## 3 Results  
### Matching between the Footprints of Spectral and Flux Observations  
To investigate the matching between the footprints of spectral and flux observations, the footprint of the flux measurements needs to be modeled. In contrast to spectral observations, estimating the footprint of flux measurements is more complex due to the influence of the atmosphere.  
Figure 3: Variation of the transmittance of up-welling radiation at 761.1 nm with the RTPL according to simulations made by MODTRAN 5. The AOD\({}_{550}\) is set as 0.1, 0.3, and 0.5; the sensor height is 20 m and the range of the view zenith angle is 0–72\({}^{\circ}\); the other parameters are set as given in Table 1.  
[PERSON] et al. (2015) presented a two-dimensional parameterisation for flux footprint prediction (FFP). Unlike other existing fast analytical footprint models, the FFP parameterisation is valid for a wide range of boundary layer stratifications and receptor heights, as well as for non-Gaussian turbulence. Therefore, in this study, FFP was employed for the simulation of the flux measurement footprint. The Xiao Tangshan EC site, located at the National Precision Agriculture Demonstration Base in the town of Xiao Tangshan, north of Beijing, China (40.17\({}^{\circ}\) N,116.39\({}^{\circ}\) E), was selected as a test site, and parameters measured on 18 April 2016 were used (details listed in Table 2). Using the online FFP ([[http://footprint.kljun.net/](http://footprint.kljun.net/)]([http://footprint.kljun.net/](http://footprint.kljun.net/))), a two-dimensional discrete footprint function at a height of 20 m for convective conditions was then modeled--shown as the red lines in Figure 3.  
According to Equation (4), it is possible to model the cumulative footprint contours of the hemispherical spectral observations made at nadir at a height of 20 m above the target surface. These are shown as the black lines in Figure 3. On the other hand, for the conical observations, the radiance measured by the bare fiber at nadir comes from a circular area on the ground with a radius of \(H\cdot\tan\left(\frac{FOV}{2}\right)\), where \(H\) is the height of the sensor above the target surface. The source area for these measurements is marked as the blue circular area in Figure 3.  
As Figure 4 shows, for a typical sensor height above the target surface of 20 m, 90% of the total radiation comes from an FOV lying within 72\({}^{\circ}\) (the corresponding footprint radius is 61.55 m), which can cover 75.68% of the source area of the total flux signal under convective conditions. In contrast, the total surface source area of the conical observations (FOV of 25\({}^{\circ}\)) is a circle with a radius of 4.43 m, which covers only 1.93% of the flux footprint. Therefore, compared to the conical observation, the hemispherical observation has its advantages in the coordinated measurements of spectra and flux.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Description** & **Value** & **Unit** \\ \hline zm & Receptor height & 20 & m \\ L & Obukhov length & \(-\)100 & m \\ \(\sigma_{\mathrm{v}}\) & Standard deviation of lateral velocity fluctuations & 0.45 & m/s \\ u- & Friction velocity & 0.3 & m/s \\ h & Planetary boundary layer height & 2000 & m \\ u\({}_{\mathrm{(zm)}}\) & Mean wind velocity at measurement height & 0.74 & m/s \\ \hline \hline \end{tabular}
\end{table}
Table 2: The FFP inputs and their values, as used for modeling the flux footprint at our test site.  
Figure 4: Cumulative footprint contours of the flux (red lines) and hemispherical spectral observations made at nadir (black circles) at the Xiao Tangshan EC site for a height above the target surface of 20 m. The blue circular area represents the total surface source area of the conical spectral observations (FOV of 25\({}^{\circ}\)). The center of this circle is the location of the EC tower. The cross marks the location of the flux footprint peak.