Description Usage Arguments Details Value Author(s) References See Also Examples

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

1 |

`X,Xhat` |
m by n matrices giving the “observed” and forecast fields, respectively. |

`threshold,rule` |
The threshold and rule arguments to the |

`...` |
Not used. |

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.

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

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.

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

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