4  Metric selection and redundancy check

This chapter explains which metrics were calculated and how the final metric set was selected. At first, a larger set of green-space, FWEI derived flood, distance to green, and DEM metrics was produced for both Delft and Xi’an. However, not all of these metrics were used in the later analysis, because some of them described almost the same spatial pattern.

4.1 Collected metrics

The analysis used three main groups of metrics: green space, FWEI flood indicators, and DEM variables. The green space metrics describe how much green is present and how it is arranged. The flood metrics describe where surface water increase was detected and what pattern it forms. The DEM metrics describe elevation and slope, because lower or flatter areas can be more likely to hold water.

The flood metrics in this chapter were derived from the binary flood change mask, the clipped FWEI change raster thresholded at 0.05 in R. Each metric describes the amount or spatial structure of newly detected surface water per 100 m grid cell, tracing back to the FWEI based satellite detection described in the FWEI chapter.

Metric group	Metric	Meaning
Green-space metrics	green_percent	Percentage of each grid cell covered by green space.
Green-space metrics	area	Average size of green patches.
Green-space metrics	gyrate	Spatial spread of green patches.
Green-space metrics	contig	Compactness and internal connectedness of green patches.
Green-space metrics	enn	Distance to the nearest neighbouring green patch.
Flood metrics	fwei_change_mean	Average FWEI after-minus-before change per grid cell.
Flood metrics	flood_share	Share of each grid cell with detected surface-water increase.
Flood metrics	pland_flood	Percentage of each grid cell covered by detected flood pixels.
Flood metrics	np_flood	Number of separate detected flood patches.
Flood metrics	flood_cohesion	Connectedness of detected flood patches.
Flood metrics	flood_clumpy	Clustering of detected flood pixels.
Flood metrics	flood_lpi	Dominance of the largest detected flood patch.
Distance-to-green metrics	mean_dist_green	Average distance from detected water pixels to the nearest green pixel.
Distance-to-green metrics	min_dist_green	Minimum distance from detected water pixels to the nearest green pixel.
DEM metrics	elevation_mean	Average elevation per grid cell.
DEM metrics	elevation_min	Lowest elevation value per grid cell.
DEM metrics	slope_mean	Average slope per grid cell.

4.2 Metric redundancy check

Before selecting the final metrics, the candidate metrics were checked for redundancy. This was necessary because clustering is sensitive to the input variables. If two metrics describe almost the same pattern, including both of them would give that pattern too much influence.

Pearson correlation was used to compare the candidate metrics. A correlation close to 1 or -1 means that two metrics are strongly related. In this analysis, metric pairs with an absolute correlation above about 0.80 were treated as highly redundant.

Metric redundancy heatmap.

The redundancy check showed that several variables were strongly related. This was especially clear for flood extent metrics and elevation metrics. For example, flood_share and pland_flood had a correlation of 1.00, meaning they were identical in practice. elevation_mean and elevation_min were also almost identical.

Highly correlated metric pairs.

metric_1	metric_2	correlation	abs_correlation
flood_share	pland_flood	1.000	1.000
elevation_mean	elevation_min	1.000	1.000
flood_share	flood_lpi	0.979	0.979
pland_flood	flood_lpi	0.979	0.979
mean_dist_green	min_dist_green	0.924	0.924
gyrate	contig	0.885	0.885
area	gyrate	0.873	0.873
green_percent	area	0.837	0.837

4.3 Redundant metrics

The table below shows the final decisions for the highly correlated metric pairs. In most cases, one metric was kept and the other was removed from the final metric set.

Metric redundancy decision table.

Metric redundancy decisions.

correlated_metrics	correlation	decision	reason
flood_share + pland_flood	1.000	keep flood_share, remove pland_flood	both measure detected water extent
elevation_mean + elevation_min	1.000	keep elevation_mean, remove elevation_min	both describe almost the same elevation pattern
flood_share + flood_lpi	0.979	keep flood_share, remove flood_lpi	largest flood patch mostly follows flood extent
pland_flood + flood_lpi	0.979	remove pland_flood and flood_lpi	both overlap strongly with flood extent
mean_dist_green + min_dist_green	0.924	remove both from typology, keep only for interpretation	both measure distance to green space
gyrate + contig	0.885	keep contig, remove gyrate	patch spread overlaps with compactness
area + gyrate	0.873	keep contig, remove gyrate	patch size overlaps with patch spread
green_percent + area	0.837	keep green_percent, remove area	green amount overlaps with patch size

The main decisions were as follows. flood_share was kept instead of pland_flood, because both metrics measure detected surface water extent. flood_lpi was removed because it was also strongly related to flood extent. elevation_mean was kept instead of elevation_min, because both showed almost the same elevation pattern. gyrate was removed because it strongly overlapped with other green patch metrics. area was also removed from the final metric set because it strongly correlated with green_percent.

The distance to green metrics, mean_dist_green and min_dist_green, were not used in the final metric set. They are still useful for interpretation, but they describe the relationship between detected water and green space rather than the main green, flood, or topographic condition of the grid cell.

4.4 Final selected metrics

After the redundancy check, the final metric set was reduced. The aim was to keep one representative metric for each important dimension of the analysis: green amount, green compactness, green isolation, FWEI derived water change, flood extent, flood fragmentation, flood clustering, elevation, and slope.

Metric group	Final metric	Why it was kept
Green amount	green_percent	Represents how much green space is present in each grid cell.
Green configuration	contig	Represents the compactness and internal connectedness of green patches.
Green isolation	enn	Represents how isolated green patches are from nearby green patches.
Surface-water change	fwei_change_mean	Represents the average FWEI-derived surface-water change.
Flood extent	flood_share	Represents the share of each cell with detected surface-water increase.
Flood fragmentation	np_flood	Represents the number of separate detected flood patches.
Flood clustering	flood_clumpy	Represents whether detected water is clustered or scattered.
Topography	elevation_mean	Represents average elevation conditions.
Topography	slope_mean	Represents average terrain steepness or flatness.

These selected metrics were then used as the basis for the combined typology analysis. The metric set keeps the main dimensions of the research question while avoiding double counting strongly overlapping variables.

4.5 Final metric maps

The maps below show the final metrics that were kept after the redundancy check. They are shown in tabs so that the spatial patterns can be compared without making the chapter too long.

Green percent

green_percent shows the amount of green space in each grid cell.

Contiguity

contig shows whether green patches are compact and internally connected.

Nearest-neighbour distance

enn shows how isolated green patches are from other green patches.

FWEI change

fwei_change_mean shows the average FWEI-derived surface-water change per grid cell.

Flood share

flood_share shows the proportion of each grid cell where surface-water increase was detected.

Number of flood patches

np_flood shows whether detected water appears as one patch or many separate patches.

Flood clumpiness

flood_clumpy shows whether detected water pixels are clustered or scattered.

Elevation

elevation_mean shows the average elevation per grid cell.

Slope

slope_mean shows the average slope per grid cell.

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