"""Frequency spectral shapes."""
import numpy as np
import xarray as xr
from scipy.constants import g, pi
from wavespectra.core.utils import scaled, check_same_coordinates, wavenuma, to_coords
from wavespectra.core.attributes import attrs
from wavespectra.core import npstats
[docs]
def pierson_moskowitz(freq, fp, alpha=0.0081, hs=None, **kwargs):
"""Pierson and Moskowitz spectrum for fully developed seas (Pierson and Moskowitz, 1964).
Args:
- freq (DataArray, 1darray, list): Frequency array (Hz).
- fp (DataArray, float): Peak wave frequency (Hz).
- alpha (DataArray, float): Phillip's fetch-dependent scaling coefficient.
- hs (DataArray, float): Significant wave height (m), if provided the spectra
are scaled so that :math:`4\\sqrt{m_0} = hs`.
Returns:
- efth (SpecArray): Pierson-Moskowitz frequency spectrum E(f) (m2s).
Note:
- If `hs` is provided the spectra are scaled so that :math:`4\\sqrt{m_0} = hs`
and the scaling parameter `alpha` becomes irrelevant.
- If two or more input args other than `freq` are DataArrays,
they must share the same coordinates.
"""
check_same_coordinates(fp, alpha)
if not isinstance(freq, xr.DataArray):
freq = to_coords(freq, "freq")
dsout = alpha * g**2 / (2 * pi) ** 4 / freq**5 * np.exp(-1.25 * (freq / fp) ** -4)
if hs is not None:
dsout = scaled(dsout, hs)
dsout.name = attrs.SPECNAME
return dsout
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def jonswap(
freq, fp, alpha=0.0081, gamma=3.3, sigma_a=0.07, sigma_b=0.09, hs=None, **kwargs
):
"""Jonswap frequency spectrum for developing seas (Hasselmann et al., 1973).
Args:
- freq (DataArray, 1darray, list): Frequency array (Hz).
- fp (DataArray, float): Peak wave frequency (Hz).
- alpha (DataArray, float): Phillip's fetch-dependent scaling coefficient.
- gamma (DataArray, float): Peak enhancement parameter.
- sigma_a (DataArray, float): width of the peak enhancement parameter for f <= fp.
- sigma_b (DataArray, float): width of the peak enhancement parameter for f > fp.
- hs (DataArray, float): Significant wave height (m), if provided the Jonswap
spectra are scaled so that :math:`4\\sqrt{m_0} = hs`.
Returns:
- efth (SpecArray): Jonswap spectrum E(f) (m2s).
Note:
- If `hs` is provided than the scaling parameter `alpha` becomes irrelevant.
- If two or more input args other than `freq` are DataArrays,
they must share the same coordinates.
"""
check_same_coordinates(fp, alpha, gamma, sigma_a, sigma_b, hs)
if not isinstance(freq, xr.DataArray):
freq = to_coords(freq, "freq")
sigma = xr.where(freq <= fp, sigma_a, sigma_b)
term1 = alpha * g**2 * (2 * pi) ** -4 * freq**-5
term2 = np.exp(-(5 / 4) * (freq / fp) ** -4)
term3 = gamma ** np.exp(-((freq - fp) ** 2) / (2 * sigma**2 * fp**2))
dsout = term1 * term2 * term3
if hs is not None:
dsout = scaled(dsout, hs)
dsout.name = attrs.SPECNAME
return dsout
[docs]
def tma(
freq,
fp,
dep,
alpha=0.0081,
gamma=3.3,
sigma_a=0.07,
sigma_b=0.09,
hs=None,
**kwargs,
):
"""TMA frequency spectrum for seas in water of finite depth (Bouws et al., 1985).
Args:
- freq (DataArray, 1darray, list): Frequency array (Hz).
- fp (DataArray, float): Peak wave frequency (Hz).
- dep (DataArray, float): Water depth (m).
- alpha (DataArray, float): Phillip's fetch-dependent scaling coefficient.
- gamma (DataArray, float): Peak enhancement parameter.
- sigma_a (float): width of the peak enhancement parameter for f <= fp.
- sigma_b (float): width of the peak enhancement parameter for f > fp.
- hs (DataArray, float): Significant wave height (m), if provided the Jonswap
spectra are scaled so that :math:`4\\sqrt{m_0} = hs`.
Returns:
- efth (SpecArray): TMA frequency spectrum E(f) (m2s).
Note:
- If `hs` is provided than the scaling parameter `alpha` becomes irrelevant.
- If two or more input args other than freq are DataArrays,
they must share the same coordinates.
"""
check_same_coordinates(fp, dep, alpha, gamma, sigma_a, sigma_b, hs)
if not isinstance(freq, xr.DataArray):
freq = to_coords(freq, "freq")
dsout = jonswap(freq, fp, alpha, gamma, sigma_a, sigma_b, hs)
k = wavenuma(freq, dep)
phi = np.tanh(k * dep) ** 2 / (1 + (2 * k * dep) / np.sinh(2 * k * dep))
dsout = dsout * phi
if hs is not None:
dsout = scaled(dsout, hs)
dsout.name = attrs.SPECNAME
return dsout
[docs]
def gaussian(freq, hs, fp, gw, **kwargs):
"""Gaussian frequency spectrum (Bunney et al., 2014).
Args:
- freq (DataArray): Frequency array (Hz).
- hs (DataArray, float): Significant wave height (m).
- fp (DataArray, float): Peak wave frequency (Hz).
- gw (DataArray, float): Gaussian width parameter :math:`\sigma` (m2s).
Returns:
- efth (SpecArray): Gaussian frequency spectrum E(f) (m2s).
Note:
- The spectra are scaled so that :math:`4\\sqrt{m_0} = hs`.
- If two or more input args other than `freq` are DataArrays,
they must share the same coordinates.
"""
check_same_coordinates(hs, fp, gw)
if not isinstance(freq, xr.DataArray):
freq = to_coords(freq, "freq")
mo = (hs / 4) ** 2
dsout = mo / (gw * np.sqrt(2 * pi)) * np.exp(-0.5 * ((freq - fp) / gw) ** 2)
dsout = scaled(dsout, hs)
dsout.name = attrs.SPECNAME
return dsout
def conditional(
freq, hs, fp, cond, when_true="jonswap", when_false="gaussian", **kwargs
):
"""Conditional frequency spectrum selecting a given shape based on a boolean array.
Args:
- freq (DataArray): Frequency array (Hz).
- hs (DataArray, float): Significant wave height (m).
- fp (DataArray, float): Peak wave frequency (Hz).
- cond (DataArray, bool): .
- when_true: spectral shape function when cond == True.
- when_false: spectral shape function when cond == False.
- kwargs: kwargs must have all arguments for both when_true and when_false functions.
Returns:
- efth (SpecArray): Conditional frequency spectrum E(f) (m2s).
Note:
- The spectra are scaled so that :math:`4\\sqrt{m_0} = hs`.
- If two or more input args other than `freq` are DataArrays,
they must share the same coordinates.
"""
check_same_coordinates(hs, fp, cond)
if not isinstance(freq, xr.DataArray):
freq = to_coords(freq, "freq")
import inspect
arg_vals = inspect.getargvalues(inspect.currentframe())
arguments = {a: arg_vals.locals[a] for a in arg_vals.args}
arguments.update(arg_vals.locals["kwargs"])
true_func = globals()[when_true]
false_func = globals()[when_false]
ds_true = true_func(**arguments)
ds_false = false_func(**arguments)
dsout = xr.where(cond, ds_true, ds_false)
dsout.name = attrs.SPECNAME
return dsout
