## 2 Materials and Methods
### Data Source  
In this study, the datasets used included OCO-2 products, EC Flux Tower datasets and MODIS data. We used SIF and XCO\({}_{2}\) data from OCO-2. The data versions of SIF and XCO\({}_{2}\) are OCO2_L2_Lite_SIF.8r and OCO2_L2_Lite_FP.8r, respectively. The SIF product was calculated using the IMAP-DOAS algorithm. The SIF product was retrieved using two Fraunhofer lines centering at 757 nm and 771 nm, respectively. There are three observation modes for OCO-2, namely, nadir, glint and target mode. In order to avoid additional errors, we only select SIF products in the same observation mode for each site. If there are SIF products with more than two observation modes for a single site, the observation mode with the largest amount of data was selected. With that criterion, we used SIF data of target mode for US-PFA and US-WCr, used those of glint mode for CA-TPD. For the rest of the sites, we used SIF data of nadir mode. Moreover, we extracted XCO\({}_{2}\) data and their corresponding quality identification from OCO-2 datasets spanning from 2014 to 2019.  
In this study, we used land cover classification 2 (University of Maryland UMD format) of MCD12Q1 from MODIS as auxiliary data to evaluate the study area. Land cover types of North America contain 17 different types. Different vegetation types are represented by different colors. (Figure 1). Due to the proximity of several selected study areas to each other, we have expanded some of the study areas to provide a clear description of the locations of these flux towers. In addition to remote sensing products, we also used GPP and surface CO\({}_{2}\) concentrations from EC flux towers. Both of these products were downloaded from the Ameriflux website.  
We did a preliminary processing of the data. XCO\({}_{2}\) data with \"xCO\({}_{2}\)_quality_flag\" equal to 1 were also eliminated. For EC tower's products, there are several missing measurements in the original products of the surface CO\({}_{2}\) mole fraction and GPP measurements. We have applied spline interpolation to fill these missing values. For the CO\({}_{2}\) data of the flux tower, we take the frictional wind speed 0.2 as the threshold value. Only when the frictional wind speed is greater than 0.2 can we consider the CO\({}_{2}\) data to be valid [33].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Site** & **Lat (\({}^{\circ}\))** & **Lon (\({}^{\circ}\))** & **Year** & **Type** & **Institution** \\ \hline CA-TP3 & 42.71 & \(-\)80.35 & 2014–2017 & ENF & McMaster University \\ CA-TP4 & 42.71 & \(-\)80.36 & 2014–2017 & ENF & McMaster University \\ US-Los & 46.09 & \(-\)89.98 & 2014–2019 & WET & University of Wisconsin \\ CA-TPD & 42.64 & \(-\)80.56 & 2014–2015 & DBF & McMaster University \\ US-Srr & 38.20 & \(-\)122.03 & 2014–2017 & WET & USGS \\ US-Syr & 46.24 & \(-\)89.35 & 2014–2018 & MF & University of Wisconsin \\ US-Pra & 45.95 & \(-\)02.77 & 2014–2018 & MF & University of Wisconsin \\ US-SCC & 61.31 & \(-\)121.30 & 2014–2016 & ENF & University of California \\ US-EML & 63.88 & \(-\)149.25 & 2014–2018 & OSH & University of Northern Arizona \\ US-Ro4 & 44.68 & \(-\)122.03 & 2014–2019 & GRA & USDA-ARS \\ US-PHM & 42.47 & \(-\)70.83 & 2014–2018 & WET & Marine Biological Laboratory \\ US-WCr & 45.81 & \(-\)90.27 & 2014–2018 & DBF & University of Wisconsin \\ \hline \hline \end{tabular}
\end{table}
Table 1: Detailed information of eddy covariance (EC) Flux Towers, including site’s name, latitude, longitude, the year of data used and its institution (ENF: Evergreen Needleleaf Forests, DBF: Deciduous Broadleaf Forests, GRA: grasslands, OSH: Open shrulands, MF: Mixed Forest, WET: Permeland Wetlands).  
Figure 1: Location and attribute of selected EC sites. (**a**) An enlarged image showing sites of US-PFa, US-Syr, US-WCr, US-Los and US-Ro4. (**b**) An enlarged image showing sites of CA-TP3, CA-TP4 and TPD. (**c**) The location map of the study area; the five-pointed star indicates the location of the study area, and the base map is created in ARCGIS using MCD12Q1 data.