A. D. Kirwan

Blending HF radar and model velocities in Monterey Bay through normal mode analysis

Nowcasts of the surface velocity field in Monterey Bay are made for the period August 1–9, 1994, using HF radar observations blended with results from a primitive equation model. A spectral method called normal mode analysis was used. Objective spatial and temporal filtering were performed, and stream function, velocity potential, relative vorticity, and horizontal divergence were calculated over the domain. This type of nowcasting permits global spectral analysis of mode amplitudes, calculation of enstrophy, and additional analyses using tools like empirical orthogonal functions. The nowcasts reported here include open boundary flow information from the numerical model. Nowcasts using no open boundary flow information, however, still provide excellent results for locations within the observation footprint. This method, then, is useful for filtering high-resolution data like HF radar observations, even when open boundary flow information is unavailable. Also, since the nowcast velocity gradient fields were much less noisy than the observations, this may be an effective method for preconditioning high-resolution observation sets for assimilation into a numerical model.

The Loop Current and adjacent rings delineated by Lagrangian analysis of the near-surface flow

Evolution of the Loop Current and the adjacent mesoscale rings was investigated over a 20-day period, starting June 1, 1998. Model sea-surface height and near-surface velocity fields from the Colorado University Princeton Ocean Model of the Gulf of Mexico were used along with drifter data in the study. A Lagrangian analysis provided detailed information about ring interaction and revealed features that were not apparent in the Eulerian picture. During the observation period, a new ring was formed in the meander of the Loop Current and a large anticyclonic ring to the west was cleaved by a cyclonic eddy. The coherent structures were identified in the Lagrangian framework by means of material curves (manifolds) that act as their boundaries. Concurrent drifter trajectories were in qualitative agreement with the results of the Lagrangian analysis.

Can general circulation models be assessed and their output enhanced with drifter data

Drifter data from the Gulf of Mexico are used to assess and enhance the output of a primitive equation general circulation model. The analysis is made in a 450 km × 450 km open subdomain encompassing a Loop Current ring. The model velocity field is compared with position data from four drifters at the drogue depth of 50 m using geometrical orthogonal functions (GOF). An Eulerian velocity field is reconstructed from the model velocity field and drifter velocities. This reconstructed velocity improves 8-day numerical trajectories relative to the model field by at least an order of magnitude, as quantified by two Lagrangian error metrics referenced to the real drifter paths. An Eulerian metric that compares the two fields, however, does not exceed 7% for the 20-day assessment period. Thus the drifter data may be reproduced with modest impact on the model velocity. Enhancement of the model velocity field is determined by two tests: the ability of the GOF velocity field to (1) improve the forecast of drifter positions using only a posteriori data and (2) improve the forecast of withheld drifter data. Using a posteriori data, the 20-day temporal mean of the position error is improved for all drifters by 87–89% for 6-hour and 26–38% for 30-hour forecasts. For 6 days, a withheld drifter is 35–40 km from a drifter whose velocity is used in the reconstructed velocity field. The temporal mean of the position error during this period is improved by 20% for 6-hour and 26% for 30-hour forecasts.

On the Transport of Buoyant Coastal Plumes

Abstract The role of discharge conditions and shelf geometry on the transport of coastal plumes is studied with a fully nonlinear, primitive equation hydrodynamic model. The physical setting is an estuarine channel with a small discharge Rossby number. By simulating different discharge magnitudes, buoyant plumes are shown to be succinctly described by a simple coastal front model. Three results emerge from the model analysis. First, the plume transport is given by T = γ0(g′ph2/2f ), where γ0 is a parameter dependent on the ratio of the front and the plume widths, g′p is the plume reduced gravity, h is the plume maximum depth, and f is the Coriolis parameter. Second, this model links the plume transport directly to upstream river conditions with T = γQr, where Qr is the river outflow and γ is a parameter that relates to entrainment, the geometry of the plume front and shelf slope, and the fraction of freshwater carried downshelf. Third, these equations reduce to analytic results previously established for ...

Predictability, uncertainty, and hyperbolicity in the ocean

Lagrangian predictability of an ocean flow is studied using ideas from dynamical systems theory. Finite-time analogues of invariant manifolds and attractors are utilized to parse the flow field into regions with distinct advective fates or destinations. These analogues take the form of inflowing and outflowing material curves emanating from hyperbolic trajectories. Applications are made to the Gulf of Mexico using a high resolution, data assimilating, primitive equation hydrodynamic model.

Reconstructing basin-scale Eulerian velocity fields from simulated drifter data

Abstract A single-layer, reduced-gravity, double-gyre primitive equation model in a 2000 km × 2000 km square domain is used to test the accuracy and sensitivity of time-dependent Eulerian velocity fields reconstructed from numerically generated drifter trajectories and climatology. The goal is to determine how much Lagrangian data is needed to capture the Eulerian velocity field within a specified accuracy. The Eulerian fields are found by projecting, on an analytic set of divergence-free basis functions, drifter data launched in the active western half of the basin supplemented by climatology in the eastern domain. The time-dependent coefficients are evaluated by least squares minimization and the reconstructed fields are compared to the original model output. The authors find that the accuracy of the reconstructed fields depends critically on the spatial coverage of the drifter observations. With good spatial coverage, the technique allows accurate Eulerian reconstructions with under 200 drifters deploy...

Ocean processes underlying surface clustering

Ageostrophic ocean processes such as frontogenesis, submesoscale mixed-layer instabilities, shelf break fronts, and topographic interactions on the continental shelf produce surface-divergent flows that affect buoyant material over time. This study examines the ocean processes leading to clustering, i.e., the increase of material density over time, on the ocean surface. The time series of divergence along a material trajectory, the Lagrangian divergence (LD), is the flow property driving clustering. To understand the impacts of various ocean processes on LD, numerical ocean model simulations at different resolutions are analyzed. Although the relevant processes differ, patterns in clustering evolution from the deep ocean and the continental shelf bear similarities. Smaller-scale ocean features are associated with stronger surface divergence, and the surface material clustering is initially dominated by these features. Over time, the effect of these small-scale features becomes bounded, as material traverses small-scale regions of both positive and negative divergence. Lower-frequency flow phenomena, however, continue the clustering. As a result, clustering evolves from initial small-scale to larger-scale patterns.

Filtering noise from oceanographic data with some applications for the Kara and Black Seas

Abstract If a reconstruction process is reduced to the solution of ill-posed algebraic systems, we suggest several procedures to improve the accuracy of reconstruction from noisy and irregular data. These procedures transform ill-posed equations to their well-posed analogies, thereby reducing both the contribution of noise to the equation system and the condition number of the system matrix. One of the techniques, the so-called “regularizing filter”, can be applied to observation samples of limited size when the ratio of the number of estimated field parameters to the number of field observations and noise to signal ratio are under 0.5–0.6 and 4–5, respectively. Furthermore, the filter is constructed without any preliminary knowledge of low-order noise statistics. The regularizing filter combined with a conventional function fitting procedure is illustrated through linear mapping scalar oceanographic fields, such as the surface temperature in the Black Sea observed from the NOAA-11, SiO2 in the Kara Sea, cesium and chlorophyll in the Black Sea. Herein comparing our approach to optimal interpolation, generalized cross-validation and smoothing spline-interpolation is also given.

Clusters, deformation, and dilation: Diagnostics for material accumulation regions

Clusters of material at the ocean surface have been frequently observed. Such accumulations of material play an important role in a variety of applications, from biology to pollution mitigation. Identifying where clusters will form can aid in locating, for example, hotspots of biological activity or regions of high pollutant concentration. Here cluster strength is introduced as a new metric for defining clusters when all particle positions are known. To diagnose regions likely to contain clusters without the need to integrate millions of particle trajectories, we propose to use dilation, which quantifies area changes of Lagrangian patches. Material deformation is decomposed into dilation and area-preserving stretch processes to refine previous approaches based on finite-time Lyapunov exponents (FTLE) by splitting the FTLE into fundamental kinematic properties. The concepts are developed theoretically and illustrated in the context of a state-of-the-art data-assimilating predictive ocean model of the Gulf of Mexico. Regions of dilation less than one are shown to be much more likely (6 times more likely in the given example) to be visited by particles than those of dilation greater than one. While the relationship is nonlinear, dilation and cluster strength exhibit a fairly good correlation. In contrast, both stretch and Eulerian divergence are found to be uncorrelated with cluster strength. Thus, dilation maps can be used as guides for identifying cluster locations, while saving some of the computational cost of trajectory integrations.

Statistical properties of the surface velocity field in the northern Gulf of Mexico sampled by GLAD drifters

The Grand LAgrangian Deployment (GLAD) used multiscale sampling and GPS technology to observe time series of drifter positions with initial drifter separation of O(100 m) to O(10 km), and nominal 5 min sampling, during the summer and fall of 2012 in the northern Gulf of Mexico. Histograms of the velocity field and its statistical parameters are non-Gaussian; most are multimodal. The dominant periods for the surface velocity field are 1–2 days due to inertial oscillations, tides, and the sea breeze; 5–6 days due to wind forcing and submesoscale eddies; 9–10 days and two weeks or longer periods due to wind forcing and mesoscale variability, including the period of eddy rotation. The temporal e-folding scales of a fitted drifter velocity autocorrelation function are bimodal with time scales, 0.25–0.50 days and 0.9–1.4 days, and are the same order as the temporal e-folding scales of observed winds from nearby moored National Data Buoy Center stations. The Lagrangian integral time scales increase from coastal values of 8 h to offshore values of approximately 2 days with peak values of 3–4 days. The velocity variance is large, O(1)m2/s2, the surface velocity statistics are more anisotropic, and increased dispersion is observed at flow bifurcations. Horizontal diffusivity estimates are O(103)m2/s in coastal regions with weaker flow to O(105)m2/s in flow bifurcations, a strong jet, and during the passage of Hurricane Isaac. The Gulf of Mexico surface velocity statistics sampled by the GLAD drifters are a strong function of the feature sampled, topography, and wind forcing