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  • Author or Editor: D. L. Hartmann x
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Eric D. Maloney
and
Dennis L. Hartmann

Abstract

Low-level barotropic dynamics may help to explain the modulation of eastern and western North Pacific tropical cyclones by the Madden–Julian oscillation (MJO) during Northern Hemisphere summer. The MJO is characterized by alternating periods of westerly and easterly 850-mb zonal wind anomalies across the tropical Pacific Ocean. When MJO 850-mb wind anomalies are westerly, small-scale, slow-moving eddies grow through barotropic eddy kinetic energy (EKE) conversion from the mean flow. These growing eddies, together with strong surface convergence, 850-mb cyclonic shear, and high mean sea surface temperatures, create a favorable environment for tropical cyclone formation. Periods of strong MJO easterlies over the Pacific are characterized by lesser EKE and negligible eddy growth by barotropic conversion.

The term − u2 u /∂x is a leading contributor to low-level barotropic EKE conversion during MJO westerly periods across the Pacific, indicating the importance of zonal variations in the westerly jet for producing concentrations of eddy energy. This mechanism can be described as wave accumulation associated with variations of the low-level zonal flow. The conversion term − uυ u /∂y contributes a smaller portion of the total conversion over the eastern Pacific, but is of comparable importance to − u2 u /∂x during westerly MJO events in the western Pacific.

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Dennis L. Hartmann
and
Eric D. Maloney

Abstract

A stochastic barotropic model linearized about the 850-mb flow is used to investigate the relationship between wind variations associated with the Madden–Julian oscillation (MJO) and eddy kinetic energy variations in the Tropics. Such a model is successful in predicting the observed location of eddy kinetic energy maxima during the westerly phase of the MJO and the suppression of eddy activity during the easterly phase of the MJO. The concentration of eddy energy during the westerly phase results from the strong east–west and north–south gradients of the large-scale wind fields. The model shows that barotropic wave propagation and wave mean–flow interaction tend to concentrate small-scale Rossby wave energy in regions of convergence, which may be an important mechanism for organizing convection into tropical cyclones. The structure and barotropic energetics of the wave activity are similar to those observed, but the modeled eddies are smaller in scale and do not move westward as do the observed eddies. The eddies that dominate the observed correlations are heavily modified by convection, but barotropic processes can explain the localization of eddy energy by the MJO that is observed.

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Mark D. Borges
and
Dennis L. Hartmann

Abstract

An eigenvalue analysis of a divergent barotropic model on a sphere is extended to the formulation of a global optimization problem, whose solution selects an initial perturbation that evolves into the most energetic structure at a finite time interval, τ. The evolution of this perturbation is obtained from companion linear and nonlinear global spectral time-dependent models, and the optimization prediction of perturbation size at time τ is verified. Two zonally asymmetric flows defined by time-mean ECMWF global 300-mb analyses during winter 1985/86 are used to illustrate the application and insights provided by the optimization problem.

The dependence of the optimal perturbations on the parameter τ is examined. The optimal perturbations become increasingly localized as τ is decreased to periods on the order of three days. The initial growth rates of these perturbations greatly exceed that of the most unstable normal mode, and also exceed the growth rate of a disturbance with maximum projection onto the most unstable mode (i.e., the adjoint structure). Furthermore, the development of the optimal perturbations in the nonlinear model is in reasonable agreement with the available observations. The optimal perturbations may thus be more important than either the eigenmode or adjoint structure for determining the stability and expected behavior of anomalies to some time-mean flows.

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Carlos R. Mechoso
,
Dennis L. Hartmann
, and
John D. Farrara

Abstract

The climatology and interannual variability of wave–mean flow interaction in the Southern Hemisphere (20–80°S, 0–55 km) is described for the winter months of June–September based on a sample of four years, 1979–82. The stratospheric jet stream shifts downward and poleward over the course of the winter in response to seasonal variations in thermal forcing. The shift occurs at different times in different years, however, so that the months of July and August show substantial interannual variability of monthly mean zonal winds. The poleward and downward shift of the jet axis in an individual year is usually abrupt and occurs in association with a burst of upwardly propagating planetary waves. The driving of the mean flow in the stratosphere generally has a dipolar structure with easterly accelerations near 40°S and westerly accelerations in polar latitudes. The structure of the wave driving is consistent with the structure of the observed mean flow accelerations.

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D. L. Hartmann
,
R. Buizza
, and
T. N. Palmer

Abstract

The scale dependence of rapidly growing perturbations is investigated by studying the dominant singular vectors of T21 and T42 versions of the ECMWF model, which show the most linear energy growth in a 3-day period. A spectral filter is applied to the optimization process to determine which spatial scales are most effective in promoting energy growth. When the initial perturbation is confined to the top half of the total spherical harmonic wavenumber spectrum (high wavenumber end), the growth rates and final structures of the disturbances are changed very little from the case in which all wavenumbers are included. These results indicate that synoptic waves that become fully developed in a period of three days can arise from initial perturbations that are entirely contained at subsynoptic scales. Rapid growth is associated with initial perturbations that consist of smaller spatial scales concentrated near the effective steering level. The linear evolution of these initial perturbations in a highly complex basic flow leads to disturbances of synoptic scale that extend through most of the depth of the troposphere. Growth rates are approximately doubled when the model resolution is increased from T21 to T42, which is consistent with greater growth being associated with smaller spatial scales. When the initial perturbation is confined to the lower half of the total wavenumber spectrum, which describes the larger horizontal scales, the growth rates are significantly reduced and the initial and final structures are very different from the case in which all wavenumbers are included. These low wavenumber perturbations tend to be more barotropic in structure and in growth characteristics. As expected from their linear growth rates, when the low-wavenumber perturbations are inserted in the T63 forecast model, they grow more slowly and result in less forecast dispersion than the high wavenumber perturbations.

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D. L. Hartmann
,
T. N. Palmer
, and
R. Buizza

Abstract

The linear structures that produce the most in situ energy growth in the lower stratosphere for realistic wintertime flows are investigated using T21 and T42 calculations with the ECMWF 19-level forecast model. Significant growth is found for relatively large scale structures that grow by propagating from the outer edges of the vortex into the strong jet features of the lower-stratospheric flow. The growth is greater when the polar vortex is more asymmetric and contains localized jet structures. If the linear structures are properly phased, they can induce strong nonlinear interactions with the polar vortex, both for Northern Hemisphere and Southern Hemisphere flow conditions, even when the initial amplitudes are small. Large extensions from the main polar vortex that are peeled off during wave-breaking events give rise to a separate class of rapidly growing disturbances that may hasten the mixing of these vortex extensions.

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