# Scaling of FAPAR from the Field to the Satellite
## 4 Results and Analysis
### Temporal Corrections
#### 4.1.2 Validating Temporal Normalization Method
In estimating \(k_{1}\) and \(k_{2}\) from input LAI, the uncertainties of the result \(k_{1}\) and \(k_{2}\) were less  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Fitted**} & \multicolumn{3}{c}{**RMSE of FAPAR**} & \multirow{3}{*}{**LAI**} & \multicolumn{3}{c}{**Fitted**} & \multicolumn{3}{c}{**RMSE of FAPAR**} \\  & & & & **from the Fitted \(k\)_vs._** & & & **from the Fitted \(k\)_vs._** \\ \cline{2-10} \multirow{2}{*}{**LAI**} & \multirow{2}{*}{\(k_{1}\)} & \multirow{2}{*}{\(k_{2}\)} & **Fitted** & **Modelled** & \multirow{2}{*}{**FAPAR**} & \multirow{2}{*}{\(k_{1}\)} & \multirow{2}{*}{\(k_{2}\)} & **Fitted** & **Modelled** \\  & & & **FAPAR** & & & & **FAPAR** & **FAPAR** \\ \hline
0.2 & 0.256 & 0.248 & 0.0007 & 0.0006 & 3 & 0.913 & 1.094 & 0.0010 & 0.0016 \\
0.4 & 0.408 & 0.408 & 0.0084 & 0.0084 & 4 & 0.947 & 1.214 & 0.0010 & 0.0012 \\
0.6 & 0.525 & 0.529 & 0.0050 & 0.0054 & 5 & 0.964 & 1.307 & 0.001 than 10%, while the SZA correction using the resulted \(k_{1}\), \(k_{2}\) and input FAPAR values lead to further reductions of uncertainty, less than 0.02 under all cases. This clearly verified that both errors and uncertainties in the measurement were reduced in the temporal normalization. A series of real _in-situ_ data from one day with continuous observations were used to validate the proposed temporal normalization method. The data were obtained at 10 min interval on 5 July 2012. The diurnal variations measured at the fixed position of the field showed dramatic irregular fluctuations (gray square in Figure 8) because of the small representative area of the measurement device and the heterogeneity within canopy. Thus, we smoothed the data by a simple moving-window averaging algorithm with 100 min window to reduce the random turbulence (red line in Figure 8). The LAI was 2.56, from which the diurnal cycle was modeled by the integrated model at VIS = 30 km (blue dotted line in Figure 8). The temporally smoothed _in-situ_ FAPAR were highly consistent with the simulated diurnal cycle. The temporal normalization method was applied to correct the temporally smoothed _in-situ_ data to 10:30 a.m. (red asterisk in Figure 8). The VIS was estimated as clear condition (30 km) by visual inspection. The mean of the corrected FAPAR values was 0.805 with STD = 0.009. The average FAPAR measured between 10:00 a.m. and 11:00 a.m. was 0.792, taken as the true FAPAR value at 10:30 a.m. The mean error is thus 0.013 with an uncertainty of 0.009. The error and uncertainty from the real _in-situ_ data were consistent with the theoretical analysis of the model accuracy. The uncertainty analysis based on the simulated and the measured data both validated that the proposed temporal normalization method was highly accurate and reliable. The errors from the modeling and the two-round fittings in all were below 0.02 theoretically. Figure 7: Sensitivity of FAPAR correction to random noises in input LAI and FAPAR measurement under VIS = 30 km given FAPAR = (1% \(\pm\) 20%) of the truth FAPAR at different SZAs and: (**a**) LAI = 1.073 \(\pm\) 0.223; (**b**) LAI = 2.180 \(\pm\) 0.344; (**c**) LAI = 3.182 \(\pm\) 0.853; and (**d**) LAI = 4.103 \(\pm\) 1.011.