Exploration of spatial patterns in raster data
2024-12-03
Importance of spatial patterns
A relationship between an area’s pattern composition and configuration and ecosystem characteristics (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..)
Defining spatial patterns
- Extent: the extent of the study area
- Scale: the size of the area over which the metrics are calculated
- Resolution: the size of the cells in the raster
- Categorization: the categories used in the analysis
Landscape metrics
SHDI - Shannon’s diversity index: takes both the number of classes and the abundance of each class into account
AI - Aggregation index
Boltzmann-entropy-inspired metrics
How to measure the complexity of a landscape pattern?
One of the possible solutions is to use the Boltzmann entropy, which is a measure of the disorder in a system (Cushman, S. A. (2015), https://doi.org/10.1007/s10980-015-0305-2; Cushman, S. A. (2021). https://doi.org/10.3390/e23121616; Zhao, Y., & Zhang, X. (2019). https://doi.org/10.1007/s10980-019-00876-x)
Zhao’s entropy - Boltzmann entropy-inspired metric
IT-based metrics
Marginal entropy [H(x)] - diversity (composition), from monothematic patterns to multithematic patterns
Relative mutual information [U] - clumpiness (configuration), from fragmented to consolidated patterns
Two areas
The binary difference between two rasters
Overlapping regions, non-spatial context, raster outcome
The difference between a focal measure of two rasters
Overlapping regions, spatial context, raster outcome
Single value measure (e.g., proportion of changed pixels, overall comparison)
Overlapping regions, non-spatial context, single value outcome
Propotion of changed pixels: 0.08
Overall comparison: 0.89
The difference between a measure of two rasters
Arbitrary regions, non-spatial or spatial context, single value outcome
Difference in Zhao’s entropy: 0.002
Difference in marginal entropy: 0.33
Difference in relative mutual information: 0.06
Dissimilarity of a spatial signature between two rasters
Arbitrary regions, non-spatial or spatial context, single value outcome
Spatial signature of the 1st raster: 0.007, 0.011, 0.979, 0, 0.002, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.001, 0, 0, 0, 0, 0, 0, 0
Spatial signature of the 2nd raster: 0.027, 0.032, 0.909, 0.008, 0.004, 0.005, 0.001, 0.008, 0, 0.005, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Analysis of categorical spatial patterns
Each method returning single value can be used in an analysis of spatial patterns
It enables:
- searching for spatial patterns that are similar or different in terms of the selected metric
- clustering of spatial patterns based on the selected metric
Searching
Study area:
{supercells}
Searching
Study area:
Top 9 most similar areas to the study area
Clustering
(For example)
Hierarchical clustering:
- based on a distance matrix
- spatial signature
- dissimilarity measure
Non-hierarchical clustering (e.g., k-means):
- based on the set of derived spatial signatures
Spatial signatures may represent specific properties or general characteristics of the spatial pattern
Additionally, they can be also calculated for a moving window or multiple windows
Spatial signatures depend on the selected extent, scale, resolution, and categorization
Clustering
Land cover raster
Clustering (k-means, k = 5, based on a co-occurrence matrix spatial signature in a 10 by 10 window)
Generalizing and extending
These ideas can be generalized and extended to other types of spatial patterns (e.g., continuous, time-series)
Other signatures, their selection, and application: signatures for multiple spatial scales or signatures for multiple information layers
Selection of appropriate distance measures (for the given problem, data, and used signature)
Information about the spatial pattern can be used in various ways, for example, in spatial modeling, spatial prediction, or spatial optimization
Some tools for exploring spatial patterns: R packages landscapemetrics, bespatial, motif, spquery, patternogram, supercells
PRISM
Preservation and RecognItion of Spatial patterns using Machine learning
Marie Skłodowska-Curie Actions Postdoctoral Fellowship (August 2024 – August 2026)
- “Current machine learning methods, like random forest, are effective but often overlook intricate spatial patterns inherent in ecological processes”
- “The PRISM project tackles this by integrating and validating spatial patterns within machine learning models”
Get in touch if you want to talk about such topics!
Summary
- Spatial patterns are important in environmental sciences
- Theirs different aspects can be described using landscape metrics, Boltzmann-entropy-inspired metrics, and IT-based metrics
- Comparing spatial patterns can be done in various ways, depending on their spatial location and extent, context, and outcome
- Spatial patterns can be searched and clustered based on their properties
- These ideas can be generalized and extended to other types of spatial patterns (e.g., continuous, time-series)
Contact
Website: https://jakubnowosad.com
Materials
- Slides: https://jakubnowosad.com/giforum2024
- Software: R packages landscapemetrics, motif, spquery, patternogram, supercells, bespatial
- Blog posts: https://jakubnowosad.com/posts.html#category=spatial-patterns
