Towards space-borne monitoring of localized CO2 emissions: an instrument concept and first performance assessment

The UNFCCC (United Nations Framework Convention on Climate Change) requires the nations of the world to report their carbon dioxide (CO2) emissions. Independent verification of these reported emissions is a corner stone for advancing towards emission accounting and reduction measures agreed upon in the Paris agreement. In this paper, we present the concept and first performance assessment of a compact space-borne imaging spectrometer that could support the task of “monitoring, verification, reporting” (MVR) of CO2 emissions worldwide. With a single spectral window in the short-wave infrared spectral 5 region and a spatial resolution of 50× 50 m, the goal is to reliably estimate the CO2 emissions from localized sources down to a source strength of approx. 1 MtCO2 yr−1, hence complementing other planned CO2 monitoring missions, like the planned European Carbon Constellation (CO2M). Resolving CO2 plumes also from medium-sized power plants (1–10 MtCO2 yr−1) is of key importance for independent quantification of CO2 emissions from the coal-fired power plant sector. Through radiative transfer simulations, including a realistic instrument noise model and a global trial ensemble covering 10 various geophysical scenarios, it is shown that an instrument noise error of 1.1 ppm (1σ) can be achieved for the retrieval of the column-averaged dry-air mole fraction of CO2 (XCO2). Despite limited amount of information from a single spectral window and a relatively coarse spectral resolution, scattering by atmospheric aerosol and cirrus can be partly accounted for in the XCO2 retrieval, with deviations of at most 4.0 ppm from the true abundance for 68 % of the scenes in the global trial ensemble. 15 We further simulate the ability of the proposed instrument concept to observe CO2 plumes from single power plants in an urban area using high-resolution CO2 emission and surface albedo data for the city of Indianapolis. Given the preliminary instrument design and the corresponding instrument noise error, emission plumes from point sources with an emission rate down to the order of 0.3 MtCO2 yr−1 can be resolved, i.e. well below the target source strength of 1 MtCO2 yr−1. Hence, the proposed instrument concept could be able to resolve and quantify the CO2 plumes from localized point sources responsible 20 for approx. 90 % of the power plant CO2 emission budget, assuming global coverage through a fleet of sensors and favourable conditions with respect to illumination and particle scattering. 1 https://doi.org/10.5194/amt-2019-414 Preprint. Discussion started: 16 January 2020 c © Author(s) 2020. CC BY 4.0 License.


Introduction
Despite the broad consensus on the negative long-term effects of carbon dioxide (CO 2 ) emissions and the proclaimed efforts reducing these emissions, the atmospheric CO 2 concentrations continue to rise. During the course of 2018, the average CO 2 concentration increased from 407 to 410 ppm at the Mauna Loa observatory, representing the fourth-highest annual growth ever  (Wheeler and Ummel, 2008;Ummel, 2012), together with the corresponding To advance towards emission accounting and reduction measures, agreed upon in the Paris agreement in force since 2016, independent verification of reported emissions is of significant importance. To this end space-borne instruments provide a suitable platform where continuous long-term measurements can potentially be combined with a near-global coverage with no 5 geopolitical boundaries.
Most of the currently operating, planned and proposed instruments for passive CO 2 observations from space measure the reflected short-wave infrared (SWIR) solar radiation in several spectral windows covering the oxygen-A (O 2 A) band near 750 nm as well as the weak and strong CO 2 absorption bands near 1600 and 2000 nm, respectively, e.g. GOSAT (Greenhouse Gases Observing Satellite; Kuze et al., 2009Kuze et al., , 2016, OCO-2 (Orbiting Carbon Observatory-2; Crisp et al., 2004, TanSat 10 (Liu et al., 2018), GOSAT-2 (Nakajima et al., 2012), OCO-3 (Eldering et al., 2019), MicroCarb (Buil et al., 2011), GeoCarb (Moore III et al., 2018), CarbonSat (Bovensmann et al., 2010;Buchwitz et al., 2013) and G3E (Geostationary Emission Explorer for Europe; Butz et al., 2015). These instruments and instrument concepts further rely on a comparatively high spectral resolution on the order of approx. 0.05 − 0.3 nm representing resolving powers (ratio of wavelength over the full-width halfmaximum of the instrument spectral response function) ranging from approx. 3600 for the strong CO 2 absorption bands near 15 2000 nm for CarbonSat (Buchwitz et al., 2013) up to > 20 000 for the OCO and GOSAT instruments. Such advanced instruments, like for example GOSAT and OCO-2 that have been operating since 2009 and 2014, respectively, generally target an accuracy and coverage sufficient to study the natural CO 2 cycle on a regional to continental scale (e.g. Guerlet et al., 2013;Maksyutov et al., 2013;Parazoo et al., 2013;Eldering et al., 2017;Chatterjee et al., 2017;Liu et al., 2017), but have also been used to observe and quantify CO 2 gradients on the regional scale caused by anthropogenic CO 2 emissions in urban areas (Kort 20 et al., 2012;Hakkarainen et al., 2016;Schwandner et al., 2017;Reuter et al., 2019). OCO-2 data have further been used to observe strong CO 2 plumes from localized natural and anthropogenic CO 2 sources like volcanoes and coal-fired power plants (Nassar et al., 2017;Schwandner et al., 2017;Reuter et al., 2019), demonstrating the capabilities of imaging spectrometers to monitor CO 2 from space. The spatial resolution of OCO-2 and similar instruments like e.g. OCO-3, TanSat and the planned European CO 2 satellite constellation for CO 2 monitoring CO2M (on the order of approx. 2-4 km 2 ) does, however, pose a 25 difficulty for the routine monitoring of localized power plant CO 2 emissions, since the plume is usually only sampled by a handful of pixels, where CO 2 plume enhancements cannot be fully separated from the background, making quantitative CO 2 emission rate estimates difficult and vulnerable to cloud contamination and instrument noise propagating into CO 2 retrieval errors. For this reason CO2M will only address isolated large power plants ( 10 MtCO 2 yr −1 ) and large urban agglomerations ( Berlin) (Kuhlmann et al., 2019) and thus, a large fraction of the emission total will be missed.

30
To contribute to closing this gap and expanding on the future CO 2 monitoring from space, we here present the concept and a first performance assessment of a space-borne imaging spectrometer that could be deployed for the dedicated monitoring of localized CO 2 emissions. By targeting power plants with an annual emission rate down to approx. 1 MtCO 2 yr −1 , a substantial fraction (on the order of 90 %) of the CO 2 emissions from power plants and hence a significant part of the global manmade CO 2 emission budget in total could be observed (given a global coverage through a fleet of instruments). As shown 35 3 https://doi.org/10.5194/amt-2019-414 Preprint. Discussion started: 16 January 2020 c Author(s) 2020. CC BY 4.0 License.
in Fig. 1, it is of key importance to cover also the medium-sized power plants (1-10 MtCO 2 yr −1 ) as they alone contributed to approx. 64 % of the CO 2 emissions from power plants in 2009, according to the CARMA v3.0 data. To achieve this, the proposed instrument has an envisaged spatial resolution of 50×50 m 2 . With such a dense spatial sampling, averaging of plume enhancements and background concentration fields is avoided. This leads to an enhanced contrast compared to a coarser spatial resolution. To increase the number of collected photons and hence the signal-to-noise ratio (SNR) and relative precision of the 5 CO 2 concentration retrievals, such a high spatial resolution has to be compensated for with a rather coarse spectral resolution.
To further compensate for the limited spatial coverage of a single instrument, a comparatively compact and low-cost instrument design is an important aspect, as it would allow for a fleet of instruments to be deployed, increasing the spatial coverage. Wilzewski et al. (2019) recently demonstrated that atmospheric CO 2 concentrations can be retrieved with an accuracy < 1 % using such a comparatively simple spectral set-up with one single spectral window and a relatively coarse spectral resolution of 10 approx. 1.3-1.4 nm (resolving power of 1400-1600). Thompson et al. (2016) demonstrated the ability to resolve and quantify methane (CH 4 ) plumes, posing a similar remote sensing challenge as CO 2 , using data from the space-borne Hyperion imaging spectrometer, with a spectral and spatial resolution of 10 nm (resolving power around 230) and 30 m, respectively. Observation of emission plumes, from plume detection to enhancement quantification and flux estimation, using imaging spectroscopy with a single narrow spectral window and a spectral resolution as coarse as 5 to 10 nm (resolving power around 200-500) 15 has further been repeatedly demonstrated using airborne imaging spectroscopy data for both CO 2 (Dennison et al., 2013;Thorpe et al., 2017) and CH 4 (Thorpe et al., 2014; Thompson et al., 2015;Thorpe et al., 2016Thorpe et al., , 2017Jongaramrungruang et al., 2019). For an airborne instrument primarily dedicated to the quantitative imaging of CH 4 , but also CO 2 plumes, Thorpe Canadian company GHGSat Inc. was launched in 2016 as a demonstrator for a satellite constellation concept targeting the detection of CH 4 plumes from individual point sources within selected approx. 10 × 10 km 2 target regions at a spectral and spatial resolution of 0.1 nm (resolving power around 16 000) and 50 m, respectively (Varon et al., 2018). Varon et al. (2019) recently showed how anomalously large CH 4 point sources can be discovered with GHGSat-D observations.
Given the results from previous studies and the technology at hand, we are confident that the proposed instrument concept 25 presented here could be realised and that it would be an important complement to the fleet of current and planned space-borne CO 2 instruments, allowing for the routine quantitative monitoring of CO 2 emissions from large and medium-sized power plants and the estimation of corresponding CO 2 emission rates. The proposed instrument concept would also serve as a good complement and companion to CO2M, by targeting also medium-sized power plants and providing high-resolution images with finer CO 2 plume structures. The added value of such an instrument would be of interest, both in terms of advancing science 30 as well as in providing independent emission estimates that could be used to verify reported CO 2 emission rates at facility level and inform policy makers on the progress of reducing man-made CO 2 emissions. The proposed instrument concept is described in Sect. 2, followed by a description of the instrument noise model in Sect. 3. A global performance assessment addressing instrument noise and the errors introduced by atmospheric aerosol is presented in Sect. 4. The ability to monitor  Offner-type spectrometer.
single CO 2 emission plumes at urban scale is further simulated in Sect. 5. A short summary and our concluding remarks are finally presented in Sect. 6.

Mission and instrument concept
The instrument concept presented in this paper is based on a space-borne push-broom imaging grating spectrometer, measuring spectra of reflected solar radiation in one single SWIR spectral window, from which the column-averaged dry-air mole fraction 5 of CO 2 (XCO 2 ) can be retrieved. With an expected instrument mass of approx. 90 kg, it is suitable for the deployment on small satellite buses. Since the proposed instrument is targeting the quantification of localized CO 2 emissions from e.g. coal-fired power plants, a high spatial resolution of 50 × 50 m 2 is envisaged. The instrument is designed to fly in a sun-synchronous orbit at an altitude of 600 km and a local equatorial crossing time at 13:00.
The preliminary optical design assumes a 15 cm aperture and is based on a Three-Mirror-Anastigmat (TMA) telescope, 10 combined with an Offner-type spectrometer, as shown in Fig. 2. The optic system relies on metal-based mirrors and is designed as an athermal configuration for a wide temperature range onboard the satellite. The three mirrors of the TMA are standard aspheres aligned on a single optical axis. The efficiency of the optical bench (throughput), including e.g. transmittance and grating efficiency, is estimated to 0.48 and the f-number (f num ), equal to the ratio of focal length to aperture diameter, amounts to 2.4. The dispersed electromagnetic radiation is then focused onto a two-dimensional array detector that captures the spatial In order to reach a sufficient signal-to-noise ratio (SNR), the proposed spatial resolution only allows for a relatively coarse spectral resolution. Wilzewski et al. (2019) used spectrally degraded GOSAT soundings to demonstrate the capability of retrieving XCO 2 from a single spectral window at such a coarse spectral resolution using a spectral set-up (in terms of spectral range, resolution and oversampling ratio) compact enough to fit onto 256 detector pixels. They evaluate two alternative spectral set-ups covering the spectral ranges 1559-1672 nm (hereafter also referred to as SWIR-1) and 1982-2082 nm (hereafter also 5 referred to as SWIR-2), each with a spectral resolution (full-width half-maximum (FWHM) of the instrument spectral response function) of 1.37 nm and 1.29 nm, respectively and an oversampling ratio of three. The resolving power of the SWIR-1 and and SWIR-2 set-ups amounts to approx. 1200 and 1600, respectively. For optics design reasons, we use a spectral oversampling ratio of 2.5 in this study, resulting in a spectral sampling distance of approx. 0.55 and 0.52 nm for SWIR-1 and SWIR-2, respectively. Simulated synthetic measurements of spectral radiances for the two prospective spectral set-ups are shown in 10 Fig. 3, assuming a Gaussian instrument response function with FWHM of 1.37 nm and 1.29 nm, respectively, as proposed by Wilzewski et al. (2019). The SWIR-1 window (Fig. 3a) exhibits two weak CO 2 absorption bands around 1568-1585 nm and 1598-1615 nm and has the advantage of a stronger top-of-atmosphere (TOA) signal due to higher solar irradiance and surface albedo at these wavelengths. It also allows for the simultaneous retrieval of CH 4 using the CH 4 absorption band near 1666 nm. The SWIR-2 window, on the other hand, exhibits two stronger CO 2 absorption bands around 1995-2035 nm and 15 2045-2080 nm and has higher sensitivity to atmospheric aerosol that can potentially be exploited during the XCO 2 retrieval  (2019) showed similar performance for SWIR-1 and SWIR-2, respectively, but suspect SWIR-2 to be the favourable spectral set-up given the stronger CO 2 absorption bands, the ability to account for particle scattering and the lower radiance SNR required to reach sufficiently small XCO 2 noise errors. In this paper, we further investigate the performance of the two spectral set-ups in order to finally conclude on the more suitable one given the preliminary instrument design and realistic instrument SNR assumed here.

5
The instrument is designed to have a radiance SNR of 100 at the continuum for a reference scene with a Lambertian surface albedo of 0.1 and solar zenith angle (SZA) of 70 • . Given the altitude of 600 km and the corresponding orbital velocity of 7562 m s −1 , the instrument traverses along one 50 m ground pixel in approx. 7.2 ms. The amount of photons collected over the course of 7.2 ms is, however, not enough to reach a SNR of 100. To increase the SNR, we suggest to increase the integration time to 70 ms. This would normally lead to elongated ground pixels (approx. 50 × 500 m 2 ), but by using forward motion 10 compensation (FMC), the instrument can be periodically altered in the along-track direction, such that each ground pixel is sampled for a time period longer than the actual satellite overpass time (see e.g. Sandau, 2010;Abdollahi et al., 2014). FMC has the evident drawback that the coverage along the satellite track is discontinuous, since no data are sampled when the instrument returns to the starting forward position. A second disadvantage is the geometrical distortion of the ground pixels, that increases with the maximum off-nadir angle. The baseline design assumes 1000 measurements to be made in the along-track dimension https://doi.org/10.5194/amt-2019-414 Preprint. Discussion started: 16 January 2020 c Author(s) 2020. CC BY 4.0 License.
for each FMC repetition, leading to off-nadir angles up to approx. 20 • . Further assuming a 1000 detector pixels in the spatial dimension would consequently result in observed tiles on the order of 50 × 50 km 2 . Table 1 summarizes the preliminary mission concept and instrument design parameters assumed for this study. It should be clear that this is a preliminary baseline design used to demonstrate the CO 2 monitoring abilities and added value of the proposed instrument concept. Alternative instrument designs will be further investigated and the exact instrument design will 5 most likely be subject to change before the instrument would be realized. The continuum SNR for our reference scene should, nevertheless, remain at roughly 100, ensuring a similar performance as presented in this paper.

Instrument noise model
To assess the performance of the proposed instrument concept w.r.t. retrieving XCO 2 and monitoring localized CO 2 emissions, the expected instrument noise levels that accompany the measurements have to be quantified. To this end a numerical instrument 10 noise model that calculates the instrument's SNR is developed, following a similar approach as e.g. Bovensmann et al. (2010) and Butz et al. (2015). The SNR is given by where S is the signal, i.e. the number of photons emerging from a 50×50 m 2 ground pixel that generate a charge in the detector and σ tot is the corresponding instrument noise. The signal S is calculated as where L λ is the simulated reflected solar spectral radiance at the telescope, A det the detector pixel area, f num the instrument's f-number, η the efficiency of the optical bench, Q e the detector's quantum efficiency, ∆λ the wavelength range covered by a single detector pixel and t int the integration time between the detector pixel read-outs. Following the thin lens equation (for large distances between lens and object) and the magnification formula, the term π·Adet 4·f 2 num can also be expressed as A ap · Ω, where 20 A ap is the area of the aperture and Ω the instrument's solid angle i.e. the squared ratio of the ground sampling distance (50 m) over the orbit altitude (600 km). Apart from L λ that is calculated for each scene using a forward radiative transfer model, all quantities in Eq. 2 and their corresponding values were introduced in Sect. 2.
The total noise σ tot in Eq. 1 accounts for the noise contribution from five separate instrument noise sources 25 where σ ss = √ S is the signal shot noise, σ bg is the noise due to thermal background radiation incident on the detector, σ dc is the noise due to dark current in the detector, σ ro is the noise upon detector read-out and σ qz the quantization noise that arises when the analog signal is digitized. The thermal background signal per detector pixel is approximated as where E BB is the thermal black-body irradiance incident on the detector. E BB is determined by integrating the black-body spectral radiance L λ,BB (T bg ) emitted by the background over the detector's cut-off wavelengths λ 1 and λ 2 and hemispheric opening angle For this study, detector cut-off wavelengths of 900 and 2500 nm are assumed and the background temperature T bg is estimated 5 to 200 K. The thermal background noise is then calculated as σ bg = S bg . Similarly, the dark current noise is given by σ dc = √ S dc , where S dc = I dc · t int · Q is the per-pixel detector signal due to dark current. While Q = 6.242 · 10 18 electrons Coulomb −1 is constant, the dark current I dc strongly depends on the detector's operating temperature and is estimated to 1.6 fA pix −1 s −1 (assuming 150 K detector temperature), yielding a dark current signal of approx. 10 000 electrons (e − ) per detector pixel and second. Finally, the read-out noise (σ ro ) and quantization noise (σ qz ) are estimated to 100 and 40 e − , respectively. These noise 10 levels are preliminary estimates used to test and evaluate the instrument concept, but are comparable to those of state-of-the-art detectors for space applications. Figure 4a shows the continuum SNR (calculated with Eqs. (1)- (5)) as a function of the scene brightness for the two prospective spectral set-ups SWIR-1 and SWIR-2. The scene brightness describes the conversion from incident solar irradiance to reflected solar radiance and is calculated as the product of the surface albedo and the cosine of the SZA, divided by π, hence 15 assuming a Lambertian surface. Furthermore, Fig. 4b visualizes the individual contributions from the different noise sources for the SWIR-2 set-up. Since the instrument design is assumed to be similar, independent of whether the SWIR-1 or SWIR-2 set-up is finally used, the SNR is consistently higher for SWIR-1 compared to SWIR-2, as a result of the higher surface albedo at these wavelengths. For the reference scene (albedo = 0.1, SZA = 70 • ), the continuum SNR is approx. 180 and 100 for SWIR-1 and SWIR-2, respectively. When looking at the contributions from the different instrument noise sources, it is clear that the readout noise and signal shot noise are the major contributors, whereas the noise arising from quantization errors, dark current and thermal background radiation has a small or even negligible contribution in comparison. The signal shot noise is, however, smaller than the dark current, read-out noise and quantization noise inside the CO 2 absorption bands, where the signal, and hence the signal shot noise, decreases. Note that all noise terms, except for the signal shot noise σ ss , are constant.

4 Generic performance evaluation
In this section we conduct a first performance evaluation of the proposed instrument concept by assessing the XCO 2 retrieval errors expected on a global scale. Such errors arise due to instrument noise and because of inadequate knowledge about the light path through the atmosphere due to scattering aerosol and cirrus particles. For this purpose we use a global trial ensemble with a large collection of geophysical scenarios with varying atmospheric gas concentrations, meteorological conditions, surface 10 albedo, SZA as well as aerosol and cirrus compositions, that can be expected to be observed by a polar orbiting instrument. The same methodology and dataset have been used in several previous studies to assess the greenhouse gas retrieval performance of different satellite instruments (Butz et al., 2009(Butz et al., , 2012(Butz et al., , 2015.
The global trial ensemble contains geophysical data representative for the months of January, April, July and October. Imaging Spectroradiometer) MCD43A4 product (Schaaf et al., 2002). Aerosol optical properties are calculated (assuming Mie scattering) for an aerosol size distribution, superimposed from seven log-normal size distributions and five chemical types at 19 vertical layers, as provided by the ECHAM5-HAM model (Stier et al., 2005). Cirrus optical properties are calculated for 20 randomly orientated hexagonal columns and plates following the ray tracing model of Hess and Wiegner (1994) and Hess et al. (1998). In total the global trial ensemble consists of approx. 10 000 scenes with XCO 2 ranging from 340 to 400 ppm with an average of 382 ppm, albedo ranging from 0 to 0.7 with an average of 0.13 (SWIR-2 window), aerosol optical thickness (AOT) ranging from 0 to 1.1 with an average of 0.18 (SWIR-2 window) and cirrus optical thickness (COT) ranging from 0 to 0.8 with an average of 0.13 (SWIR-2 window). Thus, the global trial ensemble contains challenging scenes with scattering loads that 25 would be filtered out by current satellite retrievals, such as those applied to OCO-2 and GOSAT data which typically screen scenes with scattering optical thickness greater than 0.3 (at the O 2 A band around 760 nm). All data in the global trial ensemble are re-gridded to a spatial resolution of approx. 2.8 • × 2.8 • . This is, of course, much coarser than the envisaged 50 × 50 m 2 , but for investigating the propagation of instrument noise into the target quantity XCO 2 on a global scale, this dataset serves its purpose. See previous studies (e.g. Butz et al., 2009Butz et al., , 2010 for further details on the content of the global trial ensemble.

30
The geophysical data for each scene are fed to our radiative transfer software RemoTeC (Butz et al., 2011;Schepers et al., 2014) in order to simulate corresponding synthetic measurements. The measurement noise is calculated by propagating the 2000). Simulations are conducted globally for the 16th day of each of the four months January, April, July and October, hence covering SZA conditions ranging from 0 to 86 degrees.
By retrieving XCO 2 from the simulated synthetic spectra, the range of XCO 2 retrieval errors that can be expected with the proposed instrument concept can be estimated, as can the ability to account for atmospheric aerosol. The RemoTeC retrieval algorithm (e.g. Butz et al., 2011) is based on a Philipps-Tikhonov regularization scheme (Phillips, 1962;Tikhonov, 1963) 5 that uses the first-order difference operator as a side-constraint to retrieve the CO 2 partial column profiles, from which XCO 2 can be determined. Additional retrieval parameters are the total column concentrations of H 2 O and CH 4 (only for SWIR-1), surface albedo (as second-order polynomial), spectral shift, solar shift and, possibly, information on scattering aerosol. Here we assume knowledge about the airmass (needed to calculate XCO 2 ), in reality meteorological and topography data would be required to estimate the airmass.

Instrument noise induced XCO 2 errors
In a first step, we assess XCO 2 retrieval errors that are induced by instrument noise. To this end, for now, we neglect scattering by aerosol and cirrus. These so-called non-scattering simulations assume no scattering particles to be present in the atmosphere and simply compute the transmittance along the geometric light path (Rayleigh scattering is included). Figure 5a shows the cumulative distribution of the random XCO 2 noise error, i.e. the instrument noise propagated into 15 scene as a function of the corresponding scene brightness. The noise errors are significantly smaller for the SWIR-2 set-up (blue) when using the proposed integration time t int of 70 ms. The dashed lines in Fig. 5b show that on average 68 % and 95 % (1σ and 2σ respectively) of the retrievals have noise errors of less than 1.1 and 2.0 ppm, respectively. For the SWIR-1 set-up (green), the corresponding numbers are 2.9 and 5.0 ppm. For the SWIR-2 set-up it is only retrievals over scenes that are darker than our reference scene (albedo = 0.1, SZA = 70 • ) that are expected to have instrument noise induced errors larger 5 than approx. 2 ppm. For comparison, and as a reference, we also investigate how much the integration time has to be increased for the SWIR-1 set-up, in order to reach a SNR sufficient to yield XCO 2 noise errors comparable to those obtained with the SWIR-2 set-up. We find that with the preliminary instrument design assumed here, the integration time has to be increased to at least 350 ms (i.e. by a factor five) for SWIR-1 (grey) in order to reach a similar performance.
Despite the advantage of being able to retrieve XCH 4 alongside XCO 2 using the SWIR-1 set-up, the much longer integration 10 time required to reach sufficiently low CO 2 noise errors is not feasible for the purpose of the proposed instrument concept.
Hence, we conclude that the SWIR-2 set-up is superior for the passive satellite based CO 2 monitoring instrument proposed in this paper. Consequently, the remainder of this paper is limited to the SWIR-2 set-up, covering the spectral range 1982-2092 nm with a spectral resolution (FWHM) 1.29, resolving power around 1600 and a spectral sampling distance of 0.52 nm.

15
Atmospheric aerosol and cirrus particles modify the light path of the reflected solar radiation to a certain degree, depending on the particle abundance, optical properties, height and surface albedo. Consequently, this can cause large errors in the retrieved XCO 2 if the effect of CO 2 absorption and particle scattering on the measured reflected solar radiation cannot be adequately separated during the retrieval process. In this section the ability to account for atmospheric aerosol and cirrus during the retrieval is investigated by including scattering by atmospheric particles in the simulation of the synthetic measurements as 20 well as in the corresponding XCO 2 retrievals. This is done by using a more complex forward model and representation of the aerosol and cirrus particles when simulating the spectra, and a comparatively simple representation and forward model for the corresponding retrievals. More precisely, the full physical representation of vertical profiles of hexagonal cirrus particles and spherical aerosol particles of the five chemical types characterized by the seven log-normal size distributions with known micro-physical properties for each aerosol and cirrus particle type is used when simulating the synthetic measurement for 25 each scene in the global trial ensemble. On the contrary, only three aerosol parameters are fitted during the corresponding retrieval: the total column number density, the size parameter of a single mode power-law size distribution and the center height of a Gaussian height distribution. Such differences in the aerosol/cirrus representation lead to forward model errors that, alongside the instrument noise induced errors, propagate into the retrieved quantity XCO 2 . Previous studies have shown that this approach gives a good approximation of how well a satellite sensor can account for scattering by atmospheric aerosol 30 while retrieving target gas concentrations (e.g. Butz et al., 2009Butz et al., , 2010. Figure 6a shows the difference between the XCO 2 retrieved ("retr") from the synthetic measurements and the corresponding "true" XCO 2 used as input to simulate these synthetic measurements. This deviation from the truth, contains information on both random instrument noise error (Sect. 4.1) and systematic errors arising from insufficient modelling of the aerosol and cirrus properties. For comparison, Fig. 6b shows the corresponding results achieved when using a non-scattering retrieval, i.e. where the scattering by atmospheric aerosol and cirrus, now present in the atmosphere and the simulated synthetic spectra, is neglected (similar to Sect. 4.1). The retrieval errors are strongly reduced when the RemoTeC retrieval algorithm accounts for the scattering by atmospheric aerosol. When scattering is considered, 50 %, 68 % and 95 % of the XCO 2 retrievals deviate from the true abundance by less than 2.5, 4.0 and 11 ppm, respectively, with a mean bias of -2.0 ppm and no clear error-correlation 5 with the optical thickness of the scattering particles. For the non-scattering retrieval, the corresponding numbers are 16, 29 and 78 ppm, with a mean bias of -25 ppm that increases with optical thickness, exposing the necessity of accounting for atmospheric aerosol and cirrus when retrieving the XCO 2 .
Scattering particles can modify the light path and hence the XCO 2 retrieval in primarily two ways. Firstly, an elevated layer of aerosol or cirrus will scatter parts of the incoming solar radiation towards the observing sensor at a higher altitude compared 10 to the Earth's surface, leading to a reduced light path. Secondly, aerosol and cirrus will extend the light path to some degree as a result of multiple scattering between scattering particles and the surface. Such modifications of the light path will be understood 13 https://doi.org/10.5194/amt-2019-414 Preprint. Discussion started: 16 January 2020 c Author(s) 2020. CC BY 4.0 License. as either too low (overall reduced light path) or too high (overall extended light path) CO 2 concentrations in the atmosphere if scattering cannot be accounted for in the retrieval. Which effect that is dominating, is primarily driven by the surface albedo. This is visualized in Fig. 6d that shows the difference between retrieved and true XCO 2 as a function of the surface albedo when scattering by aerosol and cirrus is neglected in the retrieval. Over darker surfaces, where the effect of multiple-scattering between aerosol and surface is limited, aerosol and cirrus particles scattering the incoming solar radiation towards the sensor 5 higher up in the atmosphere becomes the dominating effect, leading to a reduced light path and underestimation of the XCO 2 .
Over brighter surfaces, where the effect of multiple scattering becomes dominant, the non-scattering retrieval is more likely to overestimate the CO 2 abundance, because the loss of radiation due to an extended light path, resulting from the multiple scattering, is assumed to be caused by more absorbing CO 2 molecules in the atmosphere. Fig. 6c shows the difference between retrieved and true XCO 2 as a function of the surface albedo when scattering by aerosol and cirrus is accounted for when 10 retrieving XCO 2 from the synthetic measurements of the proposed satellite concept. It clear that when aerosol properties are retrieved alongside the CO 2 abundance, the curve-shaped relationship between the XCO 2 error and surface albedo vanishes with no clear error-correlation other than that XCO 2 errors increase with decreasing albedo (and thus SNR).

Performance evaluation for an urban case study
While the previous section assessed XCO 2 errors for the range of geophysical conditions to be encountered over the globe, this 15 section evaluates the CO 2 monitoring capabilities at urban scale using high-resolution CO 2 concentration and surface albedo data. Similar to Sect. 4, the high-resolution data are used to simulate synthetic measurements, from which synthetic XCO 2 abundances can be retrieved in order to make a first assessment of the CO 2 monitoring ability of the proposed instrument concept. The Hestia CO 2 emission data are used as input to a Gaussian dispersion model in order to compute a three-dimensional CO 2 concentration field. For a given CO 2 emission rate Q (in g s −1 ), the CO 2 concentration C (in g m −3 ) at a given position (x, y, z) downwind of the emitter is calculated as

Datasets
where u is the horizontal wind speed in the x-direction (along-wind), h is the height of the emitting source (in m above ground level) and σ y and σ z are the standard deviations of the concentration distribution (in m) in the horizontal across-wind and vertical dimension, respectively. σ y and σ z , and hence the spread of the emission plume, depend on the atmospheric instability i.e. the degree of atmospheric turbulence as well as the downwind distance x from the emitting source. Here, we calculate 10 σ y and σ z assuming the Pasquill-Gifford stability class C (slightly unstable atmosphere). Furthermore, a constant wind speed u = 3 m s −2 and an emitting source height h = 75 m (for all sources) are assumed. This model set-up is comparable to similar studies (e.g. Bovensmann et al., 2010;Dennison et al., 2013).
Downwind CO 2 concentrations from each emitting source (pixel) in the Hestia dataset are calculated across an equidistant grid at 50 m resolution in all dimensions and the contributions from all individual emitting sources (pixels) are subsequently combined to form a three-dimensional CO 2 concentration field over Indianapolis. Figure 7b shows the resulting (vertically integrated) two-dimensional field of (noise-less) XCO 2 enhancements at 50 × 50 m 2 spatial resolution over a constant background with a surface pressure of 1013 hPa. While weaker diffuse sources like streets cannot be identified, the plumes from stronger point sources are clearly pronounced given the high spatial resolution that allows for a detailed mapping of the plumes.
For comparison, Fig. 7c shows the corresponding XCO 2 enhancements assuming a coarser spatial resolution of 2 × 2 km 2 . Al-5 though the stronger plumes can still be identified at the coarser resolution, the XCO 2 enhancements are significantly lower and each plume is only sampled by a few pixels. Figure 7d further shows these XCO 2 enhancements in more detail for three along- enhancements reaching approx. 18, 6 and 3 ppm, respectively. This clearly demonstrates the benefit of an instrument with a high spatial resolution when resolving CO 2 emission plumes from space.

Surface albedo data from Sentinel-2 15
To accurately simulate the instrument SNR and hence the measurement noise, it is important to know how large a fraction of the solar radiation incident on the Earth's surface is reflected back towards space. To get realistic estimates of the surface albedo within the Hestia Indianapolis domain, data from the European Sentinel-2 satellite are used. The multi-spectral instrument aboard Sentinel-2 measures the TOA radiance in 13 spectral bands with a spatial resolution ranging from 10 × 10 m 2 to 60 × 60 m 2 . For this study, we use the Sentinel-2 L1C radiances measured in the spectral band 12 (centred at approx. 2200 nm) 20 at a spatial resolution of 20 × 20 m 2 . The software Sen2Core (ESA, 2018) is employed to compute corresponding L2 surface reflectances from the L1C TOA radiances, through a so-called atmospheric correction.
Surface reflectance data for the month of July 2018 are computed and re-gridded (using nearest neighbour) to the envisaged spatial resolution of 50×50 m 2 . The surface reflectance for Sentinel-2 pixels classified as vegetation are scaled by a factor 0.82 in order to account for the generally lower reflectance by vegetation in the SWIR-2 window compared to Sentinel-2's band 12. 25 The scaling factor has been derived using spectral reflectance data from the ECOSTRESS spectral library (Baldridge et al., 2009;Meerdink et al.). Figure 8b shows the gridded surface reflectance data for Indianapolis together with a corresponding RGB composite (Fig. 8a), using the Sentinel-2 data from the bands centred at red, green and blue wavelengths, as reference.
The scaled and gridded Sentinel-2 surface reflectance data are taken as representative for the Lambertian surface albedo within the SWIR-2 window.

Background data from CarbonTracker
Background data, including vertical profiles of CO 2 , H 2 O, temperature and pressure, are taken for the 15th of July 2016 from the CarbonTracker CT2017 dataset (Peters et al., 2007, with updates documented at http://carbontracker.noaa.gov). The CarbonTracker CT2017 data over Indianapolis are provided at a spatial resolution of 1 • × 1 • , meaning that the entire Hestia Indianapolis domain is covered by one single CarbonTracker pixel leading to a constant background data field. 5

Simulated CO 2 plume observations
As in Sect. 4, the above sets of input data are used to simulate synthetic measurements (spectral radiances) and corresponding instrument noise of the proposed instrument concept using the forward model and the instrument noise model (Sect. 3). The SZA is calculated for the given coordinates in the Hestia domain assuming the sun-synchronous orbit described in Sect. 2 and an observation date of July 15, 2018, which translate to a SZA of about 18 • . Corresponding XCO 2 abundances are then 10 retrieved from the simulated spectral radiances, such that the ability to observe the CO 2 emission plumes from the Hestia Indianapolis data can be evaluated. In this first assessment we focus solely on the instrument performance in terms of its CO 2 plume quantification capabilities and hence we perform the high-resolution simulations with the expected instrument noise induced errors only, i.e. by assuming a non-scattering atmosphere. Figure 9a shows the retrieved field of XCO 2 enhancements w.r.t. the retrieved background XCO 2 over the Hestia domain. 15 The CO 2 plume from the strongest point source, E 1 , with an annual CO 2 emission rate of Q 1 = 3.24 MtCO 2 yr −1 , is clearly resolved with local XCO 2 enhancements well above 100 ppm close to the emitting source. Although they emit considerably  (Fig. 7b). Dark scenes with albedo < 0.05 have been filtered out due to unreliable XCO2 retrievals. less CO 2 , the plumes from the second and third strongest point sources, E 2 and E 3 , with annual CO 2 emission rates of Q 2 = 0.55 MtCO 2 yr −1 and Q 3 = 0.48 MtCO 2 yr −1 , respectively, can be clearly separated from the background as well. The plume from the fourth strongest point source, E 4 , with an annual CO 2 emission rate of Q 4 = 0.32 MtCO 2 yr −1 can also be observed, but is partly obscured by filtered out dark surface areas, where retrieval errors are too high. Plumes from weaker point sources ( 0.1 MtCO 2 yr −1 ) and other sources like e.g. streets and highways cannot be identified given the spatial resolution 5 and instrument noise errors of the proposed instrument.
One concern with high-resolution CO 2 remote sensing is the impact of the albedo heterogeneity at urban scale at such a high spatial resolution. For the non-scattering scenario simulated here, the second-order polynomial albedo fitted by the retrieval algorithm matches the reference input albedo with an average (absolute) deviation of 0.14 %, and there is consequently no spatial variability in the accuracy of the albedo retrieval that in turn affect the XCO 2 retrieval accuracy. There is, however, the 10 evident effect that a higher albedo leads to a higher SNR and hence a generally lower noise error. This is evident from Fig. 9b showing the difference between the retrieved and true XCO 2 , thus illustrating an instantaneous noise error field that would be expected for a single satellite overpass. Generally, the deviations from the true XCO 2 are smaller over areas of brighter surfaces like concrete, whereas the deviations are larger over dark surfaces like forests (see also Fig. 8). The effect of albedo heterogeneity in combination with scattering particles is not addressed in this paper and will have to be analysed in future 15 studies.
Across the entire Hestia domain (but excluding dark scenes with albedo < 0.05) 68 % and 95 % of the XCO 2 retrievals deviate from the true XCO 2 by less than 1.1 and 2.3 ppm, respectively. This is slightly lower than the noise error obtained for the global trial ensemble in Sect   The plume of the strongest emitter E 1 in Indianapolis with an annual emission rate of Q 1 = 3.24 MtCO 2 yr −1 (Fig. 10, left panels) is clearly resolved. Within the area 200-2200 m downwind of the emitting source (blue square), maximum enhancements exceed 25 ppm, and in total, approx. 200 (60) pixels have enhancements above 4 (8) ppm, representing enhancements of approx. 1 (2) % w.r.t. the background. The average along-track XCO 2 enhancement 200-2200 m downwind of the emitting source (blue/white line) reaches 12 ppm. The plumes from the second and third strongest emitters E 2 and E 3 , approx. six times 10 weaker than E 1 , with annual emission rates of Q 2 = 0.55 and Q 3 = 0.48 MtCO 2 yr −1 , respectively (Fig. 10, center panels) has considerably lower XCO 2 enhancements, but can nevertheless be clearly separated from the background with distinct increments in both per-pixel and average XCO 2 enhancements within the area 200-2200 m downwind of the emitters (blue squares). While the background fields varies from approx. -1 to 1 ppm due to instrument noise, the per-pixel plume enhancements vary from approx. 0.5 to 3 ppm, with single enhancements exceeding 4 ppm close to the emitting source. The average along-track XCO 2 enhancements 200-2200 m downwind of the emitting sources (blue/white lines) reach 1.9 and 1.5 ppm for 5 E 2 and E 3 , respectively. Despite being partly obscured by filtered out dark surfaces (water), also the plume from the fourth strongest emitter E 4 , with an annual emission rate of Q 4 = 0.32 MtCO 2 yr −1 (Fig. 10, right panels) can be separated from the background, both when looking at the two-dimensional field and the per-pixel enhancements within the area 200-2200 m downwind of the emitter. With maximum average XCO 2 enhancements of at most approx. 1.3 ppm, the proposed instrument concept is, however, approaching the limit of what it could achieve in terms of CO 2 plume observation under favourable 10 conditions, i.e. where the effect of aerosol induced errors are neglected and the SZA is relatively low. A second peak in the average along-track XCO 2 enhancements is observed approx. 850 m above (north of) the fourth strongest emitter E 4 . This enhancement stems from the CO 2 plume from the seventh strongest emitter in Indianapolis (labelled as E 7 in the top-right panel of Fig. 10) with an annual emission rate of Q 7 = 0.1 MtCO 2 yr −1 . Quantifying the CO 2 emission rate from such a weak source is, however, not realistic given the low sampling density (especially further downwind) in combination with the weak 15 per-pixel enhancements.

Conclusions
To follow the progress on reducing anthropogenic CO 2 emissions worldwide, independent monitoring systems are of key importance. In this paper, we show how a proposed concept of an imaging spectrometer, to be employed on a space-borne platform, can be used to map CO 2 emission plumes from localized point sources at a spatial resolution of 50 × 50 m 2 for target 20 tiles on the order to 50 × 50 km 2 and, hence, contribute to the independent large-scale verification of reported CO 2 emission rates at facility level.
Through radiative transfer simulations using a global trial ensemble, a preliminary, yet realistic, instrument design and an instrument noise model, we show that the expected instrument noise induced XCO 2 errors are smaller than 1.1 and 2.0 ppm for 68 % and 95 % of the retrievals, respectively, using the SWIR-2 spectral set-up covering the CO 2 absorption bands near 25 2000 nm. For the SWIR-1 spectral set-up, covering the weaker CO 2 absorption bands near 1600 nm, the instrument noise induced XCO 2 errors are significantly higher, making it inadequate for the proposed instrument concept. Although the main focus in this paper is on the performance of the proposed CO 2 monitoring instrument concept, we could also show that despite the usage of a single spectral window and a relatively coarse spectral resolution of 1.29 nm, scattering by highly complex atmospheric aerosol compositions can be partly accounted for during the XCO 2 retrieval on the global scale, limiting the 30 deviation from the true XCO 2 to at most 4.0 ppm for 68 % of the retrievals. This gives us confidence that accurate twodimensional fields of XCO 2 enhancements could be retrieved from real spectra measured by the proposed instrument concept. https://doi.org/10.5194/amt-2019-414 Preprint. Discussion started: 16 January 2020 c Author(s) 2020. CC BY 4.0 License.
A reasonable a-priori state vector w.r.t. the aerosol properties (e.g. provided through models or a companion aerosol instrument (Hasekamp et al., 2019)) would, however, still be important.
Using high-resolution CO 2 emission data for the city of Indianapolis together with a Gaussian dispersion model, corresponding high-resolution albedo data and additional radiative transfer simulations, we have clearly demonstrated that the instrument is well suited for the task of space-borne CO 2 monitoring of large and medium-sized power plants and can (only limited by its 5 own instrument noise) resolve and quantify emission plumes from point sources with an emission source strength down to the order of 0.3 MtCO 2 yr −1 . This is well below the target emission source strength of 1 MtCO 2 yr −1 , hence leaving some margin for additional error sources (not yet addressed here) and lower instrument SNR.
The high spatial resolution implies limitations in terms of spatial coverage, arising from the narrow swath (50 km assuming 1000 detector pixels in the spatial dimension) and the forward motion compensation. Hence, a single instrument of the proposed 10 concept could not map CO 2 concentrations at local to regional scale with dense global coverage, but would have to be restricted to some pre-defined targets, where independent estimates of CO 2 emissions are of highest interest. The relatively compact design with a single spectral window, however, allows for the deployment of a fleet of instruments and hence independent monitoring of localized CO 2 emissions on a larger scale. For real measurements, the proposed instrument concept would rely on meteorological and topography data to compute the airmass and thus XCO 2 , indicating the demand for a high instrument 15 pointing accuracy in order to avoid erroneous XCO 2 estimates (Kiel et al., 2019). The proposed instrument could also prove useful in synergy with a space-borne CO 2 lidar (e.g. Kiemle et al., 2017), where the passive spectrometer would benefit from the lidar's accuracy and knowledge on the light path and the lidar would benefit from the spectrometer's imaging capability.
For this first performance assessment of the proposed instrument concept, the analysis on the local scale (Indianapolis) was constrained to one day in July using a rather simplistic Gaussian dispersion model that assumes constant atmospheric stability 20 and (unidirectional) horizontal wind speed. As a next step, the CO 2 monitoring capabilities on the local scale of the instrument concept will be evaluated further for different seasons (with varying surface albedo and solar zenith angles), atmospheric states and emission source strengths using large eddy, rather than Gaussian, modelling of the CO 2 plumes, also including the inverse CO 2 flux estimates from the two-dimensional fields of synthetically retrieved XCO 2 . Although the effect of aerosols has partly been assessed on the global scale in this study, it is of key importance to also include information on the properties and distri- 25 bution of aerosols in the local scale simulations in order to better understand the instrument's ability to resolve and quantify localized CO 2 emissions under realistic conditions. Such an in-depth aerosol analysis is, however, the task of further future studies looking into realistic emission scenarios w.r.t. aerosol abundances in and around the CO 2 plumes, also in combination with high-resolution surface albedo.