DirectionalSpectrum

The DirectionalSpectrum class provides an interface for handling 2-D directional spectra. DirectionalSpectrum extends Grid, and contains spectrum density values on a two-dimentional frequency/(wave)direction grid.

\[S(\omega, \theta)\]

The DirectionalSpectrum is initialized with a frequency list (1-D array), a direction list (1-D array) and corresponding spectrum density values (2-D array).

import numpy as np
from waveresponse as wr


freq = np.linspace(0.0, 1.0, 50)
dirs = np.linspace(0.0, 360.0, endpoint=False)
vals = np.random.random((len(freq), len(dirs)))

spectrum = wr.DirectionalSpectrum(
    freq,
    dirs,
    vals,
    freq_hz=True,
    degrees=True,
    clockwise=False,
    waves_coming_from=False,
)

The DirectionalSpectrum class extends the Grid class with the following:

Calculate the variance (i.e., integral) and standard deviation of the spectrum:

# Variance
var = spectrum.var()

# Standard deviation
std = spectrum.std()

Integrate over one of the axes to obtain a one-dimentional spectrum. You can specify whether to integrate over the frequency axis (axis=0), or the direction axis (axis=1), by setting the appropriate axis parameter.

# "Non-directional" spectrum
spectrum_nondir = spectrum.spectrum1d(axis=1)

# Directional "distribution"
spectrum_dir = spectrum.spectrum1d(axis=0)

Calculate spectral moments by calling the moment() method with the desired order, n.

# Zeroth-order moment
m0 = spectrum.moment(0)

# First-order moment
m1 = spectrum.moment(1)

# Second-order moment
m2 = spectrum.moment(2)

# Etc.

Calculate the mean zero-crossing period, Tz:

spectrum.tz

Calculate extreme values using the extreme() method. The method takes three arguments: the duration of the process (in seconds), the quantile, q, and a boolean flag, absmax, determining whether to compute absolute value extremes (or only consider the maxima (default)).

duration = 3 * 3600   # 3 hours

# Extreme maximum
mpm = spectrum.extreme(duration, q=0.37)   # most probable maximum (MPM)
q90 = spectrum.extreme(duration, q=0.90)   # 90-th quantile

# Extreme absolute value maximum (i.e., minima are taken into account)
mpm = spectrum.extreme(duration, q=0.37, absmax=True)   # most probable maximum (MPM)
q90 = spectrum.extreme(duration, q=0.90, absmax=True)   # 90-th quantile