# TheBigG: The Spatial Alignment Summary Measure Called G In SpatialVx: Spatial Forecast Verification

## Description

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

## Usage

 `1` ```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.

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.

`Gbeta`
 ```1 2 3 4``` ```data( "obs0601" ) data( "wrf4ncar0531" ) res <- TheBigG( X = obs0601, Xhat = wrf4ncar0531, threshold = 2.1 ) res ```