# Understanding Forest Health with Remote Sensing-Part II--A Review of Approaches and Data Models
## 4 Physical vs. Empirical Models
Typically, these models are designed to predict the directional spectral reflectance of a canopy based on the known spectral behaviour of the geometric-optical and biophysical properties or parameters of the vegetation and the environment. Hence, for RS applications, CR models must be inverted to estimate one or more canopy parameters as a function of the canopy reflectance. All approaches to modelling the radiation in a canopy are based on the geometrical optics, the radiative transfer or the canopy transmittance theory. They can be summarized by four categories after [PERSON] [229]. (1) Geometrical models; (2) Turbid medium models; (3) Hybrid models; and (4) Computersimulation models. Geometrical models consider the canopy to be a compilation of geometrical objects with known shapes and dimensions that have distinct optical properties in terms of transmission, absorption and reflectance [230; 231]. By contrast, turbid medium models regard the canopy as a collection of absorbing and scattering particles, with given optical properties that are distributed randomly in horizontal layers [229]. Hybrid models combine the first two approaches and account for geometrical-optical properties as well as the absorption and scattering of plant elements (e.g., leaves or trunks). Finally, computer-simulation models completely model the arrangement and orientation of plant elements and the interference of spectral radiative energy by one of these elements based on computer vision. The advantage of computer models is that they enable a systematic configuration and analysis of radiation regimes and canopy structure (e.g., size, orientation, position of leaves). The application of a certain model is mostly determined by the availability of parameters. With regard to saturation, geometrical models are more appropriate for sparse canopies, whereas turbid medium models more adequately represent dense and homogenous forest stands. The main limitation of CR models is the complexity of the model due to the complex physical nature of the relations between spectral reflectance and vegetation parameters. The inversion of CR models to target variables requires knowledge of all auxiliary model parameters. The choice between physical and empirical models depends on the target application. Physical models are widely used for the quantitative modelling of biophysical vegetation parameters on a global scale (e.g., MODIS LAI, see [232]; Landsat LAI, see [233]). They rely on the physical description of the energy-matter interaction. However, every physical model strongly depends on empirical data for calibration and validation and also faces problems of saturation in regions with high biomass (see, e.g., [234] for MODIS GPP modelling). Semi-empirical approaches combine both empirical and physical modelling, e.g., by using the output from CR models to train neural networks to estimate biophysical parameters [235]. \begin{table}
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Similar modelling approaches are available based on SAR remote-sensing data. SAR-based empirical modelling approaches are conceptually the same as for optical data and make use of the backscatter, coherence or polarization information of the processed microwave signal as explained in Section 3.2. The physically-based models rely on the coherence-amplitude conversion of the complex SAR signal at different wavelengths and polarizations. In contrast to optical RS, SAR-based physical models are more related to the vertical structure of vegetation and, hence, provide a more direct approach for modelling parameters of the global carbon budget, e.g., AGB. The most widely used microwave scattering models for forest stands are the Random Volume over Ground (RVoG, [236] and the Water Cloud Model (WCM, [237]) and a number of adaptations [238].