CHAPTER 3 GEOGRAPHIC INFORMATION SYSTEM (GIS)
3.2 Materials and methods
3.2.4 GIS analysis
Table 3.11: Description of the map units of vegetation (SANBI, 2012) found at the significant areas of the NWP (continued).
Map Unit Description
Kimberley Thornveld Plains often slightly irregular with well-developed tree layer dominated by Acacia species
Klerksdorp Thornveld Plains or slightly irregular undulating plains with open to dense V.
karroo bush clumps in dry grassland Mafikeng Bushveld Well-developed tree and shrub layers
Marikana Thornveld Open Vachellia karroo woodland, occurring in valleys and slightly undulating plains and some lowland hills. Shrubs are denser along
drainage lines and rocky outcrops or areas protected from fire Moot Plains Bushveld Open to closed, low, often thorny savanna dominated by Acacia
species in the bottomlands and plains
Norite Koppies Bushveld A low, semi-open to closed woodland up to 5 m tall, consisting of dense deciduous shrubs and trees with very sparse undergrowth on shallow
soils, with large areas covered by vegetation Northern Afrotemperate
Forest
Low, relatively species-poor forests of Afromontane origin and some of them still showing clear Afromontane character
Pilanesberg Mountain Bushveld
Broad-leaved deciduous bushveld with trees and shrubs with grass layer on slopes of mountains and hills
Schmidtsdrif Thornveld Mostly a closed shrubby thornveld dominated by S. mellifera and V.
tortilis. Vegetation is sometimes very disturbed due to overgrazing by goats and other browsers
Schweizer-Reneke Bushveld
Plains, slightly undulating plains and some hills, supporting open woodland with a fairly dense shrub layer, with Acacia trees dominant Waterberg-Magaliesberg
Summit Sourveld
Higher slopes and summit positions including crests and steep rocky scarps and cliff faces, covered with grassland dominated by wiry
tussock grasses Western Highveld Sandy
Grassland
Flat to gently undulating plains with short, dry grassland, with some woody species occurring in bush clumps
Zeerust Thornveld Deciduous, open to dense short thorny woodland, dominated by Acacia species with herbaceous layer of mainly grasses
3.2.4 GIS analysis
“Raster Calculator” tool in ArcGIS 10.8.1. These new layers indicate the % woody cover change, which occurred between the different years. To determine specific bush spread that occurred for each time frame, the % woody cover layers for the years 1993, 1998 and 2018 (Symeonakis et al., 2020) and % woody cover change layers were superimposed on the same grid extent in SAGA 2.1.4. Thereafter, the layers were exported as text files using the “Export Grid to XYZ” tool. Python 3 (Van Rossum & Drake, 1995) and the Matplotlib Package (Hunter, 2007) were used to calculate each bush spread and the % distribution of each bush spread, for each time frame, by using the specific constrains (Table 3.1).
The calculated bush spread for each time frame (1993-1998, 1998-2018 and 1993-2018) were exported as three comma-separated values (CSV) files, using Python 3 and Matplotlib Package and included the X- and Y-coordinates of each data point (all 114 million). The CSV files were imported into FME desktop software 2021.1 (Safe Software Inc., 2020) and this software were used to convert the three CSV files to shapefiles (seven for each CSV file), using the “Writers”
tool, in order for bush spread maps to be created. The shapefiles (containing all points) were imported into SAGA 2.1.4 and were converted to raster data (30 m pixel size), using the “Point Cloud to Grid” tool. The seven rasters were then merged, using the “Mosaicking” tool and the single (merged) file exported as a ASCII file, which was imported into ArcGIS 10.8.1. In ArcGIS 10.8.1, the symbology was changed to match the specific bush spread and the bush spread maps created.
3.2.4.2 Determining drivers of bush encroachment
The % woody cover layers for the years 1993, 1998 and 2018 (Symeonakis et al., 2020), % woody cover change layers and potential driving factors of BE layers were all superimposed on the same grid extent in SAGA 2.1.4. The bush spread was calculated as explained in 1.2.4.1 and thereafter, Python 3, PhiK code (Baak et al., 2020) and the Matplotlib Package were used to calculate the correlation of the potential driving factors of BE with one another and with the bush spread for each time frame. Thereafter, a correlation matrix was created of each bush spread for each time frame, using Python 3 and the Matplotlib Package. The correlation matrixes were exported as CSV files and Microsoft Excel were used to manually combine all the correlation matrixes into just three (representing each time frame).
The correlation calculation of the potential driving factors of BE with one another and with bush spread are explained as follows:
Each of the 114 million pixels contained a specific map unit for each potential driving factor and a specific bush spread value for all three time frames. As the layers were exported as a text file,
the format of the map data (raster data) changed from pixels to data points. The data points (containing values of two variables, i.e. bush spread and land cover) were then used to fill the cells of contingency tables (similar to Baak et al., 2020) for each variable pair (i.e. bush spread and land cover). However, the amount of data points in the cells of a contingency table do not present true correlation. Therefore, a correlation coefficient ΦK needed to be calculated, which would indicate the true correlation of the variables with one another. Values from an “expected”
contingency table were needed to calculate a correlation coefficient ΦK and therefore, Equation 3-1 was used to calculate the expected contingency tables from the already created or “observed”
contingency tables. For equation 1, the sum of values for each row (i) and sum of values for each column (j) for each “observed” contingency table (O) were calculated, divided by the amount of data points (N) in the contingency table.
Values from the columns (j) (i.e. bush spread) and rows (i) (i.e. land cover) of the observed contingency table (O) and expected contingency table (E) were then used in Equation 3-2 (Baak et al., 2020) to calculate a χ2 value. The χ2 values and ΦK code (equations 12-17 in Baak et al., 2020) was then used to calculate the correlation coefficient ΦK, for each contingency table, representing the correlation between each variable pair. Finally, a correlation matrix was created, presenting the true correlation (correlation coefficient ΦK) between each variable pair. The correlation coefficient ΦK and corresponding criteria (Table 3.12) were selected based on similar criteria from Baak et al. (2020). From Table 3.11, only correlation coefficients ΦK > 0.39 (Moderate and higher) were regarded as significant and were accepted as a very likely driver of the specific bush spread.
Equation 3.1: 𝑬𝒊𝒋 = (∑𝒌𝒏=𝟏𝑶𝒊𝒋)(∑𝒓𝒎=𝟏𝑶𝒎𝒋)
𝑵
Where 𝐸 is the expected contingency table, 𝑂 is the observed contingency table, 𝑖 and 𝑗 is the columns and rows of the contingency tables, 𝑁 is the amount of data points in the observed contingency table, 𝒏 is the index for the columns, 𝒎 is the index for the rows, 𝒌 is the amount of columns and 𝒓 is the amount of rows.
Equation 3.2: χ2 = ∑ (𝑶𝒊𝒋− 𝑬𝒊𝒋)𝟐
𝑬𝒊𝒋 𝒊,𝒋
Where χ2 is Pearson’s chi-squared test, 𝐸 is the expected contingency table, 𝑂 is the observed contingency table and 𝑖 and 𝑗 is the columns and rows of the contingency tables.
Table 3.12: The correlation coefficient ranges and the corresponding criteria (from Baak et al., 2020).
Correlation coefficient ΦK range
Correlation criteria
0.00 None
0.001 – 0.19 Insignificant
0.20 – 0.39 Slight
0.40 – 0.59 Moderate
0.60 – 0.79 Good
0.80 – 0.99 Great
1 Perfect
3.2.4.3 Significant areas
The “create feature” tool (ESRI, 2016) was used to select the area boundaries and create four polygons. Within the created polygons, bush spread and bush spread distribution (%) were calculated (3.2.4.1) and the driving factors of BE determined (3.2.4.2). For the long-term precipitation data, the MAP were calculated for each year and thereafter, the mean MAP calculated for each time frame, using Microsoft Excel.