# Retrieval of Biophysical Crop Variables from Multi-Angular Canopy Spectroscopy
## 2 Materials and Methods
### In Situ Measurements
#### 2.2.1 Spectral Data
Spectral information from each of the 3 \(\times\) 3 ESUs was compiled to pseudo-images with a ground sampling distance of 10 m. Furthermore, the processed signatures were converted into simulated EnMAP spectra via the EnMAP-end-to-end-Simulator (EeteS) [37]. In this process, the sensor-specific radiometric and spectral properties were adapted. The spatial resolution in this case was retained at 10 m to preserve the data population. The gap fraction is a measure for the probability of a ray of light to penetrate through the canopy undisturbedly [38]. Accordingly, this parameter decreases with density and/or height of a canopy. Canopy height can also be seen as a path length on which energy can interact with plant traits. Assuming identical canopy height, the path length is shortest for nadir views and increases with OZA \(>0^{\circ}\). For a \(30^{\circ}\) deflection from nadir, the travelled path is longer by factor \(\cos\) (\(30^{\circ}\))\({}^{-1}\) which is 15.5%. This leads to a weaker influence of soil background and to an apparently higher portion of visible leaf surface. Figure 1: Sun–target–sensor-geometry. The three arrows illustrate the three different observer zenith angles (OZA). A positive OZA is associated with backscatter and commonly shows higher rates of reflectance than negative OZAs (forward scatter). The anisotropy factor (ANIF) [39] yields useful information about the sensitivity of different wavebands towards changes in illumination geometry. It is simply defined as Equation (1):  
\[\text{ANIF}=\frac{\text{R}_{\text{off}-\text{nadir}}}{\text{R}_{\text{nadir}}} \tag{1}\]  
Since the experimental setup covers two different viewing directions, two ANIFs were obtained: one for forward scatter (ANIFs) and one for backscatter (ANIFbs). Additionally, a third ANIFfs/bs was calculated as the ratio between reflectances per waveband in forward and backscatter direction. If spectral information of the same target is available for multiple angles, it was found useful to combine them and thus raise predictability. This has been done with surface-near spectrometers that are handheld [40], mounted on a tower [41], on hemispherical devices [42] or UAVs [11]. A prominent example for multi-angular optical remote sensing from space is CHRIS/Proba which allows to record narrowband spectra in the VNIR-domain from five different viewing angles (e.g., [43,44]). EnMAP will be able to perform an across-track satellite tilt, but will keep up this slanting position for longer time than its view upon the target. If the same target shall be observed under different zenith angles, more than just one acquisition will have to be made with a time gap of at least several days or possibly several weeks or months. Canopy parameters that are strongly influencing the bidirectional reflectance distribution function (BRDF) change diurnally as well as during the seasonal growth cycle. For this reason, in this study we concentrated on single looks only, regardless of the possible improvement of results for a _combined_ multi-angular approach.