waves | R Documentation |
Perform a fourier transform of the data and return the
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)
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) |
FitWave
uses fft to make a fourier transform of the
data and then 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
.
FitWaves
returns a a named list with components
wavenumbers
amplitude of each wavenumber
phase of each wavenumber in radians
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
wavenumbers
the vector of locations
the reconstructed signal of each wavenumber
FilterWave
returns a vector of the same length as y
'
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, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1175/1520-0493(2003)131<1011:EEORWP>2.0.CO;2")}
Other meteorology functions:
Derivate()
,
EOF()
,
GeostrophicWind()
,
WaveFlux()
,
thermodynamics
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")
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