calcWOI (version 1.0.3)

LW: Calculates the wavelet-based organization index with the dualtree wavelet transform

Description

This function calculates the locally wavelet-based organization index (LW) as defined in Brune et al. (2020) based on the dualtree complex wavelet transform.

Usage

LW(x, thres = 0.1, Nx = 2^ceiling(log2(max(dim(x)))), 
  Ny = 2^ceiling(log2(max(dim(x)))), boundaries = "pad", verbose = FALSE)

Arguments

x

2D numeric array with dimensions larger than 16 x 16. dim(x)[1] has not to be equal to dim(x)[1], but NA and/or NaN are not allowed.

thres

0 or a positive number. Threshold for rain rate. Default is 0.1 mm/h, because we calculate LWOI only for grid points, where rain rate is >= 0.1 mm/h. For brightness temperatures we use 245 K.

Nx

The number of grid points in x direction of the array, which is put into the dualtree wavelet transform. The default is the log2 of maximum dimension of the ingoing array. Nx must be equal or larger than the first dimension of x.

Ny

The number of grid points in y direction of the array, which is put into the dualtree wavelet transform. The default is the log2 of maximum dimension of the ingoing array. Nx must be equal or larger than the second dimension of x.

boundaries

Handles the boundary conditions, either "pad", "mirror" or "periodic".

verbose

Default FALSE. Set TRUE for print statements.

Value

This functions returns a list with follwing elements:

LWsc

LWOI scale calculated with dualtrees. The array is masked with thres. The dimension of LWsc is equal to the dimension of x, if the boundaries are only padded with zeros.

LWin

LWOI intensity calculated with dualtrees. The array is masked with thres. The dimension of LWsc is equal to the dimension of x, if the boundaries are only padded with zeros.

LWai

LWOI anisotropy calculated with dualtrees. The array is masked with thres. The dimension of LWsc is equal to the dimension of x, if the boundaries are only padded with zeros.

LWuu

LWOI u component calculated with dualtrees. The array is masked with thres. The dimension of LWsc is equal to the dimension of x, if the boundaries are only padded with zeros.

LWvv

LWOI v component with dualtrees. The array is masked with thres. The dimension of LWsc is equal to the dimension of x, if the boundaries are only padded with zeros.

angle

Angle of spectrum. The array is masked with thres. The dimension of angle is equal to the dimension of x, if the boundaries are only padded with zeros. Angle ranges between 0 degree and 180 degree.

thres

Threshold of LW calculation.

mask

Mask defined by thres.

x

Ingoing array.

ts

Computation time in seconds.

Warning

The input array must be numeric without NA or NaN and maximal of size 1024 x 1024.

References

Brune, S., Kapp, F., & Friederichs, P. (2018). A wavelet-based analysis of convective organization in ICON large-eddy simulations. Quarterly Journal of the Royal Meteorological Society, 144(717), 2812-2829. Brune, S., Buschow, S., & Friederichs, P. (2020). Observations and high-resolution simulations of convective precipitation organization over the tropical Atlantic. Quarterly Journal of the Royal Meteorological Society. Brune, S., Buschow, S., & Friederichs, P. (2020). The Local Wavelet-based Organization Index - Quantification, Localization and Classification of Convective Organization from Radar and Satellite Data.

Examples

# NOT RUN {
# Random array of dim 230 x 200
x <- array((rnorm(230*200)), dim = c (230, 200))
thres <- 0.1
LWres <- LW(x, thres = thres, Nx = 2^ceiling(log2(max(dim(x)))), 
  Ny = 2^ceiling(log2(max(dim(x)))), boundaries = "pad")
print(paste("The LWOI calculation took", LWres$ts, "seconds."))
# plot data
par(mfrow = c(3, 2))
# original data
image(LWres$x, main = "Original data", zlim = 0:1)
# scale component
image(LWres$LWsc, main = "Scale", zlim = 0:1)
# intensity component
image(LWres$LWin, main = "Intensity", zlim = 0:1)
# anisotropy component
image(LWres$LWai, main = "Anisotropy", zlim = 0:1)
# u component
image(LWres$LWuu, main = "u direction", zlim = 0:1)
# v component
image(LWres$LWvv, main = "v direction", zlim = 0:1)
# }