netsse.analys.buoy

Functions to process wave buoy motion signals into directional wave spectra.

Copyright (C) 2023-2026 Technical University of Denmark, R.E.G. Mounet

This code is part of the NetSSE software.

NetSSE is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

NetSSE is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see https://www.gnu.org/licenses/.

To credit the author, users are encouraged to use below reference:

Mounet, R. E. G., & Nielsen, U. D. NetSSE: An open-source Python package
for network-based sea state estimation from ships, buoys, and other
observation platforms (version 2.2). Technical University of Denmark,
GitLab. February 2026. https://doi.org/10.11583/DTU.26379811.

Last updated on 20-02-2026 by R.E.G. Mounet

Functions

Fourier2spread_dist_params(a1, b1, a2, b2)	Infers the parameters of the directional spreading distribution function
Shannon_MEMII_Newton(a1, a2, b1, b2, freq, theta, ...)	Reconstructs the directional spreading function based on the first four Fourier
cross_spec2Fourier_coef(Gf)	Computes the Fourier coefficients from the cross-spectra of a
spread_dist_params2Fourier(alpha, sigma, gamma, delta)	Infers the Fourier coefficients from the parameters of the directional

Module Contents

netsse.analys.buoy.Fourier2spread_dist_params(a1, b1, a2, b2)

Infers the parameters of the directional spreading distribution function from the Fourier coefficients, as per Kuik et al. (1988).

Parameters:

• a1 (array_like of shape (Nf,)) – First four Fourier coefficients of the directional wave spectrum.

• b1 (array_like of shape (Nf,)) – First four Fourier coefficients of the directional wave spectrum.

• a2 (array_like of shape (Nf,)) – First four Fourier coefficients of the directional wave spectrum.

• b2 (array_like of shape (Nf,)) – First four Fourier coefficients of the directional wave spectrum.

Returns:

• alpha (array_like of shape (Nf,)) – Wave direction [rad].

• sigma (array_like of shape (Nf,)) – Directional spread [rad].

• gamma (array_like of shape (Nf,)) – Skewness of the directional distribution [-].

• delta (array_like of shape (Nf,)) – Kurtosis of the directional distribution [-].

See also

spread_dist_params2Fourier

Infers the Fourier coefficients from the parameters of the directional spreading distribution function.

References

Kuik, A. J., van Vledder, G. P., & Holthuijsen, L. H. (1988). A Method for the Routine Analysis of Pitch-and-Roll Buoy Wave Data. Journal of Physical Oceanography, 18(7), 1020–1034.

Example

>>> [alpha, sigma, gamma, delta] = Fourier2spread_dist_params(a1,b1,a2,b2)

netsse.analys.buoy.Shannon_MEMII_Newton(a1, a2, b1, b2, freq, theta, maxiter, tol_error, miniter=50, approx=False)

Reconstructs the directional spreading function based on the first four Fourier coefficients of a directional wave spectrum.

The function implements the Maximum Entropy Principle (Hashimoto, 1997), either via running the Newton local linearisation method or following the approximation method by Kim et al. (1994).

Parameters:

• a1 (array_like of shape (Nf,)) – First four Fourier coefficients of the directional wave spectrum.

• a2 (array_like of shape (Nf,)) – First four Fourier coefficients of the directional wave spectrum.

• b1 (array_like of shape (Nf,)) – First four Fourier coefficients of the directional wave spectrum.

• b2 (array_like of shape (Nf,)) – First four Fourier coefficients of the directional wave spectrum.

• freq (array_like of shape (Nf,)) – Vector of (discretized) wave frequencies [Hz].

• theta (array_like of shape (Ntheta,)) – Vector of wave headings [deg].

• maxiter (int) – Maximum number of iterations.

• tol_error (float) – Tolerance in the relative error.

• miniter (int, default 50) – Minimum number of iterations.

• approx (bool, default False) – Boolean which indicates whether the approximation method should be used for finding the Lagrangian multipliers.

Returns:

• D (array_like of shape (Nf,Ntheta)) – Directional spreading function.

• flag (array_like of shape (Nf,)) – Boolean flag indicating unconverged frequencies (flag = 0 for unconverged)

• L1, L2, L3, L4 (array_like of shape (Nf,)) – Optimized Lagrange multipliers.

See also

cross_spec2Fourier_coef

Computes the Fourier coefficients from the cross-spectra of a heave-East-North wave buoy.

netsse.analys.emep.emep

Extended Maximum Entropy Principle (EMEP) method for reconstructing the directional spreading function based on the cross-power spectra of measured wave-induced responses.

References

1. Benoit, M., Frigaard, P., & Schäffer, H. A. (1997). Analysing Multidirectional Wave Spectra: A tentative classification of available methods. Proceedings of the 27th IAHR Congress, San Francisco, CA, USA (pp. 131–158). Canadian Government Publishing.

2. Hashimoto, N. (1997). Analysis of the Directional Wave Spectrum from Field Data. Advances in coastal and ocean engineering. 3:103-44.

3. Kim, T., Lin, L.-H., & Wang, H. (1994). Application of Maximum Entropy Method to the Real Sea Data. In Coastal Engineering (pp. 340–355).

Example

>>> D, flag, L1, L2, L3, L4 =
...     Shannon_MEMII_Newton(a1,a2,b1,b2,freq,theta,maxiter,tol_error,miniter=50,False)

netsse.analys.buoy.cross_spec2Fourier_coef(Gf)

Computes the Fourier coefficients from the cross-spectra of a heave-East-North wave buoy, as per Benoit et al. (1997).

Parameters:

Gf (array_like of shape (3,3,Nf)) – Cross-spectra (Heave-East-North), as a function of frequency in Hertz.

Returns:

• Sf (array_like of shape (Nf,)) – One-sided variance spectrum of the waves [m^2.s], as a function of frequency in Hertz.

• a1, a2, b1, b2 (array_like of shape (Nf,)) – Frequency-dependent Fourier coefficients of the directional wave spectrum.

See also

Shannon_MEMII_Newton

Reconstructs the directional spreading function based on the first four Fourier coefficients of a directional wave spectrum.

References

Benoit, M., Frigaard, P., & Schäffer, H. A. (1997). Analysing Multidirectional Wave Spectra: A tentative classification of available methods. Proceedings of the 27th IAHR Congress, San Francisco, CA, USA (pp. 131–158). Canadian Government Publishing.

Example

>>> Sf, a1, a2, b1, b2 = cross_spec2Fourier_coef(Gf)

netsse.analys.buoy.spread_dist_params2Fourier(alpha, sigma, gamma, delta, unit='rad')

Infers the Fourier coefficients from the parameters of the directional spreading distribution function, as per Kuik et al. (1988).

Parameters:

• alpha (array_like of shape (Nf,)) – Wave direction [rad, or deg].

• sigma (array_like of shape (Nf,)) – Directional spread [rad, or deg].

• gamma (array_like of shape (Nf,)) – Skewness of the directional distribution [-].

• delta (array_like of shape (Nf,)) – Kurtosis of the directional distribution [-].

• unit ({'rad','deg'}, optional) – Unit of the wave direction and directional spread: 'deg' or 'rad' (default).

Returns:

a1, b1, a2, b2 – First four Fourier coefficients of the directional wave spectrum.

Return type:

array_like of shape (Nf,)

See also

Fourier2spread_dist_params

Infers the parameters of the directional spreading distribution function from the Fourier coefficients.

Shannon_MEMII_Newton

Reconstructs the directional spreading function based on the first four Fourier coefficients of a directional wave spectrum.

References

Kuik, A. J., van Vledder, G. P., & Holthuijsen, L. H. (1988). A Method for the Routine Analysis of Pitch-and-Roll Buoy Wave Data. Journal of Physical Oceanography, 18(7), 1020–1034.

Example

>>> [a1,b1,a2,b2] = spread_dist_params2Fourier(alpha,sigma,gamma,delta,unit)