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P. Klein
and
J. Pedlosky

Abstract

The effect of three different parameterizations of dissipation on the nonlinear dynamics of unstable baroclinic waves is studied. The model is the two-layer f-plane model and the dynamics is quasigeostrophic. The dissipation mechanisms are 1) dissipation due to Ekman layers at the horizontal boundary surfaces, 2) the addition of interfacial Ekman friction, or 3) dissipation proportional to the perturbation potential vorticity.

We find, as anticipated by weakly nonlinear theory, a strong effect on the nonlinear amplitude dynamics for supercriticalities as large as four times the threshold value for instability. The use of interfacial friction or potential vorticity damping expunges the vacillating behavior common to the system with type 1 dissipation.

At high supercriticality a barotropic vacillation involving the mean flow and harmonics of the fundamental is superimposed on the basic baroclinic wave dynamics. Examination of the critical transition for the emergence of the barotropic oscillation reveals that the enhanced linear instability of the higher harmonics is responsible for the self-sustained vacillation.

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J. Pedlosky
and
P. Klein

Abstract

The nonlinear dynamics of a slightly unstable baroclinic wave is studied for a two-layer f-plane system in which the basic flow is strongly sheared in the horizontal direction. The basic flow is purely baroclinic, i.e., equal and opposite in each layer. In addition, the basic flow vanishes on the channel walls containing the flow. Weakly nonlinear theory predicts that for small supercriticality, the basic wave eigenfunction has the same horizontal structure as the basic flow although it is vertically barotropic. Moreover, weakly nonlinear theory predicts growth of the wave amplitudes, which is unrestrained by wave–mean flow interaction. This prediction is verified by direct numerical calculation. The numerical calculations further reveal the manner by which the wave eventually equilibrates. The strongly growing wave cascades energy to higher zonal harmonics. These harmonics alter the meridional structure of the fundamental that allows wave–mean flow interaction to operate, leading finally to equilibration. If the cascade to higher zonal wavenumbers is artificially blocked by truncating the numerical model to a single zonal wavenumber, equilibration artificially requires the annihilation of the basic shear.

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G. Lapeyre
and
P. Klein

Abstract

In this study, the relation between the interior and the surface dynamics for nonlinear baroclinically unstable flows is examined using the concepts of potential vorticity. First, it is demonstrated that baroclinic unstable flows present the property that the potential vorticity mesoscale and submesoscale anomalies in the ocean interior are strongly correlated to the surface density anomalies. Then, using the invertibility of potential vorticity, the dynamics are decomposed in terms of a solution forced by the three-dimensional (3D) potential vorticity and a solution forced by the surface boundary condition in density. It is found that, in the upper oceanic layers, the balanced flow induced only by potential vorticity is strongly anticorrelated with that induced only by the surface density with a dominance of the latter. The major consequence is that the 3D balanced motions can be determined from only the surface density and the characteristics of the basin-scale stratification by solving an elliptic equation. These properties allow for the possibility to reconstruct the 3D balanced velocity field of the upper layers from just the knowledge of the surface density by using a simpler model, that is, an “effective” surface quasigeostrophic model. All these results are validated through the examination of a primitive equation simulation reproducing the dynamics of the Antarctic Circumpolar Current.

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P. Klein
and
A. M. Treguier

Abstract

The dynamics of the mixed layer in the presence of an embedded geostrophic jet has been investigated using a simple 1½-layer model and a two-dimensional primitive equation model. The jet vorticity induces a spatial variability of the wind-driven inertial motions that can have some important consequences on the mixed-layer dynamics. With a steady wind stress parallel to the front, the main effect is the generation of steady upwellings and downwellings due to the divergence of the mean Ekman drift (as reported by Niiler). With a cross-front wind, however, a dramatic exponential amplification of the inertial oscillations caused by an inertial resonance mechanism is found: this mechanism can increase the inertial waves amplitude by a factor up to 10 within ten inertial periods. Competition between this resonance mechanism and the dispersion mechanisms (mainly the horizontal and vertical propagation of inertial waves) that can limit its effects has been assessed. A consequence of horizontal propagation is that energetic waves can propagate well away from the jet while continuing to absorb energy from the wind. Downward propagation disperses this energy to a depth of at least 500 m in a few days.

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P. Klein
and
A. M. Treguier

Abstract

No abstract available

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Cédric P. Chavanne
and
Patrice Klein

Abstract

A quasigeostrophic model is developed to diagnose the three-dimensional circulation, including the vertical velocity, in the upper ocean from high-resolution observations of sea surface height and buoyancy. The formulation for the adiabatic component departs from the classical surface quasigeostrophic framework considered before since it takes into account the stratification within the surface mixed layer that is usually much weaker than that in the ocean interior. To achieve this, the model approximates the ocean with two constant stratification layers: a finite-thickness surface layer (or the mixed layer) and an infinitely deep interior layer. It is shown that the leading-order adiabatic circulation is entirely determined if both the surface streamfunction and buoyancy anomalies are considered. The surface layer further includes a diabatic dynamical contribution. Parameterization of diabatic vertical velocities is based on their restoring impacts of the thermal wind balance that is perturbed by turbulent vertical mixing of momentum and buoyancy. The model skill in reproducing the three-dimensional circulation in the upper ocean from surface data is checked against the output of a high-resolution primitive equation numerical simulation.

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Jerome P. Charba
and
William H. Klein

All known long-term records of forecasting performance for different types of precipitation forecasts in the National Weather Service were examined for relative skill and secular trends in skill. The largest upward trends were achieved by local probability of precipitation (PoP) forecasts for the periods 24–36 h and 36–48 h after 0000 and 1200 GMT. Over the last 13 years, the skill of these forecasts has improved at an average rate of 7.2% per 10-year interval. Over the same period, improvement has been smaller in local PoP skill in the 12–24 h range (2.0% per 10 years) and in the accuracy of “Yes/No” forecasts of measurable precipitation. The overall trend in accuracy of centralized quantitative precipitation forecasts of ≥0.5 in and ≤1.0 in has been slightly upward at the 0–24 h range and strongly upward at the 24–48 h range. Most of the improvement in these forecasts has been achieved from the early 1970s to the present. Strong upward accuracy trends in all types of precipitation forecasts within the past eight years are attributed primarily to improvements in numerical and statistical centralized guidance forecasts.

The skill and accuracy of both measurable and quantitative precipitation forecasts is 35–55% greater during the cool season than during the warm season. Also, the secular rate of improvement of the cool season precipitation forecasts is 50–110% greater than that of the warm season. This seasonal difference in performance reflects the relative difficulty of forecasting predominantly stratiform precipitation of the cool season and convective precipitation of the warm season.

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Tommaso Benacchio
,
Warren P. O’Neill
, and
Rupert Klein

Abstract

A blended model for atmospheric flow simulations is introduced that enables seamless transition from fully compressible to pseudo-incompressible dynamics. The model equations are written in nonperturbation form and integrated using a well-balanced second-order finite-volume discretization. The semi-implicit scheme combines an explicit predictor for advection with elliptic corrections for the pressure field. Compressibility is implemented in the elliptic equations through a diagonal term. The compressible/pseudo-incompressible transition is realized by suitably weighting the term and provides a mechanism for removing unwanted acoustic imbalances in compressible runs.

As the gradient of the pressure is used instead of the Exner pressure in the momentum equation, the influence of perturbation pressure on buoyancy must be included to ensure thermodynamic consistency. With this effect included, the thermodynamically consistent model is equivalent to Durran’s original pseudo-incompressible model, which uses the Exner pressure.

Numerical experiments demonstrate quadratic convergence and competitive solution quality for several benchmarks. With the inclusion of an additional buoyancy term required for thermodynamic consistency, the “pρ formulation” of the pseudo-incompressible model closely reproduces the compressible results.

The proposed unified approach offers a framework for models that are largely free of the biases that can arise when different discretizations are used. With data assimilation applications in mind, the seamless compressible/pseudo-incompressible transition mechanism is also shown to enable the flattening of acoustic imbalances in initial data for which balanced pressure distributions are unknown.

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M.-I. Pujol
,
G. Dibarboure
,
P.-Y. Le Traon
, and
P. Klein

Abstract

An Ocean System Simulation Experiment is used to quantify the observing capability of the Surface Water and Ocean Topography (SWOT) mission and its contribution to higher-quality reconstructed sea level anomaly (SLA) fields using optimal interpolation. The paper focuses on the potential of SWOT for mesoscale observation (wavelengths larger than 100 km and time periods larger than 10 days) and its ability to replace or complement altimetry for classical mesoscale applications. For mesoscale variability, the wide swath from SWOT provides an unprecedented sampling capability. SWOT alone would enable the regional surface signal reconstruction as precisely as a four-altimeter constellation would, in regions where temporal sampling is optimum. For some specifics latitudes, where swath sampling is degraded, SWOT capabilities are reduced and show performances equivalent to the historical two-altimeter constellation. In this case, merging SWOT with the two-altimeter constellation stabilizes the global sampling and fully compensates the swath time sampling limitations. Benefits of SWOT measurement are more important within the swath. It would allow a precise local reconstruction of mesoscale structures. Errors of surface signal reconstruction within the swath represent less than 1% (SLA) to 5% (geostrophic velocities reconstruction) of the signal variance in a pessimistic roll error reduction. The errors are slightly reduced by merging swath measurements with the conventional nadir measurements.

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P. Y. Le Traon
,
P. Klein
,
Bach Lien Hua
, and
G. Dibarboure

Abstract

In high-eddy-energy regions, it is generally assumed that sea level wavenumber spectra compare well with quasigeostrophic (QG) turbulence models and that spectral slopes are close to the expected k −5 law. This issue is revisited here. Sea level wavenumber spectra in the Gulf Stream, Kuroshio, and Agulhas regions are estimated using the most recent altimeter datasets [the Ocean Topography Experiment (TOPEX)/Poseidon, Jason-1, the Environmental Satellite (Envisat), and the Geosat Follow-On]. The authors show that spectral slopes in the mesoscale band are significantly different from a k −5 law, in disagreement with the QG turbulence theory. However, they very closely follow a k −11/3 slope, which indicates that the surface quasigeostrophic theory (SQG) is a much better dynamical framework than the QG turbulence theory to describe the ocean surface dynamics. Because of the specific properties of the SQG theory, these results offer new perspectives for the analysis and interpretation of satellite data.

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