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Nili Harnik

Abstract

This work examines the extent to which a few basic concepts that apply to plane waves, for example, the refraction of waves up the gradient of the index of refraction, apply to stratospheric planetary waves. This is done by studying the relation between group velocity (C g) and the wave activity velocity, which is defined as the Eliassen–Palm flux divided by the wave activity density (V a = F/A). It is shown that although in the limit of plane waves V a equals C g, the two velocities are not equal for stratospheric waves, because of reflection, tunneling, and superposition. The use of conservation of wave activity to understand the spatial variations of wave structure is explored. This is done by defining a wave activity packet as part of the wave that moves with V a. Integral lines of V a are then used to keep track of the wave packet location and volume. In the idealized case of an almost-plane wave, conservation of wave activity leads to variations in the amplitude of the wave when it is refracted by the slowly varying basic state. This effect is related to changes in wave packet volume. The wave activity packet framework is used to examine the importance of the “volume effect” for explaining the spatial variations of stratospheric waves.

The wave packet formulation is also used to study the evolution of a wave propagating from the troposphere to the stratosphere. It is shown that the consequence of the polar night jet being a leaky waveguide is that perturbations initially concentrate up into the waveguide and only later leak out to the equatorial region. This can explain the observed stratospheric wave life cycle of baroclinic growth followed by a barotropic stage. Finally, integral lines of V a are used to estimate vertical propagation timescales of an observed wave, and it is shown that this estimate is consistent with linear wave dynamics.

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Orli Lachmy and Nili Harnik

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A quasi-linear two-layer quasigeostrophic β-plane model of the interaction between a baroclinic jet and a single zonal wavenumber perturbation is used to study the mechanics leading to a wave amplitude bifurcation—in particular, the role of the critical surfaces in the upper-tropospheric jet flanks. The jet is forced by Newtonian heating toward a radiative equilibrium state, and Ekman damping is applied at the surface. When the typical horizontal scale is approximately the Rossby radius of deformation, the waves equilibrate at a finite amplitude that is comparable to the mean flow. This state is obtained as a result of a wave-induced temporary destabilization of the mean flow, during which the waves grow to their finite-equilibrium amplitude. When the typical horizontal scale is wider, the model also supports a state in which the waves equilibrate at negligible amplitudes. The transition from small to finite-amplitude waves, which occurs at weak instabilities, is abrupt as the parameters of the system are gradually varied, and in a certain range of parameter values both equilibrated states are supported.

The simple two-layer quasi-linear setting of the model allows a detailed examination of the temporary destabilization process inherent in the large-amplitude equilibration. As the waves grow they reduce the baroclinic growth by reducing the vertical shear of the mean flow, and reduce the barotropic decay by reducing the mean potential vorticity gradient at the inner sides of the upper-layer critical levels. Temporary destabilization occurs when the reduction in barotropic decay is larger than the reduction in baroclinic growth, leading to a larger total growth rate. Ekman friction and radiative damping are found to play a major role in sustaining the vertical shear of the mean flow and enabling the baroclinic growth to continue. By controlling the mean flow potential vorticity gradient near the critical level, the model evolution can be changed from one type of equilibration to the other.

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Judith Perlwitz and Nili Harnik

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Recent studies have pointed out the impact of the stratosphere on the troposphere by dynamic coupling. In the present paper, observational evidence for an effect of downward planetary wave reflection in the stratosphere on Northern Hemisphere tropospheric waves is given by combining statistical and dynamical diagnostics. A time-lagged singular value decomposition analysis is applied to daily tropospheric and stratospheric height fields recomposed for a single zonal wavenumber. A wave geometry diagnostic for wave propagation characteristics that separates the index of refraction into vertical and meridional components is used to diagnose the occurrence of reflecting surfaces. For zonal wavenumber 1, this study suggests that there is one characteristic configuration of the stratospheric jet that reflects waves back into the troposphere—when the polar night jet peaks in the high-latitude midstratosphere. This configuration is related to the formation of a reflecting surface for vertical propagation at around 5 hPa as a result of the vertical curvature of the zonal-mean wind and a clear meridional waveguide in the lower to middle stratosphere that channels the reflected wave activity to the high-latitude troposphere.

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Judith Perlwitz and Nili Harnik

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Wave and zonal mean features of the downward dynamic coupling between the stratosphere and troposphere are compared by applying a time-lagged singular value decomposition analysis to Northern Hemisphere height fields decomposed into zonal mean and its deviations. It is found that both zonal and wave components contribute to the downward interaction, with zonal wave 1 (due to reflection) dominating on the short time scale (up to 12 days) and the zonal mean (due to wave–mean-flow interaction) dominating on the longer time scale. It is further shown that the two processes dominate during different years, depending on the state of the stratosphere. Winters characterized by a basic state that is reflective for wave 1 show a strong relationship between stratospheric and tropospheric wave-1 fields when the stratosphere is leading and show no significant correlations in the zonal mean fields. On the other hand, winters characterized by a stratospheric state that does not reflect waves show a strong relationship only between stratospheric and tropospheric zonal mean fields. This study suggests that there are two types of stratospheric winter states, characterized by different downward dynamic interaction. In one state, most of the wave activity gets deposited in the stratosphere, resulting in strong wave–mean-flow interaction, while in the other state, wave activity is reflected back down to the troposphere, primarily affecting the structure of tropospheric planetary waves.

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Ori Adam and Nili Harnik

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The interaction of midlatitude eddies and the thermally driven Hadley circulation is studied using an idealized shallow-water model on the rotating sphere. The contributions of the annually averaged differential heating, vertical advection of momentum from a stationary boundary layer, and the gross effect of eddies, parameterized by Rayleigh damping, including a hemispherically asymmetric damping, are examined at steady state.

The study finds that the relative dominance of eddies, as quantified by the local Rossby number, is predicted by an effective macroturbulent Hadley circulation Prandtl number Pr. In addition, viscous solutions of the Hadley circulation width and strength, subtropical jet amplitude, and equator-to-pole temperature difference scale as deviations from the respective inviscid solutions.

Semianalytic solutions for the steady circulation are derived in the limit of weak eddy dominance (small Pr) as deviations from the respective inviscid solutions. These solutions follow a three-region paradigm: weak temperature gradient at the ascending branch of the Hadley circulation, monotonically decreasing angular momentum at the descending branch, and modified radiative–convective equilibrium at the extratropics. Using the three-region solutions, scaling relations found in the full solutions are reproduced analytically. The weak eddy-dominance solutions diverge from the full solutions as Pr increases and may become invalid for Pr > 1 due to the breakdown of the three-region global circulation structure.

The qualitative predictions of the response of the Hadley circulation to heating based on the weak eddy-dominance solutions and Pr are in agreement with the findings of more complex models and the observed atmosphere.

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Orli Lachmy and Nili Harnik

Abstract

An abrupt transition from a merged jet regime to a subtropical jet regime is analyzed using a two-layer modified quasigeostrophic (QG) spherical model. Unlike the common version of QG models, this model includes advection of the zonal mean momentum by the ageostrophic mean meridional circulation, allowing for a relatively realistic momentum balance in the tropics and subtropics. The merged jet is a single jet inside the Ferrel cell created by a merging of the subtropical and eddy-driven jets, and the subtropical jet is a mainly thermally driven jet at the Hadley cell edge. The maintenance of each type of jet depends on the dominant baroclinic modes. In the merged jet regime, the spectrum is dominated by intermediate-scale (wavenumbers 4–6) fast waves at the midlatitudes that grow close to the jet maximum. In the subtropical jet regime, the spectrum is dominated by long (wavenumbers 1–3) slow westward-propagating waves at high latitudes and somewhat weaker intermediate-scale slow waves at the midlatitudes. In the subtropical jet regime, waves equilibrate at weaker amplitudes than in the merged jet regime. A mechanism is found that explains why baroclinic instability is weaker in the subtropical jet regime, although the vertical shear of the mean flow is stronger, which has to do with the lower-level potential vorticity (PV) structure. The relevance of these results to the real atmosphere seams to hold in local zonal sections but not for the zonal mean.

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Nili Harnik and Richard S. Lindzen

Abstract

The effects of an upper-stratospheric reflecting surface on the vertical structure of stratospheric planetary waves are considered. A diagnostic of the basic-state wave propagation characteristics, which is particularly useful for determining the existence and location of turning surfaces for meridional and vertical propagation, is developed. The diagnostic used is a more accurate indicator of wave propagation regions than the index of refraction because it diagnoses meridional and vertical propagation separately.

The diagnostic is tested on a series of simple models, both steady state and time dependent. It is found that the stratospheric waveguide sets the meridional wavenumber of the waves, regardless of the characteristics of their tropospheric forcing, making it easier to understand the effects of damping and turning surfaces on the vertical structure of the waves. The diagnostic is then applied to observations of the Southern Hemisphere winter of 1996. It is shown that the differences in vertical wave structure between middle and late winter can be explained as a linear response to the seasonal evolution of the basic state, which involves a formation of a reflecting surface in late winter. It is also shown that on daily timescales wave–mean flow interactions cause significant changes in the basic-state propagation characteristics for periods of a few days. These changes, along with the time variations in the forcing of the waves, are responsible for the observed daily timescale variations in wave structure. The fact that the observed evolution of the waves and the basic state are consistent with linear or quasi-linear wave theory (depending on the timescale looked at) supports the applicability of the theory, as well as the validity of the observations.

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Chaim I. Garfinkel and Nili Harnik

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The distribution of near-surface and tropospheric temperature variability in midlatitudes is distinguishable from a Gaussian in meteorological reanalysis data; consistent with this, warm extremes occur preferentially poleward of the location of cold extremes. To understand the factors that drive this non-Gaussianity, a dry general circulation model and a simple model of Lagrangian temperature advection are used to investigate the connections between dynamical processes and the occurrence of extreme temperature events near the surface. The non-Gaussianity evident in reanalysis data is evident in the dry model experiments, and the location of extremes is influenced by the location of the jet stream and storm track. The cause of this in the model can be traced back to the synoptic evolution within the storm track leading up to cold and warm extreme events: negative temperature extremes occur when an equatorward propagating high–low couplet (high to the west) strongly advects isotherms equatorward over a large meridional fetch over more than two days. Positive temperature anomalies occur when a poleward propagating low–high couplet (low to the west) advects isotherms poleward over a large meridional fetch over more than two days. The magnitude of the extremes is enhanced by the meridional movement of the systems. Overall, horizontal temperature advection by storm track systems can account for the warm/cold asymmetry in the latitudinal distribution of the temperature extremes.

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Orli Lachmy and Nili Harnik

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The wave spectrum and zonal-mean-flow maintenance in different flow regimes of the jet stream are studied using a two-layer modified quasigeostrophic (QG) model. As the wave energy is increased by varying the model parameters, the flow transitions from a subtropical jet regime to a merged jet regime and then to an eddy-driven jet regime. The subtropical jet is maintained at the Hadley cell edge by zonal-mean advection of momentum, while eddy heat flux and eddy momentum flux convergence (EMFC) are weak and concentrated far poleward. The merged jet is narrow and persistent and is maintained by EMFC from a narrow wave spectrum, dominated by zonal wavenumber 5. The eddy-driven jet is wide and fluctuating and is maintained by EMFC from a wide wave spectrum. The wave–mean flow feedback mechanisms that maintain each regime are explained qualitatively.

The regime transitions are related to transitions in the wave spectrum. An analysis of the wave energy spectrum budget and a comparison with a quasi-linear version of the model show that the balance maintaining the spectrum in the merged and subtropical jet regimes is mainly a quasi-linear balance, whereas in the eddy-driven jet regime nonlinear inverse energy cascade takes place. The amplitude and wavenumber of the dominant wave mode in the merged and subtropical jet regimes are determined by the constraint that this mode would produce the wave fluxes necessary for maintaining a mean flow that is close to neutrality. In contrast, the equilibrated mean flow in the eddy-driven jet regime is weakly unstable.

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Nili Harnik and Richard S. Lindzen

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The stability characteristics of normal mode perturbations on idealized basic states that have meridional potential vorticity (PV) gradients that are zero in the troposphere, very large at the tropopause, and order β in the stratosphere are checked. The results are compared to the corresponding models that have a lid at the tropopause. The dispersion relations and the vertical structures of the modes are similar in the two models, thus confirming the relevance of the Eady problem to unbounded atmospheres. The effect of replacing the lid with a more realistic tropopause is to complicate the interaction of tropopause and surface waves, such as to inhibit phase locking for a range of wavenumbers. This causes the short-wave cutoff of the Eady model to move to longer waves. Also, there is a slight destabilization of the long waves, which have large amplitudes in the stratosphere.

The effect of gradually changing the tropospheric PV gradients from zero (Eady-type profile) to β (Green- type profile) on the stability of normal modes is checked. The dispersion relations show a smooth transition from the Green profiles to the Eady profiles, and a short-wave cutoff is gradually formed.

Finally, the possibility of neutralizing the atmosphere through the short-wave cutoff of the Eady model by lifting the tropopause while keeping PV gradients zero in the troposphere is examined. It is found that instability depends on some minimal amount of tunneling of waves between the surface and the tropopause. The amount of tunneling depends on the vertical integral of N in the troposphere. It is necessary for ∫ N dz to increase for the short-wave cutoff to move to longer waves. For reasonable Brunt–Vä∩älä frequency profiles, lifting the tropopause causes the short-wave cutoff to move to longer wavelengths, but the details are sensitive to boundary values of N 2 and wind shear.

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