Calculate the shape index (Sindex) as described in AghaKouchak et al. (2011)
Sindex(x, thresh = NULL, ...)# S3 method for default
Sindex(x, thresh = NULL, ...,
loc = NULL)
# S3 method for SpatialVx
Sindex(x, thresh = NULL, ...,
time.point = 1, obs = 1, model = 1)
numeric with named components:
the shape index
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.
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”.
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.
(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.
numeric or character indicating which time point from the “SpatialVx” verification set to select for analysis.
numeric indicating which observation/forecast model to select for the analysis.
Not used.
Eric Gilleland
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.
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.
Cindex, Aindex
# 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)
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