Tracking city CO 2 emissions from space using a high resolution inverse modeling approach: A case study for Berlin, Germany

. Currently 52% of the world’s population resides in urban areas and as a consequence, approximately 70% of fossil fuel emissions of CO 2 arise from cities. This fact in combination with large uncertainties associated with 10 quantifying urban emissions due to lack of appropriate measurements makes it crucial to obtain new measurements useful to identify and quantify urban emissions. This is required, for example, for the assessment of emission mitigation strategies and their effectiveness. Here we investigate the potential of a satellite mission like Carbon Monitoring Satellite (CarbonSat), proposed to the European Space Agency (ESA) − to retrieve the city emissions globally, taking into account a realistic description of the expected retrieval errors, the spatiotemporal distribution of 15 CO 2 fluxes, and atmospheric transport. To achieve this we use (i) a high-resolution modeling framework consisting of the Weather Research Forecasting model with a greenhouse gas module (WRF-GHG), which is used to simulate the atmospheric observations of column averaged CO 2 dry air mole fractions (XCO 2 ), and (ii) a Bayesian inversion method to derive anthropogenic CO 2 emissions and their errors from the CarbonSat XCO 2 observations. We focus our analysis on Berlin in Germany using CarbonSat’s cloud-free overpasses for one reference year. The dense (wide 20 swath) CarbonSat simulated observations with high-spatial resolution (approx. 2 km x 2 km) permits one to map the city CO 2 emission plume with a peak enhancement of typically 0.8-1.35 ppm relative to the background. By performing a Bayesian inversion, it is shown that the random error (RE) of the retrieved Berlin CO 2 emission for a single overpass is typically less than 8 to 10 MtCO 2 yr -1 (about 15 to 20% of the total city emission). The range of systematic errors (SE) of the retrieved fluxes due to various sources of error (measurement, modeling, and 25 inventories) is also quantified. Depending on the assumptions made, the SE is less than about 6 to 10 MtCO 2 yr -1 for most cases. We find that in particular systematic modeling-related errors can be quite high during the summer months due to substantial XCO 2 variations caused by biogenic CO 2 fluxes at and around the target region. When making the extreme worst-case assumption that biospheric XCO 2 variations cannot be modeled at all (which is overly pessimistic), the SE of the retrieved emission is found to be larger than 10 MtCO 2 yr -1 for about half of the 30 sufficiently cloud-free overpasses, and for some of the overpasses we found that SE may even be on the order of magnitude of the anthropogenic emission. This indicates that biogenic XCO 2 variations cannot be neglected but must be considered during forward and/or inverse modeling. Overall, we conclude that CarbonSat is well suited to obtain city-scale CO 2 emissions as needed to enhance our current understanding of anthropogenic carbon fluxes and that CarbonSat or CarbonSat-like satellites should be an important component of a future global carbon emission system. and the uncertainty in a priori knowledge of the surface flux of CO 2 . For this, we used WRF-GHG forward simulations as the “true” representation of the atmospheric CO 2 concentrations and the associated fluxes as the “true fluxes” to be retrieved. Hence the deviation in the retrieved fluxes (via inverse 45 rush hours, difference in power demand between weekdays and weekends, domestic heating, and air conditioning (Pregger and Friedrich, 2007). While utilizing the IER year 2000 database to represent the simulation year (2008), we apply scaling factors in a manner similar to that in Pillai et al. (2011) to preserve the temporal emission pattern differences between 45 emission plume corresponding to the anthropogenic CO 2 emission in the target region. Although the error arising from these unknown spatial emission structures is not directly related to CarbonSat measurement errors, we attempt to perform an experiment using two different flux inventories, with one of the flux inventories representing the prior fluxes and the other as the “true” fluxes. The experiment is designed 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 set-up cannot provide posterior estimates for each pixel or emission sector within the target region. In other words, the flexibility to 45 capture the true spatial variation of fluxes is more limited in our simple inversion system than in pixel- or parameter-Atmos. random swath CarbonSat simulated of flux when fluxes fluxes structural variations of extended state state vector (adjoint regional A preliminary analysis over the target using the “clean-pixel” method as followed encouraging results in XCO the present study demonstrates that an instrument like CarbonSat has high potential to provide important 40 information on city CO 2 emissions when exploiting the atmospheric XCO 2 observations using a high-resolution inverse modeling 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. Acknowledgements. We thank all principle investigators involved in the eddy covariance measurements, and all scientists involved in the L4 eddy covariance dataset that has been accessed from http://www.europe-fluxdata.eu/. This study has received funding from ESA (projects LOGOFLUX-I and LOGOFLUX-II) and the State and the University of Bremen.

satellite mission, OCO-2, has been launched in 2014, with the aim of measuring global XCO 2 with the precision, resolution, and coverage needed to characterize CO 2 sources and sinks at regional scales (≥ 1000km) (Crisp et al., 2004). In additional to these, there have been some recent attempts to utilize ground-based measurements of XCO 2 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 XCO 2 observations with the precision and accuracy, 5 spatiotemporal coverage, resolution, and sensitivity to near-surface concentration variations that are required to derive emissions at urban scales, a satellite mission has been proposed to the European Space Agency (ESA): Carbon Monitoring Satellite (CarbonSat) (Bovensmann et al., 2010). CarbonSat aims to measure XCO 2 and XCH 4 at a high spatial resolution (approx. 2 km × 2 km), with good spatial coverage via continuous imaging across a wide swath. The goal swath width is 500 km, but a smaller swath width will likely be implemented to limit cost (ESA, 10 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 CO 2 and CH 4 from localized sources such as cities, power plants, methane seeps, and landfills, by utilizing its unique greenhouse gas imaging capability achieved by its 15 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 an instrument like CarbonSat's capability 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 CO 2 emissions, and atmospheric transport. Here we 20 present results focusing on Berlin in Germany, being 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 CO 2 emission plume of Berlin 25 from a single CarbonSat "XCO 2 image". We use a high-resolution modeling 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 CO 2 mixing ratios for a domain centered on Berlin. An analysis is carried out for CarbonSat's cloud-free overpasses for one reference year by applying a simple Bayesian inversion scheme to estimate the emission budget with associated uncertainty. A preliminary analysis 30 using a least-squares-fitting algorithm was reported in Buchwitz et al. (2013b), but here we present 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.

WRF-GHG inverse modeling system
A high-resolution inverse modeling system, utilizing atmospheric XCO 2 measurements at high spatial and temporal resolution, is used to retrieve the CO 2 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 CO 2 mixing ratios, and a Bayesian inversion technique to optimize the fluxes. One primary objective is to quantify the 40 uncertainties in the retrieved anthropogenic CO 2 emission fluxes resulting from typical and reasonable estimates of the systematic and random error of the XCO 2 measurements for an instrument like CarbonSat for the spatial resolution of 2km x 2km and the uncertainty in a priori knowledge of the surface flux of CO 2 . For this, we used WRF-GHG forward simulations as the "true" representation of the atmospheric CO 2 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 modeling errors (including the use of different emission inventories) depending on different scenarios analyzed. Each component of the inverse modeling system is described in the following.

WRF-GHG forward model simulations
The present study uses the WRF-GHG (version WRFv3.4) forward simulations of CO 2 concentrations at high spatial 5 (10 km × 10 km) and temporal (1 hour) resolutions for all of CarbonSat's overpasses over Berlin in the year 2008. The WRF-GHG modeling system has already been used in several regional studies and has shown remarkable performance in capturing fine-scale spatial variability of CO 2 mixing ratios (e.g. Ahmadov et al., 2007Ahmadov et al., , 2009Pillai et al., 2010Pillai et al., , 2011Pillai et al., , 2012. The model domain describes a region (spatial extent of ~ 900 km × 900 km) centered over Berlin ( Fig.1) and the simulations use 41 vertical levels (the thickness of the lowest layer is about 18 m).

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Simulations are conducted separately for each day for a period of 30 hours, including a meteorological spin-up time of 6 hours starting at 18 UTC the previous day.
The initial and lateral boundary conditions of the meteorological variables, the sea surface temperature (SST) and the soil initialization fields for each run are prescribed from the European Centre for Medium-Range Weather Forecasts (ECMWF) model analysis data (http://www.ecmwf.int) with a spatial resolution of about 25 km and 6-15 hourly temporal intervals. As initial atmospheric CO 2 fields and the lateral boundary concentrations, simulations use global CO 2 concentration simulations by the atmospheric Tracer transport Model 3 (TM3) with a spatial resolution of 4° × 5°, 19 vertical levels and a temporal resolution of 3 hours (Heimann and Körner, 2003). TM3 simulations used for this study are generated by a forward transport simulation of fluxes that have been optimized using a global network of CO 2 observing stations (Rödenbeck, 2005). Biospheric fluxes within the regional domain are calculated 20 online in WRF-GHG with a diagnostic biospheric model, the Vegetation and Photosynthesis and Respiration Model (VPRM), utilizing remote sensing products and meteorological data at high temporal and spatial resolutions (Mahadevan et al., 2008). To obtain more realistic estimates of biospheric fluxes, a set of parameters in the VPRM, specific for each vegetation class, have been optimized against eddy flux observations obtained during the CarboEurope IP experiment at various sites (21 measurements sites) under different vegetation types within Europe 25 (Pillai et al., 2012). An overview of the flux optimization is shown in Fig. 2. Regional oceanic fluxes are neglected here since their contribution is insignificant in the context of the present study.

Fossil fuel emission fluxes
The anthropogenic CO 2 emission fluxes are based on the EDGAR (Emission Database for Global Atmospheric

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Research, version 4.1, year 2008) global inventory with a spatial resolution of 0.1° x 0.1°. EDGAR is an annually varying database, but we apply time factors in order to provide hourly emissions. The time factors for seasonal, daily, and diurnal variations are based on the step-function time profiles published on the former EDGAR website: http://themasites.pbl.nl/images/temporal-variation-TROTREP_POET_doc_v2_tcm61-47632.xls (see Kretschmer et al. (2014);Steinbach et al. (2011) for further details). WRF-GHG simulations using these EDGAR emissions are 35 treated as the real distribution of atmospheric CO 2 (hereafter referred to as "true CO 2 conc."), and the associated EDGAR fluxes as "true fluxes".
In order to examine the impact of the spatio-temporal distribution of fossil fuel emission structures on atmospheric CO 2 and to quantify the associated uncertainties in the optimized fluxes, we use different emission data as the prior emissions, namely those compiled by the Institut für Energiewirtschaft und Rationelle Energieanwendung (IER 40 inventory), University of Stuttgart, (http://carboeurope.ier.uni-stuttgart.de) for the year 2000, at a spatio-temporal resolutions of 10 km and 1 hour. Temporal variations in the IER inventory include traffic rush hours, difference in power demand between weekdays and weekends, domestic heating, and air conditioning (Pregger and Friedrich, 2007). While utilizing the IER year 2000 database to represent the simulation year (2008), we apply scaling factors in a manner similar to that in Pillai et al. (2011) to preserve the temporal emission pattern differences between weekdays and weekends. Simulations using the IER database are used as the current knowledge about the atmospheric concentration for the inverse optimization described in Sec. 4.3.
Both these emission fluxes are re-gridded to WRF-GHG's 10 km Lambert Conformal Conic projection grid, conserving the total mass of emissions. These hourly fluxes are added separately to the first model layer, and transported separately as tagged tracers. Figure 3 shows a spatial map of the averaged EDGAR and IER emission 5 fluxes over all the cloud-free overpasses at a certain hour as well as their differences for the model domain. Strong emissions associated with large industrial areas and cities can be seen well in both inventories. In general, both emission inventories show good consistency in terms of spatial emission structures; however significant differences in emission intensities (magnitude) between the inventories, especially for large cities and power plants, are common (Fig. 3c). These differences are larger for emissions resulting from power plants than for those from cities. Figure 4 shows the temporal variability of urban-scale emission fluxes in hourly, weekly and monthly averaged time scales for a region around Berlin (~ 100 km × 100 km). For Berlin emissions, considerable differences in temporal variations are found between both inventories, with maximum values of 22. 5, 18.5, and 24.0 MtCO 2 yr -1 for hourly, weekly and monthly averaged timescales respectively. As compared to the IER inventory, the EDGAR inventory shows consistently larger emissions for Berlin. The seasonal variability exhibited by EDGAR Berlin emissions is 15 substantially larger than that of the IER inventory. Larger emissions are seen in the EDGAR inventory in winter months, with values approximately a factor of 1.5 higher than those in summer months. This results from the increased demand of domestic heating in winter. In terms of the seasonal variability of the Berlin city emissions, the IER inventory shows a relatively small difference in winter-summer emission patterns (temporal) as compared to EDGAR, and shows overall larger emissions in winter. Both inventories show lower emissions during weekends, 20 consistent with the reduced demand of transportation and power consumption. The hourly averaged Berlin emissions provided by both inventories display peak values during 7 to 9 am and 5 to 7 pm (local times), reflecting morning and evening rush hours in terms of city traffic. Interestingly the IER Berlin emissions show "delayed" morning rush hours on weekends, with a maximum value around 11 am (local time).

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The significant difference between these inventories in both temporal and spatial scales implies that our current 25 knowledge of urban-scale emissions is inadequate, even for Central Europe, which is relatively well characterized in terms of emissions compared to many other parts of the world. Note that a part of these emission differences is likely due to the different data compilation years of the IER and EDGAR inventories. This "knowledge gap" is also important in inverse-modeling-based estimations of the source-sink distribution of CO 2 , in which fossil fuel fluxes are generally assumed to be known. How critical the effect of this assumption is depends on the impact of these 30 differences in emissions (emission uncertainties) on modeled atmospheric mixing ratios, as well as on the transport errors that are included in the model-data mismatch error in the inverse modeling framework. The impact of emission uncertainties is further discussed in Sec. 4.1.

Inverse optimization technique
The inverse optimization utilizes observational constraints to adjust a subset of parameters out of model 35 parameters in the surface flux model in order to obtain a modeled concentration consistent with the observations. Hence the anthropogenic atmospheric concentration (column averaged dry air mole fraction) at different locations and times can be represented as: Here, the matrix links the atmospheric concentration to a vector whose dimension is equal to the total 40 number of surface flux elements, multiplied by total time steps. The vector !" is the background column averaged dry air mole fraction i.e. the concentration due to the advection of upstream tracer concentrations. For the inversion, is assumed to be linearly dependent on and is expressed as: where represents a vector of daily scaling factors of surface fluxes, and represents the surface flux field over the model domain.
A linear model is obtained by combining Eq(s). 1 and 2: where the measurement vector is given by and, !" is obtained by linearizing the model with a reference state ! = 0 (see Eq. 1).
The Jacobian matrix that represents the sensitivity of the observations to the state vector is given by The state vector and the Jacobian matrix are further described in Sec. 3.2. A priori knowledge of the surface fluxes, !"#$" , along with their uncertainties is incorporated in the Bayesian formulation. The term, !""#" , is assumed to follow the Gaussian distribution described by the error covariance matrices of the measurements, and the prior estimate, . The posterior estimate of is obtained by minimizing the cost function, , which is given as:

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Analytically solving for the minimum of Eq. (4) gives the optimal estimate of the state vector of the scaling factors , as well as the associated error covariance matrix of , termed as the posterior uncertainty, ! . These are expressed as follows (Rodgers, 2000):

Pseudo observations
The inversion utilizes a one year dataset of CarbonSat simulated observations at a spatial resolution of 2 km × 2 km, generated using the WRF-GHG forward model (10 km × 10 km) as described in Sect. 2.1 and CarbonSat's retrieval error (2 km × 2 km), estimated using an error parameterization scheme based on the measurement characteristics as 25 described in Buchwitz et al. (2013a). The error parameterization scheme, described in detail in Buchwitz et al.(2013a), is based on six parameters consisting of solar zenith angle (SZA) and scattering-related parameters such as albedo in the near-infrared (NIR) and the first shortwave-infrared (SWIR-1) bands, cirrus optical depth (COD), cirrus top height (CTH), and aerosol optical depth (AOD) at 550 nm. We use the "Level 2 error dataset" (L2e files), described in Buchwitz et al. (2013a), that contains the random and systematic errors of CarbonSat's XCO 2 retrievals 30 based on the error parameterization scheme. CarbonSat is assumed to follow an orbit similar to NASA's Terra satellite (www.nasa.gov/terra/), but with an equator crossing time of 11:30 a.m. Hence, for specifying the CarbonSat's geolocation, the L2e files utilize the geolocation provided in the Terra Level 1 dataset for the year 2008, but modified to consider the difference in equator crossing time. This dataset contains fields such as geodetic coordinates, ground elevation, and solar and satellite zenith angles etc., determined using the spacecraft attitude and 35 orbit, a digital elevation model, and information derived from various other datasets such as the Filled Land Surface Albedo Product, generated from MOD43B3 (http://modis-atmos.gsfc.nasa.gov/ALBEDO/) at a spatial resolution of 1 minute (2 km at equator, and < 1 km at the poles), which is used to account for surface albedo. The cirrus Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-960, 2016 Manuscript under review for journal Atmos.  Winker et al., 2009). Global aerosol data products from the "GEMS project" (http://gems.ecmwf.int/) at a spatiotemporal resolution of 1.125 o × 1.125 o and 12 hourly are used to account for aerosols (AOD). This dataset is based on the assimilation of MODIS data and we use the 5 AOD at 550 nm. As described in Buchwitz et al. (2013a), the L2e dataset only contains those Carbonsat simulated observations which are approximately cloud-free as determined using a cloud mask obtained from MODIS Terra (using the MODIS cloud cover data product (MOD35) at a spatial resolution of about 1 km × 1 km). As the remaining ground pixels may still suffer from cloud contamination (e.g., due to "too high" amounts of thin cirrus) or other disturbances, a quality filtering scheme is applied which is based on retrieved (e.g., COD and AOD) and 10 known quantities (e.g., SZA). The quality filtering scheme is described in Buchwitz et al. (2013a) and we use here only those ground pixels which are considered "good" according to this scheme.
Initially, we have identified all the potentially useful Berlin overpasses, i.e., overpasses where at least some CarbonSat simulated observations are present over Berlin and surroundings for a given CarbonSat orbit. We found that the maximum number of observations is obtained during the summer months due to most favorable observation 15 conditions (less clouds for extended time periods and regions, high SZA, etc.). In total, there are 41 days (orbits) of potentially useful overpasses over Berlin for the year 2008 for a swath width of 500 km. Note that the number of overpasses are smaller in the figures shown later. This is because of an additional quality filtering procedure applied after the inverse optimization that is based on retrieved random errors, as explained later.

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In the present study, the state vector (the scalable parameter of the emission flux) corresponds to the scaling factor of emission fluxes for a trimmed model domain, i.e., a region around Berlin (spatial extent: approximately 100 km × 100 km, hereafter referred to as the "target region" (TR). The temporal resolution of is set to be daily, assuming no spatial variations within the target region. The prior value of this scaling factor, !"#$" , is set to unity.

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The Jacobian matrix relates the measurement vector to the state vector , and has elements that represent the response in mixing ratios to the emission fluxes (see Eq. 5). Since we do not have an adjoint model, these sensitivity functions are derived by perturbing each element of the emission flux field over the target region by small increment and applying the forward model (WRF-GHG) to obtain the resulting perturbed concentration field ( + ∆ ) over the target region. Hence, is calculated as follows: The posterior estimate of the scaling factor, , is derived by minimizing the cost function, , as given in Eq.7.

Error covariance matrices
Bayesian inversion utilizes error covariance matrices to account for the measurement error and the prior flux error variances and co-variances. The measurement error covariance matrix, , is constructed by specifying the XCO 2 35 random errors (single measurement precision) derived using the error parameterization scheme described in Sect.
3.1. Note that the XCO 2 random error is primarily determined by the instrument signal-to-noise performance (but also to some extent by the retrieval algorithm, see Buchwitz et al. (2013a)) and is typically about 1.2 ppm (for the assumed threshold requirement signal-to-noise ratio performance assumption used by Buchwitz et al., 2013a)  is neglected here since the objective of current study is to quantify the uncertainty in the retrieved fluxes due to CarbonSat's retrieval errors only.
The prior flux uncertainty, , is set uniformly to 40 % of the total emission over the target region to ensure that the difference between the "true" and prior fluxes is appropriately considered. We consider the fact that the increased variability of emissions at the high resolution (as it is used in this study) leads to increased uncertainty due 5 to the lack of information about the emission processes at the required spatial and temporal resolutions. The magnitude of is specified here based on the approximate difference between the IER and the EDGAR inventories over the target region. Any error correlations are neglected; hence is set to be a diagonal matrix.

Results: Estimation anthropogenic XCO 2 enhancement and retrieved flux uncertainty over Berlin
In this study, we use anthropogenic XCO 2 enhancement, which is defined as the enhancement in XCO 2 resulting 10 from local anthropogenic emissions relative to the background concentration. The tagged tracer option in WRF-GHG stores XCO 2 enhancement resulting from EDGAR emissions separately, and we use this field to represent anthropogenic XCO 2 enhancement. The uncertainty in the retrieved emission attributed by CarbonSat's retrieval error is a function of the anthropogenic XCO 2 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 15 account the influence of these parameters to achieve a robust estimation of the retrieved surface emission uncertainty or error.

Local anthropogenic XCO 2 enhancement
The XCO 2 enhancements resulting from anthropogenic emissions over Berlin are estimated in order to assess whether these emission enhancements are detectable by an instrument having the performance of CarbonSat i.e. to 20 assess whether the resulting plumes are statistically significant and robust, thereby enabling the changes or trends in anthropogenic emission over the cities. Figure 5 shows the "true" anthropogenic XCO 2 enhancement on a reference day (24 th June 2008), the anthropogenic XCO 2 enhancement based on the IER inventory, and the difference in XCO 2 enhancement due to the difference in emission inventories. From Fig. 3a and Fig. 5a, it can be concluded that, given the availability of a satellite 25 instrument which is able to precisely detect the associated XCO 2 mixing ratio enhancements ranging from 0.80 to 1.35 ppm at a high spatial resolution and adequate spatial coverage, anthropogenic emissions from a city the size of Berlin and other localized emission sources can be estimated from space with sufficient accuracy. It should be noted that the magnitude of detectable anthropogenic XCO 2 enhancements is likely to be underestimated in our study because the "true" fields of XCO 2 variations are simulated at a 10 km spatial resolution instead of CarbonSat's 30 resolution (~2 km × 2 km).
Noteworthy is that the spatial and temporal difference in EDGAR and IER emission inventories gives rise to a notable XCO 2 mixing ratio difference between 0.4 and 1.0 ppm. For Berlin, this is about 40% of the total "true" XCO 2 enhancement. It should be noted that surface concentrations show larger relative differences than the column dry mole fraction for CO 2 , XCO 2 , because of their higher sensitivity to the change in surface fluxes. Hence this 35 result indicates the importance of characterizing emission uncertainties, even for the region where fossil emissions are often considered to be "well-quantified" in comparison to the biospheric carbon balance. Neglecting this uncertainty term would lead to significant biases in the net carbon exchange estimations, particularly when assimilating concentration measurements closer to emission sources such as cities.
In this section, we show the results obtained by inverting CarbonSat simulated observations over the target region, taking into account different sources of possible errors including CarbonSat measurement errors and modeling errors. Inversions are performed separately for each potentially useful CarbonSat overpass (see above) to derive the total emission flux and its error over the target region.
The systematic error (SE) of the retrieved emission fluxes, which are specific for each source of errors or 5 combination of errors, are determined separately by defining six scenarios represented by S01 through S06 (Table  1). These scenarios are described in the following subsections, while additional scenarios S07 -S11 are presented and discussed separately in Sect. 4.3. Note that the distance from the center of the target region to one of its boundaries is roughly 50 km, which corresponds to a time of approximately 3 hours for air parcels travelling with a velocity of 4.5 ms −1 . This means that the observed local CO 2 emission plume is not only determined by the emission 10 at the time of the overpass, but also during a time interval of several hours before the time of the overpass. This is taken into account when modeling the CO 2 emission plume. For the inversion, it is assumed that the time dependence of the emissions in the time period of up to several hours (3 to 6 hours) before the overpass is at least reasonably well known except for the scenarios S07 to S11. As noted earlier, the "true" XCO 2 variations in this study are based on 10 km spatial resolution instead of 2 km in CarbonSat simulated observations. For the inversion 15 results, we assume negligible representation error arising from these spatial scale mismatches. Based on meteorological conditions, the representation error introduced by decreasing the horizontal resolution from 2 km to 10 km can be approximately 0.5 ppm on average for CO 2 concentrations at the surface (Tolk et al., 2008). However, it is expected that the representation error for XCO 2 between these horizontal scales will be much lower than that for CO 2 concentration at surface (see Pillai et al., 2010).

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Before analyzing SE for the different scenarios, we first present the random error (RE) of the retrieved emission. RE is caused by the measurement noise, i.e., by the random part of the measurement error; hence it is independent of the above-mentioned SE scenarios. In the optimal case, the instrument noise is determined by the shot noise of the detector arrays. In practice, there are additional sources of noise such as read out noise, digitization noise etc. Figure  7 shows the random errors of the retrieved emissions over the target region, obtained by inverting the entire one-year 25 data set of simulated CarbonSat XCO 2 retrievals. As explained above, we have investigated two different swath widths, 500 km and 240 km. The results are shown only for the days where the number of CarbonSat simulated observations around the target region is sufficiently dense (covering the emission plume and its surroundings) to obtain a retrieved emission random error of less than 25 %, i.e., we use the a posteriori random error of the retrieved emission as a quality criterion (as also done in Buchwitz et al. (2013b)). This number, labeled as "N" useful 30 overpasses, is 25 for a swath width of 500 km and 17 for a swath width of 240 km. As can be seen in Fig. 7, decreasing the swath width not only reduces the number of useful overpasses, but also increases the RE of the retrieved fluxes for some overpasses. The RE of the retrieved emission (from a single overpass) is usually found to be less than 20% (approximately 10 MtCO 2 yr −1 ) of the emission fluxes for both swath widths.

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Here, we focus on scenario S01, and estimate the uncertainty in the retrieved emission fluxes caused exclusively by CarbonSat measurement errors. For this, we assume that the XCO 2 variability in the target region is dominated by the anthropogenic CO 2 emission and that there is negligible XCO 2 variability due to biogenic fluxes over the target region, or that this biogenic component can be modeled well, and thus can be subtracted from the observations without introducing any modeling-related errors.

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The systematic measurement error of the CarbonSat simulated observations over the target region for a typical day (24 th June 2008) for S01 is shown in Fig. 8a. This is estimated using the error parameterization scheme of Buchwitz et al. (2013a), as shortly described in Sec. 3.1. The mean systematic measurement error over the target region is about 0.25 ppm for this day. For the scenario S01, the "observed" anthropogenic XCO 2 by CarbonSat is thus the sum of this measurement error (Fig. 8a) and the "true" anthropogenic XCO 2 . Fig. 9a shows the observed 45 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-960, 2016 Manuscript under review for journal Atmos. Chem. Phys.
anthropogenic XCO 2 enhancement for S01 over the target region during the overpass on 24 th June 2008. For the comparison, the corresponding "true" anthropogenic XCO 2 enhancement, i.e. without any source of errors, is shown in Fig. 9g. The "true" emission plume, originating almost from the centre of the target region, can be clearly seen with a maximum value of about 0.90 ppm. As can be seen, the observed CarbonSat XCO 2 pattern (Fig. 9a) differs from the "true" XCO 2 pattern (Fig. 9g) by the measurement errors (Fig. 8a); hence the retrieved emission via 5 inversion typically differs from the "true" emission that results in a systematic error (SE) of the retrieved emission. The extent of this systematic error depends on how well the systematic measurement error correlates with the "true" XCO 2 pattern. Figure 10 shows the systematic errors of the retrieved emissions for CarbonSat overpasses over the target region obtained by inverting the entire one-year data set of simulated CarbonSat XCO 2 retrievals for the scenario S01.

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Shown are the results for swath widths of 500 km and 240 km for all "N" useful overpasses (days). Overall, the absolute magnitude of the systematic errors of the retrieved emissions for both swath widths for the scenario S01 is found to be less than 10% for most of the overpasses (about 75% of the "N" useful overpasses for the year 2008), which corresponds to about 5.3 MtCO 2 yr −1 . For the 500 km swath width in S01, the mean and standard deviation of the SE for all "N" useful overpasses is -2.4 MtCO 2 yr -1 (-4.5%) and 3.2 MtCO 2 yr -1 (6.2%), respectively (see also 15 Table 1). In general, we find that the two different swath widths have a negligible impact on the daily SE of the retrieved emissions.

Impact of CarbonSat measurement errors with worst-case aerosol related biases (scenarios S02 and S04)
Note that in the previous section we have used the CarbonSat systematic XCO 2 retrieval errors as provided by the 20 error parameterization scheme described in Buchwitz et al. (2013a). However, as explained in Buchwitz et al. (2013b), this scheme may underestimate aerosol related biases if the spatially (not aggregated) high-resolution CarbonSat simulated observations are used for applications like the one used here. The reason is that aerosol-related retrieval biases have been computed using quite smooth model aerosol input data sets, which might not be sufficient to represent the aerosol plume over Berlin.

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To consider this, an additional error term has been defined which is referred to as "high resolution aerosol error" in this manuscript. In this sub-section we present results for scenario S02, where the measurement error used for S01 described in the previous section has been replaced by the high-resolution aerosol error contribution to the systematic measurement error. We also present results for scenario S04, where the measurement error is the sum of the S01 and S02 errors.

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The method of computing the "high resolution aerosol error" is described in detail in Buchwitz et al. (2013b). Here we describe it briefly as follows. A local AOD enhancement has been computed by scaling the observed anthropogenic XCO 2 spatial pattern, i.e., the AOD enhancement is assumed to be perfectly correlated with the CO 2 emission plume of interest (see Fig. 8b and Fig. 9b). Furthermore, a quite high scaling factor has been used (the AOD change, ∆AOD at 550 nm is 0.2 per 4 ppm of local anthropogenic ∆XCO 2 ). Overall, these are worst-case 35 assumption that are supposed to result in upper limits of systematic XCO 2 errors due to aerosols and resulting errors of the retrieved emissions. For a more detailed discussion see Buchwitz et al. (2013b).
The resulting SEs of the retrieved emissions for scenario S02 are found to be negative, indicating systematic underestimation of retrieved emissions (see Fig. 11). As can be seen, the absolute magnitudes of errors are slightly higher than those for S01. The mean and standard deviation of SE for S02, considering all "N" useful overpasses performed by utilizing these two sources of error, i.e. the XCO 2 systematic error for S04 is the sum of XCO 2 systematic error specified in S01 and S02 (see Fig(s). 8d and 9d)). As expected, the SE of the retrieved emission for S04 is found to be higher than those of S01 and S02, and their values are close to the linear sum of systematic emission errors for S01 and S02 (see Table 1). As already explained, the definition of S04 likely represents the possible worst-case measurement scenario in particular with respect to aerosol related errors. In this section, we explore the impact of modeling error on retrieving Berlin city emissions. In the last two sections, it is assumed that the spatial variability introduced by the biogenic component of XCO 2 in the target region is well known or sufficiently small that it can be ignored. However, in reality there are notable perturbations caused by the spatial variability of biogenic XCO 2 in the target region that cannot be ignored. As an example, Fig. 8c illustrates the 10 biogenic XCO 2 variability in the target region during a CarbonSat overpass. Most critical in terms of this uncertainty is how well the biogenic XCO 2 pattern is correlated with the anthropogenic XCO 2 pattern. In this case, the uncertainty in the retrieved emissions depends on how accurately the biogenic fluxes can be modeled, as well as the associated transport model uncertainty in simulating the biogenic XCO 2 pattern. Note that we assume negligible transport uncertainty for the anthropogenic XCO 2 pattern in order to distinguish the retrieved emission errors due 15 only to the biogenic XCO 2 pattern. In order to account for this modeling-related error, we consider scenario S03. In S03, we assume an extreme case where biogenic XCO 2 cannot be modeled at all; hence biogenic XCO 2 is treated as the "perturbation" seen in the measurement vector ( ) of the inversion system (see Fig(s). 8c and 9c). However, it should be noted that in reality biospheric modeling uncertainty is not expected to be as high as this assumption. As can be seen in Fig. 2, a simple biosphere model such as VPRM used in this study could capture 50 to 65% of the 20 biospheric flux variability in most of the cases (squared correlation coefficient (VPRM vs. observations), R 2 ~ 0.50-0.65).
The systematic errors of the retrieved emissions for S03 are found to be significantly higher compared to the errors for the above-mentioned scenarios than those for S01 and S02 (see Fig. 12). Noteworthy is that this uncertainty is not related to CarbonSat measurement errors, but arises due to the inability of the model to simulate the biospheric 25 contribution. Hence this uncertainty should be treated as model-related error. Due to the extreme assumption of modeling error in S03, the uncertainty values reported in this section have to be considered as the extreme upper limits of the possible total uncertainties in the retrieved fluxes due to biogenic modeling error. Despite this, the SE of the retrieved emission for S03 is within the range of 20 to 25% (10 to 15 MtCO 2 yr −1 ) for most of the scenes although we assumed the largest uncertainty in modeling biogenic XCO 2 . The reason for this is that the spatial 30 biospheric XCO 2 pattern in the target region that "disturbs" the inverse system typically differs from the anthropogenic XCO 2 pattern in many of the good CarbonSat overpasses, enabling these two sources/sinks (anthropogenic and biogenic) to be disentangled reasonably well.
Additionally, we define other scenarios, S05 and S06, to investigate the impact of the biogenic modeling errors in combination with other error sources, such as CarbonSat measurement errors and high-resolution aerosol related 35 errors. Systematic error estimations for these scenarios are summarized in Table 1 and these results suggest that a dominant part of the retrieved emission error is caused by the unknown biogenic variability.

Inversion Experiment using different prior emission fluxes (S07-S11)
The inversion results presented so far have not taken into account the impact of imperfect knowledge of the spatial pattern of emission fluxes and the different time dependences of the emissions; hence the inverse optimization 40 adjusts only the amplitude of the emission plume corresponding to the anthropogenic CO 2 emission in the target region. Although the error arising from these unknown spatial emission structures is not directly related to CarbonSat measurement errors, we attempt to perform an experiment using two different flux inventories, with one of the flux inventories representing the prior fluxes and the other as the "true" fluxes. The experiment is designed with an inversion set-up, which is essentially the same as that described in Sect. 3.3, but with the following exception: Here the prior emission fluxes are prescribed from the IER emission inventory (Fig. 3b); hence the modeled anthropogenic XCO 2 is based on IER emission fluxes (see Fig. 5b and Sec. 2.1.1). Similar to the sections above, the EDGAR emission inventory is considered to be the "true" fluxes and the measurement vector ( ) which corresponds to CarbonSat simulated observations is based on the EDGAR emission inventory as described in sec.

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3.1. The retrieved posterior fluxes of this inversion optimization are compared with "true" fluxes to estimate the retrieved posterior flux errors and to assess how well inversion studies can benefit from CarbonSat measurements in the case of discrepancy between "true" and prior fluxes in terms of spatial patterns of distribution.
Similar to the above section, systematic errors of the retrieved fluxes are estimated specifically for each source of errors or combination of errors by defining scenarios S07 through S11 (see Table 1). It should be noted that the IER 10 and EDGAR fluxes are not entirely different in terms of temporal variations, though the magnitude of the emissions in the target region is notably different. However, there exists a dissimilarity of approximately 70% of the spatial patterns between these two inventories (based on the correlation of spatial variability between two inventories, R 2 ~ 0.30) in the target region.
For most of the overpasses, the random errors of the retrieved emission fluxes over the target region (single 15 overpass) are found to be less than 20% (approximately 10 MtCO 2 yr −1 ) of the emission fluxes for both swath widths (not shown). These values are comparable to those shown in Fig. 7, indicating the potential of CarbonSat simulated observations to retrieve surface fluxes, even when uncertainties in the spatial pattern of the prior emission fluxes are present. Figure 13 shows the SE of the retrieved emissions estimated for the scenario S08, where CarbonSat measurement errors are considered in addition to the uncertainty in the spatial pattern of the prior fluxes. For both 20 swath widths, the estimated SE for S08 is found to be less than 10 MtCO 2 yr −1 in many instances (for about 55 to 75% of useful overpasses). Systematic errors for other scenarios are summarized in Table 1. Depending on the error sources, the inversion experiment shows that the mean and standard deviation of SE, considering all "N" useful overpasses and the 500 km swath width, ranges from -0.12 to -9.0 MtCO 2 yr -1 and 14.6 to 19.2 MtCO 2 yr -1 respectively. Furthermore, the systematic errors of the retrieved emission fluxes for both swath widths are found to 25 be lower than the systematic error of the prior fluxes (estimated based on "true" fluxes) except for a very few cases, providing confidence in the inverse results although only a simple inverse optimization methodology is used.

Discussion and clean pixel method
In this section, we discuss the merits of instrument like CarbonSat for retrieving emission fluxes and its potential in disentangling anthropogenic and biogenic CO 2 fluxes over cities like Berlin. Caveats related to the simple inversion 30 approach used here are discussed.
For the study of CO 2 emissions, it is necessary to assess whether local anthropogenic XCO 2 enhancements are large enough to be detected by using the retrieved XCO 2 data products from the satellite-borne instrument, taking into account the measurement noise. Figure 14 presents an overview of "true" anthropogenic XCO 2 emission enhancements together with the associated CarbonSat retrieval uncertainty over the target region around Berlin for a 35 one year time period. The analysis shows that anthropogenic XCO 2 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. 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 modeling.

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In a real scenario the question arises whether it is possible to clearly separate local anthropogenic XCO 2 enhancements from CarbonSat's total column measurements, which are in addition influenced by biospheric sources or sinks. Moreover, in order to isolate the XCO 2 enhancement caused by local sources (such as city emissions), it is necessary to specify the "background" signal, representing the CO 2 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 5 anthropogenic sources, one can utilize additional tracers (e.g. CO, NO X ) and/or isotopic ratios (e.g. ∆ 14 C) as demonstrated by Newman et al. (2013). In the time frame of a potential CarbonSat mission, Sentinel-5 will be providing data on CO and tropospheric NO 2 (Ingmann et al., 2012), which when combined with CarbonSat data allows 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 10 differentiate different source-sink contributions.
In this study, we describe an approach to estimate the anthropogenic Berlin XCO 2 enhancements from measurements made by and data products retrieved from the proposed instrument CarbonSat. In this manner, we assess its capability to track the anthropogenic enhancements in our target region and thereby retrieve or infer emissions. As our target region around Berlin is mostly isolated from other urban sources, we use a simple "clean-

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pixel" method, similar to that used by Kort et al. (2013) to differentiate local anthropogenic XCO 2 from other background and biospheric surface fluxes. We have chosen boundary pixels of our target region in the upwind direction as "clean pixels", assuming that the observations from these pixels typically represent background XCO 2 values without any local influence. The WRF simulated wind direction in the lower atmosphere yields the upwind direction of the target region. Berlin XCO 2 enhancements are estimated by differentiating these plumes in the 20 simulated CarbonSat observations over the target region (see Fig. 14). As is shown, the temporal patterns of the estimated anthropogenic enhancement are in general consistent with those of the true anthropogenic enhancement. This approach is thus able to isolate anthropogenic XCO 2 enhancements with a mean bias (mean of the difference between estimated and "true" enhancements) of 0.12 ppm, a standard deviation of the difference σ d = 0.17 ppm, and a squared correlation coefficient R 2 = 0.92.

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One source of bias on the XCO 2 enhancement estimated by the clean-pixel method is when the dominant biogenic perturbations in the target region have different patterns than those of the chosen "clean" boundary region. Another possibility is the failure of the clean-pixel method to represent background XCO 2 concentration based on clean boundary pixels. The tagged tracer option in WRF-GHG allows us to investigate this further by utilizing the modeled biogenic and background CO 2 concentrations generated by WRF-GHG. We found that most of the 30 deviations in the estimated XCO 2 enhancement are caused by the background "noise", indicating that the XCO 2 from the "clean" boundary pixels do not always represent the background values in our case. Note that the abovementioned bias is not related to any CarbonSat measurement errors, but due to the simplicity of the approach adopted to estimate anthropogenic XCO 2 enhancements. We found negligible influence of biospheric fluxes in the target region, which can bias the XCO 2 enhancement estimated by the clean-pixel method (not shown).

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By assuming that the biospheric patterns are accurately modeled and that these biogenic signals can be subtracted from the measurement vector to isolate the anthropogenic contribution of XCO 2 , 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 set-up is not well suited for this purpose since we have not taken into account additional 40 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 Sec. 4.2.3).
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 set-up cannot provide posterior estimates for each pixel or emission sector within the target region. In other words, the flexibility to 45 capture the true spatial variation of fluxes is more limited in our simple inversion system than in pixel-or parameter-Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-960, 2016 Manuscript under review for journal Atmos. Chem. Phys.
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, 5 need to be taken into account when estimating the total flux uncertainty via inverse modeling.

Conclusion
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 CO 2 . A significant contribution by the CarbonSat greenhouse gas (GHG) observations will be the ability to retrieve the emissions of localized (moderate to strong CO 2 10 and CH 4 ) 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 wide swath. To demonstrate this, 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-centered target region investigated here: ~100 km × 100 km) from CarbonSat simulated observations.

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The study utilizes a Bayesian inversion approach based on the WRF-GHG modeling system at a high spatial resolution to optimize anthropogenic CO 2 emissions for the target region using CarbonSat simulated observations for a time period of one 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 XCO 2 measurement and modeling errors. The CarbonSat measurement errors are estimated using the error parameterization scheme of Buchwitz et al.

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(2013a), which takes into account different sources of uncertainties including scattering related errors. Based on the EDGAR emission inventory, the local anthropogenic XCO 2 enhancement over Berlin is found to be approximately 0.80 to 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 km 25 and 500 km). By performing a Bayesian inversion based on one year of CarbonSat simulated observations, we show that the random error of the retrieved Berlin CO 2 emissions is typically less than 15 to 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 to 10 MtCO 2 yr -1 .
In order to quantify the systematic error (SE) of the retrieved fluxes, we use different scenarios in terms of various 30 sources of systematic error in the inversion system. For scenario S01, we use CarbonSat's "default" XCO 2 systematic errors (retrieval biases) from Buchwitz et al. (2013a), and assume no biogenic XCO 2 modeling error. For S01, we find that SE is in the range of 3 to 6 MtCO 2 yr −1 for most of the cases (40 to 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 one-year period of CarbonSat simulated observations, we

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show that narrowing the swath width (from 500 km 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 XCO 2 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

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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 CO 2 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 "high resolution aerosol error" in this manuscript. The estimated emission uncertainty for this Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-960, 2016 Manuscript under review for journal Atmos. Chem. Phys.
Published: 17 February 2016 c Author(s) 2016. CC-BY 3.0 License. scenario (S04) is found to be higher than that of S01, with mean and standard deviation of approximately -6.4 and 4.2 MtCO 2 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 modeled very well. By further investigating the extreme case in which the biospheric contribution is assumed to 5 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 8.5 ± 10.8 MtCO 2 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 models' inability in 10 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 15 modeling 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 set-up 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 20 results from this experiment in which the modeled and true XCO 2 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 that of the prior fluxes (estimated based on 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

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MtCO 2 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 on 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 30 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 nonnegligible and should be properly addressed in the inverse modeling applications of satellite data.
Using the dense CarbonSat measurements in an inverse modeling framework at high resolution is expected to 35 improve the inference of CO 2 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. A preliminary analysis over the target region using the "clean-pixel" method as followed by Kort et al. (2013) provides encouraging results in isolating temporal patterns of local anthropogenic XCO 2 enhancement.
Overall, the present study demonstrates that an instrument like CarbonSat has high potential to provide important 40 information on city CO 2 emissions when exploiting the atmospheric XCO 2 observations using a high-resolution inverse modeling 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.