## 2 Materials and Methods
### Data Filtering and to Compute Daily VIs and GPP  
After computing the half-hourly VIs (GCC, CamNDVI, CamNIRv, CamRVI) at ecosystem scale, we applied a series of steps to derive robust time series of daily VIs:  
1. We discarded VIs measured with PAR below 600 umol m\({}^{-2}\) s\({}^{-1}\). This procedure was used, on one hand, to filter out the VI values measured during adverse meteorological conditions (i.e., rainy, foggy, or overcast half-hours [48; 34]), and on the other hand, [PERSON] et al. [29] suggests to apply a threshold on PAR to reduce the variability of CamNDVI due to changes in illumination conditions. Here, we selected a more conservative threshold than [PERSON] et al. [29].
2. A _max.density_ filter method was developed to filter and retrieve daily VIs. We constructed the probability density function (PDF) of VIs in 3-day moving windows (30 observations), and assigned the value that has highest probability density as the filtered daily value. We did not apply the widely used _max_ method [22; 36], which uses the 90 th percentile of the VIs value from  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Site** & **VIs** & **N** & **Intercept** & **Slope** & \(\mathbf{R^{2}}\) \\ \hline \multirow{3}{*}{ES-LM1} & NDVI & 4000 & 0.60 & 1.51 & 0.69 \\  & NIRv & 3282 & 0.06 & 0.01 & 0.60 \\  & RVI & 3389 & \(-\)2.03 & 6.61 & 0.54 \\ \hline \multirow{3}{*}{ES-LM2} & NDVI & 4340 & 0.56 & 1.12 & 0.77 \\  & NIRv & 4223 & 0.04 & 0.01 & 0.55 \\  & RVI & 4268 & \(-\)0.14 & 3.55 & 0.57 \\ \hline \multirow{3}{*}{ES-LMa} & NDVI & 3549 & 0.67 & 0.89 & 0.89 \\  & NIRv & 3522 & 0.06 & 0.01 & 0.73 \\  & RVI & 3515 & \(-\)0.20 & 5.17 & 0.84 \\ \hline \multirow{3}{*}{ES-Abr} & NDVI & 3560 & 0.64 & 1.18 & 0.83 \\  & NIRv & 3361 & 0.06 & 0.01 & 0.82 \\ \cline{1-1}  & RVI & 3564 & \(-\)0.78 & 5.39 & 0.80 \\ \hline \hline \end{tabular} \({}^{1}\) ES-LM1, ES-LM2, ES-LMa, and ES-Abr are the FLUXNET-IDs of four experimental sites, respectively. \(N\), number of observations used for each regression; Intercept and slope: the parameters of the linear regression between indexes retrieved from the PhenoCam and SRS; \(R^{2}\): determination coefficient of linear regression. Regression coefficients are all statistically significant (\(p<0.001\)).  
\end{table}
Table 1: Results of the linear regression between normalized difference vegetation index (NDVI), near-infrared reflectance of vegetation index (NIRv), ratio vegetation index (RVI) retrieved from PhenoCam and spectral reflectance sensor (SRS) at four experimental sites \({}^{1}\).  
a 3-day moving window as the filtered daily value. This is because the variability of NIRDN is larger compared to other channels (i.e., RDN, GDDN, BDN) in the PhenoCam, which would result in large variability of VIs (i.e., CamNDVI, CamNIRv and CamRVI) that is especially obvious for Mediterranean ecosystems compared to other ecosystems (some comparison using data retrieved from [34], results are not shown in this study). Hence, we chose to apply the _max.density_ filter to retrieve time series of VIs with less variability, which were not always retrieved by applying _max_ filter in our study. We used an example to demonstrate the better filter performance of _max.density_ compare to _max_ filter methods in our study (Figure A1).
3. Daily VIs were gap-filled using the Singular Spectrum Analysis (SSA) method implemented in the \"spectral.methods\" R package [60].
4. Similar to the processing of VIs, the daily GPP was derived from half-hourly data following the step (2) and step (3).