One of the main objectives of any climate policy initiative is to limit atmospheric greenhouse gas emissions resulting from anthropogenic activity to a level that minimizes adverse modification of the climate system. An essential component in attaining this goal is the accurate quantification of emissions at national and state levels in order to independently verify the implemented climate change mitigation and adaptation measures. In the context of CO2, cities are significant contributors of emissions, giving rise to approximately 70 % of the total anthropogenic emissions (Canadell et al., 2010). However, there exist large uncertainties associated with quantifying urban emissions. This makes it difficult to assess the efficacy of any emission management schemes at urban scales.

While mitigation efforts are being taken in some cities around the globe, they lack objective, observation-based methods to verify their outcomes (Pacala et al., 2010). Some observation-based attempts have been made with a focus on deriving city-scale emissions in a variety of urban environments (Bergeron and Strachan, 2011; Levin et al., 2011; Mays et al., 2009; Wang et al., 2010; Zimnoch et al., 2010). However, none of these approaches is able to account for CO2 emissions from urban areas with the accuracy required for verification, nor are they easily adaptable to other locations. As a result, our current emission estimates are purely based on inventories (bottom-up approach), which have large uncertainties due to many unresolved processes related to spatial and temporal heterogeneity of emission fluxes and local transport phenomena (Van Amstel et al., 1999; Gregg et al., 2008; Marland, 2008; White et al., 2011). Recent revelations about the inaccuracy of the knowledge of motor vehicle emissions emphasize this point.

The reporting of the emissions of CO2 is currently determined by national and regional agreements and legislation. This is an evolving topic for policy makers. For example, there exists an emission inventory which accounts for total annual US emissions between 1990 and 2014 (EPA, 2016). In the European Union, the monitoring and reporting of greenhouse gas emissions are performed and regulated under the Commission Regulation (EU) no. 601/2012 (European Commission, 2012). Similarly, the UK government has announced, under the Companies Act 2006 (Strategic Report and Directors' Report) Regulations 2013, that companies are required to report their annual greenhouse gas emissions in their directors' report (see http://www.legislation.gov.uk/uksi/2013/1970/pdfs/uksi_20131970_en.pdf). There is also a guideline for national greenhouse inventories prepared by a task force of the IPCC (IPCC, 2006). Following the agreement of the UNFCCC COP21 in Paris in 2015, it is likely that new guidelines for reporting the emissions of greenhouse gases will be required.

The uncertainties, i.e. the sum of systematic and stochastic error, in the national average of annual fossil fuel CO2 emissions from the United States is estimated to be 2–5 % (EPA, 2016). The corresponding values for countries without well-developed energy sector statistics are even higher, giving rise to uncertainties of about 10–20 % at the national level (Gregg et al., 2008). When disaggregating these national emissions at fine scales (e.g. city scale) based on conventional accounting methods, the associated uncertainties are expected to be significantly higher compared to those of national averages (Oda and Maksyutov, 2011). Hence, reliable emission estimates are not often available at a scale relevant for urban emissions and the associated uncertainties. This is problematic in terms of judging the effectiveness of emission reduction schemes or designing new management strategies for emission trading. Furthermore, uncertainties in emission estimates impose important limitations on regional carbon budget estimations derived by most atmospheric inverse frameworks (top-down approach), in which anthropogenic emission fluxes are assumed to be well known (Corbin et al., 2010; Göckede et al., 2010; Gurney et al., 2002, 2005).

In order to assess accurately the contribution of a city or other emission hotspot to CO2 or other GHG emission, accurate knowledge of the surface fluxes at high spatial and temporal resolutions is needed. Ideally, the accuracy of the estimated flux needs to be high for unambiguous attribution of source strength. The uncertainty of these estimations is required to be reduced to the extent that is feasible. In ESA (2015) it is noted (see their Sect. 4.1.2) that accuracies better than 10 % would be useful for providing important additional information for cities where inventories exist, and accuracies better than 20 % would contribute knowledge for cities where inventories do not exist.

The key limitations to constrain emission fluxes at urban scales via inverse modelling are the unavailability of direct, continuous, and high-frequency atmospheric CO2 measurements representing CO2 enhancement in urban domains, as well as the inability of current inverse modelling systems to capture the fine-scale variability caused by the atmospheric transport and emission processes at a scale relevant for urban emissions (e.g. Bréon et al., 2015). An assessment study based on ground-based measurements indicated potential drawbacks of using CO2 surface measurements for emission verification, and strongly recommended the use of sufficiently accurate column-averaged CO2 dry air mole fractions, denoted as XCO2, measured from the ground and/or space as the best approach to detect and quantify emissions and emission trends from urban regions (McKain et al., 2012). An effective observation-based scheme is able to disentangle anthropogenic emissions from CO2 fluxes originating from biosphere–atmosphere exchange.

Despite its importance, none of the existing satellites has been specifically designed and focused on observing XCO2 at urban scales. However, the first attempt to detect and quantify anthropogenic urban area CO2 emissions from space was initiated with the launch of SCIAMACHY onboard ENVISAT (2002–2012) (Burrows et al., 1995; Bovensmann et al., 1999), which had a variety of atmospheric trace gas targets and applications. This has been followed by TANSO onboard GOSAT (launched in 2009) (Kuze et al., 2009).

Analysis of SCIAMACHY XCO2 retrievals revealed that regionally elevated atmospheric XCO2 over highly populated regions correlates well with anthropogenic CO2 emissions in terms of relative emission increase per year (Schneising et al., 2008, 2013). However, these analyses are limited to large and intense emission regions, owing to the coarse spatial resolution (∼ 60 km × 30 km) of the SCIAMACHY measurements. Reuter et al. (2014) also presents results related to anthropogenic CO2 emissions for large areas using an assessment of SCIAMACHY XCO2 and NO2 retrievals.

By using GOSAT observations, Kort et al. (2013) reported significant enhancements of XCO2 over megacities (3.2± 1.5 ppm for Los Angeles and 2.4± 1.2 ppm for Mumbai), and argued that these enhancements can be exploited to track anthropogenic emission trends over megacities. However, constraining fossil fuel CO2 emissions by using GOSAT XCO2 retrievals is limited by the sparseness of the GOSAT data (Keppel-Aleks et al., 2013). Another satellite mission, OCO-2, has been launched in 2014, with the aim of measuring global XCO2 with the precision, resolution, and coverage needed to characterize CO2 sources and sinks at regional scales (≥ 1000 km) (Crisp et al., 2004). In additional to these, there have been some recent attempts to utilize ground-based measurements of XCO2 to constrain emissions from cities such as Los Angeles (Wong et al., 2015) and Berlin (Hase et al., 2015).

In an effort to overcome these limitations and to achieve XCO2 observations with the precision and accuracy, spatiotemporal coverage, resolution, and sensitivity to near-surface concentration variations that are required to derive emissions at urban scales, a satellite mission was proposed to the European Space Agency (ESA): Carbon Monitoring Satellite (CarbonSat) (Bovensmann et al., 2010). CarbonSat aimed to measure XCO2 and XCH4 at a high spatial resolution (approximately 2 km × 2 km), with good spatial coverage via continuous imaging across a wide swath. The goal swath width for the proposed CarbonSat mission was 500 km, but smaller swath widths were also considered to limit cost (ESA, 2015).

In this study, we investigated two potential measurement swath widths: 500 km (goal requirement) and 240 km (breakthrough requirement). As a result of its relatively wide swath and high spatial resolution, CarbonSat is designed to disentangle natural and anthropogenic sources of CO2 and CH4 from localized sources, such as cities, power plants, methane seeps, and landfills, by utilizing its unique greenhouse gas imaging capability achieved by its high spatiotemporal coverage and resolution. More details on the mission and the current instrument concept are given in Buchwitz et al. (2013a) and in ESA (2015).

The goal of the present study is to assess the capability of an instrument like CarbonSat to quantify emission patterns of moderate to strong localized sources, taking into account a realistic description of the retrieval errors as given in Buchwitz et al. (2013a), the spatiotemporal distributions of CO2 emissions, and atmospheric transport. Here, we present results focusing on Berlin (Germany), a large city but not a megacity. According to the classification of Globalization and World Cities (GaWC) for the year 2012 (http://www.lboro.ac.uk/gawc/gawcworlds.html), Berlin is categorized as a beta-level city that provides a moderate economic contribution to the world economy. Berlin is located in the northeast of Germany (see Fig. 1) and is relatively isolated, i.e. it is not a part of a large agglomeration of several cities. This permits us to clearly identify the anthropogenic CO2 emission plume of Berlin from a single CarbonSat XCO2 image. We use a high-resolution modelling framework, comprising the Weather Research Forecasting (WRF) model combined with a greenhouse gas module (WRF-GHG, Beck et al., 2011) and the Vegetation Photosynthesis Respiration Model (VPRM) to simulate CO2 mixing ratios for a domain centred on Berlin. An analysis is carried out for CarbonSat's cloud-free overpasses for 1 reference year by applying a simple Bayesian inversion scheme to estimate the emission budget with associated uncertainty. A preliminary analysis using a least-squares-fitting algorithm was reported in Buchwitz et al. (2013b), but here we present a more detailed analysis, which differs from the previous study as follows: the present study (1) uses high-resolution model simulations for each cloud-free CarbonSat overpass over Berlin for the simulated year 2008, (2) prescribes the updated emission inventory including hourly variations, (3) utilizes a Bayesian inversion approach, and (4) examines more scenarios to extend the error analysis study.

A high-resolution inverse modelling system, utilizing atmospheric XCO2 measurements at high spatial and temporal resolution, is used to retrieve the CO2 emissions at an urban scale. It comprises two components: the WRF-GHG model linking atmospheric transport and the fluxes to realistically represent the distribution of atmospheric CO2 mixing ratios, and a Bayesian inversion technique to optimize the fluxes. One primary objective is to quantify the uncertainties in the retrieved anthropogenic CO2 emission fluxes resulting from typical and reasonable estimates of the systematic and random error of the XCO2 measurements for an instrument like CarbonSat for the spatial resolution of 2 km × 2 km and the uncertainty in a priori knowledge of the surface flux of CO2. For this, we used WRF-GHG forward simulations as the true representation of the atmospheric CO2 concentrations and the associated fluxes as the true fluxes to be retrieved. Hence, the deviation in the retrieved fluxes (via inverse optimization) relative to the true fluxes is caused by the CarbonSat simulated observation errors and the modelling errors (including the use of different emission inventories) depending on different scenarios analysed. Each component of the inverse modelling system is described in the following.

In this study, we use anthropogenic XCO2 enhancement, which is defined as the enhancement in XCO2 resulting from local anthropogenic emissions relative to the background concentration. The tagged tracer option in WRF-GHG stores XCO2 enhancement resulting from EDGAR emissions separately, and we use this field to represent anthropogenic XCO2 enhancement. The uncertainty in the retrieved emission attributed by CarbonSat's retrieval error is a function of the anthropogenic XCO2 enhancement over Berlin, the number of potential observations in and around Berlin, and the retrieval uncertainty (random and systematic components). In this manner, we take into account the influence of these parameters to achieve a robust estimation of the retrieved surface emission uncertainty or error.

In this section, we discuss the merits of instruments like CarbonSat for retrieving emission fluxes and its potential in disentangling anthropogenic and biogenic CO2 fluxes over cities like Berlin. Caveats related to the simple inversion approach used here are discussed.

For the study of CO2 emissions, it is necessary to assess whether local anthropogenic XCO2 enhancements are large enough to be detected by using the retrieved XCO2 data products from the satellite-borne instrument, taking into account the measurement noise. Our analysis shows that anthropogenic XCO2 enhancements around Berlin are well above the retrieval biases for most of the overpasses and the number of potential observations, after filtering out the contaminated pixels, is large enough to minimize the random error component (not shown). Given the availability of such a dense sampling coverage with similar retrieval biases, one can be confident in utilizing CarbonSat's observations for retrieving city emission trends or absolute emission fluxes via appropriate inverse modelling.

In a real scenario, the question arises whether it is possible to clearly separate local anthropogenic XCO2 enhancements from CarbonSat's total column measurements, which are in addition influenced by biospheric sources or sinks. Moreover, in order to isolate the XCO2 enhancement caused by local sources (such as city emissions), it is necessary to specify the background signal, representing the CO2 column without any influence of local fluxes. These additional biospheric and background influences can be ignored if the target city is well isolated from other strong urban sources and/or active biospheric regions as well as has negligible local biospheric activity. However, only a few cities or urban areas meet the above criteria, and a typical European city, in general, has considerable local or nearby biogenic influences. Under these conditions, it is necessary to disentangle biogenic, anthropogenic and background contributions from CarbonSat's observations. To assess the relative contribution of biogenic and anthropogenic sources, one can utilize additional co-emitted tracers such as CO and NOx (Newman et al., 2013; Silva et al., 2013; Berezin et al., 2013; Reuter et al., 2014). In the time frame of a potential CarbonSat mission, Sentinel-5 will be providing data on CO and tropospheric NO2 (Ingmann et al., 2012), which, when combined with CarbonSat data, are expected to provide information for the attribution of air masses originating from fossil fuel combustion. Depending on the extent of the variability and the possible uncertainties, we can also rely on the biospheric and global model simulations to differentiate different source-sink contributions.

By assuming that the biospheric patterns are accurately modelled and that these biogenic signals can be subtracted from the measurement vector to isolate the anthropogenic contribution of XCO2, our simple inversion system is constructed such that it takes into account the impact of CarbonSat sampling errors on the retrieved city emissions over Berlin. The applicability of our results to a scenario where these assumptions are not valid needs to be examined, but the current setup is not well suited for this purpose since we have not taken into account additional state vectors for biospheric contributions. On the other hand, the current setup allows us to investigate the extremely pessimistic scenario where we assume that we cannot model the biospheric contribution at all (see Sect. 4.2.3).

When using observations at CarbonSat's 2 km spatial resolution, as mentioned in Sect. 4.1, it is likely that the magnitude and variability of local anthropogenic XCO2 enhancement would be higher than our estimation that is based on simulations at 10 km spatial resolution. One of the main advantages of CarbonSat's resolution is its ability to provide a large number of cloud-free observations and this study identified the potential observations over Berlin by utilizing CarbonSat's 2 km spatial resolution.

Although we utilize high-resolution forward simulations, at present our inversion system uses only one scaling factor for the entire target region for each useful overpass. This means that the current setup cannot provide posterior estimates for each pixel or emission sector within the target region. In other words, the flexibility to capture the true spatial variation of fluxes is more limited in our simple inversion system than in pixel- or parameter-wise inversions. Using this simple inversion system may thus overestimate the retrieved flux uncertainty. While interpreting our results, one should keep in mind that we do not specify other important sources of errors in the inversion system, such as transport error. As previously noted, the main focus of this study is to estimate the retrieved flux uncertainties that are caused only by CarbonSat's measurement errors. However, these transport-related errors, which provide proper weight to the observations depending on the capability of the transport model, need to be taken into account when estimating the total flux uncertainty via inverse modelling.

In the present study, we examine the potential of a satellite mission like CarbonSat for improving the current knowledge on the surface–atmosphere exchange of atmospheric CO2. A significant contribution by the CarbonSat GHG observations will be the ability to retrieve the emissions of localized (moderate to strong CO2 and CH4) emission sources such as cities, power plants, methane seeps, etc., as a result of its unique sampling capability at high spatial resolution (approximately 2 km × 2 km) with a good spatial coverage using a much wider swath. To demonstrate this, we have investigated the error on the retrieved fluxes using synthetic data which are similar to that expected from CarbonSat. We have simulated emissions from a medium-size city (in terms economic contribution and trade) and assessed the capability to retrieve anthropogenic emission fluxes for the city and its surrounding region (Berlin-centred target region investigated here: ∼ 100 km × 100 km) from CarbonSat simulated observations. The results show that these potential space-based, top-down flux estimates have high accuracy; hence, this study contributes to the definition of achievable targets for emission fluxes at the city scale.

The study utilizes a Bayesian inversion approach based on the WRF-GHG modelling system at a high spatial resolution to optimize anthropogenic CO2 emissions for the target region using CarbonSat simulated observations for a time period of 1 year. The inverse system is designed in such a way that one can quantify the random and systematic errors of the retrieved anthropogenic emission fluxes for a given set of XCO2 measurement and modelling errors. The CarbonSat measurement errors are estimated using the error parameterization scheme of Buchwitz et al. (2013a), which takes into account different sources of uncertainties, including scattering-related errors. Based on the EDGAR emission inventory, the local anthropogenic XCO2 enhancement over Berlin is found to be approximately 0.80–1.35 ppm. The latter is similar to the detectable limit of single CarbonSat ground pixels. However, typically there will be several hundred observations available per overpass, sampling the emission plume and its surrounding. The impact of CarbonSat measurement errors on the retrieved emissions is assessed for two swath widths (240 and 500 km). By performing a Bayesian inversion based on 1 year of CarbonSat simulated observations, we show that the random error of the retrieved Berlin CO2 emissions is typically less than 15–20 % of the total city emissions. In other words, the CarbonSat measurements can be utilized in atmospheric top-down approaches to quantify emissions of medium-sized cities such as Berlin with a precision better than 8–10 Mt CO2 yr-1.

In order to quantify the SE of the retrieved fluxes, we use different scenarios in terms of various sources of systematic error in the inversion system. For scenario S01, we use CarbonSat's default XCO2 systematic errors (retrieval biases) from Buchwitz et al. (2013a), and assume no biogenic XCO2 modelling error. For S01, we find that SE is in the range of 3–6 Mt CO2 yr-1 for most of the cases (40–80 % of the good overpasses as identified by the quality filtering procedure), indicating a high potential of utilizing CarbonSat's measurements to retrieve city emissions. Based on the analysis using a 1-year period of CarbonSat simulated observations, we show that narrowing the swath width (from 500 to 240 km) decreases the total number of useful overpasses, as expected, but we do not find any significant difference between the single-overpass SEs estimated for the two swath widths investigated here.

As explained in Buchwitz et al. (2013b), the default XCO2 systematic errors only reflect aerosol-related biases at quite low spatial resolution. On the spatial scale of the city of Berlin, aerosol-related biases may be larger. To consider this, we use the worst-case measurement scenario as used by Buchwitz et al. (2013b), in which we assume that the aerosol-related biases may be perfectly correlated with the signal of interest, which is the city CO2 emission plume in combination with a high amount of aerosols in the plume. For this, we define a scenario S04 and refer to this as a high-resolution aerosol error in this paper. The estimated emission uncertainty for this scenario (S04) is found to be higher than that of S01, with a mean and standard deviation of approximately -6.1 and 3.8 Mt CO2 yr-1, respectively.

The above-mentioned results, however, are mostly dominated by the assumption that there is a negligible influence of biospheric fluxes that perturb the emission plume over the target region, or that these biospheric contributions can be modelled very well. By further investigating the extreme case in which the biospheric contribution is assumed to be totally unknown and treated as perturbation in the inversion system (scenario S03), we find that the single-overpass SE of the retrieved emission is significantly increased to 7.5±9.5 Mt CO2 yr-1 (mean ± standard deviation). Nevertheless, the magnitude of the uncertainty is not overwhelmingly large over the target region, despite the worst-case assumption used here. It should be kept in mind that the above-mentioned uncertainty is not directly related to the performance of CarbonSat measurements, but more towards the model's inability in simulating the biospheric contribution well. Hence, for the effective utilization of these measurements, the noises induced from other sources have to be taken into account, which requires careful design of the inverse optimization methodology using transport models at high resolution, enabling them to handle the information contained in those measurements. On comparing the results from different scenarios, we show that the systematic error of the retrieved fluxes depends largely on the accuracy of the CarbonSat simulated observations and more importantly on the modelling-related errors.

Further investigation by designing a synthetic inversion experiment is motivated by the possible impact of spatial structural variability of the emission fluxes, which is not considered in the above-mentioned inversions. We acknowledge that our current inversion setup is too simple to examine how suitable CarbonSat measurements are for this purpose, as we use only one scaling factor for the entire target region. Nevertheless, we find promising results from this experiment in which the modelled and true XCO2 concentrations are based on two distinct emission inventories (IER and EDGAR) differing in spatiotemporal patterns. By showing that the systemic error of the retrieved fluxes is lower than the difference between the prior fluxes and the true fluxes in most of the cases, the results from the inversion experiment build confidence in our uncertainty estimations and ensure that the optimization is done correctly. The random error of the retrieved emissions for a single overpass is estimated to be less than 10 Mt CO2 yr-1 for both swath widths. Hence, it is expected that given the availability of the high-resolution CarbonSat simulated observations, it is likely to deduce the structural patterns of the emission fluxes. Based on the above analysis, however, no firm conclusion can be made regarding the magnitude of the retrieved flux uncertainty when prior fluxes significantly deviate from true fluxes in representing the structural variations of emissions. For this purpose, a more sophisticated inverse methodology involving additional extended state vectors and calculation of the response function of the elements of the state vector (adjoint calculation) is required. Since we use the same transport model to generate the (pseudo) observations and the influence functions, the inversion results shown here may be slightly optimistic. Although it is not within the scope of this study, the transport-related errors are expected to be non-negligible and should be properly addressed in the inverse modelling applications of satellite data.

Using the dense CarbonSat measurements in an inverse modelling framework at high resolution is expected to improve the inference of CO2 fluxes by disentangling different sources of variations. But to what extent one can differentiate regional contributions from different sources should be investigated in further detail.

Overall, the present study demonstrates that an instrument like CarbonSat has high potential to provide important information on city CO2 emissions when exploiting the atmospheric XCO2 observations using a high-resolution inverse modelling system. Utilizing these measurements together with in situ, airborne, and other satellite measurements is expected to provide more detailed and reliable information on natural and anthropogenic fluxes, facilitating the monitoring of future climate mitigation strategies.

The L4 eddy covariance data set has been accessed from http://www.europe-fluxdata.eu/.