A Parameter-Free Spectral Clustering Approach to Coherent Structure Detection in Geophysical Flows

Abstract

In Lagrangian dynamics, the detection of coherent clusters can help understand the organization of transport by identifying regions with coherent trajectory patterns. Many clustering algorithms, however, rely on user-input parameters, requiring a priori knowledge about the flow and making the outcome subjective. Building on the conventional spectral clustering method of Hadjighasem et al (2016), a new parameter-free spectral clustering approach is developed that automatically identifies parameters and does not require any user-input choices. A noise-based metric for quantifying the coherence of the resulting coherent clusters is also introduced. The parameter-free spectral clustering is applied to two benchmark analytical flows, the Bickley Jet and the asymmetric Duffing oscillator, and to a realistic, numerically-generated oceanic coastal flow. In the latter case, the identified model-based clusters are tested using observed trajectories of real drifters. In all examples, our approach succeeded in performing the partition of the domain into coherent clusters with minimal inter-cluster similarity and maximum intra-cluster similarity. For the coastal flow, the resulting coherent clusters are qualitatively similar over the same phase of the tide on different days and even different years, whereas coherent clusters for the opposite tidal phase are qualitatively different.

Uncertainty Quantification of Trajectory Clustering Applied to Ocean Ensemble Forecasts

“…We highlighted in the previous section how the similarity radius σ is closely related to the sparsification threshold used by Hadjighasem et al [2016]. While the sparsification threshold selection was mentioned in [Hadjighasem et al, 2016], the clustering results are highly sensitive to this parameter [Filippi et al, 2020], and we now address this sensitivity.…”

“…During the summer months, the region experiences a mean westward surface current that reaches velocities of 15 cm s −1 [Rypina et al, 2016]. The drifter deployment experiments targeting predicted coherent structures [Filippi et al, 2020], presented in Section 5.2, took place around the 2.5 km 2 uninhabited island of Nomans Land, south of Martha's Vineyard. The channel between the two islands has a width of approximately 5 km and an average depth of 10 m.…”

“…The model is used to forecast the three-dimensional velocity field for the coastal region near Martha's Vineyard, an island located south of Cape Cod, Massachusetts, USA. Trajectories from drifters deployed [Filippi et al, 2020] for the corresponding day are then compared to the cluster behaviors. Section 5.1 presents characteristics of the Martha's Vineyard region, the model used to forecast the velocity field, and the results of the clustering uncertainty quantification analysis applied to the ensemble forecast.…”

“…We used the MIT Multidisciplinary Simulation, Estimation, and Assimilation Systems (MIT-MSEAS) primitive equation ocean modeling system [Haley and Lermusiaux, 2010;Haley Jr et al, 2015] to compute ocean surface velocity forecasts in the Martha's Vineyard coastal region during August 2018. The modeling system provided forecasts of the ocean state variable fields (three-dimensional velocity, temperature, salinity, and sea-surface height) every hour, with a spatial resolution of 200 m. More details about the model forecast initialization, tidal forcing, atmospheric flux forcing, and CTD data assimilation can be found in [Serra et al, 2020;Filippi et al, 2020]. The deterministic two-way nesting ocean forecast initialized from the estimated ocean state conditions at a particular time is referred to as the central forecast, and ensemble forecasts were initialized using Error Subspace Statistical Estimation procedures [Lermusiaux, 2002].…”

“…Few studies, however, have used Lagrangian methods to plan and execute field experiments [Haza et al, 2007[Haza et al, , 2010Serra et al, 2020]. The drifter-release experiment presented in [Filippi et al, 2020], whose drifter data is used in this paper, is one of the first experiments targeting coherent structures based on an a priori trajectory clustering obtained from forecast simulations.…”