## 4 Discussion
### Significance of Understanding Spatial Heterogeneity and Footprint Modeling  
The spatial heterogeneity of underlying surfaces contributes largely to the differences and uncertainties of flux measurements and also greatly affects the spatial representativeness [71; 72]. The spatial heterogeneity can be inferred by the detailed information on vegetation or land cover properties derived from high spatial resolution satellite images within the flux source area [27]. Therefore, the spatial heterogeneity of flux can be better recognized by integrating high spatial resolution remote sensing images and footprint analyses [73]. The spatial representation of flux data can be improved by utilizing footprint information and high spatial resolution remote sensing images. [PERSON] et al. extracted crop-specific flux by applying a detailed footprint analysis [74]. [PERSON] et al. improved the energy closure by 5% after filtering out the flux data from bare soil in a boreal forest flux site in Finland [23]. [PERSON] et al. decomposed methane flux of Siberianundra into land-cover-specific data by footprint weighting and wind direction [27]. Mismatching between the local scale EC observations with a temporally varying flux footprint and regional scale gridded estimation is a major issue in model-data comparisons [75]. To solve this issue, a feasible way is to acquire daily \"ground truth\" data based on footprint models at a remote sensing pixel scale [76]. Meanwhile, footprint modeling has been widely used in recent years to solve another mismatch issue between measurements from plot-scale chambers and footprint-scale ECs. [PERSON] et al. used a footprint-weighted average method to evaluate a plot-scale methane emission model with EC measurements [77]. With the help of this footprint-weighted method, the daily dynamics of EC flux were properly captured by the plot-scale model. [PERSON] et al. improved the consistency of the measurements from the chamber and EC by using detailed vegetation maps and footprint analyses [78]. The footprint modeling is expected to be a bridge connecting the flux observations from the plot, EC footprint and regional grid scale. On the other hand, the change in remote sensing gird can also lead to the mismatch issue. Many studies show that solar-induced chlorophyll fluorescence (SIF) is closely related to the plant photosynthetic rate and plant physiological state [79; 80; 81; 82]. Here, SIF pixels from the Global Ozone Monitoring Experiment-2 (GOME-2) [83; 84], in October 2010, were chosen to be compared with the footprint-weighted EVI and FTVT on the same day to demonstrate to what degree the change in remote sensing pixel position can lead to in mismatch issue (Figures 9 and 10). There is little difference in the EVIs between the two, but there is a great difference in the FTVT (Tables 2 and 3). This indicates that the flux information of the two with similar fluxes may not come from the same vegetation type, and the heterogeneity between vegetation types should be fully considered when addressing the mismatch issue. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Date**} & **EVI of the** & **Mean EVI within** & \multirow{2}{*}{**Bias**} \\  & **Source Area** & **the Pixel** & \\ \hline
2010.10.3 & 0.4482 & 0.4548 & \(-\)0.0066 \\
2010.10.8 & 0.4489 & 0.4620 & \(-\)0.0136 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of EVI within the flux source area and the pixels of GOME-2 SIF data. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Date**} & \multicolumn{2}{c}{**FIVT of the**} & \multicolumn{2}{c}{**Mean FIVT within**} \\  & **Source Area** & **the Pixel** & **Bias** \\ \hline
2010.10.15 & 0.4566 & 0.4585 & \(-\)0.0019 \\
2010.10.17 & 0.4521 & 0.4676 & \(-\)0.0155 \\
2010.10.20 & 0.4607 & 0.4605 & 0.0002 \\
2010.10.27 & 0.4536 & 0.4687 & \(-\)0.0151 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._