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  • Author or Editor: Maarten H. P. Ambaum x
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Maarten H. P. Ambaum

Abstract

A novel statistic for local wave amplitude of the 500-hPa geopotential height field is introduced. The statistic uses a Hilbert transform to define a longitudinal wave envelope and dynamical latitude weighting to define the latitudes of interest. Here it is used to detect the existence, or otherwise, of multimodality in its distribution function. The empirical distribution function for the 1960–2000 period is close to a Weibull distribution with shape parameters between 2 and 3. There is substantial interdecadal variability but no apparent local multimodality or bimodality.

The zonally averaged wave amplitude, akin to the more usual wave amplitude index, is close to being normally distributed. This is consistent with the central limit theorem, which applies to the construction of the wave amplitude index. For the period 1960–70 it is found that there is apparent bimodality in this index. However, the different amplitudes are realized at different longitudes, so there is no bimodality at any single longitude.

As a corollary, it is found that many commonly used statistics to detect multimodality in atmospheric fields potentially satisfy the assumptions underlying the central limit theorem and therefore can only show approximately normal distributions. The author concludes that these techniques may therefore be suboptimal to detect any multimodality.

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Maarten H. P. Ambaum
and
David P. Marshall

Abstract

Separation of stratified flow over a two-dimensional hill is inhibited or facilitated by acceleration or deceleration of the flow just outside the attached boundary layer. In this note, an expression is derived for this acceleration or deceleration in terms of streamline curvature and stratification. The expression is valid for linear as well as nonlinear deformation of the flow. For hills of vanishing aspect ratio a linear theory can be derived and a full regime diagram for separation can be constructed. For hills of finite aspect ratio scaling relationships can be derived that indicate the presence of a critical aspect ratio, proportional to the stratification, above which separation will occur as well as a second critical aspect ratio above which separation will always occur irrespective of stratification.

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Maarten H. P. Ambaum
and
Panos J. Athanasiadis

Abstract

The response of a uniform horizontal temperature gradient to prescribed fixed heating is calculated in the context of an extended version of surface quasigeostrophic dynamics. It is found that for zero mean surface flow and weak cross-gradient structure the prescribed heating induces a mean temperature anomaly proportional to the spatial Hilbert transform of the heating. The interior potential vorticity generated by the heating enhances this surface response. The time-varying part is independent of the heating and satisfies the usual linearized surface quasigeostrophic dynamics. It is shown that the surface temperature tendency is a spatial Hilbert transform of the temperature anomaly itself. It then follows that the temperature anomaly is periodically modulated with a frequency proportional to the vertical wind shear. A strong local bound on wave energy is also found. Reanalysis diagnostics are presented that indicate consistency with key findings from this theory.

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Panos J. Athanasiadis
and
Maarten H. P. Ambaum

Abstract

An isentropic potential vorticity (PV) budget analysis is employed to examine the role of synoptic transients, advection, and nonconservative processes as forcings for the evolution of the low-frequency PV anomalies locally and those associated with the North Atlantic Oscillation (NAO) and the Pacific–North American (PNA) pattern. Specifically, the rate of change of the low-frequency PV is expressed as a sum of tendencies due to divergence of eddy transport, advection by the low-frequency flow (hereafter referred to as advection), and the residual nonconservative processes. The balance between the variances and covariances of these terms is illustrated using a novel vector representation.

It is shown that for most locations, as well as for the PNA pattern, the PV variability is dominantly driven by advection. The eddy forcing explains a small amount of the tendency variance. For the NAO, the role of synoptic eddy fluxes is found to be stronger, explaining on average 15% of the NAO tendency variance. Previous studies have not assessed quantitively how the various forcings balance the tendency. Thus, such studies may have overestimated the role of eddy fluxes for the evolution of teleconnections by examining, for example, composites and regressions that indicate maintenance, rather than evolution driven by the eddies. The authors confirm this contrasting view by showing that during persistent blocking (negative NAO) episodes the eddy driving is relatively stronger.

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Benjamin J. Harvey
,
Maarten H. P. Ambaum
, and
Xavier J. Carton

Abstract

The stability characteristics of the surface quasigeostrophic shielded Rankine vortex are found using a linearized contour dynamics model. Both the normal modes and nonmodal evolution of the system are analyzed and the results are compared with two previous studies. One is a numerical study of the instability of smooth surface quasigeostrophic vortices with which qualitative similarities are found and the other is a corresponding study for the two-dimensional Euler system with which several notable differences are highlighted.

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Yvonne B. L. Hinssen
and
Maarten H. P. Ambaum

Abstract

It is shown that a quantitative relation exists between the stratospheric polar cap potential vorticity and the 100-hPa eddy heat flux. A difference in potential vorticity between years is found to be linearly related to the flux difference integrated over time, taking into account a decrease in relaxation time scale with height in the atmosphere.

This relation (the PV–flux relation) is then applied to the 100-hPa flux difference between 2008/09 and the climatology (1989–2008) to obtain a prediction of the polar cap potential vorticity difference between the 2008/09 winter and the climatology. A prediction of the 2008/09 polar cap potential vorticity is obtained by adding this potential vorticity difference to the climatological potential vorticity. The observed polar cap potential vorticity for 2008/09 shows a large and abrupt change in the potential vorticity in midwinter, related to the occurrence of a major sudden stratospheric warming in January 2009; this is also captured by the potential vorticity predicted from the 100-hPa flux and the PV–flux relation.

The results of the mean PV–flux relation show that, on average, about 50% of the interannual variability in the state of the Northern Hemisphere stratosphere is determined by the variations in the 100-hPa heat flux. This explained variance can be as large as 80% for more severe events, as demonstrated for the 2009 major warming.

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Lenka Novak
,
Maarten H. P. Ambaum
, and
Rémi Tailleux

Abstract

The North Atlantic eddy-driven jet exhibits latitudinal variability with evidence of three preferred latitudinal locations: south, middle, and north. Here the authors examine the drivers of this variability and the variability of the associated storm track. The authors investigate the changes in the storm-track characteristics for the three jet locations and propose a mechanism by which enhanced storm-track activity, as measured by upstream heat flux, is responsible for cyclical downstream latitudinal shifts in the jet. This mechanism is based on a nonlinear oscillator relationship between the enhanced meridional temperature gradient (and thus baroclinicity) and the meridional high-frequency (periods of shorter than 10 days) eddy heat flux. Such oscillations in baroclinicity and heat flux induce variability in eddy anisotropy, which is associated with the changes in the dominant type of wave breaking and a different latitudinal deflection of the jet. The authors’ results suggest that high heat flux is conducive to a northward deflection of the jet, whereas low heat flux is conducive to a more zonal jet. This jet-deflecting effect was found to operate most prominently downstream of the storm-track maximum, while the storm track and the jet remain anchored at a fixed latitudinal location at the beginning of the storm track. These cyclical changes in storm-track characteristics can be viewed as different stages of the storm track’s spatiotemporal life cycle.

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Ben Harvey
,
John Methven
, and
Maarten H. P. Ambaum

Abstract

The amplitude of ridges in large-amplitude Rossby waves has been shown to decrease systematically with lead time during the first 1–5 days of operational global numerical weather forecasts. These models also exhibit a rapid reduction in the isentropic gradient of potential vorticity (PV) at the tropopause during the first 1–2 days of forecasts. This paper identifies a mechanism linking the reduction in large-scale meander amplitude on jet streams to declining PV gradients. The mechanism proposed is that a smoother isentropic transition of PV across the tropopause leads to excessive PV filamentation on the jet flanks and a more lossy waveguide. The approach taken is to analyze Rossby wave dynamics in a single-layer quasigeostrophic model. Numerical simulations show that the amplitude of a Rossby wave propagating along a narrow but smooth PV front does indeed decay transiently with time. This process is explained in terms of the filamentation of PV from the jet core and associated absorption of wave activity by the critical layers on the jet flanks, and a simple method for quantitatively predicting the magnitude of the amplitude reduction without simulation is presented. Explicitly diffusive simulations are then used to show that the combined impact of diffusion and the adiabatic rearrangement of PV can result in a decay rate of Rossby waves that is 2–4 times as fast as could be expected from diffusion acting alone. This predicted decay rate is sufficient to explain the decay observed in operational weather forecasting models.

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Lenka Novak
,
Maarten H. P. Ambaum
, and
Ben J. Harvey

Abstract

The steady-state response of a midlatitude storm track to large-scale extratropical thermal forcing and eddy friction is investigated in a dry general circulation model with a zonally symmetric forcing. A two-way equilibration is found between the relative responses of the mean baroclinicity and baroclinic eddy intensity, whereby mean baroclinicity responds more strongly to eddy friction whereas eddy intensity responds more strongly to the thermal forcing of baroclinicity. These seemingly counterintuitive responses are reconciled using the steady state of a predator–prey relationship between baroclinicity and eddy intensity. This relationship provides additional support for the well-studied mechanism of baroclinic adjustment in Earth’s atmosphere, as well as providing a new mechanism whereby eddy dissipation controls the large-scale thermal structure of a baroclinically unstable atmosphere. It is argued that these two mechanisms of baroclinic adjustment and dissipative control should be used in tandem when considering storm-track equilibration.

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Paolo Ruggieri
,
Maarten H. P. Ambaum
, and
Jonas Nycander

Abstract

Large-scale overturning mass transport in the stratosphere is commonly explained through the action of potential vorticity (PV) rearrangement in the flank of the stratospheric jet. Large-scale Rossby waves, with their wave activity source primarily in the troposphere, stir and mix PV and an overturning circulation arises to compensate for the zonal torque imposed by the breaking waves. In this view, any radiative heating is relaxational and the circulation is mechanically driven. Here we present a fully thermodynamic analysis of these phenomena, based on ERA-Interim data. Streamfunctions in a thermodynamic, log(pressure)–temperature space are computed. The sign of a circulation cell in these coordinates directly shows whether it is mechanically driven, converting kinetic energy to potential and thermal energy, or thermally driven, with the opposite conversion. The circulation in the lower stratosphere is found to be thermodynamically indirect (i.e., mechanically driven). In the middle and upper stratosphere thermodynamically indirect and direct circulations coexist, with a prominent semiannual cycle. A part of the overturning in this region is thermally driven, while a more variable indirect circulation is mechanically driven by waves. The wave driving does not modulate the strength of the thermally direct part of the circulation. This suggests that the basic overturning circulation in the stratosphere is largely thermally driven, while tropospheric waves add a distinct indirect component to the overturning. This indirect overturning is associated with poleward transport of anomalously warm air parcels.

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