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Self-contribution of each source cell in a stream-mode random walk

rw_self_retention.Rd

Computes G_cc, the stream-mode residence time in cell c per unit of release from cell c (see random_walk()). This is each source's contribution to its own value, which can be subtracted for a leave-one-out surface, e.g. to avoid a site predicting itself.

Usage

rw_self_retention(
  rose,
  half_life = Inf,
  timescale = 1,
  latitude_correction = TRUE,
  cells = NULL,
  exact = FALSE,
  chunk = 200
)

Arguments

rose

A wind_rose.

half_life

Half-life of airborne mass, in hours. Must match the value used for the stream-mode walk; see random_walk().

timescale

Time step scaling factor; see random_walk(). Affects only the approximate values; exact values are independent of timescale.

latitude_correction

Logical. Must match the value used for the stream-mode walk; see random_walk().

cells

Cell numbers, or a two-column matrix of coordinates, at which to compute G_cc. Optional for the approximation (which defaults to every cell); required if exact = TRUE.

exact

Logical: compute exact values rather than the approximation? Exact values are a sparse solve per cell (sharing one factorization), practical for a set of occupied cells but not for every cell of a large grid. The approximation is a lower bound. Default FALSE.

chunk

With exact = TRUE: number of cells to solve for at once. Larger values are faster but use more memory.

Value

G_cc in hours per unit of release: a SpatRaster of approximate values for every cell if cells is NULL, otherwise a numeric vector with one value per cell. For a leave-one-out surface, residence_loo = residence - init * G_cc and deposition_loo = log(2) / half_life * residence_loo, using the residence layer from random_walk() and init values at the source cells.

Details

The approximation G_cc ~ (1 - lambda) * t / (1 - (1 - lambda) * p_cc) counts only paths in which mass never leaves the cell (p_cc is the retention probability; see random_walk()). It omits mass that leaves and returns, which is substantial in a nearest-neighbor walk, especially in fast cells where p_cc is near zero.