A Methodology for Scaling Biophysical Models

<p>The science of remote sensing is based on analyses of the spectral and spatial information contained in electromagnetic radiation reflected or emitted from the earth's surface. The development of predictive analytical and semi-analytical models defining radiative-transfer processes associated with earth surface processes and structures are based on the relationship between the biophysical variables of interest and the signal received by an airborne or satellite sensor. This forward modelling approach provides a mathematical basis to enable researchers to understand and predict the relationships between an object's properties and the resulting digital image. Of greater interest to environmental managers is the inverse problem, where the object properties are estimated from the remotely sensed image data. The availability of this type of information facilitates monitoring and management of terrestrial and aquatic environments. Due to the complex and often non-linear nature of the interactions modelled in the forward approach, the inversion of such a model is often ill-posed, resulting in a solution that is not unique or not a continuous function of the data. This uncertainty limits the efficacy of remotely sensed data for repeatable and robust environmental monitoring, which is unfortunate given the scope and relatively low cost of this product. Although significant research into spatial scaling and data integration has been completed, there has been limited work into scale integration of spectral and spatial data for multiple scale linkage and estimation of biophysical variables. This dissertation, through an analysis of the spatial and spectral dimensions of digital images, endeavours to mitigate the difficulties involved in model inversion by establishing a generic framework to generate well-posed extensions to previously ill-posed biophysical inverse problems, resulting in a solution that is unique and depends continuously on the data.</p> <p>The framework was developed in two parts, covering the extraction of spectral and spatial information, and was applied to a series of case studies in tropical and subtropical forests. Since the high-spatial resolution image data used in this project was provided by an airborne digital camera, there was a requirement to first build an image processing chain to link the specialised radiometric calibration, vignetting, sensor linearity and viewing/illumination geometry correction routines developed for this system. The spectral framework was used to develop a set of sensor spectral response functions, while the spatial framework was used to develop the system spatial response functions. The result of the system integration is an image processing system that outputs calibrated, ready to mosaic corrected image data sets in a GIS ready image format.</p> <p>The spectral framework was then tested using a case study that mapped the location of individual tree canopies that provided suitable fodder for Koalas. Field spectrometer samples were used to transform hyperspectral data into four components representing within-pixel proportions of target and non-target species, background and shade. A canopy detection routine was then used to produce canopy scale maps of individual species. This approach was tested using hyperspectral image data in a mixed coastal eucalypt forest and was found to be 90.1% accurate when compared to field located species.</p> <p>The spatial framework was tested using two case studies that inverted a simple disk model of spatial variance. The high-spatial resolution data provided by the airborne digital camera system was used to test the applicability of the disk model in tropical rainforests. Results indicated that this model accurately captured the spatial structure of real digital images of this environment. Analysis of variograms extracted from these data was used to estimate the optimal spatial scale at which to acquire images of tropical rainforests for various monitoring tasks. The disk model was then used to invert a geometrical-optical model of rainforest canopy structure, where gaps within the canopy were modelled as cylinders of varying sizes. The inversion of this model, using moderate spatial resolution image data, predicted canopy cover, mean gap size, gap distribution and canopy height, and was found to be accurate in regions where the elevation model accurately represented the terrain, but it overestimated gap size and canopy height in regions where the illumination variability cannot be adequately corrected.</p> <p>The spectral and spatial frameworks were then synthesised, providing a tool to regularise a large class of biophysical inverse problems. The application of this synthesised framework to an ill-posed problem in aquatic remote sensing was used to engender a well-posed extension that would allow stable inversion given moderate spatial resolution hyperspectral data. In conjunction with the next generation imaging platforms that offer ever-increasing spectral and spatial resolutions, this framework offers a suite of techniques that facilitate the extraction of information from image data. Implementation of the framework has shown how the relationship between the spectral and spatial scales of image and field data can be exploited. In addition, results presented here have identified opportunities for future research in the areas of tropical forest geometrical-optical modelling, spectral mixture analysis, spatial variance analysis and the selection and integration of multiple scale ancillary data. Limitations of this work include the restricted geographic range over which it has been tested, the inability to include multitemporal data and the lack of a specific method for the inclusion of synthetic aperture radar data in the framework.