Nevertheless, the inversion flux used as the prior in this study was optimised for the different years, which introduced a certain level of uncertainty. In future analysis, an effort for reducing uncertainties will be made by performing a global inverse analysis by combining ground-based stations and CONTRAIL data.

Conclusions 540
In this study, an inverse system was developed to estimate high-spatiotemporal resolution fluxes in a focused area and incorporate CO as a proxy for combustion sources. We performed the inverse analysis for carbon fluxes in Equatorial Asia during the historic El Niño of 2015.
In contrast to many studies that used aircraft data for evaluating inversion results as independent data (e.g., Chevallier et al. 2019), we extensively used the CONTRAIL aircraft data in the inverse analysis and demonstrated that the aircraft data 545 could constrain flux estimates efficiently. It is essential for Equatorial Asia because there are insufficient ground-based observations in the region. Furthermore, the upward airflow, which is typical in the tropics, makes it difficult for remote ground-based stations to capture flux signals (Niwa et al., 2012).
We estimated the fire-induced carbon flux to be 273 Tg C for September-October. This number accounts for 75% of the annual fire emission and 45% of the annual net carbon flux in Equatorial Asia, demonstrating that fire emission is a major 550 driving force of the carbon flux in the region. Although the inversions have a certain degree of sensitivity to prior fire-emission data, they coherently estimated smaller amounts than the prescribed biomass burning data. One cause could be that peatland fires were not as severe in 2015 as expected, as suggested by the model overestimation of the enhancement ratios ΔCO/ΔCO2 captured by the NIES VOS observation. Nevertheless, this study is compatible with previous studies because a significantly smaller amount of carbon was released in 2015 than in 1997, of which the El Niño intensity was comparable to that of 2015. 555 This could be because the intensity of land-use change has decreased in recent decades (Kondo et al., 2018). Another possible underlying mechanism is the difference in precipitation patterns and amounts between 2015 and 1997 (Fanin and van der Werf, 2017). However, further investigation is needed by combining process-based terrestrial biosphere models, biomass burning emission models and inverse estimates, as in this study.
Although it is smaller than 1997, our estimate of the fire-induced emissions in 2015 is still notably high. Field et al. 560 (2016) pointed out that the fire emissions estimated by GFED for Equatorial Asia in 2015 are higher than the annual fossil fuel emissions of Japan. Our estimate is smaller than that of GFED, but still comparable to the latest Japanese inventory (338 TgC yr −1 for 2018 (GIO and MOE, 2020)). Using an atmospheric climate model, Shiogama et al. (2020) projected that Equatorial Asia would experience stronger droughts than that in 2015 in a future warmer climate condition. To reduce fire-induced carbon emissions from such drought events, chances of ignition must be reduced. The continuous monitoring of carbon emissions 565 with high-precision atmospheric observations is indispensable for mitigation measures against fires. The ongoing activity of aircraft-and ship-based observations used in this study will continue to provide practical implications and reliable quantitative estimates of carbon emissions from Equatorial Asia along with an inverse analysis.

Data Availability 570
The CO2 mole fraction data of CONTRAIL  and NIES VOS used in this study are available from the Global Environmental Database (GED) of NIES (http://db.cger.nies.go.jp/portal/geds/atmosphericAndOceanicMonitoring).
The CO observational data of NIES VOS are available on request to H. Nara.
This study was supported mainly by the Environment Research and Technology Development Fund of the Ministry of the Environment, Japan, and the Environmental Restoration and Conservation Agency of Japan (JPMEERF20142001 and JPMEERF20172001), whose project leader was Nobuko Saigusa of NIES. The work was also supported by the JSPS KAKENHI, Grant Number 19K03976. The inverse simulations in this study were performed on the NIES supercomputer 585 system (NEC SX-ACE). The observations from the CONTRAIL project are conducted under great supports of Japan Airlines, JAMCO and the JAL Foundation. The observational projects of CONTRAIL and NIES VOS are financially supported by the research fund by Global Environmental Research Coordination System of the Ministry of the Environment, Japan (E1253, E1652, E1851). YN is grateful to the NICAM developers of the University of Tokyo, JAMSTEC, RIKEN and NIES for maintaining and developing NICAM. Our appreciation is also extended to Tomoko Shirai and Yoko Fukuda of NIES for 590 developing and maintaining GED, through which we make our observational data publicly available.