Collaborative Research: Global Estimation of Lagrangian Characteristics of the Ocean Circulation

海洋是一种复杂的湍流，可以在传统的固定（欧拉）坐标系或运动（拉格朗日）参考系中研究，这些参考系遵循主要的洋流。可以从拉格朗日数据中测量的四个关键量是扩散率，拉格朗日积分时间标度，自旋参数和谱斜率或（等效）分形维数。前三个是海洋学界的积极兴趣，因为它们与提高大尺度海洋和气候模式中海洋环流的保真度有关。第四个量，光谱斜率，可能同样重要，但它的值和意义在很大程度上都没有被探索过，而且还没有在全球范围内进行检验。这些拉格朗日特征是许多重要假设的核心；然而，从数据中估计它们的困难是众所周知的，并导致了突出的不确定性。如图所示，这四个量紧密相连，因为它们描述了拉格朗日速度频谱的四个最重要的特征——这一事实表明，通过直接研究频谱本身的细节，可以采用一种新的统一方法来分析它们。拟议的研究将应用大数据的严格技术，从所有可用的拉格朗日数据中同时估计所有四个拉格朗日特征。其结果将是迄今为止在地表和深处绘制的最高分辨率的拉格朗日特征图。提高气候模式中海洋环流真实性的总体目标是一个引起社会极大兴趣的话题，因为它将加强适应和减缓气候变率的努力。更直接的是，该项目将有助于维护、改进和更广泛地分发唯一活跃的声学跟踪浮子数据档案，这是海洋环流最有价值的现场窗口之一。在整个项目中开发或改进的创新分析算法将与社区公开共享，为支持科学研究的软件基础设施做出贡献。在这个项目中，将进一步开发一种新的、高度优化的地球物理流体动力学理想数值模型，并将其分发给社区。将大数据技术应用于建模输出，可以将非常大的数据集减少到更少的参数，这将在未来的模型/数据相互比较中特别有用。最后，该项目将支持一名研究生，该研究生将接受大数据技术应用于分析数值模型输出的培训，以及一名早期职业科学家。该方法将在几个重要方面以以前的工作为基础：(i)最好地利用现有的统计信息，从而提高有效的空间分辨率，可能会大大提高；（ii）避免四个参数相互作用可能产生的严重估计误差；（iii）允许对不确定性进行量化；（四）允许对一些重要的物理假设进行正式和系统的检验。对来自现实模型的更大的轨迹集合进行并行分析，将允许量化由数据稀疏引起的不确定性，并将使模型在再现观察到的拉格朗日特征方面的技能得到仔细审查。最后，理想化的数值模拟和理论将为直接将拉格朗日轨迹的可观测特征与基础物理联系起来提供桥梁。主要的智力贡献将是回答一些重要的问题，在这里详细列出，例如：表面准营养、内部准营养和其他过程的影响能否在拉格朗日光谱的基础上加以区分？拉格朗日谱斜率告诉我们关于海洋湍流的本质是什么？何时何地各向异性是有效描述扩散率所必需的？自旋参数是否准确地捕捉了相干涡流对背景光谱的影响？通过对拉格朗日速度谱的首次全面研究，通过对误差的量化和对不同状态下控制参数的正确物理解释，可以回答这些问题和其他问题。

The ocean is a complex turbulent fluid that can be studied in the traditional fixed (Eulerian)coordinate system or a moving (Lagrangian) reference frame that follow the major ocean currents. Four key quantities that may be measured from Lagrangian data are the diffusivity, the Lagrangian integral timescale, the spin parameter and the spectral slope or (equivalently) the fractal dimension. The first three are of active interest to the oceanographic community due to their relevance for increasing the fidelity of the ocean circulation in large-scale ocean and climate models. The fourth quantity, the spectral slope, is potentially of equal importance, yet both its values and it meaning are largely unexplored, and it has yet to be examined on global scale. These Lagrangian characteristics are central to a number of important hypotheses; yet the difficulties in estimating them from data are well known and lead to outstanding uncertainties. As shown herein, these four quantities are tightly connected because they describe the four most important features of the frequency spectrum of Lagrangian velocities - a fact which suggests a new and unified approach to their analysis, by directly investigating the details of the spectrum itself. The proposed study will apply rigorous techniques from Big Data to estimate all four Lagrangian characteristics simultaneously from all available Lagrangian data. The result will be the highest resolution maps yet made of the Lagrangian characteristics, both at surface and at depth. The overarching goal of increasing the realism of the ocean circulation in climate models is a topic of great societal interest, because it would bolster climate variability adaptation and mitigation efforts. More immediately, this project will contribute to the maintenance, improvement, and broader distribution of the only active archive of acoustically tracked float data, one of the most valuable in situ windows into the ocean circulation. Innovative analysis algorithms developed or refined throughout this project will be openly shared with the community, contributing to the software infrastructure that supports scientific research. A new, highly optimized implementation of idealized numerical models for geophysical fluid dynamics will similarly be further developed, and distributed to community, during this project. The application of Big Data techniques to model output, allowing very large datasets to be reduced to much smaller numbers of parameters, will be particularly useful in future model/data intercomparisons. Finally, this project will support a graduate student, who will be trained in the application of Big Data techniques to analyzing numerical model output, as well as an early-career scientist.The approach will build on previous work in several important ways: (i) by making best use of available statistical information, thereby increasing the effective spatial resolution, perhaps dramatically; (ii) by avoiding potentially serious estimation errors arising from interactions of the four parameters; (iii) by allowing quantification of uncertainty; and (iv) by permitting the formal and systematic testing of a number of important physical hypothesis. A parallel analysis of a vastly larger ensemble of trajectories from a realistic model will allow quantification of uncertainties arising from data sparsity, and will enable the model's skill at reproducing observed Lagrangian features to be closely scrutinized. Finally, idealized numerical modeling and theory will provide the bridge to directly connect the observable features of Lagrangian trajectories with the underlying physics. The main intellectual contribution will be to answer a number of important questions, framed in detail herein, such as: Can the influence of surface quasigeostrophy, interior quasigeostrophy, and other processes be distinguished on the basis of their Lagrangian spectra? What does the Lagrangian spectral slope tell us about the nature of ocean turbulence? When and where is anisotropy necessary to effectively describe diffusivity? Does the spin parameter accurately capture the effect of coherent eddies on the background spectrum? These and other questions can be answered with the first global study of Lagrangian velocity spectra, with careful attention to quantifying errors and to establishing the correct physical interpretations of the controlling parameters in different regimes.