## 2 Materials and Methods
### Data Acquisition and Preprocessing
#### 2.2.3 Satellite Remote Sensing Data  
The spatiotemporal variation of FCO\({}_{2}\) is strongly affected by both biotic (vegetation productivity) and abiotic (soil temperature and soil moisture) factors [5; 13; 14; 34; 39; 58; 59]. Given this, 10 explanatory variables representing plant productivity, soil temperature, and soil moisture were derived from the RS products and used for predicting FCO\({}_{2}\) (Table 2). These data sets were obtained from the MODIS products and the Soil Moisture Active Passive (SMAP) root-zone soil moisture [5; 34]. All the products are continuously updated and can be obtained from the the NASA's Land Processes Distributed Active Archive Center (LP DAAC) ([[https://lpdaac.usgs.gov/data/](https://lpdaac.usgs.gov/data/)]([https://lpdaac.usgs.gov/data/](https://lpdaac.usgs.gov/data/)) (accessed on 7 October 2020)) and EARTHDATA ([[https://search.earthdata.nasa.gov/](https://search.earthdata.nasa.gov/)]([https://search.earthdata.nasa.gov/](https://search.earthdata.nasa.gov/)) (accessed on 26 October 2020)). The first MODIS data is the 8-day Terra MODIS surface reflectance product (MOD09A1, V6), which has spatial resolutions of 500 m and provides 7 wavelength bands. Each pixel value of the MOD09A1 data is produced by selecting all the acquisitions within the 8-day composite based on high observation coverage, low view angle, the absence of clouds, and aerosol loading [39; 60]. The MOD09A1 surface reflectance products in this study are used to calculate the VIs (Normalized Difference Vegetation Index (NDVI) [61] and Enhanced Vegetation Index (EVI) [62] that representing vegetation productivity as shown in Equations (2) and (3). \[\text{NDVI}=\frac{\rho_{2}-\rho_{1}}{\rho_{2}+\rho_{1}} \tag{2}\]  
\[\text{EVI}=2.5\times\frac{\rho_{2}-\rho_{1}}{\rho_{2}+(6\times\rho_{1}-7.5 \times\rho_{3})+1} \tag{3}\]  
where \(\rho_{1}\), \(\rho_{2}\) and \(\rho_{3}\) are the red band, near-infrared (NIR) band, and blue band (centered at 645, 858, and 469 nm, respectively) in the MODIS surface reflectance products, respectively. Besides, the MODIS leaf area index (LAI) (MCD15A3H, 500 m, 4 days) and gross primary production (GPP) (MOD17A2H, 500 m, 8 days) products are also considered in our study, because they are the two robust indicators of vegetation productivity [34; 39]. Finally, the MOD09A1, MOD17A2H, and MCD15A3H products were processed and acquired to match the timing of FCO\({}_{2}\) measurements. The daily 1-km Terra and Aqua MODIS Land Surface Temperature (LST) (MOD11A1 and MYD11A1) products are also obtained, which are produced by the generalized split-window algorithm [63]. Both Terra and Aqua MODIS LST have two data layers of daytime and nighttime, respectively. In this study, two LST temperature variables (LSTtd and LSTad) were adopted. Among them, the LSTtd and LSTad represent the Terra MODIS LST \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Types** & **Fullname** & **Indices** & **Data Source** \\ \hline \multirow{4}{*}{Plant productivity} & Normalized Difference Vegetation Index & NDVI & Calculated from MOD09A1 \\  & Enhanced Vegetation Index & EVI & Calculated from MOD09A1 \\  & Leaf Area Index & LAI & MCD15A3H \\  & Gross Primary Production & GPP & MOD17A2H \\ \hline \multirow{2}{*}{Soil temperature} & Terra MODIS Land Surface Temperature & LSTd & MOD11A1 \\  & Aqua MODIS Land Surface Temperature & LSTad & MYD11A1 \\ \hline \multirow{4}{*}{Soil moisture} & Evapotranspiration & ET & MOD16A2 \\  & Soil Moisture & SM & SMAP Level 4 Global EASE-Grid root zone SM \\ \cline{1-1}  & Land Surface Water Index & LSWI & Calculated from MOD09A1 \\ \cline{1-1}  & Surface Water Capacity Index & SWCI & Calculated from MOD09A1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of all remote sensing indices used in this study. and Aqua MODIS LST with daytime overpasses at approximately 10:30 a.m. and 1:30 p.m. local time, respectively.