# Retrieval of Biophysical Crop Variables from Multi-Angular Canopy Spectroscopy
## 1 Introduction  
The retrieval of biophysical plant variables from optical imagery has been playing an important role in remote sensing and ecosystem modelling for more than 30 years. With ongoing technical progress of the sensors, there is also a steady demand for improved extraction of information from the gathered data. Especially in the agricultural context, many studies have pointed out the suitability of multispectral data (e.g., [1; 2; 3; 4; 5]), hyperspectral data (e.g., [6; 7; 8; 9; 10; 11]) and a combination of both (e.g., [12; 13; 14]) for an assessment of crop characteristics. In order to make these benefits available to modern farming, scientific tools and algorithms need to be directly applicable for a broader user community. Variables like the leaf area index (LAI) or leaf chlorophyll content (LCC) are of prime importance for a proper characterization of the canopy and plant biochemistry [15]. Several approaches are known to successfully retrieve hyperspectral canopy variables from measured spectra. The approaches can be divided into empirical and generic methods. The formerbuild up a statistical relationship between vegetation spectral signatures and in situ measured variables as parametric or non-parametric regressions [4]. Due to this site-specific linkage, empirical methods are not transferable in space or time [16; 17]. To become independent of in situ measurements, more generic approaches often make use of radiative transfer models (RTMs). They are the intermediate link between biophysical characteristics of the canopy and its geometry, radiometric interaction and the reflected radiation [18]. Location, intensity and quality of the radiation source, atmosphere, vegetation/canopy, soil as well as position and properties of the sensor are important subsystems for the remote sensing of vegetation [19]. RTMs separate exterior parameters from the influence of the target itself, allowing quantitative analysis and the establishment of distinct relationships between signal and object variables [18]. One of the major improvements in RTMs was the incorporation of arbitrarily inclined leaves instead of a representation by plates. The resulting SAIL model [18] (Scattering by Arbitrarily Inclined Leaves) was later coupled with the leaf optical properties model PROSPECT [20] to form the new fusion model PROSAIL [21]. In the direct or forward mode, PROSAIL simulates synthetic spectra from input variables that describe plant physiology and canopy architecture. In the indirect or inverse mode, these variables are obtained from spectral signatures. Inversion techniques are either based on optimization methods, artificial neural networks (ANN), machine learning algorithms (MLA) or look-up-tables (LUT) (see [22] for overview). Their advantages and drawbacks vary with purpose of use. Optimization methods aim at minimizing deviations between modelled and measured spectra [23]. Such minimization algorithms continuously change the input variables of the RTM until the modelled result matches the observation as closely as possible, leading to comparatively long computation times [24]. ANNs and MLAs on the other hand are quicker in training and execution, but they require a priori information, calibration and lack of mathematical transparency [12; 25]. Look-up-tables are databases of modelled spectra and their associated input parameter configurations. LUTs are known to be fast and robust methods producing reasonable results (e.g., [3; 6; 26; 27; 28]). In a first step, the LUT is built up in forward mode before it can be browsed in inverse mode. For the compilation of the LUT, the user has the choice of size (number of simulations), artificial noise type and noise level of the spectral model output as well as distribution type and constraints for all input parameters. Inversion of RTMs is impeded by the fact that more than one combination of variables can lead to the same model result.