Distance to habitat

In this first part of the series you measure distances in a real forest landscape of south-western Oregon. You turn a satellite image of greenness into a forest map, measure how far every forest cell lies from the forest's edge and how far every open cell lies from the nearest forest, and divide the open land among the large forests nearest to it. At the end you will have three maps and two curves that answer everyday questions of restoration and conservation: how much of the forest is exposed to edge effects, how much of the cleared land is close enough to the forest to regrow by itself, and which forest each part of the matrix "belongs" to.

The idea#

Distance is the simplest spatial variable there is, and one of the most useful in ecology. Many processes fade with distance from a habitat's edge:

Inside a forest, light, wind, temperature and humidity change near the edge, and so do the plants and animals that live there. These edge effects reach tens of metres for microclimate and up to several hundred metres for some species (Murcia, 1995). The distance of a forest cell to the edge says how deep in the interior it lies.
Outside a forest, most seeds fall close to their parent trees or are carried short distances by birds and bats. The chance that cleared land regrows naturally falls quickly with distance from the forest, so land near forest can often be restored by letting it regrow, at a fraction of the cost of planting (Chazdon & Guariguata, 2016). The distance of an open cell to the nearest forest says how close it is to a seed source.

A raster is a map made of a grid of square cells, each holding one number. A distance map is a raster in which each cell holds the straight-line (Euclidean) distance from its centre to the nearest cell of some kind. GuidosToolbox, the image analysis software of the European Commission's Joint Research Centre (Vogt & Riitters, 2017), computes it on both sides of an edge at once and gives it a sign: positive inside the habitat, negative outside it.

A toy map of 8 by 10 cells: forest in green, open land in beige, and in each cell its signed distance to the edge in cells — The signed distance cell by cell. Each forest cell (green) holds its distance to the nearest open cell; each open cell (beige) the distance to the nearest forest cell, with a minus sign. Cells next to the edge are at 1; a diagonal neighbour is at √2 ≈ 1.4. Multiply by the cell's side (30 m here) for metres.

Key idea

For a cell \(i\) of the habitat \(H\), the signed distance is

\[ d_i = \min_{j \notin H} \lVert c_i - c_j \rVert \]

and for a cell outside it \( d_i = -\min_{j \in H} \lVert c_i - c_j \rVert \), where \(c_i\) is the centre of cell \(i\) (in cells) and \(\lVert \cdot \rVert\) the straight-line distance. A cell on the edge is at 1 (its neighbour across the edge is one cell away); multiplied by the cell's side it is in metres.

Two related tools answer "which forest is nearest?". A zone of influence is the part of the open land nearer to one forest object than to any other, the raster version of a Voronoi diagram (or of Thiessen polygons around points). GuidosToolbox draws the zones as the basins of the distance map: the lines between zones run where two forests are equally far.

When to use it#

Edge exposure. The share of a forest within 50 or 100 m of its edge is a direct, easily explained indicator of edge effects, and the distance map is a covariate for species that avoid or seek edges.
Natural regeneration potential. Studies of the Atlantic Forest and other tropical regions map land within a few hundred metres of forest as the cheapest to restore (Chazdon & Guariguata, 2016). The distance to the nearest forest is the first layer of such a map.
Drivers of land change. Distance to roads, rivers, towns or existing farmland is among the most common explanatory variables of deforestation and land change models; distance.proximity computes it for any set of values.
Buffer zones and catchments. The zones of influence assign every part of the matrix to its nearest reserve, for planning buffer zones or for sharing the management of the land between them.

What it is not for: a straight line ignores what lies between two places. When the land in between is easier or harder to cross (a river, a highway, a pasture), use an accumulated cost instead: the next part does, and so do the grid distances and circuit connectivity tutorials. Distances also say nothing about how connected the forest is as a whole: for that see habitat networks.

What you need#

A habitat map. Here, ndvi.tif: summer greenness (the normalised difference vegetation index, NDVI, from 0 for bare ground to about 0.9 for dense canopy) of 371 × 371 cells of about 30 m in south-western Oregon, a composite of the summers of 2000 to 2016 from landschaft's example data. Your own map can be a land cover classification, a forest mask from Global Forest Watch, or any map of the habitat of a species.
A projected coordinate system. A coordinate reference system (CRS) says what the numbers of the grid mean on the ground. ndvi.tif is in degrees of latitude and longitude (EPSG:4326), and a degree of longitude is shorter than a degree of latitude away from the equator: at 43° N its cells are about 31 m tall and 23 m wide. Distances need square cells of a known size in metres, so the first step reprojects the map to UTM zone 10 N (EPSG:32610) with cells of 30 m.

In the application

The operators of this series are under Distance & restoration in the library (the left pane). Click one to add it to the graph, drag from an output port (right side of a node) to an input port (left side) to connect them, and set its settings in the Node pane. Ctrl+Enter runs the model up to the selected node, and clicking a node shows its output in the Viewer. Plots › Save as a new plot, in the Viewer's header, keeps a view with the model.

Build the model#

Read and project the map#

Start with a raster.read node whose path is ndvi.tif, then a raster.reproject node. Connect ndvi.raster to projected.raster and set crs to EPSG:32610 and resolution to 30. Reprojection resamples the values to the new grid; for a continuous map like NDVI Terraflux uses bilinear interpolation, a weighted mean of the four nearest cells (for a map of classes it would take the nearest cell instead).

Define the forest#

GuidosToolbox's operators read maps coded 0 missing, 1 background, 2 foreground. The foreground is the habitat whose distances you measure, the background everything else on the map, and missing the cells without data (outside the study area, clouds). A raster.calc node makes that code from the NDVI:

0 if isnull(n) else 2 if n >= 0.7 else 1

Its input n is projected.raster. Cells without a value (the corners that the reprojection leaves empty) become 0, cells with an NDVI of 0.7 or more forest (2), the rest open land (1). The threshold of 0.7 is a choice, not a fact: a later section shows how much it matters.

Read the NDVI, project it to metres, and code it as GuidosToolbox expects: 0 missing, 1 open land, 2 forest.

Model file (TOML)

format = "terraflux/1"

[[nodes]]
id = "ndvi"
op = "raster.read"
params = { path = "ndvi.tif" }
note = "Summer NDVI of south-western Oregon, cells of about 30 m, in degrees."

[[nodes]]
id = "projected"
op = "raster.reproject"
inputs = { raster = "ndvi.raster" }
params = { crs = "EPSG:32610", resolution = 30 }
note = "UTM zone 10 N: square cells of 30 m."

[[nodes]]
id = "forest"
op = "raster.calc"
inputs = { n = "projected.raster" }
params = { expression = "0 if isnull(n) else 2 if n >= 0.7 else 1" }
note = "0 missing, 1 open land, 2 forest."

NDVI ≥ 0.7: forest — Summer NDVI, projected

The signed distance to the edge#

Add distance.euclidean and connect forest.map to its map input. With no foreground setting it takes the map's own codes (2 the foreground); for a land cover map with other codes, list the habitat's classes in foreground (for example [1, 3]). It has three outputs:

map: the signed distance in cells (positive in the forest, negative outside).
display: GuidosToolbox's byte version of it (130 plus the distance inside, 130 minus it outside, up to 120 cells), for viewing in GuidosToolbox.
stats: per side (1 the foreground, 0 the background) the number of cells and the mean and largest distance.

The distance to the nearest forest, in metres#

distance.proximity is GDAL's proximity tool: the distance from every cell to the nearest cell holding some values, here values = [2]. Connect forest.map to its raster input. Its distances are in the map's units (metres, after the projection) unless units = "cells", and max_distance leaves the cells beyond it without a value. Unlike distance.euclidean it works on the file in blocks, whatever its size, so it is the one to use for a country-wide map of the distance to roads or to forest.

Zones of influence#

Add distance.influence_zones with forest.map as its map. It labels the forest's objects (groups of forest cells touching by a side or a corner, holes filled), keeps those of at least min_area cells, and divides the rest of the map among them. GuidosToolbox's default min_area of 5,000 cells suits large maps; this one has about 100,000 cells, so set min_area = 1000 (90 ha at 30 m). The outputs are map (GuidosToolbox's codes), ids (the object of every cell), zones (the zone of every cell, 0 on the lines between them) and objects (the area of each object).

The full model: the signed distance to the edge, the distance to the nearest forest in metres, and the zones of influence of the forests of 1,000 cells or more.

Model file (TOML)

format = "terraflux/1"

[[nodes]]
id = "ndvi"
op = "raster.read"
params = { path = "ndvi.tif" }

[[nodes]]
id = "projected"
op = "raster.reproject"
inputs = { raster = "ndvi.raster" }
params = { crs = "EPSG:32610", resolution = 30 }

[[nodes]]
id = "forest"
op = "raster.calc"
inputs = { n = "projected.raster" }
params = { expression = "0 if isnull(n) else 2 if n >= 0.7 else 1" }

[[nodes]]
id = "distance"
op = "distance.euclidean"
inputs = { map = "forest.map" }
note = "Signed distance to the edge, in cells."

[[nodes]]
id = "to_forest"
op = "distance.proximity"
inputs = { raster = "forest.map" }
params = { values = [2] }
note = "Metres to the nearest forest cell."

[[nodes]]
id = "zones"
op = "distance.influence_zones"
inputs = { map = "forest.map" }
params = { min_area = 1000 }

[[plots]]
id = "plot_distance"
title = "Signed distance (cells)"
layers = [{ from = "distance.map" }]

[[plots]]
id = "plot_zones"
title = "Zones of influence"
layers = [{ from = "zones.map" }]

From the command line, save the model as distance.toml next to ndvi.tif and run it. To keep a map, add a raster.write node, or make a table an output of the model so that terraflux run writes it as a CSV:

[outputs.distance_stats]
from = "distance.stats"

terraflux run distance.toml --out results

Read the results#

Inside and outside the forest#

The signed distance to the forest's edge in metres: green inside the forest, pink outside — The signed distance in metres (the map's cells times 30). Green: inside the forest, darker deeper in it; pink: open land, darker further from any forest. White: the edge.

The map is mostly pale: this is a fine-grained landscape where almost nothing is far from an edge. The deepest forest cell lies 13 cells (390 m) from open land, and the most remote open cell 13.3 cells (400 m) from forest. The stats table gives the means: forest cells lie on average 2.1 cells (64 m) from the edge, open cells 2.7 cells (81 m) from the forest.

The distance from every open cell to the nearest forest cell, in metres — distance.proximity: metres from every cell to the nearest forest cell (0 in the forest). The darkest patches are the open land furthest from any seed source.

The two maps agree (the proximity map is the negative half of the signed one, in metres), but the proximity map is the one to give a regeneration model or to threshold ("open land within 100 m of forest").

The most useful summary is a curve: for every distance, the share of each side within it.

Cumulative distances from the real run. Half of the open land lies within 60 m of a forest and 96% within 210 m; 64% of the forest lies within 60 m of its edge.

Read the curves with an ecological threshold in mind. If edge effects on the microclimate reach about 60 m, then 64% of this forest is edge habitat and only about a third is interior. If natural regeneration is likely within about 100 m of a seed source, then about three quarters of the open land could regrow without planting (the real distances depend on the species and the region: take them from the local literature).

In the literature

Haddad et al. (2015) computed the distance of every forest point on Earth to the nearest edge and found that 70% of the world's remaining forest lies within 1 km of an edge, where fragmentation's effects on species and ecosystems accumulate. The same distance, on your map, is what distance.euclidean computes.

Zones of influence#

Eight forest objects reach 1,000 cells; the largest has 9,508 cells (8.6 km²), the smallest of the eight 1,067. Each gets the land nearest to it. Large objects next to small ones get large zones, and a zone's line falls halfway between two objects. Use the zones map as you would use Thiessen polygons: to sum the open land, the people or the pressure that each forest has around it.

Experimental

The zones of influence follow GuidosToolbox's method, but its distance transform is not yet reproduced exactly, so the lines can differ in detail from GuidosToolbox's own maps (the operator's description says so).

How to report it#

Report the habitat definition (the data, the threshold, the cell size and the CRS), then the distances in metres: the mean and largest distance on each side, and the share of each side within the thresholds that matter for your question (for example "64% of the forest lies within 60 m of an edge"). The curve above is a good figure for a paper, and the proximity map a good layer for the next steps of a restoration plan.

Settings that change the answer#

The definition of the habitat#

The threshold that turns NDVI into forest is rarely given by the ecology, and the distances depend on it more than on anything else. Move the slider: each frame is a real run of the model with another threshold.

NDVI threshold of the forest 0.6 — The signed distance in metres (green inside the forest, pink outside; the colours are fixed from -600 to 600 m) for four thresholds. At 0.6 the forest covers almost everything and its interior is deep; at 0.75 a few scattered stands remain and open land lies up to 1.7 km from them.

NDVI threshold of the forest 0.65 — The signed distance in metres (green inside the forest, pink outside; the colours are fixed from -600 to 600 m) for four thresholds. At 0.6 the forest covers almost everything and its interior is deep; at 0.75 a few scattered stands remain and open land lies up to 1.7 km from them.

Between 0.65 and 0.70 the forest falls from 80% to 41% of the map, because most cells have an NDVI between those two values: the threshold cuts through the bulk of the distribution. When a result depends this much on a threshold, report it for two or three plausible values, or use a definition of habitat from field data.

The least object of the zones#

min_area decides which forests get a zone. With a larger value fewer, larger zones remain; at 0.75 no object reaches 1,000 cells and the operator stops with the message that no object is kept. Choose it from the ecology (the smallest forest that holds a population, or the smallest reserve that counts) rather than from the map.

Common pitfalls#

Degrees are not metres. Distances on a map in latitude and longitude are in degrees, and the cells are not square. Project the map first (here to UTM), or give the cells' size where an operator asks for it.
Cells, not metres. distance.euclidean gives distances in cells; distance.proximity in the map's units. Multiply the first by the cell's side before you compare them or report them.
The edge of the map is not an edge of the forest. A forest cut by the map's border looks smaller and its interior shallower than it is, and the open land near the border may be close to a forest just outside. Give the analysis a margin around the study area, or code the outside as missing (0), as here.
Missing cells. Clouds or gaps coded as open land create false edges. Code them 0 (missing) in the GuidosToolbox coding, as the expression above does for empty cells.
Resolution. At 30 m a hedge or a narrow riparian strip may be forest; at 250 m it disappears. Distances to the nearest forest grow as the cells grow, so compare landscapes at the same resolution.

Going further#

Distances that account for what lies between: Costs, paths and corridors, the next part, finds the cheapest route between two forests and what restoring it would gain.
The edges and cores of the forest as classes: habitat patterns (MSPA).
How fragmented the forest is at many scales: fragmentation.
The operators: distance.euclidean, distance.proximity, distance.influence_zones and distance.objects_proximity, which measures the gap between neighbouring objects along the lines between their zones.

References#

Chazdon, R. L., & Guariguata, M. R. (2016). Natural regeneration as a tool for large-scale forest restoration in the tropics: prospects and challenges. Biotropica, 48(6), 716–730. https://doi.org/10.1111/btp.12381
Haddad, N. M., Brudvig, L. A., Clobert, J., Davies, K. F., Gonzalez, A., Holt, R. D., et al. (2015). Habitat fragmentation and its lasting impact on Earth's ecosystems. Science Advances, 1(2), e1500052. https://doi.org/10.1126/sciadv.1500052
Murcia, C. (1995). Edge effects in fragmented forests: implications for conservation. Trends in Ecology & Evolution, 10(2), 58–62. https://doi.org/10.1016/S0169-5347(00)88977-6
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