## 2 Materials and Methods  
### Carbon Cycle Data Assimilation System (CCDAS) and Simulation Experiments  
A Carbon Cycle Data Assimilation System (CCDAS) was used to optimize ecosystem fluxes in this study. CCDAS is based on the BETHY model and combined with an atmospheric transport model (TM2 [51]). CCDAS utilizes a variational method to optimize the process parameters as well as variables by assimilating in situ and remotely sensed observations. The BETHY model simulates carbon cycling as well as the water and energy balance in an ecosystem. Plants are categorized into 13 plant function types (PFTs) and each grid can be represented by at most 3 PFIs, which sum up to be 100% coverage of the area in the grid [19]. Photosynthesis is simulated with the Farquhar equation and C3 and C4 are separately modeled. Soil hydrology is represented by a two-layer bucket model [22] and the first layer which is 4 cm thick corresponds to the soil layer detected by the microwave remote sensing techniques.  
Net ecosystem exchange (NEE) simulated by BETHY was then used as an input together with prescribed background fluxes (fossil fuel, ocean and land use change fluxes) for the TM2 [19], which simulates atmospheric CO\({}_{2}\) concentrations at the flask sample stations from National Oceanic and Atmospheric Administration (NOAA) observation networks (NOAA CO\({}_{2}\) networks). The fossil fuel fluxes were from [PERSON], et al. [52] for the year 1980, and a scaling factor was used for each year from 1981 to 2015 based on ratios of the global annual total fluxes from the Global Carbon Budget (GCB, [53]) to the those by [PERSON], et al. [52] in 1980. The ocean fluxes were taken from two sources. The fluxes from [PERSON], et al. [54] were used to describe the flux climatology, and we added the anomalies derived from the inversed ocean fluxes with atmospheric TM3 [55] for 1980-2015. For land use change fluxes, we used the flux from 1980 by [PERSON], et al. [56] and rescaled it to the other years based on the ratios of the annual total land use change fluxes estimated from GCB to the values from 1980 at the respective grid.  
Three experiments were conducted with CCDAS: a \"_prior_\" simulation experiment with default model parameters, a \"_co\({}_{2}\)_\" simulation experiment with atmospheric CO\({}_{2}\) concentrations from 8 stations (Table A1) assimilated, and a \"_sm + co\({}_{2}\)_\" simulation experiment with surface soil moisture data from ESA-CCI and atmospheric CO\({}_{2}\) data from 8 stations simultaneously assimilated. The simulation period is 1980 to 2015, with daily soil moisture and monthly carbon fluxes (GPP, NEP, and CO\({}_{2}\) concentrations) as output. The spatial resolution for the simulations is 8\({}^{\circ}\times\) 10\({}^{\circ}\) both for BETHY and TM2.  
In total, CCDAS optimizes 101 parameters related to different processes and different PFTs and soil textures using a variational method which minimizes the cost function with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method [57]:  
\[J(x)=\frac{1}{2}\left[\begin{matrix}(M_{co2}(p)-O_{co2})^{T}c_{co2}^{-1}(M_{co2}( p)-O_{co2})+\\ (M_{sm}(p)-O_{sm})^{T}c_{sm}^{-1}(M_{sm}(p)-O_{sm})+\\ (p-p_{0})^{T}C_{p}^{-1}(p-p_{0})\end{matrix}\right] \tag{1}\]  
where \(M\) and \(O\) stand for model and observation, respectively; subscripts \(co_{2}\) and \(sm\) stand for atmospheric CO\({}_{2}\) concentrations and soil moisture, respectively; \(C\) stands for the uncertainty covariance matrices for observations and parameters; \(p\) stands for the parameters; \(p_{0}\) denotes the prior control vector.