The Province of British Columbia is developing a suite of attributes to assess and monitor forest sustainability. Each attribute is in turn evaluated using a variety of indicators. Recently, digital remote sensing technologies have emerged as both alternative and supplement to traditional monitoring techniques, with light detection and ranging (lidar) in particular showing great promise for estimating a variety of indicators. The goal of this thesis was to review and assess the ability of lidar to estimate selected indicators of forest sustainability. Specifically, digital elevation model (DEM) interpolation (from which indicators are extracted both directly and indirectly) and wildlife tree class distributions were examined. Digital elevation models are a key derivative of lidar data, and their generation is a critical step in the data processing stream. A validation exercise was undertaken to determine which combination of interpolation routine and spatial resolution was the most accurate. Ground returns were randomly subsetted into prediction and validation datasets. Linear, quintic, natural neighbour, spline with tension, regularized spline, inverse distance weighting, and ANUDEM interpolation routines were used to generate surfaces at spatial resolutions of 0.5, 1.0, and 1.5 m. The 0.5 m natural neighbour surface was found to be the most accurate (RMSE=0.17 m). Classification and regression tree analysis indicated that slope and ground return density were the best predictors of interpolation error. The amount and variability of living and dead wood in a forest stand is an important indicator of forest biodiversity. In the second study, the capacity of lidar to estimate the distribution of living and dead trees within forests is investigated. Twenty-two field plots were established in which each stem (DBH>10cm) was assigned to a wildlife tree (WT) class. For each plot, a suite of lidar-derived predictor variables were extracted. Ordinal logistic regression was then employed to predict the cumulative proportions of stems within the WT classes. Results indicated that the coefficient of variation of the lidar height data was the best predictor variable (r = 0.85, p <0.000, RMSE = 4.9%). The derived relationships allowed for the prediction of the proportion of stems within WT classes across the landscape.

The Province of British Columbia is developing a suite of attributes to assess and monitor forest sustainability. Each attribute is in turn evaluated using a variety of indicators. Recently, digital remote sensing technologies have emerged as both alternative and supplement to traditional monitoring techniques, with light detection and ranging (lidar) in particular showing great promise for estimating a variety of indicators. The goal of this thesis was to review and assess the ability of lidar to estimate selected indicators of forest sustainability. Specifically, digital elevation model (DEM) interpolation (from which indicators are extracted both directly and indirectly) and wildlife tree class distributions were examined. Digital elevation models are a key derivative of lidar data, and their generation is a critical step in the data processing stream. A validation exercise was undertaken to determine which combination of interpolation routine and spatial resolution was the most accurate. Ground returns were randomly subsetted into prediction and validation datasets. Linear, quintic, natural neighbour, spline with tension, regularized spline, inverse distance weighting, and ANUDEM interpolation routines were used to generate surfaces at spatial resolutions of 0.5, 1.0, and 1.5 m. The 0.5 m natural neighbour surface was found to be the most accurate (RMSE=0.17 m). Classification and regression tree analysis indicated that slope and ground return density were the best predictors of interpolation error. The amount and variability of living and dead wood in a forest stand is an important indicator of forest biodiversity. In the second study, the capacity of lidar to estimate the distribution of living and dead trees within forests is investigated. Twenty-two field plots were established in which each stem (DBH>10cm) was assigned to a wildlife tree (WT) class. For each plot, a suite of lidar-derived predictor variables were extracted. Ordinal logistic regression was then employed to predict the cumulative proportions of stems within the WT classes. Results indicated that the coefficient of variation of the lidar height data was the best predictor variable (r = 0.85, p <0.000, RMSE = 4.9%). The derived relationships allowed for the prediction of the proportion of stems within WT classes across the landscape.

Digital Elevation Models (DEMs) are fundamental datasets for environmental modelling. They provide the basic data from which terrain indices that represent or influence environmental phenomena are derived, for example slope gradient and hydrological contributing area, and also the source from which specific morphometric features are quantified and characterised, for example mountains and drainage basins. This thesis focuses on the latter, with the aim being to develop an algorithm to characterise the landscape in terms of five morphometric features (peaks, passes, pits, ridges and valleys) and to assess its validity and effectiveness for characterising landform from DEMs. The research in this thesis is divided into two parts. First, an algorithm of morphometric characterisation of landform from OEMs is developed based on a locally fitted quadratic surface and its positional relationship with the analysis window. Five requirements are taken into account within the algorithm: (1) the ideal cases of different morphometric features are simply and clearly defined; (2) the output is spatially continuous to reflect the inherent fuzziness of landform features; (3) the output is easily combined into a multi-scale index across a range of operational scales; (4) the standard general morphometric parameters can be easily quantified due to the easy calculation of first and second order derivatives from the quadratic surface; and (5) the algorithm is applicable to the different data structures used to represent DEMs. An additional benefit of the quadratic surface is the derivation of the R?? goodness-of-fit statistic, which allows both an assessment of the reliability of the results and the complexity of the terrain. Of the five morphometric features identified using the algorithm, valleys are perhaps the most commonly used. Therefore the second part of this thesis is a more detailed comparison between the Multi-Scale Valleyness (MSV) and three existing algorithms (D8, D∞ and MrVBF). D8 and D∞ are global flow accumulation algorithms, and perform well when characterising valley centre lines. However, they do not identify the valley areas themselves, although this is to be expected given their formulation. MrVBF focuses on characterising valley bottoms and so performs well when characterising valleys in broad and topographically flat areas. It does not identify valleys in the steeper upland parts of a catchment, although this too is something to be expected given its formulation. MSV directly characterises valley areas from a geomorphometric point of view, and performs well for both upland and lowland catchments, irrespective of their width. Overall, the results show that the single- and multi-scale terrain indices developed in this research perform well when characterising the five morphometric features. The approach has considerable potential for use in environmental modelling and terrain analysis.

M.Sc. / Real-time terrain rendering (RTTR) is an exciting eld in computer graphics. The algorithms and techniques developed in this domain allow immersive virtual environments to be created for interactive applications. Many di culties are encountered in this eld of research, including acquiring the data to model virtual worlds, handling huge amounts of geometry, and texturing landscapes that appear to go on forever. RTTR has been widely studied, and powerful methodologies have been developed to overcome many of these obstacles. Complex natural terrain features such as detailed vertical surfaces, overhangs and caves, however, are not easily supported by the majority of existing algorithms. It becomes di cult to add such detail to a landscape. Existing techniques are incredibly e cient at rendering elevation data, where for any given position on a 2D horizontal plane we have exactly 1 altitude value. In this case we have a many-to-1 mapping between 2D position and altitude, as many 2D coordinates may map to 1 altitude value but any single 2D coordinate maps to 1 and only 1 altitude. In order to support the features mentioned above we need to allow for a many-to-many mapping. As an example, with a cave feature for a given 2D coordinate we would have elevation values for the oor, the roof and the outer ground. In this dissertation we build upon established techniques to allow for this manyto- many mapping, and thereby add support for complex terrain features. The many-to-many mapping is made possible by making use of geometry images in place of height-maps. Another common problem with existing RTTR algorithms is texture distortion. Texturing is an inexpensive means of adding detail to rendered terrain. Many existing technique map texture coordinates in 2D, leading to distortion on steep surfaces. Our research attempts to reduce texture distortion in such situations by allowing a more even spread of texture coordinates. Geometry images make this possible as they allow for a more even distribution of sample positions. Additionally we devise a novel means of blending tiled texture that enhances the important features of the individual textures. Fully sampled terrain employs a single global texture that covers the entire landscape. This technique provides great detail, but requires a huge volume of data. Tiled texturing requires comparatively little data, but su ers from disturbing regular patterns. We seek to reduce the gap between tiled textures and fully sampled textures. In particular, we aim at reducing the regularity of tiled textures by changing the blending function. In summary, the goal of this research is twofold. Firstly we aim to support complex natural terrain features|speci cally detailed vertical surfaces, over-hangs and caves. Secondly we wish to improve terrain texturing by reducing texture distortion, and by blending tiled texture together in a manner that appears more natural. We have developed a level of detail algorithm which operates on geometry images, and a new texture blending technique to support these goals.

The Province of British Columbia is developing a suite of attributes to assess and monitor forest sustainability. Each attribute is in turn evaluated using a variety of indicators. Recently, digital remote sensing technologies have emerged as both alternative and supplement to traditional monitoring techniques, with light detection and ranging (lidar) in particular showing great promise for estimating a variety of indicators. The goal of this thesis was to review and assess the ability of lidar to estimate selected indicators of forest sustainability. Specifically, digital elevation model (DEM) interpolation (from which indicators are extracted both directly and indirectly) and wildlife tree class distributions were examined. Digital elevation models are a key derivative of lidar data, and their generation is a critical step in the data processing stream. A validation exercise was undertaken to determine which combination of interpolation routine and spatial resolution was the most accurate. Ground returns were randomly subsetted into prediction and validation datasets. Linear, quintic, natural neighbour, spline with tension, regularized spline, inverse distance weighting, and ANUDEM interpolation routines were used to generate surfaces at spatial resolutions of 0.5, 1.0, and 1.5 m. The 0.5 m natural neighbour surface was found to be the most accurate (RMSE=0.17 m). Classification and regression tree analysis indicated that slope and ground return density were the best predictors of interpolation error. The amount and variability of living and dead wood in a forest stand is an important indicator of forest biodiversity. In the second study, the capacity of lidar to estimate the distribution of living and dead trees within forests is investigated. Twenty-two field plots were established in which each stem (DBH>10cm) was assigned to a wildlife tree (WT) class. For each plot, a suite of lidar-derived predictor variables were extracted. Ordinal logistic regression was then employed to predict the cumulative proportions of stems within the WT classes. Results indicated that the coefficient of variation of the lidar height data was the best predictor variable (r = 0.85, p <0.000, RMSE = 4.9%). The derived relationships allowed for the prediction of the proportion of stems within WT classes across the landscape. / Forestry, Faculty of / Graduate

There has been a marked increase in melt season length over the past two decades on glaciers and ice caps within Canada’s Queen Elizabeth Islands (QEI). Prior to the year ~2000 land ice was in a state of slightly negative mass balance (-11 +/- 11.5 Gt yr⁻¹ over 1958-1995), but recent GRACE measurements suggest that mass losses averaged -33 +/- 5 Gt yr⁻¹ between 2003-2015. These losses have primarily been attributed to meltwater runoff, making the QEI one of the largest recent contributors to sea level rise outside of the ice sheets. Despite these losses, there is a lack of information concerning how a warming climate is affecting small (<1 km²) ice bodies, which are considered sensitive indicators of change due to their short response time. In this study, historical and contemporary aerial photographs, high resolution optical satellite imagery, and ground penetrating radar (GPR) surveys are used to determine area, thickness, mass and volume changes of Adams Icefield within Expedition Fiord, Axel Heiberg Island, Nunavut, over the past seven decades (1948/59-2019). Area changes are determined from a comparison of air photos acquired in 1948/59 with satellite images acquired since 1979. Contemporary (2001, 2012, 2019) digital elevation models (DEMs) were either collected or created from stereo satellite images, and via aerial photo surveys using Structure from Motion photogrammetry. DEM of Difference maps calculated from these DEMs provide volume and mass changes. Results illustrate a steady reduction in glacier area, thickness, and volume prior to the year ~2000, followed by a rapid increase in losses over the past two decades. As a result, Adams Icefield is now rapidly declining and is likely to completely disappear early in the twenty-second century.

We present a statistical model of recreational trails, and a method to infer trail routes from geophysical data, namely aerial imagery and terrain elevation. We learn a set of textures (textons) that characterize the imagery, and use the textons to segment each image into super-pixels. We also model each texton's probability of generating trail pixels, and the direction of such trails. From terrain elevation, we model the magnitude and direction of terrain gradient on-trail and off-trail. These models lead to a likelihood function for image and elevation. Consistent with Bayesian reasoning, we combine the likelihood with a prior model of trail length and smoothness, yielding a posterior distribution for trails, given an image. We search for good values of this posterior using both a novel stochastic variation of Dijkstra's algorithm, and an MCMC-inspired sampler. Our experiments, on trail images and groundtruth collected in the western continental USA, show substantial improvement over those of the previous best trail-finding methods.

The method described here for recovering the shape of a surface from a shaded image can deal with complex, wrinkled surfaces. Integrability can be enforced easily because both surface height and gradient are represented. The robustness of the method stems in part from linearization of the reflectance map about the current estimate of the surface orientation at each picture cell. The new scheme can find an exact solution of a given shape-from-shading problem even though a regularizing term is included. This is a reflection of the fact that shape-from-shading problems are not ill-posed when boundary conditions are available or when the image contains singular points.

The most widely used classification method for statistical mapping is Jenks’s natural breaks. However, it has been found that natural breaks is not good at classifying data which have scaling property. Scaling property is ubiquitous in many societal and natural phenomena. It can be explained as there are far more smaller things than larger ones. For example, there are far more shorter streets than longer ones, far more smaller street blocks than bigger ones, and far more smaller cities than larger ones. Head/tail breaks is a new classification scheme that is designed for values that exhibit scaling property. In Digital Elevation Models (DEMs), there are far more lower elevation points than higher elevation points. This study performs both head/tail breaks and natural breaks for values from five resolutions of DEMs. The aim of this study is to examine advantages and disadvantages of head/tail breaks classification scheme compared with natural breaks. One of the five resolutions of DEMs is given as an example to illustrate the principle behind the head/tail breaks in the case study.The results of head/tail breaks for five resolutions are slightly different from each other in number of classes or level of details. The similar results of comparisons support the previous finding that head/tail breaks is advantaged over natural breaks in reflecting the hierarchy of data. But the number of classes could be reduced for better statistical mapping. Otherwise the top values, which are very little, would be nearly invisible in the map.A main conclusion to be drawn from this study is that head/tail breaks classification scheme is advantaged over natural breaks in presenting hierarchy or scaling of elevation data, with the top classes gathered into one. Another conclusion is when the resolution gets higher; the scaling property gets more striking.

This thesis evaluates the potential for using line of sight returns and return signals from underneath a forest canopy using X-band, airborne synthetic aperture radar (SAR) tomography. Approximately 30% of the Earth’s land surface is covered by vegetation, therefore global digital elevation models (DEMs) contain a signal from the forest canopy and not the ground. By uncovering new techniques to find the ground signals, using data collected from airborne platforms as verification, such procedures could be applied to currently operational and future X-band, spaceborne systems with the aim of resolving much of the vegetation bias on an international scale. Data from three sources is presented; data collected from Selex ES’s SAR systems, the GOTCHA dataset and simulated data. Before carrying out tomography it is shown that SAR interferometry (InSAR) can successfully be applied to X-band, helicopter data. A scatterer defined as a candidate persistent scatterer (CPS) is introduced, where the pixels are stable and coherent over a matter of days. An algorithm for selecting CPSs is developed by exploiting sparsity and a novel choice of hard thresholding operator. Using simulated forestry and SAR information the effects of changing input parameters on the outcome of the tomographic profile is analysed. What is found in this study is that model simulations demonstrate that ground points can be detected if the platform motion is relatively stable and that temporal decorrelation over the forest volume is kept to a minimal. An understory can confuse the tomographic profile since less line of sight observations can be made. By combining line of sight observations alongside new tomography techniques on high resolution SAR data this thesis shows it is possible to detect ground scatterers, even at X-band.