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Viewing Sea Level by a One-Dimensional Random Function with Long Memory

机译：通过长记忆的一维随机函数查看海平面

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摘要

Sea level fluctuation gains increasing interests in several fields, such as geoscience and ocean dynamics. Recently, the long-range dependence (LRD) or long memory, which is measured by the Hurst parameter, denoted by H, of sea level was reported by Barbosa et al. (2006). However, reports regarding the local roughness of sea level, which is characterized by fractal dimension, denoted by D, of sea level, are rarely seen. Note that a common model describing a random function with LRD is fractional Gaussian noise (fGn), which is the increment process of fractional Brownian motion (fBm) (Beran (1994)). If using the model of fGn, D of a random function is greater than 1 and less than 2 because D is restricted by H with the restriction D = 2 - H. In this paper, we introduce the concept of one-dimensional random functions with LRD based on a specific class of processes called the Cauchy-class (CC) process, towards separately characterizing the local roughness and the long-range persistence of sea level. In order to achieve this goal, we present the power spectrum density (PSD) function of the CC process in the closed form. The case study for modeling real data of sea level collected by the National Data Buoy Center (NDBC) at six stations in the Florida and Eastern Gulf of Mexico demonstrates that the sea level may be one-dimensional but LRD. The case study also implies that the CC process might be a possible model of sea level. In addition to these, this paper also exhibits the yearly multiscale phenomenon of sea level.
机译：海平面波动在诸如地球科学和海洋动力学等多个领域中越来越引起人们的兴趣。最近，Barbosa等人报道了通过海平面的Hurst参数（用H表示）测量的长期依赖关系（LRD）或长时记忆。 （2006）。然而，很少有关于海平面局部粗糙度的报道，其特征在于以D表示的海平面的分形维数。注意，描述带有LRD的随机函数的通用模型是分数高斯噪声（fGn），它是分数布朗运动（fBm）的增量过程（Beran（1994））。如果使用fGn模型，则随机函数的D大于1且小于2，因为D受H约束且约束D = 2-H。在本文中，我们引入一维随机函数的概念LRD基于称为“柯西级”（Cauchy-class，CC）过程的特定过程类别，旨在分别表征局部粗糙度和海平面的长期持续性。为了实现此目标，我们以封闭形式介绍了CC过程的功率谱密度（PSD）函数。由国家数据浮标中心（NDBC）在佛罗里达州和墨西哥东部海湾的六个站点收集的海平面真实数据建模的案例研究表明，该海平面可能是一维的，但是LRD。案例研究还暗示，CC过程可能是海平面的一种可能模型。除了这些，本文还展示了每年的海平面多尺度现象。

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  • 来源
    《Mathematical Problems in Engineering》 |2011年第2期|p.1-13|共13页
  • 作者

    Ming Li; Carlo Cattani; Seng-Yong Chen;

  • 作者单位

    School of Information Science & Technology, East China Normal University, Shanghai 200241, China;

    Department of Pharmaceutical Sciences (DiFarma), University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, SA, Italy;

    College of Computer Science, Zhejiang University of Technology, Hangzhou 310023, China;

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