# Understanding Forest Health with Remote Sensing-Part II--A Review of Approaches and Data Models
## 4 Physical vs. Empirical Models
Table 9 summarizes the types of models that are frequently used for such purposes, ranging from different adaptations of linear regression (e.g., ordinary least squares regression, OLS; reduced major axis regression, RMA), non-linear regression (e.g., exponential, logarithmic), multivariate techniques such as canonical correlation analysis or redundancy analysis to non-parametric regression models. In classification, parametric techniques such as the Maximum Likelihood classification were traditionally used but more recently, non-parametric classifiers such as k-Nearest Neighbours (kNN), Classification and Regression Trees (CART), and the related ensemble classifier, Random Forests (RF), and Support Vector Machine (SVM) algorithms have been widely adopted. In particular, RF [226] has gained popularity because it: (i) can take input parameters that are continuous, interval or class-based; (ii) can process large numbers of input variables with complex interactions, although variable correlations and spatial autocorrelation have been shown to affect output accuracy [227]; (iii) incorporates bootstrapping for training and validation (out-of-bag) sample selection from a set of reference data in each of many iterations and their associated assessment of internal (out-of-bag) error; and (iv) can be used as a variable selection tool to identify the most important variables that discriminate a set of classes. Although little has been reported on RF use in FH applications, there is significant potential for its use in classification of FH classes, or in RF regression to model and estimate FH traits. The aim of empirical models in RS is to use relationships between image and field data for the spatially explicit estimation of biophysical attributes. Thus, empirical models are most frequently used in regional case studies. They provide the most straightforward way of estimating biotic traits from RS. On the other hand, they are limited in transferability because the nature of the statistical relation between biotic traits and RS indices changes with the modification of the underlying RS data, calibration processes, date of acquisition and phenological state of the vegetation. Moreover, any empirical model is considerably influenced by other external conditions such as the atmosphere, sun angle, geometric resolution, and the accuracy of both the RS and field data. It is also evident that the relation varies between different species (even within a forest stand) and that it is sensitive to the canopy's horizontal and vertical structure. In addition, many studies have shown that some empirical relations reach a level of saturation that is often caused by the nature of the underlying vegetation indices, especially in stands with a high biomass [224; 228]. There is only slight agreement about which algorithm, and which set of independent variables is best suited for the prediction of forest biophysical attributes and their changes over time that can be related to FH conditions. In spite of these limitations, empirical models are the foundation for an era of civilian earth RS studies based on medium resolution satellite images like Landsat, SPOT and others. They are the appropriate choice if no detailed knowledge about the geometric and optical properties of the vegetation exist, and the information about the radiative path from the object to the sensor is incomplete, or if the direct physical relationship between the biotic trait (e.g., biomass) and the reflected spectral energy is not known [224]. Canopy reflectance (CR) models, as part of the more generalized approach of radiative transfer (RT) modelling build on the comprehensive description of the nature of interactions between incoming radiation, vegetation parameters and environmental factors [229]. They assume a logical and direct connection between biotic traits (e.g., LAI), the geometric properties of a canopy or leaf and the directional reflected energy.