Simplified patterns, objects and distances

MSPA's seven classes are not always what a question needs. A map for a planning meeting may need three classes, not twenty codes. A forest report asks how much of the forest is in large blocks and how much in small woods. A study of edge effects wants the distance of every tree to the nearest field, not a class at one edge width. This part covers the tools GuidosToolbox offers around MSPA, on the same forest map as part 2: the simplified pattern analysis (SPA), the objects by size (Accounting), the parcellation of the landscape, the contortion of the patches, the Euclidean distance to the forest's edge, and the zones of influence and proximity of the large forests. All of them read the same binary map, so they hang off one raster.read node side by side.

The idea#

All the tools of this page look at the same thing, a map of foreground (forest) and background, but each asks a different question of it:

Three ideas run through them.

An object is a group of foreground cells connected to each other (by their sides, or also by their corners with 8-connectivity): what an ecologist calls a patch. Counting objects and measuring them is the oldest way to describe fragmentation, and still one of the most useful: is most of the forest in a few large blocks or spread over many small woods?

Division. Jaeger (2000) proposed to measure how divided a landscape is by a probability: pick two points at random; how likely is it that they are not in the same patch?

Distance. The edge width of MSPA is a threshold on a distance: a forest cell is core when it is further than the edge width from the background. Measuring that distance for every cell gives, in one map, the answer for every edge width at once.

When to use it#

• SPA when the audience is not specialist, or when only interior versus the rest matters. SPA5 and SPA6 are close to MSPA without the bridge, loop and branch distinction; SPA2 and SPA3 are the bluntest summaries.
• Accounting to report the forest by patch size classes. FAO's global analysis of forest fragmentation for The State of the World's Forests 2020 reported the world's forest in six size classes, from under 100 ha to over 1,000,000 ha, with exactly this method, alongside the forest area density of the fragmentation tutorials (Vogt et al., 2019; FAO & UNEP, 2020). Thresholds can come from species' area requirements: the minimum area for a territory, or for a viable population.
• Parcellation to compare how finely divided different landscapes, classes or dates are.
• Contortion to find the patches with the most convoluted outlines: much edge for their area, more exposed to edge effects, and often shaped by human use.
• The Euclidean distance when edge effects decline gradually with distance rather than stopping at a depth, or to model a response (bird density, temperature, carbon stock) as a function of the distance to the edge; Chaplin-Kramer et al. (2015) found the biomass of tropical forests 25% lower within 500 m of an edge than in their interiors, and still 10% lower 1.5 km in.
• Influence zones and proximity to see which large forest every part of the land is closest to, and where the gaps between large forests are narrowest: a first look for restoring links.

What you need#

GuidosToolbox's sample forest map, input.tif, as in part 2 (0 missing, 1 background, 2 forest). In the application, the template Patterns and objects (Templates > Patterns (GuidosToolbox)) has SPA and Accounting on a forest drawn by chance; replace its first node by a raster.read of your map.

Build the model#

format = "terraflux/1"

[[nodes]]
id = "forest"
op = "raster.read"
params = { path = "input.tif" }
note = "0 missing, 1 background, 2 forest."

[[nodes]]
id = "spa"
op = "landscape.spa"
inputs = { map = "forest.raster" }
params = { variant = 6 }
note = "Core, islet, edge, perforation, margin."

[[nodes]]
id = "objects"
op = "landscape.accounting"
inputs = { map = "forest.raster" }
params = { thresholds = [50, 250, 1000, 5000, 20000], highlight_largest = true }
note = "The forest's objects in six size classes."

[[nodes]]
id = "parcels"
op = "landscape.parcellation"
inputs = { map = "forest.raster" }
note = "Parcels of the forest and of the background."

[[nodes]]
id = "contortion"
op = "landscape.contortion"
inputs = { map = "forest.raster" }
params = { min_area = 100 }

[[nodes]]
id = "distance"
op = "distance.euclidean"
inputs = { map = "forest.raster" }

[[nodes]]
id = "zones"
op = "distance.influence_zones"
inputs = { map = "forest.raster" }
params = { min_area = 5000 }

Every tool takes the same input, forest.raster: connect node 1's output map to the input map of each. They do not depend on each other, so Terraflux runs them in parallel. The tables they give (stats, objects, summary) show in the Viewer when the node is selected, and in a model run from the command line they are written as CSV files when you make them outputs of the model:

[outputs.objects_by_size]
from = "objects.stats"

Each tool also takes foreground (the classes of the forest in a map of many classes), like MSPA, except parcellation, which works on every class of the map at once.

SPA: the pattern in fewer classes#

landscape.spa is a simplified MSPA of the 8-connected foreground with edges one cell wide, in four variants (variant):

• SPA2: contiguous foreground (17, the objects that have a core) and small linear features (1, the rest).
• SPA3: core (17), core-opening (100) and margin (1, everything that is not core).
• SPA5: core, edge (3), perforation (5) and margin (1, bridges, loops and branches together, and islets).
• SPA6: SPA5 with the islets (9) apart from the margin.

On the whole map, SPA6 gives: core 75.1% of the forest, edge 13.5%, margin 6.0%, islet 3.3% and perforation 2.1%. SPA2 puts 90.8% of the forest in contiguous objects and 9.2% in small linear features. SPA also reports the porosity, \(100 - 100 \times \text{contiguous} / (\text{contiguous} + \text{core-openings})\): the share of holes in the forest's interior, here 1.4% (SPA5 and SPA6). A forest pierced by clearings has a high porosity.

The objects table of SPA counts the objects of each class as GuidosToolbox does: here 2,850 forest objects, of which 2,443 islets.

Accounting: the forest's objects by size#

landscape.accounting labels every object of the forest, measures it in cells and puts it in one of up to six size classes. The thresholds are the upper bounds of the classes in cells: with the default [50, 250, 1000, 5000, 20000] (GuidosToolbox's batch), class 1 holds the objects of up to 50 cells, class 2 those of 51 to 250, and so on, class 6 those above 20,000. thresholds = "auto" proposes bounds at 0.1, 1, 10, 50 and 90% of the range of the objects' areas, as GuidosToolbox does. highlight_largest paints the three largest objects apart.

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The stats table reads:

This is how most forests in farmed landscapes look: very many small woods and a few large blocks holding most of the area. The two halves of the table answer different questions. The large objects hold the interior habitat and most of the forest's connectivity; the small ones are numerous stepping stones, and their number tells you how scattered the forest outside the blocks is. Report both columns.

Parcellation: how divided is the landscape?#

landscape.parcellation works on every class of the map: each connected region of one value is a parcel. Here, the forest's parcels and the background's. Its stats table gives, per class:

How to read it:

• The APS (the average parcel size) of the forest is small, 150 cells, because the many small woods weigh as much as the large blocks. The AWAPS weights each parcel by its own area: it is the size of the parcel that a forest cell picked at random belongs to, on average. 114,286 cells: a forest cell is usually in a large block.
• AWAPS over the area with data divides by the whole map rather than by the forest: this is Jaeger's (2000) effective mesh size of the forest, 48,984 cells.
• Division 0.733 for the forest: two forest cells picked at random are in different parcels three times in four. The background (fields, villages) is much less divided (0.198): it is one large connected matrix.
• PARC, GuidosToolbox's degree of parcellation, summarises the same thing on a logarithmic scale: higher is more finely parcelled.

Parcellation is most useful to compare: two dates, two regions, two classes. The effective mesh size and the division of the forest are also among the class metrics of the landscape metrics.

Contortion: how convoluted are the outlines?#

landscape.contortion measures how much the outline of each patch turns, relative to its size, for the patches with a core and of min_area cells at least (here 100). Compact patches score low, elongated and dendritic ones high. Its display output scales the values to 3–255 over the map's range for drawing; its map keeps GuidosToolbox's values (0 missing, 1 background, 2 forest left out, from 3 the contortion plus one).

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Contortion depends on the resolution (a finer map draws a more ragged outline) and on the size of the patch; compare patches of similar size, and maps of the same resolution.

The distance to the forest's edge#

distance.euclidean gives every cell its straight-line distance, in cells, to the forest's edge: positive inside the forest, negative outside it. Its display output is GuidosToolbox's byte version (130 plus the distance inside, 130 minus it outside, up to 120 cells), and its stats table the mean and largest distance on each side: here a forest cell is on average 6.0 cells from the edge, and the deepest is 37 cells in; a non-forest cell is on average 5.0 cells from the forest, and the furthest 33.5 cells.

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The distance map holds every MSPA core at once. The share of the forest at least \(w + 1\) cells from the background is MSPA's core at an edge width \(w\): we compared it with the MSPA runs of part 2 and the two differ by fewer than 20 cells in 200,000 for every width from 1 to 6. So one map gives the whole curve:

This is a good figure for a paper: it shows how the amount of interior habitat depends on the depth of edge effects, without committing to one depth.

Zones of influence and proximity#

distance.influence_zones takes the large objects of the forest (8-connected, holes filled, of min_area cells or more: GuidosToolbox's default is 5,000) and divides the whole map among them: every cell goes to the object it is closest to (the watershed of the distance to the objects). The lines between the zones are where two objects are equally far.

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distance.objects_proximity follows those lines and measures, along them, the gap between the two objects and the connected area gain (CAG) of joining them. On this map it finds 18 pairs of neighbouring objects, and its lines table lists, for every cell of the lines, the two objects, their areas, the connector length and the CAG; sorted by the connector length, the narrowest gaps come first, here a few cells wide. Such short gaps between large forests are the first places to look when planning to restore a link, before the more detailed tools of the restoration planner.

Settings that change the answer#

• Connectivity. Accounting, parcellation and SPA's object counts depend on it: with 4 neighbours, woods that touch at a corner are separate objects, and the counts of small objects grow.
• Thresholds of Accounting. Classes in cells change meaning with the resolution; set them in hectares and convert.
• min_area of contortion and of the zones: which patches count as large enough.
• The map's extent. Every object cut by the map's border is smaller than it really is; the largest objects of a map are the most likely to be cut.

Common pitfalls#

• Comparing APS between maps. The average patch size is dominated by the number of small patches, which depends on the map's detail; prefer AWAPS or the effective mesh size.
• Cells versus hectares. All these tools count cells. Multiply by the area of a cell, and on a map in degrees (like this sample) project first: cells of degrees have different areas at different latitudes.
• Parcellation of a binary map coded 0 and 1. Parcellation reads the classes 1 to 255 and takes 0 as missing: a forest map coded 0 and 1 would lose its background. Reclassify first.
• Distances in cells. The Euclidean distance is in cells; multiply by the cell size for metres.

Going further#

• Part 4: MSPA's cores and bridges as a network, change between two dates, maps larger than memory.
• Landscape metrics: patch, class and landscape metrics, many of them close relatives of these (core area, mesh size, shape).
• Distance and restoration: the restoration planner, least-cost corridors and isochrones.
• The operator reference: landscape.spa, landscape.accounting, landscape.parcellation, landscape.contortion, distance.euclidean, distance.influence_zones, distance.objects_proximity.

References#

• Chaplin-Kramer, R., Ramler, I., Sharp, R., Haddad, N. M., Gerber, J. S., West, P. C., Mandle, L., et al. (2015). Degradation in carbon stocks near tropical forest edges. Nature Communications, 6, 10158. https://doi.org/10.1038/ncomms10158
• FAO & UNEP. (2020). The State of the World's Forests 2020: Forests, biodiversity and people. FAO. https://doi.org/10.4060/ca8642en
• Jaeger, J. A. G. (2000). Landscape division, splitting index, and effective mesh size: new measures of landscape fragmentation. Landscape Ecology, 15(2), 115–130. https://doi.org/10.1023/A:1008129329289
• Soille, P., & Vogt, P. (2009). Morphological segmentation of binary patterns. Pattern Recognition Letters, 30(4), 456–459. https://doi.org/10.1016/j.patrec.2008.10.015
• Vogt, P., & Riitters, K. (2017). GuidosToolbox: universal digital image object analysis. European Journal of Remote Sensing, 50(1), 352–361. https://doi.org/10.1080/22797254.2017.1330650
• Vogt, P., Riitters, K. H., Caudullo, G., & Eckhardt, B. (2019). FAO – State of the World's Forests: Forest fragmentation (EUR 29972 EN). Publications Office of the European Union. https://doi.org/10.2760/145325
• Vogt, P., Riitters, K., Rambaud, P., d'Annunzio, R., Lindquist, E., & Pekkarinen, A. (2022). GuidosToolbox Workbench: spatial analysis of raster maps for ecological applications. Ecography, 2022(3), e05864. https://doi.org/10.1111/ecog.05864