Spatial stratification of landscapes allows for the development of efficient sampling surveys, the inclusion of domain knowledge in data-driven modeling frameworks, and the production of information relating the spatial variability of response phenomena to that of landscape processes. This work presents the rassta package as a collection of algorithms dedicated to the spatial stratification of landscapes, the calculation of landscape correspondence metrics across geographic space, and the application of these metrics for spatial sampling and modeling of environmental phenomena. The theoretical background of rassta is presented through references to several studies which have benefited from landscape stratification routines. The functionality of rassta is presented through code examples which are complemented with the geographic visualization of their outputs.
The application of robust, quantitative approaches for the spatial modeling of environmental phenomena has increased in the past few decades mainly due to an increase in computational power, advances in statistical modeling, and the availability of geospatial layers of environmental information (Scull et al. 2003; Elith and Leathwick 2009). Most of these approaches aim at building explicit quantitative relationships between environmental controls and response phenomena through statistical learning. Examples of these approaches include digital soil mapping (DSM) (McBratney et al. 2003), species distribution modeling (SDM) (Guisan and Zimmermann 2000), land use/land cover classification (Ham et al. 2005), and forest fire modeling (Chuvieco et al. 2010). Despite the extensively documented success of these approaches, there are still some challenges that limit their application. For instance, poor statistical performance is often reported in studies where input data is too limited to accurately represent control-response relationships (Araújo and Guisan 2006). Moreover, model parsimony and interpretation of results can be compromised when using ‘black-box’ algorithms (Arrouays et al. 2020). Similarly, including a priori knowledge about natural processes in purely statistical approaches can be challenging to achieve (Heuvelink and Webster 2001).
Several studies have suggested embedding spatial stratification routines within approaches such as DSM, SDM, land use/cover mapping, forest fire modeling, and others to overcome the challenges limiting their application. In such studies, the spatial stratification of landscapes creates units with reduced spatial variability of environmental phenomena as compared to the overall variability across a landscape. The use of these units allows the researcher to (a) obtain balanced representations of control-response relationships (Guisan and Zimmermann 2000; West et al. 2016); (b) include expert knowledge of physical processes for improving modeling with limited data (Zhu et al. 2008); (c) improve the performance of parameterization of mechanistic models (Park and Van De Giesen 2004; Baldwin et al. 2017); and, (d) facilitate the interpretation of environmental conditions and their influence on the spatiotemporal variability of processes of interest (Rodrigues et al. 2019).
In general, landscape stratification routines follow fundamental ecological concepts that explain the hierarchical and multi-scale nature of relationships between environmental phenomena across space (Allen and Starr 1982). Therefore, landscape stratification methods have been applied in many studies that use geospatial information for environmental modeling, such as those previously cited. However, few packages exist in the R environment with functions strictly aimed at landscape stratification routines using geospatial data. Although one could implement custom stratification algorithms using multiple all-purpose geospatial analysis packages such as terra (Hijmans 2021) and sf (Pebesma 2018), the ease of use, reproducibility, and replicability of analysis is often enhanced when algorithms are implemented as part of a dedicated package. The motif package (Nowosad 2021) is the only example the authors could find of a package that is fully dedicated to landscape stratification in R using geospatial data. Although the methods offered by motif are effective for large-scale studies (Jasiewicz et al. 2015; Nowosad 2021), their application is currently limited to rasters of categorical data. Thus, motif is not practical for the modeling of spatially continuous environmental phenomena, which is often a goal of landscape stratification routines.
This work presents the rassta package as a collection of algorithms for the spatial stratification of landscapes, sampling, and modeling of environmental phenomena. The rassta package is not intended as a drop-in replacement for statistically-robust environmental modeling approaches. Rather, it is intended to serve as a generalized framework to derive geospatial information that can be used to improve inference with these statistical approaches.
The algorithms in the rassta package assist in the analysis of
environmental information related to the spatial variability of natural
phenomena across landscapes. These functions focus on integrating standard
geospatial techniques and quantitative analysis in a generalized framework for
landscape stratification, sampling, and modeling. All of the functions in the
rassta package take geospatial data in raster format as input. In the
context of geographic information systems (GIS), the raster format can be
considered a graphical representation of a matrix that is organized in rows and
columns, and which may be stacked in multiple layers (e.g., multi-band satellite
imagery). Each cell (pixel) in the raster contains a value representing a
spatially-varying phenomenon, such as elevation or precipitation. A few
functions in rassta also produce geospatial data in vector format. Vector
data represents geometric entities in the form of points, lines, and polygons.
The rassta package uses the highly efficient terra package as the
backbone for handling raster and vector data. Most of the geospatial data
manipulation with terra is performed in C++ and is based on two main R
data types (classes): SpatRaster and SpatVector. Note that terra
imports the Rcpp package (Eddelbuettel and François 2011) since terra uses
C++ (including external pointers) to manipulate these classes.
Most of the functions implemented in rassta are interrelated in the sense
that the outputs from some functions can be used as the inputs for others. This
functional interrelation allows for a generalized framework to conduct spatial
stratification, sampling, and modeling in a single package following a
project-oriented approach. In general, the functions of rassta can be
grouped into five categories: (a) landscape stratification; (b) landscape
correspondence metrics; (c) stratified sampling; (d) spatial modeling; and (e)
miscellaneous (Figure 1). Each category and its corresponding
functions (except for miscellaneous) are theoretically founded on several
studies focused on understanding spatially-varying natural phenomena across
landscapes. In the next sections, the rationale behind each category and its
functions is described. This description is complemented with references to
corresponding scientific literature and includes code examples showing the
application of each function with extensive use of plotting functions (for
visualization purposes only). Most of the plotting functions are derived from
the terra package using the SpatRaster and SpatVector classes. [Note:
To reduce the extension of code examples, all the map and graph plotting
functions were consolidated in the function figure()].