Julia Levin

A three-dimensional spectral element model for the solution of the hydrostatic primitive equations

We present a spectral element model to solve the hydrostatic primitive equations governing large-scale geophysical flows. The highlights of this new model include unstructured grids, dual h–p paths to convergence, and good scalability characteristics on present day parallel computers including Beowulf-class systems. The behavior of the model is assessed on three process-oriented test problems involving wave propagation, gravitational adjustment, and nonlinear flow rectification, respectively. The first of these test problems is a study of the convergence properties of the model when simulating the linear propagation of baroclinic Kelvin waves. The second is an intercomparison of spectral element and finite-difference model solutions to the adjustment of a density front in a straight channel. Finally, the third problem considers the comparison of model results to measurements obtained from a laboratory simulation of flow around a submarine canyon. The aforementioned tests demonstrate the good performance of the model in the idealized/processoriented limits. 2003 Elsevier Science B.V. All rights reserved.

Spatiotemporal path planning in strong, dynamic, uncertain currents

This work addresses mission planning for autonomous underwater gliders based on predictions of an uncertain, time-varying current field. Glider submersibles are highly sensitive to prevailing currents so mission planners must account for ocean tides and eddies. Previous work in variable-current path planning assumes that current predictions are perfect, but in practice these forecasts may be inaccurate. Here we evaluate plan fragility using empirical tests on historical ocean forecasts for which followup data is available. We present methods for glider path planning and control in a time-varying current field. A case study scenario in the Southern California Bight uses current predictions drawn from the Regional Ocean Monitoring System (ROMS).

Chaotic Advection in an Archipelago

Abstract Techniques from dynamical systems theory have been applied to study horizontal stirring of fluid in the Philippine Archipelago. The authors’ analysis is based on velocity fields produced by two high-resolution (3 and 6 km) numerical models. Particular attention is paid to identifying robust surface flow patterns and associating them with dominant Lagrangian coherent structures (LCSs). A recurrent wind-driven dipole in the lee of the coastline is considered in detail. The associated LCSs form a template for stirring, exchange, and biological transport in and around the dipole. Chaotic advection is argued to provide a relevant framework for interpreting mesoscale horizontal stirring processes in an archipelago as a whole. Implications for the formation of filaments, the production of tracer variance, and the scale at which stirring leads to mixing are discussed in connection with an observed temperature record.

An Adjoint Sensitivity Study of Buoyancy- and Wind-Driven Circulation on the New Jersey Inner Shelf

Adjoint sensitivity analysis is used to study the New York Bight circulation for three idealized situations: an unforced buoyant river plume, and upwelling and downwelling wind forcing. A derivation of adjoint sensitivity is presented that clarifies how the method simultaneously addresses initial, boundary, and forcing sensitivities. Considerations of interpretation and appropriate definitions of sensitivity scalar indices are discussed. The adjoint method identifies the oceanic conditions and forcing that are ‘‘dynamically upstream’’ to a region or feature of interest, as well as the relative roles of the prior ocean state, forcing, and dynamical influences. To illustrate the method, which is quite general, the authors consider coastal sea surface temperature (SST) variability and define the adjoint scalar index as the temporal‐spatial mean squared SST anomaly on a segment of the New Jersey coast at the conclusion of a 3-day period. In the absence of wind, surface temperature advection dominates the SST anomaly with two sources of surface water identified. Downwelling winds amplify upstream advective influence. Sensitivity to temperature is separated into direct advection and the dynamic effect on density stratification and mixing. For upwelling conditions, this decomposition shows that coastal SST is controlled by both advection from the south and subsurface, but above the 5-m depth, and temperature-related density stratification between 5 and 15 m to 10 km offshore. By identifying the timing and location of ocean conditions crucial to subsequent prediction of specific circulation features, the adjoint sensitivity method has application to quantitative evaluation of observational sampling strategies.

The Inverse Ocean Modeling System. Part II: Applications

The Inverse Ocean Modeling (IOM) System is a modular system for constructing and running weakconstraint four-dimensional variational data assimilation (W4DVAR) for any linear or nonlinear functionally smooth dynamical model and observing array. The IOM has been applied to four ocean models with widely varying characteristics. The Primitive Equations Z-coordinate-Harmonic Analysis of Tides (PEZHAT) and the Regional Ocean Modeling System (ROMS) are three-dimensional, primitive equations models while the Advanced Circulation model in 2D (ADCIRC-2D) and Spectral Element Ocean Model in 2D (SEOM-2D) are shallow-water models belonging to the general finite-element family. These models, in conjunction with the IOM, have been used to investigate a wide variety of scientific phenomena including tidal, mesoscale, and wind-driven circulation. In all cases, the assimilation of data using the IOM provides a better estimate of the ocean state than the model alone.

A Spectral Finite-Volume Method for the Shallow Water Equations

A spectral finite-volume (SFV) method is proposed for the numerical solution of the shallow water equations. This is the first phase in the development of a layered (isopycnal) ocean model. Its target applications include, in particular, the simulation of the wind-driven oceanic circulation in geometrically complex basins where layer outcropping and/or isopycnal‐bathymetry intersection must be handled explicitly. The present formulation is geometrically flexible and can extend accuracy to arbitrary high order with no change to the basic algorithm. A flux-corrected transport (FCT) algorithm ensures the stability of the computations in regions of vanishing layer thickness and in areas where the flow features are underresolved. The spatial discretization is based on a two-level grid: a globally unstructured elemental grid and a locally structured grid consisting of N 3 N quadrilateral cells within each element. The numerical solution is continuous within each element but discontinuous across elements; the discontinuity is resolved by upwinding along characteristics. The accuracy and convergence rate of the SFV method are verified on two linearized problems amenable to analytical solution; the SFV solution exhibits a convergence order of N 1 1 for smooth solutions. The FCT portion of the model is tested by simulating the formation of an oblique hydraulic jump in a supercritical channel flow. The model is then applied to simulate, in reduced-gravity mode, the double-gyre and wind-driven upper-ocean circulations in a square basin. Finally, the previous experiment is repeated in the North Atlantic basin to illustrate the application of the model in a realistic geometry.

Interannual variability of the surface summertime eastward jet in the South China Sea

The summertime eastward jet (SEJ) located around 12°N, 110°E–113°E, as the offshore extension of the Vietnam coastal current, is an important feature of the South China Sea (SCS) surface circulation in boreal summer. Analysis of satellite-derived sea level and sea surface wind data during 1992–2012 reveals pronounced interannual variations in its surface strength (SSEJ) and latitudinal position (YSEJ). In most of these years, the JAS (July, August, and September)-mean SSEJ fluctuates between 0.17 and 0.55 m s−1, while YSEJ shifts between 10.7°N and 14.3°N. These variations of the SEJ are predominantly contributed from the geostrophic current component that is linked to a meridional dipole pattern of sea level variations. This sea level dipole pattern is primarily induced by local wind changes within the SCS associated with the El Nino-Southern Oscillation (ENSO). Enhanced (weakened) southwest monsoon at the developing (decaying) stage of an El Nino event causes a stronger (weaker) SEJ located south (north) of its mean position. Remote wind forcing from the tropical Pacific can also affect the sea level in the SCS via energy transmission through the Philippine archipelago, but its effect on the SEJ is small. The impact of the oceanic internal variability, such as eddy-current interaction, is assessed using an ocean general circulation model (OGCM). Such impact can lead to considerable year-to-year changes of sea level and the SEJ, equivalent to ∼20% of the observed variation. This implies the complexity and prediction difficulty of the upper ocean circulation in this region.

Multi-scale geophysical modeling using the spectral element method

The spectral element method offers distinct advantages for geophysical simulations, including geometric flexibility, accuracy and scalability. Developers of atmospheric and oceanic models are capitalizing on these properties to create new models that can accurately and effectively simulate multi-scale flows in complex geometries.

Four-Dimensional Variational Assimilation of Satellite Temperature and Sea Level Data in the Coastal Ocean and Adjacent Deep Sea

Incremental, Strong constraint, 4-dimensional variational data assimilation is used to initialize operational forecast models of mesoscale ocean circulation in continental shelf and associated boundary current regimes. In the East Australia Current and the Mid-Atlantic Bight, data assimilation in the deep ocean adjacent to the shelf imposes the influence of remote-ocean forcing on coastal dynamics. Observations assimilated are satellite surface temperature (SST), satellite altimeter sea level anomalies (SLA), and subsurface temperature and salinity from ships, autonomous underwater vehicles and/or profiling floats. The models use boundary data from operational basin-scale circulation models and weather forecast meteorological forcing. Control variables of the data assimilation are the initial conditions of each assimilation window, and the model trajectory through each interval is deemed the best-estimate analysis for initializing the subsequent forecast. We evaluate model skill from a large set of multi-day forecasts starting from different initial mesoscale states. Forecast skill is enhanced, and uncertainty reduced, when empirical statistical subsurface pseudo-observations and/or so-called balance constraints are used to augment surface satellite data.

Examining the Accuracy of GlobCurrent Upper Ocean Velocity Data Products on the Northwestern Atlantic Shelf

This study provides a regional coastal ocean assessment of global upper ocean current data developed by the GlobCurrent (GC) project. These gridded data synthesize multiple satellite altimeter and wind model inputs to estimate both Geostrophic and Ekman-layer velocities. While the GC product was mostly devised and intended for open ocean studies, the present objective is to assess whether its data quality nearer the coast is suitable for other applications. The key ground truth sources are long-term mean and time series observations on the Northwestern Atlantic (NWA) shelf derived from Acoustic Doppler Current Profilers (ADCP) and high frequency (HF) radar networks in both the Mid-Atlantic Bight (MAB) and the Gulf of Maine (GoM). Results indicate that mean geostrophic currents across the MAB and the offshore GoM agree to roughly 10% in speed and 10 degree in direction with the in situ depth-averaged currents, with correlation levels of 0.5–0.8 at seasonal and longer time scales. Interior GoM comparisons at 5 coastal buoys show much less agreement. One likely source of GoM error is shown to be the GC mean dynamic topography near the coast. Comparison to near-surface MAB HF radar current measurements on the MAB shelf shows significant GC data improvement when including the surface Ekman term. Overall, the study results imply that application of GlobCurrent data may prove useful in coastal seas with broad continental shelves such as the MAB or Scotian shelf, but that large inaccuracies inside the GoM diminish its utility there.