SpatialVx (version 0.1-7)

FQI: Forecast Quality Index

Description

Functions for calculating the Forecast Quality Index (FQI) and its components.

Usage

FQI(object, surr = NULL, k = 4, time.point = 1, model = 1, ...)
UIQI(X, Xhat, ...)
ampstats(X, Xhat, only.nonzero = FALSE)
## S3 method for class 'fqi':
print(x, ...)
## S3 method for class 'fqi':
summary(object, ...)

Arguments

object

list object of class SpatialVx. In the case of the summary method, object is the list object returned by FQI.

X,Xhat

numeric matrices giving the fields for the verification set.

x

list object of class fqi as returned by FQI.

surr

three-dimesnional array containing surrogate fields for X, e.g. as returned by surrogater2d. If NULL, these will be calculated using surrogater2d.

only.nonzero

logical, should the means and variances of only the non-zero values of the fields be calculated (if so, the covariance is returned as NA)?

k

numeric vector for use with the partial Hausdorff distance. For k that are whole numerics or integers >= 1, then the k-th highest value is returned by locmeasures2d. If 0

time.point

numeric or character indicating which time point from the SpatialVx verification set to select for analysis.

model

numeric indicating which forecast model to select for the analysis.

...

In the case of FQI, additional arguments to surrogater2d. Only used if surr is NULL. In the case of UIQI, additional arguments to ampstats. In the case of summary.fqi, these

Value

• FQI returns a list with with the following components:
• phd.norm
  matrix of normalized partial Hausdorff distances for each value of k (rows) and each threshold (columns).
• uiqi.norm
  numeric vector of modified UIQI values for each threshold.
• fqi
  matrix of FQI values for each value of k (rows) and each threshold (columns).
• It will also have the same attributes as the SpatialVx object with additional attributes defining the arguments specific to parameters used by the function.

  UIQI returns a list with components:

• data.name
  character vector giving the names of the two fields.
• cor
  single numeric giving the correlation between the two fields.
• brightness.bias
  single numeric giving the brightness (bias) value.
• distortion.variability
  single numeric giving the distortion (variability) value.
• UIQI
  single numeric giving the UIQI (or modified UIQI if only.nonzero is set to TRUE) value.
• ampstats returns a list object with components:
• mean.fcst,mean.vx
  single numerics giving the mean of Xhat and X, resp.
• var.fcst,var.vx
  single numerics giving the variance of Xhat and X, resp.
• cov
  single numeric giving the covariance between Xhat and X (if only.nonzero is TRUE, this will be NA).

Details

The FQI was proposed as a spatial verification metric (a true metric in the mathematical sense) by Venugopal et al. (2005) to combine amplitude and displacement error information in a single summary statistic. It is given by

FQI = (PHD_k(X, Xhat)/mean( PHD_k(X, surr_i); i in 1 to number of surrogates)) / (brightness * distortion)

where the numerator is a normalized partial Hausdorff distance (see help file for locperf), brightness (also called bias) is given by 2*(mu1*mu2)/(mu1^2+mu2^2), where mu1 (mu2) is the mean value of X (Xhat), and the distortion term is given by 2*(sig1*sig2)/(sig1^2+sig2^2), where sig1^2 (sig2^2) is the variance of X (Xhat) values. The denominator is a modified UIQI (Universal Image Quality Index; Wang and Bovik, 2002), which itself is given by

UIQI = cor(X,Xhat)*brightness*distortion.

Note that if only.nonzero is TRUE in the call to UIQI, then the modified UIQI used in the FQI formulation is returned (i.e., without multiplying by the correlation term).

The print method so far just calls the summary method.

References

Venugopal, V., Basu, S. and Foufoula-Georgiou, E. (2005) A new metric for comparing precipitation patterns with an application to ensemble forecasts. J. Geophys. Res., 110, D08111, 11 pp., doi:10.1029/2004JD005395.

Wang, Z. and Bovik, A. C. (2002) A universal image quality index. IEEE Signal Process. Lett., 9, 81--84.

See Also

locperf, surrogater2d, locmeasures2d

Examples

data(ExampleSpatialVxSet)

x <- ExampleSpatialVxSet$vx
xhat <- ExampleSpatialVxSet$fcst

# Now, find surrogates of the simulated field.
z <- surrogater2d(x, zero.down=TRUE, n=10)

u <- cbind( quantile( c(x), c(0.75, 0.9)),
            quantile( c(xhat), c(0.75, 0.9)))
hold <- make.SpatialVx(x, xhat, thresholds=u,
            field.type="Example", units="none",
            data.name=c("ExampleSpatialVxSet", "X", "Xhat"))
FQI(hold, surr=z, k=c(4, 0.75))