Implemented Lomb-Scargle periodogram: a valuable tool for improving cyclostratigraphic research on unevenly sampled deep-sea stratigraphic sequences

One important handicap when working with stratigraphic sequences is the discontinuous character of the sedimentary record, especially relevant in cyclostratigraphic analysis. Uneven palaeoclimatic/palaeoceanographic time series are common, their cyclostratigraphic analysis being comparatively difficult because most spectral methodologies are appropriate only when working with even sampling. As a means to solve this problem, a program for calculating the smoothed Lomb-Scargle periodogram and cross-periodogram, which additionally evaluates the statistical confidence of the estimated power spectrum through a Monte Carlo procedure (the permutation test), has been developed. The spectral analysis of a short uneven time series calls for assessment of the statistical significance of the spectral peaks, since a periodogram can always be calculated but the main challenge resides in identifying true spectral features. To demonstrate the effectiveness of this program, two case studies are presented: the one deals with synthetic data and the other with paleoceanographic/palaeoclimatic proxies. On a simulated time series of 500 data, two uneven time series (with 100 and 25 data) were generated by selecting data at random. Comparative analysis between the power spectra from the simulated series and from the two uneven time series demonstrates the usefulness of the smoothed Lomb-Scargle periodogram for uneven sequences, making it possible to distinguish between statistically significant and spurious spectral peaks. Fragmentary time series of Cd/Ca ratios and ??¹⁸O from core AII107-131 of SPECMAP were analysed as a real case study. The efficiency of the direct and cross Lomb-Scargle periodogram in recognizing Milankovitch and sub-Milankovitch signals related to palaeoclimatic/palaeoceanographic changes is demonstrated. As implemented, the Lomb-Scargle periodogram may be applied to any palaeoclimatic/palaeoceanographic proxies, including those usually recovered from contourites, and it holds special interest in the context of centennial- to millennial-scale climatic changes affecting contouritic currents.     

Bound waves and triad interactions in shallow water

Boussinesq type equations with improved linear dispersion characteristics are derived and applied to study wave-wave interaction in shallow water. Weakly nonlinear solutions are formulated in terms of Fourier series with constant or spatially varying coefficients for two purposes: to derive higher order boundary conditions for regular and irregular wave trains and to derive evolution equations on constant or variable water depth. Wave transformation of monochromatic, bichromatic and irregular waves is studied and comparison with measurements and direct time domain solutions shows good agreement. The improvement relative to classical models from the literature is discussed.     

A shipborne wave-recording system with digital data processing

A shipborne wave-recording system which consists of a sonic wave gauge, accelerometers, gyroscopes and a computer system is described. Signals from the measuring apparatus are fed directly into a shipborne digital computer system at a prescribed sampling rate. The time series of wave heights and the acceleration are transformed into Fourier series using an algorithm of Fast Fourier Transform. Errors contained in the observed wave heights due to ship motion are corrected in the Fourier series by using the Fourier coefficients for the vertical acceleration. Power spectra and waveforms can also be calculated in a short time with this system from Fourier coefficients. Examples of the observational results obtained in the central part of the East China Sea in 1969 are presented.     

纬度正反解问题的傅里叶级数解算方法

讨论了一种在一般闭区间上连续的无穷级数展开方法,针对测量和地图学中常用纬度间正反解等一类问题,给出了一种傅里叶级数解算方法,并进行了相应的理论分析和计算。基于Mathematica计算机代数系统,推导出常用纬度与大地纬度间正反解的级数展开式,表明运用傅里叶级数解法可以简单表示和计算一类复杂奇函数的正反解无穷展开式。算例分析验证表明,该方法推导出的纬度正反解展开式是正确的。傅里叶级数方法为分析一类正反解问题无穷展开式的一般系数和形式提供了理论分析依据,具有通用性,丰富了纬度正反解变换的相关理论。     

时间不连续压力序列的傅立叶分析方法

提出了一种用于对不连续压力采样序列的傅立叶分析方法.此方法将周期函数展开成傅立叶级数,但在数值积分时取函数周期内有采样值的区间作为积分域,然后求解线性方程组得到傅立叶级数的系数值.为了检验本方法的有效性,利用此方法对解析函数进行了拟合,当一个周期内的取样时间大于1/2周期时,利用此方法能够得到满意的结果.利用实验方法研究了波浪作用下截断圆柱表面的压力分布.在波浪作用下静水面附近的测点在露出水面时没有压力值.利用所提出的傅立叶分析方法对略低于静水面位置的实测压力进行了分析,拟合结果与实测结果吻合很好,说明此方法在处理物理模型实验中间断采样得到的数据是有效的.利用数值方法对波浪压力进行了计算,并将一阶和二阶波压力的数值结果与实测值进行了比较.     

Padé coefficients for the solution of the wave dispersion equation under ice

The equations governing the propagation of linear gravity waves in ice-covered waters of finite depth is delineated for the linear elastic deformation of the ice plates that are modeled as elastically supported. The possible limiting condition for the validity of the assumptions involved in the formulation of the problem is discussed. A solution procedure for the solution of the wave dispersion equation under ice is discussed and a set of coefficients synthesized using the properties of infinite series and Padé approximants. Direct application of these coefficients for the calculation of wave characteristics in ice-covered sea will eliminate the need for iterative procedure, and hence will reduce the computational time. The derived coefficients were used for the computation of the wave characteristics of laboratory simulated waves and compared with the values obtained through iteration and the error was found to be less than 2%.     

Experimental researches on reflective and transmitting performances of quarter circular breakwater under regular and irregular waves

A series of regular and irregular wave experiments are conducted to study the reflective and transmitting performances of quarter circular breakwater (QCB) in comparison with those of semi-circular breakwater (SCB). Based on regular wave tests, the reflection and transmission characteristics of QCB are analyzed and a few influencing factors are investigated. Then, the wave energy dissipation as wave passing over the breakwater is discussed based on the hydraulic coefficients of QCB and SCB. In irregular wave experiments, the reflection coefficients of QCB and their spectrums are studied. Finally, the comparisons between the experimental results and numerical simulations for QCB under regular and irregular wave conditions are presented.     

马蹄波波形特征和对圆柱作用实验研究

为了研究真实海洋表面马蹄波特性以及对建筑物的作用,通过物理模型实验研究了马蹄波的波形特征参数以及马蹄波对圆柱体的作用。实验中通过对浪高仪采集的波面升高时间历程曲线进行分析得出了不同水深情况下马蹄波的垂向几何特征,并通过快速傅里叶变换得出了马蹄波波幅谱的特征,研究了马蹄波各组成波波幅沿空间的变化从而得出了圆柱存在对马蹄波演化的影响,同时给出马蹄波绕射形成的波面分布和不同频率谐波在圆柱周围的分布,讨论了马蹄波不同于Stokes波对圆柱作用的特征。结果表明,马蹄波波形受水深影响较大,水深越浅,马蹄波的波面形状越接近椭圆余弦波。圆柱体的存在干扰了马蹄波不稳定的增长,使其在接近圆柱时呈下降趋势,导致不稳定幅值最大值的位置提前并且出现在偏离圆柱迎浪点的侧表面,从而使圆柱受到侧向力的作用。     

稳恒水波的Fourier近似解研究

A computational method for steady water waves is presented on the basis of potential theory in the physical plane with spatial variables as independent quantities. The finite Fourier series are applied to approximating the free surface and potential function. A set of nonlinear algebraic equations for the Fourier coefficients are derived from the free surface kinetic and dynamic boundary conditions. These algebraic equations are numerically solved through Newton＇s iterative method, and the iterative stability is further improved by a relaxation technology. The integral properties of steady water waves are numerically analyzed, showing that （1） the set-up and the set-down are both non-monotonic quantities with the wave steepness, and （2） the Fourier spectrum of the free surface is broader than that of the potential function. The latter further leads us to explore a modification for the present method by approximating the free surface and potential function through different Fourier series, with the truncation of the former higher than that of the latter. Numerical tests show that this modification is effective, and can notably reduce the errors of the free surface boundary conditions.     

Efficient processing of water wave records via compressive sensing and joint time-frequency analysis via harmonic wavelets

A methodology is proposed for efficient processing of sea wave field data via compressive sensing (CS), and joint time-frequency analysis via harmonic wavelets (HWs) based evolutionary power spectrum (EPS) estimation. In this regard, it is possible to record and store relatively long wave data sequences, whereas the commonly adopted in-practice assumption of stationary data is abandoned. Currently, most wave records are measured by buoys, which acquire data for a time interval representative of stationary time series. Next, following a Fourier transform processing, only few spectral parameters are stored. Thus, detailed information about localized-in-time phenomena are completely lost. Herein, it is shown that CS can be adopted for efficiently compressing and reconstructing wave data, while retaining localized information. For this purpose, CS is used in conjunction with a HW basis for processing long time series. In particular, storage capacity demands are drastically decreased as only the HW coefficients need to be saved. These are determined from a randomly-sampled record by invoking a L_1/2 norm minimization procedure. The resulting reconstructed record, being longer than conventional wave time series, can no longer be regarded as stationary; thus, a HW based EPS estimate is employed for describing the joint time-frequency features of the record. Finally, the reliability of the methodology is assessed by analyzing wave field data measured at the Natural Ocean Engineering Laboratory (NOEL) of Reggio Calabria. Specifically, comparisons between original and reconstructed records demonstrate a satisfactory agreement regarding the time-histories, and the estimated EPS and relevant statistical quantities, even for up to 60% missing/removed data.     

Research on the spectral analysis and test method of period signals in monthly mean sea level

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Hydrodynamics of A Flexible Riser Undergoing the Vortex-Induced Vibration at High Reynolds Number

This study proposed a method to obtain hydrodynamic forces and coefficients for a flexible riser undergoing the vortex-induced vibration (VIV), based on the measured strains collected from the scale-model testing with the Reynolds numbers ranging from 1.34E5 to 2.35E5. The riser is approximated as a tensioned spatial beam, and an inverse method based on the FEM of spatial beam is adopted for the calculation of hydrodynamic forces in the cross flow (CF) and inline (IL) directions. The drag coefficients and vortex-induced force coefficients are obtained through the Fourier Series Theory. Finally, the hydrodynamic characteristics of a flexible riser model undergoing the VIV in a uniform flow are carefully investigated. The results indicate that the VIV amplifies the drag coefficient, and the drag coefficient does not change with time when the CF VIV is stable. Only when the VIVs in the CF and IL directions are all steady vibrations, the vortex-induced force coefficients keep as a constant with time, and under “lock-in” condition, whether the added-mass coefficient changes with time or not, the oscillation frequency of the VIV keeps unchanged. It further shows that the CF excitation coefficients at high frequency are much smaller than those at the dominant frequency, while, the IL excitation coefficients are in the same range. The axial distributions of the excitation and damping region at the dominant frequency and high frequency are approximately consistent in the CF direction, while, in the IL direction, there exists a great difference.     

中国海洋水色遥感器瑞利散射定标研究

水色遥感是海洋环境监测的主要技术手段之一.对于任何海洋水色遥感器来说,监测其在轨期间的定标系数变化是非常重要的,否则无法得到精确的定量产品.以我国“HY-1B”卫星水色遥感器为研究对象,开展了基于大洋水体上空的瑞利散射定标方法研究,利用通过对SeaWiFS数据叶绿素、离水辐亮度和气溶胶产品进行分析,选择了符合条件的7个海区实施大气瑞利散射定标,根据2010年12月份选定的4个区域定标结果得到不同海区/不同时间获得的定标系数一致性较好,CH1至CH6的定标系数标准差分布在0.9％～2.1％的范围内,因此瑞利散射定标是有效的非现场定标方法,具有较高的定标精度,其总误差在4.09％.     

基于矢耳石形态分析的凤鲚(Coilia mystus) 群体识别研究

以长江口、胶州湾、渤海湾和辽东湾4个地理群体的凤鲚(Coilia mystus)矢耳石样本为研究对象,采用形状指数和椭圆傅里叶系数分析相结合的方法研究了该4个凤鲚群体的矢耳石形态特征及差异性。方差分析结果表明,大部分形态变量存在显著的群体差异,引入协变量(耳石长)之后除形状因子外这种差异依然显著。基于协方差校正的判别分析只保留了耳石重量及9个傅里叶系数用于群体识别,而非参数检验的判别分析则保留了耳石重量、分形维数、环状度、矩形趋近率、圆度和19个傅里叶系数用于群体识别。相应地,基于非参检验的凤鲚群体的总体识别成功率(68.2%)明显高于协方差校正的判别分析结果(46.2%),表明前者比后者更能提高耳石形态分析的群体识别能力。     

A Probability Distribution of Surface Elevation for Wind Waves in Terms of the Gram-Charlier Series

Laboratory experiments are conducted to study the probability distribution of surface elevation for wind waves and the convergence is discussed of the Gram-Charlier series in describing the surface elevation distribution. Results show that the agreement between the Gram-Charlier series and the observed distribution becomes better and better as the truncated order of the series increases in a certain range, which is contrary to the phenomenon observed by Huang and Long (1980) . It is also shown that the Gram-Charlier series is sensitive to the anomalies in the data set which will make the agreement worse if they are not preprocessed appropriately. Negative values of the probability distribution expressed by the Gram-Charlier series in some ranges of surface elevations are discussed, but the absolute values of the negative values as well as the ranges of their occurrence become smaller gradually as more and more terms are included. Therefore the negative values will have no evident effect on the form of t     

A Study on the Maneuvering Motion of a Low Speed Submersible

In this paper,the maneuvering characteristics of a low speed submersible are investigated.First,the captive model tests are carried out to obtain the hydrodynamic forces acting on the submersibleusing a Planar Motion Mechanism(PMM).For the hydrodynamic forces within a wide range of attack an-gles,the hydrodynamic coefficients which are usually used in the conventional maneuvering motion arequite difficult to be applied.In this case,a Fourier series is adopted to represent the hydrodynamic forcesand it fits the experimental data well.Then,based on the experimental results the simulation calculationsare made to predict some of the maneuvering performance of the low speed submersible.     

Climate-based Monte Carlo simulation of trivariate sea states

Accurate wave climate characterization, which is vital to understand wave-driven coastal processes and to design coastal and offshore structures, requires the availability of long term data series. Where existing data are sparse, synthetically generated time series offer a practical alternative. The main purpose of this paper is to propose a methodology to simulate multivariate hourly sea state time series that preserve the statistical characteristics of the existing empirical data. This methodology combines different techniques such as univariate ARMAs, autoregressive logistic regression and K-means clusterization algorithms, and is able to take into account different time and space scales. The proposed methodology can be broken down into three interrelated steps: i) simulation of sea level pressure fields, ii) simulation of daily mean sea conditions time series and iii) simulation of hourly sea state time series. Its effectiveness is demonstrated by synthetically generating multivariate hourly sea states from a specific location near the Spanish Coast. The direct comparison between simulated and empirical time series confirms the ability of the developed methodology to generate multivariate hourly time series of sea states. Finally, the potential of the proposed methodology to simulate multivariate time series at multiple locations and incorporate climate change issues is discussed.     

On the Statistical Structure of Hydrometeorological Fields in the North Atlantic

We study the possibility of detection of statistically significant trends as a characteristic of low-frequency variability of hydrometeorological fields in the North Atlantic on the basis of relatively short time series. We use the monthly data of the Russian Hydrometeorological Center for 1957–1990 and analyze their statistical structure. It is shown that significant linear and quadratic trends can be detected in the fields of most hydrometeorological characteristics of the North Atlantic. The residual signal is approximated by using the first-order autoregressive model. Typical values of the coefficient of autoregression vary within the range 0.3–0.6 (for different hydrometeorological characteristics of the North Atlantic). The maximum correlation is observed for the fields of sea-surface temperature and humidity, whereas the minimum correlation is typical of the fields of wind velocity and the difference between the temperatures of water and air.     

基于支持向量回归的海面高度统计预报方法研究

本文提出一种基于支持向量回归的统计预报方法,通过经验正交分解对原始数据矩阵进行时空分解,提取出空间模态和时间系数。由于海面高度变化具有非线性、大惯性的特点,对时间系数进行小波分析,能有效滤除其中的高频信号,得到表征海面高度变化的低频信号。利用支持向量回归方法对小波分解后的低频信号构建预报模型。最后,进行小波重构,还原时间序列长度,实现未来7天的海面高度预报。通过黑潮附近海域的海面高度预报结果验证,该预报方法的预报效果优于整合滑动平均自回归预报方法。本文通过机器学习的算法实现了海面高度的预报,为海洋预报方法提供了新的思路。