Monitoring Carbon Dioxide from Space: Retrieval Algorithm and Flux Inversion Based on GOSAT Data and Using CarbonTracker-China

Atmospheric carbon dioxide (CO₂) is the most important anthropogenic greenhouse gas and is considered to be the primary cause of global warming. A lack of knowledge regarding global CO₂ emissions has introduced significant uncertainties into studies of climate change. The CO₂ flux at the surface cannot be measured directly from in-situ or satellite remote sensing, but it can be inversed from the atmospheric column-averaged CO₂ dry-air mole fraction (XCO₂) by data assimilation. Simulation studies have indicated that uncertainties in the atmospheric CO₂ balance could be reduced if a precision of 1% for global measurement data of XCO₂ can be achieved (Miller et al., 2007). Sparsely distributed in situ measurements, such as the Total Carbon Column Observing Network (TCCON) (Wunch et al., 2011a) cannot meet the global coverage requirements, especially in areas without in situ CO₂ measurements. Hence, measurements from space are a more effective way to obtain XCO₂ data for flux inversion.

The thermal infrared (TIR) measurement of CO₂ has been well studied for many years. Unfortunately, TIR measurements are only sensitive in the middle and upper troposphere, which limits their application to CO₂ surface flux studies. Hyperspectral near infrared (NIR) and shortwave infrared (SWIR) measurements, however, are able to capture the CO₂ signal in the total column, being especially sensitive to near-surface CO₂, which enables information regarding the surface flux to be collected. The SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Chartography) instrument onboard the European Space Agency's ENVISAT is the pathfinder of NIR/SWIR CO₂ monitoring (Reuter et al., 2010). However, the low spectral resolution and large field-of-view result in measurements being affected by interference factors such as cloud and aerosol. The Greenhouse Gases Observing Satellite (GOSAT) was the first NIR/SWIR greenhouse gas observing satellite, having been successfully launched in 2009 (Kuze et al., 2009). Its Thermal and Near-infrared Sensor for Carbon Observation (TANSO) Fourier Transform Spectrometer (FTS) is a state-of-the-art hyperspectral spectrometer that can capture O₂ A (0.76 μm) and CO₂ (1.61 and 2.04 μm) spectra from surface reflected sunlight (Table 1). The CO₂ information is obtained from the weak CO₂ band, while the O₂ A band and strong CO₂ band are used to correct aerosol and cloud scattering and water vapor interference (Mao and Kawa, 2004; Aben et al., 2007; Butz et al., 2009; Uchino et al., 2012).

There have been many studies on XCO₂ retrieval algorithms, such as the National Institute for Environmental Studies Full Physics algorithm (NIES-FP) (Yoshida et al., 2013), the Atmospheric CO₂ Observations from Space algorithm (ACOS) (O'Dell et al., 2012), the University of Leicester Full Physics algorithm (UoL-FP) (Böesch et al., 2011), the RemoTeC algorithm (Butz et al., 2009), and the Institute of Atmospheric Physics Carbon Dioxide Retrieval Algorithm for Satellite Remote Sensing (IAPCAS) (Yang et al., 2015). The global TCCON validation experiment confirmed that these algorithms have a precision of 1.5-2.0 ppm after the correction of systematic errors (Oshchepkov et al., 2013; Yang et al., 2015). In addition to the precision and accuracy, the total number of high quality data points is the key factor determining carbon flux inversion.

Satellite-based observations of XCO₂ have enabled a better understanding of global carbon cycling and offer an additional constraint on the estimated CO₂ fluxes used in the atmospheric inversion method (Hammerling et al., 2012a; Zhang et al., 2015). These satellite-based measurements can enhance the spatial coverage of CO₂ data and allow for better characterization of large-scale temporal, spatial, and seasonal variations of surface CO₂ sources and sinks using Bayesian inverse modeling techniques (Hammerling et al., 2012a; Inoue et al., 2013). Many studies have carried out inversion analyses of GOSAT XCO₂ measurements, with various retrieval algorithms, revealing that such retrievals are particularly useful for improving estimates of CO₂ and decreasing the uncertainties of CO₂ sources and sinks——especially in tropical regions, where the coverage of surface networks is sparse (Hammerling et al., 2012b; Basu et al., 2014, 2016;Chevallier et al., 2014; Takagi et al., 2014; Feng et al., 2015, 2016; Houweling et al., 2015; Wang et al., 2015). However, different GOSAT XCO₂ retrievals have different impacts on surface flux estimations. (Takagi et al., 2014) presented five retrieval algorithms for GOSAT XCO₂ and suggested that the influence of these five XCO₂ retrievals on regional surface flux estimates is not uniform. Also, it is dependent on the availability of both XCO₂ retrievals and surface observations within and around each region.

As a rapidly developing country, China plays an important role in the global carbon budget, due to its significant emissions of CO₂. The Chinese government is striving to find a balance between development and emissions. The "Strategic Priority Research Program of the Chinese Academy of Sciences——Climate Change: Carbon Budget and Relevant Issues" commenced in 2010 with a focus on the scientific aspects of both global and Chinese carbon emissions. The determination of methods for space-based measurement of CO₂ and its flux is a main objective of this program. With the support of this program, we have developed an advanced carbon flux inversion system for the purpose of applying satellite measurements in carbon flux inversion. The system can be considered as comprising two independent parts: the IAPCAS XCO₂ retrieval algorithm, and CarbonTracker-China (CT-China), developed at the Chinese Academy of Sciences (Peters et al., 2007, 2010; Zhang et al., 2014). The algorithm provides XCO₂ retrieval product from satellite measurements, and then CT-China uses the XCO₂ product to inverse the carbon flux (Fig. 1).

Figure 1.  Framework of the carbon flux inversion system from satellite measurements.

In this paper, we introduce our experiment by using GOSAT measurements in carbon flux inversion over China, presenting results on the distribution and seasonal variation of XCO₂ and carbon flux. The theoretical basis and method applied in the inversion system are introduced briefly in section 2. In section 3, results regarding the quality control of data and the bias correction of the GOSAT retrieval are presented. The inversed carbon flux and further discussion are given in sections 4 and 5, respectively.

As an application of the optimal estimation method (OEM) (Rodgers, 2000), a "full physics (FP)" XCO₂ retrieval algorithm called IAPCAS was developed by (Yang et al., 2015). The FP retrieval simulates the radiative transfer of a solar beam precisely by a forward model, and then adjusts the simulation F(x) to the measurement y iteratively (left part of Fig. 1). An OEM provides a convenient way to determine the solution by weighting the true state and the a priori knowledge: \begin{equation} \hat{x}={Ax}+({I}-{A}){x}_{a} , \ \ (1)\end{equation}

where x and x _a are the true state and the a priori knowledge of state vectors, respectively. I is unit matrix. Besides the CO₂ concentration, water vapor, temperature, surface pressure, aerosol, and cirrus cloud are approached synchronously in retrieval, which has been introduced in a previous paper (Yang et al., 2015). The matrix A is an averaging kernel that indicates the retrieval sensitivity derivative of a true state, \(A=\partial\hat{x}/\partial x\). The final solution is approached as a minimized cost function: \begin{equation} \chi^2=[{y}-F({x})]^{ T}{S}_\epsilon^{-1}[{y}-F({x})]+[{x}-{x}_{ a}]^{ T}{S}_{ a}^{-1}[{x}-{x}_{ a}] , \ \ (2)\end{equation} where S\(_{\epsilon}\) and S _a are the measurement error and a priori covariance matrix, respectively.

The VLIDORT (Vector Linearized Discrete Ordinate Radiative Transfer) code was used in the forward model (Spurr, 2006) to simulate the radiative transfer process. This linearization-based radiative transfer model can provide the weighting functions of state vectors along with the spectrum at the top of the atmosphere (TOA). A line-by-line (LBL) computation, with a very high spectral resolution (0.01 cm^-1), is required in the radiative transfer computation to reduce the forward model error to as low as possible. However, adopting an online LBL method is computationally very expensive, and hence cannot be used for the huge amount of daily satellite data that needs processing. Here, we use the linear-k method, which was developed and implemented successfully in the RemoTeC algorithm (Hasekamp and Butz, 2008) to improve the retrieval efficiency. The application of linear-k results is extremely effective in terms of computation speed for most observation conditions. The residuals induced by linear-k are less than 0.13%, 0.06% and 0.12% in the O₂ A, weak CO₂, and strong CO₂ bands, respectively.

The a priori CO₂ vertical mixing ratio (VMR) is most likely to be the true state before the measurement, and is usually obtained from a simulation by a chemical transfer model. However, the direct use of model gridded data will introduce a simulation bias into retrievals. To reduce this error, we have developed a monthly and latitude-varied climatology model from analysis of NOAA CarbonTracker CT2013 data (http://carbontracker.noaa.gov) (Peters et al., 2007). The interannual variation has been removed by an 11-year (2001-11) low-pass filtering technique, and the seasonal variation is described by a two-order Fourier series, with a set of fitted coefficients. The covariance matrix that constrains the retrieval is the key factor used to weight the information from the a priori knowledge and measurement. A large covariance indicates more loss constraints on the CO₂ VMR, which means that more information has to be obtained from measurements, and vice versa. Statistically, there is a very small covariance due to the slow and smooth variation of CO₂. However, we have enlarged the covariance tenfold to place more emphasis on the measurement than the a priori knowledge.

The CO₂ flux is determined using CT-China, which has been used in many carbon flux estimations studies with a focus on areas such as North America, Europe, and East Asia (Peters et al., 2007, 2010; Zhang et al., 2014). The global chemistry and transport of CO₂ is simulated by TM5 (Krol et al., 2005) in off-line mode as a forward operator, in an ensemble fixed-lag Kalman smoother (Peters et al., 2005). CT-China estimates carbon surface fluxes by minimizing the cost function of the simulation and observation of CO₂ concentration (right part of Fig. 1), \begin{equation} J=\dfrac{1}{2}[{y}_0-H({x})]^{ T}{R}^{-1}[{y}_0-H({x})]+\dfrac{1}{2}({x}-{x}_0)^{ T}{B}^{-1}({x}-{x}_0) ,\ \ (3) \end{equation} where R and B represent the covariance of the measurement and the a priori knowledge, respectively; y₀ is the measured CO₂ concentration observations, including ground-based and satellite-based CO₂; and H(x) is the modeled CO₂ mixing ratio values, corresponding to the observation operator in flux x. The carbon flux can be divided into four types: fossil fuel combustion, fire emissions, land biosphere, and ocean fluxes. The atmospheric transport model TM5, which is used in CT-China, has a global horizontal resolution of 6^°× 4^° (lat × lon), with a nested grid of 3^°× 2^° (lat × lon) over Asia and a further nested grid of 1^°× 1^° over China. The flux is optimized by a scaling factor in the inversion; and only the terrestrial biosphere and ocean fluxes, rather than fossil fuel combustion and fire emissions, are optimized.

We use ECMWF ERA-Interim data to drive TM5. The first guess and a priori knowledge of the terrestrial biosphere exchange data are acquired from the CASA-GFED2 [Global Fire Emissions Database (version 2), Carnegie-Ames Stanford Approach) biogeochemical modeling system (van der Werf et al., 2006). Ocean surface fluxes are calculated based on the difference in air-sea CO₂ partial pressure from ocean interior inversion calculations (Jacobson et al., 2007). The fire emissions are from the GFED2. The global fossil fuel emission inventory data are constructed based on China's total fossil fuel emissions from the Carbon Dioxide Information and Analysis Center (Miller, personal communication, 2010).

In situ CO₂ flask mole fraction data, provided by NOAA-ESRL (http://www.esrl.noaa.gov/gmd/ccgg/obspack/, data version 1.0.2) and the World Data Centre for Greenhouse Gases (http://ds.data.jma.go.jp/gmd/wdcgg/) are assimilated in the inversion experiment. The nine Asian in situ sites involved in these studies are listed in Table 5. For most of the continuous sampling sites at the surface, we derive an average afternoon CO₂ concentration (1200-1600 LST) for each day from the time series, while at mountain-top sites we construct an average based on nighttime hours (0000-0400 LST) to reduce the local influence and compare modeled with observed values only for well-mixed conditions.

In this study, we use GOSAT V161.160 L1B (http://data. gosat.nies.go.jp/) in the global retrieval experiment. However, the L1B data have to be well calibrated before they can be used in retrievals. TANSO-FTS/GOSAT uses a double side diffuser for solar calibration. The front side is exposed in the routine calibration during each orbit when the satellite flight path is towards the sun and the overpass is the northern polar region, and the back side is only used to calibrate the front side once a month. Degradation of the front side diffuser leads to a systematic bias in the calibrated spectra. We calibrate the degradation with a series of coefficients recommended by (Kuze et al., 2014) from a long-term vicarious calibration.

Potentially poor measurements caused by serious contamination from cloud and aerosol or complicated surface roughness have a large impact on the retrieval precision or, worse, cause the inversion to collapse (Yang et al., 2014). Hence, we need to screen out any of these measurements before retrieval, thus minimizing the chance of inefficient computation and low-quality retrievals. ERA-Interim data provide reliable surface pressure, and by comparing it with the retrieval data the modification of the light path can be determined. The computational cost is expensive if the exact retrieval is applied to surface pressure, and it is not always necessary. As an alternative, we select a couple of very narrow spectral regions in the O₂ A band, which only includes two temperature-insensitive lines. Surface pressure, surface albedo, and wave number dispersion are determined in the retrieval. A surface pressure threshold of 20 hPa is used to screen out any seriously contaminated measurements.

Before being used in the flux inversion experiment, the XCO₂ product has to be carefully validated. To achieve this, we apply a two-step optimization that includes post-processing screening and bias correction to select data with high confidence. All of the filters are shown in Table 2, with a strong constraint. The fitting residual is the primary factor that should be considered in the evaluation of retrievals. As described in section 2.1 and Eq. (2), the fitting residual can be represented well by χ². A large χ² means that the simulation is very different from the measurement and is marked as an unsuccessful retrieval, and vice versa. The ideal value of χ² is around 1, which means that the residual is almost the same level as the measurement noise. However, for GOSAT, the realistic measurement noise is worse than the official theoretical model, which causes the χ² to be much larger than 1. In our retrieval, the mean χ² is calculated separately for each band, and we recommend the use of a value lower than 5 as a threshold to indicate the low residual of the fitting spectrum. Statistical results indicate that global mean χ² of the O₂ A, CO₂ weak, and CO₂ strong band is 3.01, 2.25 and 2.77, respectively. Surface pressure (P₀) is used to estimate the light path in radiative transfer that could be modified by aerosol, cloud, and molecular scattering, and also by the interactions with surface reflectance. ERA-Interim provides an accurate global distribution of P₀. The difference in surface pressure between the retrieval and ∆ P=|P _0,retrieval-P _{0,ERA-Interim}| represents a significant light path modification. Analysis of the global retrieval indicates the standard deviation (1σ) of ∆ P to be 5.17 hPa. In this study, we abandon retrievals with a ∆ P larger than 2σ (∼ 10 hPa). The blend albedo filter, which was recommended by (Wunch et al., 2011b), is used to indicate the ice- and snow-covered surfaces. (O'Dell et al., 2012) used another form, introduced as the ratio of the albedo of the O₂ A and strong CO₂ bands. A retrieval test indicates the blend albedo to be more appropriate for use in this study, and a blend albedo of greater than 1 is recognized as an ice- and snow-covered surface that is inappropriate for further use as high quality data.

Figure 2.  The post-screening processing filters (a-k) for retrieval quality control. Chi² and Delta P0 mean χ² and ∆ P in section 2.3. The grey- and blue-colored histograms indicate the frequency for each 0.5 ppm error bin before and post filtering, respectively. The red histogram in (l) shows the final result after post-screening processing.

Figure 3.  Seasonal variation of IAPCAS-GOSAT (blue) against the TCCON (grey) XCO₂ product globally. (a) Bialystok (53.23^°N, 23.03^°E), (b) Caltech (34.14^°N, 118.13^°W), (c) Darwin (12.43^°S, 130.89^°E), (d) Garmisch (47.48^°N, 11.06^°E), (e) Karlsruhe (49.1^°N, 8.44^°E), (f) Lamont (36.6^°N, 97.49^°E), (g) Lauder (45.04^°S, 169.68^°E), (h) Orleans (47.97^°N, 2.11^°E), (i) ParkFalls (45.95^°N, 90.27^°W), (j) Saga (33.24^°N, 130.29^°W), (k) Tuskuba (36.05^°N, 140.12^°E), (l) Wollongong (34.41^°S, 150.88^°E).

We also use three other simple filters: (1) a solar zenith angle filter to remove measurements with very slanted solar incident light conditions; (2) a particle optical depth (including aerosol and cirrus) filter to remove any highly contaminated scattering scenes; and (3) a post-prior XCO₂ uncertainty filter to remove measurements with little information. In summary, the χ² screens out most of the "bad" retrievals, and the post-posterior XCO₂ and total optical depth [total OD includes aerosol optical depth (AOD) and cloud optical depth (COD)] are the second- and third-most important factors, respectively (Fig. 2). In the validation experiment, about 43% of the data are marked as "bad" by the filters. However, the proportion of "bad" retrievals grows when a post-screening process is applied to the global retrievals, with only 25%-30% of data remaining.

A ppm bias is apparent in the raw statistical data, and this bias remains after the post-screening process, with no significant changes, suggesting it is not caused by a "bad" fitting of the spectrum. Most atmospheric and surface parameters that have a significant impact on TOA radiance are corrected in the retrieval. Unfortunately, there are still some errors that remain in the calibration, forward model, and atmospheric and surface model, which display systematic error when validated against global TCCON measurements. We select all of the TCCON sites for the validation when there are coupled measurements (Fig. 3). TCCON measurements made within 2 hours of the satellite overpass over a 550 km distance are selected for the validation experiment. The error of the retrieval is calculated by subtracting the 2-hour mean of the TCCON measurement. We investigate the error correlation of latitude, time, air mass [1/cosθ+1/cosφ, in which θ and φ represent the solar zenith angle and view angle, respectively], surface pressure, aerosol optical depth, cloud optical depth, χ² of each band, albedo ratio, and blend albedo, and find that only surface pressure, air mass, and blend albedo have an obvious correlation with the retrieval errors (Fig. 4). A polynomial fitting is used to correct the systematic bias: \begin{eqnarray} \Delta { XCO_2}_{ bias}&\!=\!&c_{P_0}(P_0-\bar{a}_{P_0})+c_{ Airmass}(X_{ Airmass}-\bar{a}_{ Airmass})+ c_{ Blend_albedo}(X_{ Blend_albedo}-\bar{a}_{ Blend_albedo})+c ,\quad\ (4)\end{eqnarray} where c and \(\bar{a}\) are the polynomial coefficient and reference value of the subscript parameter, respectively (Table 3). X _Airmass and X _{Blend_albedo} is the value of airmass and blend albedo for each measurement. The root-mean-square error (RMSE) and correlation coefficient (r) are shown in Fig. 3, along with the total sample quantity (N). The mean RSME and r of all 12 TCCON sites improves from 3.03 ppm and 0.49 to 1.47 ppm and 0.76, respectively, after the bias correction is performed. Further validation results of the IAPCAS XCO₂ product are reported in (Yang et al., 2015).

The seasonal variations of XCO₂ compared with the TCCON measurements are shown in Fig. 4. Most retrievals agree well with the TCCON measurements, although a small bias is apparent at Darwin and Garmisch in winter and summer, respectively, and hence needs to be improved in further investigations. In the Northern Hemisphere, the satellite captures the seasonal variation over all TCCON sites, which are distributed across Europe, the United States, and Japan. Only a slow increase is found throughout the whole year in the Southern Hemisphere. The daily average XCO₂ correlation coefficient between the IAPCAS-GOSAT retrieval and all 12 TCCON site measurements is 0.59, with a maximum value of 0.84 at Park Falls and minimum value of 0.28 at Saga.

Figure 4.  The relation between XCO₂ error and (a) ∆ P₀ (delta P₀), (b) air mass residual, and (c) blend albedo. The validation of bias correction is indicated in (d). Grey and blue points indicate before and after bias correction, and the dark grey line shows the 1:1 ratio. The RSME and correlation coefficient (r) are shown along with the quantity of "good" data (N).

The CO₂ concentration in the atmosphere is balanced, and is significantly impacted by anthropogenic emissions, ecosystem uptake by photosynthesis, and respiration. Land cover and population data can be used in analyses of XCO₂ seasonal variation. The MODIS (Moderate Resolution Imaging Spectroradiometer) instrument onboard the Aqua and Terra satellites provides global 0.05^° grid land cover data for the International Geosphere Biosphere Programme (IGBP), with 17 land cover classifications. GOSAT observations have a 10 km circular footprint at 150 km intervals on average. The original IGBP classification is not appropriate for such coarse spatial resolutions and sparse sampling. We combine similar types of land cover and reclassify them into seven types (Table 4). Because the GOSAT nadir observation has limitations over water and snow surfaces, we only study the seasonal variation of forests, small plants, barren land, ploughed areas, and built-up land (Fig. 5a). Population has a strong correlation with anthropogenic activity, and is also connected to urban and industrial areas. NASA's SocioEconomic Data and Applications Center (SEDAC) provides Gridded Population of the World V3.0 (GPW V3.0) forecast data for 2010-12. Population studies in the social sciences have suggested that population density can be classified into five levels of 0-1, 1-25, 25-100, 100-250, and more than 250 persons km^-2 (Fig. 5c).

Assessment of the monthly variation of XCO₂ reveals a smooth increase from early autumn to late spring and a rapid decrease in early summer. A significant difference in XCO₂ appears in autumn and winter. Ploughed and built-up land have XCO₂ values that are 2 ppm larger than those for barren areas and sparsely vegetated land on average. Similar results were obtained in an ensemble average analysis study of the XCO₂ distribution in China in 2010 (Yang et al., 2016). The presence of ploughed and built-up land indicates a high level of anthropogenic activity, with a similar pattern observed in densely populated areas (>25 persons km^-2). The XCO₂ over forests displays a similar trend as that over barren areas and sparsely vegetated land in the autumn and winter, but in summer the rate of increase slows down, and in April it is more similar to ploughed and built-up areas. Figure 5d also indicates that the XCO₂ is 10 ppm lower in summer than in late spring, but for densely populated areas (>100 persons km^-2) the value is still high. The XCO₂ indicates anthropogenic activity and ecosystem-related variations in China. However, due to the transfer and mixing of CO₂ by atmospheric dynamic processing, the accuracy of carbon emissions and sinks must be analyzed through a data assimilation and inversion system.

Two inversion experiments are conducted for the year 2012. The first (in situ-only) was run with only in situ CO₂ flask concentration data (Table 5), and the second (Case IAPCAS-GOSAT) is run with in situ CO₂ flask data and IAPCAS-GOSAT XCO₂ measurements. The only difference between the in situ-only and IAPCAS-GOSAT inversion is the application of satellite measurements. As mentioned in the previous section, for each experiment, only the biosphere and ocean fluxes are optimized in CT-China. The CO₂ flux shown in the following section is the net ecosystem CO₂ exchange (NEE), which includes a constant fire emission rate of 0.01 Pg C yr^-1, but excludes a fossil fuel emission rate of 2.63 Pg C yr^-1 (the same thereafter). Note that a negative signal indicates a CO₂ sink, while a positive sign denotes a source.

Figure 5.  The distribution of (a) reclassified IGBP land cover and (b) SEDAC-GPW V3.0 population in China against the monthly variation of XCO₂. The cyan, green, blue, red, and black lines in (b) indicate forest, sparse vegetation, ploughed land, barren area, and built-up land, respectively, corresponding to the classification in (a) and Table 4. The cyan, green, blue, red, and black lines in (d) show the population in the regions with a density of 0-1, 1-25, 25-100, 100-250, and >250 persons km^-2, respectively, corresponding to the classification in (c).

Figure 6.  The distribution of NEE in China from spring (March-May, MAM), summer (June-August, JJA), autumn (September-November, SON), and winter (December-February, DJF) (columns 1-4). The first line is a priori knowledge from before data assimilation; the second and third lines indicate the in situ-only and IAPCAS GOSAT flux inversions; and the final line shows the difference between the in situ-only and IAPCAS GOSAT results.

Table 6 shows the Chinese annual variations of the prior/ posterior land sinks of the two experiments. In 2012, we estimate a net terrestrial CO₂ uptake (a postieriori) of -0.34 Pg C yr^-1 in the IAPCAS-GOSAT inversion over China, with Gaussian uncertainties of 0.08 Pg C yr^-1 (1δ). This estimate is very close to the previous results of (Piao et al., 2009) (-0.35 Pg C yr^-1, 1996-2005 annual average), (Zhang et al., 2014) (-0.33 Pg C yr^-1, 2001-10 annual average), and (Jiang et al., 2016) (-0.35 Pg C yr^-1, 2006-09 annual average). Comparing the IAPCAS-GOSAT and in situ-only experiments, although similar prior carbon flux (-0.05 Pg C yr^-1) is used, they show large differences (∼ 0.17 Pg C yr^-1) in the posterior uptake values of China, with a carbon uptake of -0.34 Pg C yr^-1 for IAPCAS-GOSAT inversions and CO₂ flux of -0.51 Pg C yr^-1 for the in situ-only experiment. This is generally consistent with other GOSAT inversion experiments insofar as including additional GOSAT XCO₂ observations into the atmospheric inversion will change the regional carbon flux estimates significantly, particularly for areas with sparse observational coverage (e.g., China) (Chevallier et al., 2014; Basu et al., 2016; Deng et al., 2016; Feng et al., 2016). We further examine the impacts of the GOSAT XCO₂ data on Chinese flux estimation by comparing the flux uncertainty results from IAPCAS-GOSAT and in situ-only inversions. The Gaussian uncertainties of flux inversion with and without GOSAT data are listed in Table 6, with posterior uncertainty estimates of 0.08 and 0.38 Pg C yr^-1 (1δ) averaged weekly background covariance over the whole year of 2012. Compared to their previous error levels, both inversions' uncertainties display obvious uncertainty reduction, with 22% and 84% error reduction for the in situ-only and GOSAT assimilations, respectively. It is also clear, however, that by including the additional GOSAT data into the IAPCAS-GOSAT inversion, the uncertainty reduction of the posterior flux over China is greater (∼60%) than that of the in situ-only inversion. This suggests that current surface CO₂ observational data alone do not sufficiently constrain Chinese regional flux estimations, and the additional GOSAT XCO₂ observations impose an extra constraint that can help reduce uncertainty in inferred Chinese CO₂ fluxes (Fig. 6).

Figure 7.  The IAPCAS-GOSAT retrieval product spatial coverage and frequency in China in spring, summer, autumn and winter. Blue points indicate the in situ sites used in the in situ-only inversion experiment. There are three far-away sites (Asian surface CO₂ sites, but outside of China)——namely, BKT, WIS and MNM——not shown in the figure.

The seasonal spatial distributions of the inversed CO₂ surface flux for the IAPCAS-GOSAT and in situ-only inversions are shown in Fig. 7. The amplitude of Chinese terrestrial ecosystem CO₂ flux displays a clear seasonal cycle in these two experiments, with the strongest sink in summer and weakest sink in winter. This seasonal variation is reasonable and agrees with many previously studies in which it has been reported that suitable temperature, precipitation, and solar radiation may result in high carbon uptake in summer, while negative effects of climate factors induce a strong source in winter (Jiang et al., 2013; Qu et al., 2013; Zhang et al., 2015). The inferred surface land flux also shows obvious spatial variations in the IAPCAS-GOSAT and in situ-only experiments, with the strongest carbon uptake over the northeast of China in summer. It is well known that the spatial distribution of terrestrial carbon sinks is largely related to land cover types (Peters et al., 2007, 2010; Zhang et al., 2014). For the northeast of China, a large area (155 710 km²) is dominated by old-warm coniferous forests and theropencedrymion of a cool temperature region, which contributes strong gross primary production and low respiration to a high amount of carbon flux in Northeast China.

A large seasonal difference is found between the APCAS-GOSAT and in situ-only inversions, especially for the spatial distribution pattern of the North China Plain in winter, which is a strong sink in the in situ-only estimate but a carbon source in the IAPCAS-GOSAT result. This discrepancy in spatial distribution is mainly due to the lack of CO₂ surface measurement in the in situ-only assimilation, which in turn leads to an overestimation of carbon uptake in the North China Plain. This issue was also raised in (Zhang et al., 2014), i.e. that the atmospheric inversion system implements a limited optimization of a priori knowledge without any constraint from observation over the North China Plain, inducing an apparent anomaly for the strong sink of the North China Plain in winter. In fact, there is only sparse vegetation and some ploughed land over this area due to the extremely cold and dry weather at that time. Thus, satellite measurements improve the data coverage in spatial terms significantly, and provide an additional constraint on the estimated CO₂ concentrations and fluxes of the atmospheric inversion method.

This study introduces a carbon flux inversion system for estimating the carbon flux from satellite measurements, developed with support from "The Strategic Priority Research Program of the Chinese Academy of Sciences——Climate Change: Carbon Budget and Relevant Issues". The carbon flux inversion system is composed of two separate parts: an XCO₂ retrieval algorithm (IAPCAS), and an inversion tool (CT-China).

Here, IAPCAS is used for XCO₂ retrieval from GOSAT measurements. We introduce a post-screening and bias correction method developed for improving the quality of the product, before applying it in flux inversion. After post-screening, 25%-30% of the data remain and are marked as "good" retrievals. Global validation studies with TCCON measurements indicate a better than 1.47 ppm regional-scale precision after the bias correction. The trend in XCO₂ agrees with TCCON measurements, which display a seasonal variation in the Northern Hemisphere and smooth increase in the Southern Hemisphere. The seasonal variation of XCO₂ against land cover and population over China is analyzed. Average differences of 2 ppm between winter and spring indicate the impact of anthropogenic activity on CO₂ concentrations in the atmosphere.

Next, we introduce a carbon flux inversion experiment that applies the IAPCAS-GOSAT product in CT-China. Based on this, NEE is estimated as -0.34 Pg C yr^-1, with a large error reduction of 84%, which is a significant improvement in error reduction when compared with the in situ-only inversion. The results also indicate that satellite measurements can provide a global coverage dataset for the estimation of carbon fluxes, if the required accuracy and precision can be met. The amount of valid data has a significant impact on carbon flux inversions. A set of extremely strict quality control thresholds are established to ensure the data quality. However, the small quantity of data that remains cannot significantly improve the amount of information, because the information has been already provided by in situ measurements, which means that information is still lost for some key regions, e.g., mega cities. In contrast, a very loose post-screening cannot filter out any risky data and may therefore induce errors in the flux inversion. In this study, we use three sets of quality control thresholds, with levels set from high to low. The inversed flux is very sensitive to both data quality and quantity. In addition, a data quality control process is applied in the flux inversion before use. Control experiments also indicate that the inversed flux is very sensitive to the constraint of a data filter. Therefore, the lack of valid measurements is still a source of error in carbon flux inversions; this needs to be improved in future studies.

There is an anomaly in the seasonal variation of ecosystem carbon fluxes, as indicated in Fig. 6. For example, a weak sink appears in Inner Mongolia and the Tibetan Plateau in spring (March-May, MAM), and a strong source appears in Sichuan and the North China Plain in winter and autumn. In addition to the quality of satellite measurements and constraints in data assimilation, there are two main reasons for these errors. First, in this study, we assume that the difference between measured and a priori knowledge for CO₂ is only due to uptake and emissions in ecosystems, with a fixed emission from anthropogenic activity. In reality, there is large uncertainty in emissions from industry and fossil fuel combustion, and the inversion result could therefore be influenced by these sources. The XCO₂ measurement can only provide information regarding the total CO₂ flux, which cannot distinguish between natural and anthropogenic sources. Therefore, in future studies, accurate measurements of associated greenhouse gases (e.g., carbon monoxide and methane) are required to provide more information on different sources of carbon emissions. The second reason is the bias that remains in the retrieval product. There are many factors that could induce a bias, e.g., retrieval algorithms, forward simulations, and systematic measurement errors. We correct the global bias using TCCON measurements; however, this is not suitable for China because of the complicated atmospheric (e.g., aerosol) and surface conditions. A validation in China could make a contribution to bias correction and subsequently improve the flux inversion.