Intensity Scale (IS) verification based on Casat et al (2004) and Casati (2010).
waveIS(x, th = NULL, J = NULL, wavelet.type = "haar", levels
= NULL, max.n = NULL, smooth.fun = "hoods2dsmooth",
smooth.params = NULL, rule = ">=", verbose = FALSE,
...)# S3 method for SpatialVx
waveIS(x, th = NULL, J = NULL, wavelet.type = "haar", levels
= NULL, max.n = NULL, smooth.fun = "hoods2dsmooth",
smooth.params = NULL, rule = ">=", verbose = FALSE,
..., time.point = 1, obs = 1, model = 1 )
# S3 method for default
waveIS(x, th = NULL, J = NULL, wavelet.type = "haar", levels
= NULL, max.n = NULL, smooth.fun = "hoods2dsmooth",
smooth.params = NULL, rule = ">=", verbose = FALSE,
...)
# S3 method for waveIS
plot(x, main1 = "X", main2 = "Y",
which.plots = c("all", "mse", "ss", "energy"),
level.label = NULL, ...)
# S3 method for waveIS
summary(object, ...)
A list object of class “waveIS” that contains the entire prep object passed in by obj, as well as additional components:
J by q matrices giving the energy for the verification and forecast fields, resp., for each threshold (columns) and scale (rows).
J by q matrices giving the mean square error and IS skill score for each threshold (column) and scale (rows).
numeric vector of length q giving the frequency bias of the original fields for each threshold.
plot.waveIS does not return any value. A plot is created on the current graphic device. summary.waveIS returns a list invisibly with the same components as returned by waveIS along with extra components:
length q numeric vectors giving the MSE, SS, and Vx and Fcst energy for each threshold (i.e., ignoring the wavelet decomposition).
J by q numeric matrices giving percentage form of MSE, Vx Energy and Fcst Energy values, resp.
J by q numeric matrix giving the energy relative difference.
For waveIS either a list object of class “SpatialVx”, a two-component list giving the two fields to be compared (the verification field is assumed to be the first one) or a named list with components “X” and “Xhat” giving the two fields to be compared. list object returned by waveIS.
list object returned by waveIS.
character giving labels for the plots where main1 refers to the verification field and main2 to the forecast field.
character vector naming one or more specific plots to do.
optional character vector to use for level names on the plot(s).
numeric integer giving the number of levels to use. If NULL and the field is dyadic, this will be log2(min(dim(X))), where X is a field from the verification set. If NULL and the field is not dyadic, then J is set equal to 4. Note that if the fields are not dyadic, the function will be much slower.
character giving the name of the wavelet type to use as accepted by dwt.2d and modwt.2d.
list object with named components “X” and “Xhat” giving the thresholds to use for each field. If null, taken from teh thresholds attribute for “SpatialVx” objects.
numeric or character indicating which time point from the “SpatialVx” verification set to select for analysis.
numeric indicating which observation/forecast model to select for the analysis.
numeric vector giving the successive values of the smoothing parameter. For example, for the default method, these are the neighborhood lengths over which the levels^2 nearest neighbors are averaged for each point. Values should make sense for the specific smoothing function. For example, for the default method, these should be odd integers.
(optional) single numeric giving the maximum neighborhood length to use. Only used if levels are NULL.
character giving the name of a smoothing function to be applied. Default is an average over the n^2 nearest neighbors, where n is taken to be each value of the levels argument.
list object containing any optional arguments to smooth.fun. Use NULL if none.
If type is “binary”, return 0 when the rule applied to a grid point's value is not true in relation to the threshold value, and 1 elsewhere. If type is “replace.below”, then return replace.with wherever the rule is not true and return the original value otherwise. By default, it replaces values below the threshold with zero (hence its name), but if rule is, e.g., “<=”, then it will replace values above with zero; or whatever value is chosen for replace.with.
logical, should progress information be printed to the screen?
Not used by waveIS (or its method functions) or plot.waveIS. Only sort of used by summary.waveIS. One can put the argument silent=TRUE so that nothing is printed to the screen (useful if you just want the values calculated and stored without writing to the screen).
Eric Gilleland
This function applies various statistics to the detail fields (in wavelet space) of a discrete wavelet decomposition (DWT) of the binary error fields for a verification set. In particular, the statistics described in Casati et al (2004) and Casati (2010) are calculated. This function depends on the waverify2d or mowaverify2d function (depending on whether the fields are dyadic or not, resp.), which themselves depend on the dwt.2d and idwt.2d or modwt.2d and imodwt.2d functions.
See the references herein and the help files and references therein for dwt.2d and modwt.2d for more information on this approach, as well as Percival and Guttorp (1994) and Lindsay et al. (1996).
Casati, B., Ross, G. and Stephenson, D. B. (2004) A new intensity-scale approach for the verification of spatial precipitation forecasts. Meteorol. Appl. 11, 141--154.
Casati, B. (2010) New Developments of the Intensity-Scale Technique within the Spatial Verification Methods Inter-Comparison Project. Wea. Forecasting 25, (1), 113--143, doi:10.1175/2009WAF2222257.1.
Lindsay, R. W., Percival, D. B. and Rothrock, D. A. (1996) The discrete wavelet transform and the scale analysis of the surface properties of sea ice. IEEE Transactions on Geoscience and Remote Sensing, 34 (3), 771--787.
Percival, D. B. and Guttorp, P. (1994) Long-memory processes, the Allan variance and wavelets. In Wavelets in Geophysics, Foufoula-Georgiou, E. and Kumar, P., Eds., New York: Academic, 325--343.
data( "UKobs6" )
data( "UKfcst6" )
data( "UKloc" )
hold <- make.SpatialVx( UKobs6, UKfcst6,
thresholds = c(0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50),
loc = UKloc, map = TRUE, field.type = "Rainfall", units = "mm/h",
data.name = "Nimrod", obs.name = "UKobs6", model.name = "UKfcst6" )
look <- waveIS(hold, J=8, levels=2^(8-1:8), verbose=TRUE)
plot(look, which.plots="mse")
plot(look, which.plots="ss")
plot(look, which.plots="energy")
summary(look)
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