Inventory of methods for comparing spatial patterns in raster data

Comparison of spatial patterns in raster data is a part of many types of spatial analysis. With this task, we want to know how the physical arrangement of observations in one raster differs from the physical arrangement of observations in another raster.

This blog post series will explain the motivation for comparing spatial patterns in raster data, the general considerations when selecting a method for comparison, and the inventory of methods for comparing spatial patterns in raster data. Next, it will show how to use R to compare spatial patterns in continuous and categorical raster data. Lastly, it will discuss the methods’ properties, their applicability, and how they can be extended.

Motivation

In general, four main reasons for comparing spatial patterns in raster data were identified by Long and Robertson (2018, https://doi.org/10.1111/gec3.12356):

1. Study of change (i.e., how the spatial pattern of a landscape has changed over time)
2. Study of similarity (i.e., how similar the spatial pattern of two landscapes is)
3. Study of association (i.e., how the spatial pattern of one theme is associated with the spatial pattern of another theme)
4. Spatial model assessment (i.e., how well a model output matches the spatial pattern of the reference data)

For now, I want to focus on the situation in which only two rasters are compared at a time.¹ Then, we can think about comparing spatial patterns in raster data as the type of operation that is performed:

1. Comparison of the same variable for two different areas
2. Comparison of two different variables (or e.g., sensors) for the same area
3. Comparison of the same variable for the same area at two different times

Visual inspection

To think about this topic, let’s consider the examples of the Corine Land Cover (CLC) data for Tartu, Estonia in 2000 and 2018, and for Poznan, Poland in 2018:

We can start comparing the spatial patterns in these rasters just by looking at them: the land cover for Tartu in 2000 and 2018 looks similar, but it is different for Poznan in 2018 (much more urban areas, less forests). A comparison of Tartu in 2000 and 2018 suggests that urban areas have expanded into areas that were previously mostly covered by agricultural land. Visual inspection is a good starting point, as the human eye can detect multiple patterns that are not easily quantifiable. At the same time, it is subjective and may not be suitable for large datasets.

Generalization of the main aspects to consider

Alternatively, we can use quantitative methods to compare the spatial patterns in these rasters. Figure 1 shows general considerations when thinking about the properties of the methods for comparing spatial patterns in raster data.

flowchart TB
  A[Arbitrary regions] ---|Yes| B(Spatial context)
  A ---|No| C(Spatial context)
  B ---|Yes| D{{Outcome}}
  B ---|No| E{{Outcome}}
  C ---|Yes| F{{Outcome}}
  C ---|No| G{{Outcome}}
  D --> H([Single value])
  E --> I([Single value])
  F --> J([Single value]) 
  F --> K([Multiple values])
  F --> L([Raster]) 
  G --> M([Single value])
  G --> N([Multiple values])
  G --> O([Raster])
  
  style D stroke:transparent
  style E stroke:transparent
  style F stroke:transparent
  style G stroke:transparent

The first main aspect to consider when comparing spatial patterns in raster data is whether or not we are dealing with arbitrary regions. Working on overlapping (i.e., non-arbitrary) regions, e.g., CLC in Tartu in 2000 and 2018, allows for different approaches than working on arbitrary regions, e.g., CLC in Tartu in 2018 and Poznan in 2018. With non-arbitrary regions, each cell in one raster (or each cell in a moving window) can be compared to a corresponding cell in another raster. Thus, one possible outcome of the comparison is another raster, which highlights where the spatial patterns are similar or different. This is not possible with arbitrary regions, and the comparison usually includes spatial patterns of whole rasters.

The second main aspect to consider when comparing spatial patterns in raster data is whether the method used allows the integration of the spatial context of the analysis. A difference between the values of two cells is straightforward to calculate and interpret, but it does not consider the other local values. Alternatively, some methods use the spatial context of the analysis, e.g., by comparing the values in a moving window or a local neighborhood.

It is also worth noting that the comparison of spatial patterns in raster data can result in different types of data. For overlapping regions, the outcome can be a single value, multiple values, or a raster, and for arbitrary regions, it is usually a single value (multiple values are also possible, but often as a collection of single values’ results).

The above considerations can be applied to both continuous and categorical raster data, but the methods used for comparing spatial patterns in these two types of data are different.

Inventory of methods

An inventory of methods for comparing spatial patterns in raster data is presented in the following tables.² Methods for comparing two layers of spatial continuous raster data are shown in Table 1, and methods for spatial categorical raster data are in Table 2.

Both tables are adapted from the “Comparing spatial patterns in raster data using R” paper published in the ISPRS Archives (Nowosad, 2024, https://doi.org/10.5194/isprs-archives-XLVIII-4-W12-2024-127-2024).³ There you can find the complete list of the references for the methods presented in the tables.

In the next blog posts, I will focus on the practical aspects of comparing spatial patterns: how to use R to compare spatial patterns in continuous and categorical raster data. It will include the interpretation of the results and the discussion of the characteristics of the methods. Stay tuned!

@online{nowosad2024,
  author = {Nowosad, Jakub},
  title = {Inventory of Methods for Comparing Spatial Patterns in Raster
    Data},
  date = {2024-10-13},
  url = {https://jakubnowosad.com/posts/2024-10-13-spatcomp-bp1/},
  langid = {en}
}