SpatialVx (version 1.0-3)

S1: S1 Score, Anomaly Correlation

Description

Calculate the S1 score and anomaly correlation for a verification set.

Usage

S1(x, ...)
# S3 method for default
S1(x, ..., xhat, gradFUN = "KernelGradFUN")
# S3 method for SpatialVx
S1(x, ..., xhat, gradFUN = "KernelGradFUN",
    time.point = 1, obs = 1, model = 1)
ACC(x, ...)
# S3 method for default
ACC(x, ..., xhat, xclim = NULL, xhatclim = NULL)
# S3 method for SpatialVx
ACC(x, ..., xclim = NULL, xhatclim = NULL,
    time.point = 1, obs = 1, model = 1)

Value

single numeric

Arguments

x,xhat

m by n matrices giving the verification and forecast fields, resp.

For S1.SpatialVx and ACC.SpatialVx, x is an object of class “SpatialVx”.

xclim, xhatclim

m by n matrices giving the climatologies for X and Y, resp. If NULL, the result is simply a usual correlation.

gradFUN

character identifying a function used to calculate the gradient fields for X and Y. The default KernelGradFUN is to use a Laplacian of Gaussian kernel.

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.

...

optional arguments to the gradFUN function. In the case of the default, the kernel can be changed (e.g., if only “laplacian” is desired), and optional arguments to the kernel2dmeitsjer function (in this case, nx, ny and sigma). Not used by ACC.

Author

Eric Gilleland

Details

The S1 score is given by

S1 = 100*sum(abs(DY_i - DX_i))/sum(max(abs(DY_i),abs(DX_i))),

where DY_i (DX_i)is the gradient at grid point i for the forecast (verification). See Brown et al. (2012) and Thompson and Carter (1972) for more on this score.

The ACC is just the correlation between X - Xclim and Y - Yclim.

References

Brown, B.G., Gilleland, E. and Ebert, E.E. (2012) Chapter 6: Forecasts of spatial fields. pp. 95--117, In Forecast Verification: A Practitioner's Guide in Atmospheric Science, 2nd edition. Edts. Jolliffee, I. T. and Stephenson, D. B., Chichester, West Sussex, U.K.: Wiley, 274 pp.

Thompson, J. C. and Carter, G. M. (1972) On some characteristics of the S1 score. J. Appl. Meteorol., 11, 1384--1385.

See Also

smoothie::kernel2dmeitsjer

Examples

data( "UKobs6" )
data( "UKfcst6" )

S1( UKobs6, xhat = UKfcst6 )
ACC( UKobs6, xhat = UKfcst6 )

if (FALSE) {
data( "obs0601" )
data( "wrf4ncar0531" )
data( "ICPg240Locs" )

hold <- make.SpatialVx( obs0601, wrf4ncar0531, loc = ICPg240Locs,
    projection = TRUE, map = TRUE, loc.byrow = TRUE,
    field.type = "Precipitation", units = "mm/h",
    data.name = "ICP NSSL/SPC Spring 2005 Cases",
    obs.name = "obs0601", model.name = "wrf4ncar0531" )

plot( hold )

S1( hold )
ACC( hold )
}