Potential of a geostationary geoCARB mission to estimate surface emissions of CO 2 , CH 4 and CO in a polluted urban environment : case study Shanghai

This paper describes a numerical experiment to test the ability of the proposed geoCARB satellite to estimate emissions of trace gases (CO2, CH4 and CO) in the polluted urban environment of Shanghai. The meteorology over Shanghai is simulated with the Weather Research and Forecasting (WRF) model for a 9-day period in August 2010. The meteorology includes water and ice clouds. The chemistry version of WRF (WRF-Chem V3.6.1) is used to predict the chemical composition, mass density and number density of aerosol species. Spectra in the bands measured by geoCARB are calculated, including the effects of polarisation and multiple scattering of radiation by clouds, aerosols and molecules. Instrument noise is added, and column-averaged trace-gas mole fractions are estimated from the noisy spectra using an algorithm based on that for the Greenhouse Gases Observing Satellite (GOSAT) and the Orbiting Carbon Observatory-2 (OCO-2) but adapted to geoCARB. As expected, the high aerosol loadings are challenging. However, when the retrieval algorithm is provided with regionally adjusted aerosol optical properties, as might be determined from observations of dark targets within the field of regard, the accuracies of retrieved concentrations are comparable to those reported earlier for geoCARB. Statistics of the errors in the retrieved column-averaged concentrations are used to predict the reduction in uncertainty of surface emissions possible with remotely sensed data.


Introduction
Emissions of CO 2 , CH 4 and CO from cities and power plants potentially may be monitored from space, using columnaveraged concentrations of the gases inferred from highresolution spectra of reflected sunlight in absorption bands of CO 2 , CH 4 , CO and O 2 .Bovensmann et al. (2010b) examined CarbonSat (Bovensmann et al., 2010a), an instrument proposed to the European Space Agency, that would make spatially dense observations over power plants and cities from sun-synchronous orbit, and they found that the observations could provide valuable emission estimates, especially under conditions of low wind speed.Polonsky et al. (2014) examined geoCARB (Sawyer et al., 2013;Mobilia et al., 2013;Kumer et al., 2013b;Rayner et al., 2014), which would provide wall-to-wall coverage of continents with high spatial and temporal resolution, again with encouraging results.Gerilowski et al. (2011) flew an airborne CH 4 and CO 2 mapper over a German power plant and successfully estimated emissions from the plant.Kort et al. (2012) estimated emissions from megacities using data from Japan's Greenhouse Gases Observing Satellite (GOSAT), even though GOSAT only provides sparse spatial and temporal coverage.
The ability to measure emissions relies on many factors: 1. the concentration measurements must be precise because local sources generally will make only small perturbations to the column-averaged concentrations; 2. the observations must be spatially dense and highly resolved to capture plumes from local sources; Published by Copernicus Publications on behalf of the European Geosciences Union.3. the measurements must be frequent in order to track varying winds; 4. the wind fields must be known well if plumes are to be traced reliably back to spatially diverse sources, although this requirement might be weakened if only the integrated emissions from cities are required; 5. the fluxes of trace gases across the boundary of the city must be known, because the boundary fluxes control the background level upon which the contributions from local sources are imposed.
The principal impediment to accurate concentration measurements using reflected sunlight comes from scattering of photons by aerosols and clouds, because scattered photons travel different paths through the atmosphere and therefore suffer varying degrees of absorption.Thus, urban complexes, where emissions are large and observations would be most valuable, are locations where measurements are especially difficult because city atmospheres are polluted.This point was recognised clearly by Bovensmann et al. (2010b) and Polonsky et al. (2014), and they attempted to incorporate particulate emissions in their studies.
To some extent, obscuration by clouds and degraded accuracy caused by aerosols can be overcome if observations are spatially dense and frequent, as is possible with an instrument such as geoCARB observing from geostationary orbit.The spatial density allows the instrument to peek through gaps in clouds, while periods with cleaner air are captured by the frequent measurements.However, quantifying the extent is a complex task that must address all the issues listed above.
This paper is a first step, using the city of Shanghai as an example (Fig. 1).First the urban environment and the concentration measurements possible with geoCARB are simulated.Next the impact of those measurements is investigated in the context of perfect meteorology using the methods developed by Rayner et al. (2014).As a measure of impact, we use the reduction of the prior uncertainty of the surface emission fluxes gained from the (pseudo) satellite observations.In a later paper the errors caused by imperfect knowledge of the meteorology will be examined.
At the outset we emphasise that the forward models used on one hand to simulate polarised spectra at the top of the atmosphere and on the other hand to retrieve trace-gas concentrations have major differences, the chief of which are listed below.
1.In the simulation, the distributions of aerosol mass in space and time are derived from Weather Research and Forecasting model (WRF-Chem), as are the particle size distributions.The aerosol particles are assumed to be spherical, and their optical properties are calculated using Mie's theory.For the retrieval algorithm, the optical properties of aerosols are both prescribed and fixed and almost never coincide with the "truth".It is well known that scattering by aerosols is the most serious source of error for OCO-like instruments.
2. Similarly, in the simulations the mass distributions of cloud water and cloud ice and the corresponding particle size distributions were derived from WRF-Chem.The optical properties of water clouds were based on Mie calculations, while those for ice clouds accounted for nonspherical particles.In the retrieval algorithm, water and ice clouds were assumed to consist of particles with preassigned effective radii.Again, the assigned values almost never coincide with the "truth" in the simulations.
3. The vertical distributions of CO 2 , CH 4 and CO in the simulations are those predicted by WRF-Chem.Whereas a vertical profile of CO 2 is retrieved, only scaling factors are retrieved for CH 4 and CO.The shapes of the profiles of CH 4 and CO are preassigned and fixed in the retrievals.
4. The surface in the simulations is represented by a polarised bidirectional reflectance distribution.In the retrievals, it is assumed to be non-polarising and Lambertian.
Thus, the simulations exploit the "true" information provided by WRF-Chem, while the retrievals, limited in the variables that can be estimated reliably from the data, must rely on prior guesses for the remainder, as is currently the practice with Orbiting Carbon Observatory-2 (OCO-2) and GOSAT.The structure of the paper is as follows.Section 2 describes the simulation of the atmosphere over Shanghai, including carbon fluxes, clouds and aerosols, for a 9-day period in August 2010.Section 3 outlines the optical properties of clouds, aerosols and the surface assumed in generating geoCARB spectra, while Sect. 4 discusses the noise model for geo-CARB.Section 5 describes the inversion procedure by which column-averaged concentrations are derived from the noisy spectra.Section 6 estimates the reduction of uncertainty in surface fluxes gained from the relatively sparse set of observations that survive after rigorous screening for cloud and aerosol, and the implications are discussed.Finally, Sect.7 presents the results.
2 Simulation of the atmosphere over Shanghai

Time window
Observations of cloud and aerosol optical depth (AOD) from MODIS were used to select a suitable period for the study in the northern hemispheric summer of 2010, that year being chosen because greenhouse gas emissions at high spatial resolution were readily available.This preliminary step simply ensured that Shanghai was not obscured by cloud for the selected period.The period selected was from 1 through 9 August 2010.

Meteorology
The chemistry version of the WRF-Chem was run for a total of 10 days, allowing the extra day at the start for model spin-up, to simulate the winds and trace-gas concentrations over the target.The initial spin-up period allows time for transients caused by inconsistencies between the initial and boundary conditions to decay.A three-nested domain (18, 6 and 2 km resolution) was used with the innermost domain covering an area 200 × 200 km 2 centred close to Changzhou on the west of Shanghai.The innermost domain is entirely over land, apart from the Yangtze River, Lake Taihu in the south and numerous small lakes.Output files were written at 30 min intervals.The number of vertical layers was limited to 29 to reduce the numerical cost of the simulations.
The radiative transfer requires temperature and gas profiles to the top of the atmosphere, whereas the top of the grid used by WRF-Chem was located at p t = 50 hPa.Therefore, one more layer, extending from 50 hPa to the top of the atmosphere, was added to the output generated by WRF-Chem.The temperature and trace-gas concentrations for this extra layer were set to those for the top WRF-Chem layer.The extra layer was assumed to be free of cloud and aerosol.

Surface and boundary carbon fluxes
Surface fluxes of CO 2 and CO were derived from the Fossil Fuel Data Assimilation System (FFDAS) (Asefi-Najafabady et al., 2014), but the temporal structure was not modelled.Surface fluxes for CH 4 came from the Emission Database for Global Atmospheric Research (EDGAR; Olivier et al., 2005).Boundary fluxes of CO 2 were derived from the ECMWF Monitoring Atmospheric Composition and Climate (MACC) program (Panareda et al., 2014), while the global Model for OZone And Related chemical Tracers (MOZART-4; Emmons et al., 2010) provided fluxes for the other trace gases.
Because FFDAS uses night lights to help distribute regional CO 2 fluxes at finer spatial resolution, it can shift emis-  sions from point sources like power plants to users who consume the electrical power.For example, the large power plant (red dot) on the Yangtze River near the centre of Fig. 2 does not coincide with the peaks in the surface fluxes from FFDAS (green dots).For the purpose of the numerical experiment described in this paper, the mislocation of the emissions is not important, but for an analysis of real geoCARB data the locations of power plants would have to be specified correctly.

Aerosol
Primary aerosol emissions over Shanghai were derived from EDGAR (Olivier et al., 2005), which provides fluxes of organic carbon (OC), black carbon (BC), particulates less than 2.5 µm in diameter (PM 2.5 ) and particulates less than 10 µm in diameter (PM 10 ).No other primary emissions of particulates were included.In particular, sulfate and biomassburning aerosols were advected from the boundary and were not generated locally.This restriction will be removed in later work.
Because the spatial resolution of EDGAR (0.1 • × 0.1 • ) is roughly 5 times coarser than the spatial resolution of the inner domain of the WRF-Chem simulations, a method to distribute the EDGAR particulate fluxes over the finer WRF-Chem grid was required.Following Asefi-Najafabady et al. (2014), the downscaling of particulate fluxes was based on the Defense Meteorology Satellite Program (DMSP) nightlight product, whose native resolution is 30 arcsec.For each emitted species the high-resolution (30 arcsec) flux F high was assumed to be where F low is the low-resolution (0.1 • ) flux, L the 30 arcsec DMSP night-light field and L the same field averaged over the 0.1 • grid cell of the low-resolution flux.This approach was applied to all fluxes except CO 2 emissions themselves.The low-resolution flux F low was taken from the EDGAR V4.2 emissions (Olivier et al., 2005).For CO 2 emissions, the high-resolution version of the fossil-fuel data assimilation (FFDAS) data set was used (Asefi-Najafabady et al., 2014).The "other" sector of Asefi-Najafabady et al. ( 2014) EDGAR does not provide size-resolved particulate fluxes (apart from the broad PM 2.5 and PM 10 categories), whereas the MOdel for Simulating Aerosol Interactions and Chemistry (MOSAIC) embedded in WRF-Chem uses eight size bins: r 0 < r 1 < . . .< r i < . ..r s with r i = 2 i−s r s and s = 8.In practice the maximum bin limit is r s = 5 µm, leading to r 0 ≈ 19 nm. 1 The ith bin represents the combined mass of particulates with radii in the range [r i−1 , r i ].Because r 0 , the lower limit of the smallest bin, exceeds the upper limit for Aitken particles (5 nm), MOSAIC accounts only for accumulation and coarse mode particulates.
Particulate fluxes from EDGAR were partitioned between Aitken, accumulation and coarse modes using the ad hoc factors listed in Table 1; real data would assist if they were available.The fraction of the EDGAR flux assigned to the Aitken mode is lost from the subsequent calculations because Aitken particles are smaller than the smallest MOSAIC bin.Next the accumulation and coarse modes were partitioned between the MOSAIC size bins with a fixed assignment for each mode, as specified in Table 2.
Lateral boundary conditions for aerosol species were obtained from MOZART-4 (Emmons et al., 2010).Boundary values and fluxes for sea salt and dust were carried in sectional size bins, while those for organic carbon, black carbon, sulfate and ammonium nitrate were not size-resolved.

Cloud
WRF-Chem generated three-dimensional cloud fields.In each cell of the model domain, the number density and mass density were predicted for each cloud type (water or ice).The effective radius was derived using conservative models for 1 Whereas this paper consistently uses radius, MOSAIC mostly uses diameter to characterise particles.the size distributions for water and ice clouds, as described in Appendix C.
3 Simulation of geoCARB spectra

Scan box and sample times
GeoCARB is assumed to be in geostationary orbit at longitude 110 • E. When viewing to nadir, the east-west scan step is 3.0 km, and the north-south spacing of pixels is 2.7 km.These spacings increase when viewing away from nadir.For the Shanghai simulations, the optic axis, after reflection in the east-west and north-south scan mirrors, hits the geoid at 31.8 • N latitude and 120.0 • E longitude, just to the west of Shanghai and close to the city of Changzhou.The simulated data consist of 51 frames, each with 51 pixels, covering the scan box shown in Fig. 1.The time between frames was taken to be 4.625 s.2 GeoCARB observations of Shanghai were simulated three times per day at 00:15, 04:15 and 08:15 UTC, corresponding to 08:15, 12:15 and 16:15 local time (LT) in Shanghai.

Optical properties of aerosol and cloud
Size-resolved mass mixing ratios of nine aerosol species were predicted by MOSAIC during the simulations.The species and the procedures by which the optical properties of the aerosol mixtures were computed in the geoCARB spectral bands are detailed in Appendix A.
Figure 3 illustrates the AOD computed for the target region in the geoCARB spectral bands.The simulation is for   GeoCARB observations of Shanghai were simulated three times per day at 00:15, 04:15 and 08:15 UTC, corresponding to 08:15, 12:15 and 16:15 local time (LT) in Shanghai.

Optical properties of aerosol and cloud
Size-resolved mass mixing ratios of nine aerosol species were predicted by MOSAIC during the simulations.The species and the procedures by which the optical properties of the aerosol mixtures were computed in the geoCARB spectral bands are detailed in Appendix A.
Figure 3 illustrates the aerosol optical depth (AOD) com-10 puted for the target region in the geoCARB spectral bands.The simulation is for 9 August 2010 at 08:15 UTC, corresponding to 16:15 LT in Shanghai.All four panels use the same dynamic range, which makes the differences between bands easier to see.There is a steady decrease in optical depth with wavelength, indicating small aerosol particles.Histograms of AOD in the O 2 A-band predicted by WRF-Chem and observed by MODIS are compared in Fig. 4. The MODIS data were adjusted from the measured optical thickness at 550 to 770 nm using MODIS Ångström coefficients.

20
The histograms present the probabilty of each optical thickness bin without regard for the spatial distributions.Only the near-noon WRF-Chem simulations are included, because these provide an approximation to the MODIS Terra obser-vations at 10:30 and Aqua at 13:30 LT.The peaks of the two histograms coincide at approximately 0.3, but the MODIS observations contain a longer tail extending to 1.0, whereas the WRF-Chem tail extends only to 0.8.Generally the correspondence is good, so the scenarios encountered in the simulated geoCARB are not unrealistic.
Three-dimensional distributions of the mass and number of cloud liquid water and ice particles, all per unit mass of moist air, were predicted by WRF-Chem.In order to estimate the corresponding effective radii, needed to compute the optical properties of the clouds, the particle sizes were assumed to follow modified gamma distributions (Deirmendjian, 1969).Optical properties in the geoCARB bands were calculated using Mie theory for spherical water drops, while for ice cloud the extinction coefficient and phase matrix were interpolated from data published by Baum (2007) and Baum et al. (2005a, b).

Surface properties
Surface properties, such as polarized bidirectional reflectance distribution function (BRDF, derived from MODIS and POLDER), were interpolated to the wavelengths of the geoCARB spectral bands.The method was similar to that described by O'Brien et al. (2009) andPolonsky et al. (2014).In the geoCARB spectral bands at 765, 1606 and 2065 nm, the surface BRDF was interpolated linearly from the MODIS BRDF at 645, 859, 1240, 1640 and 2130 nm.The BRDF in the geoCARB band at 2323 nm was assumed to be the same as the MODIS BRDF at 2130 nm, because MODIS BRDF is not available at longer wavelengths.The polarised component of the BRDF was assumed to be independent of wavelength.Surface heights from the WRF-Chem topography were interpolated to the centres of the geoCARB pixels.

Radiative transfer calculations
Using the three-dimensional fields of CO 2 , CH 4 , CO, clouds, aerosols and meteorology, spectra in the geoCARB bands were simulated for all geoCARB pixels within the target area for early morning, noon and late afternoon observations on each of the non-spin-up days selected for the study.These simulations used the correct observation geometry.However, neither variations of trace gas concentrations nor variations of surface properties were modelled within the geoCARB Atmos.Meas.Tech., 9, 1-22, 2016 www.atmos-meas-tech.net/9/1/2016/  9 August 2010 at 08:15 UTC, corresponding to 16:15 LT in Shanghai.All four panels use the same dynamic range, which makes the differences between bands easier to see.There is a steady decrease in optical depth with wavelength, indicating small aerosol particles.Histograms of AOD in the O 2 A-band predicted by WRF-Chem and observed by MODIS are compared in Fig. 4. The MODIS data were adjusted from the measured optical thickness at 550 to 770 nm using MODIS Ångström coefficients.The histograms present the probability of each optical thickness bin without regard for the spatial distributions.Only the near-noon WRF-Chem simulations are included, because these provide an approximation to the MODIS Terra observations at 10:30 and Aqua at 13:30 LT.The peaks of the two histograms coincide at approximately 0.3, but the MODIS observations contain a longer tail extending to 1.0, whereas the WRF-Chem tail extends only to 0.8.Generally the correspondence is good, so the scenarios encountered in the simulated geoCARB are not unrealistic.
Three-dimensional distributions of the mass and number of cloud liquid water and ice particles, all per unit mass of moist air, were predicted by WRF-Chem.In order to estimate the corresponding effective radii, needed to compute the optical properties of the clouds, the particle sizes were assumed to follow modified gamma distributions (Deirmend-jian, 1969).Optical properties in the geoCARB bands were calculated using Mie theory for spherical water drops, while for ice cloud the extinction coefficient and phase matrix were interpolated from data published by Baum (2007) and Baum et al. (2005a, b).

Surface properties
Surface properties, such as polarised bidirectional reflectance distribution function (BRDF, derived from MODIS and POLDER), were interpolated to the wavelengths of the geo-CARB spectral bands.The method was similar to that described by O'Brien et al. (2009) and Polonsky et al. (2014).In the geoCARB spectral bands at 765, 1606 and 2065 nm, the surface BRDF was interpolated linearly from the MODIS BRDF at 645, 859, 1240, 1640 and 2130 nm.The BRDF in the geoCARB band at 2323 nm was assumed to be the same as the MODIS BRDF at 2130 nm, because MODIS BRDF is not available at longer wavelengths.The polarised component of the BRDF was assumed to be independent of wavelength.Surface heights from the WRF-Chem topography were interpolated to the centres of the geoCARB pixels.

Radiative transfer calculations
Using the three-dimensional fields of CO 2 , CH 4 , CO, clouds, aerosols and meteorology, spectra in the geoCARB bands were simulated for all geoCARB pixels within the target area for early morning, noon and late afternoon observations on each of the non-spin-up days selected for the study.These simulations used the correct observation geometry.However, neither variations of trace-gas concentrations nor variations of surface properties were modelled within the geoCARB pixels.Instead, the atmosphere above each pixel was assumed to consist of plane parallel layers, each uniform horizontally.Thus, the concentrations and optical properties of the atmosphere at any point along the line of sight from the centre of a pixel to the satellite were assumed to be the same as those at the same height vertically above the centre of the pixel.Similarly, the surface properties were assumed to be horizontally uniform with values set at the centre of the pixel.These approximations are expedient, because they permit the use of plane-parallel radiation codes, but their justification is questionable for sensors (like geoCARB) with moderate spatial resolution, comparable to that of WRF-Chem.Fortu-Table 3. Noise parameters for the geoCARB bands.The units of N 0 and N 1 are nW (cm 2 sr cm −1 ) −1 .

Band
N 0 N 1 (µm) 0.765 0.1819 0.003295 1.606 0.1172 0.002107 2.065 0.0814 0.001452 2.323 0.0811 0.001303 nately, the approximation is immaterial for the numerical experiments over Shanghai, because the same approximation is employed in the forward simulation and the inverse retrieval, but for geoCARB in flight this issue should be addressed.
An outline of the radiative transfer calculations is provided by O'Brien et al. (2015).Polarisation by the surface and by scattering within the atmosphere is included, but the polarisation effects of geoCARB's gratings are bypassed, because they may be corrected during analysis of the spectra using radiometric and polarimetric calibration data acquired before launch (O'Brien et al., 2015).Thus, the Stokes vector (I, Q, U, V ) was computed at the top of the atmosphere, and the intensity I was assumed to be the measured signal.

Simulation of instrument noise
The noise model for geoCARB is based on both laboratory characterisation and airborne trials with the Tropospheric Mapping Imaging Spectrometer (TIMS) developed by Lockheed Martin (Kumer et al., 2009(Kumer et al., , 2011)).TIMS was used to demonstrate the feasibility of measuring CH 4 and CO in the 2.323 µm band.Details of the noise model and further information on the detector performance are provided by Kumer et al. (2013a).
The noise equivalent spectral radiance N (in units nW (cm 2 sr cm −1 ) −1 ) for a representative spectral sample consists of shot noise due to the observed signal radiance I and a signal-independent noise floor radiance N 0 .It is given by where N 0 and N 1 are constants for each band. 3Their numeric values, listed in Table 3, were derived from geoCARB instrumental and operational parameters by Kumer et al. (2013a).
For each spectrum, the root-mean-square noise was computed using Eq. ( 2) and was provided to the inversion algorithm.In addition, for each spectrum a random sample of noise was drawn from a Gaussian distribution with zero mean and the appropriate standard deviation at each frequency within each band.The noise sample was added to the spectrum prior to inversion.

Inversion of noisy spectra
The basic inversion algorithm developed by the Jet Propulsion Laboratory and Colorado State University for OCO, GOSAT and OCO-2, as described by O'Dell et al. ( 2012), was adapted to the spectral bands of geoCARB and applied to the simulated spectra.The results reported in Sect.7 were obtained by fitting the intensity component of the Stokes vector rather than the signal that includes the polarising effects of the gratings.

Instrument
The instrument line shape (ILS) function in each band was assumed to be Gaussian in wavelength (and therefore slightly non-Gaussian in frequency).The band limits (λ − and λ + ), dispersion per pixel (δ) and resolution are listed in Table 4.
The number n of pixels in each band was defined to be where [x] denotes the integer part of x.The spectral sample points were with corresponding frequencies where λ p is expressed in nanometres and ν p in cm −1 .Lastly, ν p was represented as a cubic dispersion polynomial: The dispersion coefficients are listed in Table 5.With these definitions, the inversion code works entirely in frequency, rather than wavelength."Observed" and calculated spectra were compared in the reference frame of geoCARB, after allowing for the Doppler shifts arising from the motion of the target relative to the sun.

Prior gas profiles
The prior gas vertical profiles were based on the simulated profiles for the morning of the first day.Once computed, the same prior profiles were used for all subsequent times and days.The prior profiles are shown in Fig. 5.The prior for the CO 2 field was taken to be the average of the background CO 2 field across the target region.In calculating the average, the background values from WRF-Chem on 29 layers firstly were interpolated to the 20 levels of the retrieval algorithm.The background represents the CO 2 advected into the domain but does not include the contributions from local sources and sinks.To the extent that the broad scale features of the global CO 2 field can be predicted reliably by transport models, this is a reasonable prior for CO 2 .
The prior for CO was averaged similarly over the Shanghai domain.However, the logic was convoluted because the background field for CO initially was not available in the WRF-Chem output.Instead the "true" CO field was taken to be the field generated with the FFDAS emission sources but evolved with chemistry disabled, while the prior was generated with FFDAS emissions and active chemistry.Thus, the prior and the truth had the same emission sources and differed only in the chemistry.However, it emerged that the prior profile of CO determined at the first observation time on the first day was on average 40 % higher than the profiles on other days.
For CH 4 the background field was not available initially, so the average of the true CH 4 field over the domain was used for the prior.
For H 2 O, CH 4 and CO, the retrieval algorithm optimised scalar multiples of the prior profiles, while for CO 2 a full vertical profile was retrieved.The prior uncertainties for the scaling factors are shown in  probably unrealistically so, but it was necessary because with larger uncertainties the retrieval algorithm frequently failed to converge.This issue is discussed later.

Prior meteorology
Previous studies (O'Dell et al., 2012;Polonsky et al., 2014) suggest that the accuracy of the meteorology prior does not have a large impact upon the retrieved trace-gas concentrations.Therefore, in this preliminary study, the prior for the meteorology was taken to be the truth, apart from the minor errors introduced by interpolating from the 29 layers of WRF-Chem to the 20 levels of the retrieval algorithm.The prior uncertainty assumed for surface pressure was 4 hPa, a relatively large value, so the prior has only a secondary effect upon the retrieval.Similarly, the uncertainty assumed for the temperature offset was large (5 K).

Prior aerosol
The algorithm to retrieve concentration profiles is based on that used for GOSAT and OCO-2.It assumes four particulate types, water drops with effective radius 8 µm, ice crystals with effective radius 70 µm and two aerosol types, Kahn 2b and Kahn 3b, as described by Kahn et al. (2001).
For each particulate, the extinction coefficient, single scattering albedo and phase matrix were precalculated and provided to the retrieval algorithm.The underlying assumption is that a mixture of the two aerosol types can represent the optical properties of real aerosol with sufficient accuracy.However, in practice this assumption frequently fails; the mixture cannot reproduce the optical properties, the retrieval algorithm fails to converge or produces estimates seriously in error, and the fits to the spectra (measured by the reduced χ 2 ) are poor.The obvious remedy is to use more appropriate aerosol models.
Although aerosol loadings can be highly variable in space and time, in the absence of other data it is common to assume that the aerosol type is the same over a limited region.Of the extinction coefficient, single scattering albedo and phase matrix, the most important to capture reliably for the retrieval algorithm is the wavelength dependence of the extinction coefficient.Therefore, after retrieving column-averaged gas concentrations from the simulated spectra with the standard algorithm, the retrievals were repeated with the wavelength dependence of the aerosol extinction coefficients adjusted to represent the regional aerosols more accurately.The adjustment was performed for each scene using the minimum and maximum of the simulated AOD over the whole scene.
1.The minimum and maximum AOD over the scene, denoted τ min (λ) and τ max (λ), were computed for the geo-CARB bands.
2. The extinction coefficient, single scattering albedo and phase matrix of Kahn type 3b aerosol were replaced by those for type 2b.
3. For Kahn aerosol type 2b, the extinction coefficient γ (λ) was replaced by where λ 0 denotes the wavelength at the blue end of the O 2 A-band.
4. For Kahn aerosol type 3b (initially equal to type 2b), γ (λ) was replaced by Neither the single scattering albedo nor the phase matrix was changed for two reasons.Firstly, in practice it is unlikely that information to guide such changes would be available.Secondly, the adjustment to the extinction coefficient ensures that aerosol contributions to the radiance are correctly proportioned across the geoCARB bands.
As justification for this replacement, other sensors (or perhaps geoCARB itself) are likely to provide independent information on aerosols.Furthermore, when there is a dark target in the region, such as Lake Taihu near Shanghai, robust measurements of aerosol properties are possible, because photons scattered by aerosols over the dark target are not masked by photons reflected from the surface.
Thus, two options were considered, the first with standard aerosol and the second with regionally adjusted aerosol.In addition, the threshold for retrieved aerosol optical thickness in the post-processing filter (PPF) was increased from 0.1 to 0.15 for the experiment with regionally adjusted aerosol.Details of the PPF are provided by Polonsky et al. (2014).

Estimation of surface fluxes
To test the capacity of the retrieved concentrations to constrain surface fluxes we extended the work of Rayner et al. (2014).That paper calculated the reduction in uncertainty for fluxes in an idealised urban box with a single isolated power plant.Here we replaced the idealised environment with a realistic representation of the Shanghai-Nanjing region.The emissions are the same as that used to generate the atmospheric state used in the trace-gas retrieval calculations.Six days of observations were considered.The diurnal cycle of emissions was assumed to be the same for each day and was represented in four 6 h blocks.Fluxes were retrieved at 5 × 5 km resolution.Every pixel within the 200×200 km target area was considered as a source, so there were 4 × 40 × 40 = 6400 unknown flux elements for CO 2 .Following Rayner et al. (2014) we also solved for a constant emission factor for CO for each pixel.This approach is more difficult than the tracer correlations used by Palmer et al. (2006) since it renders the inversion nonlinear.It better reflects the source processes that link the two species, and also allows future use of bottom-up emission factors to provide more information.For methane we assumed no diurnal cycle of emissions, yielding 1600 unknown flux components.For each trace gas we also solved for a constant bias across the region.If concentrations are linearly related to source fluxes and Gaussian statistics are assumed, then the posterior flux error covariance A is where B is the prior flux error covariance, H is the Jacobian matrix mapping fluxes to observed concentrations, and R is the error covariance of the observations.This model predicts the reduction in flux errors brought about by the observations.In this form it does not address the impact of transport errors.The percentage uncertainty reduction for component j of the flux is taken to be where A jj and B jj are the corresponding diagonal elements of the posterior and prior flux error covariances respectively.Following Rayner et al. (2014) we use the simplified transport model SatPlume to calculate H. Justification of the Sat-Plume Jacobian depends on whether or not it overestimates the structure of the retrieved field; the more structured the plumes, the stronger the error reduction because sources are less smeared together.Rayner et al. (2014) argued that the statistics of column dilution from SatPlume are plausible.
Apart from H, the other two ingredients for the error reduction calculation are B and R. Prior flux uncertainties for CO 2 are set at 25 % of the fluxes themselves.For the calculation using CO measurements we also require an emission factor for CO.Its uncertainty is set at 30 % following Rayner et al. (2014).The posterior errors in X CO 2 and X CH 4 measurements are taken directly from the L2 retrieval algorithm.For X CO the L2 retrieval algorithm underestimates the errors, as will be discussed later in Fig. 11, so experiments were conducted with values 15, 10 and 2.5 ppb.

Trace-gas concentrations
The optical depths of cloud water, cloud ice and aerosol in the O 2 A-band are plotted in Fig. 6.These histograms include all samples over Shanghai in the 9-day period of the simulation.Although the period selected generally had skies that a casual observer would call clear, relatively few pixels had optical depths sufficiently low to permit reliable retrieval of trace gases.Thus, even an instrument like geoCARB with its high spatial density of samples cannot provide wall-towall coverage of a polluted urban environment, and retrieval of accurate surface fluxes is challenging.
Three experiments were conducted, as indicated in the first three columns of Table 7.In experiment 1, the aerosol over Shanghai was simulated, but the optical thicknesses of water and ice clouds were set to 0. The retrieval algorithm used the ACOS aerosol scheme with water cloud, ice cloud and two types of aerosol.The retrieval algorithm did not assume that the atmosphere was cloud free; it retrieved optical thickness profiles of aerosol, cloud water and cloud ice, layer by layer.Experiment 2 was similar, except that the radiance sim-  .Histograms of errors in retrieved surface pressure p s , X CO 2 , X CH 4 and X CO for experiment 1 with cloud-disabled and standard aerosol.The PPF has been applied to the coloured histograms, but not to those in light grey.The biases (b) and standard deviations (SD) quoted are for the histograms after the PPF.Of the total of 55 387 cases that converged, 10 995 passed the PPF (19.9 %).
ulations of the forward model included the contributions of cloud water and cloud ice.Lastly, the forward simulations for experiment 3 included both aerosol and cloud, but the retrieval algorithm used adjusted optical properties for aerosol as described under Sect.5.2.3 above.
Table 7 lists the success rate of the retrieval algorithm, presenting the fraction of soundings for which the retrieval algorithm converged and the fraction that passed the PPF.The total number of soundings is the same for all the experiments (70 227), being the product of the number of days ( 9), the number of times per day (3), the number of geoCARB frames (51) and the number of pixels per frame (51).The two experiments with cloud enabled had approximately the same numbers of converged pixels, but experiment 3 with adjusted aerosol properties had many more pass the PPF.There are two reasons.First, the threshold for AOD was increased in experiment 3 from the default of 0.10 to 0.15.Probably more important were the superior aerosol optical properties, which permitted better fits to the spectra.Histograms of errors in the retrieved surface pressure p s , X CO 2 , X CH 4 and X CO are presented in Fig. 7 for experiment 1 with standard aerosol but without cloud.In each panel, the grey histogram (partly obscured) describes the errors with the PPF disabled; the foreground coloured histogram has the PPF active.Generally the results are poor.
1.The histograms without the PPF are very broad, far exceeding the range thought necessary to retrieve surface fluxes.
2. In the case of X CO , the histogram has multiple peaks, the origin of which is unknown.They indicate that the retrieval algorithm is failing in several distinct modes.
3.Even after the PPF, the surface pressure is biased low by 1.7 hPa, while X CO 2 is high by 2.2 ppm.This effect of anticorrelated errors is often observed in retrievals with simulated spectra, though the underlying cause is poorly understood.It seems to occur in the presence of high aerosol loadings, particularly when the optical properties (single scattering albedo and phase matrix) .Histograms of errors in retrieved surface pressure p s , X CO 2 , X CH 4 and X CO for experiment 2 with cloud-enabled and standard aerosol.The PPF has been applied to the coloured histograms, but not to those in light grey.The biases (b) and standard deviations (SD) quoted are for the histograms after the PPF.Of the total of 36 000 cases that converged, 666 passed the PPF (1.9 %).For clarity, the vertical scale in the coloured histograms has been multiplied by 5.
assumed for the aerosol in the retrieval algorithm do not match those in the simulated data.
When cloud is enabled in experiment 2 with standard aerosol (Fig. 8), the histograms broaden, even those with the PPF.The low bias in surface pressure and high bias in X CO 2 persist, and the distributions are not bell-shaped, suggesting that competing factors contribute to the error.
Figure 9 shows the corresponding results for experiment 3 in which the retrieval algorithm was provided with regionally adjusted optical properties for aerosol (but not cloud).Although the histograms after the PPF are slightly skewed, they are more bell-shaped, and the mean values are close to 0. These results are comparable to those found in earlier studies for less polluted environments (Polonsky et al., 2014).
CO is particularly difficult to retrieve, because the absorption lines of CO are masked by lines of H 2 O and CH 4 .Only with spectral resolution much finer than that provided by geoCARB is it possible to probe CO lines without interference from H 2 O and CH 4 .Compounded with this spectrographic difficulty is an algorithmic limitation.In order to estimate the atmospheric state, the current version of the L2 retrieval algorithm performs unconstrained optimisation of a cost function that measures the difference between the observed and computed spectra, consistent with the instrument noise.However, in the course of the optimisation, the algorithm can produce unphysical states, a common example being negative values for optical depth.In an attempt to control this behaviour for aerosol, the optimised variable is the log-arithm of the optical depth, which may take any value, but which compresses the dynamic range.Consequently the retrieval algorithm frequently aborts because the state vector has strayed into an unphysical region of state space.Further soundings are lost due to lack of convergence, a problem exacerbated by logarithms of optical depth.For example, several iterations may be wasted with tiny steps in AOD, even though the steps in the logarithm are significant.In order to secure convergence of the algorithm, a tight prior error for the CO scaling factor was imposed.While that probably is acceptable if the prior CO profile is close to the truth, it clearly is not if the initial guess is poor.In that case, the profile is clamped to the prior profile by the tight prior error, and the final answer for X CO will be biased towards that of the prior.This might explain the positive bias in X CO in experiment 3, because the prior CO profile was higher than the truth for most pixels.
The reason why a tight prior uncertainty for the CO profile assists convergence is not clear, but we offer the following conjecture.In response to an amplitude shift that varies slowly with frequency, such as that produced by aerosol, the retrieval algorithm mistakenly attempts to compensate by adjusting the gas concentrations.However, because the effect of CO on the spectrum is much smaller than that of CH 4 and H 2 O in geoCARB's 2323 nm band, the adjustment to CO concentrations made by the algorithm is too large and results in negative X CO , which in turn causes the radiative transfer code to fail.With a tight prior uncertainty, the CO .Histograms of errors in retrieved surface pressure p s , X CO 2 , X CH 4 and X CO for experiment 3 with cloud-enabled and regionally adjusted aerosol.The PPF has been applied to the coloured histograms, but not to those in light grey.The biases (b) and standard deviations (SD) quoted are for the histograms after the PPF.Of the total of 34 664 cases that converged, 3107 passed the PPF (9.0 %).For clarity, the vertical scale in the coloured histograms has been multiplied by 2.
profile cannot deviate far from the prior profile, resulting in fewer unphysical values.If this conjecture is correct the problem can be ameliorated by preconditioning the optimisation so that steps in X CO are smaller.We note also that the masking of CO lines by CH 4 and H 2 O lines will be reflected in the linear error analysis.It is reasonable to hope, then, that once numerical problems with the optimisation algorithm are overcome, the error statistics for X CO will improve, perhaps considerably.
These problems might be alleviated by constraining state variables to ensure that all internally generated variables have physically reasonable values.For example, optical depth should be positive.When the state vector encounters a constraint boundary, the optimisation algorithm should require the state to move along the constraint boundary as it continues its search rather than crossing the boundary and aborting.At each iteration, the optimisation algorithm should check whether a better reduction in the cost function could be achieved by releasing the state from the boundary or by retaining it there.Robust code to implement constrained optimisation is available.
Of particular interest are the histograms of errors for retrieved AOD, shown in Fig. 10 for experiments 1, 2 and 3.In each case the mean error is negative, so the retrieval algorithm underestimates the true AOD.Furthermore, the standard deviation is close to the magnitude of the mean, suggesting that the prior value for the AOD is too low and that the prior uncertainty is too tight.

Errors vs. S/N
Statistics of the errors as functions of the signal-to-noise ratio (S/N) are needed to conduct observational system simulation experiments (OSSEs) for geoCARB.They allow the measurement error to be predicted from the surface albedo, which is known by the OSSE, because to a good approximation the albedo and the solar zenith angle determine the S/N .The small dots in Fig. 11 are the posterior errors in the column-averaged mole fractions of CO 2 , CH 4 and CO estimated by the L2 retrieval algorithm for the ensemble of soundings over Shanghai that passed the PPF in experiment 3.They were derived from the posterior covariance, given by where S is the covariance of instrument noise, S a is the covariance of the distribution about the prior state and K is the Jacobian of the transformation from states to measurements (Rodgers, 2000, Eq. 3.31).Thus, the posterior errors include both retrieval noise and smoothing errors.The range of S/N is wide (although not as wide as that expected by geoCARB), because the ensemble includes morning and afternoon observations when the solar zenith angle is large and the incident solar flux density is low.The solid curves have the form where σ denotes the uncertainty (in ppm for CO 2 and ppb for CH for Shanghai, many functional forms could have been chosen to fit the data.However, it was decided to choose a functional form that would be conservative should it be abused by applying it to S/N outside the range over Shanghai.The form in Eq. ( 8) decreases monotonically from a, its value when x is 0, so parameter a should represent the prior un- certainty.For large x the function decays to 0 at a rate determined by the exponent c.Conservative values of 10 ppm, 100 and 100 ppb for X CO 2 , X CH 4 and X CO were assigned to a, and parameters b and c were determined by fitting the model to the posterior errors from the L2 algorithm.Table 8 lists the parameters so determined.
The points in Fig. 11 with error bars represent the actual error, defined to be the retrieved value minus the truth, with the latter weighted by the averaging kernel.The error bars in Fig. 11 were derived using a bootstrap algorithm.In this procedure, bootstrap data sets were generated by randomly  sampling with replacement from the set of actual errors incurred in the retrievals over Shanghai.The variance of the distribution of actual errors was estimated from the ensemble of bootstrap data sets.This technique is common in the statistics literature; one reference is Horowitz (2001).The actual errors are larger than the estimates of posterior error from the retrieval algorithm; for X CO 2 and X CH 4 the actual errors are about 1.5 times larger than the estimated errors, but for X CO the factor is closer to 8, although most of the X CO difference is due to bias rather than a serious underestimation of the random error by the L2 algorithm.Possible causes of the bias are the differences between the forward models used for simulation and retrieval, nonlinearities in the retrieval (Kulawik et al., 2008) and the interplay of a consistently low prior for CO with an unrealistically small prior error.In future work we will investigate these issues using atmospheres that can be described perfectly by the retrieval forward model.

Reduction of uncertainty in surface fluxes
Of the 3107 soundings that converged and passed the PPF in the full 9-day simulation for experiment 3, only 2751 fell within the selected 6-day window and also had rays from the target to the sun and satellite passing through the top rather than the sides of the model domain.With only 2751 observations for 6401 flux components, any attempt to determine the posterior fluxes is under-constrained.However, the observations will not be uniformly distributed through the day, so fluxes at some times may be determined well.
Figure 12 shows the reduction of error in the 00:00 UTC time period for the case using both X CO 2 and X CO measurements, the latter with uncertainty 10 ppb.The spatial structure is quite similar to that of the prior fluxes.This is a common result following from Eq. ( 5) in which larger prior uncertainties are preferentially reduced.This relationship weakens towards the east of the domain.Here the sunearth ray is likely to pass through the eastern wall of the domain and hence be excluded (observation time is 08:15 LT).The maximum error reduction is 30 %, corresponding to one of the strongest prior sources.
Two other periods of the day are quite well constrained.This is not surprising for the local afternoon (14:00-20:00 LT) since there is an observation made during that period.The block from 02:00 to 08:00 LT is also reasonably constrained by the observation made at 08:15 LT.As in Rayner et al. (2014), the block corresponding to the unobserved night is completely unconstrained by observations.We conducted four experiments, the first without X CO observations and the remainder including X CO with errors of 15, 10 and 2.5 ppb.The largest value (15 ppb) is approximately the mean of the true error, defined to be the difference between X CO retrieved and X CO simulated.The middle value (10 ppb) is a slightly optimistic estimate, while the lowest (2.5 ppb) is included to explore benefits that might accrue from improved spectral resolution in the CO band.For each experiment we performed four variations: 1. σ (X CO 2 ) reduced by a factor of 5 2. σ (X CO 2 ) inflated by a factor of 5 3. observations thinned by a factor of 2 4. observations thinned by a factor of 4. Spatial patterns of error reduction are similar, so we summarise the statistics of the results in Table 9.The row labelled "Base" describes the four experiments; the following four rows cover the variations on the experiments.
The base case demonstrates the importance of the X CO observations.For the X CO 2 -only experiment, the maximum reduction of uncertainty is 17 % and occurs at 00:00 UTC (locally 08:00).The maximum rises with the addition of X CO observations, reaching 24, 30 and 58 % for the three levels assumed for σ (X CO ).8.2 8.5 0.0 5.7 11.7 12.9 0.0 9.1 17.7 15.0 0.0 9.9 41.1 43.9 0.0 31.7 The variations explore trade-offs among precision and data density.For example, adding X CO observations with accuracy 2.5 ppb outweighs improving the X CO 2 accuracy by a factor of 5 in the X CO 2 -only case.Similarly, X CO observations with 15 ppb error more than compensate for loss of half the observations in the X CO 2 -only case.Lastly, X CO observations with 15 ppb error roughly compensate for a 5-fold loss of accuracy in the X CO 2 -only case.

Discussion
This work is intended as part of an evolution from the notional study of Rayner et al. (2014) towards a mission definition.It parallels the development from Rayner and O'Brien (2001) to the definitions of global missions.The main step we have made here is a more serious treatment of the concentration retrieval errors that can be expected from a real instrument, informed by previous experience with low-earth orbiting missions OCO-2 and GOSAT.Only the random component of the instrument error is considered; non-random errors, such as those arising from imperfect radiometric calibration and imperfect characterisation of the ILS function, will be considered in future work.We caution that the estimates of posterior flux errors are likely to be optimistic because the calculation assumes perfect meteorology along with other idealisations.
The results are less dramatic than those of Rayner et al. (2014).This is particularly clear if one notes that the flux retrieval uncertainties here are at a spatial resolution of 5×5 km while those of Rayner et al. (2014) for CO 2 sources were at 3 × 3 km.The main reason for the weakened constraint of fluxes is the reduction in the number of available soundings.Detailed simulations including aerosol and cloud give a more pessimistic picture of sampling density than the simple statistical approach of Rayner et al. (2014).
Given the sensitivity of the results to contamination by clouds and aerosols we need to improve our confidence in these fields.Our simulations seem to perform quite well against available data, but there are many aspects we cannot test.Data on the diurnal cycle of cloudiness at this resolution are surprisingly lacking for example.
As with the study of Rayner et al. (2014), X CO measurements provide much information on fluxes.It is important, therefore, to understand their error characteristics.We noted already that the uncertainties generated by the L2 algorithm were a poor guide to the errors (retrieval minus truth).The differences between experiments with 15 and 2.5 ppb for σ (X CO in Table 9) underline the importance of the question; if we could generate measurements with the characteristics implied by the L2 algorithm, the flux constraint would be far stronger.However, the mechanism we believe is causing the larger X CO errors shows that eliminating bias will require substantial improvements to the L2 algorithm.Because there is interference between the CO lines and both CH 4 and H 2 O lines in geoCARB's 2323 nm band, at the spectral resolution of geoCARB the sensitivity of the spectrum to changes in CO concentration is relatively small.In response to slowly varying amplitude changes in the spectrum (such as those caused by aerosol or cloud), the L2 algorithm frequently makes large adjustments to the CO concentration, making it negative and causing the radiative transfer algorithm to fail.Our ad hoc remedy for this paper, tightening the prior error on the CO profile, improved the success rate for retrievals, but also added bias.Thus, the posterior uncertainty from the L2 algorithm understated the actual error, because the latter is the sum of both the bias and the random error.Future work should ensure that variables such as optical thickness always assume feasible values.
Higher resolving power in the 2323 nm band probably would reduce the posterior error in X CO and thereby improve the flux inversions, provided the associated reduction in S/N is not too large.However, the present design for geoCARB uses the same grating in two orders for the 2323 and 2065 nm bands, so the resolving powers will be the same for these bands.Furthermore, the parameters for geoCARB's 2065 nm band were selected to approximate the spectral performance of the 2065 nm band of OCO-2.Consequently, to obtain higher resolving power in geoCARB's 2323 nm band would require significant changes to the proposed instrument.
Because the algorithm to retrieve trace-gas concentrations assigns fixed values to some physical variables, such as the optical properties of aerosols, the Jacobians for the retrieved variables will be imperfect and a source of bias.Consequently, the posterior distribution of the retrieved state will be broader than expected.In future work we will investigate the impact on flux inversions of larger posterior errors in X CO 2 and X CH 4 , based on the results of OCO-2.
Finally we must ask what the more physically based calculations of this paper tell us about the value of a future mission with the characteristics described here.The weaker constraint on fluxes means that longer averaging periods are required before a given signal (such as an emission reduction) can be detected.However, these times remain short compared to the required timescale for policy.More important may be the reduction in spatial resolution from 3 to 5 km.This takes the results further from the scale of most businesses.

Conclusions
WRF-Chem was used to model the dynamics and composition of the atmosphere over Shanghai for a 9-day period.Models were developed for the optical properties of aerosols and clouds in the spectral bands of geoCARB, and the predicted distributions of AOD were broadly consistent with those from MODIS.The simulated urban environment should provide a rigorous case on which to test retrievals of surface fluxes.
GeoCARB observations were simulated at three times per day for each of the 9 days.The simulated spectra were degraded with noise expected for geoCARB, and columnaveraged concentrations of CO 2 , CH 4 and CO were retrieved from the spectra.Experiments were conducted to assess the accuracy of the retrieved concentrations.
1.Even though a comparatively cloud-free period was selected, many soundings were too contaminated by aerosol or cloud to permit accurate determination of the column-averaged concentrations.The experiments suggest that the number of successful retrievals might be as low as 5 %.This places a strong constraint on the complexity of the surface flux model.
2. Retrievals using preassigned aerosol optical properties, similar to those used for GOSAT and OCO-2, gave poor results.Surface pressure was biased high, while X CO 2 was low.The distributions were non-normal.Retrieval of X CO had several unidentified modes of failure.
3. When the aerosol optical properties provided to the retrieval algorithm were regionally adjusted, the results improved dramatically.Surface pressure and X CO 2 no longer had large, anticorrelated biases; distributions were closer to normal; the throughput of the retrieval algorithm improved.As justification for the regional adjustment, dark targets in the vicinity of the urban complex (such as Lake Taihu near Shanghai) could be used by other sensors (or even geoCARB) to characterise the wavelength dependence of aerosol optical thickness.This complex experiment suggests the advantages would be significant.Further examination of this idea is a priority.Appendix A: Optical properties of aerosols Within the WRF-Chem model domain, MOSAIC tracked the aerosol chemistry and predicted the spatial distributions of size-resolved mass concentrations of the aerosol species listed in Table A1.Because refractive indices are not known (or are unreliable) for some of the species, proxies were nominated, as indicated in the third column of Table A1.For example, the refractive index for sulfate ions was assumed to be the same as that for ammonium sulfate (NH 4 SO 4 ), for which laboratory data are available.The real and imaginary parts of the refractive indices of the proxies are listed in Tables A2  and A3.
Given an ensemble of aerosols, including any water coating the aerosols, the refractive index n of the composite was assumed to be the volume-weighted average of the constituents: where n a and v a denote the refractive index and volume occupied by aerosols of the species indexed by a.The volumes v a = c a /ρ a were obtained from MOSAIC's mass mixing ratios c a (µg of aerosol per kg of dry air) using densities ρ a listed in Table A4.The density of black carbon is the midpoint of the values quoted by Bond and Bergstrom (2006).
Table A3.Imaginary parts of the refractive indices of the proxies listed in Table A1 at the centres of the geoCARB spectral bands.Because the advection scheme in WRF-Chem may cause the mass and number prognostic equations to give inconsistent values, usually at sharp gradients of these quantities, MOSAIC checks internally that the predicted number density of aerosol lies between bounds determined by the limits of the size bin.For particles in the ith size bin, whose lower and upper radius limits are Similarly, let N + denote the number if the particles have the smallest size r − .In this calculation, v d is the total volume occupied by all aerosol species with the exception of condensed water; thus, v d is the total dry volume.If N, the number of particles per unit mass of dry air, falls outside the range [N − , N + ], then it is clamped: In subsequent calculations of the optical properties, N is replaced by N .
Table B1.Bin limits for the imaginary part of the refractive index.
q ν q q ν q q ν q 0 0.0000 5 0.0100 10 0.2500 1 0.0010 6 0.0250 11 0.5000 2 0.0025 7 0.0500 12 0.7500 3 0.0050 8 0.0750 13 1.0000 4 0.0075 9 0.1000 Lastly, the wet radius r w is estimated from where v w is the wet volume, given by The calculations above were performed for each size bin, providing a volume-averaged refractive index n and wet radius r w , henceforth denoted simply by r.The refractive index could vary from band to band, but within each band it was assumed to be constant.Thus, the aerosol in size bin j was characterised by one real and four complex numbers, (r, n 1 , n 2 , n 3 , n 4 ).

Figure 1 .
Figure 1.Target area around Shanghai showing the geoCARB footprints (skewed grid) and the centres of the Weather Research and Forecasting model cells (small red dots).The large red dots indicate power plants as listed by CARMA (Carbon Monitoring for Action, http://carma.org),with the sizes of the dots proportional to the annual CO 2 emissions from the plants.The distance from the south-western to the south-eastern corner of the geoCARB grid is approximately 158 km, while from the south-eastern to the north-eastern corner it is approximately 176 km.

Figure 2 .
Figure 2. The red dots show the locations of power plants as listed by CARMA (Carbon Monitoring for Action, http://carma.org).The sizes of the dots are proportional to the annual CO 2 emissions of the plants.The green dots are the emissions used in the WRF simulations, redistributed using FFDAS.

Figure 3 .
Figure 3. Aerosol optical depth over Shanghai on 8 September 2010 at 08:15 UTC in the geoCARB spectral bands.The horizontal and vertical axes are labelled by geoCARB frames and pixels.

Figure 4 .
Figure 4. Histograms of aerosol optical depth over Shanghai from the WRF-Chem simulations (grey) and from MODIS (red).The wavelength is 770 nm.

Figure 4 .
Figure 4. Histograms of aerosol optical depth over Shanghai from the WRF-Chem simulations (grey) and from MODIS (red).The wavelength is 770 nm.

Figure 5 .
Figure 5. Prior vertical profiles for volume mixing ratios of CO 2 , CH 4 and CO.

Figure 6 .
Figure 6.Histograms of the optical depths of cloud water, cloud ice and aerosol in the O 2 A-band for the cloudy simulations over Shanghai.The histogram of the optical thickness of cloud water extends to 40, but only the range [0, 10] is plotted for clarity.The biases (b) and standard deviations (SD) quoted are for the ensemble of soundings.
Figure7.Histograms of errors in retrieved surface pressure p s , X CO 2 , X CH 4 and X CO for experiment 1 with cloud-disabled and standard aerosol.The PPF has been applied to the coloured histograms, but not to those in light grey.The biases (b) and standard deviations (SD) quoted are for the histograms after the PPF.Of the total of 55 387 cases that converged, 10 995 passed the PPF (19.9 %).

D
Figure8.Histograms of errors in retrieved surface pressure p s , X CO 2 , X CH 4 and X CO for experiment 2 with cloud-enabled and standard aerosol.The PPF has been applied to the coloured histograms, but not to those in light grey.The biases (b) and standard deviations (SD) quoted are for the histograms after the PPF.Of the total of 36 000 cases that converged, 666 passed the PPF (1.9 %).For clarity, the vertical scale in the coloured histograms has been multiplied by 5.
Figure9.Histograms of errors in retrieved surface pressure p s , X CO 2 , X CH 4 and X CO for experiment 3 with cloud-enabled and regionally adjusted aerosol.The PPF has been applied to the coloured histograms, but not to those in light grey.The biases (b) and standard deviations (SD) quoted are for the histograms after the PPF.Of the total of 34 664 cases that converged, 3107 passed the PPF (9.0 %).For clarity, the vertical scale in the coloured histograms has been multiplied by 2.

Figure 10 .
Figure10.Histograms of the errors in retrieved aerosol optical depth in the O 2 A-band for experiments 1, 2 and 3 (top, middle and bottom).The PPF has been applied to the dark grey histograms, but not to those in light grey.The bias (b) and standard deviation (SD) quoted are for the histogram after the PPF.

Figure 11 .
Figure11.Posterior errors estimated by the retrieval algorithm (small dots) and actual errors (points with error bars, retrieved minus the truth weighted by the averaging kernel) plotted as functions of signal-to-noise ratio for the ensemble of soundings in the Shanghai data set that passed the PPF in experiment 3.

Figure 12 .
Figure12.Spatial distribution of E, the reduction in uncertainty in the CO 2 flux, at 00:00 UTC as determined using both X CO 2 and X CO data.

Table 1 .
Fractional assignment of EDGAR particulates to Aitken, accumulation and coarse modes.

Table 2 .
Assignment of EDGAR particulate fluxes to MOSAIC bins.

Table 3 .
Assignment of EDGAR particulate fluxes to MOSAIC bins.

Table 4 .
Spectral ranges and resolutions of the geoCARB bands for the baseline configuration.The bands at 1.606 and 2.065 µm are referred to in the text as the "weak" and "strong" CO 2 bands.

Table 6 .
The uncertainties for the scaling factors for H 2 O and CH 4 are very large, imposing almost no restraint.The uncertainty for CO is much tighter,

Table 6 .
Prior uncertainties σ (standard deviations) for the scaling factors applied to the prior profiles for H 2 O, CH 4 and CO.

Table 7 .
Success rates for converged soundings and soundings that passed the PPF.

Table 8 .
Parameters for the model of posterior error in terms of signal-to-noise ratio.

Table 9 .
Maximum error reduction (in percent).The labels 00, 06, 12 and 18 refer to the UTC time slot.

Table A2 .
Real parts of the refractive indices of the proxies listed in TableA1at the centres of the geoCARB spectral bands.

Table A4 .
Densities assumed for MOSAIC aerosol species.