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J. A. Barth, J. S. Allen, and P. A. Newberger

Abstract

As part of a program to improve understanding of the dynamics of the complicated, vigorous eddy and jet flow fields recently observed over the continental shelf and slope, we investigate the potential of intermediate models for use in both process and data assimilation studies of these flows. Intermediate models incorporate physics simpler than that contained in the full primitive equations yet more complete than in the quasi-geostrophic equations, and are capable of representing subinertial flows over O(1) bottom topographic variations and/or with O(1) isopycnal slopes. In addition, intermediate models dynamically filter out high-frequency gravity- inertial motions leading, potentially, to higher computational efficiency and well-posed limited area forecast/hindcast models. Initial studies focus on single layer flows on an f-plane with a free surface, governed by the shallow-water equations. In Part I, various intermediate models are formulated and their accuracy assessed by comparing some exact nonlinear analytical solutions that exist for the shallow-water equations with corresponding analytical solutions of the intermediate models. Here in Part II, an extensive set of numerical finite-difference solutions to initial-value problems in doubly periodic domains (to isolate model differences from the influence of boundary condition implementation on solid walls) is used to determine the accuracy of various intermediate models by comparing their predictions with those of a shallow-water equation model that uses a potential enstrophy and energy conserving numerical scheme (SWE). Intermediate model results are also contrasted with those from a quasi-geostrophic (QG) model. The intermediate models considered are based on the geostrophic momentum (GM) approximation, the derivation of Salmon utilizing Hamilton's principle (HP), a geostrophic vorticity (GV) approximation, a combination of the quasi-geostrophic momentum and full continuity equations (IM), the linear balance equations (LBE), the balance equations (BE), the related balance-type (HBE, BEM, NBE) and modified linear balance equations (LQBE), and on Lynch's slow equations in their original form (SE) and in a modified form (MSE). In addition, a semi-implicit version (SEMI) of the shallow-water equations, which numerically filters high-frequency motions, is included in the study. The basic initial-value problem used to test the various intermediate models involves sinusoidal flow over a symmetric Gaussian-shaped bottom topographic feature. Comparisons are made for a range of the relevant dimensionless model parameters including the strength of the flow (as measured by the Rossby number), the square of the ratio of a characteristic horizontal length scale to the Rossby radius of deformation, and the height of the topographic feature. A second initial-value problem involves the evolution of a rotating elliptical vortex over both flat and variable bottom topography. Results show that in cases with low local Rossby number flow, but with large topographic height, most of the intermediate models are substantially more accurate than QG. Even for flows with O(1) local Rossby numbers, some of the intermediate models continue to give excellent results. Specifically, BE, BEM and SEMI consistently do the best in the comparisons. Although the relative ordering of the remaining models is somewhat parameter-dependent, in general the next most accurate models are MSE and LQBE followed by HP and NBE. These are followed in quality by GV and GM while the remaining models, HBE, IM and LBE, perform least accurately for the range of parameters studied. Generally, intermediate models that have an integral invariant corresponding to conservation of potential enstrophy do better than those without, with the best results coming from models which have this property and a nonlinear balance equation.

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J. S. Allen, J. A. Barth, and P. A. Newberger

Abstract

The study of intermediate models for barotropic continental shelf and slope flow fields initiated in Parts I and II is continued. The objective is to investigate the possible use of intermediate models for process and data assimilation studies of nonlinear mesoscale eddy and jet current fields over the continental shelf and slope. Intermediate models contain physics between that in the primitive equations and that in the quasi-geostrophic equations and are capable of representing subinertial frequency motion over the O(1) topographic variations typical of the continental slope while filtering out high-frequency gravity–inertial waves. We concentrate on the application of intermediate models to the f-plane shallow-water equations. The accuracy of several intermediate models is evaluated here by a comparison of numerical finite-difference solutions with those of the primitive shallow-water equations (SWE) and with those of the quasi-geostrophic equations (QG) for flow in a periodic channel. The intermediate models that we consider are based on the balance equations (BE), the balance equations derived from momentum equations (BEM), the potential vorticity conserving linear balance equations (LQBE), the hybrid balance equations (HBE), the near balance equation (NBE), a geostrophic vorticity (GV) approximation, the geostrophic momentum (GM) approximation, and the quasi-geostrophic momentum and full continuity equations (IM). The periodic channel provides a basic geometry for the study of physical flow processes over the continental shelf and slope. Wall boundary conditions are formulated for the intermediate models and implemented in the numerical finite-difference approximations. The ability of intermediate models to represent linear ageostrophic coastally trapped waves, i.e., Kelvin and continental shelf waves, is verified by numerical experiments. The results of numerical solution intercomparisons for initial-value problems involving O(1) topographic variations are as follows. For flow at small local Rossby number |εL| < 0.2, where εL is given by the magnitude of the vorticity divided by f, all of the intermediate models do well, while the QG model does poorly. For flows with larger values of |εL|, e.g., |εL| ≈ 0.5, the performance of the different intermediate models varies. BEM and BE consistently give extremely accurate solutions while the solutions from LQBE are almost as good. The other models are substantially less accurate with errors generally increasing in the order NBE, HBE, GV, GM, IM. The QG solution always has the largest errors. Consistent with the results from the studies in Part II in a doubly periodic domain, the balance equations BE and BEM, followed closely by LQBE, appear to be the most accurate intermediate models.

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J. S. Allen, J. A. Barth, and P. A. Newberger

Abstract

Motivated by the general objective of pursuing oceanographic process and data assimilation studies of the complex, nonlinear eddy and jet current fields observed over the continental shelf and slope off the west coast of the United States, we investigate the use of intermediate models for that purpose. Intermediate models contain physics between that in the primitive equations and that in the quasigeostrophic equations and are capable of representing subinertial frequency motion over the O(1) topographic variations typical of the continental slope, while filtering out high-frequency gravity-inertial waves. As an initial step, we compare and evaluate several intermediate models applied to the f-plane shallow-water equations for flows over topography. The accuracy and utility of the intermediate models are assessed by a comparison of exact analytical and numerical solutions with those of the primitive shallow-water equations (SWE) and with those of the quasi-geostrophic equations (QG). The intermediate models that we consider are based on the geostrophic momentum (GM) approximation, the derivation of Salmon (1983) utilizing Hamilton's principle (HP), a geostrophic vorticity (GV) approximation, the quasi-geostrophic momentum and full continuity equations (IM), the linear balance equations (LBE), the balance equations (BE), the related balance-type (HBE, BEM, NBE) and modified linear balance equations (LQBE), the slow equations (SE) of Lynch (1989), and the modified slow equations (MSE). In Part I, we discuss the intermediate models and develop formulations that are suitable for numerical solution in physical coordinates for use in Parts II and III. We investigate the capability of the intermediate models to represent linear ageostrophic coastally trapped waves, i.e., Kelvin and continental shelf waves, and demonstrate that they do so with accuracy consistent with standard linear low-frequency approximations. We also assess the accuracy of the models by a comparison of exact nonlinear analytical solutions to the SWE for steady flow in an elliptic paraboloid and for unsteady motion of elliptical vortices in a circular paraboloid with corresponding analytical solutions to the intermediate models and to QG. General results from the exact solution comparisons include the following. Many of the intermediate models are capable of producing more accurate solutions than QG over a range of Rossby numbers 0 < ε < 1. In some cases, the intermediate models provide accurate approximate solutions where QG is not applicable and fails to give a relevant solution. Considerable parameter-dependent variation in quality exists, however, among the different intermediate models. For the particular problems considered here, BE, HBE, BEM, NBE, and MSE reproduce the exact results of the SWE while LBE and LQBE give the same approximation as QG. The accuracy of the models is typically in the order GV, GM, IM, HP, and QG, with GV most accurate and IM and HP sometimes less accurate than QG.

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Anthony R. Kirincich, Steven J. Lentz, and John A. Barth

Abstract

Recent work by documents offshore transport in the inner shelf due to a wave-driven return flow associated with the Hasselmann wave stress (the Stokes–Coriolis force). This analysis is extended using observations from the central Oregon coast to identify the wave-driven return flow present and quantify the potential bias of wind-driven across-shelf exchange by unresolved wave-driven circulation. Using acoustic Doppler current profiler (ADCP) measurements at six stations, each in water depths of 13–15 m, observed depth-averaged, across-shelf velocities were generally correlated with theoretical estimates of the proposed return flow. During times of minimal wind forcing, across-shelf velocity profiles were vertically sheared, with stronger velocities near the top of the measured portion of the water column, and increased in magnitude with increasing significant wave height, consistent with circulation due to the Hasselmann wave stress. Yet velocity magnitudes and vertical shears were stronger than that predicted by linear wave theory, and more similar to the stratified “summer” velocity profiles described by S. Lentz et al. Additionally, substantial temporal and spatial variability of the wave-driven return flow was found, potentially due to changing wind and wave conditions as well as local bathymetric variability. Despite the wave-driven circulation found, subtracting estimates of the return flow from the observed across-shelf velocity had no significant effect on estimates of the across-shelf exchange due to along-shelf wind forcing at these water depths along the Oregon coast during summer.

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T. M. Dillon, J. A. Barth, A. Y. Erofeev, G. H. May, and H. W. Wijesekera

Abstract

A new high-frequency turbulence measuring instrument, MicroSoar, has been developed, tested, and used to make scalar variance dissipation rate measurements. MicroSoar was mounted on the undercarriage of SeaSoar, a depth-programmable winged platform, and towed by a ship, at speeds up to 7 kt, in a depth range of the sea surface to 120 m. Sensors carried by MicroSoar were a fast thermistor, a pressure sensor, a microscale capillary conductivity sensor, and a three-axis accelerometer. With appropriate assumptions about the local TS relation, measurements of microscale conductivity fluctuations can often be used to directly determine temperature variance dissipation rate (χ T), the Cox number (C x), and the scalar diathermal turbulent diffusivity (K T). Compared to conventional quasi-free-fall tethered vertically profiling instruments, MicroSoar's major advantage lies in its ability to sample large fluid volumes and large geographic areas in a short time, and to provide, rapidly and simply, two-dimensional (horizontal–vertical) representations of the distribution of oceanic mixing rates.

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R. Kipp Shearman, John A. Barth, J. S. Allen, and Robert L. Haney

Abstract

Several diagnoses of three-dimensional circulation, using density and velocity data from a high-resolution, upper-ocean SeaSoar and acoustic Doppler current profiler (ADCP) survey of a cyclonic jet meander and adjacent cyclonic eddy containing high Rossby number flow, are compared. The Q-vector form of the quasigeostrophic omega equation, two omega equations derived from iterated geostrophic intermediate models, an omega equation derived from the balance equations, and a vertical velocity diagnostic using a primitive equation model in conjunction with digital filtering are used to diagnose vertical and horizontal velocity fields. The results demonstrate the importance of the gradient wind balance in flow with strong curvature (high Rossby number). Horizontal velocities diagnosed from the intermediate models (the iterated geostrophic models and the balance equations), which include dynamics between those of quasigeostrophy and the primitive equations, are significantly reduced (enhanced) in comparison with the geostrophic velocities in regions of strong cyclonic (anticyclonic) curvature, consistent with gradient wind balance. The intermediate model relative vorticity fields are functionally related to the geostrophic relative vorticity field; anticyclonic vorticity is enhanced and cyclonic vorticity is reduced. The iterated geostrophic, balance equation and quasigeostrophic vertical velocity fields are similar in spatial pattern and scale, but the iterated geostrophic (and, to a lesser degree, the balance equation) vertical velocity is reduced in amplitude compared with the quasigeostrophic vertical velocity. This reduction is consistent with gradient wind balance, and is due to a reduction in the forcing of the omega equation through the geostrophic advection of ageostrophic relative vorticity. The vertical velocity diagnosed using a primitive equation model and a digital filtering technique also exhibits reduced magnitude in comparison with the quasigeostrophic field. A method to diagnose the gradient wind from a given dynamic height field has been developed. This technique is useful for the analysis of horizontal velocity in the presence of strong flow curvature. Observations of the nondivergent ageostrophic velocity field measured by the ADCP compare closely with the diagnosed gradient wind ageostrophic velocity.

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Peter R. Oke, J. S. Allen, R. N. Miller, G. D. Egbert, J. A. Austin, J. A. Barth, T. J. Boyd, P. M. Kosro, and M. D. Levine

Abstract

Sixty-day simulations of the subinertial continental shelf circulation off Oregon are performed for a hindcast study of summer 1999. Model results are compared with in situ currents, high-frequency radar–derived surface currents, and hydrographic measurements obtained from an array of moored instruments and field surveys. The correlations between observed and modeled alongshore currents and temperatures in water depths of 50 m are in excess of 0.8. A study designed to test the model's sensitivity to different initial stratification, surface forcing, domain size, and river forcing demonstrates that surface heating is important, and that the model results are sensitive to initial stratification. An objective criterion for assessing the skill of a model simulation relative to a control simulation is outlined, providing an objective means for identifying the best model simulation. The model–data comparisons demonstrate that temperature fluctuations off Newport are primarily in response to surface heating and that subsurface density fluctuations are controlled by the wind-forced circulation through salinity. Experiments with river forcing indicate that, in the vicinity of Newport, the Columbia River plume is typically greater than 15 km from the coast and is confined to the top few meters of the water column. Additionally, the model–data comparisons suggest that the strongest upwelling occurs to the north of Newport where the continental shelf is relatively narrow and uniform in the alongshore direction. Part II of this study investigates the modeled three-dimensional circulation and dynamical balances.

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M. S. Spydell, S. H. Suanda, D. J. Grimes, J. Becherer, J. M. Mcsweeney, C. Chickadel, M. Moulton, J. Thomson, J. Lerczak, J. Barth, J. Macmahan, J. Colosi, R. Romeiser, A. F. Waterhouse, J. Calantoni, and Falk Feddersen

Abstract

Off the central California coast near Pt. Sal, a large-amplitude internal bore was observed for 20 h over 10 km cross shore, or 100–10-m water depth (D), and 30 km along coast by remote sensing, 39 in situ moorings, ship surveys, and drifters. The bore is associated with steep isotherm displacements representing a significant fraction of D. Observations were used to estimate bore arrival time t B, thickness h, and bore and nonbore (ambient) temperature difference ΔT, leading to reduced gravity g′. Bore speeds c, estimated from mapped t B, varied from 0.25 to 0.1 m s−1 from D = 50 to 10 m. The h varied from 5 to 35 m, generally decreased with D, and varied regionally along isobath. The bore ΔT varied from 0.75° to 2.15°C. Bore evolution was interpreted from the perspective of a two-layer gravity current. Gravity current speeds U, estimated from the local bore h and g′, compared well to observed bore speeds throughout its cross-shore propagation. Linear internal wave speeds based on various stratification estimates result in larger errors. On average bore thickness h = D/2, with regional variation, suggesting energy saturation. From 50- to 10-m depths, observed bore speeds compared well to saturated gravity current speeds and energetics that depend only on water depth and shelf-wide mean g′. This suggests that this internal bore is the internal wave analog to a saturated surfzone surface gravity bore. Along-coast variations in prebore stratification explain variations in bore properties. Near Pt. Sal, bore Doppler shifting by barotropic currents is observed.

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C. A. Barth, R. W. Sanders, G. E. Thomas, G. J. Rottman, D. W. Rusch, R. J. Thomas, G. H. Mount, G. M. Lawrence, J. M. Zawodny, R. A. West, and J. London
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Russ E. Davis, Lynne D. Talley, Dean Roemmich, W. Brechner Owens, Daniel L. Rudnick, John Toole, Robert Weller, Michael J. McPhaden, and John A. Barth

Abstract

The history of over 100 years of observing the ocean is reviewed. The evolution of particular classes of ocean measurements (e.g., shipboard hydrography, moorings, and drifting floats) are summarized along with some of the discoveries and dynamical understanding they made possible. By the 1970s, isolated and “expedition” observational approaches were evolving into experimental campaigns that covered large ocean areas and addressed multiscale phenomena using diverse instrumental suites and associated modeling and analysis teams. The Mid-Ocean Dynamics Experiment (MODE) addressed mesoscale “eddies” and their interaction with larger-scale currents using new ocean modeling and experiment design techniques and a suite of developing observational methods. Following MODE, new instrument networks were established to study processes that dominated ocean behavior in different regions. The Tropical Ocean Global Atmosphere program gathered multiyear time series in the tropical Pacific to understand, and eventually predict, evolution of coupled ocean–atmosphere phenomena like El Niño–Southern Oscillation (ENSO). The World Ocean Circulation Experiment (WOCE) sought to quantify ocean transport throughout the global ocean using temperature, salinity, and other tracer measurements along with fewer direct velocity measurements with floats and moorings. Western and eastern boundary currents attracted comprehensive measurements, and various coastal regions, each with its unique scientific and societally important phenomena, became home to regional observing systems. Today, the trend toward networked observing arrays of many instrument types continues to be a productive way to understand and predict large-scale ocean phenomena.

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