Biomass burning combustion efficiency observed from space using measurements of CO and NO2 by TROPOMI

Abstract. The global fire emission inventories depend on ground and airborne measurements of species-specific emission factors (EFs), which translate dry matter losses due to fires to actual trace gas and aerosol emissions. The EFs of nitrogen oxides (NOx) and carbon monoxide (CO) can function as a proxy for combustion efficiency to distinguish flaming from smoldering combustion. The uncertainties on these EFs remain large as they are limited by the spatial and temporal representativeness of the measurements. The global coverage of satellite observations has the advantage to fill this gap, making these measurements highly complementary to ground-based or airborne data. We present a new analysis of biomass burning pollutants using space-borne data to investigate the spatiotemporal efficiency of fire combustion. Column measurements of nitrogen dioxide and carbon monoxide (XNO2 and XCO) from the TROPOspheric Monitoring Instrument (TROPOMI) are used to quantify the relative atmospheric enhancements of these species over different fire-prone regions around the world. We find spatial and temporal patterns in the ΔXNO2 / ΔXCO ratio that point to distinct differences in biomass burning behavior. Such differences are induced by the burning phase of the fire (e.g. high temperature flaming vs. low temperature smoldering combustion) and burning practice (e.g. the combustion of logs, coarse woody debris and soil organic matter vs. the combustion of fine fuels such as savanna grasses). The sampling techniques and the signal-to-noise of the retrieved ΔXNO2 / ΔXCO signals were quantified with WRF-CHEM experiments and showed similar distinct differences in combustion types. The TROPOMI measurements show that the fraction of surface smoldering combustion is much larger for the boreal forest fires in the upper northern hemisphere and peatland fires in Indonesia. These types of fires cause a much larger increase (3 to 6 times) in ΔXCO relative to ΔXNO2 than elsewhere in the world. The high spatial and temporal resolution of TROPOMI also enables the detection of spatial gradients in combustion efficiency at smaller regional scales. For instance, in the Amazon, we found higher combustion efficiency (up to 3-fold) for savanna fires than for the nearby tropical deforestation fires. Out of two investigated fire emission products, the TROPOMI measurements support the broad spatial pattern of combustion efficiency rooted in GFED4s. Meanwhile, TROPOMI data also add new insights on regional variability in combustion characteristics that are not well represented in the different emission inventories, which can help the fire modeling community to improve their representation of the spatiotemporal variability in EFs.


debris and soil organic matter vs. the combustion of fine fuels such as savanna grasses). The sampling techniques and the signal-to-noise of the retrieved ΔXNO2/ΔXCO signals were quantified with  CHEM experiments and showed similar distinct differences in combustion types. The TROPOMI measurements show that the fraction of surface smoldering combustion is much larger for the boreal forest fires in the upper northern hemisphere and peatland fires in Indonesia. These types of fires cause a much larger increase (3 to 6 times) in ΔXCO relative to ΔXNO2 than elsewhere in the world. The high spatial and temporal resolution of TROPOMI also enables the detection of spatial gradients in combustion 30 efficiency at smaller regional scales. For instance, in the Amazon, we found higher combustion efficiency (up to 3-fold) for savanna fires than for the nearby tropical deforestation fires. Out of two investigated fire emission products, the TROPOMI measurements support the broad spatial pattern of combustion efficiency rooted in GFED4s. Meanwhile, TROPOMI data also add new insights on regional variability in combustion characteristics that are not well represented in the different emission inventories, which 35 can help the fire modeling community to improve their representation of the spatiotemporal variability in EFs.

Introduction
The importance of biomass burning as a source of atmospheric trace gases and aerosols has been 40 increasingly studied and recognized in the past decades (Andreae, 2019). To quantitatively assess the influence of biomass burning on atmospheric chemistry and climate the atmospheric modeling community requires accurate estimates of fire emissions. Important scientific efforts have led to the development of a number of biomass burning emission products by combining satellite derived datasets of burned area with biogeochemical models and biomass density datasets that enabled more accurate 45 emission estimates (e.g. Hoelzemann et al. 2004;Ito and Penner, 2004;van der Werf et al., 2003). Since then much progress has been made to reduce uncertainties of the involved datasets (e.g. burned area, fuel loads, combustion factors, and emission factors), but the uncertainties in the emission estimates remain substantial especially at the more detailed regional scales (van der Werf et al., 2017). The recent emergence of new space-based instruments that measure different trace gases could provide additional 50 top-down constraints on biomass burning emissions and combustion characteristics.
Since the 1980s numerous field measurement campaigns have provided information on biomass burning characteristics and emissions for different biomes and vegetation types around the world (e.g. Andreae et al., 1988;Lacaux et al., 1996;Yokelson et al., 1999). Most of these studies derived so-called emission 55 factors (EF or EFs) for different chemical compounds to quantify the number of grams of a trace gas or aerosol emitted per kilogram of biomass burned. These EFs are combined with biogeochemical models such as used in the Global Fire Emissions Database (GFED; van der Werf et al., 2010) to provide global biomass burning emission estimates, which in turn are used as input for atmospheric transport models (e.g. CarbonTracker data-assimilation system; Peters et al., 2007). The main function of these 60 biogeochemical models is to help predict the spatiotemporal combustion rate of biomass dry matter based on the fuel load, combustion completeness and / or remotely-sensed products like burned area or fire radiative power (FRP). A number of EF databases have been published providing biome-average EFs derived from the large collection of available field and laboratory measurements. The first widely used biomass combustion efficiency, i.e., the fraction of biomass combustion by flaming and smoldering.
Flaming combustion is hotter and cleaner and produces relatively large amounts of NO2 and relatively small amounts of CO, whereas smoldering combustion happens at fairly low temperatures at the surface and produces predominantly CO (Andreae and Merlet, 2001).

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Previous applications of joint trace gas analysis, including CO and NO2, focused mostly on constraining anthropogenic and fossil fuel emissions, using either surface observations (e.g. Lopez et al., 2013;Hassler et al., 2016) or satellites (e.g. Silva et al., 2013;Reuter et al., 2014;Konovalov et al., 2016). Mebust and Cohen (2013) demonstrated the detection of seasonal variations of fire EFs in the African savannas using satellite measurements of NO2. Silva and Arellano (2017) used satellite observations of CO,CO2 and NO2 95 in a novel way to distinguish combustion types around the world. This study provided new insights on emission inventories as they found distinct differences in the ratios of CO/CO2 and CO/NO2 between different biomass and urban combustion regions, which are often not well represented in emission inventories.

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In this study we aim to demonstrate the capabilities of the new space-borne TROPOspheric Monitoring Instrument (TROPOMI, launched in October 2017; Veefkind et al., 2012) to provide new information about biomass burning characteristics and efficiency in different regions around the globe. The main advantage of TROPOMI is that it delivers co-located column densities of several trace gases, including CO and NO2. It extends the capability of legacy instruments like MOPITT and OMI by measuring trace 105 gases at improved accuracy, surface sensitivity, and spatial resolution providing daily global coverage.
The wealth of data that TROPOMI provides offers the unique opportunity to monitor seasonal changes in the relative amount of flaming and smoldering combustion, even in remote regions where ground-based measurements of fire properties are sparse. For instance, under relatively clear-sky conditions, the Amazon basin can now be examined for trace gases in much more detail on a day-to-day basis during 110 annual dry season fire spells. TROPOMI surmounts some of the limitations of previous joint trace gas analysis studies where measurements were often taken from various instruments, each with their own intrinsic limitations such as a clear-sky-only retrieval requirement (e.g. with MOPITT), and with widely different spatial resolutions and repeat cycles, i.e. the number of days between two satellite overpasses over the same region. The improved consistency among the different TROPOMI data products in terms 115 of overpass time and location, retrieval sensitivity and spatiotemporal resolution might also help to suppress aggregation errors and biases in the derived ratios of trace gases, improving the capability to distinguish differences in combustion types at the regional scale. The aim of this study is two-fold: (1) To demonstrate the detection of spatial variations in the regional enhancements of CO and NO2 for different fire prone areas that are either dominated by smoldering or flaming fires, or a combination of both. (2) 120 To investigate the use of TROPOMI CO and NO2 to verify the current set of biome-specific EFs used in the atmospheric and climate modeling community.

GFED4s and GFAS Emission Factor Ratio
We used two well-established biomass burning emission datasets to interpret and validate TROPOMI 125 inferred combustion characteristics and efficiencies: the Global Fire Emission Database version 4 with small fires (GFED4s; van der Werf et al., 2017) and the Global Fire Assimilation System version 1 (GFAS; Kaiser et al., 2012). Both datasets provide global fire emission fluxes for a large number of chemical species but use different methods.

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GFED4s is based on Carnegie-Ames-Stanford Approach (CASA) biogeochemical model (Potter et al., 1993) to predict the amount of above and below ground biomass at monthly temporal resolution. The MODIS Collection 5.1 MCD64A1 500 m burned area satellite product  is used to estimate the daily dry matter combustion rate at 0.25°×0.25° spatial resolution from 2001 up to 2016.
GFED4s also includes 1×1 km 2 thermal anomalies (active fire counts) from Terra and Aqua MODIS, and 135 500×500 m 2 surface reflectance observations, providing a statistical estimate of the burned area associated with small fires (Randerson et al., 2012;van der Werf et al., 2017). The GFED4s flux estimates from 2017 onward (used in this study) are not directly derived from the burned area product because the underlying MODIS algorithm was upgraded from Collection 5.1 to Collection 6. Instead, flux estimates are simply derived from MODIS active fire detections and their FRP and the climatological ratio between 140 them derived from the overlapping 2003-2016 period. The GFAS product calculates emissions by assimilating FRP observations from the MODIS Terra and Aqua satellites and is tuned to match the dry matter combustion rate of GFED3 per biome (Kaiser et al., 2012). The version we used provides daily emissions at 0.1°×0.1° spatial resolution.

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Both biomass burning products are combined with EFs to translate the derived dry matter combustion rate to specific trace gas and aerosol emissions. These EFs are based on a large number of trace gas measurement campaigns in the field, in the air or in the laboratory, and are subdivided for dominant biome/burning categories without specifying any variability in space and time. GFAS uses the older EF dataset compiled by Andreae and Merlet (2001) with additional updates from the literature and EFs of 150 peatland fires from Christian et al. (2003). In this dataset boreal and temperate forest fires form together a single category named extratropical forest fires (ETF). GFED4s uses EFs largely based on the dataset compiled by Akagi et al. (2011). This dataset is based on trace gas measurements from fresh smoke sampled in close proximity of the fire source and cooled to ambient temperature but with minimal photochemical processing. This provides a better representation of the initial emissions without chemical 155 disturbances (to aid assessment of biomass burning in atmospheric chemistry models). The Akagi et al. (2011) dataset makes a distinction between boreal and temperate forest fires. For boreal fires they used the average of airborne and ground-based measurements that is roughly equivalent of assuming 70% of dry matter consumption is originating from smoldering combustion. Therefore, the EFs for the boreal latitudes are relatively high for carbon monoxide (EFCO: 127.0 g kg -1 ) and low for nitrogen oxides (EFNOx: 160 0.9 g kg -1 ). The EFs for the temperate fires are 88.0 and 1.9 g kg -1 , respectively for CO and NOx, and represent a larger fraction of flaming combustion similar to the ETF category used in the Andreae and Merlet (2001) dataset. Other variations in EFs between Akagi et al. (2011) and Andreae and Merlet (2001) are due to variations in the averaging and weighting methods of the measurements. In addition, GFED4s includes sub-grid cell partitioning of burned area to account for different fire types within a grid cell, 165 which affects the grid-average emissions of CO and NOx. Because NO is usually the most abundant Nspecies emitted to the atmosphere and because NO and NO2 are rapidly interconverted in the atmosphere both datasets report EFs for NOx as NO. Henceforth, the EFs are reported in units of mmol kg -1 and mol kg -1 for EFNOx and EFCO, respectively, to make ratios of EFs of similar magnitude as the ratios of column densities measured by TROPOMI (see Sect. 2.2). Table 1 shows an overview of EFs of CO and NOx used 170 by GFAS and GFED4s.
The spatial stratification of the different biomass burning categories is apparent in the ratio between NOx and CO EFs. This ratio exhibits a distinct "fingerprint" that carries information on combustion efficiency, combustion practice, and fuel type. In this study, we call this dimensionless metric the Emission Factor 175 Ratio (EFR = EFNOx/EFCO). EFR is a relative measure of how much millimoles of NOx are released to the atmosphere for each mole of CO. This metric is a proxy for the modified combustion efficiency (MCE) parameter that is often used in fire emission quantification studies but more difficult to derive from space given the relatively small departures of CO2 concentrations over biomass burning regions from background conditions. The MCE is defined as ΔCO2/(ΔCO+ΔCO2) to indicate combustion efficiency of 180 a fire by measuring the amount of excess in CO2 in comparison to total emitted C from CO2 and CO (Yokelson et al, 1999). Table 1 gives the EFR for the different combustion types based on the ratio between the EFs of NOx and CO used by GFED4s and GFAS. Figures 1a and 1b show the spatial distribution of EFR in both datasets. For GFED4s, we subdivided EFR into three different categories: high EFR above 50 for savanna fires, EFR between 10 and 50 for temperate forest fires, tropical 185 deforestation fires and agricultural waste burning, and EFR lower than 10 for boreal and peatland fires.
High EFR is thus related to the flaming type of combustion that is hotter and more efficient as it produces relatively less CO alongside CO2 and relatively more NOx by combustion of N in the biomass itself.
Conversely, low EFR is generally related to slow smoldering type of combustion. The EFR categories are similar for GFAS, however, due to differences between the EFs datasets (for reasons discussed in the 190 previous paragraph) EFRs are classified differently: high EFR above 30 for savanna fires, EFR between 10 and 30 for ETF fires, tropical deforestation fires and agricultural waste burning, and EFR lower than 10 for peatland fires. Fig. 1 are various regions of interest studied in this paper with strong seasonal occurrences 195 of biomass burning. Regions that have been selected for detailed analysis using TROPOMI: two boreal fire regions in North America, one boreal fire region in Siberia, five savanna fire regions on the African continent, one savanna fire region in Australia, two peatland fire regions in Indonesia, and 15 regions in South America to more specifically study spatial gradients in combustion efficiency between tropical deforestation and savanna fires. 200

TROPOMI CO and NO2
The TROPOMI instrument was launched on 13 October 2017 onboard the Sentinel-5 Precursor satellite to monitor the chemical composition of the atmosphere (Veefkind et al., 2012). It measures a range of trace gases at unprecedented spatial resolution with a daily global coverage. Sect. 2.2.1 and 2.2.2 provide further details about the TROPOMI operational level 2 column density data products of carbon monoxide 205 (XCO) and nitrogen dioxide (XNO2). Figure 2 shows a few examples of monthly and daily average maps of XCO and XNO2 for a number of biomass burning regions together with CO emissions from GFED4s (Sect. 2.1). Enhancements in XCO and XNO2 correspond well with local fire emissions based on independently derived burned area. Note that the chemical lifetime of NOx is much shorter than for CO (minutes to hours vs. weeks to months). The main chemical driver during daytime is the photochemical 210 balance between NO2 photolysis and NO oxidation by ozone converting NO into NO2 and makes NO2 a robust measure for NOx. The NOx lifetime is limited by the conversion of NO2 to HNO3 in reaction with hydroxyl (OH) radicals. The short chemical lifetime results in a precise alignment between the enhancements of XNO2 and the location of fire emissions, while enhancements of XCO are more affected by atmospheric transport due to its longer chemical lifetime. These differences in lifetime can cause biases 215 in the joint analysis of XNO2 and XCO and its ratio. That limits our ability to make direct quantitative comparisons between EFs and column densities. Nonetheless, assuming the lifetime does not vary greatly from fire to fire and from region to region, it is probable that it does not affect our ability to the detect variations in fire characteristics around the world. This limitation is further discussed in Sect. 4 of the paper. 220

XCO
The carbon monoxide total column density from TROPOMI is retrieved from reflected and backscattered solar radiance around 2.3 μm measured by the shortwave infrared module of the spectrometer. The Shortwave Infrared Carbon Monoxide Retrieval algorithm (SICOR, Landgraf et al., 2016) is used to translate spectral radiances to XCO column densities, with high sensitivity to the planetary boundary layer 225 for clear-sky conditions over land. For cloudy conditions over land and ocean, the XCO has a stronger sensitivity at higher altitude. To account for cloud interferences SICOR retrieves an effective cloud optical depth and cloud height, and provides a column averaging kernel as part of the product which represents the height sensitivity of the measurement.

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A good agreement was found between TROPOMI XCO and TCCON XCO ground measurements for clear and cloudy sky conditions (Borsdorff et al., 2018a). Mean biases amount to: 6.0 ppb for clear-sky, 6.2 ppb for cloudy-sky retrievals and 5.8 ppb for the combination of both. The station-to-station standard deviation of the bias was 3.9 ppb for clear-sky, 2.4 ppb for cloud-sky, and 2.9 ppb for the combination of both. Thereby, TROPOMI achieves its mission requirements on precision (<10%). 235 The XCO column density for 2018 is observed with daily global coverage at a spatial resolution of 7×7 km 2 in nadir. The data is selected for clear-sky and cloudy-sky conditions with a cloud top height limited to 5000 m and an aerosol optical thickness equal or larger than 0.5 (TROPOMI CO level 2 README Document, 2018). In addition, the two most westward pixels of the swath were excluded due to 240 performance issues (Borsdorff et al., 2018b). The XCO column density is presented in units of mole per square meter (mol m -2 ).

XNO2
The tropospheric nitrogen dioxide column density from TROPOMI is retrieved from spectrometer measurements of direct and backscattered solar radiance between 405 and 465 nm. The XNO2 retrieval 245 algorithm uses the DOAS approach and is an adapted version of the algorithm used for the DOMINO v2.0 (Boersma et al., 2011) and QA4ECV XNO2 products (van Geffen et al., 2015, Boersma et al., 2018. In the retrieval procedure, NO2 slant columns are derived from the measured spectra using the DOAS method. Then the tropospheric component of the slant columns is separated from the stratospheric component, and finally the tropospheric slant columns are converted to vertical columns XNO2 based on 250 the tropospheric air mass factor (AMF).
XNO2 is observed with daily global coverage at a spatial resolution of 3.5×7 km 2 in nadir. The spectrometer's near infrared band provides additional information on cloud characteristics and allows a better cloud correction, i.e., improving the measurement precision under cloudy conditions. XNO2 255 column densities have been compared with ground-based MAX-DOAS measurements at 14 stations. In general, TROPOMI underestimates the tropospheric column at polluted sites. The daily median negative biases are generally less than 50%, within the required measurement precision, but vary from station-tostation (TROPOMI NO2 level 2 README Document, 2018). Because this bias is largely systematic, it is not expected to deteriorate our ability to differentiate between fire characteristics. This is further 260 For this study, we use the recommended filter settings outlined in the README document, removing cloud-covered scenes with a cloud radiance fraction exceeding 0.5, scenes covered by snow or ice, and other problematic retrievals (qa_value > 0.75). The XNO2 column density is presented in units of 265 millimole per square meter (mmol m -2 ).

Mole Fraction Ratio: sampling methods
For our analysis, we selected important hotspots of biomass burning according to the GFED4s database.
To prevent contamination with urban trace gas emissions large population centers were avoided. The regions are outlined in Fig. 1  To derive the regional enhancements in XCO and XNO2 relative to the background, ΔXCO and ΔXNO2 respectively, we used two main sampling methods depending on the scale and severity of the fires in the 275 region. A statistical bulk method (SBM) is used for regions that are characterized by extensive seasonal burning over a large area and where upwind background levels of XCO and XNO2 are difficult to define.
A local sampling method (LSM) is used for regions where we could identify local fires and plumes of enhanced trace gas abundance for which the wind direction and background column density upwind of the fires could be determined. Each method is discussed in more detail in Sect. 2.3.1 and 2.3.2, 280 respectively. With daily estimates for ΔXNO2 and ΔXCO we were able to derive a new dimensionless metric: the Mole Density Ratio (MDR = ΔXNO2/ΔXCO). The MDR is the atmospheric equivalent to EFR and provides a remotely sensed proxy for biomass combustion efficiency.

Statistical bulk method
The statistical bulk method (SBM) is based on the method discussed in Silva and Arellano (2017) who 285 used it to distinguish urban and industrial trace gas enhancements from biomass burning. It provides a simple measure of regional trace gas enhancements when background column densities are difficult to determine. For this method, the daily TROPOMI data were regridded at 0.1°×0.1° resolution from which co-located XCO and XNO2 data within 5°×5° boxes were sampled each day over the selected regions (see Fig. 1 and 2). The size of these boxes allows for a sufficient number of trace gas observations each 290 day (more than 1000). To determine the regional trace gas enhancement relative to the background (ΔXCO and ΔXNO2 are here jointly indicated by ΔX) we assume that the sampled data exhibits a Gaussian normal distribution. A trace gas enhancement of one standard deviation above the daily mean of the distribution is assumed to be due to fires, i.e., Xfire = μX + σX. Conversely, a column density of one standard deviation below the mean is assumed to represent the trace gas background, i.e., XBG = μX − σX. This 295 implies that the regional trace gas enhancement is assumed to be two times the standard deviation of the distribution, i.e., ΔX = Xfire − XBG = 2σX. Figure 3a displays an idealized normal distribution of sampled column densities of XCO indicating the values of XCOfire, XCOBG, ∆XCO, μXCO, and σXCO along the distribution. The MDR between ΔXNO2 and ΔXCO is therefore equal to the ratio between two standard deviations σXNO2/σXCO. As discussed by Silva and Arellano (2017), this assumption is only valid if both 300 species are highly correlated with each other. This is the case for this study given the strong co-location of the sampled XCO and XNO2 data, the daily sampling interval for both species, and because we carefully selected strong biomass burning source regions. SBM was used for the following regions: 15 regions over the southern Amazon basin of South America, where data was sampled between July and September 2018, 2 regions over Northern Africa, where data was sampled in December 2018, and 3 305 regions over Southern Africa, where data was sampled between July and September 2018. Deriving ΔX as outlined above, may not reflect a formally correct estimate of the regional trace gas enhancement relative to the actual background, but that is also not our main goal. The purpose is to have a consistent method among the two trace gases that provides a reasonable proxy for regional fire induced column enhancements. Therefore, this method was only used for regions where we have a very high density of 310 fires within our study area and where it is difficult to investigate individual fire plumes and their background mole density levels. Some of the errors introduced by this method are systematic and have a similar impact on ΔXNO2 and ΔXCO (e.g. error due to atmospheric transport) and will cancel out in the estimate of MDR. Other errors may introduce new uncertainties and biases on top of the TROPOMI column uncertainty unevenly between XNO2 and XCO, potentially affecting our ability to differentiate 315 between combustion characteristics. For instance, the assumption of a Gaussian normal distribution of the sampled data might not hold for one or both of the trace gases. To assess the importance of these uncertainties, we developed two alternative methods to derive ΔX that are closely related to SBM. The first alternative method (SBM_alt1) assumes that ΔX is not determined by the standard deviation but by the difference between the 15.9 and 84.1 percentile ranks around the median of the distribution. Figure  320 3b shows an example of such a distribution. Only if the sampled data is perfectly normally distributed, SBM_alt1 and SBM will yield the same result because the two percentile ranks will align with the minus one and plus one standard deviations. Variations from the standard normal could for instance deteriorate our ability to differentiate between combustion characteristics as it will affect the estimates for ΔX and MDR. The second alternative method (SBM_alt2) derives ΔX by taking the difference between Xfire from 325 the standard SBM method and an alternative XBG derived from a distribution of samples from an adjacent 5°×5° region. Naturally that means the SBM_alt2 ΔX value is only identical to the standard SBM ΔX value if both estimates for XBG are identical. Figure 3c shows an example of this method with an idealized background and source distribution of sampled XCO.

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SBM and the two alternative methods have been validated for two source regions in South America (see Sect. 3.2). The first region is located south of the Amazon river over the Brazilian state of Amazonas in the tropical rainforest and is dominated by deforestation fires, i.e. the practice of burning logs and debris that remain on the landscape after initial clearing to create new agricultural land. The second region is located over the central Brazilian state of Goias in an ecoregion called the Cerrado, which is a savanna-335 like fire-adapted ecosystem with frequent fires that mostly consume the grass layer but where the expansion of agriculture is also an important cause of fires. These two areas are shown in Fig. 4, in green and blue, respectively. In the 3-month dry season between July-September 2018, the parameters Xfire, XBG, ΔX were determined every day for XCO and XNO2 using SBM, SBM_alt1, and SBM_alt2. The latter method used the two adjacent background regions shown in purple in Fig. 4. These two background 340 regions were chosen for a number of reasons. First of all, the background region for the Cerrado savanna fires was on average upwind of the source area. The average wind direction in the planetary boundary layer of the domain was predominantly from the east during the 3-month period (see Fig. 4), based on a WRF-CHEM simulation nudged to NCEP re-analysis boundary conditions. Moreover, the CO and NOx emissions from fires were about two times smaller in the background region than in the source region 345 according to the GFED4s database (0.6 Gg CO region -1 day -1 vs. 1.1 Gg CO region -1 day -1 ). Similarly, we opted for a 'clean air' background area just northeast of the deforestation region where CO and NOx emissions from fires were very small during our study period.

Local sampling method
The local sampling method (LSM) is a more straightforward approach to determine local enhancements 350 in trace gas densities in close proximity of the actual fire hotspot. This method was specifically used for fires in the North American boreal biome in July 2018, the Siberian boreal biome in July and August 2018, the central Australian savanna biome in November and December 2018, and the Indonesian peatland biome in August and September 2018 (see Fig. 1 and 2). All events were relatively isolated from other fires, a prerequisite for using this method. For predefined 5°×5° and 10°×10° boxes, TROPOMI 355 data were regridded at 0.1°×0.1° resolution. Subsequently, co-located XCO and XNO2 data each day are sampled within a radius of 10 km from a location where CO and NOx was emitted according to GFED4s.
For each fire hotspot, Xfire is defined as the average of these sampled column densities. The background column density XBG is determined each day by taking the average of all sampled column densities inside a smaller subregion upwind of the fire hotspot within the larger predefined box. The location of the 360 background subregion was determined by visual inspection, looking at the predominant direction of the individual trace gas plumes. For each day, we averaged ΔXCO and ΔXNO2 over active hotspots in the predefined boxes, which were subsequently used to derive a daily average MDR. Days with insufficient data upwind of the fire hotspots were excluded from the analysis as well as days with enhanced trace gas levels that were advected into the region from outside. For instance, we had to filter out by visual 365 inspection a number of days for the North American regions because high amounts of CO were advected from the Eurasian continent to Alaska obscuring most of the local enhancements in CO.
We show in Fig. 5a and 5b an example of TROPOMI XCO and XNO2 measured over Australia for fire was likely short-lived and only detected in the morning with MODIS Terra satellite (local 10:30am overpass), three hours before the TROPOMI overpass. For the other hotspots, Fig. 5a and 5b show a good correlation between the magnitude of the trace gas enhancements, the plume distances, and the spatial extent and magnitude of the fire emissions. America stretching over 6000 km in the east-west direction and 3900 km in the north-south direction (see Fig. 4). We used a horizontal resolution of 30×30 km 2 with 32 vertical levels. We chose the 'tropical' suite of physics options that includes Yonsei University (YSU) scheme for planetary boundary layer physics (Hu et al., 2013), WSM 6-class scheme for microphysics (Hong and Lim, 2006), Tiedtke-scheme 390 for cloud physics (Tiedtke, 1989), and Rapid Radiative Transfer Method (RRTM, Mlawer et al., 1997) for short-and longwave radiation. We included gas-phase chemistry mechanisms from the Regional Acid Deposition Model version 2 (Stockwell et al., 1990), but without aerosol chemistry. Boundary and input meteorological fields for September 2018 came from NCEP FNL Operational Global Analysis dataset prepared on a 1°×1° grid every 6 hours. Boundary and initial trace gas concentrations were taken from 395 CAMS model and were interpolated to WRF vertical levels. GFED4s (see Sect. 2.1) provided the biomass burning dry matter combustion rate based on real fire events for South America in September 2018. These were multiplied with a set of EFs to acquire a synthetic estimate of biomass burning emissions for the entire domain that is associated with a single combustion type: either boreal fires, mixed peat fires, tropical deforestation fires or savanna fires. For the EFs of the mixed peat fires we assumed 60% is 400 combusted by tropical deforestation (to mimic overstory consumption) and 40% is combusted by peat soils. As a consequence, each of these four emission estimates carried a different (but in space constant) EFR between NOx and CO over the entire domain for each of the respective fire types. In addition, we used a spatial characterization of injection height profiles based on space-based stereo-height information from smoke plumes (Martin et al., 2018). 405 WRF-CHEM was executed four times for September 2018 under the exact same conditions and settings described above, except that we used for each run one of the four modified biomass burning emissions.
Each simulation provided hourly 3-dimensional fields of CO and NO2 concentrations for the entire month.
Close to the center of the domain we collected within a 5°×5° region each day at 2pm local time (half an 410 hour later than the actual TROPOMI overpass) all CO and NO2 data. These were translated into XCO and XNO2 column mole densities using a daily mean estimate of TROPOMI's averaging kernel (AK) of the two respective species, derived from September 2018 data over the same 5°×5° collection region. This assured realistic differences in column sensitivity for simulated XCO and XNO2, even under cloudy conditions. The collection of column densities was used to derive daily ΔXCO, ΔXNO2, and MDR using 415 the three SBM sampling methods discussed in Sect. 2.3.1.

Results
In Sect. 3.1 we provide an overview of all retrieved MDR signatures and compare them with the regional patterns in EFR and with WRF-CHEM simulations. In Sect. 3.2 we present a detailed analysis of XCO and XNO2 data focusing on the Amazon basin. This analysis includes the errors associated with the 420 different sampling methods, the significance of the retrieved MDR signatures in relation to the instrument precision of TROPOMI, and a comparison of retrieved MDR signatures between TROPOMI and two biomass burning datasets.

Global fire characteristics
By combining ΔXCO and ΔXNO2 data from all investigated regions we can identify a four-way split in 425 regional combustion activity and efficiency (see Fig. 6a). According to the TROPOMI data, there is a group of boreal and peatland regions that emit relatively much CO per gram of NOx in comparison to the other regions and are in the literature typically characterized as smoldering fires. For these regions we determined MDR values ≤1.4. At the opposite end of the spectrum are the savanna regions on three different continents that emit relatively much NOx generated from nitrogen in the biomass and possibly 430 from thermal decomposition of atmospheric N2 at very high combustion temperatures. The MDR values for savanna fires are much higher than for the boreal and peatland fires, and range between 3.6-6.2 among the different savanna regions and sampling methods (SBM for South America and Africa, LSM for Australia). In between these two extremes lie 4 different South American deforestation regions with MDR values that range between 1.6 and 2.5, which is less efficient than the savanna combustion but still more 435 efficient than boreal and peat combustion. In particular for the boreal regions we observe a 3 to 6 times larger increase in ΔXCO relative to ΔXNO2 than for the deforestation and savanna regions. It consistently translates to a much lower monthly average MDR (<1) for the boreal fires on two different continents, with higher MDR values over boreal North America compared to boreal Siberia.

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A similar four-way split in regional combustion characteristics is shown in Fig. 6b using the four synthetic WRF-CHEM simulations, each driven by a different set of modified biomass burning emissions to mimic different ecosystems with frequent occurring fires (see Sect. 2.4). The estimates in ΔXCO and ΔXNO2 were derived with SBM and while day-to-day variability is quite substantial just like in the real 445 TROPOMI data in Fig. 6a, it demonstrates that the SBM method can provide a robust monthly average estimate of MDR. The MDR estimates and the relative differences between the four different fire types compare quite well with the actual derived signals in TROPOMI. The simulated savanna fires have consistently the highest MDRs, which are about twice as high than the simulated tropical deforestation fires, and 3 to 4 times as high than the simulated peatland and boreal fires, respectively. 450 The pattern of combustion signatures in MDR determined with TROPOMI across the different fire types compare well with the spatial patterns in GFED4s EFR (see Fig. 7a). The Pearson correlation coefficient between estimates of MDR and EFR across the 5 continental areas implies a strong linear relationship exist (r=0.90). It demonstrates that the regional combustion efficiency that is detected with TROPOMI is 455 generally consistent with the worldwide spatial distribution of EFs used by GFED4s (mostly based on Akagi et al., 2011). For the savanna fires we have consistently the highest estimates for MDR and EFR.
The MDR and EFR for tropical deforestation fires are about half those of savanna fires. The peatland fires in turn have 3 times lower MDR and EFR. The lowest values in MDR and EFR (4 times lower than savanna fires), which suggest the least efficient type of biomass combustion, is shown for the North 460 American and Siberian boreal regions. Note that the retrieved linear relationship in Fig. 7a between GFED4s EFR and TROPOMI MDR is similar to the linear relationship and slope found between EFR and MDR based on the 4 synthetic WRF-CHEM simulations. Even with the aforementioned caveat that these simulations are simple in design, it does demonstrate quite convincingly that satellite and groundbased measurements of trace gas ratios are related to one another through a simple linear relationship. 465 The pattern of combustion signatures in MDR is somewhat different from EFR of GFAS (see Fig. 7b), which is mostly based on the older set EFs from Andreae and Merlet (2001). The Pearson correlation coefficient between MDR and EFR is lower (r=0.49) and the slope across the different fire regions is less steep. One reason is that the boreal fire characteristics in GFAS were lumped together with the temperate 470 fires into a single category called extratropical fires, which reflects a much smaller smoldering combustion component and thus a higher EFR (see Table 1). As a consequence, Siberian boreal NOx emissions are in GFAS approximately four times larger than in GFED4s. This confirms the findings in the CAMS validation activity: Comparisons with GOME-2 indicated largely overestimated Boreal NO2 concentrations in the CAMS forecasts driven by GFAS (Ramonet et al., 2019). Another reason for the 475 mismatch is that the combustion efficiency of savanna fires in GFAS is of the same order of magnitude as the combustion efficiency in the boreal regions, which seems less realistic given the current body of EFs measurements from savanna ecosystems that claim the contrary. For peatland fires in Borneo, Indonesia, GFAS assumes a much larger fraction of smoldering combustion than GFED4s also. This large fraction of smoldering combustion would probably be more accurate during the drier years, e.g. during 480 El Niño, than for the relatively wet year 2018.

South American deforestation and savanna fire characteristics
The joint analysis of ΔXCO and ΔXNO2 column densities in Fig. 8a-c shows a clear distinction between the deforestation and savanna regions during the 3-month dry season. For the deforestation burning region 485 we observe much larger increased levels of ΔXCO (up to 0.030 mol m -2 ) relative to ΔXNO2 mostly in September indicating a substantial fraction of smoldering combustion later in the season. This is consistent with ground-based measurements of tropical forest fires that usually show a persistent smoldering phase that can continue for days, in particular when woody debris is ignited that is piled together (Carvalho et al., 2001;Morton et al., 2008). The day-to-day variability in ΔXCO is large but 490 remains quite proportional to the variability in ΔXNO2 in September, indicating that the relative amount of smoldering and flaming combustion remains relatively constant throughout the month. For the deforestation region ΔXCO and ΔXNO2 are correlated in September with a Pearson correlation coefficient of r=0.82, r=0.84, and r=0.68 for respectively SBM, SBM_alt1 and SBM_alt2. The estimates of ΔXNO2 are quite similar for the deforestation and the savanna region (between 0.005-0.05 mmol m -2 ). 495 However, lower ΔXCO values (up to 0.010 mol m -2 ) point to a much cleaner combustion of savanna biomass, which is common for savanna fires where the flaming phase typically dominates (Andreae and Merlet, 2001). In contrast to deforestation fires, ΔXCO and ΔXNO2 for savanna fires are less correlated (r<0.66), i.e. the trace gases do not change consistently on a day-to-day time scale.
In September, at the peak of the fire season, the monthly average MDR is significantly different for the two fire types, irrespective of the sampling method used (see Fig. 8c). The MDR estimates for deforestation fires range between 1.06 and 1.55 whereas the MDR estimates for savanna fires are higher, ranging between 2.97 and 3.17. The separation between deforestation and savanna fires remains also quite robust to the different bulk sampling methods used (SBM, SBM_alt1 or SBM_alt2). For each fire type, 505 the monthly average ΔXCO and ΔXNO2 estimates of the three sampling methods lay well within the 1σ uncertainty level of each method (the standard deviation of day-to-day variability in ΔXCO and ΔXNO2).
The differences in MDR between SBM and SBM_alt1 are quite small in August and September (within 15% for both fire types) indicating that SBM is not so sensitive to a possibly non-Gaussian shape of the distribution. Much larger differences in MDR exist between SBM and SBM_alt2 (up to 35% for 510 deforestation fires), with much larger day-to-day variability in MDR using SBM_alt2. It indicates the background estimates of XCO and XNO2 in the adjacent regions are not necessarily consistent with the background densities derived with the Gaussian fit. These uncertainties can be attributed to the incorrect assumption that the sampled trace gases are Gaussian distributed or by the somewhat arbitrary choice of the background regions for SBM_alt2, which do not necessarily characterize the true background each 515 day in September. As discussed in Sect. 2.3.1, it is not our goal to determine the best possible background estimate, which is difficult for these kinds of regions that are continuously surrounded by fires. Instead, we opted for a mathematical method that is consistent in application for both trace gases and provides a reasonable proxy for regional fire induced trace gas enhancements.

520
The influence of instrument precision on the ΔXCO, ΔXNO2 and MDR estimates was also quantified.
The instrument precision of XCO under relatively clear-sky conditions is primarily a function of surface albedo (Landgraf et al., 2016). The low albedo of the tropical deforestation region yields an average XCO precision of 0.0014 mol m -2 , which is two times larger than for the savanna region with an average XCO precision of 0.0007 mol m -2 . The precision of XNO2 is around 0.011 mmol m -2 for both regions and is 525 dominated by air mass factor uncertainties under polluted conditions (Lorente et al., 2017). The contribution of instrument/retrieval precision to the uncertainty in ΔXCO, ΔXNO2 and MDR was estimated using a synthetic distribution of daily measurements for both trace gases in September 2018.
This was done as follows: assuming no systematic errors or biases, each single TROPOMI measurement was randomly perturbed by its precision value or decreased by its precision value or remained unchanged. 530 Subsequently, the SBM method was applied on this distribution, yielding an uncertainty range around ΔXCO, ΔXNO2 and MDR values due to instrument or retrieval noise (see Fig. 9). While the XNO2 uncertainty is quite substantial in comparison to XCO, their contribution to ΔXNO2, and in the resulting MDR, is actually quite small on a monthly time scale. There is barely any overlap in the range of monthly MDR estimates of the deforestation and savanna fires, which means that differences in combustion 535 characteristics easily exceed the precision. Only for smaller ΔXCO and ΔXNO2 values, TROPOMI's precision will become a more limiting factor in terms of signal-to-noise and could explain the lower correlation between daily ΔXCO and ΔXNO2 noted before for savanna fires.
The September daily estimates of ΔXCO and ΔXNO2 are shown in Fig. 10a for the deforestation region, 540 along with the smoothed estimates of the MDR, and the smoothed GFED4s and GFAS CO fire emissions.
In September, when the enhancements of the two trace gases and the CO emissions are at their maximum, the MDR is also at its lowest level around 1.5, indicating persistent less efficient combustion in the region (relatively less NO2 and more CO release to the atmosphere). The same set of daily estimates are also shown for the savanna region in Fig. 10b. The peaks in ΔXCO and ΔXNO2 correspond with peaks in the 545 GFAS CO emissions and the MDR is quite constant between 3.0 and 3.5, i.e. about twice as high as the MDR for the deforestation region.
It is worthwhile to note that the GFAS and GFED4s emission products do not necessarily align well in hand, used the FRP associated with those active fires and is tuned to match GFED3 emissions but not for each grid cell but for each biome (Kaiser et al., 2012). In addition, the used EFs between the two products are different (see Table 1). For the large deforestation fires the estimates of CO emissions from GFAS and GFED4s are more similar although the timing is somewhat different (see Fig. 10a).

560
We also demonstrate the detection of subcontinental scale gradients in biomass burning efficiency from space. The September average MDR (derived with the standard SBM) is shown in Fig. 11a for 15 5°×5° regions south of the Amazon river that cover the two main biomes: tropical rainforest (dominated by deforestation fires) and Cerrado savanna (dominated by savanna fires). For the same 15 regions we also derived the EFR from the monthly average GFED4s NOx and CO fire emissions shown in Fig. 11b. These 565 emissions are essentially based on the Akagi et al. (2011) EF database that is compiled from ground and airborne measurements. Although the relationship is not perfect, MDR responds fairly linearly to EFR (r=0.59 shown in Fig. 11c). A very similar west-east relationship also exists between the 15 EFR estimates from GFAS and MDR (r=0.61, not shown). However, GFAS EFR values are generally lower across the entire domain which can be traced back to differences in EFs (see Table 1). In general, we see lower MDR 570 and EFR values over the western part of the domain (where deforestation fires dominate) and higher MDR and EFR values over the eastern part of the domain (where savanna fires are more prevalent). The relationship becomes much more significant (r=0.89) if three outliers are excluded from the analysis. One of these outliers represents a mountainous region in the southwest corner of the domain, where fire activity was much lower than elsewhere in the domain. The other two outliers represent regions that are located 575 in between the tropical rain forest and the Cerrado savanna (highlighted in Fig. 11a and 11b). It is possible that the MDR and EFR do not align well at these locations because the biome-specific EFs are not representative for a more complex transition region. One would expect here more diversity in burning practices, vegetation types and climate conditions, resulting in a mixture of different burning characteristics that are not accounted for in the EF in neither GFED4s nor GFAS, which are based on 580 coarser resolution land cover data. Another factor that plays a role is atmospheric transport as it affects the column mole densities that are measured downwind of dominant fire type. The wind direction was predominantly from the east in September (see Fig. 4) and could as well carried the savanna-like combustion characteristics from the most eastern regions more towards the west (see Fig. 11a).

Discussion 585
In this paper, we demonstrated the capability of new high-quality XCO and XNO2 column observations from the space-borne TROPOMI instrument to detect and quantify spatial variations in biomass combustion efficiency from a top-down perspective. The TROPOMI observations of XCO and XNO2 (a good proxy for NOx) and the Mole Density Ratio (MDR) between the local enhancements of the two species have an important advantage over ground or airborne-based measurements due to the daily global 590 spatial coverage, and as such are complementary to bottom-up derived EFR signatures.
We found distinct spatial patterns in MDR across different regions and continents which signify very different combustion efficiency characteristics. Irrespective of the utilized sampling method, these patterns in MDR compare well with EFR signatures around the world from existing fire emission datasets. 595 In principle, these findings are not new but confirm from a remote sensing perspective the general spatial distribution of combustion efficiency of the current body of EF measurements. Based on the TROPOMI measurements of just one year we derived a first (but still preliminary) linear relationship between TROPOMI column observations of CO and NO2, and EFs of CO and NOx near the fire source (see Fig.   7). This approach provides an additional anchor to help constrain combustion characteristics and can for 600 instance be used to estimate and quantify the spatiotemporal variability of combustion efficiency around the world, even over regions where there is a deficiency of detailed information on fuel load, combustion practice and EFs.
The combustion in all savanna regions in South America, Africa and Australia were consistently cleaner 605 and more efficient (i.e. highest MDR) than for all the other regions investigated. The MDR for Australia was determined by studying individual fire plumes with LSM and yielded the highest MDR estimate, but also the largest day-to-day uncertainty. The other three savanna regions were determined with SBM and yielded smaller MDR values but were still significantly larger than the MDRs derived for the other fire types. The LSM method may be inclined to higher MDRs because ΔXNO2 is derived from mole density 610 measurements in close proximity of the actual fire sources where XNO2 is at its highest level before any significant removal with OH occurs. On the other hand, the area sampled was very arid and mostly consisted of grasses. Therefore, smoldering combustion products like CO and CH4 tend to be lower (Hurst et al., 1994). Our study also shows a relatively clean combustion process for the Northern and Southern African savanna fires, in agreement with the current EF datasets. In contrast to Zheng et al. (2018), we 615 did not find evidence of a seasonal transition from flaming to smoldering combustion for the different African regions. They inverted multi-year XCO column measurements from the MOPITT instrument and found that GFED4s significantly underestimates the CO emissions by 12 to 62% later in the fire season.
They partly attributed this outcome to the static EFs that are currently in use that omit seasonal variations in burning conditions. We therefore argue that the underestimation of GFED4s CO emissions is more 620 likely the result of missing burned area detections in the late dry season.
In comparison to the savanna fires, lower MDR values were derived for the South American deforestation regions, indicating a larger contribution from smoldering combustion of organic soils and woody debris that is piled together at the surface. These spatial differences in combustion efficiency between 625 deforestation and savanna fires agree with the study of Silva and Arellano (2017), however, a one-on-one comparison between the two studies is difficult. They derived estimates of MDR based on the ratio of ΔXCO/ΔXNO2 (instead of ΔXNO2/ΔXCO), and they did their analysis for a different year, probably under somewhat different meteorological and chemistry regimes.

630
The least efficient type of combustion with the lowest MDR values were detected for the Indonesian peatland fires and boreal fires of North America and Siberia. In Indonesia, peatland fires are a recurring seasonal phenomenon that generates severe atmospheric pollution and impacts public health (Marlier et al., 2013). In many lowland regions, forest clearing occurs along with drainage of peat-swamp forest exposing peat to fire. During the dry season, the boreal forest fires consume large amounts of above-and 635 especially belowground biomass, including the burning of organic soils, peat, and woody debris (Ottmar and Sandberg, 2003;French et al., 2004). Typically, such ecosystems burn by residual smoldering combustion which can continue long after the initial flaming phase of the fires (Akagi et al. 2011).
The difference in MDR between the North American and Siberian boreal fires in Fig. 6a suggest different fire dynamics between the two boreal regions. These differences do not appear in the EFR estimates of 640 GFAS and GFED4s because the EF datasets lack spatial and temporal variability for each fire type. The lower average MDR value for Siberia indicates generally more smoldering combustion (less NOx, more CO) than the combustion in North America. This result supports independently the findings of Wooster and Zhang (2004) and Rogers et al. (2015), who found compelling evidence for smaller fire intensity and burn severity in the Siberian boreal forests across multiple satellite datasets (but not TROPOMI) and 645 forest inventories. Rogers et al. (2015) related the differences in fire dynamics between these two regions to their dominant tree species. Pine trees in Eurasia have evolved to resist and suppress crown fires.
Therefore, the fires in these areas are usually reported as surface fires, which burn mostly in the smoldering phase. The trees in the northern parts of North America have evolved to spread and be consumed by more intense crown fires, killing most trees. Yet, we remain cautious to fully attribute the 650 detected differences between the North American and Siberian MDR to the burning characteristics of specific tree species until we have analyzed multiple years of TROPOMI data. The uncertainties in MDR for 2018 (based on day-to-day variability) are still quite substantial for the boreal regions as is shown in Fig. 6a.

655
Our estimates of MDR across the world compared most favorably with the spatial distribution of biomass burning efficiency prescribed in GFED4s, where the proxy of efficiency is carried through the EFs of CO and NOx. The remotely sensed measurements confirm the addition of a dedicated boreal forest fire type as a key improvement that was implemented in the more recent Akagi et al. (2011) EF database (used by GFED4s). It underlines the need for EFs that reflect a large component of smoldering combustion of 660 organic soils and boreal peat in this part of the world (Yokelson et al., 1997;Bertschi et al., 2003). This was specifically done in the Akagi et al. (2011) EF dataset where they applied an equal weighting scheme for the boreal region airborne measurements (which have a bias towards flaming fires) and ground-based measurements (which have a bias towards smoldering fires). Our MDR estimate for the two Indonesian peatland regions is lower than MDR for deforestation fires but higher than the MDR for boreal fires. 665 Therefore, it is likely that it represents a combination of peat soil combustion (usually consumed almost entirely by smoldering) and overstory combustion of tropical forests, grasslands, and agriculture (usually consumed by flaming and smoldering). This relative pattern is in agreement with a more mixed combustion efficiency prescribed in GFED4s for Indonesia (both for Borneo and Sumatra). The Borneo fires in GFAS exhibited a much larger smoldering component, which may be more common during El 670 Niño years when fires spread out of control, consuming a significant portion of the underlying peat soils.
However, 2018 was not an El Niño year, and evidence of excessive smoldering combustion was not found in the TROPOMI data (see Fig. 6a). In fact, the TROPOMI data suggest more complete combustion efficiency in Borneo than in Sumatra (1.43 vs. 0.94 MDR).

675
The day-to-day variations in MDR (shown in Fig. 6a) point to a considerable amount of uncertainty. An important source of this uncertainty is first of all the SBM sampling method. Estimates of ΔXCO and ΔXNO2 can deviate substantially on a daily basis depending on how much the sampled data is skewed to either side of the scale, away from a perfect Gaussian normal distribution. It was demonstrated for South American fires (see Fig. 8) that the SBM and the two alternative sampling methods can produce quite a 680 range in MDR. Similarly, the instrument/retrieval precision of TROPOMI's XNO2 was also a small source for uncertainty in MDR (see Fig. 9). However, regardless of the sampling method or precision, we were still able to distinguish clearly the deforestation fires from savanna fires using the monthly aggregated ΔXCO and ΔXNO2 data. The alternative sampling methods were also used to derive MDR from the synthetic WRF-CHEM simulations, and similarly, it did not deteriorate our ability to distinguish 685 the four different fire types (not shown in paper).
Another source of uncertainty in MDR is the difference in surface sensitivity of TROPOMI's XCO and XNO2 measurements. A comparison of the column averaging kernel (AK) of both species shows that tropospheric XNO2 measurements are generally less sensitive to sources in the planetary boundary layer 690 than XCO measurements. From the surface to approximately 800hPa is the sensitivity of XNO2 smaller than for XCO but increases from the mid-troposphere to tropopause . This is one of the reasons why our daily estimates of ΔXNO2 are biased low. Potentially, it has an effect on most of our MDR estimates because it has been demonstrated, using stereo-height measurements of smoke plumes, that most fires are typically emitted inside the planetary boundary layer (Martin et al., 2018). The 695 estimates of ΔXCO, ΔXNO2 and MDR derived from the simulated XCO and XNO2 column data (WRF-CHEM experiments in Fig. 6b and 7) were calculated with a daily region-average AK for September 2018. This provided more realistic column estimates for both species (and thus a more realistic MDR estimate) that allowed a better one-to-one comparison to TROPOMI MDR estimates, even under cloudy conditions (Borsdorff et al. 2018b). Not using the AKs to derive MDR with WRF-CHEM, and instead 700 simply using the simulated total XCO and the tropospheric XNO2 column densities, would yield higher MDR estimate. This is because simulated XNO2 enhancements from surface fire sources are, in comparison to TROPOMI's limited measurement sensitivity in the PBL, unrealistically overrepresented in WRF-CHEM.
In general, a large part of the biases in ΔXNO2 (and thus in MDR), either caused by the sampling techniques or the precision and sensitivity, were in all likelihood somewhat similar in magnitude in the regions we studied. Hence, we believe it did not impair the detection of differences in fire characteristics.
The uncertainty related to chemistry and transport may have played a larger role region-to-region as it affected tropospheric NO2 more differently than CO, and thus our ability to derive a robust MDR. In 710 particular, on shorter day-to-day time scales the MDR estimates can vary greatly. The amount of OH radicals in the atmosphere acts as the primary daytime sink of NO2 and can vary substantially depending on the amount of tropospheric O3, water vapor and incoming sunlight (source of OH), and the presence of other chemical species such as volatile organic compounds (sink of OH). Overall, it reduces the lifetime of NO2 to several hours, much shorter than the lifetime of CO. As a consequence, daily estimates of 715 ΔXNO2 will always be biased low. In addition, daily variations in ΔXNO2 that are driven by transport and chemistry are naturally exacerbated in ΔXNO2/ΔXCO ratio-space. Therefore, to interpret MDR, it is currently necessary to collect multiple days of data (e.g. for an entire month) to retrieve a more robust combustion efficiency signature that cancels out some of the day-to-day variations in transport and chemistry. Potentially we could minimize these variations retroactively by inverting the measured MDR 720 back to a daily EFR estimate, where we take the removal of NO2 into account. This could provide a more direct top down estimate of EFR and could improve the detection of seasonal (and maybe even daily) changes in fire characteristics. For instance, the transition from flaming to the more smoldering fires, as suggested to occur in the African savanna (Zheng et al., 2018) or the supposed differences between North American and Siberian boreal fires (Rogers et al., 2015) might be detected more easily that way. Future 725 research could explore this but requires a more elaborate analysis for each region separately, with emphasis on acquiring a better understanding of the daily variations of regional OH content, windspeed and direction, and the chemical rate constant of NO2 removal.

Conclusion
We have investigated regional biomass burning characteristics and efficiency using the new space-based 730 TROPOMI measurements of XCO and XNO2. The mole density ratios (MDR) between regional enhancements of XNO2 and XCO have been quantified using different sampling techniques, which have been tested using WRF-CHEM simulations accounting for realistic atmospheric transport, chemistry and the limited instrument sensitivity to the lower atmosphere. TROPOMI provides independent support for the more recent Akagi et al. (2011) set of EFs used in fire emission products like GFED4s. We have found 735 spatial variations in combustion efficiency that match the ground and airborne measurements of EFs quite accurately. Generally, boreal fires show a much larger fraction of smoldering combustion than savanna grassland and tropical deforestation fires (boreal ecosystem cause a 3 to 6 larger increase in ΔXCO than ΔXNO2). On smaller spatial scales of a thousand kilometers, we also found gradients in combustion characteristics from west to east over Brazil. In the state of Amazonas, the practice of tropical 740 deforestation, where woody debris after initial clearing is ignited during the dry season, is clearly distinguishable from fires in the savanna-like ecosystem in central Brazil, where fires mostly consume the grass-layer by flaming combustion. We have found deforestation fires to cause a 1.5 to 2 times larger increase in ΔXCO relatively to ΔXNO2 than the savanna fires, mainly because these fires reflect a larger fraction of surface smoldering combustion. The detected differences interregional (e.g. boreal vs. 745 savanna) and intraregional (e.g. North America vs. Eurasia boreal region) underline that TROPOMI can provide new top-down constraints on biomass burning characteristics and EFs.

Author Contributions
IvdV did the data analysis, designed and ran the model simulations and wrote the paper. GvdW, SH, and IA provided science advise and detailed comments on the manuscript. HE, JPV, and TB provided additional comments on the manuscript and TROPOMI retrieval products. 760

The linear regression derived from the MDR-EFR data is shown for both panels (black solid and dashed lines). The MDR-EFR relationship from the four WRF-CHEM simulations is shown by the colored open circles and the linear regression through these four markers
is shown by the red dashed line. The slope, Pearson correlation coefficient and the two-sided p-value (for a hypothesis test whose null hypothesis is that the slope is zero) is reported for each regression line.