Abstract. The basin-wide surface transport of tracers such as heat, nutrients and plastic in the North Atlantic Ocean is organized into large-scale flow structures such as the Western Boundary Current and the Subtropical and Subpolar gyres. Being able to identify these features from drifter data is important for studying tracer dispersal but also for detecting changes in the large-scale surface flow due to climate change. We propose a new and conceptually simple method to detect groups of trajectories with similar dynamical behaviour from drifter data using network theory and normalized cut spectral clustering. Our network is constructed from conditional bin-drifter probability distributions and naturally handles drifter trajectories with data gaps and different lifetimes. The eigenvalue problem of the respective Laplacian can be replaced by a singular value decomposition of a related sparse data matrix. The construction of this matrix scales with O(NM+Nτ) , where N is the number of particles, M the number of bins and τ the number of time steps. The concept behind our network construction is rooted in a particle's symbolic itinerary derived from its trajectory and a state space partition, which we incorporate in its most basic form by replacing a particle's itinerary by a probability distribution over symbols. We represent these distributions as the links of a bipartite graph, connecting particles and symbols. We apply our method to the periodically driven double-gyre flow and successfully identify well-known features. Exploiting the duality between particles and symbols defined by the bipartite graph, we demonstrate how a direct low-dimensional coarse definition of the clustering problem can still lead to relatively accurate results for the most dominant structures and resolve features down to scales much below the coarse graining scale. Our method also performs well in detecting structures with incomplete trajectory data, which we demonstrate for the double-gyre flow by randomly removing data points. We finally apply our method to a set of ocean drifter trajectories and present the first network-based clustering of the North Atlantic surface transport based on surface drifters, successfully detecting well-known regions such as the Subpolar and Subtropical gyres, the Western Boundary Current region and the Caribbean Sea.

中文翻译：

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使用源自符号行程的网络检测稀缺轨迹数据中的流动特征：在北大西洋表面漂流者的应用

摘要。北大西洋中示踪剂（例如热量、营养物质和塑料）的整个盆地表面传输被组织成大规模流动结构，例如西边界流和亚热带和亚极地环流。能够从漂流器数据中识别这些特征对于研究示踪剂扩散很重要，而且对于检测由于气候变化引起的大规模地表流量变化也很重要。我们提出了一种新的概念上简单的方法，使用网络理论和归一化切割谱聚类从漂移数据中检测具有相似动态行为的轨迹组。我们的网络由条件 bin-drifter 概率分布构建，并自然地处理具有数据间隙和不同生命周期的漂移轨迹。各个拉普拉斯算子的特征值问题可以用相关稀疏数据矩阵的奇异值分解来代替。该矩阵的构造与 O(NM+Nτ) 成比例，其中 N 是粒子数，M 是箱数，τ 是时间步长。我们网络构建背后的概念植根于从其轨迹和状态空间分区得出的粒子符号行程，我们通过用符号上的概率分布替换粒子的行程，以最基本的形式将其合并。我们将这些分布表示为二部图的链接，连接粒子和符号。我们将我们的方法应用于周期性驱动的双环流并成功识别出众所周知的特征。利用二部图定义的粒子和符号之间的二元性，我们展示了聚类问题的直接低维粗定义如何仍然可以为最主要的结构产生相对准确的结果，并将特征解析到远低于粗粒度尺度的尺度。我们的方法在检测具有不完整轨迹数据的结构方面也表现良好，我们通过随机删除数据点来证明双环流。我们最终将我们的方法应用于一组海洋漂流者轨迹，并提出了基于表面漂流者的第一个基于网络的北大西洋地面传输聚类，成功检测了众所周知的区域，如副极地和亚热带环流、西部边界流区域和加勒比海。