TheBigG: The Spatial Alignment Summary Measure Called G

In SpatialVx: Spatial Forecast Verification

The Spatial Alignment Summary Measure Called G

Description

The spatial alignment summary measure, G, is a summary comparison for two gridded binary fields.

Usage

TheBigG(X, Xhat, threshold, rule = ">", ...)

Arguments

X, Xhat	m by n matrices giving the “observed” and forecast fields, respectively.
threshold, rule	The threshold and rule arguments to the binarizer function.
...	Not used.

Details

This function is an alternative version of Gbeta that does not require the user to select a parameter. It is not informative about rare events relative to the domain size. It is the cubed root of the product of two terms. If A is the set of one-valued grid points in the binary version of X and B those for Xhat, then the first term is the size of the symmetric difference between A and B (i.e., an area with grid points squared as the units) and the second term is MED(A,B) * nB with MED(B,A) * nA, where MED is the mean-error distance and nA, nB are the numbers of grid points in each of A and B, respectively. The second term has units of grid squares so that the product is units of grid squares cubed; hence, the reason for taking the cubed root for G. The units for G are grid squares with zero being a perfect score and increasing scores imply worsening matches between the sets A and B. See Gilleland (2021) for more details.

Value

An object of class “TheBigG” is returned. It is a single number giving the value of G but also has a list of attributes that can be accessed using the attributes function. This list includes:

components	A vector giving: nA, nB, nAB (number of points in the intersection), number of points in the symmetric difference, MED(A,B), MED(B,A), MED(A,B) * nB, MED(B,A) * nA, followed by the asymmetric versions of G for G(A,B) and G(B,A).
threshold	If a threshold is provided, then this component gives the threshold and rule arguments used.

Author(s)

Eric Gilleland

References

Gilleland, E. (2020) Novel measures for summarizing high-resolution forecast performance. Advances in Statistical Climatology, Meteorology and Oceanography, 7 (1), 13–34, doi: 10.5194/ascmo-7-13-2021.

See Also

Gbeta

Examples

data( "obs0601" )
data( "wrf4ncar0531" )
res <- TheBigG( X = obs0601, Xhat = wrf4ncar0531, threshold = 2.1 )
res

SpatialVx documentation built on May 29, 2024, 9:31 a.m.