2. The Global Digital Elevation Model (GTOPO30) of Great Basin Location: latitude 38  15’ to 42  N, longitude 118  30’ to 115  30’ W Grid size: 925 m Elevation range: 1,005 – 3,651 m (rescaled to the interval of 0 to 255 - the brightest pixel has the highest elevation)

3.  One of the primaries issues in dealing with DEMs are uncertainties caused by: Data errors: ○ Data capture errors: Cloud or forest cover Instable remote sensing equipment Atmospheric refraction ○ Analysis and visualization errors: Interpolation procedures The limited horizontal and vertical resolution of terrain models Scale ○ Spatial resolution ○ Spatial extent Lack of standardization  These factors lead to uncertainties in the extracted landforms and features

4. Multiscale DEMs generated using the lifting scheme, using scales of 1 to 20 Scale: 1 Scale: 3 Scale: 5 Scale: 10Scale: 15Scale: 20

5. Multiscale DEMs generated using the lifting scheme, using scales of 1 to 20 Scale: 1 Scale: 3 Scale: 5 Scale: 10 Scale: 15 Scale: 20

6. Scale: 1Scale: 3 Scale: 5 Scale: 10Scale: 15Scale: 20

7.  Segmentation of the terrain of the DEM of Great Basin into the predominant physiographic features; mountains, basins and piedmont slopes Mountains Piedmont slopes Basins

8. MountainsBasins Piedmont slopes

9. Basins Scale: 1 Scale: 3 Scale: 5 Scale: 10 Scale: 15 Scale: 20

10. Piedmont slopes Scale: 1 Scale: 3 Scale: 5 Scale: 10 Scale: 15 Scale: 20

11.  A number of studies have been conducted on classification of various landforms extracted from multiscale DEMs, including: Physiographic features (mountain, basin & piedmont slope) Morphometric features (plane, channel, ridge, pass, peak & pit) Hydrological features (drainage networks & catchments) Beach landforms (foreshors, beach & foredune) Soil properties (anthrosols, flovisols, cambisols & podzols)  However, not much attention has been provided on the effect of multiscaling on elevation variances.

12.  To conduct the statistical analysis of elevation variances of cells of physiographic features extracted from multiscale DEMs.  The statistical parameters analysed are: Measures of centrality and variability: mean & standard deviation Measures of distribution shape: skewness & kurtosis Measures of complexity: energy & entropy

13.  The most common method to extract statistical parameters of an image is by employing the first order distribution P(b) of the intensities of the image.  DEMs are greyscale images with the intensity of each cell representing elevation at the corresponding location.  For each elevation b in the elevation range (b min to b max ) of a region with area of M cells, P(b) is computed as follows:  where N(b) is the number of cells with elevation b.

14.  Measures of Centrality and Variability Mean S M provides the numerical average of the set of elevation values of the DEM, and indicates where the distribution of the elevations is centred. Standard deviation S D : Indicates the variability of the distribution from the mean. It is often used as a measure of surface roughness, quantifying the vertical deviations of the surface from its best-fit plane, represented by the mean

15.  Measures of Distribution Shape Skewness S S : Characterises the degree of asymmetry of the elevation distribution around the mean. A distribution that is symmetric about the mean has skewness of 0. Values greater than 0 indicate skewness of distributions to the right of the mean, while values less than 0 indicate skewness to the left.

16.  Measures of Distribution Shape Kurtosis S K : A measure the relative peakedness of a distribution relative to the normal distribution. The kurtosis of a normal distribution is 0. Distributions that are more outlier-prone than the normal distribution have kurtosis greater than 0, while lower outlier- prone distributions have kurtosis less than 0.

17.  Measures of Complexity Energy S N : Provides a measure of repeated transitions in the distributions. Energy is a measure of surface roughness, with a higher value indicating a higher rate of repeated transitions and hence, decreased surface roughness, and vice versa.

18.  Measures of Complexity Entropy S E : Is a measure of randomness that can be used to characterise the elevation variation of a DEM. It provides a low value when the elevations have similar values, and a high value when the elevations vary significantly. Entropy is also often used as a measure of surface roughness

19.  For the respective DEMs and physiographic features, varying patterns are observed in the plots due to varying surface profiles, and the changes that occur over the scales.  For all the parameters, with the exception of mean elevation, the DEMs and mountains exhibit similar patterns at the initial scales, indicating that mountains are the more dominant of the three predominant physiographic features in deciphering terrain character. Mean Standard deviationSkewness Kurtosis Energy Entropy

20.  Mean: Mountains have the highest mean elevations as compared to the other features over the scales. The mean elevations for the DEMs and mountains decrease with increasing scale due to the removal of fine detail. However, for basins, the mean elevations increase over scale, as the removal of fine detail causes the removal of concave regions, resulting in increased elevations in the basin regions. The mean elevations of the piedmont slopes increase at the initial scales due to the removal of concave regions, but then decrease drastically due to the removal of fine detail in these regions.

21.  Surface roughness: Standard deviation, energy and entropy are measures of surface roughness. It is expected that increase in scale will result in decreased surface roughness for the DEMs and physiographic features due to the removal of curvature regions, and hence, reduced vertical deviations from the best-fit plane Standard deviation Energy Entropy

22.  Entropy: Decreasing values over scale The DEMs and mountains have higher entropy values compared to the basins and piedmont slopes until the final three scales, where the mountains regions have largely been removed

23.  Energy: The energies of the DEMs and physiographic features increase over the scales, indicating increased occurrences of repeated elevation transitions between the cells and hence, reduced surface roughness. The DEMs and mountains exhibit lower energies, and hence, higher surface roughness, as compared to the basins and piedmont slopes.

24.  Standard deviation: The standard deviations of the DEMs and mountains decrease with increasing scale. While both show similar values at the initial scales, the standard deviations of the mountains then decrease drastically, having significantly lower values than the basins and piedmont slopes. Despite the removal of curvature regions, the basins and piedmont slopes have increasing standard deviations at the initial scales, after which the basins have reducing values and the piedmont slopes have fluctuating values. The accuracy of standard deviation of elevation as a measure of surface roughness has been called into question as it fails to quantitatively discriminate between surfaces of different amplitudes, frequencies and correlations, and is sensitive to abrupt strong variations in elevation

25.  Distribution shape: Values of skewness and kurtosis over the scales indicate that elevation distributions decrease at: Higher rates as compared to mean elevations for the DEMs and mountains Lower rates for the piedmont slopes Similar rates for the basins. Skewness Kurtosis

26.  This study has provided key insights into the statistical behaviour of elevation variances of cells of physiographic features extracted from multiscale DEMs.  For all the parameters, with the exception of mean elevation, the DEMs and mountains exhibit similar patterns at the initial scales, indicating that mountains are the more dominant of the three predominant physiographic features in deciphering terrain character.  Mean elevation: The loss of fine detail during multiscaling causes the mean elevations of the DEMs and mountains to decrease. Elevation gain due to removal of concave regions causes the mean elevation of the basins to increase. The mean elevation of the piedmont slopes initially increases due to the removal of concave regions, but then decreases drastically due to the removal of fine detail.

27.  Surface roughness: Energy and entropy prove to be effective surface roughness measures, providing decreasing roughness values for the DEMs and physiographic features over the scales. On the other hand, standard deviation of elevation is found to be an ineffective surface roughness measure as it fails to quantitatively discriminate between surfaces of different amplitudes, frequencies and correlations, and is sensitive to abrupt strong variations in elevation.  Values of skewness and kurtosis over the scales indicate that elevation distributions decrease at higher rates as compared to mean elevations for the DEMs and mountains, lower for the piedmont slopes, and similar for the basins.  Scope for future work:  For the purposes of this study, the analysis was conducted for a mountainous terrain, with rough surface profile.  For future work, the analysis will be extended to terrains of varying profiles and character.