Preliminary data analysis

Prior to further analysis, a first step is to calculate the correlation between TM bands. As one would normally expect, there is a high correlation between the three visible bands, and between bands 5 and 7 in the middle infrared (table 4.3). Other correlations are medium, although the therm al band (6) is almost completely uncorrelated with the visible bands. One may conclude that TM data is essentially three- dimensional among the reflected bands and four dimensional when the therm al band is included. Band 6 is also distinguished by substantially

higher m ean values and low variance, both indicative of its fundamentally different nature. These tables are used further both in interpreting the results of principal component analysis and in assessing appropriate spectral band ratios.

Table 4.2 TM band statistics

Band Mean Standard

1 27.27 30.36 2 18.67 19.18 3 23.95 26.78 4 51.91 23.62 5 60.58 43.17 6 119.05 7.21 7 28.26 27.34

Table 4.3 Between band correlations for TM bands (significant

TM 1 2 3 4 5 6 Band 1 2 .972 3 .976 .993 4 .468 .564 .568 5 .637 .603 .658 .629 6 -.059 -.025 .012 .423 .466 7 .720 .663 .720 .484 .968 .356 4.3 Band ratios

W ith six TM bands, it is possible to generate 15 different ratios and their reciprocals but ratios between bands that are highly correlated such as 1, 2 and 3 yield little useful information, leaving the eleven ratios in table 4.4 . All ratios were calculated first using the 8-bit digital numbers of the TM bands and secondly their raw radiance values, as

some authors claim this is important for 'true' ratio values. However no significant difference was found either in the visual appearance of the ratio images, nor in the statistical distribution of their pixel values. As a result, it was not considered necessary to look any further into the radiance values.

Table 4.4 Main band ratios products eocamined

nd ratio Mean Std. de)

4/1 39.72 25.75 4/2 68.19 37.37 4/3 70.10 42.29 5/1 48.65 22.16 5/2 54.74 19.57 5/3 101.05 36.75 7/1 52.77 20.08 7/2 33.52 12.60 7/3 76.44 22.94 7/4 22.31 11.49 5/4 24.14 11.93

Table 4.5 Class Correlation Matrix for selected band ratios

Ratio 4/1 4/2 4/3 5/1 5/2 5/3 7/1 7/2 7/3 4/1 4/2 .96 4/3 .96 .96 5/1 .88 .85 .80 5/2 .67 .75 .63 .90 5/3 .84 .86 .85 .94 .90 7/1 .53 .52 .42 .89 .84 .76 7/2 .06 .14 .001 .46 .72 .45 .83 7/3 .34 .38 .32 .66 .82 .72 .90 .90 5/4 -.70 -.70 -.74 -.40 -.14 -.38 .074 .50 .26 7/4 -.72 -.72 -.75 -.46 -.22 -.46 .026 .46 .22 5/4 .97

This still leaves a possible 165 combinations of three ratios (11*10*9/ 6), which can be reduced since while all band ratios elim inate the topographic effect to some degree, many are highly correlated, displaying the same features as other ratio channels. It is possible to find the best 3 ratio band combination in term s of non-redundancy and information content by determining the 'Optimum Index Factor' (OIF) for potential combinations. This is given for any 3-band combination as the sum of their three standard deviations, divided by the sum of the three correlations between each pair, added absolutely, without regard to positive or negative sign (Sheffield, 1985). It can be written thus:

OIFabc - ^ (®a ®c) / I X (r ah + rbc + rac) I

The optimum then is likely to result from a combination that provides a high num erator and/or a low denominator. Ratios which tend to have larger variance will reduce the need to stretch the data values which can induce more noise. Ratios which are not highly correlated to each other will contain different information. Logically, sim ilar ratios which combine bands from the same two of the three spectral groups (1-2-3, 4 and 5-7) will be highly correlated, for example 7/1 , 5/2 and 7/3. An optimum combination would thus consist of three ratios, where each one

represents a ratio between two of the three groups, e.g. 4/1, 7/1 and 5/4.

The possibilities can be further reduced by ackowledging the similarity of 4/1, 4/2 and 4/3 and also 5/4 and 7/4. We will accept 4/3 given its importance in vegetation discrimination as a ratio and vegetation index, and also because in this instance both 4/1 and 4/2 appeared to retain some topographic effect. We will also accept 5/4 over 7/4 as it has a higher variance, and because band 5 has greater application than band 7

in vegetation sensing. In this case 5/4 is also visually less noisy than 7/4. OIF scores are tabulated below for the resulting possible combinations:

Table 4.6 Optimum Index Factor scores for 3-ratio combinations

Ratio 1 Ratio 2 Ratio 3 XNum XDenom OIF

4/3 5/1 5/4 76.38 1.94 39.37 4/3 6/2 5/4 73.79 1.47 50.20 4/3 5/3 5/4 90.97 1.97 46.18 4/3 7/1 5/4 74.30 1.23 60.41 4/3 7/2 5/4 66.82 1.26 53.02 4/3 7/3 5/4 75.73 1.29 58.71

On this basis, it can be concluded th at the best 3 channel band ratio combination containing the most information is 4/3, 5/4 and 7/1. These are displayed in figures 4.1 and 4.2. Ratio images of this landscape, while clearly differentiating between vegetated and non-vegetated areas, generally appear to be inherently noisy within forested areas, in that they contain random variations in pixel intensity. The 4/3 ratio however contains a particularly useful feature, in that it naturally separates land cover into four general groupings, if the process truncates the real numbers generated by dividing the digital numbers in band 4 by band 3. These appear in increasing lightness from black to near white, although the distinction may not have reproduced as clearly in figure 4.2b:

DN Shade Vegetation cover

0: black no vegetation- rock and water

1: dark gray alpine tundra and grassland, including roadsides

2: light gray coniferous forests

These groups can potentially be further refined to separate vegetated and non-vegetated surfaces by setting more precise threshold boundaries or by using the normalised ratio, also known as the normalised difference vegetation index or ’NDVI' (figure 4.3a). Small 'outliers' can be elim inated by using a 'filter' or 'sieve' that removes those below a selected threshold size (figure 4.3b). This can also be performed using similar operations in a raster geographic information system (GIS), that recognise contiguous groupings of similar pixels and allows the user to select desired groupings by number.

Bare rock and water surfaces, while similar in lacking vegetation are obviously fundamentally different in surface type; bare rock is strongly influenced by the effects of topography, while water surfaces have zero slope and aspect. They can be separated by combining the above 'density slice', with a density slice of an infra-red band, in which water surfaces have very low or zero reflectance. Band 4 is often the best in mountainous environments as ice and snow also have low reflectance in bands 5 and 7. By overlaying this image with the 4/3 ratio, water can be separated from bare rock since water is low or zero in both, while bare rock has zero values in the ratio but high values in band 4 (figure 4.4 ).

Figure 4.1 Band ratios: 5 /4 (above) and 7/1 (below)

Note that undesirable striping on the lakes can be removed by overlaying the ratio with a binary mask for water (see figure 4.4b)

Figure 4.2 Band ratios 4/3:

8-bit stretched values (above) and unstretched values 0-4 (below)

Figure 4.3 Binary mask from 4/3 separating vegetation from non- vegetated, initial image (above) and 'sieved'(below): black = vegetated

Figure 4.4 Binary mask for vegetation (above) and water (below) above: Black is water and bare rock; hence vegetated = white

4.4 Principal Component Analysis (PCA)