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R. M. Samelson
and
E. D. Skyllingstad

Abstract

A numerical simulation is analyzed that resolves the full range of motions from rotationally dominated, growing baroclinic waves to quasi-isotropic, three-dimensional shear instabilities. The results confirm a 40-yr-old prediction, made by B. Hoskins and F. Bretherton, that frontogenetic collapse of cross-frontal spatial scales, driven by baroclinic-wave deformation fields, will continue to the Kelvin–Helmholtz (K–H) turbulent transition. This process of frontal collapse followed by K–H transition provides a mechanism for spontaneous loss of balance in an initially geostrophic flow, and a direct, spectrally nonlocal pathway for downscale energy transfer that is phenomenologically distinct from traditional concepts of turbulent cascades and can contribute substantially to total kinetic energy dissipation. These results, which neglect surface drag and several other potentially relevant atmospheric processes, would suggest that the turbulence associated with collapsing fronts in the atmosphere can extend upward from the surface through roughly one-third of the troposphere.

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R. M. Samelson
and
S. J. Lentz

Abstract

The horizontal momentum balance in the marine atmospheric boundary layer during the Coastal Ocean Dynamics Experiment (CODE) is analyzed, using meteorological data from an array of surface moorings. Previous studies have indicated the presence of orographically generated mesoscale features that are induced by strong southward flow around Point Arena. The present analysis demonstrates that during periods of strong southward flow, the cross-shore momentum equation is dominated by a balance between the ageostrophic acceleration associated with the flow curvature around Point Arena, and the cross-shore pressure gradient, while the along-shore momentum equation is dominated by a balance between vertical stress divergence and alongshore pressure gradient. These balances are consistent with results from a shallow water model of the marine layer. The calculations provide evidence for orographic modification of the horizontal structure of the boundary layer under a broader range of southward flow conditions than had been indicated by previous studies.

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J. Pedlosky
and
R. M. Samelson

Abstract

A recently developed nonlinear inviscid model of the equatorial undercurrent is coupled to wind-driven surface layer. Wind stress drives a poleward Ekman flow, causing equatorial divergence of surface layer transport. This divergence is balanced by upwelling of fluid supplied by zonal convergence of the undercurrent. In this manner, the imposed wind stress controls the zonal structure of the undercurrent transport. The meridional structure of the undercurrent is determined from the undercurrent transport, the thermocline structure outside the undercurrent, and conservation of potential vorticity and Bernoulli function by the inviscid undercurrent. Solutions are presented for two zonal profiles of zonal wind stress. For westward wind stress increasing linearly westward, eastward transport increases nearly linearly westward. For westward wind stress with a midbasin maximum, eastward transport has a maximum just west of the basin middle, and there is recirculation along the equator. Solutions are also presented for uncoupled models with several layers and with a deep constant potential vorticity layer.

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R. M. Samelson
and
Geoffrey K. Vallis

Abstract

A simple friction and diffusion scheme is proposed for use with the time-dependent planetary geostrophic equations, which in their proper asymptotic form cannot be solved in a closed basin. The resulting set of equations admits boundary conditions of no-normal flow and no-normal heat flux at all rigid boundaries, is amenable to efficient numerical solution, and may be solved with small heat (and salt) diffusivities. The scheme is formally a minor modification of several others that have recently been proposed but differs in significant details. Friction is represented by linear drag in the horizontal momentum equations, while the hydrostatic balance is retained exactly. The Laplacian vertical and horizontal heat (and salt) diffusion are supplemented by biharmonic horizontal diffusion. The latter is necessary in order that the smoothness of the solution can be maintained up to and along the boundary, which is particularly important because the no-normal-flow condition is enforced as a differential equation that must be solved along the boundary. The equations support a frictional western boundary current that is nearly adiabatic.

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Sangil Kim
,
R. M. Samelson
, and
Chris Snyder

Abstract

Estimates of three components of an uncertainty budget for a coastal ocean model in a wind-forced regime are made based on numerical simulations. The budget components behave differently in the shelf regime, inshore of the 200-m isobath, and the slope-interior regime, between the 200-m isobath and a fixed longitude (126°W) that is roughly 150 km offshore. The first of the three budget components is an estimate of the uncertainty in the ocean state given only a known history of wind stress forcing, with errors in the wind forcing estimated from differences between operational analyses. It is found that, over the continental shelf, the response to wind forcing is sufficiently strong and deterministic that significant skill in estimating shelf circulation can be achieved with knowledge only of the wind forcing, and no ocean data, for wind fields with these estimated errors. The second involves initial condition error and its influence on uncertainty, including both error growth with time from well-known initial conditions and error decay with time from poorly known initial conditions but with well-known wind forcing. The third component is that of boundary condition error and its influence on the interior solutions, including the dependence of that influence on the specific location along the boundary of the boundary condition error. Boundary condition errors with amplitude comparable to the root-mean-square variability at the boundary lead eventually to errors equal to the root-mean-square variability in the slope-interior regime, and somewhat smaller errors in the shelf regime. Covariance estimates based on differences of the wind-forced solutions from the ensemble mean are not dramatically different from those based on the full fields, and do not show strong state dependence.

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Sangil Kim
,
R. M. Samelson
, and
Chris Snyder

Abstract

The predictability of coastal ocean circulation over the central Oregon shelf, a region of strong wind-driven currents and variable topography, is studied using ensembles of 50-day primitive equation ocean model simulations with realistic topography, simplified lateral boundary conditions, and forcing from both idealized and observed wind time series representative of the summer upwelling season. The main focus is on the balance, relevant to practical predictability, between deterministic response to known or well-predicted forcing, uncertainty in initial conditions, and sensitivity to instabilities and topographic interactions. Large ensemble and single-simulation variances are found downstream of topographic features, associated with transitions between along-isobath and cross-isobath flow, which are in turn related both to the time-integrated amplitude of upwelling-favorable wind forcing and to the formation of small-scale eddies. Simulated predictability experiments are conducted and model forecasts are verified by standard statistics including anomaly correlation coefficient, and root-mean-square error. A new variant of relative entropy, the forecast relative entropy, is introduced to quantify the predictive information content in the forecast ensemble, relative to the initial ensemble. The results suggest that, even under conditions of relatively weak wind forcing, the deterministic response is stronger than instability growth over the 3–7-day forecast intervals considered here. Consequently, important elements of the coastal circulation should be accessible to predictive, dynamical forecasts on the nominal 7-day predictability time scale of the atmospheric forcing, provided that sufficiently accurate initializations are available. These results on predictability are consistent with inferences drawn from recent modeling studies of coastal ocean circulation along the central Oregon shelf, and should have general validity for other, similar regions.

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Jeffrey Shaman
,
R. M. Samelson
, and
Eli Tziperman

Abstract

This paper presents a methodology for performing complex wavenumber ray tracing in which both wave trajectory and amplitude are calculated. This ray-tracing framework is first derived using a scaling in which the imaginary wavenumber component is assumed to be much smaller than the real wavenumber component. The approach, based on perturbation methods, is strictly valid when this scaling condition is met. The framework is then used to trace stationary barotropic Rossby waves in a number of settings. First, ray-traced Rossby wave amplitude is validated in a simple, idealized system for which exact solutions can be calculated. Complex wavenumber ray tracing is then applied to both solid-body rotation on a sphere and observed climatological upper-tropospheric fields. These ray-tracing solutions are compared with similarly forced solutions of the linearized barotropic vorticity equation (LBVE). Both real and complex wavenumber ray tracings follow trajectories matched by LBVE solutions. Complex wavenumber ray tracings on observed two-dimensional zonally asymmetric atmospheric fields are found to follow trajectories distinct from real wavenumber Rossby waves. For example, complex wavenumber ray tracings initiated over the eastern equatorial Pacific Ocean during boreal summer propagate northward and northeastward into the subtropics over the Atlantic Ocean, as well as southeastward into the Southern Hemisphere. Similarly initiated real wavenumber ray tracings remain within the deep tropics and propagate westward. These complex wavenumber Rossby wave trajectories and ray amplitudes are generally consistent with LBVE solutions, which indicates this methodology can identify Rossby wave effects distinct from traditional real wavenumber tracings.

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Jeffrey Shaman
,
R. M. Samelson
, and
Eric Skyllingstad

Abstract

The intraseasonal variability of turbulent surface heat fluxes over the Gulf Stream extension and subtropical mode water regions of the North Atlantic, and long-term trends in these fluxes, are explored using NCEP–NCAR reanalysis. Wintertime sensible and latent heat fluxes from these surface waters are characterized by episodic high flux events due to cold air outbreaks from North America. Up to 60% of the November–March (NDJFM) total sensible heat flux and 45% of latent heat flux occurs on these high flux days. On average 41% (34%) of the total NDJFM sensible (latent) heat flux takes place during just 17% (20%) of the days. Over the last 60 years, seasonal NDJFM sensible and latent heat fluxes over the Climate Variability and Predictability (CLIVAR) Mode Water Dynamic Experiment (CLIMODE) region have increased owing to an increased number of high flux event days. The increased storm frequency has altered average wintertime temperature conditions in the region, producing colder surface air conditions over the North American eastern seaboard and Labrador Sea and warmer temperatures over the Sargasso Sea. These temperature changes have increased low-level vertical wind shear and baroclinicity along the North Atlantic storm track over the last 60 years and may further favor the trend of increasing storm frequency over the Gulf Stream extension and adjacent region.

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R. M. Samelson
,
M. G. Schlax
, and
D. B. Chelton
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R. M. Samelson
,
M. G. Schlax
, and
D. B. Chelton

Abstract

It is shown that the life cycles of nonlinear mesoscale eddies, a major component of low-frequency ocean physical variability, have a characteristic structure that differs fundamentally from that which would be expected on the basis of classical interpretations of ocean eddy evolution in terms of mean flow instability and equilibration followed by frictional, radiative, or barotropic decay, or of vortex merger dynamics in quasigeostrophic turbulent cascades. Further, it is found that these life cycles can be accurately modeled in terms of the large-amplitude excursions of a stochastic process. These conclusions, which apply in the corresponding global-mean context, follow from the examination of ensemble-mean and standard deviation time series of normalized eddy amplitude from an automated eddy identification and tracking analysis of a nearly two decade–merged satellite altimeter record of global sea surface height (SSH). The resulting series are found to have several striking and unexpected characteristics, including time-reversal symmetry and approximate self-similarity. Consistent results are obtained from a similar analysis of a 7-yr record of global SSH from a numerical ocean circulation model. The basic qualitative and quantitative statistical properties of these series can be remarkably well reproduced with an extremely simple stochastic model, in which the SSH increments between successive time points are random numbers, and the eddy life cycles are represented by excursions exceeding a given threshold. The stochastic model is found also to predict accurately the empirical autocorrelation structure of the underlying observed SSH field itself, when the autocorrelations are computed along long planetary (Rossby) wave characteristics.

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