# Retrieval of Biophysical Crop Variables from Multi-Angular Canopy Spectroscopy
## 2 Materials and Methods
### Step-Wise Inversion of the LUT
In doing so, the model is calibrated to site-specific characteristics and might not be able to help retrieve variables for other fields, crop types or phenological stages. The step-wise hierarchical variable retrieval was achieved by several consecutive complete LUT-inversions. A motivation for this approach is the dominance of some parameters (e.g., LAI) that may suppress the signal of others (e.g., LCC) affecting similar spectral domains. For the first inversion run, all available spectral bands were included except for those influenced by the atmospheric water vapor absorptions (1359 nm-1465 nm and 1731 nm-1998 nm) and the VNIR-bands in the detector overlap of the EnMAP-HSI (911 nm-985 nm). Although all variables were obtained in this first step, LAI was the only one of interest at that time. The average inclination of leaves is an important regulation parameter that describes the visibility of photosynthetically active parts of the vegetation for the sensor. Erectophile canopies reveal larger parts of the underlying soil, especially for low SZAs. Planophile and plagiophile canopies on the other hand cover more of the background and lead to stronger signals just like an increased LAI would. ALIA and LAI therefore counterbalance each other. In an attempt to separate their influences on the measured spectra, another pre-selection is investigated  
Figure 2: Impact of the choice of number of best fits for the retrieval accuracy. The measured winter wheat spectrum was obtained on 10 April 2014, with an Analytical Spectral Devices (ASD) FieldSpec 3 Jr and then converted into pseudo-EnMAP reflectances. The other signatures are the closest 100 members of the LUT, as simulated by the PROSAIL model. The best estimate, i.e., the model run with least distance to the measured spectrum, is drawn in green. With increasing statistical distance the colors fade from green to yellow until the 100 th best estimate is finally plotted in red. for the first inversion run, selecting only those LUT members with an ALIA close to the one estimated in the field. For the second inversion run, the LAI values resulting from the first run were fixed. A pre-analysis selected only those LUT members containing the retrieved LAI \(\pm\) an absolute tolerance of 0.01 (m\({}^{2}\) m\({}^{-2}\)). If this pre-selection left fewer members than two times the size of n\({}_{\mathrm{bf}}\), the valid tolerance was expanded by increments of 0.01 until the minimum condition was met. Only then the second run was started during which LCC was retrieved by separately applying the cost function to the variable-specific sensitive wavelengths (LCC @ 423-705 nm). According to the authors of [51] the performance of an inversion setting shall ideally be assessed by multiple statistical quality criterions when comparing retrieved model parameters to in situ measured values. Most importantly, the relative Root Mean Squared Error (rRMSE) and the slope of the regression line (m) were considered in this study. The coefficient of determination (R\({}^{2}\)) played a minor role, since it measures the strength of the correlation according to the linear regression rather than the 1:1 relationship between model parameter and in situ variable. A regression model was calculated nonetheless and its slope served as an indicator of the inversion accuracy. A slope of 1.0 suggests a perfectly outbalanced relationship. Slopes > 1.0 reveal an underestimation for low and overestimation for high values. The reverse relationship applies for slopes <1.0. For all following analyses, model runs with a slope <0.7 or >1.3 were not considered in the final results.