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

海洋是一种复杂的湍流流体，可以在传统的固定（欧拉）坐标系或移动（拉格朗日）参考系中进行研究，这些参考系遵循主要洋流。可以从拉格朗日数据测量的四个关键量是扩散率、拉格朗日积分时间尺度、自旋参数和谱斜率或（等效地）分形维数。前三个是积极感兴趣的海洋学社区，因为它们的相关性，以增加大规模的海洋和气候模式的海洋环流的保真度。第四个量，光谱斜率，可能同样重要，但它的值和它的意义在很大程度上是未经探索的，它还有待于在全球范围内进行检查。这些拉格朗日特性是许多重要假设的核心，但从数据中估计它们的困难是众所周知的，并导致突出的不确定性。如本文所示，这四个量是紧密相连的，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。这项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由拉格朗日特征制成的最高分辨率的地图，无论是在表面还是在深度。提高气候模型中海洋环流的真实性这一总体目标是一个具有重大社会意义的主题，因为它将加强适应和减缓气候变异的努力。更直接的是，该项目将有助于维护、改进和更广泛地传播声学跟踪浮子数据的唯一有效档案，这是了解海洋环流的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。一个新的，高度优化的实现地球物理流体动力学的理想化数值模型将同样进一步开发，并分发给社区，在这个项目。将大数据技术应用于模型输出，可以将非常大的数据集缩减为数量少得多的参数，这在未来的模型/数据相互比较中将特别有用。最后，该项目将支持一名研究生，他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建立在以前的工作基础上：（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，也许会显着提高;（ii）避免因四个参数的相互作用而可能产生的严重估计错误;（iii）允许量化不确定性;（iv）允许对一些重要的物理假设进行正式和系统的检验。从一个现实的模型的轨迹的一个更大的合奏的并行分析将允许量化的数据稀疏性所产生的不确定性，并将使模型的技能，在复制观察到的拉格朗日功能进行仔细检查。最后，理想化的数值模型和理论将提供桥梁，直接连接拉格朗日轨迹的可观测特征与基础物理。主要的智力贡献将是回答一些重要的问题，在这里详细框，如：表面准地转，内部准地转，和其他过程的影响可以区分的基础上，他们的拉格朗日谱？关于海洋湍流的本质，拉格朗日谱斜率告诉我们什么？何时何地各向异性是有效描述扩散率所必需的？自旋参数能准确地反映相干涡旋对背景光谱的影响吗？这些和其他问题可以回答的第一个全球性的研究拉格朗日速度谱，仔细注意量化误差，并建立正确的物理解释的控制参数在不同的制度。

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.