Pairwise random walk connectivity among sites

For every pair of sites, computes how strongly particles released at one site reach the other under a stream-mode random walk (see random_walk()): by default, the probability that a particle released at the first site is deposited at the second. This is the random walk counterpart to pairwise_least_cost().

Usage

pairwise_random_walk(
  rose,
  sites,
  half_life = NULL,
  value = c("deposition", "residence"),
  density = TRUE,
  timescale = 1,
  latitude_correction = TRUE,
  chunk = 200
)

Arguments

rose

A wind_rose.

sites

A two-column matrix (or data frame) of site coordinates, or a SpatVector of points.

half_life

Half-life of airborne mass, in hours of transport time; see random_walk(). Required for value = "deposition", which is zero without deposition.

value

"deposition" (the default) or "residence"; see Value.

density

Logical: divide by the area of the destination site's grid cell, giving values per km^2? Default TRUE. Without this, values depend on cell size: a larger cell receives more of the particles passing nearby. On a longitude/latitude grid, cell area shrinks toward the poles (by about 25 percent from 30 to 50 degrees latitude), so raw values are biased toward lower-latitude destinations even within a single analysis. Dividing by area removes that bias, and also makes values comparable across grid resolutions (though see Details).

timescale, latitude_correction

See random_walk(). Results do not depend on timescale.

chunk

Number of sites to solve for at once. Larger values are faster but use more memory.

Value

A square matrix with one row and column per site, giving connectivity from the row's site (the origin) to the column's site (the destination). Large values mean strong connectivity, the opposite orientation from the travel times of pairwise_least_cost(). With value = "deposition", entries are the probability that a particle released at the origin is deposited in the destination's grid cell (per km^2 if density = TRUE). With value = "residence", they are the time, in hours, that a unit release at the origin spends airborne over the destination's cell (per km^2 if density = TRUE). Because wind is directional, the matrix is generally asymmetric. The diagonal is each site's self-connectivity: release that is deposited (or stays airborne) in its own cell, which can be large; see rw_self_retention(). Sites are treated as the centers of their grid cells, so sites in the same cell get identical rows and columns; see check_cell_distance().

Details

Each origin's row is the destination values of a stream-mode random walk released from that origin, so it equals the result of random_walk(rose, origin, mode = "stream", ...) read at each destination. All origins share one matrix factorization, so the cost grows slowly with the number of sites.

density = TRUE removes the direct effect of cell size on how much a destination receives, but the random walk's spread itself depends somewhat on grid resolution (see random_walk()), so values are not fully resolution-independent.

Examples

rose <- windscape_example("wind_rose")
sites <- cbind(c(-110, -105, -100, -95), c(40, 42, 38, 44))
pairwise_random_walk(rose, sites, half_life = 24)
#>              [,1]         [,2]         [,3]         [,4]
#> [1,] 1.249959e-04 9.325450e-07 7.104573e-10 1.513116e-10
#> [2,] 3.550546e-15 5.577307e-05 4.317434e-09 2.141014e-09
#> [3,] 4.053452e-17 6.038675e-11 7.086970e-05 1.498152e-08
#> [4,] 3.191795e-21 1.232927e-12 2.449646e-12 7.976103e-05