SpatialVx (version 0.1-7)

Sindex: Shape Index

Description

Calculate the shape index (Sindex) as described in AghaKouchak et al. (2011)

Usage

Sindex(x, thresh = NULL, ...)
## S3 method for class 'default':
Sindex(x, thresh = NULL, ...,
    loc = NULL)
## S3 method for class 'SpatialVx':
Sindex(x, thresh = NULL, ...,
    time.point = 1, model = 1)

Arguments

x

Default: m by n numeric matrix giving the field for which the shape index is to be calculated.

Sindex.SpatialVx: list object of class SpatialVx.

thresh

numeric giving a threshold under which (and including, i.e.,

loc

(optional) mn by 2 numeric matrix giving the grid point locations. If NULL, the expanded grid with x=1:m and y=1:n is used.

time.point

numeric or character indicating which time point from the SpatialVx verification set to select for analysis.

model

numeric indicating which forecast model to select for the analysis.

...

Not used.

Value

• numeric with named components:
• Sindex
  the shape index
• Pmin,P
  the numerator and denominator (perimeter) that make the Sindex.
• For SpatialVx objects, the routine is applied to both the verification and forecast objects so that a two-row matrix is returned containing the above vectors for each field.

Details

The shape index introduced in AghaKouchak et al. (2011) is defined as

Sindex = Pmin/P,

where for n = the number of positive-valued grid points, Pmin = 4*sqrt(n) if floor(sqrt(n)) = sqrt(n), and Pmin = 2 * floor(2*sqrt(n)+1) otherwise. P is the permieter of the non-zero grid points. Range is 0 to 1. Values closer to 1 indicate shapes that are closer to circular.

References

AghaKouchak, A., Nasrohllahi, N., Li, J., Imam, B. and Sorooshian, S. (2011) Geometrical characterization of precipitation patterns. J. Hyrdometeorology, 12, 274--285, doi:10.1175/2010JHM1298.1.

See Also

Cindex, Aindex

Examples

# Re-create Fig. 7a from AghaKouchak et al. (2011).
tmp <- matrix(0, 8, 8)
tmp[3,2:4] <- 1
tmp[5,4:6] <- 1
tmp[7,6:7] <- 1
Sindex(tmp)

# Two separate areas with highly structured shapes, but far away from each other.
data(pert000)
data(pert006)
data(ICPg240Locs)

hold <- make.SpatialVx(pert000, pert006, loc=ICPg240Locs,
    projection=TRUE, map=TRUE,
    field.type="Precipitation", units="mm/h",
    data.name=c("ICP Perturbed Cases", "pert000", "pert006"))

plot(hold, set.pw=TRUE)

Sindex(hold)