Sindex: Shape Index

In SpatialVx: Spatial Forecast Verification

Shape Index

Description

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

Usage

Sindex(x, thresh = NULL, ...)

## Default S3 method:
Sindex(x, thresh = NULL, ...,
    loc = NULL)

## S3 method for class 'SpatialVx'
Sindex(x, thresh = NULL, ...,
    time.point = 1, obs = 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., <=) all values are set to zero, and the shape index is calculated for the non-zero (positive-valued) grid-points.
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.
obs, model	numeric indicating which observation/forecast model to select for the analysis.
...	Not used.

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.

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.

Author(s)

Eric Gilleland

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)

SpatialVx documentation built on Nov. 10, 2022, 5:56 p.m.