To optimise South American fire emissions using satellite retrievals, we apply a two-step inversion framework consisting of a long-window (LW) and a short-window (SW) inversion. The LW inversion resolves monthly to inter-annual variability in the global CO budget, while the SW inversion targets daily variability in fire emissions. Decoupling the system in this way allows each step to use a set of observations that target spatio-temporal scales for source/sink processes of interest through the design of a statevector. We implement this approach in the CarbonTracker Data Assimilation Shell CTDAS;, building on the CarbonTracker Europe (CTE) ensemble Kalman smoother around the TM5 transport model .

The long-window inversion approach was recently developed for CO₂ and related tracers . Here, we present the first application that expands this LW system to CO. Subsequently, we designed and performed a short-window inversion for CO and refer to the combined system as CTE-LW/SW. We model atmospheric CO using the following the mass balance equation: 1dCO(x,y,z,t)dt=λr,tfire︷short-window⋅E(x,y,t)fire+λr,tNMVOC︷⋅P(x,y,z,t)NMVOC+λr,tCH4︷⋅P(x,y,z,t)CH4+λr,tant︷︷long-window⋅E(x,y,t)ant-L(x,y,z,t)CO+OH-D(x,y,t)dry

where Efire, Eant represent emissions from fires and anthropogenic activities. PNMVOC, and PCH4 stand for the chemical CO production through the oxidation of methane (CH₄) and non-methane volatile organic compounds (NMVOCs). Chemical loss of CO by the hydroxyl radical (OH; LCO+OH) and dry deposition (Ddry) are calculated online in the atmospheric transport model that acts as observation operator (details in Sect. ). The λ's represent a set of linear scaling factors for each source term for a given set of statevector elements (r) that are optimised in the indicated assimilation step (Table ).

First, we optimise λr,tNMVOC, λr,tCH4, and λr,tant in the global-scale long-window inversion using flask observations from the National Oceanic and Atmospheric Administration Global Monitoring Laboratory (NOAA-GML) GLOBALVIEWplus v4.0 ObsPack . This step focuses on the capturing the monthly to inter-annual variation in the CO budget components (excluding fire emissions) using the background flask network. The long-window inversion then provides a set of optimised fluxes that serve as the prior for the second step: the short-window inversion. The short-window inversion optimises 3-daily scaling factors for fast varying fire emissions with satellite XCO data that contain clear fire plume-like structures, while the other budget terms from the long-window optimisation are imposed.

A more detailed overview of the long-window inversion can be found in Appendix . The next sections further describe the short-window inversion configuration.

We start our inversions from two distinct fire emission inventories: GFED5.1 and the GFAS v1.2 . Burned area-based inventories, such as GFED , calculate emissions by combining satellite-based burned area with biogeochemical model outputs and emission factors. The new GFED5.1 inventory has improved detection of small fires by including higher-resolution burned area inputs from based on corrections derived mostly from Sentinel-2 and Landsat. Globally, this nearly doubled burned area estimates relative to MODIS alone. For Brazil this resulted in a 61 % increase for 2019, particularly during the late dry season (July–October).

GFAS uses satellite-derived FRP observed by MODIS (both Terra and Aqua), to calculate fire emissions. Biome-level scaling factors based on GFED3 are used to convert fire radiative energy (FRE) to total dry matter burned , which are then combined with emissions factors that vary between biomes, mostly from , to calculate fire emissions.

All inventories use emission factors to convert total dry matter burned to trace gas emissions. Traditionally, these factors have been static biome averages while in reality they depend on fuel type, fuel moisture content, and meteorological conditions . Recently, combined a large set of savanna fire emission factor measurements across the world with geospatial proxies for these conditions (e.g. tree cover fraction, soil moisture, vapour pressure deficit) and a machine learning algorithm to derive dynamic savanna fire emission factors. GFED5.1 is the first inventory to operationally introduce spatio-temporal dynamic emission factors for savanna fires that allow a more realistic representation of temporal and regional variability.

GFED5.1 and GFAS v1.2 yield considerably different emission estimates for the 2019 fire season in Brazil of 41 and 25 TgCO, respectively. Expressed as total carbon, this difference translates to a factor of roughly 1.5. At the biome scale, the contrasts become even more pronounced. In the Amazon biome, for example, the two inventories differ by up to a factor of two in both their CO and total carbon emissions. Beyond underscoring the need for observations, these differences provide a means to assess the robustness of our inversions by examining how the optimised emissions respond to each prior.

We use the Transport Model 5 Massive-Parallel (TM5-MP; ) model to transport the CO emissions and production fields, from which vertical profiles of CO mole fractions and pressure are sampled. These profiles, combined with averaging kernels, are subsequently used in CTDAS to derive XCO.

The short-window TM5 simulations were performed globally at a horizontal resolution of 1° × 1°, with 34 vertical levels, driven by three-hourly meteorological fields from the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 ERA5;. Dry deposition is computed online. CO chemistry is linearised by prescribing three-hourly OH fields from the Copernicus Atmosphere Monitoring Service (CAMS) ECMWF Atmospheric Composition Reanalysis 4 (EAC4) dataset , as well as the CO production from CH₄ and NMVOC oxidation optimised by the long-window. Fire emissions are distributed vertically using injection heights from the IS4FIRES dataset .

Each statevector element (r) in λr,tfire from Eq. () represents a 1°×1° grid box over land in South America between 22.5° S, 9.5° N, 79.5° W, and 34.5° W, resulting in a total of 1023 spatial unknowns (Fig. ). At the start of each 3 d cycle, λrfire are set to 1.0. We run the SW system with a 3 d assimilation window and 2 lags (i.e. 3 d lag). The scaling factors are optimised with a square root ensemble Kalman Smoother . We minimise the cost-function equation as defined in . In each cycle, a total of (2×1023) optimised scaling factors are thus calculated in the SW inversion. The optimised mean state of each cycle is propagated to inform the next cycle's mean state. This mean state is determined as the average between the current cycle's optimised state and a state filled with λ values of 1.0 (which represent the prior fluxes that are calculated by the long-window system). This procedure ensures that the scaling factors quickly revert back to the unscaled prior value of 1.0 when no CO observations are present.

The degree of uncertainty on each scaling factor and their spatial correlations are described by the prior covariance structure. This covariance structure reflects our assumption that the errors in emission inventories are related to emissions factors and fuel characteristics or conditions, which often have some biome-dependency. We set the prior uncertainty to 100 % of the prior emission (variance = 1.0) and impose spatial correlations within biogeographical biomes using an e-folding distance correlation of 300 km (see also Fig. ). Note that our inversion system is not designed to resolve emissions from individual fire plumes, a.o. due to the 1° × 1° resolution of our transport model and scaling factors, as well as biome level error correlations. Instead, it provides top-down constraints on fire emissions at the aggregated biome level.

Given that only a subset of the gridded fire emission state contains non-zero values within a 3 d cycle, we restrict the state-space to these active grid cells. This targeted state reduction mitigates the impact of zero-signal elements, which can otherwise dilute the ensemble covariance estimate.

Fire emissions are inherently non-negative and represent a bounded quantity. However, in practice, the optimisation algorithm may generate negative λ values that correspond to physically impossible negative emissions. We apply a semi-exponential transformation (Eq. ), similar to , to the optimized scaling factors where λ<1.0. We acknowledge that this transformation introduces non-linearity in the relationship between the statevector deviations and XCO deviations (x′ and H(x′) respectively, see ), yet we consider the use of the transformation to be more physically consistent, as it ensures the exclusion of unrealistic negative emissions. Besides, because we run a lagged system, subsequent lags can compensate for any non-linear effects introduced by this transformation. 2λ=e(λ-1)forλ<1

We conducted a series of inversion experiments to quantify Brazilian fire emissions and to assess the robustness of the estimates. These experiments test the sensitivity of the inversion results to the choice of prior fire emission inventory and the assimilated satellite instrument. The different configurations are summarised in Table .

In addition to testing the sensitivity to different priors and observational constraints, we quantified how uncertainties in OH chemistry and in CO production from NMVOC oxidation influence the inferred fire emissions. Rather than performing a new suite of inversions, we base this on a set of sensitivity experiments that was targeted to do this for the same region and for four fire seasons, by (see their Fig. S2). ran their inversions with two sets of OH fields, and two sets of chemical production fields. For each season that ran the experiments, we calculate the ensemble standard deviation across their sensitivity experiments and then average these values over all four years. This approach yields an estimated structural uncertainty of 15 TgCO per season in the posterior fire emissions. We consider this estimate conservative for two reasons: (1) their inversion domain extends beyond Brazil, whereas our reported emissions are limited to the Brazilian portion of the domain, and (2) our system includes an intermediate long-window inversion step.

In this section, we demonstrate the performance of our inversions by comparing against observations. We start with a comparison to satellite-based XCO and compare to surface observations (in-situ and aircraft). We focus these comparisons on our “base inversion” which started from GFED5.1 and assimilated TROPOMI superobservations.

According to the GFAS v1.2 and GFED5.1 inventories, total CO emissions from fires in Brazil during the 2019 fire season (22 July–30 November) were 25 and 41 TgCO, respectively, as indicated in Fig. . Our inversions suggest that fire emissions are 474648 TgCO (meanminmax). The posterior emissions deviate by less than 20 % from the GFED5.1 prior. For GFAS v1.2 however, the inversions imply that an 81 % increase of emissions is needed. This prior-posterior increase is substantially higher than the average 50 % increase that found for the 2003–2018 fire seasons and will be discussed in more detail (Sect. ).

Despite starting from substantially different prior fire-emission totals, the inversions converge to nearly the same posterior fire-emission integral over the season (46.0 and 47.7 TgCO). Likewise, inversions that assimilate either TROPOMI or MOPITT data end up with similar fire season totals (47.7 and 48.2 TgCO), underscoring the robustness of the posterior estimates to both the choice of prior and the choice of satellite instrument.

On more local scales (bar-stacks in Fig. ) or shorter time intervals, the posterior emission spread becomes larger in a relative sense but still demonstrates strong convergence from multiple priors and instruments down to 3 d intervals for most periods analysed (Fig. ).

To better understand the origin and dynamics of posterior–prior differences, we analyse CO emissions at the biome level and their temporal evolution. Given the contrasting fire dynamics and the shifting position of the arc of deforestation relative to biome boundaries, we further subdivided the Amazon emissions into the season’s dominant fire types following . As shown in Figs.  and , savanna fires make a substantial contribution within the Amazon biome (21 %–32 %), and their temporal evolution aligns more closely with Cerrado fires than with deforestation events, supporting this subdivision.

The temporal evolution of fire CO emissions during the 2019 dry season is characterised by a clear succession of different fire regimes (Fig. ). Both prior and posterior estimates reproduce this phasing, but the posterior estimates highlight important discrepancies in the magnitude of emissions for several biomes – most notably the Caatinga and Cerrado, where optimised emissions differ by a factor of 2–3 from their priors. Figure  illustrates this evolution, which we divide into three phases: early-season (mid-August), mid-season (mid-September), and a widespread late-season tail (October–November).

When comparing our inversion results with existing bottom-up inventories, we find encouraging progress in fire emission modelling. This is demonstrated by the good agreement with the new GFED5.1 dataset (posterior within < 20 % of GFED5.1), as opposed to the older GFAS v1.2 product (posterior deviates > 80 %). The agreement with GFED5.1 suggests that recent updates, such as the inclusion of the new small-fire burned area dataset, help to better capture regional fire regimes.

When analysed at biome level, the inversion suggests large fire emission changes for fires in the Amazon, ranging between 3–9 TgCO, with a reduction and increment compared to GFED5.1 and GFAS v1.2 respectively. However, the posterior mean (23.5 TgCO) ends up well within the large prior range of 14.3–26.8 TgCO as inventories in tropical forest regions remain uncertain. Detection of emissions from understory fires remains inherently challenging due to persistent cloud cover and dense canopies . It should be acknowledged that our posterior spread remains relatively large for this region (20.9–25.5 TgCO) in part due to limited observational constraints from MOPITT during the peak of the fire season here and that our system has limited capacity to account for a lack of emissions due to missed detections, as will be discussed later.

In contrast, we find systematic emission increments for the Cerrado and the Caatinga biomes. The inversion adjusts the prior by a factor two, resulting in a 7–8 TgCO prior-posterior gap. This result is unexpected, as fire dynamics in these savanna-dominated ecosystems are typically considered relatively well captured and constrained by global inventories due to availability of ground measurements and relatively straightforward fire dynamics. Our findings however, are in line with previous work by , who also reported a systematic underestimation of savanna and shrubland fire emissions by GFAS v1.2. In their work the median difference between the prior and posterior emissions also approached a factor of two, while using a different inversion algorithm (4D-var v. EnKS), meteorological driver data (ERA-Interim v. ERA5), and different CO source/sink datasets. The remainder of this discussion will investigate the potential drivers of this large and systematic discrepancy between our inverse results and the fire inventories.

To understand the source of the discrepancy between the prior and posterior Cerrado/Caatinga emissions, we first assess potential errors in our inversion framework before discussing the prior inventories.

First, transport modelling errors can play a role. The comparison of TM5 simulated vertical profiles of CO against observed CO from aircraft flights near Manaus suggest that convective mixing of surface signals aloft is too strong in TM5 (Fig. ). At the same time, major errors in vertical transport seem unlikely given the strong consistency between TROPOMI- and MOPITT-based inversions despite their different vertical sensitivities and overpass times. Nonetheless, transport modelling errors remain a source of uncertainty in atmospheric inversions. These uncertainties are challenging to quantify and would benefit from for instance an inter-comparison study with different transport models over South America, which is beyond the scope of this work.

Second, showed that African fires contribute up to 25 % of tropospheric CO mass over eastern Brazil. The good agreement between TROPOMI observations and TM5 simulated fields over the main inflow regions (Sect. , B2 in Fig. d) suggests, however, that long-range transport biases are small. Moreover, the good agreement negates the hypothesis that the high emissions are a compensation for a lack of CO inflow from distant fire emissions or CO production from CH₄ oxidation in the background atmosphere.

Third, weak correlations between the posterior Cerrado emission ensembles with other regions suggest that the inferred increments over the Cerrado are genuine local signals rather than the inversion compensating for omitted emissions in neighbouring biomes or countries (Appendix ).

Fourth, localised chemical sources or sinks – such as CO production from NMVOC oxidation or loss through OH – remain an alternative explanation for the differences over the Cerrado and Caatinga. However, the magnitude of the sub-regional changes required makes this unlikely. To close the emission gap, NMVOC-derived CO production in these regions would need to increase two- to fourfold. Besides, this assumes a 1:1 compensation between NMVOC-CO and fire-CO, but as demonstrated, the relationship is closer to 2:1, implying an even larger and less plausible adjustment would be needed. Furthermore, such a large, localised change in the NMVOC source would require compensating biases elsewhere and degrade the current good agreement with independent CO budget estimates .

Following the same reasoning, we think that large OH biases in the Cerrado/Caatinga are improbable. Moreover, the CAMS state-of-the-art chemical data assimilation system has constraints on species important for OH-chemistry through extensive assimilation of satellite observations, making such systematic biases in our imposed OH fields unlikely. Also, a recent inter-comparison by shows that CAMS EAC4 surface ozone (a key OH precursor) lies at the low end of current reanalyses, suggesting that EAC4 could more likely underestimate than overestimate OH. More OH in our inversion would, if anything, increase inferred fire emissions, further stretching the prior-posterior Cerrado/Caatinga emission gap.

While structural uncertainties in the representation of the chemical sources and sinks are substantial, ±15 TgCO (see Sect. ), we argue that the current chemical source and sink terms cannot fully account for the Cerrado/Caatinga posterior estimates without degrading agreement with observations in downwind regions (e.g. Sect. ). Therefore, the adjustment in the Cerrado/Caatinga seems to be plausible not only because it is independent of the data assimilated in our inversions, but also because it is consistent with other top-down studies that found larger CO and CO₂ emissions in the Cerrado and Caatinga biomes .

This study and our new modelling framework open the path for future research. For example, we want to highlight the potential of leveraging CO to improve fire detection and quantification, particularly for small and cloud- or canopy-obscured fires that traditional bottom-up methods may still under-represent. Although our current framework effectively constrains regional emissions, it has only limited capability to assign emissions locations where the priors have no or low emissions because the errors we assign to each location depend on the magnitude of the local fire emission itself. Future studies could build on our work by implementing more flexible prior error structures. For example, adopting approaches that allow the inversion to allocate emissions more freely, such as in , could allow a more complete exploitation of downwind CO observations and refine emission estimates for low-intensity fire regimes.

Furthermore, our data selection strategy focused on fresh fire plumes by using a 125 ppb threshold, which proved effective in constraining peak fire emissions without introducing strong biases in CO background mole fractions. Future work should explore more dynamic data selection methods or consider assimilation of background XCO in the long-window inversion step. Such advancements would allow for the assimilation of all available observations, which could help to capture more diffuse, widespread fire emissions that lead to lower yet detectable XCO increases.

In addition, we acknowledge that our 3×R rejection strategy, while standard practice, may have led to the exclusion of some valid high-concentration observations. As a result, the most extreme fire enhancements that were simulated and not observed, or vice versa, may be partially filtered out. The prior residuals of these rejected samples do not suggest that we systematically under- or overestimate the posterior fire emissions. Nonetheless, we may have rejected some valid data and we recommend future studies to consider exploring more sophisticated, possibly non-Gaussian outlier detection methods that are better suited to process fire plumes.

Aerosol-induced XCO retrieval biases are a potential concern in dense smoke plumes because aerosols modify the light path of photons which might affect retrieval sensitivity. However, aerosol scattering effects are explicitly accounted for in the SICOR retrieval and sensitivity tests presented in the algorithm theoretical baseline document that include cases with high aerosol loads, suggest the algorithm remains within 1 % uncertainty . In addition, a validation campaign during a wildfire suggests that uncertainties remain within mission performance requirements even in optically thick smoke plumes (10 % accuracy, 15 % precision) . Aerosol radiative effects in the 4.7 µm thermal-infrared absorption band are weak and therefore not explicitly accounted for in the retrieval . tested for a shift of the mean in bias against two AERONET sites under high and low aerosol conditions, but did not find a significant shift. This finding, however, related to version 6 of the MOPITT algorithm. Especially since version 9 coverage increased, particularly under elevated aerosol conditions. Nonetheless, since aerosol properties, such as size and mixing state, are generally more complex than assumed in radiative transfer models , the effects of aerosols on retrievals remains a source of uncertainty.

Ultimately, our goal is to accurately quantify total carbon release. We convert the CO emissions to total carbon using pre-determined CO2CO ratios, as done in previous studies e.g.. Assuming the prior CO2CO ratios, our posterior CO estimates translate to fire carbon emissions of 270–278 TgC for the 2019 Brazilian fires, compared to 141–205 TgC according to GFAS v1.2 and GFED5.1, respectively. This is roughly 100 TgC larger than previous estimates . Approximately 50 %–70 % of this prior-to-posterior increase stems from the Cerrado and Caatinga. This not only highlights the importance of savanna fire carbon emissions but also the critical uncertainty in CO2CO emission ratios. To include the uncertainty arising from the assumed prior emission factor ratios, we performed a sensitivity analysis perturbing the assumed CO2CO ratios by ±20 % (Fig. ). This widens the estimates by ∼ 55 TgC in both directions and results in a range of 216–334 TgC. The downside of CO-only inversions for total carbon emission quantification is that we must rely on the accuracy of the emission factors that vary by fuel type, fuel moisture content, and meteorological conditions. Future work would benefit from further investigation of the CO2CO emission factor ratios, and potential constraints thereon. For instance, joint CO/CO2 inversions would allow the co-optimisation of the emission ratios using alternative combustion efficiency proxies like ΔXNO2ΔXCO .

With continuing advances in computational capacity, increasing availability of large atmospheric datasets, as well as capacity to efficiently analyse these, multi-tracer, multi-instrument approaches are on the rise e.g.. From a fire-emissions inversion perspective, exploration of joint observation constraints from CO, CO₂, NO₂, aerosols, HCHO, and CH₄, may not just benefit total fire emission quantification, but also help to partition in terms of fire type or burning phase, as well as the ability to separate source-background signals.