Background

Data collected in streams frequently exhibit unique patterns of spatial autocorrelation resulting from the branching network structure, longitudinal (i.e., upstream/downstream) connectivity, directional water flow, and differences in flow volume upstream of junctions (i.e., confluences) in the network (Peterson et al., 2013). In addition, stream networks are embedded within geographic (i.e., 2-D) space, with the terrestrial landscape often having a strong influence on observations collected on the stream network. Ver Hoef & Peterson (2010) describe how to fit spatial statistical models on stream networks (i.e., spatial stream-network models) that capture the unique and complex spatial dependencies inherent in streams. These stream network models can be fit using the ‘SSN2’ R package (Dumelle, Peterson, Ver Hoef, Pearse, & Isaak, 2024). To use ‘SSN2’, however, users must provide the spatial, topological, and attribute data in a specific format called an SSN object. The ‘SSNbler’ R package, which we introduce here, is an adaptation of the STARS ArcGIS toolset (Peterson & Ver Hoef, 2014) for the R programming language. ‘SSNbler’ generates formats, assembles, and validates SSN objects that can be used for statistical modeling in ‘SSN2’.

In this vignette, we use ‘SSNbler’ to create the SSN object MiddleFork04.ssn used by ‘SSN2’. First, we load ‘SSNbler’ into our current R session.

library(SSNbler)

A few input datasets are included in the ‘SSNbler’ package:

• MF_streams: An sf object with LINESTRING geometry representing a portion of the Middle Fork stream network in Idaho, USA.
• MF_obs: An sf object with POINT geometry containing observed summer mean stream temperature observations at 45 unique locations on MF_streams.
• MF_pred1km: An sf object with POINT geometry containing unsampled locations spaced at one-kilometer intervals throughout MF_streams. This prediction dataset represents 175 locations where predictions of some response variable (i.e., temperature) may be desired.
• MF_CapeHorn: An sf object with POINT geometry containing 654 unsampled locations spaced at 10-meter intervals throughout Cape Horn Creek in MF_streams.

To provide context, the observed data in MF_obs will be used to build statistical models and make predictions at the locations in MF_pred1km and MF_CapeHorn using the R package ‘SSN2’. Documentation for each dataset can be found by running help(). For example, to learn more about MF_streams, run help("MF_streams", package = "SSNbler").

While these datasets come with ‘SSNbler’ and can be loaded via data(), we focus here on a more realistic workflow for the user. We start with a collection of spatial datasets installed alongside ‘SSNbler’ in the streamsdata folder that represent the Middle Fork stream network. In streamsdata are GeoPackages (more on this later) representing the stream network, observed data, and prediction data (optional) required to create an SSN object. To prevent ‘SSNbler’ functions from reading and writing to this folder, we copy it to R’s temporary directory and store the path to this folder:

copy_streams_to_temp()
path <- paste0(tempdir(), "/streamsdata")

Then we can read in the relevant data using st_read from the ‘sf’ R package (Pebesma, 2018), which comes installed alongside ‘SSNbler’. Note that the input data can be in any vector data format that can be imported into R and stored as an sf object with LINESTRING or POINT geometry (e.g., shapefile, GeoJSON, GeoPackage, SpatiaLite, PostGIS).

library(sf)
MF_streams <- st_read(paste0(path, "/MF_streams.gpkg"))
MF_obs <- st_read(paste0(path, "/MF_obs.gpkg"))
MF_pred1km <- st_read(paste0(path, "/MF_pred1km.gpkg"))
MF_CapeHorn <- st_read(paste0(path, "/MF_CapeHorn.gpkg"))

Notice that the line (MF_Streams) and point features (MF_obs, MF_pred1km, and MF_CapeHorn) have LINESTRING and POINT geometry types, which are required in ‘SSNbler’. If these datasets had MULTILINESTRING or MULTIPOINT geometry types, the ‘sf’ function st_cast could be used to convert to the required geometry types. All of the input data have an Albers Equal Area Conic projection (EPSG 102003) and distances are measured in meters. It is important that all input datasets have the same map projection, which must be a projected coordinate system and not a geographic coordinate system measured in Latitude and Longitude. The ‘sf’ function st_transform can be used to reproject sf objects in R.

We previously mentioned these data are stored in streamsdata in a GeoPackage format. GeoPackages, like shapefiles, are a way to store spatial data. We prefer GeoPackages over shapefiles because they offer better support for high precision numeric data compared to the traditional DBF (dBASE) format (used in shapefiles), which limits the precision to 10 decimal places when writing (not reading) to local files from R. This is problematic because several important columns ‘SSNbler’ adds and ‘SSN2’ uses contain very small values ranging from zero to one. If these columns are truncated it can lead to difficult-to-diagnose errors when models are fit in ‘SSN2’. GeoPackages do not have this limitation. To learn more about GeoPackages, visit here.

Before working with any of the input files, we visualize the stream network, observed sites, and prediction sites using the R package ‘ggplot2’ (Wickham, 2016).

library(ggplot2)
ggplot() +
  geom_sf(data = MF_streams) +
  geom_sf(data = MF_CapeHorn, color = "gold", size = 1.7) +
  geom_sf(data = MF_pred1km, colour = "purple", size = 1.7) +
  geom_sf(data = MF_obs, color = "blue", size = 2) +
  coord_sf(datum = st_crs(MF_streams))

In the figure above, there are two subnetworks from MF_Streams (black lines). Point features from MF_obs (blue dots) and MF_pred1km (purple dots) are found on both networks, while MF_CapeHorn point features (yellow dots) are only found on one of the two networks.

The Landscape Network

‘SSNbler’ makes use of a data structure called a Landscape Network (LSN), which is a type of graph used to represent spatial context and relationships with additional geographic information (Theobald et al., 2006). In a LSN, streams are represented as a collection of directed edges, where the directionality is determined by the digitized direction of the line features. Nodes are located at the end points of edges (i.e., end nodes) and represent topologic breaks in the edges. For a more detailed description of the LSN, see Peterson & Ver Hoef (2014).

There are four topologically valid node categories in a LSN:

• Source: Water flow originates at these nodes and flows downstream. An edge that begins at a source node is called a headwater segment. Source nodes do not receive flow from any upstream edges.
• Outlet: Flow terminates at these nodes. This node is the most downstream point in an edge network. We refer to an edge that terminates at an outlet as an outlet segment. Note that a streams dataset may contain multiple subnetworks with associated outlets.
• Confluence: Multiple edges converge, or flow into, a single node.
• Pseudonode: One edge flows in and one edge flows out of a single node. While these nodes are not topologically problematic, an excessive number of pseudonodes can slow down geoprocessing operations for large datasets.

A landscape network (LSN). Nodes are denoted by blue circles, with the node category labelled. Edges are denoted by black arrows, with the arrow indicating flow direction (i.e., digitized direction).

Each edge is associated with two nodes, which correspond to the upstream and downstream end nodes of the edge. When more than one edge flows into or out of the node, they share a node. Thus, there should always be a single node at the intersection of edges. If there is more or less than one node at an intersection, it is a topological error. If these errors are not corrected, the connectivity between line features and the observed and prediction sites associated with them will not be accurately represented in the SSN object or the spatial statistical models subsequently fit to the data. In this vignette, we assume that MF_streams has already been checked and topologically corrected. Two tutorials have been created with detailed instructions about identifying and correcting topological errors in the LSN, as well as other topological restrictions that are not permitted (please see ‘Correcting topological errors using SSNbler and QGIS’ or ‘Correcting topological errors using SSNbler and ArcGIS Pro’). These tutorials are available for download within the relevant folders on GitHub at this link.

## Set path for new folder for lsn
lsn.path <- paste0(tempdir(), "/mf04")

edges <- lines_to_lsn(
  streams = MF_streams,
  lsn_path = lsn.path,
  check_topology = TRUE,
  snap_tolerance = 0.05,
  topo_tolerance = 20,
  overwrite = TRUE
)

obs <- sites_to_lsn(
  sites = MF_obs,
  edges = edges,
  lsn_path = lsn.path,
  file_name = "obs",
  snap_tolerance = 100,
  save_local = TRUE,
  overwrite = TRUE
)

preds <- sites_to_lsn(
  sites = MF_pred1km,
  edges = edges,
  save_local = TRUE,
  lsn_path = lsn.path,
  file_name = "pred1km.gpkg",
  snap_tolerance = 100,
  overwrite = TRUE
)

capehorn <- sites_to_lsn(
  sites = MF_CapeHorn,
  edges = edges,
  save_local = TRUE,
  lsn_path = lsn.path,
  file_name = "CapeHorn.gpkg",
  snap_tolerance = 100,
  overwrite = TRUE
)

Calculating Upstream Distance

The “upstream distance” represents the hydrologic distance (i.e., distance between locations when movement is restricted to the stream network) between the network outlet and each feature. For an edge, the distance is measured to the upstream end node of the line feature. The upstream distance for the jth edge, upDist_j, is:

upDist_j = ∑_k ∈ DjL_k,

where L_j is the length of each edge and D_j is the set of edges found in the path between the network outlet and the jth edge, including the jth edge.

The upstream distance for each edge is calculated using the updist_edges() function, which generally requires these arguments:

• edges: An sf object containing the edges in the LSN generated using lines_to_lsn().
• save_local: A logical indicating whether the updated edges should be saved to lsn_path in GeoPackage format. Default is TRUE.
• lsn_path: LSN pathname where edges and relationships.csv are stored locally.
• calc_length: A logical indicating whether a column representing line length should be calculated and added to edges. It is important to set calc_length = TRUE if the edge features have been edited.

edges <- updist_edges(
  edges = edges,
  save_local = TRUE,
  lsn_path = lsn.path,
  calc_length = TRUE
)

names(edges) ## View edges column names

#>  [1] "rid"        "COMID"      "GNIS_NAME"  "REACHCODE"  "FTYPE"     
#>  [6] "FCODE"      "AREAWTMAP"  "SLOPE"      "rcaAreaKm2" "h2oAreaKm2"
#> [11] "Length"     "upDist"     "geom"

Two columns are added to edges and saved in edges.gpkg. Length represents the length of each edge in map units and upDist is the upstream distance for each edge.

For sites, the upstream distance is calculated a little differently because it is the hydrologic distance between the network outlet and each site. The upstream distance for site i, upDist_i, is calculated as: upDist_i = r_iL_i + ∑_{k ∈ Dj^*}L_k,

where r_i is the ratio value for site_i, L_i is the length of the edge site_i resides on, and D_j^* is the set of edges found in the path between the network outlet and site_i, excluding the edge site_i resides on.

Upstream distance is calculated for each site using the updist_sites() function, which generally requires a few arguments:

• sites: A named list of one or more sf objects with POINT geometry, which have been incorporated into the LSN using sites_to_lsn().
• edges: An sf object representing edges that have been processed using lines_to_ssn() and updist_edges().
• length_col: The name of the column in edges that represents edge length.
• save_local: A logical indicating whether the updated sites should be saved to lsn_path in GeoPackage format. Default is TRUE.
• lsn_path: The LSN pathname where the sites and edges GeoPackages reside. Must be specified if save_local is TRUE.

site.list <- updist_sites(
  sites = list(
    obs = obs,
    pred1km = preds,
    CapeHorn = capehorn
  ),
  edges = edges,
  length_col = "Length",
  save_local = TRUE,
  lsn_path = lsn.path
)

names(site.list) ## View output site.list names

#> [1] "obs"      "pred1km"  "CapeHorn"

names(site.list$obs) ## View column names in obs

#>  [1] "rid"        "STREAMNAME" "COMID"      "AREAWTMAP"  "SLOPE"     
#>  [6] "ELEV_DEM"   "Source"     "Summer_mn"  "MaxOver20"  "C16"       
#> [11] "C20"        "C24"        "FlowCMS"    "AirMEANc"   "AirMWMTc"  
#> [16] "rcaAreaKm2" "h2oAreaKm2" "ratio"      "snapdist"   "geom"      
#> [21] "upDist"

The data stored in upDist are later used to calculate the directional hydrologic distances between observed and prediction locations in the ‘SSN2’ package. If we plot the edges and observations, assigning color based on the upDist column, it is apparent that the upstream distance increases from the outlet to headwater streams, as expected.

ggplot() +
  geom_sf(data = edges, aes(color = upDist)) +
  geom_sf(data = site.list$obs, aes(color = upDist)) +
  coord_sf(datum = st_crs(MF_streams)) +
  scale_color_viridis_c()

Calculating Additive Function Values (AFVs)

Spatial weights are used to split the tail-up covariance function upstream of network confluences, which allows for the disproportionate influence of one upstream edge over another (e.g., a large stream channel converges with a smaller one) on downstream values. Calculating the spatial weights is a three-step process: 1) calculating the segment proportional influence (PI), 2) calculating the additive function values (AFVs), and 3) calculating the spatial weights. Steps 1) and 2) are undertaken in ‘SSNbler’, while Step 3) is calculated in the package ‘SSN2’ when spatial stream-network models are fit.

The segment PI for each edge, ω_j, is defined as the relative influence of the jth edge feature on the edge directly downstream. In the following example, ω_j is based on cumulative watershed area for the downstream node of each edge, A_j, which is used as a surrogate for flow volume. However, simpler measures could be used, such as Shreve’s stream order (Shreve 1966) or equal weighting, as long as a value exists for every line feature in edges (i.e., missing data are not allowed). It is also preferable to use a column that does not contain values equal to zero, which we explain in more detail below.

When two edges, denoted j and k, converge at a node, the segment PI for the jth edge is:

$$ \omega_j=\frac{A_j}{A_j + A_k}. $$

Notice that the segment PI values are ratios. Therefore, the sum of the PI values for edges directly upstream of a single node always sum to one. Also note that ω_j = 0 when A_j = 0.

The AFVs for the jth edge, AFV_j, is equal to the product of the segment PIs found in the path between the edge and the network outlet, including edge j itself.

AFV_j = ∏_k ∈ Djω_k.

If ω_j = 0, the AFV values for edges upstream of the jth edge will also be equal to zero. This may not be problematic if the jth edge is a headwater segment without an observed site. However, it can have a significant impact on the covariance structure of the tail-up model when the jth edge is found lower in the stream network.

AFVs are calculated for every edge in the network using afv_edges(), which generally requires these arguments:

• edges: An sf object representing edges that has been processed using lines_to_lsn().
• lsn_path: The LSN pathname where the edges reside.
• infl_col: The name of the numeric column in edges used to calculate the segment PI for each edge feature. Missing values are not allowed.
• segpi_col: The name of the new column in edges where segment PI values are stored.
• afv_col: The name of the new column in edges where AFVs are stored.
• save_local: A logical indicating whether the updated edges should be saved to lsn_path in GeoPackage format. Default is TRUE.

Note that we use a variable representing cumulative watershed area that is already present in edges (h2oAreaKm2) to create the segment PI values:

summary(edges$h2oAreaKm2) ## Summarize and check for zeros

#>     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
#>   0.0036   2.4534   5.9877  22.6237  28.2600 209.8989

edges <- afv_edges(
  edges = edges,
  infl_col = "h2oAreaKm2",
  segpi_col = "areaPI",
  afv_col = "afvArea",
  lsn_path = lsn.path
)

names(edges) ## Look at edges column names

#>  [1] "rid"        "COMID"      "GNIS_NAME"  "REACHCODE"  "FTYPE"     
#>  [6] "FCODE"      "AREAWTMAP"  "SLOPE"      "rcaAreaKm2" "h2oAreaKm2"
#> [11] "Length"     "upDist"     "areaPI"     "afvArea"    "geom"

summary(edges$afvArea) ## Summarize the AFV column

#>     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
#> 0.004709 0.026168 0.066095 0.160335 0.169575 1.000000

The AFVs are a product of ratios, which means that the AFVs are always between zero and one (0 ≤ AFV ≤ 1). The AFV for the most downstream edge in a network will always be one. If AFVs do not meet this requirement, then an error has occurred.

Once the AFVs have been added to edges, they can be calculated for the observations and (if relevant) prediction sites. The AFV for any site is equivalent to the AFV of the edge it resides on. If there are multiple sites on a single edge feature, their AFVs will be equal. Also note that when the AFV for the ith site is zero, the covariance between data collected at the ith site and every other site will also be zero. For more on additive function values, see Ver Hoef & Peterson (2010) and Peterson & Ver Hoef (2010).

The afv_sites function is used to create an AFV column in a list of observed and prediction sites. The inputs include:

• sites: A named list of one or more sf objects with POINT geometry, which have been incorporated into the LSN using sites_to_lsn().
• edges: An sf object representing edges, which contains afv_col created using edges_afv().
• afv_col: The name of the column containing the AFVs in edges. A new column with this name will be added to sites.
• save_local: If TRUE (the default), the updated sites are written to lsn_path.
• lsn_path: A path to the directory where the LSN created via lines_to_lsn() is stored. Required when save_local = TRUE.

site.list <- afv_sites(
  sites = site.list,
  edges = edges,
  afv_col = "afvArea",
  save_local = TRUE,
  lsn_path = lsn.path
)

names(site.list$pred1km) ## View column names in pred1km

#>  [1] "rid"        "COMID"      "AREAWTMAP"  "SLOPE"      "ELEV_DEM"  
#>  [6] "FlowCMS"    "AirMEANc"   "AirMWMTc"   "rcaAreaKm2" "h2oAreaKm2"
#> [11] "ratio"      "snapdist"   "upDist"     "afvArea"    "geom"

summary(site.list$pred1km$afvArea) ## Summarize AFVs in pred1km and look for zeros

#>     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
#> 0.009894 0.031219 0.047469 0.104969 0.112882 1.000000

Each sf dataset in sites.list now has an AFV column, afvArea, which was generated based on cumulative watershed area. All AFVs should meet the requirement that they are between zero and one.

Assembling the SSN Object

The last data processing step is to assemble the SSN object using the ssn_assemble function.

The key arguments in ssn_assemble() include:

• edges: An sf object representing edges that has been processed using lines_to_lsn(), updist_edges(), and afv_edges().
• lsn_path: The LSN pathname where the edges and all observation and prediction site datasets reside.
• obs_sites: Optional. A single sf object representing observed sites, which has been processed using sites_to_lsn(), updist_sites(), and afv_sites(). Default is is NULL.
• preds_list: Optional. A named list of one or more sf objects representing prediction site datasets that have been processed using sites_to_lsn(), updist_sites(), and afv_sites(). Default is NULL.
• ssn_path: The path to a local directory where the output files will be saved. A .ssn extension will be added if it is not included.
• import: Logical indicating whether the output files should be imported and returned as an SSN object.
• check: Logical indicating whether the validity of the SSN object should be checked using ssn_check(). Default is TRUE.
• afv_col: Character vector containing the names of the AFV columns that will be checked when check = TRUE. Columns must be present in edges, obs_sites, and preds_list, if they are included.

mf04_ssn <- ssn_assemble(
  edges = edges,
  lsn_path = lsn.path,
  obs_sites = site.list$obs,
  preds_list = site.list[c("pred1km", "CapeHorn")],
  ssn_path = paste0(path, "/MiddleFork04.ssn"),
  import = TRUE,
  check = TRUE,
  afv_col = "afvArea",
  overwrite = TRUE
)

#> 
#> 
#> SSN object is valid: TRUE

class(mf04_ssn) ## Get class

#> [1] "SSN"

names(mf04_ssn) ## print names of SSN object

#> [1] "edges" "obs"   "preds" "path"

names(mf04_ssn$preds) ## print names of prediction datasets

#> [1] "pred1km"  "CapeHorn"

The outputs of ssn_assemble() are stored locally in a directory with a .ssn extension and in memory as an object of class SSN when import = TRUE. At a minimum, the new .ssn directory will contain:

1. edges.gpkg: edges in GeoPackage format
2. sites.gpkg: observed sites in GeoPackage format (if included)
3. Prediction datasets: (e.g., CapeHorn.gpkg and pred1km.gpkg) in GeoPackage format (if included)
4. netIDx.dat files: one text file for each unique subnetwork in edges containing information describing the topological relationships between edges.

When import = TRUE, the spatial data stored in the .ssn directory are imported into R and stored in memory as an SSN object. The netIDx.dat files are combined behind the scenes into an SQLite database named binaryID.db, which is saved in the .ssn directory. Most users will not need to access the binaryID.db or the netIDx.dat files, but a more detailed description about how the topological relationships are stored can be found in Peterson & Ver Hoef (2014).

The SSN object itself is a list containing four elements:

1. edges: An sf object representing edges.
2. obs: An sf object of observed sites.
3. preds: Named list of sf objects representing prediction site datasets.
4. path: Character string describing the path to the .ssn where the SSN components are stored locally.

Including observed sites is optional in ssn_assemble and when they are missing obs will contain NA rather than an sf object. Most users will likely include observations because they are needed to fit spatial statistical stream-network models. Nevertheless, this option provides the flexibility to include additional functionality in future ‘SSNbler’ versions. More specifically to create an SSN object based on existing stream network data, generate artificial observed locations at various locations throughout the network, and simulate data at those locations using the ‘SSN2’ function ssn_simulate.

The path element provides a critical link between the .ssn directory and the SSN object stored in R. This is important because the ‘SSN2’ package reads and writes data to this directory during the spatial stream-network modelling workflow.

The ssn_assemble function also adds several important columns to the edges, obs, and prediction datasets.

• edges:
  • netID: A unique network identifier
• obs and preds:
  • netID The network identifier value for the edge the site resides on
  • pid: A unique identifier for each measurement (i.e., point feature).
  • locID: A unique identifier for each location. Note that repeated measurements at a site will have the same locID value, but different pid values.

A netgeom (short for network geometry) column is also added to each of the sf objects stored within an SSN object. The netgeom column contains a character string describing the position of each line (edges) and point (obs and preds) feature in relation to one another. The format of the netgeom column differs depending on whether it is describing a feature with LINESTRING or POINT geometry. For edges, the format of netgeom is

ENETWORK (netID rid upDist), and for sites SNETWORK (netID rid upDist ratio pid locID).

The information stored in these columns is used to keep track of the spatial and topological relationships in the network. The data used to define netgeom is stored in the edges, observed sites, and prediction sites datasets. We store an additional copy of this critical information as text in the netgeom column because it reduces the chances that users will unknowingly make changes to these data, which in turn could change how relationships are represented in spatial stream-network models.

Plotting an SSN Object

The ‘SSNbler’ and ‘SSN2’ packages do not include generic plotting functions for SSN objects because the functionality is already available in the package ‘ggplot2’. As an example, we create a plot of the SSN object. The edges are displayed in blue, with the linewidth proportional to cumulative watershed area column, h2oAreaKm2. The summer stream temperature observations (Summer_mn) are shown using the viridis color palette, with pred1km locations shown as smaller white dots:

ggplot() +
  geom_sf(
    data = mf04_ssn$edges,
    color = "medium blue",
    aes(linewidth = h2oAreaKm2)
  ) +
  scale_linewidth(range = c(0.1, 2.5)) +
  geom_sf(
    data = mf04_ssn$preds$pred1km,
    size = 1.5,
    shape = 21,
    fill = "white",
    color = "dark grey"
  ) +
  geom_sf(
    data = mf04_ssn$obs,
    size = 1.7,
    aes(color = Summer_mn)
  ) +
  coord_sf(datum = st_crs(MF_streams)) +
  scale_color_viridis_c() +
  labs(color = "Temperature", linewidth = "WS Area") +
  theme(
    legend.text = element_text(size = 8),
    legend.title = element_text(size = 10)
  )

Mean summer stream temperature (Temperature) and cumulative watershed area (WS AREA) for the Middle Fork stream network. Prediction locations are white circles.

Notice the different ways the sf objects for the edges, obs, and pred1km datasets are accessed in the SSN object and used for plotting in the calls to geom_sf. Any valid plotting function for sf objects and ggplot in general can be used to create attractive plots of SSN object components.

Incorporating Data Into an sf or SSN Object

The edges, observations, and prediction locations are stored as sf objects, which allows these data to be accessed, manipulated, deleted, or replaced in the same way as other sf objects. The sf objects found in an SSN object can be accessed just like an element in any named list. In this example, the edges and observed sites are accessed using calls to mf04_ssn$edges and mf04_ssn$obs, respectively. The prediction sites are accessed a bit differently (e.g. mf04_ssn$preds$pred1km) because preds is itself a named list.

Users often want to incorporate additional data into the edges, observations, or prediction datasets to generate AFVs, for use as model covariates, or to create more meaningful plots. For example, the US EPA’s StreamCat database (Hill, Weber, Leibowitz, R, & Thornbrugh, 2015) contains hundreds of variables describing stream segment characteristics in the conterminous US. It is relatively easy to join these and other data to the sf objects in R before or after the SSN object is assembled. An online search will show there are numerous functions available for joining an sf object to a variety of data formats (e.g. data.frames, tibbles, vectors, sp objects). However, if the result of the join is not an sf object, it must be converted to one before running additional functions in ‘SSNbler’ and ‘SSN2’ (see st_as_sf in the ‘sf’ package).

Fitting a Spatial Stream Network Model Using SSN2

We can now use the mf04_ssn object to fit a spatial stream-network model relating mean summer temperature to elevation (ELEV_DEM) and mean annual precipitation (AREAWTMAP), with the exponential tail-up, spherical tail-down, and Gaussian Euclidean covariance functions. Notice that additive = "afvArea", which is the column we created earlier using the afv_edges and afv_sites functions.

library(SSN2)

## Generate hydrologic distance matrices
ssn_create_distmat(mf04_ssn)

## Fit the model
ssn_mod <- ssn_lm(
  formula = Summer_mn ~ ELEV_DEM + AREAWTMAP,
  ssn.object = mf04_ssn,
  tailup_type = "exponential",
  taildown_type = "spherical",
  euclid_type = "gaussian",
  additive = "afvArea"
)
summary(ssn_mod)

#> 
#> Call:
#> ssn_lm(formula = Summer_mn ~ ELEV_DEM + AREAWTMAP, ssn.object = mf04_ssn, 
#>     tailup_type = "exponential", taildown_type = "spherical", 
#>     euclid_type = "gaussian", additive = "afvArea")
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -2.73430 -1.43161 -0.04368  0.83251  1.39377 
#> 
#> Coefficients (fixed):
#>              Estimate Std. Error z value Pr(>|z|)    
#> (Intercept) 78.214857  12.189379   6.417 1.39e-10 ***
#> ELEV_DEM    -0.028758   0.005808  -4.952 7.35e-07 ***
#> AREAWTMAP   -0.008067   0.004125  -1.955   0.0505 .  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Pseudo R-squared: 0.4157
#> 
#> Coefficients (covariance):
#>               Effect     Parameter   Estimate
#>   tailup exponential  de (parsill)  1.348e+00
#>   tailup exponential         range  8.987e+05
#>   taildown spherical  de (parsill)  2.647e+00
#>   taildown spherical         range  1.960e+05
#>      euclid gaussian  de (parsill)  1.092e-04
#>      euclid gaussian         range  1.805e+05
#>               nugget        nugget  1.660e-02

As expected, there is strong evidence (p < 0.001) that elevation is negatively related to mean summer temperature, while there is moderate evidence (p ≈ 0.05) that precipitation is negatively related to mean summer temperature. To learn more about fitting spatial stream-network models using the ‘SSN2’ package, visit the package website at https://usepa.github.io/SSN2/.