The Orbiting Carbon Observatory-2 OCO-2, was launched in 2014, aiming to continue and improve XCO2 observations from space. OCO-2 is part of the A-train satellite constellation and flies in a sun-synchronous orbit whose ascending node crosses the Equator at 13:36 LT. It measures the solar backscattered radiance in three independent wavelength bands in the spectral regions of the near infrared (NIR) and shortwave infrared (SWIR): the O2-A band at around 760 nm, the weak CO2 band at around 1610 nm, and the strong CO2 band at around 2060 nm. OCO-2 is operated in a near-push-broom fashion and has eight parallelogram-shaped footprints across track with a spatial resolution at ground of ≤1.29 km × 2.25 km.

We use NASA's operational bias-corrected OCO-2 L2 Lite XCO2 product v9 (; see Fig. a for an example), which we obtained from https://daac.gsfc.nasa.gov (last access: 17 July 2019). The product is rigorously prefiltered and post-filtered for potentially unreliable soundings including, e.g., cloud and aerosol contaminated scenes. Additionally, the OCO-2 retrieval algorithm accounts for light scattering at optically thin aerosol layers by fitting the optical depth and height of two lower-atmosphere aerosol layers and the optical depth of a stratospheric aerosol layer . The OCO-2 v9 dataset has an improved bias correction approach that results in reduced biases, particularly over areas of rough topography.

The OCO-2 XCO2 product includes an uncertainty estimate which we use for our study. For the selected scenarios, the reported single sounding uncertainty lies typically in the range of 0.4 to 0.7 ppm, which is similar to estimates based on the standard deviation of the difference of succeeding soundings. The validation study of estimated that the single sounding precision relative to ground-based Total Carbon Column Observing Network (TCCON) data is about 1.3 ppm. However, this includes, e.g., the noise of the validation dataset and a larger pseudo-noise component, due to spatial and temporal representation errors when co-locating OCO-2 with the validation data and it should be noted that the study of analyzed a predecessor NASA OCO-2 XCO2 dataset (v7 instead of v9).

The TROPOspheric Monitoring Instrument (TROPOMI) on Sentinel-5 Precursor was launched in October 2017 into a sun-synchronous orbit with an ascending-node Equator crossing time of 13:30 LT . TROPOMI is a nadir-viewing grating imaging spectrometer for the UV–visible spectral region with additional channels in the NIR and SWIR, extending the existing data records of the GOME (Global Ozone Monitoring Experiment), SCIAMACHY, OMI (Ozone Monitoring Instrument), and the GOME-2 missions. It has a swath width of about 2600 km and in comparison to previous instruments a much better spatial resolution of 3.5 km × 7 km at nadir at a similar signal-to-noise ratio per measurement. Here we use radiances in the spectral region 425–465 nm to retrieve NO2 slant columns with a standard Differential Optical Absorption Spectroscopy (DOAS) retrieval developed for previous satellite instruments , followed by a de-striping step, as described by . Slant columns are defined as the absorber concentration integrated along the light path, and thus depend on both the atmospheric NO2 profile and the light path of the individual measurement.

The random noise of our S5P slant columns has been estimated from the scatter of observations over a clean Pacific region (10∘ S–10∘ N, 160–230∘ E). In order to account for the viewing-angle dependency of the slant columns, a geometric air mass factor has been computed using only the instrument's viewing zenith angle. The evaluation suggests that the random noise (1σ) of our S5P slant column product is typically 5×1014 molec. cm-2, while enhancements near sources often exceed 1016 molec. cm-2. For individual soundings, the uncertainty can differ depending on viewing geometry and surface reflectance.

Usually, in order to extract the tropospheric vertical columns, first the stratospheric contribution to the retrieved slant columns needs to be removed and then the light path dependency of the remaining tropospheric slant columns is corrected for by dividing through a scene dependent air mass factor. In this study, another approach is taken as only localized enhancements are evaluated. By subtracting the surrounding background values (Sect. ), both the stratospheric contribution and any tropospheric background are removed from the signal as they are both smooth on the scale of a few tens of kilometers discussed here. What remains is the slant column plume signal of the lower troposphere from which we derive information on the CO2 plume.

OCO-2 and S5P both fly in sun-synchronous orbits with similar Equator crossing times of their ascending nodes and with orbit times of about 100 min. S5P has a swath width of about 2600 km, which provides nearly global coverage each day. For these reasons, each scene observed by OCO-2 is also observed by S5P within a maximum time difference of about 50 min. We project the S5P and OCO-2 data of the same day in a surroundings of a potential target on a high-resolution (0.001∘×0.001∘) grid to compute NO2 averages representative for the footprints of the CO2 soundings (see Fig. c for an example).

As input for the computation of the cross-sectional fluxes (Sect. ), we compute the number of dry air particles in the atmospheric column from meteorological profiles which we read at the same time with the wind information from the ECMWF (European Centre for Medium range Weather Forecast) ERA5 (fifth-generation of ECMWF atmospheric reanalyses) data archive at 0.25∘×0.25∘ hourly resolution. This data archive also provides an uncertainty estimate of the wind information from an ensemble statistic but at a reduced resolution of about 0.5∘×0.5∘ over 3 h.

We compare the inferred cross-sectional CO2 fluxes with the following emission databases. The Emissions Database for Global Atmospheric Research (EDGAR v4.3.2, https://edgar.jrc.ec.europa.eu, last access: 17 July 2019) provides information on anthropogenic CO2 emissions at 0.1∘×0.1∘ annual resolution. EDGAR v4.3.2 ends in 2012 and we use the data of that year for our comparisons. The Open-Data Inventory for Anthropogenic Carbon dioxide ODIAC v2017, http://db.cger.nies.go.jp/dataset/ODIAC (last access: 17 July 2019), also provides information on annual anthropogenic CO2 emissions but at a finer resolution (1 km × 1 km monthly), and the database ends in 2016. For the reason of comparability, we re-gridded the ODIAC emissions to the EDGAR resolution (0.1∘ × 0.1∘ annually) and use 2012 data as baseline. Additionally, we use ODIAC v2017 data re-gridded to 0.1∘ × 0.1∘ monthly resolution. The Global Fire Emissions Database (GFED v4.1s, https://www.globalfiredata.org, last access: 17 July 2019) provides information on CO2 emissions from wildfires at a resolution of 0.25∘ × 0.25∘ over 3 h, which we re-gridded to 0.1∘ × 0.1∘ resolution for a 6 h average, ending approximately at the time of the overpass.

S5P's spatial resolution is considerably coarser than that of OCO-2. Consequently for our case studies, we concentrate on plumes that are significantly larger than the swath width of OCO-2. This means that for the selected scenarios, OCO-2 actually sees only a cross section of a plume (see Fig. c for an example).

We model the cross-sectional NO2 columns along the OCO-2 orbit via a linear polynomial, accounting for large-scale variations in the background values, overlaid by a Gaussian function describing the enhancement within the plume. Simultaneously, the cross-sectional CO2 concentrations are modeled in a similar manner. However, the width of the CO2 Gaussian function is constrained to equal the width of the NO2 Gaussian function. This means that the plume shape is determined from the NO2 measurements, but we allow for a shifted position of the maximum in order to account for potential plume displacements resulting from different overpass times. Additionally, it should be noted that the CO2 and NO2 plumes may have small differences, e.g., due to different decay rates of NO2 in different altitudes. These differences, however, are considered minor compared with the precision of the XCO2 soundings. Specifically, the co-located NO2 and XCO2 values along the distance in OCO-2's flight direction x are fitted with the maximum likelihood method by the following vector function: 1NO2XCO2=a0+a1x+a2e-4ln(2)(x-a3)2a4-2a5+a6x+a7e-4ln(2)(x-a8)2a4-2.

The free fit parameters a0–8 correspond to the polynomial coefficients of the background values (a0,1,5,6), the amplitudes (a2,7), shifts (a3,8), and the full width at half maximum (FWHM, a4) of the Gaussian functions. We force the FWHM to be constrained entirely by the NO2 measurements by setting the CO2 part of the corresponding Jacobian artificially to zero. However, we expect only little differences with a combined FWHM fit because of the lower relative noise of the NO2 measurements.

Integration over the Gaussian enhancement results in the cross-sectional CO2 flux FCO2 (mass of CO2 over time) of the plume depending on the FWHM a4, the amplitude of the XCO2 enhancement a7, the effective wind speed ve within the plume normal to the OCO-2 orbit, and the number of dry air particles in the atmospheric column ne:

2FCO2=12πln(2)MCO2NAnea4a7ve.

Here, MCO2 is the molar mass of CO2 (44.01 g mol-1) and NA is the Avogadro constant (6.02214076 × 1023 mol-1). We approximate the number of dry air particles ne and the effective wind speed's normal ve from ECMWF ERA5 meteorological profiles at the position of the maximum of the fitted Gaussian XCO2 function. In regions with large variations in surface elevation or wind conditions within the plume's cross section, it might be appropriate to account for variations in the number of dry air particles and/or the wind conditions when integrating over the Gaussian enhancement.

We manually adjust the ECMWF wind direction (not the wind speed) to subjectively fit the plume direction observed in the NO2 fields (e.g., Fig. a). The manual adjustment to wind direction but not wind speed is similar to the approaches of, e.g., or .

For a hydrostatic atmosphere with a standard surface pressure of 1013 hPa, ne is about 2.16 × 1025 cm-2 and the cross-sectional CO2 flux FCO2 (Eq. ) in units of MtCO2 a-1 becomes approximately

3FCO2≈0.53MtCO2aa4kma7ppmvems-1, given that the FWHM a4, the amplitude of the XCO2 enhancement a7, and the effective wind speed ve are provided in the units km, ppm, and m s-1, respectively. As ne approximately scales with the surface pressure, Eq. () may be easily adapted to other meteorological conditions.

As discussed by , the plume height (and subsequently the wind speed in plume height) depends on many aspects like emission height, stack geometry, flue gas exit velocity and temperature, meteorological conditions, etc. Some of these parameters are not known for many sources and their explicit consideration would go beyond the scope of this study focusing on demonstrating the benefits of simultaneous NO2 and XCO2 measurements rather than on most accurate flux estimates. proposed approximating the effective wind speed within the plume from the 10 m wind by applying a multiplier in the range of 1.3–1.5. Therefore, we decided to use a multiplier of 1.4 for convenience. This empirical relationship accounts for plume rise and mixing into altitudes with larger wind speeds, for example. For the present, we consider this approximation adequate for this first study, but we recognize that uncertainties (see next section) resulting from this estimate of the effective wind speed's normal may be reduced in the future by improved wind knowledge.

Additionally, it should be noted that the plume cross-sectional flux (Eq. ) is only a good approximation for the actual source emission under steady-state (temporally invariant) conditions for wind speeds greater than about 2 m s-1 , when advection dominates over diffusion . Changes in wind direction, wind speed, or atmospheric stability in the time span between emission and observation may result in differences between the plume cross-sectional flux and the source flux. Temporal variations in the source emissions of course also result in (temporally delayed) variations in the plume cross-sectional flux, which is always only a snapshot and must not be confused with, e.g., the annual average, even though it is given in the same units. In case of chemically active species (such as NO2), chemical processes along the plume path would also have to be considered in order to compute source emissions from plume cross-sectional fluxes.

In order to estimate the uncertainty of the CO2 plume cross-sectional flux (FCO2, Eq. ), we propagate the uncertainties of the FWHM (a4), the amplitude (a7), and the wind speed normal (ve) by assuming uncorrelated errors. The uncertainties of the FWHM and the amplitude result from the maximum likelihood fitting method propagating the uncertainties of the individual XCO2 and NO2 soundings as reported in the data products. The uncertainties of the wind components are read from the ECMWF ERA5 data archive resulting in total wind speed uncertainties ranging from 0.18 to 0.33 m s-1 for the analyzed scenarios. Additionally, we assume that the manual adjustment of the wind direction is accurate by ±10∘. These uncertainties propagate into the uncertainty of the wind speed normal. estimated that computing the effective wind speed from the 10 m wind introduces an additional uncertainty of 8 %–12 %. However, we analyze scenarios with larger plume structures and probably also larger variations in the injection heights, which we consider by enhancing this error component to 20 % for convenience. Uncertainties in the number of dry air particles are neglected as they are much smaller compared to the wind speed uncertainty, for example. As mentioned earlier, the assumption of constant meteorological conditions might not be valid in regions with large variations in surface elevation or wind conditions within the plume's cross section, which may result in an underestimation of the total cross-sectional flux uncertainty in such cases.

We use a semiautomatic method to select potentially interesting targets. In a first step, all co-locations of OCO-2 and S5P are computed similarly to those described in Sect.  but based on a coarser high-resolution grid (0.01∘ × 0.01∘) to improve the computational efficiency. We shift a 30 s (∼200 km) search window in time steps of 0.25 s (∼2 km) over the time series of co-locations. Only those time steps are further considered that have at least 100 co-locations without data gaps exceeding 3 s (∼20 km) within the search window. In the next step, we perform a least-squares fit of the co-located XCO2 and NO2 data with a Gaussian vector function. This fitting function corresponds to Eq. () but with independent FWHM for XCO2 and NO2 and centered within the search window (a3 and a8 set to zero), which improves the convergence rate. Only those time steps that fulfill the following criteria are considered further: the fit converges, the NO2 amplitude exceeds 1015 molec. cm-2, the XCO2 and NO2 FWHM (ac and an, respectively) do not exceed the half width of the search window (ac,an≤15 s) and do not differ by more than their average (|ac-an|≤(ac+an)/2), and the XCO2 and NO2 amplitudes are at least 2 times larger than their uncertainties and larger than the maximum variations in the backgrounds. In the last step, we decided by manual inspection of the XCO2 and NO2 co-locations plus the surrounding NO2 fields and ECMWF wind information if the scenario is a promising candidate for further flux analyses. Potential reasons to reject an automatically preselected scenario are, e.g., too low wind speed, wind direction nearly parallel to OCO-2 orbit, unclear source attribution, or poor fit quality. In total, we manually identified about 20 promising scenarios in the time period January to August 2018 of which we selected and analyzed six examples for this study.

Figure a shows the NO2 enhancement in the city plume of Moscow (approx. 12.4 million inhabitants) as retrieved from S5P overlaid by OCO-2's XCO2 measurements. The NO2 enhancement is clearly also visible in the plume's cross section along OCO-2's ground track (Fig. c). Due to the larger relative noise of the XCO2 retrievals, the XCO2 enhancement is less obvious but still visible (Fig. c). The Gaussian fit of the enhancements is excellent for NO2 and reasonable (χ2=2.2) for XCO2. There was nearly no adjustment needed (1∘) to bring the ECMWF 10 m wind in good agreement with the NO2 plume (Fig. a). The effective wind speed normal to the OCO-2 orbit amounts to 1.6±0.6 m s-1, which is a bit lower than optimal for reasonable flux estimates . The cross-sectional CO2 flux amounts to 76±33 MtCO2 a-1. This compares to 2012 average upwind emissions (white boxes in Fig. a) of 195 MtCO2 a-1 (EDGAR) and 102 MtCO2 a-1 (ODIAC). ODIAC's emission estimate for August 2016 amounts to 88 MtCO2 a-1. The NO2 far field shows no indications of overlaid CO2 plumes from other sources (Fig. b). The total flux uncertainty is dominated by the uncertainty of the wind direction followed by the uncertainty of the effective wind speed.

Figure a shows the surroundings of Lipetsk (approx. 0.5 million inhabitants) with, among other industries, the Novolipetsk steel plant and the Lipetskaya TEC-2 gas-fired power plant (515 MW) only 1 min (∼400 km) away from Moscow along OCO-2's flight track (see also Fig. b). The cross-sectional NO2 and XCO2 enhancements clearly stand out from the noise in the data (Fig. c) and the Gaussian function fits the XCO2 data reasonably well (χ2=2.4). We applied a small correction of 5∘ to the ECMWF wind direction. However, as the wind direction is similar to OCO-2's flight direction, the normal effective wind speed is unfavorably low (0.9±0.7 m s-1), which makes the cross-sectional flux estimates (69±50 MtCO2 a-1) less reliable and highly uncertain. The largest uncertainty contribution by far comes from the uncertainty of the wind direction. The 2012 average EDGAR and ODIAC upwind emissions (white marked boxes in Fig. a) are 23 and 4 MtCO2 a-1 (same for August 2016), respectively, but the NO2 far field shows no indications of overlaid CO2 plumes from other sources (Fig. b).

Figure a shows the S5P NO2 slant columns overlaid by OCO-2 XCO2 data in a surroundings of Baghdad (approx. 5.4 million inhabitants). Enhanced values are clearly visible in the cross section of the NO2 plume and less obviously also visible in the XCO2 data (Fig. c). The XCO2 enhancement is well-fitted (χ2=1.0) by the Gaussian fitting function. The manually adjusted wind direction deviates by 17∘ from the ECMWF wind direction and the normal wind speed amounts to 4.4±1.7 m s-1. From the XCO2 enhancement and the normal wind speed, we compute the cross-sectional CO2 flux to be 95±36 MtCO2 a-1. This compares to an upwind source of 22 or 13 MtCO2 a-1 (12 MtCO2 a-1 for July 2016) of EDGAR or ODIAC, respectively. The flux uncertainty is dominated by the uncertainty of the wind direction and the uncertainty of the effective wind speed. The NO2 far field shows no indications of overlaid CO2 plumes from other sources (Fig. b).

The Medupi (4764 MW) and Matimba (3990 MW) coal-fired power plants lie close to each other in South Africa, about 300 km north of Johannesburg. Their NO2 plume is shown in Fig. a overlaid by OCO2 XCO2 measurements. NO2 measurements in the larger surrounding do not suggest any additional nearby upwind sources (Fig. b). The cross-sectional NO2 values show a clear elevation within the plume that is less obvious for XCO2, which has larger relative scatter, especially south of the plume. Nevertheless, the Gaussian function fits the XCO2 values reasonably well (χ2=1.4). The wind direction (corrected by 13∘) is nearly perpendicular to the OCO-2 orbit and the effective normal wind speed is 2.6±0.6 m s-1. The cross-sectional CO2 flux amounts to 31±7 MtCO2 a-1, which is consistent with ODIAC 2012 emissions of 24 MtCO2 a-1 and ODIAC July 2016 emissions of 26 MtCO2 a-1 but EDGAR does not have significant emissions in this area. It should be noted that the Medupi power plant started operation in 2015 with limited capacity and that it still has not reached its nominal capacity. Therefore, it is no surprise that the Medupi power station is not included in either EDGAR or ODIAC 2012 data. The flux uncertainty is dominated by the uncertainty of the effective wind speed.

Figure a shows the NO2 plumes of two Australian wildfires on 5 May 2018 overlaid by an OCO-2 orbit of XCO2 measurements. Enhanced NO2 and XCO2 values are clearly visible within the plume's cross section (Fig. b). The NO2 (and also less obviously the XCO2) cross section has two maxima that cannot be accounted for by the Gaussian fitting function. However, this is not reflected in the good XCO2 fit quality (χ2=0.6) but should be taken into account when valuing the results. We applied a small manual correction of 7∘ to the wind direction and the effective wind speed normal to the OCO-2 orbit is 6.7±1.7 m s-1. For the snapshot of the overpass, we computed a cross-sectional CO2 flux of 153±40 MtCO2 a-1. Its uncertainty is driven by the uncertainty of the effective wind speed and wind direction. As the shown plumes originate from wildfires, EDGAR and ODIAC do not include their emissions. However, GFED has average emissions of 52 MtCO2 a-1 within the 6 h period 00:00–06:00 UTC including the time of the overpass (05:00 UTC). The maximum GFED emissions are approximately at the position of the largest NO2 concentrations. Figure c shows no indications that additional upwind sources explain the discrepancy between our cross-sectional flux estimate and GFED.

Figure a shows the NO2 slant columns in the surroundings of Nanjing (approx. 5.8 million inhabitants) overlaid by OCO-2 XCO2 measurements. The cross section along the OCO-2 orbit shows strong XCO2 and NO2 plume signals distinctively above the noise level that are well-fitted with the Gaussian fitting function (χ2=0.6). The ECMWF wind direction is not far from being rectangular to the OCO-2 orbit, and we applied a moderate manual correction of 11∘. The effective normal wind speed is 2.2±0.5 m s-1. This results in a cross-sectional flux estimate of 120±27 MtCO2 a-1, which lies in between the upwind emissions of EDGAR (163 MtCO2 a-1) and ODIAC (89 MtCO2 a-1 for 2012, 96 MtCO2 a-1 for March 2016). Figure b does not indicate additional major remote upwind sources. The uncertainty of the cross-sectional flux estimate is dominated by the uncertainty of the effective wind speed.