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104 Figure 3.6: Maximum Likelihood Supervised classification process

Figure 3.7: Landcover/landuse images of (a) 1990, (b) 1999, (c) 2008 (d) 2017 and (e) 2018

105 A method of calculating and comparing the area of the resulting land cover/land use types of each year was adopted for data analysis. The comparison of the landcover/landuse statistics will assist in identifying the percentage change, trend and annual rate of change between 1990 and 2017. In achieving this, table was prepared showing the areas and percentage change for each year measured against each other. To determine the rate of change of landcover/landuse, the year period 1990-2017 was divided into three sub-periods 1990 – 1999, 1999 – 2008 and 2008 - 2017 and compared against each other.

The comparative analysis in landcover/landuse change focuses on the three sub-periods and the spatial distribution of the average (annual) rate of landcover/landuse change between the three periods as proposed by Long et al. (2007).

Percentage change to determine the trend of change can be calculated by dividing the observed change by the sum of the area of the particular landcover/landuse type in that period multiplied by 100

(Trend) % change = Observed change x 100 ____________________

Total Area

Where Observed change = (Area of before year – Area of after year) Total Area = sum of total area of both years

The annual percentage rate = Trend divided by N (number of years).

A trend percentage with a value greater than zero means that the landcover/landuse type has increased over the period of years while a value less than zero shows a decrease in the landcover/landuse type over a period of time.

The transition of the landcover/landuse classes in the last 27 years was also calculated using matrix union and discriminant function change detection in Erdas imagine.

... (3.1)

106 Matrix union and discriminant function change detection was used to compute the probability of change per pixel from two images that depict the same area at different points in time. The process performs an unsupervised classification on the input before image and uses that and discriminant function analysis to compute a probability of change between the input after image to generate any of the output files.

The output images generated are grayscale images composed of single band continuous data with pixel values in the range from 0.0 to 1.0. These values represent the probability that the pixel has changed in a significant way.

I. Values near 0.0 indicate a low probability of change.

II. Values near 1.0 indicate a high probability of change.

This process was done by:

1. Input before Image: This image is the earlier of the two images (before). Enter the name, or click the dropdown arrow to open the Recent Files list.

Click to open a File Selector to navigate to the desired file, or right-click to open the Recent Files list.

2. Input after Image: This image is the more recent of your two images and reflects change over time (after). Enter the name, or click the dropdown arrow to open the Recent Files list.

Click to open a File Selector to navigate to the desired file, or right-click to open the Recent Files list.

3. Specify process Area: Specify the area of the input files to be processed.

107 4. Select Intersection Click to automatically use the intersection of the two input files.

5. Select Coordinate Type: Click the appropriate radio button to select the type of coordinates to use. If the input file does not have map coordinates, the coordinate type will automatically default to File.

6. Specify Output Options: Specify the output files to be generated.

7. Select Positive Change Image: Click to check the checkbox to generate an output image based on Input before Image.

8. Select output [file name]: Enter the output file name.

Click to open a File Selector to navigate to the desired directory, or right-click to open the Recent Files list.

9. Select Negative Change Image: Click to check the checkbox to generate an output image based on Input after Image.

10. Select output [file name]: Enter the output file name.

Click to open a File Selector to navigate to the desired directory, or right-click to open the Recent Files list.

11. Select Combined Change Image: Click to check the checkbox to generate an output image based on a combination of Input before image and Input after image, by using the maximum (highest) file values.

12. Click to open a File Selector to navigate to the desired directory, or right-click to open the Recent Files list.

108 13. Select Low Values: Remove values that are less than the specified number of standard

deviations (Sigma) from the mean of the calculated values. Click to check the checkbox to apply this option, and enter a number of standard deviations.

14. Select - [3.00] Sigma^ Enter a value to represent the number of negative standard deviations. The default is 3.00.

High Values: Remove values that are more than the specified number of standard deviations (Sigma) from the mean of the calculated values. Click to check the checkbox to apply this option, and enter a number of standard deviations.

+ [3.00] Sigma^: Enter a value to represent the number of positive standard deviations. The default is 3.00.

15. Unsupervised Options: An unsupervised classification approach measures a multivariate statistical distance of the pixel DN vectors in one image with spectral signatures derived from the other image. These are then converted into probabilities using a proprietary algorithm.

16. Select number of Classes: Specify the number of classes (categories of data) to be created.

17. Maximum Iterations: Enter the number of maximum times that the ISODATA clustering utility should recluster the data. This parameter prevents this utility from running too long, or from potentially getting "stuck" in a cycle without reaching the convergence threshold.

18. Convergence Threshold: Specify the convergence threshold. The convergence threshold is the maximum percentage of pixels whose cluster assignments can go unchanged

109 between iterations. This threshold prevents the ISODATA utility from running

indefinitely.

By selecting a convergence threshold of .95, you specify that as soon as 95% or more of the pixels stay in the same cluster between one iteration and the next, the utility should stop processing. In other words, as soon as 5% or fewer of the pixels change clusters between iterations, the utility stops processing.

19. Skip Factors: For faster (although less accurate) processing, you can enter an X and Y skip factor.

X: Enter the X skip factors to use when processing. Entering a 1 processes all pixels, 2 processes every other pixel, 3 every third pixel, and so forth.

Y: Enter the Y skip factors to use when processing. Entering a 1 processes all pixels, 2 processes every other pixel, 3 every third pixel, and so forth.

20. Click OK: Click to run this program with the options selected and close this dialog.

This process was done as shown in figure 3.8.

110 Figure 3.8: Matrix union and discriminant function change detection process

The classes i.e. vegetation and open space within the study area were also significantly tested to determine which class contributed to urban area at a probability level of 0.05. The significance level is the probability value that forms the boundary between rejecting and not rejecting the null hypothesis. This was represented as P<0.05 in which P stands for the probability of the null hypothesis. The 0.05 thus represents the probability value that separates a decision to reject null hypothesis from the decision not to reject it.

Figure 3.9: Normal curve showing critical region and significance level at 95% (0.05).

Critical region

Significance level Significance level

0

Acceptance area 47.5% 47.5%

Critical region

111 The t- test was used to determine whether two classes are significantly different. The formula used is given in equation 3.2 by Pradhan et al, (2013). Figure 4.9 shows significance level at 95%.

t = X1 – X2 ... (3.2)

Where X1& X2 -Mean of classes S - Standard deviation

n - Number of subjects in each class