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A comprehensive estimate of recent carbon sinks in China using both top-down and bottom-up approaches

Atmospheric inversions use measurements of atmospheric CO2 gradients to constrain regional surface fluxes. Current inversions indicate a net terrestrial CO2 sink in China between 0.16 and 0.35 PgC/yr. The uncertainty of these estimates is as large as the mean because the atmospheric network historically contained only one high altitude station in China. Here, we revisit the calculation of the terrestrial CO2 flux in China, excluding emissions from fossil fuel burning and cement production, by using two inversions with three new CO2 monitoring stations in China as well as aircraft observations over Asia. We estimate a net terrestrial CO2 uptake of 0.39–0.51 PgC/yr with a mean of 0.45 PgC/yr in 2006–2009. After considering the lateral transport of carbon in air and water and international trade, the annual mean carbon sink is adjusted to 0.35 PgC/yr. To evaluate this top-down estimate, we constructed an independent bottom-up estimate based on ecosystem data, and giving a net land sink of 0.33 PgC/yr. This demonstrates closure between the top-down and bottom-up estimates. Both top-down and bottom-up estimates give a higher carbon sink than previous estimates made for the 1980s and 1990s, suggesting a trend towards increased uptake by land ecosystems in China.

The carbon balance of China is characterized by the World's highest emissions of CO 2 from fossil fuel use and substantial carbon sequestration in intensively managed ecosystems. The large land area of China (6.4% of the global land mass), coupled to its rapid economic development, its large food production, and its recent large-scale afforestation practices puts its carbon cycle in the center of current global carbon cycle research. Top-down atmospheric inversions 1,2 have used globally distributed stations measuring atmospheric CO 2 mole fraction observations to provide estimates of surface-atmosphere CO 2 fluxes over large (>10 6 km 2 ) spatial areas. One limitation of inversions is the insufficient density of atmospheric stations over continental regions. In this study, we derive new top-down calculations of China's CO 2 budget, by combining new atmospheric CO 2 observations within and around China, with two independent atmospheric inversion systems. We additionally conduct a synthesis of the bottom-up carbon budget of China's terrestrial ecosystems to gauge the convergence between these independent streams of information.

Results
Top-down estimate. Atmospheric inversions 3 , quantify net CO 2 fluxes at the surface of the Earth, based on transport models and atmospheric CO 2 observations. In this process, a higher density of observations allows more detailed estimates of fluxes. In China, only one high altitude monitoring station (Mt Waliguan) in the western part of China 4 has been available to constrain the published estimates up until 2006. Since then, the Chinese Meteorological Administration (CMA) installed three additional surface GHG monitoring stations 5 . In addition, CO 2 measurements on board of passenger aircraft, with vertical profiles at selected airport locations and horizontal transects at the cruising altitude of aircraft, have been acquired over Asia and Europe 6 since July 2005 by the Comprehensive Observation Network for Trace gases by AirLiner project (CONTRAIL). These CO 2 observations form the basis for the revised top-down estimate of the CO 2 budget of China.
We use two well-established inversion systems, a nested Bayesian inversion (BI) system 7 and the CarbonTracker-China (CTC) system 8 1,[9][10][11][12] . When the three new CMA stations are assimilated into the BI and CTC systems, the inverted terrestrial CO 2 sink in China increases to 0.43 ± 0.19 and 0.29 ± 0.35 PgC yr −1 , respectively. When both CMA and CONTRAIL data are assimilated, the sink further increases to 0.51 ± 0.18 and 0.39 ± 0.33 PgC yr −1 , respectively (Fig. 1). The two inversion systems thus consistently show that when new CO 2 measurements within or around China are included, the inverted CO 2 sink in China gets larger and its uncertainty is reduced. With the new CO 2 data added, the mean inverted CO 2 sink in China is 0.45 ± 0.25 PgC yr −1 , which is a higher than previous inversions. In inversions, the inferred sinks depend on the value being assumed for CO 2 emissions from fossil fuel burning and cement production (FFCO 2 ). There is a rather large uncertainty of FFCO 2 in China, as evidenced by differences between published estimates 13,14 . In this study, we used as a reference FFCO 2 from the Carbon Dioxide Information Analysis Center (CDIAC) 15 16 , Guo et al. 17 and Pan et al. 18 estimated that forest biomass carbon stock accumulated at a rate of 0.174, 0.104, and 0.115 PgC yr −1 during the 2000s, respectively. We use the mean and standard deviation of these three estimates, which is 0.13 ± 0.038 PgC yr −1 . This is larger than the value of 0.075 ± 0.035 PgC yr −1 reported by Piao et al. 9 during the 1980s and 1990s, suggesting that forest biomass carbon gains in 2000s significantly increased from 1980s and 1990s. In addition, short rotation forests and bamboo plantations were estimated to have accumulated 0.009 ± 0.006 PgC yr −1 in total 16,17 , and woodlands, shrub, tree on non-forest lands were estimated to have a sink of 0.016 ± 0.011 PgC yr −1 in total 16 . Due to lack of more recent research results for grasslands, we use the same estimate than Piao et al. 9

Consistent top-down and bottom-up estimates.
The bottom-up estimate of carbon stock change in vegetation and soil is still much lower than the inversion results. That is because inland waters, ocean and wood products are also reservoirs for terrestrial carbon and the inverted CO 2 sink is also influenced by CO 2 from the oxidization of net imported products and reduced carbon compounds (RCC) emitted from fossil fuels and ecosystems. We then try to reconcile top-down and bottom-up results as follows: where biogenic RCC includes RCC from biomass burning and biogenic volatile organic carbon emissions. Net ecosystem productivity (NEP) is the difference between photosynthesis and respiration in terrestrial ecosystems, which is also estimated from the top-down and bottom-up results to provide a full picture of the carbon cycle in China. All items in the above equations are positive. Equations (2) and (3) are straightforward to understand, and details of equation (1) are given in the Supplementary Material. Fossil fuel emission inventories, i.e., CDIAC, are based on CO 2 emission factors that include direct emissions of CO 2 from fossil fuels and emissions of RCC, e.g., carbon monoxide (CO), methane (CH 4 ) and non-methane volatile organic carbons (NMVOCs) that are later oxidized into CO 2 22 . When the total fossil fuel emission is treated as all CO 2 emission, as done in most inversion studies including ours, the contribution of the emission to the regional near surface CO 2 concentration is overestimated. That is because, after emission to the atmosphere, NMVOCs is first oxidized to CO, which is subsequently oxidized to CO 2 . The NMVOCs oxidation process is typically fast (hours), while the CO oxidation process is rather slow (1-2 months). CH 4 is also oxidized to CO 2 at a very slow rate. Generally, these oxidation processes will occur during the air mass transport, and therefore non-CO 2 carbon species emitted from one region (e.g., China) will transform into CO 2 globally rather than locally. Hence, the treatment of non-CO 2 carbon species as direct CO 2 emission in inversions will tend to overestimate the contribution of fossil fuel emission to CO 2 concentration over China in inversions, causing overestimation of the inverted carbon sink, i.e. too high sinks needed to offset CO 2 gradients due to too high emissions 23 . During 2006-2009, China emitted RCC at a rate of 0.102 ± 0.007 PgC yr −1 , including 0.072 ± 0.005 PgC yr −1 of CO, 0.019 ± 0.001 PgC yr −1 of NMVOCs and 0.011 ± 0.001 PgC yr −1 of CH 4 on average, roughly 14% of these emissions were converted to CO 2 in the boundary layer over China, 12% were deposited to the land surface, and the remaining 74% were transported to the global atmosphere 24 . Therefore, the "fossil fuel RCC transferred to global atmosphere" term in Eq. 1 is 0.076 ± 0.0050 PgC yr −1 , and the "fossil fuel RCC deposited to land" term in Eq. 1 is 0.012 ± 0.0010 PgC yr −1 .
The Global Fire Emission Database (GFED) biomass burning emission dataset, explicitly separates CO 2 , CO, CH 4 and NMVOC emissions. Based on GFED v3.1 25 , emissions of CO 2 and RCC from biomass burning are 0.016 and 0.0020 PgC yr −1 , respectively over China. In addition, land ecosystems also directly release biogenic RCC, including NMVOC and CH 4 . Their emissions over China are estimated to be 0.021 ± 0.010 and 0.027 ± 0.013 PgC yr −1 , respectively. The "biogenic RCC emission" term in Eq. 3 is 0.050 ± 0.024 PgC yr −1 , and the "biogenic RCC deposition" term in Eq. 3 is 0.0060 ± 0.0020 PgC yr −1 , taken as 12% of the sum. The "biogenic RCC transferred to global atmosphere" term in Eq. 1 is 0.037 ± 0.018 PgC yr −1 , which is 74% of the biogenic RCC emission. It is a negative adjustment to the top-down land sink estimate because 74% of the biogenic RCC (carbon source) is lost to the global atmosphere and not captured by the inversion 24 .
The net imports of forest and crop products from outside China, which are decomposed in China and become additional sources of carbon to the atmosphere are included in the top-down sink estimates, but should be subtracted from it to be compared with the bottom-up ecosystem carbon stock change estimate, which does not count wood and crop products stocks. Moreover, carbon accumulated in forest products is a net accumulation of carbon that should be included in the bottom-up estimate 26 . Based on the Food and Agriculture Organization Scientific RepoRts | 6:22130 | DOI: 10.1038/srep22130 of the United Nations (FAO) statistical databases 27 , we estimate that 0.012 PgC of wood and 0.019 PgC of food were imported into China every year during 2000s. The net imported food is assumed to be fully consumed and oxidized to CO 2 in the same year, while only a portion of the net imported wood products is fully oxidized. The remainder goes into long-term products and is slowly oxidized over time. Using the method of Winjum et al. 28 , we calculate that during 2006-2009, the CO 2 emission due to net wood import is 0.006 PgC yr −1 , and the net accumulation of carbon in wood products made by local harvests in China during 2000s is 0.005 PgC yr −1 . Therefore, the "net import" term in Eq. 1 is 0.025 PgC yr −1 , and the "accumulation in products" term in Eq. 2 is 0.0050 PgC yr −1 .
Inland aquatic systems are now considered as a significant component of land-atmosphere CO 2 fluxes 29,30,31 . Globally, about 2.1 PgC yr −1 of carbon are transported from terrestrial landscape to inland waters, in which 1.7 PgC yr −1 is from soil erosion and 0.4 PgC yr −1 is from rock weathering 32 . In this study, we estimate that inland waters of China annually receive 0.12 ± 0.06 PgC yr −1 of carbon from land, in which 0.105 ± 0.052 PgC yr −1 is from eroded soils and 0.015 ± 0.008 PgC yr −1 is from rock weathering (half of the exported dissolved inorganic carbon (DIC) 24 ). During the inland water carbon transport processes, about 0.020 ± 0.010 PgC yr −1 of carbon is buried in aquatic sediments, and 0.062 ± 0.030 PgC yr −1 is returned to the atmosphere, and the remainder of 0.038 ± 0.019 PgC yr −1 is delivered to the coastal ocean, including 0.008 ± 0.004 PgC yr −1 of total organic carbon (TOC) and 0.030 ± 0.015 PgC yr −1 of DIC. The amounts of carbon that are transported to ocean, buried in the sediment and outgassed to the atmosphere in China are estimated to be all lower than those in Europe, but the relative fractions among burial, outgassing, and transport to the ocean are close to those in Europe 24 . Therefore, the "burial in aquatic sediments" term in Eq. 2 is 0.020 ± 0.010 PgC yr −1 , the "delivery to ocean" term in Eq. 2 is 0.023 ± 0.010 PgC yr −1 (i.e., TOC + DIC/2), and the "CO 2 outgassing" term in Eq. 3 is 0.062 ± 0.030 PgC yr −1 .
By including the various fluxes outlined above (see details in the Supplementary Material), the land sink estimates by the top-down and bottom-up methods are adjusted to 0.35 ± 0.23 (mean range 0.29-0.41) PgC yr −1 and 0.33 ± 0.14 PgC yr −1 , respectively, and the corresponding NEP estimates are 0.47 ± 0.28 PgC yr −1 and 0.45 ± 0.19 PgC yr −1 (Fig. 2).

Discussion
The top-down and bottom-up estimates are consistent within their respective uncertainties. A full picture of the carbon cycle of China is shown in Fig. 3. However, considerable sources of systematic uncertainties still exist in these estimates, and the real uncertainties of both top-down and bottom-up estimates are likely higher than those calculated above.
The top-down results for south and southwest China are very uncertain ( Supplementary Fig. S3, Fig. S4), although the results for eastern and northern China from different inversion systems are consistent within their uncertainties. Generally, significant and spatially explicit constraints on fluxes can be obtained in locations near and immediately upwind of surface measurements 33 . In south and southwest China there are no local surface CO 2 observations and very few air masses from these regions move to existing observation stations ( Supplementary  Fig. S5). Although the inverted carbon sinks are significantly sensitive to the additional CO 2 observations, the total error reduction is very limited, only about 10~14%. New atmospheric CO 2 measurements in south, southwest, and central China should be added to improve this further.
We also assume that the fossil fuel emissions from China are perfectly known, and therefore fixed in the inversions, but previous studies show that there is an uncertainty of about 7~9% in these emissions 13,14 . This amounts to ~0.12 PgC yr −1 during 2006-2009. The systematic error of emissions is thus comparable to the random uncertainty of inversion results. However, since a bias in fossil fuel estimation would influence all inversions in the same way, our finding that the inverted carbon sink in China increases when the new CO 2 observations used for China (as shown in Fig. 1) would not change if we adopted another fossil fuel estimate.
In the bottom-up approach, some estimates are very coarse and some are not included: 1) the conversion rate of 14% from non-CO 2 species to CO 2 in the boundary layer is from a simulation in Europe 24 , which may depend on air pollutants emission strength and the size of the region, and thus this value may be different for China's landmass; 2) the carbon accumulation for harvested wood is estimated based on empirical coefficients of limited cases 28 ; 3) carbon transport in inland waters is estimated based on limited measurements in main rivers and lakes of China, which do not cover the entire country, and the estimate of carbon transport from terrestrial ecosystem to rivers (0.105 ± 0.050 PgC yr −1 ) is lower than a recent result of 0.19~0.24 PgC yr −1 which was calculated using the Revised Universal Soil Loss Equation (RUSLE) model 34 ; 4) a small amount of forest and shrub soil carbon may contribute to the lateral transport of carbon in rivers but this amount is not included in models used for these ecosystems, and therefore modeled soil carbon sinks may be overestimated by this small amount; and 5) emissions from the net import of meat and cooking oil and domestic biofuel consumption are not considered. Furthermore, the top-down estimate is for the late 2000s (2006-2009), while the bottom-up estimate is mainly for the 2000s. Recent evidence suggests that warmer temperatures in China since then 7 , as well as afforestation/reforestation of previously cleared land, has lead to an intensification of Asia's land carbon sink that contributes partly to the increasing trend for the global land sink during 2000s 35 .
We conclude that the land sink in China's terrestrial ecosystems is 0.34 ± 0.19 PgC yr −1 during 2000s, which is larger than the comprehensive estimate of 0.19~0.26 PgC yr −1 by Piao et al. 9 for the 1980s and 1990s. In Piao's estimate, burial in aquatic sediments and delivery to the oceans were not included. But it is also possible that the CO 2 sink in China actually has intensified between the 1990s and the 2000s as other studies found that between 1989-1998 and 1999-2008, China's forest area and carbon density increased by 14% and 12%, respectively, causing the biomass carbon sink to increase by 0.14 PgC yr −1 16,18 . Our results show that the use of additional CO 2 observations within and around China doubles our top-down sink estimates and makes it possible to achieve the closure between top-down and bottom-up estimates.  Administration (CAMS/CMA) 5 , and aircraft CO 2 measurements from Nov 2005 to Dec 2009 over Eurasian by the Comprehensive Observation Network for Trace gases by AirLiner (CONTRAIL) project 6 are used in both systems. The three CAMS/CMA sites are all regional background stations, which are located in Northeast China (LFS), North China (SDZ), and East China (LAN), and with altitudes of 330, 293 and 139 m, respectively. The air intake height is 10 m above ground level for all three sites. The measurements in these stations are sampled and analyzed using the recommended methods of WMO/GAW, and the accuracy is comparable with that of NOAA/ESRL 5 .

Materials and Methods
Simulation for the soil carbon fluxes over forest land. The Integrated Terrestrial Ecosystem C-budget (InTEC) model 19 , which is a regional C-budget model, is used to simulate the soil carbon fluxes over forest land. It combines the CENTURY model for soil C and nutrient dynamics and Farquahar's leaf biochemical model for canopy-level annual photosynthesis implemented using a temporal and spatial scaling scheme. In this study, the InTEC model is run from 1901 to 2012. The simulation region covers the whole China, with a horizontal resolution of 1 km × 1 km. LAI, NPP, forest cover and stand age data in 2005; climate data during 1901-2012, nitrogen deposition data during 1901-2010, soil data, and CO 2 data during 1901-2012 were used to driving the InTEC model. No forest management was considered. Forest disturbance was considered according to the stand age. Carbon transport by rivers. The carbon delivered to the ocean through rivers include dissolve organic carbon (DOC), dissolve inorganic carbon (DIC) and particulate organic carbon (POC). Nine Chinese exorheic rivers are considered, including the Yangtze River, Yellow River, Pearl River, Huai River, Hai River, Liao River, Songhua River, Qiantang River and Min River. For the Yangtze River, Yellow River and Pearl River, we use the observations by respectively Wu et al. 37 , Ran et al. 38 , and Zhang et al. 39 . For the Hai and Liao rivers, we use the observations by Xia and Zhang 40 , and for the other 4 rivers there are no observations available to date. We use several simple methods to estimate the transport: for DOC, we use the mean concentration of Yellow and Yangtze River, for DIC, we use the mean DIC/DOC ratio observed in the five rivers, and for POC we use an empirical formula 41 .
The CO 2 outgassing from inland waters in China is calculated based on limited observations of CO 2 outgassing rates in the past decade and the water surface area is reported by the National Bureau of Statistics in China. For rivers and steams, the observations in Pearl River, Yangtze River and Yellow River are used [42][43][44] ; for reservoirs, the observations in five reservoirs in Yangtze River are used 45 ; and for natural lakes, the average of global natural lakes 46 is adopted directly.
The carbon burial in lakes and reservoirs are estimated using the data reported by Gui et al. 47 and Dong et al. 48 , which both covered lakes in the middle and lower reaches of the Yangtze River Basin. The mean rate of these two studies is about two times the global mean rate. For the reservoirs, due to lack of observations, we assume that the carbon burial rate in Chinese reservoirs is also about two times of the global mean rate.
Trade of food and wood. The import and export data of food and wood products from the FAO statistical databases 27 are used. The food products include cereals, roots, sugar, soybeans and pulses, oil crops, vegetables, fruits, coffee and teas. The wood products include sawn wood, wood-based panels, paper and paperboard, recovered paper, other industry roundwood, and wood fuel and charcoal. Every year, the food products and the wood products of wood fuel and charcoal are assumed to be totally consumed and oxidized to CO 2 , while the other wood products are partially oxidized and partially go into uses or long-term storage, the CO 2 release by these products are calculated using the method of Winjum et al. 28 .
Carbon accumulated in wood products. This carbon is calculated using the local production data reported in the FAO statistical databases and the method of Winjum et al. 28 .