Understanding spatial patterns: how to measure and compare them
2025-09-04
Spatial patterns
Discovering and describing patterns is a vital part of many spatial analysis However, spatial data is gathered in many ways and stored in forms, which requires different approaches to understanding spatial patterns
Spatial patterns of categorical rasters
Discovering and describing spatial patterns is an important part of many geographical studies, and spatial patterns are linked to natural and social processes.
Evaluation of the susceptibility of forest landscapes to agricultural expansion
Bourgoin et al., 2020, 10.1016/j.jag.2019.101958
Reinterpretation of histological images as categorized rasters and their use for disease classification (e.g., liver cancer)
Kendall et al., 2020, 10.1038/s41598-020-74691-9
Spatial patterns in landscape ecology
Hesselbarth, M.H.K., Nowosad, J., de Flamingh, A. et al. Computational Methods in Landscape Ecology. Curr Landscape Ecol Rep 10, 2 (2025). https://doi.org/10.1007/s40823-024-00104-6
Quantification of categorical spatial patterns
Spatial patterns can be quantified using landscape metrics (O’Neill et al. 1988; Turner and Gardner 1991; Li and Reynolds 1993; He et al. 2000; Jaeger 2000; Kot i in. 2006; McGarigal 2014).
Software such as FRAGSTATS, GuidosToolbox, or landscapemetrics has proven useful in many scientific studies (> 12,000 citations).
There is a relationship between an area’s pattern composition and configuration and ecosystem characteristics, such as vegetation diversity, animal distributions, and water quality within this area (Hunsaker i Levine, 1995; Fahrig i Nuttle, 2005; Klingbeil i Willig, 2009; Holzschuh et al., 2010; Fahrig et al., 2011; Carrara et al., 2015; Arroyo-Rodŕıguez et al. 2016; Duflot et al., 2017, many others..)
Example data
Randomly selected 16 rasters (100x100 cells) with different proportions of forest (green) areas from Land cover data for the year 2016 of the CCI-LC project (simplified into nine categories)
Landscape metrics
General assumption is that the spatial pattern of a landscape influences the processes that occur within it
In the last 40 or so years, several hundred different landscape metrics were developed
They quantify the composition and configuration of spatial patterns of categorical rasters
Landscape metrics
Landscape metrics can be calculated for three different levels: patch, class, and landscape (here we (mostly) focus on the landscape level)
Landscape metrics
- SHDI - Shannon’s diversity index - takes both the number of classes and the abundance of each class into account; larger values indicate higher diversity (diversity metric)
- AI - Aggregation index - from 0 for maximally disaggregated to 100 for maximally aggregated classes (aggregation metric)
SHDI:
AI:
Landscape metrics
Important considerations:
- Scale: the size of the area over which the metrics are calculated
- Extent: the borders of the study area
- Spatial resolution: the size of the raster cells
- Categorization: the categories used in the analysis
- Redundancy: many metrics are highly correlated
IT metrics
- Five information theory metrics based on a co-occurrence matrix exist (Nowosad and Stepinski, 2019, https://doi.org/10.1007/s10980-019-00830-x)
- Marginal entropy [H(x)] - diversity (composition) of spatial categories - from monothematic patterns to multithematic patterns
- Relative mutual information [U] - clumpiness (configuration) of spatial categories from fragmented patterns to consolidated patterns)
- H(x) and U are uncorrelated
Entropy:
Relative mutual information:
IT metrics
2D parametrization of categorical rasters’ configurations based on two weakly correlated IT metrics groups similar patterns into distinct regions of the parameters space
{landscapemetrics}
{landscapemetrics}: patch-level
# A tibble: 305 × 6
layer level class id metric value
<int> <chr> <int> <int> <chr> <dbl>
1 1 patch 1 1 perim 1200
2 1 patch 1 2 perim 1200
3 1 patch 1 3 perim 1800
4 1 patch 1 4 perim 1800
5 1 patch 1 5 perim 255000
6 1 patch 1 6 perim 1800
7 1 patch 1 7 perim 1800
8 1 patch 1 8 perim 2400
9 1 patch 1 9 perim 6600
10 1 patch 1 10 perim 6000
# ℹ 295 more rows
{landscapemetrics}: class-level
{landscapemetrics}: landscape-level
{landscapemetrics}: moving window calculations
mat_window = matrix(1, nrow = 11, ncol = 11)
w_result = window_lsm(r9, window = mat_window, what = "lsm_l_ai")
plot(r9); plot(w_result$layer_1$lsm_l_ai)
Pattern-based spatial analysis
In recent years, the ideas of analyzing spatial patterns have been extended through an approach called pattern-based spatial analysis (Long in in. 2010; Cardille in in. 2010; Cardille in in. 2012; Jasiewicz i in. 2013; Jasiewicz i in. 2015).
The fundamental idea is to divide data into a large number of smaller areas (local landscapes).
Next, represent each area using a statistical description of the spatial pattern - a spatial signature.
Spatial signatures can be compared using a large number of existing distance or dissimilarity measures (Lin 1991; Cha 2007).
This approach enables spatial analyses such as searching, change detection, clustering, or segmentation.
Pattern-based spatial analysis
Knowing the distance between spatial signatures can be used in several contexts (Nowosad, 2021, 10.1007/s10980-020-01135-0):
one-to-many
finding similar spatial structures
one-to-one
quantitative assessment of changes in spatial structures
many-to-many
clustering similar spatial structures
Examples of applications
Using spatial signatures to compare and evaluate digital soil maps (Rossiter et al., 2022, 10.5194/soil-8-559-2022)
Changes in spatial patterns resulting from the inclusion of small woody elements in land use maps (Golicz et al., 2021, 10.3390/land10101028)
Code examples
Code examples
Non-categorical rasters
WorldClim version 2.1 climate data
for 1970-2000
CMIP6 downscaled future climate projection for 2061-2080 [model: CNRM-ESM2-1; ssp: “585”]
Minimum temperature (°C)
{spquery}
https://jakubnowosad.com/spquery/
How to find and compare areas with similar spatial patterns in non-categorical rasters (e.g., raster time-series)?
{patternogram}
https://jakubnowosad.com/patternogram/, https://jakubnowosad.com/ecem-2023
How to detect and describe a range of spatial similarity (spatial autocorrelation) for multiple variables?
It can be used to:
- explore spatial autocorrelations of predictors in machine learning models
- detect spatial autocorrelation in various data structures
- compare the spatial autocorrelation of variables over time
- investigate spatial autocorrelation of categorical spatial patterns
{patternogram}
{supercells}
https://jakubnowosad.com/supercells/, https://jakubnowosad.com/foss4g-2022/
supercells: an extension of SLIC (Simple Linear Iterative Clustering; Achanta et al. (2012), doi:10.1109/TPAMI.2012.120) that can be applied to non-imagery geospatial rasters that carry:
- pattern information (co-occurrence matrices)
- compositional information (histograms)
- time-series information (ordered sequences)
- other forms of information for which the use of Euclidean distance may not be justified
Segmentation/regionalization: partitioning space into smaller segments while minimizing internal inhomogeneity and maximizing external isolation
A way to improve the output and reduce the cost of segmentation.
Code examples
library(terra)
library(supercells)
# Version 1
mintemp_zones = supercells(cmip_tmin_pl, k = 150, compactness = 4)
plot(cmip_tmin_pl[[1]]); plot(mintemp_zones, add = TRUE, col = NA)
# Version 2
mintemp_zones = supercells(cmip_tmin_pl, k = 50, compactness = 4)
plot(cmip_tmin_pl[[1]]); plot(mintemp_zones, add = TRUE, col = NA)
# Version 3
mintemp_zones = supercells(cmip_tmin_pl, k = 150, compactness = 1)
plot(cmip_tmin_pl[[1]]); plot(mintemp_zones, add = TRUE, col = NA)
Summary
- Landscape metrics are still a useful tool for quantification of spatial patterns in categorical raster data
- Pattern-based spatial analysis, on the other hand, enables searching, change detection, clustering, and segmentation of spatial patterns in categorical raster data
- Spatial patterns of non-categorical rasters (e.g., time-series) can be analyzed using the ideas of pattern-based spatial analysis, and also using new methods
- Many methods are already implemented in open-source software
- Think of what scientific problems you can tackle using these methods
Contact
Mastodon: fosstodon.org/@nowosad
Website: https://jakubnowosad.com
Materials
- Software: R packages landscapemetrics, motif, spquery, patternogram, supercells
- Blog posts: https://jakubnowosad.com/posts.html#category=motif, https://jakubnowosad.com/posts.html#category=geopat, https://jakubnowosad.com/posts.html#category=segmentation, https://jakubnowosad.com/posts.html#category=landscape-ecology
