Spatial and temporal statistics of SAR and InSAR observations for providing indicators of tropical forest structural changes due to forest disturbance

Tropical forests are extremely important ecosystems which play a substantial role in the global carbon budget and are increasingly dominated by anthropogenic disturbance through deforestation and forest degradation, contributing to emissions of greenhouse gases to the atmosphere. There is an urgent need for forest monitoring over extensive and inaccessible tropical forest which can be best accomplished using spaceborne satellite data. Currently, two key processes are extremely challenging to monitor: forest degradation and post-disturbance re-growth. The thesis work focuses on these key processes by considering change indicators derived from radar remote sensing signal that arise from changes in forest structure. The problem is tackled by exploiting spaceborne Synthetic Aperture Radar (SAR) and Interferometric SAR (InSAR) observations, which can provide forest structural information while simultaneously being able to collect data independently of cloud cover, haze and daylight conditions which is a great advantage over the tropics. The main principle of the work is that a connection can be established between the forest structure distribution in space and signal variation (spatial statistics) within backscatter and Digital Surface Models (DSMs) provided by SAR. In turn, forest structure spatial characteristics and changes are used to map forest condition (intact or degraded) or disturbance. The innovative approach focuses on looking for textural patterns (and their changes) in radar observations, then connecting these patterns to the forest state through supporting evidence from expert knowledge and auxiliary remote sensing observations (e.g. high resolution optical, aerial photography or LiDAR). These patterns are descriptors of the forest structural characteristics in a statistical sense, but are not estimates of physical properties, such as above-ground biomass or canopy height. The thesis tests and develops methods using novel remote sensing technology (e.g. single-pass spaceborne InSAR) and modern image statistical analysis methods (wavelet-based space-scale analysis). The work is developed on an experimental basis and articulated in three test cases, each addressing a particular observational setting, analytical method and thematic context. The first paper deals with textural backscatter patterns (C-band ENVISAT ASAR and L-band ALOS PALSAR) in semi-deciduous closed forest in Cameroon. Analysis concludes that intact forest and degraded forest (arising from selective logging) are significantly different based on canopy structural properties when measured by wavelet based space-scale analysis. In this case, C-band data are more effective than longer wavelength L-band data. Such a result could be explained by the lower wave penetration into the forest volume at shorter wavelength, with the mechanism driving the differences between the two forest states arising from upper canopy heterogeneity. In the second paper, wavelet based space-scale analysis is also used to provide information on upper canopy structure. A DSM derived from TanDEM-X acquired in 2014 was used to discriminate primary lowland Dipterocarp forest, secondary forest, mixed-scrub and grassland in the Sungai Wain Protection Forest (East Kalimantan, Indonesian Borneo) which was affected by the 1997/1998 El Niño Southern Oscillation (ENSO). The Jeffries- Matusita separability of wavelet spectral measures of InSAR DSMs between primary and secondary forest was in some cases comparable to results achieved by high resolution LiDAR data. The third test case introduces a temporal component, with change detection aimed at detecting forest structure changes provided by differencing TanDEM-X DSMs acquired at two dates separated by one year (2012-2013) in the Republic of Congo. The method enables cancelling out the component due to terrain elevation which is constant between the two dates, and therefore the signal related to the forest structure change is provided. Object-based change detection successfully mapped a gradient of forest volume loss (deforestation/forest degradation) and forest volume gain (post-disturbance re-growth). Results indicate that the combination of InSAR observations and wavelet based space-scale analysis is the most promising way to measure differences in forest structure arising from forest fires. Equally, the process of forest degradation due to shifting cultivation and post-disturbance re-growth can be best detected using multiple InSAR observations. From the experiments conducted, single-pass InSAR appears to be the most promising remote sensing technology to detect forest structure changes, as it provides three-dimensional information and with no temporal decorrelation. This type of information is not available in optical remote sensing and only partially available (through a 2D mapping) in SAR backscatter. It is advised that future research or operational endeavours aimed at mapping and monitoring forest degradation/regrowth should take advantage of the only currently available high resolution spaceborne single-pass InSAR mission (TanDEM-X). Moreover, the results contribute to increase knowledge related to the role of SAR and InSAR for monitoring degraded forest and tracking the process of forest degradation which is a priority but still highly challenging to detect. In the future the techniques developed in the thesis work could be used to some extent to support REDD+ initiatives

Multiscale Representations for Manifold-Valued Data

We describe multiscale representations for data observed on equispaced grids and taking values in manifolds such as the sphere $S^2$, the special orthogonal group $SO(3)$, the positive definite matrices $SPD(n)$, and the Grassmann manifolds $G(n,k)$. The representations are based on the deployment of Deslauriers--Dubuc and average-interpolating pyramids "in the tangent plane" of such manifolds, using the $Exp$ and $Log$ maps of those manifolds. The representations provide "wavelet coefficients" which can be thresholded, quantized, and scaled in much the same way as traditional wavelet coefficients. Tasks such as compression, noise removal, contrast enhancement, and stochastic simulation are facilitated by this representation. The approach applies to general manifolds but is particularly suited to the manifolds we consider, i.e., Riemannian symmetric spaces, such as $S^{n-1}$, $SO(n)$, $G(n,k)$, where the $Exp$ and $Log$ maps are effectively computable. Applications to manifold-valued data sources of a geometric nature (motion, orientation, diffusion) seem particularly immediate. A software toolbox, SymmLab, can reproduce the results discussed in this paper

Wavelet Based Analysis of TanDEM-X and LiDAR DEMs across a Tropical Vegetation Heterogeneity Gradient Driven by Fire Disturbance in Indonesia

Three-dimensional information provided by TanDEM-X interferometric phase and airborne Light Detection and Ranging (LiDAR) Digital ElevationModels (DEMs) were used to detect differences in vegetation heterogeneity through a disturbance gradient in Indonesia. The range of vegetation types developed as a consequence of fires during the 1997-1998 El Niño. Two-point statistic (wavelet variance and co-variance) was used to assess the dominant spatial frequencies associated with either topographic features or canopy structure. DEMs wavelet spectra were found to be sensitive to canopy structure at short scales (up to 8 m) but increasingly influenced by topographic structures at longer scales. Analysis also indicates that, at short scale, canopy texture is driven by the distribution of heights. Thematic class separation using the Jeffries-Matusita distance (JM) was greater when using the full wavelet signature (LiDAR: 1.29 ≤ JM ≤ 1.39; TanDEM-X: 1.18 ≤ JM ≤ 1.39) compared to using each decomposition scale individually (LiDAR: 0.1 ≤ JM ≤ 1.26; TanDEM-X: 0.1 ≤ JM ≤ 1.1). In some cases, separability with TanDEM-X was similar to the higher resolution LiDAR. The study highlights the potential of 3D information from TanDEM-X and LiDAR DEMs to explore vegetation disturbance history when analyzed using two-point statistics.</p

SIMULATING SEISMIC WAVE PROPAGATION IN TWO-DIMENSIONAL MEDIA USING DISCONTINUOUS SPECTRAL ELEMENT METHODS

We introduce a discontinuous spectral element method for simulating seismic wave in 2- dimensional elastic media. The methods combine the flexibility of a discontinuous finite element method with the accuracy of a spectral method. The elastodynamic equations are discretized using high-degree of Lagrange interpolants and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix and the use of discontinuous finite element method makes the calculation can be done locally in each element. Thus, the algorithm is simplified drastically. We validated the results of one-dimensional problem by comparing them with finite-difference time-domain method and exact solution. The comparisons show excellent agreement