Data processing

2.4.1. Spectral vegetation indices

Mathematical combinations of spectral bands represent a classic tool in the field of optical remote sensing. Owing to the characteristic spectral response of the materials contained, adequate band combinations facilitate the discrimination of different target surfaces and ideally reduce the signal variations caused by atmospheric properties, sensor viewing geometry, terrain or surface background signals (Baret and Guyot, 1991; Jones and Vaughan, 2010). With regards to green foliage, strong absorptions by chlorophyll across the visible spectrum and by cell water content in certain spectra of the SWIR, respectively, contrast with the high reflectance of vital cell tissue in the NIR. As such, the combination of spectra results in potentially useful information for the study of vegetation. For instance, combinations incorporating the red and NIR are frequently applied, as their contrast is sensitive to the amount and vitality of vegetation present. A vast list of SVIs of varying complexity and (sensor-specific) spectra have been proposed (see Bannari et al. (1995) for an overview) in order to quantitatively derive and monitor vegetation and its condition.

Considerable uncertainties are associated with the application of satellite-based SVI and real-world canopies. Firstly, as a function of spatial resolution of the sensor, the spectral signal detected is a spatial average across the entity of observation, i.e. the pixel. Secondly, radiative transfer at vegetated surfaces is complex (Jones and Vaughan, 2010; Ollinger, 2011; Sellers, 1985): foliage arrangement (e.g. leaf angles) and chemical properties, non-photosynthetic canopy components (e.g.

litter, stems, fruits, and flowers), but also shadows and background conditions (e.g. soil, understorey vegetation) all contribute to the spectral signal detected. When considering the low to moderate plant covers of dry savannas, their distinct spatial clumping of individuals, and the offset phenology (e.g. green canopy vs. senescent herbaceous understorey), the spectral signals of green vegetation are likely to be complicated. Although SVI are accepted proxies for biophysical (e.g. aboveground biomass, LAI, and fractional cover), and biochemical (e.g. nitrogen, chlorophyll) properties of vegetation, they often only yield moderate correlations with field-measured quantities (Glenn et al., 2008; Sellers, 1985). Furthermore, no single SVI has been identified as “the best” across different species, canopy architectures, and leaf structures (Huete, 2014; Viña et al., 2011). In order to relate field-measured properties of vegetation to their representation in satellite imagery, a large set of sensor-specific candidate SVI had to be considered (see Chapter 5 for a full overview).

2.4.2. Time series analysis

A distinct feature of operationally-produced remote sensing data is the potential to monitor ecological processes and phenomena based on the temporal integration of systematic discrete time steps. Each individual raster in the temporal domain covers the same spatial extent and resolution, i.e. the spatial domain. Resultantly, per-pixel analyses may be performed similar to non-spatial time series. Given a sufficient temporal record (e.g. 2000-2016 in case of the MODIS products), the typical behaviour¹³ in terms of time and magnitude of an observed variable can be characterized according to its temporal aggregation and descriptive statistics. For instance, per-pixel TAMSAT monthly precipitation sums were aggregated to annual sums¹⁴ and subsequently averaged across the full period of observation to yield MAP.

The calculation of metrics from satellite time series suffers from data gaps and quality issues.

Temporary instrument failure, limited observations due to prolonged cloud cover (in the case of land surface products), as well as atmospheric, and sensor-viewing properties may contribute to time series gaps and observations of varying quality (Eklundh and Jönsson, 2017; Goward et al., 1991). As a consequence, satellite time series are often delivered in aggregated time steps, which also holds benefits for their processing performance. MODIS products are made available with a Quality Assurance (QA) layer that indicates the quality of retrieval for each pixel. Accordingly, the MODIS time series used within this thesis (MCD45A1 and MOD13A1; see Chapter 2.3.4) were filtered to include only retrievals of highest quality. This constrained the MCD45A1 BA record (see Figure 3), while intending to increase its reliability.

Figure 3: Exemplary illustration of the MCD45A1 Quality Assurance (QA) layer for the study area in northern Otjozondjupa, Namibia. Burned area sums from April 2012 to March 2013 (in red) were filtered to highest-quality retrievals only (QA=1; in grey).

As NDVI time series, such as the MOD13A1 product, are sensitive to changes in green vegetation, they facilitate the derivation of phenological metrics. In order to close the gaps arising from quality filtering and to deal with noise in the data, smoothing functions, which are fitted per-pixel, are usually applied. Noisy observations frequently introduce a negative bias. Hence, smoothing functions intend to fit to the upper envelope of the data (Eklundh and Jönsson, 2017). The present thesis fitted

13 Different terminologies are used within scientific disciplines to describe the typical behaviour of a variable:

e.g. climatologies in atmospheric sciences, or fire regime (parameters) in fire ecology, respectively.

14 Annual sums of precipitation were calculated from September to August of the next year with regards to the initialization of the rainy season across large parts of Namibia.

the MOD13A1 NDVI record using a double logistic function (Beck et al., 2006). The suitability of the double logistic function for unimodal growing seasons has been confirmed across various canopy architectures (e.g. Atkinson et al., 2012; Butt et al., 2011; Fischer, 1994; Hird and McDermid, 2009).

Seasonally-decomposed phenological metrics were then averaged per pixel and across the NDVI record. However, a trend analysis, as has been performed on comparable datasets (e.g. Andela et al., 2017; Brandt et al., 2016; Fensholt et al., 2009; Maidment et al., 2015), was beyond the scope of this work.

2.4.3. Unmanned Aerial Vehicle photogrammetry

Photogrammetry generally aims at making measurements from imagery. Established photogrammetric methods for aerial triangulation¹⁵ were not designed for surveys using an UAV (Colomina and Molina, 2014). Their inefficiency with the use of UAV imagery arises from uncalibrated cameras in terms of lens geometry and distortion, and the irregularities in image acquisition such as variations in overlap and camera attitude, i.e. the 3D position and orientation.

Thus the determination of interior and exterior image orientations and the 3D scene reconstruction thereof are nowadays frequently accomplished by computer vision techniques (Carrivick et al., 2016; Colomina and Molina, 2014). The Structure-from-Motion (SfM) - Multi-View Stereopsis (MVS) approach provides a flexible, yet to some degree arbitrary, framework to process UAV imagery (see Westoby et al. (2012), or Carrivick et al. (2016) for detailed overviews). In brief, so-called tie points, which are based on the recognition of common scale-invariant features among the imagery (e.g. Lowe, 2004) are initially identified with SfM-MVS photogrammetry. From the tie points, camera position and orientation are estimated, and planar image points are re-projected into 3D coordinates. The product of this bundle (block) adjustment is a sparse Image-Based Point Cloud (IBPC). At this stage, spatial reference data, such as high-accuracy Ground Control Points (GCP), are introduced in order to optimize the absolute positioning of the sparse IBPC. As absolute spatial accuracy was not a priority here, only the flight telemetry data from the on-board INS/GNSS (see Chapter 2.3.8) were used for spatial referencing. Subsequently, computationally intensive MVS algorithms that iteratively optimize the 3D reconstruction using textural image information and filtering procedures were applied. The resultant dense IBPC was then spatially interpolated in order to yield a Digital Surface Model (DSM) and to derive an orthomosaic (see Figure 4).

2.4.4. Derivation of canopy height

The estimates of canopy height from 3D remote sensing data, i.e. a Canopy Height Model (CHM), may provide spatially consistent insights into stand structure. In a first step, a CHM was derived from the difference in height between the canopy and ground level (Chen et al., 2006). In order to adequately reflect the stand structure, a delineation of individuals and their maximum height from the CHM was necessary. However, this is admittedly a difficult task when it comes to connected crowns with similar heights of individuals, or irregularly shaped crowns. Hence, open and uneven canopies in savannas should be fairly well suited for an automated delineation as compared to closed forest canopies. Several methods are reported in the literature, which are reviewed by Ke and Quackenbush (2011) and, with a focus on LiDAR, by Zhen et al. (2016). Rather than a survey-grade, high-resolution DEM of the solid ground which was not available for northern Otjozondjupa, a

15 Aerial triangulation describes the process of solving orientations and positions for a set of overlapping imagery with the aim of producing a single aligned image.

separate DEM was derived from a classification of the ground points contained in the dense IBPC (Chapter 2.4.3.). Watershed segmentation was then performed on the CHM, whereby crowns were

“filled” around local maxima points.

Figure 4: Exemplary orthomosaic (left) and hill-shaded Digital Surface Model (DSM; right) near Farm Rooidag, Namibia, that were created using Unmanned Aerial Vehicle (UAV) photogrammetry.

2.4.5. Spatial aggregation and upscaling

Several datasets of different resolution and type (e.g. raster vs. vector) were included in this thesis. In order to facilitate their combined analyses, each dataset had to be aggregated to the resolution of the coarsest respective dataset. The preservation of a maximum of information across scale is a central question in these regards (Hay et al., 1997). One should be aware that different scales of observation may result in different implications drawn thereof – an issue more generally known as the Modifiable Areal Unit Problem (MAUP; Dark and Bram, 2007).

Also data conversions, such as from vector- to raster data format, are likely to introduce errors in shape as a function of the raster’s resolution. Spatial aggregation, as was achieved with resampling techniques and descriptive functions, is usually accompanied by a reduction in variance (Hay et al., 1997). Variance reduction may also be desirable for smoothing noisy data and to enhance processing performance, as was done with the output UAV CHM. A special case of spatial aggregation was the upscaling from discrete point measurements of vegetation attributes to satellite imagery where a statistical model determined the required transfer function (see Chapter 2.5.1).