netsse.analys.buoy ================== .. py:module:: netsse.analys.buoy .. autoapi-nested-parse:: Functions to **process wave buoy** motion signals into directional wave spectra. .. dropdown:: Copyright (C) 2023-2026 Technical University of Denmark, R.E.G. Mounet :color: primary :icon: law *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: .. code-block:: text 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 --------- .. autoapisummary:: netsse.analys.buoy.Fourier2spread_dist_params netsse.analys.buoy.Shannon_MEMII_Newton netsse.analys.buoy.cross_spec2Fourier_coef netsse.analys.buoy.spread_dist_params2Fourier Module Contents --------------- .. py:function:: 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). :param a1: First four Fourier coefficients of the directional wave spectrum. :type a1: array_like of shape (Nf,) :param b1: First four Fourier coefficients of the directional wave spectrum. :type b1: array_like of shape (Nf,) :param a2: First four Fourier coefficients of the directional wave spectrum. :type a2: array_like of shape (Nf,) :param b2: First four Fourier coefficients of the directional wave spectrum. :type b2: array_like of shape (Nf,) :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 [-]. .. seealso:: :py:obj:`spread_dist_params2Fourier` Infers the Fourier coefficients from the parameters of the directional spreading distribution function. .. rubric:: 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. .. rubric:: Example >>> [alpha, sigma, gamma, delta] = Fourier2spread_dist_params(a1,b1,a2,b2) .. py:function:: 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). :param a1: First four Fourier coefficients of the directional wave spectrum. :type a1: array_like of shape (Nf,) :param a2: First four Fourier coefficients of the directional wave spectrum. :type a2: array_like of shape (Nf,) :param b1: First four Fourier coefficients of the directional wave spectrum. :type b1: array_like of shape (Nf,) :param b2: First four Fourier coefficients of the directional wave spectrum. :type b2: array_like of shape (Nf,) :param freq: Vector of (discretized) wave frequencies [Hz]. :type freq: array_like of shape (Nf,) :param theta: Vector of wave headings [deg]. :type theta: array_like of shape (Ntheta,) :param maxiter: Maximum number of iterations. :type maxiter: int :param tol_error: Tolerance in the relative error. :type tol_error: float :param miniter: Minimum number of iterations. :type miniter: int, default 50 :param approx: Boolean which indicates whether the approximation method should be used for finding the Lagrangian multipliers. :type approx: bool, default False :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. .. seealso:: :py:obj:`cross_spec2Fourier_coef` Computes the Fourier coefficients from the cross-spectra of a heave-East-North wave buoy. :py:obj:`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. .. rubric:: 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). .. rubric:: Example >>> D, flag, L1, L2, L3, L4 = ... Shannon_MEMII_Newton(a1,a2,b1,b2,freq,theta,maxiter,tol_error,miniter=50,False) .. py:function:: 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). :param Gf: Cross-spectra (Heave-East-North), as a function of frequency in Hertz. :type Gf: array_like of shape (3,3,Nf) :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. .. seealso:: :py:obj:`Shannon_MEMII_Newton` Reconstructs the directional spreading function based on the first four Fourier coefficients of a directional wave spectrum. .. rubric:: 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. .. rubric:: Example >>> Sf, a1, a2, b1, b2 = cross_spec2Fourier_coef(Gf) .. py:function:: 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). :param alpha: Wave direction [rad, or deg]. :type alpha: array_like of shape (Nf,) :param sigma: Directional spread [rad, or deg]. :type sigma: array_like of shape (Nf,) :param gamma: Skewness of the directional distribution [-]. :type gamma: array_like of shape (Nf,) :param delta: Kurtosis of the directional distribution [-]. :type delta: array_like of shape (Nf,) :param unit: Unit of the wave direction and directional spread: ``'deg'`` or ``'rad'`` (default). :type unit: {'rad','deg'}, optional :returns: **a1, b1, a2, b2** -- First four Fourier coefficients of the directional wave spectrum. :rtype: array_like of shape (Nf,) .. seealso:: :py:obj:`Fourier2spread_dist_params` Infers the parameters of the directional spreading distribution function from the Fourier coefficients. :py:obj:`Shannon_MEMII_Newton` Reconstructs the directional spreading function based on the first four Fourier coefficients of a directional wave spectrum. .. rubric:: 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. .. rubric:: Example >>> [a1,b1,a2,b2] = spread_dist_params2Fourier(alpha,sigma,gamma,delta,unit)