Processing and Analysis

The captured field mapping data was transferred from paper to digital maps in QGIS. Orthophotos were also used to align the mapped elements that had not changed between the 2023 orthophoto capture and the April field visit. The resulting landscape cartography was then exported to PMTiles format so that it can be rendered in this report using MapLibre GL JS.

For the vertical relationships analysis, a grid of points separated by 100 m was drawn over the study area, resulting in 107 sample points. These are the points at which measurements were made, and they form the basis of a chi-square and Jaccard similarity analysis. Not all sample points were used in every analysis: points falling in the Zenne, on infrastructure, or in smaller land use or soil categories outside the selected classes were excluded from the relevant cross-tables.

Vertical relationships sample points

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Figure 21. Grid of 107 sample points used for the vertical relationships analysis.

The chi-square analysis compares the natural component of soil texture (clay, sandy loam and loam) with the cultural component of land use (pasture, cropland and forestry) to see whether they covary. The observed values are recorded in a table, and the expected values are calculated in a second table.

The expected frequency for each cell is calculated as:

E_{ij} = \frac{O_i \cdot O_j}{N}

where $E_{ij}$ is the expected frequency in cell $ij$ , $O_i$ is the row total, $O_j$ is the column total and $N$ is the total number of observations. The chi-square value is then calculated as:

\chi^2 = \sum_{i,j} \frac{(O_{ij} - E_{ij})^2}{E_{ij}}

where $O_{ij}$ is the observed frequency in cell $ij$ . The number of degrees of freedom is calculated as:

df = (r - 1)(c - 1)

where $r$ is the number of rows and $c$ is the number of columns.

The Jaccard similarity measure compares altitude (<40 m and >40 m) as the natural component with the residential use of the land as the cultural component. The observed values are again recorded in a table, and the Jaccard score is calculated.

For a 2x2 cross-table, the Jaccard similarity between two classes is calculated as:

J(A,B) = \frac{|A \cap B|}{|A \cup B|} = \frac{a}{a + b + c}

where $a$ is the number of sample points where both classes occur together, and $b$ and $c$ are the points where only one of the two classes occurs. For the cell-based interpretation in this report, the denominator is the union of the relevant row and column.