waves {metR} | R Documentation |
Fourier transform functions
Description
Use fft()
to fit, filter and reconstruct signals in the frequency domain, as
well as to compute the wave envelope.
Usage
FitWave(y, k = 1)
BuildWave(
x,
amplitude,
phase,
k,
wave = list(amplitude = amplitude, phase = phase, k = k),
sum = TRUE
)
FilterWave(y, k, action = sign(k[k != 0][1]))
WaveEnvelope(y)
Arguments
y |
numeric vector to transform |
k |
numeric vector of wave numbers |
x |
numeric vector of locations (in radians) |
amplitude |
numeric vector of amplitudes |
phase |
numeric vector of phases |
wave |
optional list output from |
sum |
whether to perform the sum or not (see Details) |
action |
integer to disambiguate action for k = 0 (see Details) |
Details
FitWave
performs a fourier transform of the input vector
and returns a list of parameters for each wave number kept.
The amplitude (A), phase (\phi
) and wave number (k) satisfy:
y = \sum A cos((x - \phi)k)
The phase is calculated so that it lies between 0 and 2\pi/k
so it
represents the location (in radians) of the first maximum of each wave number.
For the case of k = 0 (the mean), phase is arbitrarily set to 0.
BuildWave
is FitWave
's inverse. It reconstructs the original data for
selected wavenumbers. If sum
is TRUE
(the default) it performs the above
mentioned sum and returns a single vector. If is FALSE
, then it returns a list
of k vectors consisting of the reconstructed signal of each wavenumber.
FilterWave
filters or removes wavenumbers specified in k
. If k
is positive,
then the result is the reconstructed signal of y
only for wavenumbers
specified in k
, if it's negative, is the signal of y
minus the wavenumbers
specified in k
. The argument action
must be be manually set to -1
or +1
if k=0
.
WaveEnvelope
computes the wave envelope of y
following Zimin (2003). To compute
the envelope of only a restricted band, first filter it with FilterWave
.
Value
FitWaves
returns a a named list with components
- k
wavenumbers
- amplitude
amplitude of each wavenumber
- phase
phase of each wavenumber in radians
- r2
explained variance of each wavenumber
BuildWave
returns a vector of the same length of x with the reconstructed
vector if sum
is TRUE
or, instead, a list with components
- k
wavenumbers
- x
the vector of locations
- y
the reconstructed signal of each wavenumber
FilterWave
and WaveEnvelope
return a vector of the same length as y
'
References
Zimin, A.V., I. Szunyogh, D.J. Patil, B.R. Hunt, and E. Ott, 2003: Extracting Envelopes of Rossby Wave Packets. Mon. Wea. Rev., 131, 1011–1017, doi:10.1175/1520-0493(2003)131<1011:EEORWP>2.0.CO;2
See Also
Other meteorology functions:
Derivate()
,
EOF()
,
GeostrophicWind()
,
WaveFlux()
,
thermodynamics
Examples
# Build a wave with specific wavenumber profile
waves <- list(k = 1:10,
amplitude = rnorm(10)^2,
phase = runif(10, 0, 2*pi/(1:10)))
x <- BuildWave(seq(0, 2*pi, length.out = 60)[-1], wave = waves)
# Just fancy FFT
FitWave(x, k = 1:10)
# Extract only specific wave components
plot(FilterWave(x, 1), type = "l")
plot(FilterWave(x, 2), type = "l")
plot(FilterWave(x, 1:4), type = "l")
# Remove components from the signal
plot(FilterWave(x, -4:-1), type = "l")
# The sum of the two above is the original signal (minus floating point errors)
all.equal(x, FilterWave(x, 1:4) + FilterWave(x, -4:-1))
# The Wave envelopes shows where the signal is the most "wavy".
plot(x, type = "l", col = "grey")
lines(WaveEnvelope(x), add = TRUE)
# Examples with real data
data(geopotential)
library(data.table)
# January mean of geopotential height
jan <- geopotential[month(date) == 1, .(gh = mean(gh)), by = .(lon, lat)]
# Stationary waves for each latitude
jan.waves <- jan[, FitWave(gh, 1:4), by = .(lat)]
library(ggplot2)
ggplot(jan.waves, aes(lat, amplitude, color = factor(k))) +
geom_line()
# Build field of wavenumber 1
jan[, gh.1 := BuildWave(lon*pi/180, wave = FitWave(gh, 1)), by = .(lat)]
ggplot(jan, aes(lon, lat)) +
geom_contour(aes(z = gh.1, color = after_stat(level))) +
coord_polar()
# Build fields of wavenumber 1 and 2
waves <- jan[, BuildWave(lon*pi/180, wave = FitWave(gh, 1:2), sum = FALSE), by = .(lat)]
waves[, lon := x*180/pi]
ggplot(waves, aes(lon, lat)) +
geom_contour(aes(z = y, color = after_stat(level))) +
facet_wrap(~k) +
coord_polar()
# Field with waves 0 to 2 filtered
jan[, gh.no12 := gh - BuildWave(lon*pi/180, wave = FitWave(gh, 0:2)), by = .(lat)]
ggplot(jan, aes(lon, lat)) +
geom_contour(aes(z = gh.no12, color = after_stat(level))) +
coord_polar()
# Much faster
jan[, gh.no12 := FilterWave(gh, -2:0), by = .(lat)]
ggplot(jan, aes(lon, lat)) +
geom_contour(aes(z = gh.no12, color = after_stat(level))) +
coord_polar()
# Using positive numbers returns the field
jan[, gh.only12 := FilterWave(gh, 2:1), by = .(lat)]
ggplot(jan, aes(lon, lat)) +
geom_contour(aes(z = gh.only12, color = after_stat(level))) +
coord_polar()
# Compute the envelope of the geopotential
jan[, envelope := WaveEnvelope(gh.no12), by = .(lat)]
ggplot(jan[lat == -60], aes(lon, gh.no12)) +
geom_line() +
geom_line(aes(y = envelope), color = "red")