# Retrieval of Biophysical Crop Variables from Multi-Angular Canopy Spectroscopy
## 4 Discussion
The rRMSE for nadir appears to be comparatively high and the intercept of the linear model is t = 0.20 which is 10.6% of the data average. This constant overestimation is caused by the before mentioned overestimation of LAI and LCC from nadir spectra reducing the models accuracy. An improvement of the retrieval of these two parameters also yields an improvement for CCC, as can be seen for results from the forward scatter observations. Another focus of this work was to test different LUT-based strategies, while keeping a special focus on the zenithal-angular effects for spectral observations from the future EnMAP sensor. Most commonly, the RMSE\({}_{\text{cft}}\) is used as a merit function to find the best matching LUT members. In fact, there is only a 3.0% mean difference between RMSE\({}_{\text{cft}}\) and MAE in the resulting parameter estimation. The n\({}_{\text{bf}}\) to incorporate in the parameter retrieval has a much stronger impact on the success of the inversion. If we assess only the rRMSE as a statistical measure for the inversion performance, it could be concluded that for LCC there is a steady improvement in predictability for larger n\({}_{\text{bf}}\). It should be noted, however, that the slope responds conversely, decreasing for larger n\({}_{\text{bf}}\) and moving away from the optimal value of 1.0. Lower regression slopes indicate that the range of predicted variables becomes more level, cutting off lowest and highest inversion results. [PERSON] et al. [54] found an optimal inversion routine with n\({}_{\text{bf}}\) = 10% of the LUT-size which, in their case, was 5400 members. For larger n\({}_{\text{bf}}\) the inversion approaches the expected value of the variable as specified before the creation of the LUT, so RMSE is bound to decrease if field observations served as a reference for the original parameter distribution. For all angular settings, statistics deteriorated for n\({}_{\text{bf}}>\) 100 or 0.2% of the compared LUT-members. This suggests that the LUT composition was optimally set. Accordingly, n\({}_{\text{bf}}\) = 100 is considered as the optimal setting in the case of this study. A comparison of the performance with other studies is generally difficult, due to the exploration of different sensor data, LUT-compositions, inversion techniques, crop types and measurement ranges. However, as example, [PERSON] et al. [7] retrieved LAI with an RMSE of 0.83 (m\({}^{2}\) m\({}^{-2}\)) and CCC with RMSE 0.66 (g m\({}^{-2}\)) from winter wheat spectra by training artificial neural networks on PROSAIL which is roughly in the same accuracy range as our findings for nadir observations. Different sources of errors and uncertainties in the whole inversion process must be considered as limitations to this study: in situ measurements of biophysical variables, spectral measurements, simulation of EnMAP data, model representation and the inversion scheme. For most variables, in situ errors can be reduced by choosing an adequate sampling scheme with multiple repetitions. The median standard deviation for LAI measurements of two seasons was 0.22 (m\({}^{2}\) m\({}^{-2}\)) and 3.16 (\(\upmu\)g cm\({}^{-2}\)for LCC. Repetitions of the ALIA estimation in the field revealed a mean error of \(\pm\)7\({}^{\circ}\). Senescent canopies yielded higher uncertainties for the measurement of most variables. Standard deviation of all EnMAP-end-to-end simulations was \(\sigma\) = 0.013 (Ref.) at the NIR-plateau which is 0.28% of the mean reflectance at this wavelength. In comparison to other error sources, this uncertainty played only a minor role. LAI acts as a scaling factor for the leaf constituents. The reflectance signal is ambiguous for substances of lower concentrations within a dense canopy or substances of higher concentrations in a sparse canopy respectively. The hierarchical approach estimates LAI first, fixates it and then finds the other parameters in consecutive inversion steps. This proved to work well for LCC, but not yet for other parameters.