# Retrieval of Biophysical Crop Variables from Multi-Angular Canopy Spectroscopy
## Results
### Impact of the Observer Zenith on the Retrieval of Crop Parameters  
Results for the retrieval of LAI and LCC from different observation angles and two different cost functions are shown in Table 3. For LAI, the lowest rRMSE of 0.18 was obtained for nadir observation with MAE cost function. For OZA = \(-30^{\circ}\) (forward scatter) rRMSE was 0.24 and 0.25 for OZA = \(+30^{\circ}\) which means an error increase of 30%. The associated scatterplots are shown in Figure 5. Subplot (c) illustrates the instable model inversion for LAI from backscatter spectra. Especially for medium LAI values, PROSAIL suggested a widespread variable range and better results for nadir inversion. LCC retrieval on the other hand improved for negative observation angles (rRMSE = 0.20), as the clusters of high and low chlorophyll content moved closer to the 1:1 line. For the lower reflectances in opposite viewing direction, rRMSE = 0.27 was the best possible result. Slope and intercept of the regression line nearly reached the optimum of f(x) = x, but the scattergram shows a non-linear behavior and a reduced rRMSE. Figure 6 compares the map of in situ variables as measured at the study fields with the results of the inversion for LAI and LCC. Discrete steps in hue and saturation can be found in both in situ values and model results, indicating that the seasonal dynamics were captured in general. Within the \(3\times 3\) pixels for each field date, variations could not be fully reproduced by the inversion. For this, model uncertainties would have to be lower than the lateral disparity for the \(30\times 30\) m sub-plots. Figure 4: Illustration of the Anisotropy Factor (ANIF) for three different phenological stages of winter wheat (early: bright green, medium: dark green, late: yellow) and observation angles: ANIF for forward scatter ((a) ANIF\({}_{\rm fs}\)), backscatter ((b) ANIF\({}_{\rm bs}\)) and the off-nadir ratio ((c) ANIF\({}_{\rm fs/bs}\)). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**OZA**} & \multicolumn{4}{c}{**RMSE Cost Function**} & \multicolumn{4}{c}{**MAE Cost Function**} \\ \cline{2-9}  & \multicolumn{2}{c}{**LAI**} & \multicolumn{2}{c}{**LCC**} & \multicolumn{2}{c}{**LAI**} & \multicolumn{2}{c}{**LCC**} \\ \hline
**(deg)** & **Slope** & **rRMSE** & **Slope** & **rRMSE** & **Slope** & **rRMSE** & **Slope** & **rRMSE** \\ \hline \(-30\) & 0.81 & 0.27 & 0.95 & 0.20 & 0.84 & 0.24 & 0.82 & 0.22 \\ \(0\) & 0.94 & 0.19 & 0.87 & 0.24 & 0.92 & 0.18 & 0.89 & 0.26 \\ \(+30\) & 0.83 & 0.25 & 0.94 & 0.27 & 0.82 & 0.27 & 0.79 & 0.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Influence of angular spectral measurements, representing the tilt of the EnMAP satellite platform of \(\pm 30^{\circ}\) across track (OZA). Model inversion was conducted with relative root mean squared error (RMSE)\({}_{\rm cft}\) and mean absolute error (MAE) and different sizes of n\({}_{\rm bf}\). Best results for leaf area index (LAI) and leaf chlorophyll content (LCC) for each angle and cost function type are shown. Figure 5: (**a–f**) Evaluation of best inversion results for LAI (left column) and LCC (right column). Nadir is displayed in the top row, backscatter (OZA = +30\({}^{\circ}\)) in the middle, forward scatter (OZA = -30\({}^{\circ}\)) in the bottom row. The slope of the regression line is indicated as \(m\). By subtracting parameter estimations from in situ measurements, residuals for the inversion of LAI and LCC are obtained. Figure 7 is an illustration of these residuals as a map. For the first season in 2014, the model overestimated LCC most of the time for all angular settings, especially for the beginning of the season in April and May. In April and for one sampling date in July 2015, higher chlorophyll concentrations were measured than predicted by the model. The latter is especially striking, because estimations in nadir were quite close the week before (\(\Delta\)LCC\({}_{\rm DOY182}\) = 2.56 \(\mu\)g cm\({}^{-2}\)) and after (\(\Delta\)LCC\({}_{\rm DOY202}\) = 4.24 \(\mu\)g cm\({}^{-2}\)).