2.4 Conclusions
4.2.4. Calculating an experimental variogram from coverage data
As we mention in Section 4.2.1 and 4.2.2, the use of 'coverage data' provides us with the opportunity to subsample data to calculate the roughness index. We also sample from the raster dataset to reduce the computational load of calculating variograms.
The empirical variograms we calculate from the point data sources re use observations (as is typical of the classical empirical variogram). This is a departure from the preferred methods for calculating the Hurst exponent (from which the roughness index is derived). Typically studies that calculate the Hurst exponent use a sampling design that ensures that each pair of observations are used exclusively in a single bin.
Using coverage data allows us to control the sampling design in a way that we cannot when we are using legacy data. In the previous chapter we discuss some of the potential impacts of legacy data By selecting unique pairs at pre-specified separation distances or lags, we can avoid potential issues with autocorrelation.
We use the ‘random pairs’ sampling design described in Chapter 3. This design ensures both that unique pairs are used for the calculation of pairs (avoiding the problem with autocorrelation17), and
that the underlying distribution of points are random (avoiding potential problems with grid based sampling). This design also allows us to dictate the lags.
4.2.4.2. Coverage datasets – summary of key parameters
We selected coverage datasets that described properties of interest and that were suitable for our modelling. The calculation of the semivariogram (upon which our roughness index is based) requires that the data is numeric and ordinal, so we did not include categorical variables. We also required datasets with a reasonably fine support or resolution. For example, we chose not to use climate data available from the Australian Bureau of Meteorology comes at a 5km resolution which makes modelling below this resolution meaningless.
We present a brief summary of key properties of each of the coverage datasets that we use in Table 4.2 above, and more detail about each dataset in Sections 4.2.3.3. to 4.2.3.8.
17 There is still a minor issue with auto-correlation because pixels are not excluded after they have been sampled, so a small
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4.2.4.3. Digital Elevation Model – smoothed
A number of terrain models that model different features of terrain at high resolution have been developed by the Commonwealth Scientific and Industrial Research Organisation of Australia (CSIRO). All of these models ultimately derive from the Shuttle Radar Topography Mission (SRTM) satellite data collected by NASA during its 2000 space shuttle mission (Farr et al., 2007). We briefly describe the meaning of each layer and the basic processing/ modelling used below.
The digital elevation model represents ground surface topography. It has been filtered from vegetation features and is smoothed to reduce noise to better represent the surface shape (Geoscience Australia, accessed 2018). The smoothing processes mean that the DEM-Smooth supports calculation of local terrain shape attributes such as slope, aspect and curvature that cannot be reliably derived from the unsmoothed 1 second DEM because of artefacts (Gallant, 2011).
4.2.4.4. Percentage slope
Calculated from the smoothed digital elevation model, percentage slope measures the deviation from horizontal or flat of the land surface. Percentage slope provides information about likely run off and erosion potential.
4.2.4.5. Elevation focal range – 300m
Derived from the DEM – Smoothed data, the elevation range measures the full range of elevations within a circular window in this case 300m. This data can be used as a representation of local relief (CSIRO 2018).
4.2.4.6. Radiometric data
We use percentage of Potassium from the Radiometric map of Australia (Minty et al., 2009) as a proxy for soil mineralogy. Airborne Radiometric surveys have diffuse boundaries. The strongest signal comes from the area directly below the observation, but lateral observations continue to affect the signal. As lateral distance increases, the contribution to the signal decreases (Minty, 1997). This gradual reduction in signal influence with distance has a smoothing effect on local variability.
The map provides levelled and merged composite grids of radiometric regions of interests (ROIs) pertaining the potassium, thorium, uranium and total count over Australia at a 100m resolution. The
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raw data for the map comes from systematic airborne radiometric surveys undertaken over the last 40 years. The resolution of the airborne surveys is shown below (Figure 4.3 taken from Minty et al., 2009). The Radiometric data was aligned to a common datum, and older surveys were back calibrated using new field observations. Details of the alignment and calibration are available in Minty et al., (2009).
Figure 4.3. Left Panel: Radiometric sampling density (Minty et al. 2009) Right Panel: Potassium layer
from the radiometric map of Australia (original source Geoscience Australia).
While the soil samples are observed to a given depth, sometimes >2m, the radiometric data tends to observe only the top of the soil profile, typically the top 35cm (Minty, 1997). The footprint (which can be thought of loosely as the support) of an airborne radiometric survey will typically be around 50- 100 meters, with diffuse boundaries due to the low linear attenuation co-efficient of air18.
18
The linear attenuation co-efficient describes how many atoms there are in a cubic cm volume of material. The lower the linear attenuation co-efficient, the wider the spatial range of materials that will affect the
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4.2.4.5. Enhanced Vegetation Index
Enhanced Vegetation Index appears to be better than NDVI (the traditional vegetation indices) at discriminating in areas of high vegetation density (Didan, et al., 2015). EVI is calculated using visible and near visible spectrum (Didan et al. , 2015):
𝐸𝑉𝐼 = 𝐺 𝑁𝐼𝑅 − 𝑅𝑒𝑑
𝑁𝐼𝑅 + 𝐶1𝑅𝑒𝑑 − 𝐶2𝐵𝑙𝑢𝑒 + 𝐿
NIR, Red, and Blue are surface reflectance (full or partially atmospheric-corrected for Rayleigh
scattering and ozone absorption. L, C1, C2 and G are all coefficients. L is the canopy background adjustment for correcting the nonlinear, differential NIR and red radiant transfer through a canopy.
C1 and C2 are the coefficients of the aerosol resistance term (which uses the blue band to correct for
aerosol influences in the red band). G is a gain or scaling factor. The coefficients adopted for the MODIS EVI algorithm are, L=1, C1=6, C2=7.5, and G=2.5 (Didan et al., 2015).
The MODIS EVI that we use has a 16 day temporal resolution and a 250m spatial resolution. The best pixels from the 16 day temporal window are used. In some cases (e.g. where cloud cover is high), there will not be any quality information recorded in a given 16 day window (observations are taken daily) and the pixel values will be based on modelled data.