Nonlinear energy transfer between wind waves in a gravity wave spectrum plays a pivotal role in the evolution of waves and was included as one of the source term (named nonlinear source term) in the third-generation (3G) wave models. The main objective of this paper is to compute the energy distribution due to nonlinear quadruplet wave–wave interactions for observed wave spectrum. This is achieved by utilizing cubic spline technique to fit and represent the theoretical as well as the measured spectra at given location. This technique is further incorporated into Gauss–Legendre Quadrature Method (GLQM) [1, 2] for computing the nonlinear source term. Results were illustrated and validated for the theoretical as well as measured spectra (single- or multi-peaked spectrum) without compromising the accuracy of the method. The significance of this work includes an improvement in the computational efficiency of the method up to \(65\%\) by employing optimal set of points of input spectrum (using a procedure discussed) without affecting the nonlinear results of the original one. GLQM (spline fitted spectra) is suitable for deep and finite water depths. Also, this work does not adhere to any assumptions for the tail factor, as the measured spectrum is directly fitted using splines.

重力波谱中风波之间的非线性能量传递在波浪的演化中起着关键作用，并被作为源项之一（称为非线性源项）包含在第三代（3G）波浪模型中。本文的主要目的是计算观测到的波谱中非线性四重态波-波相互作用引起的能量分布。这是通过利用三次样条技术来拟合和表示给定位置的理论光谱和测量光谱来实现的。该技术进一步融入高斯-勒让德求积法 (GLQM) [1, 2]，用于计算非线性源项。对理论和测量光谱（单峰或多峰光谱）的结果进行了说明和验证，而不影响方法的准确性。这项工作的意义在于，通过采用输入频谱的最佳点集（使用讨论的过程），在不影响原始频谱的非线性结果的情况下，将该方法的计算效率提高到65% 。GLQM（样条拟合谱）适用于深水和有限水深。此外，这项工作不遵守尾部因子的任何假设，因为测量的光谱是使用样条直接拟合的。