## 3 Methodology
### Remote Sensing Index  
#### 3.1.1 MODIS BRDF_R  
Index  
The Ross-Li-Maignan model predicts the reflectance as the sum of three terms [9; 10]:  
\[ \begin{split}\rho(\theta_{s},\theta_{v},\phi)=k_{0}+k_{1}F_{1}( \theta_{s},\theta_{v},\phi)+k_{2}F_{2}(\theta_{s},\theta_{v},\phi)\\ =k_{0}\Big{[}1+\frac{k_{1}}{k_{0}}F_{1}(\theta_{s},\theta_{v}, \phi)+\frac{k_{2}}{k_{0}}F_{2}(\theta_{s},\theta_{v},\phi)\Big{]}\end{split}  \tag{1}\]  
where \(\theta_{s}\) and \(\theta_{v}\) are the sun and viewing zenith angles, respectively; \(\phi\) is the difference between the azimuth angles of the sun direction and the viewing direction; \(F_{1}\) is the volume-scattering kernel based on the Ross-Thick function corrected for the hot-spot process, \(F_{2}\) is the geometric kernel based on the Li-sparse-reciprocal function [9; 10]; \(k_{0}\) is the isotropic scattering component, which is equal to the bi-directional reflectance for a view zenith angle of \(\theta_{v}\) = 0 and a solar zenith angle of \(\theta_{s}\) = 0; \(k_{2}\) is the coefficient of the Li-sparse-reciprocal geometric scattering kernel \(F_{2}\), which is derived from surface scattering and the geometric shadow casting theory; and \(k_{1}\) is the coefficient for the Ross-Thick volume-scattering kernel \(F_{1}\), which is derived from radiative transfer models. The parameters \(k_{0}\), \(k_{1}\), and \(k_{2}\) are included in the MODIS MCD43 B1 data and were provided by the MODIS working team. We used MODIS remote sensing data because they represent standard data products for the BRDF model parameters and the NDVI at a spatial resolution of 1 km with the frequent simultaneous observations of the Terra and Aqua satellite constellation. Furthermore, because of the homogeneity of the underlying surface at A'rou station, as shown in Figure 1, the 1 km pixel size did not introduce the apparent uncertainty of mixed pixels to the analysis and the results presented in this study. In the future, we will attempt to develop the BRDF model parameters using Belgian Proba-V satellite data, which have a spatial resolution of 100 m, in order to reduce the influence of mixed pixel. The BRDF_R index, which reflects the geometric roughness of the land surface, is calculated as follows [12]:  
\[\text{BRDF}\_R=k_{2}/k_{0} \tag{2}\]  
The eight-day composited MODIS MCD43 B1 data covering the experimental site in 2013 and 2014 were downloaded from the National Aeronautics and Space Administration (NASA) website \begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Instrument** & **Observation Height** \\ \hline Air temperature and humidity & HMP45C, Vaisala, Vaisala Oyj, Vanha & \\ Nurmijarventie 21, 01670 Vantaa, Finland; & \\ AV-14 TH, Avalon, 35-1802 River Drive South, & \\ Jersey City, NJ 07310, USA & \\ \hline Wind speed and direction & 03002, R.M. Young, 2801 Aero Park Drive & 1 m; 2 m; \\ Traverse City, Michigan 49686 USA; & 5 m; 10 m; \\ Windsonic, Gill, Saltmarsh Park, 67 Gosport & 15 m; 25 m \\ Street, Lymington, Hampshire, UK & \\ \hline Air pressure & Model 278, Setra, 159 Swanson Rd. & \\ Boxborough, MA 01719, USA; PTB210, & \\ Vaisala, Vaisala Oyj, Vanha Nurmijarventie 21, & \\
01670 Vantaa, Finland & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Observed quantities and instrumentation at A’rou superstation [19; 20]. ([[http://ladsweb.nascom.nasa.gov](http://ladsweb.nascom.nasa.gov)]([http://ladsweb.nascom.nasa.gov](http://ladsweb.nascom.nasa.gov))). The visible, near-infrared, and shortwave broad bands cover 0.3 to 0.7 \(\upmu\)m, 0.7 to 5.0 \(\upmu\)m, and 0.3 to 5.0 \(\upmu\)m in sequence, respectively, and have a spatial resolution of 1 km. In this paper, the MODIS BRDF_R index in the near-infrared band was used to conduct the analysis according to the conclusion [12] that near-infrared and shortwave-infrared BRDF parameters show similar sensitivities for the AR to those of the visible band.