DispFieldbb {ICvectorfields}

Displacement fields based on 2D cross-covariance using bounding box

Description

Calculates a displacement field based on the cross-covariance of two input rasters presumably representing spatial population abundance or density at two different instances of time. This version differs from DispField in that the user defines a bounding box that determines a single sub-grid. The center of the bounding box is the location from whence displacement is estimated.

Usage

DispFieldbb(
  inputrast1,
  inputrast2,
  rowmn,
  rowmx,
  colmn,
  colmx,
  restricted = FALSE
)

Arguments

inputrast1

a raster as produced by terra::rast

inputrast2

a raster of equivalent dimension to inputrast1 as produced by terra::rast

rowmn

an integer denoting the minimum row index of the sub-grid

rowmx

an integer denoting the maximum row index of the sub-grid

colmn

an integer denoting the minimum column index of the sub-grid

colmx

an integer denoting the maximum column index of the sub-grid

restricted

logical (TRUE or FALSE)

Details

The input rasters are first converted to equivalent matrices. If restricted is set to FALSE (the default), the function computes cross-covariance between the sub-grid of the first input raster and the entirety of the second input raster and then uses the location of maximum cross-covariance to estimate displacement in the vertical and horizontal directions from the centre of the sub-grid.

If restricted is set to TRUE, the function uses cross-covariance between the sub-grid of the first input raster and the equivalent sub-grid of the second input raster to estimate vertical and horizontal displacement.

Reference coordinates and cell size are extracted from the first input raster such that the locations from whence displacement is estimated as well as displacement estimates can be expressed in the units of the projected coordinates.

The coordinates are assumed to increase vertically and horizontally from the lower left corner of the two-dimensional domain.

Caution is warranted when defining the bounding box because the function can produce erroneous results when the bounding box is too small.

Value

A data frame is returned with the following column names: rowcent, colcent, frowmin, frowmax, fcolmin, fcolmax, centx, centy, dispx, and dispy. The rowcent and colcent column names are the row and column indices for the center of the sub-grid; frowmin and frowmax are the sub-grid minimum and maximum row indices; fcolmin and fcolmax are the sub-grid minimum and maximum column indices; centx and centy are the projected coordinates of the centre of the subgrid derived from the raster input files; dispx and dispy are the displacement in the horizontal and vertical directions in the same units as the projected coordinates of the raster input files.

See Also

DispField for a similar function with a grid of focal regions, DispFieldSTbb for a version designed to quantify persistent directional movement when the time series features more than two time instances, DispFieldSTbball for a version designed to quantify persistent directional movement when velocity is variable in space, and Xcov2D for demonstration of how two-dimensional cross-covariance is used to determine displacement (see examples of Xcov2D function documentation).

Examples

rseq <- stats::runif(72)
Mat1 <- matrix(rep(0, 81), nrow = 9)
Mat2 <- Mat1
Mat1[1:9, 1:8] <- rseq
Mat1
Mat2[1:9, 2:9] <- rseq
Mat2

# rasterizing
rast1 <- terra::rast(Mat1)
terra::plot(rast1)
rast2 <- terra::rast(Mat2)
terra::plot(rast2)

(VFdf1 <- DispFieldbb(rast1, rast2, 2, 8, 2, 8))
# The second raster is shifted right by 1 unit relative to the first raster
# dispx = 1