SpatialVx (version 0.1-2)

hoods2dsmooth: Wrapper functions for kernel2dsmooth

Description

Wrapper functions for kernel2dsmooth to perform specific convolution smooths of 2-d fields.

Usage

hoods2dsmooth(x, lambda, W = NULL, setup = FALSE, ...)
gauss2dsmooth(x, lambda, W = NULL, setup = FALSE, ...)
disk2dsmooth(x, lambda, W = NULL, setup = FALSE, ...)
identity2dsmooth(x, lambda = 0, W = NULL, setup = FALSE, ...)

Arguments

x

numeric matrix giving the field to be smoothed.

lambda

single numeric giving the smoothing parameter. In the case of hoods2dsmooth, this is the neighborhood length so that the result is that each point is an average over the nearest lambda^2 neighbors. For gauss2dsmooth, this is th

W

(optional) if the FFT of the kernel weights have already been calculated for the smooth, they can be passed here. Not used by identity2dsmooth.

setup

logical, should only the FFT of the kernel weights be returned (i.e., instead of the smoothed x field)? Should not be used if W is supplied, or you may not get what you want (i.e., precedence is given to W's being supplied). No

...

optional arguments to the specific kernel type in the call to kernel2dsmooth, or really, to kernel2dmeitsjer. Not used by identity2dsmooth.

Value

• If W is not supplied and setup is TRUE, then a matrix is returned with dimensions chosen to optimize computational efficiency. Otherwise, a matrix of the same dimension as x is returned giving the smoothed version of the field.

Details

This is a wrapper function to kernel2dsmooth. See its help file for more details. These functions were set up to make the hoods2d function more flexible (i.e., to allow other types of smoothing besides the default nearest neighbors smoothing). Makes use of the convolution theorem with the fast Fourier transform for computational efficiency (Ritter and Wilson, 2001; Barrett and Myers, 2004). Missing values are set to zero, and borders are zero-padded to an optimal amount. See Hastie and Tibshirani (1990) for smoothing functions in teh context fo statistical analysis.

hoods2dsmooth is a wrapper to kernel2dsmooth that employs the boxcar kernel with neighborhood length n as the smoothing parameter. This is the type of kernel smoothing proposed by Roberts and Lean (2008) and used in Ebert (2008). The smoothing parameter lambda should be an odd positive integer (though it need not be an actual integer recognized by R). If it is not, then one of several things will happen depending on its value, and a warning is generated. If it is not an integer (i.e., if floor(lambda) != lambda), the floor of lambda is taken. If it is even (possibly after flooring), one is subtracted from it. If it is less than one (possibly after flooring and/or subtracting one), it is set to one (note that if lambda = 1, the field x is returned untouched).

gauss2dsmooth is a wrapper to kernel2dsmooth that employs the Gaussian kernel with smoothing parameter sigma. This is the type of smoothing applied originally for the practically perfect hindcast method (see Ebert, 2008).

disk2dsmooth is a wrapper to kernel2dsmooth that calls the disk kernel with smoothing parameter r (the radius of the disk). This is the type of smoothing applied in Davis et al. (2006a, 2006b).

identity2dsmooth simply returns the field without smoothing it. Provided for convenience.

References

Barrett, H. H. and Myers, K. J., 2004: Foundations of Image Science. Wiley Series in Pure and Applied Optics, Editor: B. E. A. Saleh, Hoboken, New Jersey, 1540pp.

Davis CA, BG Brown, and RG Bullock, 2006a. Object-based verification of precipitation forecasts, Part I: Methodology and application to mesoscale rain areas. Mon. Wea. Rev., 134, 1772--1784.

Davis CA, BG Brown, and RG Bullock, 2006b. Object-based verification of precipitation forecasts, Part II: Application to convective rain systems. Mon. Wea. Rev., 134, 1785--1795.

Ebert E. E., 2008. Fuzzy verification of high resolution gridded forecasts: A review and proposed framework. Meteorol. Appl., 15, 51--64. DOI: 10.1002/met.25. Available at http://www.ecmwf.int/newsevents/meetings/workshops/2007/jwgv/METspecialissueemail.pdf

Hastie, T. J. and Tibshirani, R. J., 1990: Generalized Additive Models. Chapman & Hall/CRC Monographs on Statistics and Applied Probability 43, 335pp.

Ritter, G. X. and Wilson, J. N., 2001: Handbook of Computer Vision Algorithms in Image Algebra. 2nd Edition, CRC Press, Boca Raton, Florida, U.S.A., 417pp.

Roberts, N. M. and H. W. Lean, 2008: Scale-selective verification of rainfall accumulations from high-resolution forecasts of convective events. Mon. Wea. Rev., 136, 78--97. DOI: 10.1175/2007MWR2123.1.

See Also

hoods2dPrep, hoods2d, kernel2dsmooth, kernel2dmeitsjer, fft

Examples

x <- y <- matrix( 0, 50, 50)
x[ sample(1:50,10), sample(1:50,10)] <- rexp( 100, 0.25)
y <- disk2dsmooth( x=x, lambda=6.5)
x <- gauss2dsmooth( x=x, lambda=3, nx=25, ny=25)
par( mfrow=c(1,2))
image.plot( x, col=tim.colors(256))
image.plot( y, col=tim.colors(256))

hold <- hoods2dPrep("y", "x", thresholds=c(0.1, 0.5), levels=c(1, 3, 20), smooth.fun="gauss2dsmooth", smooth.params=list(nx=601, ny=501))
look <- hoods2d( hold, which.methods=c("fss"))
plot( look)

data( pert000)
data(pert004)
# Do the neighborhood methods with averaging performed over a radius instead of the lambda^2 nearest neighbors.
# The smoothing parameters are determined by the levels argument, and the others are passed via smooth.params.
hold <- hoods2dPrep( "pert004", "pert000", thresholds=c(1,2,5,10,20,50), levels=c(1, 3, 9, 17, 33, 65, 129, 257),
			smooth.fun="disk2dsmooth")
look <- hoods2d(hold, verbose=TRUE)
look