Bivariate relationship modelling on bounded spaces with application to the estimation of forest foliage cover by Landsat satellite ETM-plus sensor

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

Motivation, development and validation of a new spectral greenness index: A spectral dimension related to foliage projective cover

A method is presented for the development of a regional Landsat-5 Thematic Mapper (TM) and Landsat-7 Enhanced Thematic Mapper plus (ETM+) spectral greenness index, coherent with a six-dimensional index set, based on a single ETM+ spectral image of a reference landscape. The first three indices of the set are determined by a polar transformation of the first three principal components of the reference image and relate to scene brightness, percent foliage projective cover (FPC) and water related features. The remaining three principal components, of diminishing significance with respect to the reference image, complete the set. The reference landscape, a 2200 km2 area containing a mix of cattle pasture, native woodland and forest, is located near Injune in South East Queensland, Australia. The indices developed from the reference image were tested using TM spectral images from 19 regionally dispersed areas in Queensland, representative of dissimilar landscapes containing woody vegetation ranging from tall closed forest to low open woodland. Examples of image transformations and two-dimensional feature space plots are used to demonstrate image interpretations related to the first three indices. Coherent, sensible, interpretations of landscape features in images composed of the first three indices can be made in terms of brightness (red), foliage cover (green) and water (blue). A limited comparison is made with similar existing indices. The proposed greenness index was found to be very strongly related to FPC and insensitive to smoke. A novel Bayesian, bounded space, modelling method, was used to validate the greenness index as a good predictor of FPC. Airborne LiDAR (Light Detection and Ranging) estimates of FPC along transects of the 19 sites provided the training and validation data. Other spectral indices from the set were found to be useful as model covariates that could improve FPC predictions. They act to adjust the greenness/FPC relationship to suit different spectral backgrounds. The inclusion of an external meteorological covariate showed that further improvements to regional-scale predictions of FPC could be gained over those based on spectral indices alone

Local surface temperature change due to expansion of oil palm plantation in Indonesia

A high world demand for crude palm oil has caused a reduction in the area of Indonesia’s tropical rainforests over the past several decades. Our hypothesis is that the expansion of the area devoted to oil palm plantations at the expense of primary and secondary tropical rainforests will increase the local surface temperature. While similar studies of other crops have been reported, this is the first time this particular hypothesis has been investigated and reported using the remote sensing methods described in this paper. In this study, we used remotely sensed data to quantify land use changes from tropical rainforests to oil palm plantations, calculated the surface temperature from thermal infrared data supplied by band 6 of the Landsat 5 Thematic Mapper (TM) and Landsat 7 Enhanced Thematic Mapper Plus (ETM+), examined the correlations of surface temperature to foliage cover, and conducted field work to verify the results obtained using the remotely sensed data. For this study, we used a new spectral index, Principal Polar Spectral Greenness (PPSG), that is potentially more sensitive than other index to small changes in foliage cover at high cover levels. The outcome of satellite image processing is only 0.2 °C different from direct temperature measurement in the field. Our study indicated that less density of the closed-canopy composition of oil palm trees resulted in higher surface temperature

Fitting the 4-parameter lineal basis model

This Mathematica 7 Notebook develops a novel regression method applied to bivariate data on a bounded space (we will work in the canonical {0, 1 }x{O, 1} space). This approach was developed by [Moffiet, 2008] in the context of analysis of satellite remote sensing data. A distinguishing feature of the development presented here is that the X and Y variables are treated with complete symmetry; neither variable takes dependent or independent roles. The fitted "regression line", which we call a Lineal Basis, is described parametrically, i.e., as {X= X[s, ...], y = y{s, ...}}, with 0 ≤ s ≤ 1 and the constraints {X[0, ...], Y[0, ...]} = {0, 0} and {X[1, ...], Y[1, ...]} = {1, 1}, rather than conventionally as Y = f[x, ...] with f[0] = 0 and f[1] = 1 (ellipsis ... denotes parameters). This Lineal Basis is fitted to the data according to a model in which for each observed data point {x_i, y_i} there is a corresponding "generating" point {X_i, Y_i}, which lies on the Lineal Basis. The difference vector between an {X_i, Y_i} and its corresponding {x_i, y_i} is modelled as a sample from a bivariate distribution which here is taken as a product of two independent Beta[α,β] distributions, using the notation Beta[αX, βX]xBeta[αY, βY]. Further, we will allow αX, βX, αY, and βY to vary with s, i.e., we have four functions αX[s, ...], βX[s, ...], αY[s, ...], and βY[s, ...]. Since the mean of the Beta[α, β] distribution is α / (α + β), the parameters of these four function must be such that for a given s, the joint Beta-Beta mean point {αX[s, ...] / (αX[s, ...] + βX[s, ...]), αY[s, ...] / (αY[s, ...] + βY[s, ...]) lies on the Lineal Basis. It turns out that simple linear functions suffice to fit many of the data sets typically encountered in these bounded spaces. Interesting computational issues arise when constructing the "mean prediction region" and the "single prediction region" for a Lineal Basis model, analogous to the "mean prediction bands" and the"single prediction bands" of simple linear regression. Concepts from computational geometry are employed, and in particular the logic of a key calculation is verified via a Manipulate

Airborne Laser Scanning: Exploratory Data Analysis Indicates Potential Variables for Classification of Individual Trees or Forest Stands According to Species

Understanding your data through exploratory data analysis is a necessary first stage of data analysis particularly for observational data. The checking of data integrity and understanding the distributions, correlations and relationships between potentially important variables is a fundamental part of the analysis process prior to model development and hypothesis testing. In this paper, exploratory data analysis is used to assess the potential of laser return type and return intensity as variables for classification of individual trees or forest stands according to species. For narrow footprint lidar instruments that record up to two return amplitudes for each output pulse, the usual pre-classification of return data into first and last intensity returns camouflages the fact that a number of the return signals have only “single amplitude” (singular) returns. The importance of singular returns for species discrimination has received little discussion in the remote sensing literature. A map view of the different types of returns overlaid on field species data indicated that it is possible to visually distinguish between vegetation types that produce a high proportion of singular returns, compared to vegetation types that produce a lower proportion of singular returns, at least when using a specific laser footprint size. Using lidar data and the corresponding field data derived from a subtropical woodland area of South East Queensland, Australia, map scatterplots of return types combined with field data enabled, in some cases, visual discrimination at the individual tree level between White Cypress Pine (Callitris glaucophylla) and Poplar Box (Eucalyptus populnea). While a clear distinction between these two species was not always visually obvious at the individual tree level, due to other extraneous sources of variation in the dataset, the observation was supported in general at the site level. Sites dominated by Poplar Box generally exhibited a lower proportion of singular returns compared to sites dominated by Cypress Pine. While return intensity statistics for this particular dataset were not found to be as useful for classification as the proportions of laser return types, an examination of the return intensity data leads to an explanation of how return intensity statistics are affected by forest structure. Exploratory data analysis indicated that a large component of variation in the intensity of the return signals from a forest canopy is associated with reflections of only part of the laser footprint. Consequently, intensity return statistics for the forest canopy, such as average and standard deviation, are related not only to the reflective properties of the vegetation, but also to the larger scale properties of the forest such as canopy openness and the spacing and type of foliage components within individual tree crowns

Evaluation of Different Topographic Corrections for Landsat TM Data by Prediction of Foliage Projective Cover (FPC) in Topographically Complex Landscapes

The reflected radiance in topographically complex areas is severely affected by variations in topography; thus, topographic correction is considered a necessary pre-processing step when retrieving biophysical variables from these images. We assessed the performance of five topographic corrections: (i) C correction (C), (ii) Minnaert, (iii) Sun Canopy Sensor (SCS), (iv) SCS + C and (v) the Processing Scheme for Standardised Surface Reflectance (PSSSR) on the Landsat-5 Thematic Mapper (TM) reflectance in the context of prediction of Foliage Projective Cover (FPC) in hilly landscapes in north-eastern Australia. The performance of topographic corrections on the TM reflectance was assessed by (i) visual comparison and (ii) statistically comparing TM predicted FPC with ground measured FPC and LiDAR (Light Detection and Ranging)-derived FPC estimates. In the majority of cases, the PSSSR method performed best in terms of eliminating topographic effects, providing the best relationship and lowest residual error when comparing ground measured FPC and LiDAR FPC with TM predicted FPC. The Minnaert, C and SCS + C showed the poorest performance. Finally, the use of TM surface reflectance, which includes atmospheric correction and broad Bidirectional Reflectance Distribution Function (BRDF) effects, seemed to account for most topographic variation when predicting biophysical variables, such as FPC

Prediction and validation of foliage projective cover from Landsat-5 TM and Landsat-7 ETM+ imagery

The detection of long term trends in woody vegetation in Queensland, Australia, from the Landsat-5 TM and Landsat-7 ETM+ sensors requires the automated prediction of overstorey foliage projective cover (FPC) from a large volume of Landsat imagery. This paper presents a comparison of parametric (Multiple Linear Regression, Generalized Linear Models) and machine learning (Random Forests, Support Vector Machines) regression models for predicting overstorey FPC from Landsat-5 TM and Landsat-7 ETM+ imagery. Estimates of overstorey FPC were derived from field measured stand basal area (RMSE 7.26%) for calibration of the regression models. Independent estimates of overstorey FPC were derived from field and airborne LiDAR (RMSE 5.34%) surveys for validation of model predictions. The airborne LiDAR-derived estimates of overstorey FPC enabled the bias and variance of model predictions to be quantified in regional areas. The results showed all the parametric and machine learning models had similar prediction errors (RMSE < 10%), but the machine learning models had less bias than the parametric models at greater than ~60% overstorey FPC. All models showed greater than 10% bias in plant communities with high herbaceous or understorey FPC. The results of this work indicate that use of overstorey FPC products derived from Landsat-5 TM or Landsat-7 ETM+ data in Queensland using any of the regression models requires the assumption of senescent or absent herbaceous foliage at the time of image acquisition

A statistical study on the combined effects of wall thermal mass and thermal resistance on internal air temperatures

Statistical analyses are important for real-world validation of theoretical model predictions. In this article, a statistical analysis of real data shows empirically how thermal resistance, thermal mass, building design, season and external air temperature collectively affect indoor air temperature. A simple, four-point, diurnal, temperature-by-time profile is used to summarise daily thermal performance and is used as the response variable for the analysis of performance. The findings from the statistical analysis imply that, at least for moderate climates, the best performing construction/design will be one in which insulation and thermal mass arrangements can be dynamically altered to suit weather and season

Global trends and projections for tobacco use, 1990-2025:An analysis of smoking indicators from the WHO Comprehensive Information Systems for Tobacco Control

Background: Countries have agreed on reduction targets for tobacco smoking stipulated in the WHO global monitoring framework, for achievement by 2025. In an analysis of data for tobacco smoking prevalence from nationally representative survey data, we aimed to provide comprehensive estimates of recent trends in tobacco smoking, projections for future tobacco smoking, and country-level estimates of probabilities of achieving tobacco smoking targets. Methods: We used a Bayesian hierarchical meta-regression modelling approach using data from the WHO Comprehensive Information Systems for Tobacco Control to assess trends from 1990 to 2010 and made projections up to 2025 for current tobacco smoking, daily tobacco smoking, current cigarette smoking, and daily cigarette smoking for 173 countries for men and 178 countries for women. Modelling was implemented in Python with DisMod-MR and PyMC. We estimated trends in country-specific prevalence of tobacco use, projections for future tobacco use, and probabilities for decreased tobacco use, increased tobacco use, and achievement of targets for tobacco control from posterior distributions. Findings: During the most recent decade (2000-10), the prevalence of tobacco smoking in men fell in 125 (72%) countries, and in women fell in 156 (88%) countries. If these trends continue, only 37 (21%) countries are on track to achieve their targets for men and 88 (49%) are on track for women, and there would be an estimated 1·1 billion current tobacco smokers (95% credible interval 700 million to 1·6 billion) in 2025. Rapid increases are predicted in Africa for men and in the eastern Mediterranean for both men and women, suggesting the need for enhanced measures for tobacco control in these regions. Interpretation: Our findings show that striking between-country disparities in tobacco use would persist in 2025, with many countries not on track to achieve tobacco control targets and several low-income and middle-income countries at risk of worsening tobacco epidemics if these trends remain unchanged. Immediate, effective, and sustained action is necessary to attain and maintain desirable trajectories for tobacco control and achieve global convergence towards elimination of tobacco use. Funding: Ministry of Health, Labour and Welfare, Japan; Ministry of Education, Culture, Sports and Technology, Japan; Department of Health, Australia; Bloomberg Philanthropies