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NASA NTRS1984

The Influence of Synoptic Scales on Low-frequency Modes of Variability

Model analysis and predictablity studies using an equivalent barotropic empirical orthogonal function (EOF) model described in Schubert (1984b) are dicussed. An extensive set of 10-day forecasts was produced for the 12 component version of the model. Comparisons with observed data show apparently useful forecasts for individual winters. However, when averaged over 10 winters, the improvement over persistence was marginal and only one of the EOF's (resembling North Atlantic blocking) showed a statistically significant improvement. These results suggest the need for a more realistic model which includes shorter time scale baroclinic processes and spatial modes capable of efficiently representing the characteristic structures associated with baroclinic instability.

Schubert, S. D.↗

NASA NTRS1981

Barotropic instability of zonal flows

The barotropic instability of zonal flows due to infinitesimal normal-mode perturbations is considered, with the zonal flow assumed to be continuous and either monotonic or nonmonotonic and allowed to have one or more inflection points. A sufficient condition for instability is derived for this general flow profile that complements that of Arnol'd (1965), which restricted itself to the prediction of stability only.

Tung, K. K.↗

NASA NTRS1985

A statistical-dynamical study of empirically determined modes of atmospheric variability

The observed wintertime intraseasonal variability of the northern hemisphere midtropospheric circulation is analyzed within the framework of an equivalent barotropic model. The data set and the form of the eigenvalue/vector problem in the wave domain are described, and the statistical significance of the empirical orthogonal functions (EOFs) is discussed, and some selected modes are briefly described. The anomaly model and the transformation to the EOF domain are presented together with a discussion of the model coefficients and forcing term. The fitting procedure for the parameterized terms are described and the level of correspondence between the modelled and observed streamfunction tendencies as a function of the EOFs is examined. The stability of the time mean flow and other base states is investigated.

Schubert, S. D.↗

NASA NTRS1986

Vertical structure of the wind field during the Special Observing Period I of the Global Weather Experiment

The vertical structure of the global atmosphere is analyzed for selected periods of the Special Observing Period I (SOP-I) for the Global Weather Experiment (GWE). The analysis consists of projection of the stream-function and velocity potential at 200 and 850 mb on spherical harmonics and of the wind and height fields on the normal modes of a linearized form of the primitive equations for a basic state at rest. The kinematic vertical structure is discussed in terms of correlation coefficients of the 200 mb and 850 mb winds and analysis of the internal and external normal modes of the primitive equations. The reliability of the results is checked by applying the same analysis methods to data sets obtained from three different institutions: Geophysical Fluid Dynamics Laboratory (GFDL), European Center for Medium Range Weather Forecasting (ECMWF), and Goddard Laboratory for the Atmospheres (GLA). It is found that, on a global basis, vertically reversing circulations are as important as the equivalent barotropic structures. For the verticaly reversing components, the gravity and mixed Rossby-gravity modes have contributions of the same order of magnitude as those of the Rossby modes in tropical latitudes.

Paegle, J. N.↗

NASA NTRS1994

Low-frequency modes and nonbarotropic effects in pseudo-Newtonian accretion disks

A recently developed formalism is used to reexamine the question of the existence of hydrodynamical modes that pulsate with very low frequencies in the inner regions of accretion disks. The formalism is valid in an exact sense for the adiabatic pulsations of rotating Newtonian fluids that are generally nonbarotropic (such as those with 'nonadiabatic temperature gradients,' for example), and hence its application in the present context represents an improvement over previous analyses that are more approximate. The formalism is applied to thin non-self-gravitating disks, with the gravitational potential of the central source modified in the usual way in order to simulate relativistic effects. In the barotropic limit, the analyses indicate that in many cases nearly Keplerian disks exhibit nonaxisymmetric modes of pulsation that are trapped in the inner disk regions, with pulsation periods much longer than the dynamical timescale. These results are similar to those of earlier calculations that assume disks pulsate without changing the temperature distribution. A method is developed for including lowest order nonbarotropic effects. Previous analyses have been incapable of accurately treating the nonbarotropic regime. The application of the present method to the low-frequency modes reveals that, due to unexpected cancellations among terms, the nonbarotropic correction to the pusation frequency omega is only of order tilde-omega(sub BV exp 2) omega, where tilde-omega(sub BV) is the appropriate dimensionless Brunt-Vaisala frequency. This correction is much smaller than the expected correction of order tilde-omega(sub BV) Omega, where Omega is the rotation angular velocity. The important conclusion drawn from this is that nonbarotropic corrections are generally small and hence that low-frequency modes persist into the nonbarotropic regime. For disk temperatures appropriate to X-ray emission, the adiabatic frequencies of trapped modes are of the same order as the frequencies associated with quasi-periodic oscillations (QPOs) of certain low-mass X-ray binaries and other X-ray sources. It is suggested that further consideration be given to the possiblity that modulation of emission processes by these modes can explain at least some of the QPO phenomena.

Ipser, James R.↗

NASA NTRS1978

Solitary Rossby waves in zonal shear flows and their interactions

Interactions of long-wave solitons propagating in shear flows are described by a coupled pair of Korteweg-de Vries equations. The basic equation of motion for the analysis is the quasi-geostrophic forecast equation, and the interaction of two wave modes is studied. The solution for mode 1-mode 2 interaction of solitary waves in an asymmetric shear flow of a barotropic atmosphere with divergence is constructed. Streamline patterns for certain flows are obtained. An unsteady solitary wave solution for a modified Korteweg-de Vries equation is derived.

Redekopp, L. G.↗

NASA NTRS1982

Wave instability in the polar region of Venus

Infrared and radio observations of the upper cloud region of Venus indicate that the north polar region contains features of large thermal contrast. A cold collar, encompassing a region of temperature inversions, lies between latitudes of about 65 and 75 deg, and a pair of warm features, separated by about 180 deg of longitude and centered near 80 deg latitude, rotate about the pole with a period of about 2.9 days. It is shown that the cold temperatures associated with the inversions lead to an enhancement in the mean zonal wind in a localized area near the pole, and that this enhancement makes the mean flow barotropically unstable. Since data for this region are limited, a model for the thermal structure has been used for calculating growth times and phase periods of the unstable modes. Choosing model parameters to agree as closely as possible with available data, it has been determined that the rotating warm features are likely to be manifestations of barotropically unstable waves.

Elson, L. S.↗

NASA NTRS2002

Hawaii Ocean Mixing Experiment: Program Summary

It is becoming apparent that insufficient mixing occurs in the pelagic ocean to maintain the large scale thermohaline circulation. Observed mixing rates fall a factor of ten short of classical indices such as Munk's "Abyssal Recipe." The growing suspicion is that most of the mixing in the sea occurs near topography. Exciting recent observations by Polzin et al., among others, fuel this speculation. If topographic mixing is indeed important, it must be acknowledged that its geographic distribution, both laterally and vertically, is presently unknown. The vertical distribution of mixing plays a critical role in the Stommel Arons model of the ocean interior circulation. In recent numerical studies, Samelson demonstrates the extreme sensitivity of flow in the abyssal ocean to the spatial distribution of mixing. We propose to study the topographic mixing problem through an integrated program of modeling and observation. We focus on tidally forced mixing as the global energetics of this process have received (and are receiving) considerable study. Also, the well defined frequency of the forcing and the unique geometry of tidal scattering serve to focus the experiment design. The Hawaiian Ridge is selected as a study site. Strong interaction between the barotropic tide and the Ridge is known to take place. The goals of the Hawaiian Ocean Mixing Experiment (HOME) are to quantify the rate of tidal energy loss to mixing at the Ridge and to identify the mechanisms by which energy is lost and mixing generated. We are challenged to develop a sufficiently comprehensive picture that results can be generalized from Hawaii to the global ocean. To achieve these goals, investigators from five institutions have designed HOME, a program of historic data analysis, modeling and field observation. The Analysis and Modeling efforts support the design of the field experiments. As the program progresses, a global model of the barotropic (depth independent) tide, and two models of the baroclinic (depth varying) tide, all validated with near-Ridge data, will be applied, to reveal the mechanisms of tidal energy conversion along the Ridge, and allow spatial and temporal integration of the rate of conversion. Field experiments include a survey to identify "hot spots" of enhanced mixing and barotropic to baroclinic conversion, a Nearfield study identifying the dominant mechanisms responsible for topographic mixing, and a Farfield program which quantifies the barotropic energy flux convergence at the Ridge and the flux divergence associated with low mode baroclinic waves radiation. The difference is a measure of the tidal power available for mixing at the Ridge. Field work is planned from years 2000 through 2002, with analysis and modeling efforts extending through early 2006. If successful, HOME will yield an understanding of the dominant topographic mixing processes applicable throughout the global ocean. It will advance understanding of two central problems in ocean science, the maintenance of the abyssal stratification, and the dissipation of the tides. HOME data will be used to improve the parameterization of dissipation in models which presently assimilate TOPEX-POSEIDON observations. The improved understanding of the dynamics and spatial distribution of mixing processes will benefit future long-term programs such as CLIVAR.

Ray, Richard D.↗

NASA NTRS1990

Small error dynamics and the predictability of atmospheric flows

In this paper, linear small-error theory is applied to the study of weather predictability. A simple baroclinic shear model and a barotropic channel model with a localized jet are used as examples. It is shown that increase in error on synoptic forecast time scales is controlled by rapidly growing perturbations that are not of normal mode form. Unpredictable regimes are not necessarily associated with larger exponential growth rates than are relatively more predictable regimes. Model problems illustrating baroclinic and barotropic dynamics suggest that asymptotic measures of divergence in phase space, while applicable in the limit of infinite time, may not be appropriate over time intervals addressed by present synoptic forecast.

Farrell, Brian F.↗

NASA NTRS1985

A comparison of the bounded derivative and the normal mode initialization methods using real data

A bounded derivative initialization method (BDI) formerly used only in theoretical studies to balance gravitational wave influences is extended to a real world data set and the results are compared with those from a normal mode initialization (NMI). BDI proceeds by defining the characteristic scales of motion of interest and then constraining the time derivatives to match motions on a slow scale. A global barotropic model which considers orographic forcing is initialized by the scaled balance equations of the BDI scheme, which uses vorticity alone to achieve an initial balanced state. An external mode projector is employed to realize the NMI scheme, and five Machenhauer iterations reduce the total balance by four orders of magnitude. The initial states generated with both schemes are essentially equivalent, including the time evolution of a height field and divergence behavior being centered around regions of high orographic elevation.

Semazzi, F. H. M.↗

NASA NTRS1980

Topographic coupling of surface and internal Kelvin waves

An analysis is presented for computing the diffraction of barotropic Kelvin waves by a localized topographical irregularity on flat-bottom ocean with an arbitrary vertical stratification. It was shown that all baroclinic Kelvin waves will be generated downstream of the bump, with the first baroclinic mode having the largest amplitude. The Poincare waves predominate in the lowest modes, and are more directionally anisotropic. It was concluded that baroclinic Poincare waves radiating offshore from the bump topography could contribute to the internal wave field in the open ocean and provide an alternative mechanism to dissipate the barotropic tides.

Chao, S.-Y.↗

NASA NTRS1985

Midlatitude tropical interactions during winter

Pre-FGGE and FGGE/MONEX data are used to identify short term midlatitude tropical and longitudinal interactions during the winter monsoon. These interactions occur as cold surges, which develop over the East Asian continent and penetrate deep into the tropics with fast gravity wave speed. The observed interactions that occur after a surge include cyclogenesis and enhanced convection in the equatorial region, feedback from equatorial convection to midlatitude circulation systems, tropical east-west (Walker) circulations, and cross-equatorial influence. These interactions are also studied theoretically by analytical solutions of linearized shallow water equations. Response to transient forcing (monsoon surges) are mainly in Rossby and Kelvin modes. When the forcing time scale is short, significant gravity modes are also excited. The responses closely resemble observed winter monsoon flow. Responses to stationary forcing show that deep (barotropic) motions propagate energy away into high latitudes and that shallow (baroclinic) motions are trapped around the equator. It is shown that the barotropic teleconnection-type response to tropical sources found in previous numerical studies was due to the specified vertical wind shear and surface friction.

Chang, C. P.↗

NASA NTRS1987

A comparative study of rapidly and slowly rotating dynamical regimes in a terrestrial general circulation model

As a preliminary step in the development of a general circulation model for general planetary use, a simplified vesion of thef GISS Model I GCM has been run at various rotation periods to investigate differences between the dynamical regimes of rapidly and slowly rotating planets. To isolate the dynamical processes, the hydrologic cycle is suppressed and the atmosphere is forced with perpetual annual mean solar heating. All other parameters except the rotation period remain fixed at their terrestrial values. Experiments were conducted for rotation periods of 2/3, 1, 2, 4, 8, 16, 64 and 256 days. The results are in qualitative agreement with similar experiments carried out previously with other GCMs and with certain aspects of one Venus GCM simulation. As rotation rate decreases, the energetics shifts from baroclinc to quasi-barotropic when the Rossby radius of deformation reaches planetary scale. The Hadley cell expands poleward and replaces eddies as the primary mode of large-scale heat transport. Associated with this is a poleward shift of the baroclinic zone and jet stream and a reduction of the equator-pole temperature contrast. Midlatitude jet strength peaks at 8 days period, as does the weak positive equatorial zonal wind which occurs at upper levels at all rotation periods. Eddy momentum transport switches from poleward to equatorward at the same period. Tropospheric mean static stability generally increases in the tropics and decreases in midlatitudes as rotation rate decreases, but the global mean static stability is independent of rotation rate. The peak in the eddy kinetic energy spectrum shifts toward lower wavenumbers, reaching wavenumber 1 at a period of 8 days. Implications of these results for the dynamics of Venus and Titan are discussed. Specifically, it is suggested that the extent of low-level convection determines whether the Gierasch mechanism contributes significantly to equatorial superrotation on these planets.

Del Genio, Anthony D.↗

NASA NTRS2012

Twenty Years of Progress on Global Ocean Tides: The Impact of Satellite Altimetry

At the dawn of the era of high-precision altimetry, before the launch of TOPEX/Poseidon, ocean tides were properly viewed as a source of noise--tidal variations in ocean height would represent a very substantial fraction of what the altimeter measures, and would have to be accurately predicted and subtracted if altimetry were to achieve its potential for ocean and climate studies. But to the extent that the altimetry could be severely contaminated by tides, it also represented an unprecedented global-scale tidal data set. These new data, together with research stimulated by the need for accurate tidal corrections, led to a renaissance in tidal studies in the oceanographic community. In this paper we review contributions of altimetry to tidal science over the past 20 years, emphasizing recent progress. Mapping of tides has now been extended from the early focus on major constituents in the open ocean to include minor constituents, (e.g., long-period tides; non-linear tides in shelf waters, and in the open ocean), and into shallow and coastal waters. Global and spatially local estimates of tidal energy balance have been refined, and the role of internal tide conversion in dissipating barotropic tidal energy is now well established through modeling, altimetry, and in situ observations. However, energy budgets for internal tides, and the role of tidal dissipation in vertical ocean mixing remain controversial topics. Altimetry may contribute to resolving some of these important questions through improved mapping of low-mode internal tides. This area has advanced significantly in recent years, with several global maps now available, and progress on constraining temporally incoherent components. For the future, new applications of altimetry (e.g., in the coastal ocean, where barotropic tidal models remain inadequate), and new mission concepts (studies of the submesoscale with SWOT, which will require correction for internal tides) may bring us full circle, again pushing further development of tidal models as corrections.

Egbert, Gary↗

NASA NTRS1986

The structure, energetics and evolution of the dominant frequency-dependent three-dimensional atmospheric modes

The three-dimensional structure of the dominant modes of wintertime variability are examined, and the mode structures are determined by an EOF analysis of the coupled vertical mean and shear streamfunction fields for a wide range of time-scale classes. The time mean energy conversions are determined from a two-layer quasigeostrophic model. Lag-cross correlations between the dominant low-frequency modes tend to be small and/or symmetric about zero, the high frequency modes are found to show highly asymmetric sinusoidal cross correlation functions similar to traveling waves, and some intermediate and short-time scale modes exhibit correlations indicating an association with the decaying phases of blocking in the Pacific. It is suggested that the mean flow barotropic (baroclinic) instabilities are an important source of variance for some of the lowest (highest) fluctuations considered.

Schubert, S. D.↗

NASA NTRS1993

Instability at the winter stratopause: A mechanism for the 4-day wave

Studies using climatological fields in a three-dimensional stability model show unstable modes near the polar winter stratopause with periods near 4 days. The calculated modes exhibit equatorward momentum and heat fluxes near the stratopause, similar to characteristics of observed 4-day wave events, demonstrating that both baroclinic and barotropic processes are important for this instability. The baroclinic and barotropic components are considered separately by selectively removing either horizontal or vertical shear from the background flow. Although both situations reveal instability, growth rates are very slow; realistic growth rates occur only for climatological flows including both horizontal and vertical shears. Similar unstable, fast-moving waves are found near the polar stratopause for several winter months in both hemispheres.

Manney, G. L.↗

NASA NTRS1991

Planetary-scale waves in the Southern Hemisphere winter and early spring stratosphere - Stability analysis

A barotropic stability model linearized about a zonally symmetric flow is used to examine the stability characteristics of horizontal zonal-mean flow profiles representative of the Southern Hemisphere middle stratosphere during winter and early spring, with emphasis on periods when planetary wave growth appears confined to the stratosphere. Unstable modes of eastward-travelling waves 2 and 3 are found to have period sand spatial structures, similar to observations. Wave-2 and wave-3 momentum fluxes are similar in observations and model results and are consistent with the transfer of kinetic energy from the zonal-mean flow to the wave. When a barotropic model with a zonally symmetric basic flow is used, wave 3 is usually most unstable. Including a stationary wave 1 in the basic flow destabilizes both wave 2 and wave 3, but has little effect on their periods or spatial structures. The similarity between observed fields and model results in a number of cases when wave 2 appears to grow within the stratosphere suggests that in situ instabilities play a role in the evolution of the eastward-traveling wave-2 characteristic of the Southern Hemisphere winter and early spring stratosphere.

Manney, G. L.↗

NASA NTRS1983

Charney's problem for baroclinic instability applied to barotropic instability

If barotropically unstable easterly jets may be approximated by broken line profiles, it becomes possible to use the solutions of the Charney (1947) problem for baroclinic instabilithy in order to solve the barotropic problem. Results are presented for easterly jets having an arbitrary degree of symmetry, and it is noted that the convenient calculation obtained for the growth of both localized and normal mode perturbations is important in the study of monsoon depressions over India.

Lindzen, R. S.↗