Research Doctorate - Doctor of Philosophy (PhD) / Due to the effects of global warming and climate change there is currently intense and growing international interest in suitable modelling methods for relating satellite remotely sensed spectral imagery of vegetated landscapes to the biophysical structural variables in those landscapes across regional, continental or global scales. Of particular interest here is the satellite optical remote sensing of forest foliage cover—measured as foliage projective cover (FPC)—by Landsat ETM+ (Enhanced Thematic Mapper plus) sensor. In the remote sensing literature, different empirical and physical modelling approaches exist for relating remotely sensed imagery to the landscape parameters of interest, each with their own advantages and disadvantages. These approaches, in the main, may be broadly categorised as belonging to one, or a combination of: spectral mixture analysis (SMA) modelling, canopy reflectance modelling, multiple regression (MR) modelling or, spectral vegetation index (SVI) modelling. This thesis uses the SVI approach, partly in comparison to the MR approach. Both the SVI and MR approaches require field-based data to establish the relationship between the biophysical parameter and the spectral index or spectral responses within defined spectral bandwidths. Surrogate measures of the biophysical parameter are sometimes used extensively to establish this relationship and therefore a separate calibration relationship is required.This has inherent problems when the output of one model is substituted into the next and the effects of carry-over of error from one model to the next are not considered. My main goal is therefore to develop a modelling approach that will allow a larger set of one or more surrogate measures to be combined with a smaller set of ‘true’ measures of the biophysical parameter into the one model for establishing the relationship with the SVI and hence the spectral imagery. Success in meeting the goal is the illustration of a working model using real data. In progression towards meeting the goal, two new modelling ideas are developed and synthesised into the creation of an overall modelling framework for estimating FPC from spectral imagery. The modelling framework, which has potential for use in other applications, allows for the incorporation of different types of data including different calibration relationships between variables while avoiding the usual, stepwise approach to the linking of separate relationship models and their variables. One contribution that is new to both remote sensing and statistical modelling practices involves a polar transformation of the principal components of a multi-spectral image of a local reference landscape to produce a set of empirically based, invariant three-dimensional spectral index transformations that have potential for application to the spectral images of different regional landscapes and possibly global landscapes. In particular, the vegetation index from the set has approximate bounded properties that we exploit for modelling of its contribution to residual variation in its relationships with the biophysical variables measured on the ground. The other contribution to statistical modelling practice that has potential for application by a wide range of disciplines is the direct modelling of interdependent relationships between pairs of bounded variates, each considered to have a measurement error structure that can be modelled as though it is similar to sampling variation. Associated with this particular contribution is the development of novel geometric methods to construct approximate prediction bounds and to assist with model interpretations.