Study on Separation Method for one-dimensional wind-sea and swell under different dominant wave conditions
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摘要: 海洋中的混合浪通常由风浪和涌浪以一定比例组成，因研究和应用等需求经常需要分离其中的风浪和涌浪。本文针对现有四种代表性一维谱风涌分离方法（1D法）：PM法(Pierson-Moskowitz)、改进的PM法、JP法(Jesús-Portilla)和频谱积分法，利用中法海洋卫星上搭载的波谱仪提供的二维海浪谱数据，对比分析了纯风浪、风浪为主、涌浪为主和纯涌浪4种海浪主导情况下的分离结果，结果表明：（1）PM法和改进的PM法分别在风浪为主和涌浪为主时各有更好的分离效果；（2）JP法整体表现较差，对不同海浪主导条件的响应不敏感；频谱积分法在风浪占比较大时效果更佳；（3）随着混合浪中涌浪比例的增加，适当增大PM法中分离频率的比例系数可提升分离精度。在此基础上结合波龄提出了一种分段PM法，通过调整分离频率的比例系数，在风浪主导和涌浪主导的条件下分别取1.03和1.1时，得到的分离结果更为精确。Abstract: Mixed waves in the ocean typically consist of wind waves and swell in varying proportions. Due to research and application needs, it is often necessary to separate the wind waves from the swell. This paper focuses on four existing representative one-dimensional spectral wind-sea separation methods (1D methods): the PM method (Pierson-Moskowitz), the improved PM method, the JP method (Jesús-Portilla), and the spectral integral method. Using two-dimensional wave spectrum data provided by the spectrometer onboard the China-France Oceanography Satellite, a comparative analysis of the separation results under four wave-dominant conditions—pure wind waves, wind wave-dominant, swell-dominant, and pure swell—was conducted. The results show that: (1) The PM method and the improved PM method perform better under wind wave-dominant and swell-dominant conditions, respectively. (2) The JP method performs poorly overall and is insensitive to different wave-dominant conditions; the spectral integral method performs better when wind waves dominate. (3) As the proportion of swell in mixed waves increases, appropriately increasing the frequency ratio coefficient in the PM method can improve separation accuracy. Based on this, a piecewise PM method is proposed, which adjusts the frequency ratio coefficient. Under wind wave-dominant and swell-dominant conditions, using coefficients of 1.03 and 1.1, respectively, results in more accurate separation.
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图 1 2022年11月1日4时37分SWIM二维谱及分离的3个波分量
a. 第一波分量，b. 第二波分量，c. 第三波分量，d. 3个波分量组成的总海浪谱
Fig. 1 The 2D SWIM spectrum and three separated wave components at 04:37 on November 1, 2022
a.First wave component, b. second wave component, c. third wave component, d. combined spectrum of three components
图 2 2022年11月1日04时37分SWIM一维谱风涌组成情况
a. 各波分量一维谱，b. 各频率的峰值波向和风向的余弦值分布
Fig. 2 Wind-sea and swell composition of the 1D SWIM spectrum at 04:37 on November 1, 2022
a. 1D spectra of wave components, b. distribution of the cosine of the angle between peak wave direction and wind direction across frequencies
图 3 4种1D法与2D法风涌分离结果对比
a、e. PM法分离结果，b、f. 改进的PM法分离结果，c、g. JP法分离结果，d、h. 频谱积分法分离结果；下同
Fig. 3 Comparison of wind-sea and swell separation results using four 1D methods and 2D method
a, e. Separation results using PM method, b, f. separation results using improved PM method, c, g. separation results using JP method, d, h. separation results using spectral integral method. Similar explanation for the following figures
图 4 风浪为主时的风涌分离结果
Fig. 4 Separation results of wind-sea and swell when wind-sea dominates
图 5 纯风浪时的风涌分离结果
Fig. 5 Separation results of wind-sea and swell under pure wind-sea conditions
图 6 涌浪为主时的风涌分离结果
Fig. 6 Separation results of wind-sea and swell when wind-sea dominates
图 8 4种海浪情况下分离结果的统计指标随比例系数变化的变化情况
a、e. 纯风浪时的分离结果；b、f. 风浪为主时的分离结果；c、g. 涌浪为主时的分离结果；d、h. 纯涌浪时的分离结果
Fig. 8 The variation of statistical indicators of separation results under four different wave conditions as the ratio coefficient changes
a, e. Separation results under pure wind-sea conditions, b, f. separation results when wind-sea dominates, c, g. separation results when swell dominates, d, h. separation results under pure swell conditions
图 9 分段调整比例系数后的PM法风涌分离结果
a. 分离的风浪结果对比；b. 分离的涌浪结果对比，下同
Fig. 9 Separation results of the PM method with piecewise-adjusted ratio coefficients
a. Comparison of Separated Wind-Sea Results; b. comparison of Separated Swell Results; similar for the following figures.
图 10 分段PM法的风涌分离结果
Fig. 10 Separation results of wind-sea and swell using the piecewise PM method
表 1 分段调整比例系数后的PM法与其他PM法的风涌分离结果比较
Tab. 1 Comparison of separation results between the piecewise-adjusted PM method and other PM methods
r RMSE/m Bias/m 原始的PM法（风/涌） 0.87/0.78 0.72/0.60 −0.45/0.26 改进的PM法（风/涌） 0.88/0.85 0.50/0.49 0.12/−0.13 分段调整PM法后（风/涌） 0.94/0.93 0.36/0.32 −0.06/0.02 
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表 2 分段PM法与其他PM法的风涌分离结果比较
Tab. 2 Comparison of separation results between Piecewise PM Method and other PM Methods
r RMSE/m Bias/m 原始的PM法（风/涌） 0.87/0.78 0.72/0.60 −0.45/0.26 改进的PM法（风/涌） 0.88/0.85 0.50/0.49 0.12/−0.13 分段PM法（风/涌） 0.90/0.88 0.46/0.42 −0.03/−0.04
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