Calculate Sum of Exponentially Decaying Contributions (SEDC) covariates

Usage

summarize_sedc(
  point_from = NULL,
  point_to = NULL,
  id = NULL,
  sedc_bandwidth = NULL,
  threshold = NULL,
  target_fields = NULL,
  extent_from = NULL,
  extent_to = NULL,
  ...
)

Arguments

point_from: SpatVector object. Locations where the sum of SEDCs are calculated.
point_to: SpatVector object. Locations where each SEDC is calculated.
id: character(1). Name of the unique id field in point_to.
sedc_bandwidth: numeric(1). Distance at which the source concentration is reduced to exp(-3) (approximately -95 %)
threshold: numeric(1). For computational efficiency, the nearest points in threshold will be selected. 2 * sedc_bandwidth is applied if this value remains NULL.
target_fields: character. Field names to calculate SEDC.
extent_from: numeric(4) or SpatExtent. Extent of clipping point_from. It only works with point_from of character(1) file path. See terra::ext for more details. Coordinate systems should match.
extent_to: numeric(4) or SpatExtent. Extent of clipping point_to.
...: Placeholder.

Value

data.frame object with input field names with a suffix "_sedc" where the sums of EDC are stored. Additional attributes are attached for the EDC information.

attr(result, "sedc_bandwidth"): the bandwidth where concentration reduces to approximately five percent
attr(result, "sedc_threshold"): the threshold distance at which emission source points are excluded beyond that

Details

The SEDC is specialized in vector to vector summary of covariates with exponential decay. Decaying slope will be defined by sedc_bandwidth, where the concentration of the source is reduced to $\exp(-3)$ (approximately 5 \ of the attenuating concentration with the distance from the sources. It can be thought of as a fixed bandwidth kernel weighted sum of covariates, which encapsulates three steps:

Calculate the distance between each source and target points.
Calculate the weight of each source point with the exponential decay.
Summarize the weighted covariates.

Note

Distance calculation is done with terra functions internally. Thus, the function internally converts sf objects in point_* arguments to terra. Please note that any NA values in the input will be ignored in SEDC calculation.

References

Messier KP, Akita Y, Serre ML. (2012). Integrating Address Geocoding, Land Use Regression, and Spatiotemporal Geostatistical Estimation for Groundwater Tetrachloroethylene. Environmental Science & Technology 46(5), 2772-2780.
Wiesner C. (n.d.). Euclidean Sum of Exponentially Decaying Contributions Tutorial.

Author

Insang Song

Examples

library(terra)
library(sf)
set.seed(101)
ncpath <- system.file("gpkg/nc.gpkg", package = "sf")
nc <- terra::vect(ncpath)
nc <- terra::project(nc, "EPSG:5070")
pnt_from <- terra::centroids(nc, inside = TRUE)
pnt_from <- pnt_from[, "NAME"]
pnt_to <- terra::spatSample(nc, 100L)
pnt_to$pid <- seq(1, 100)
pnt_to <- pnt_to[, "pid"]
pnt_to$val1 <- rgamma(100L, 1, 0.05)
pnt_to$val2 <- rgamma(100L, 2, 1)

vals <- c("val1", "val2")
summarize_sedc(pnt_from, pnt_to, "NAME", 1e5, 2e5, vals)
#> # A tibble: 100 × 3
#>    NAME      val1_sedc val2_sedc
#>    <chr>         <dbl>     <dbl>
#>  1 Alamance       66.3      6.71
#>  2 Alexander      98.0     11.7 
#>  3 Alleghany     135.       8.57
#>  4 Anson          50.0      5.23
#>  5 Ashe          143.       8.42
#>  6 Avery          76.1      8.76
#>  7 Beaufort       58.8      6.29
#>  8 Bertie         70.1      7.85
#>  9 Bladen         79.5      6.82
#> 10 Brunswick      54.3      5.34
#> # ℹ 90 more rows