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John Methven

Abstract

A model of the linear stability of spiral-shaped potential vorticity (PV) filaments is constructed by using the Kolmogorov capacity as a time-independent characterization of their structure, assuming that the dynamics is essentially barotropic. The angular velocity “induced” by the PV spiral has a radial profile that is approximately consistent with the advective formation of the spiral itself. The background shear in angular velocity, at a position along the filament, arising from the net effect of the remainder of the spiral, suppresses the growth rate of barotropic instability. However, it is shown here that all such spiral-shaped PV filaments are unstable in isolation and that disturbance growth rate varies only weakly with spiral shape. Contour dynamics calculations verify these predictions, as well as illustrating the strong influence of far-field strain on growth rates. The implication is that persistent vortices, associated with PV spirals and to some extent isolated from external strain, will mix the air contained within them at a rate significantly enhanced by filamentary instability. It is also concluded that the Kolmogorov capacity provides a useful geometrical characterization of atmospheric spirals.

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John Methven

Abstract

Pseudomomentum and pseudoenergy are both measures of wave activity for disturbances in a fluid, relative to a notional background state. Together they give information on the propagation, growth, and decay of disturbances. Wave activity conservation laws are most readily derived for the primitive equations on the sphere by using isentropic coordinates. However, the intersection of isentropic surfaces with the ground (and associated potential temperature anomalies) is a crucial aspect of baroclinic wave evolution. A new expression is derived for pseudoenergy that is valid for large-amplitude disturbances spanning isentropic layers that may intersect the ground. The pseudoenergy of small-amplitude disturbances is also obtained by linearizing about a zonally symmetric background state. The new expression generalizes previous pseudoenergy results for quasigeostrophic disturbances on the β plane and complements existing large-amplitude results for pseudomomentum.

The pseudomomentum and pseudoenergy diagnostics are applied to an extended winter from the European Centre for Medium-Range Weather Forecasts Interim Re-Analysis data. The time series identify distinct phenomena such as a baroclinic wave life cycle where the wave activity in boundary potential temperature saturates nonlinearly almost two days before the peak in wave activity near the tropopause. The coherent zonal propagation speed of disturbances at tropopause level, including distinct eastward, westward, and stationary phases, is shown to be dictated by the ratio of total hemispheric pseudoenergy to pseudomomentum. Variations in the lower-boundary contribution to pseudoenergy dominate changes in propagation speed; phases of westward progression are associated with stronger boundary potential temperature perturbations.

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John Methven and Brian Hoskins

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Advection in weather systems results in filamentary and spiral structures in tracers, whose complexity increases as stirring progresses. Characterizations of fine-scale structures in chemical tracers, which are typically unresolved in atmospheric analyses or models, may enable a treatment of mixing between air masses that is very different from a simple diffusion. In addition, filaments in Ertel potential vorticity (PV) and other active tracers can have a direct influence on the surrounding flow that will depend to some extent upon their spatial arrangement as well as internal structure. Here attention is focused on a particular baroclinic wave life cycle that is distinguished by the existence of an exceptionally persistent, synoptic-scale, cyclonic vortex. In this region the PV field exhibits a spiral-shaped filament that is eventually disrupted by vortex rollup due to the nonlinear development of barotropic instability. Similar spirals have been observed in satellite imagery. In this paper the characterization of the structure of PV spirals by a geometrical measure and by a spectral measure and the relationship between the two is considered.

The scale-invariant nature of a spiral can be characterized geometrically by the Kolmogorov capacity (or box-counting dimension) of the set of points of intersection between the spiral and a cut through it (DK). The capacity of the spiral in the baroclinic wave is found to be almost constant (DK ≈ 0.4) during a period when the number of turns increases from 2 to 5. The constancy of DK results from the steadiness of the radial dependence of angular velocity. Another, more traditional, measure of tracer structure is the power spectrum, which might be expected to be related to Kolmogorov capacity in the scale-invariant subrange. However, total wavenumber spectra for PV in the life cycle show two subranges with very different spectral slopes, neither of which relate to the value of capacity. It is hypothesized that the observed atmospheric kinetic energy spectrum is also not directly related to accumulating discontinuities in PV because the scale-invariant subrange of PV structures, from synoptic scales to mesoscales, is too narrow.

In conclusion, the Kolmogorov capacity is a more useful measure of structures formed by advection. For instance, the capacity of PV spirals is used as the basis for an investigation of their stability in Part II. The characterization of tracer structure with geometrically based measures, like Kolmogorov capacity, could also be helpful in studies of mixing.

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John Methven and Brian Hoskins

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The usefulness of any simulation of atmospheric tracers using low-resolution winds relies on both the dominance of large spatial scales in the strain and time dependence that results in a cascade in tracer scales. Here, a quantitative study on the accuracy of such tracer studies is made using the contour advection technique. It is shown that, although contour stretching rates are very insensitive to the spatial truncation of the wind field, the displacement errors in filament position are sensitive. A knowledge of displacement characteristics is essential if Lagrangian simulations are to be used for the inference of airmass origin. A quantitative lower estimate is obtained for the tracer scale factor (TSF): the ratio of the smallest resolved scale in the advecting wind field to the smallest “trustworthy” scale in the tracer field. For a baroclinic wave life cycle the TSF = 6.1 ± 0.3 while for the Northern Hemisphere wintertime lower stratosphere the TSF = 5.5 ± 0.5, when using the most stringent definition of the trustworthy scale. The similarity in the TSF for the two flows is striking and an explanation is discussed in terms of the activity of potential vorticity (PV) filaments.

Uncertainty in contour initialization is investigated for the stratospheric case. The effect of smoothing initial contours is to introduce a spinup time, after which wind field truncation errors take over from initialization errors (2–3 days). It is also shown that false detail from the proliferation of finescale filaments limits the useful lifetime of such contour advection simulations to ∼3σ −1 days, where σ is the filament thinning rate, unless filaments narrower than the trustworthy scale are removed by contour surgery. In addition, PV analysis error and diabatic effects are so strong that only PV filaments wider than 50 km are at all believable, even for very high-resolution winds. The minimum wind field resolution required to accurately simulate filaments down to the erosion scale in the stratosphere (given an initial contour) is estimated and the implications for the modeling of atmospheric chemistry are briefly discussed.

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John Methven and Hylke de Vries
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Johannes de Leeuw, John Methven, and Michael Blackburn

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A novel Lagrangian framework is developed to attribute monthly precipitation variability to physical processes. Precipitation variability is partitioned into a combination of five factors: airmass origin location, origin surface temperature variation, ascent intensity, mass fraction of ascending air, and the number of “wet” analysis times per month [>1 mm (6 h)−1]. Precipitation in a target region is linked to “origin” locations of air masses where the water vapor mixing ratio was last set by boundary layer moistening and is a maximum along back trajectories. Applying the technique to the England and Wales region, the factors together account for 83%–89% of the observed summer precipitation variability. The dominant contributor is the number of wet analyses, which is shown to be associated with cyclone statistics. The wettest summer months are mainly associated with anomalous cyclone duration rather than the number of cyclones. In addition, surface temperature and saturation humidity at the origin locations are found to be below their climatological averages (1979–2013). Therefore, the direct thermodynamic effect of anomalous surface temperature on marine boundary layer humidity acts to reduce monthly precipitation anomalies. The decadal precipitation change between phases of the Atlantic multidecadal oscillation is approximately 20% of the interannual variability between summer months. Changes in cyclone statistics have an effect 6 times larger than the direct thermodynamic factor in both monthly and decadal precipitation variability.

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Piero Cau, John Methven, and Brian Hoskins

Abstract

The humidity in the dry regions of the tropical and subtropical troposphere has a major impact on the ability of the atmosphere to radiate heat to space. The water vapor content in these regions is determined by their “origins,” here defined as the last condensation event following air masses. Trajectory simulations are used to investigate such origins using the 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40) data for January 1993. It is shown that 96% of air parcels experience condensation within 24 days and most of the remaining 4% originate in the stratosphere. Dry air masses are shown to experience a net pressure increase since last condensation, which is uniform with latitude, while the median time taken for descent is 5 days into the subtropics but exceeds 16 days into the equatorial lower troposphere. The associated rate of decrease in potential temperature is consistent with radiative cooling. The relationship between the drier regions in the Tropics and subtropics and the geographical localization of their origin is investigated. Four transport processes are identified to explain these relationships.

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Oscar Martínez-Alvarado, Suzanne L. Gray, and John Methven

Abstract

Extratropical cyclones are typically weaker and less frequent in summer as a result of differences in the background state flow and diabatic processes with respect to other seasons. Two extratropical cyclones were observed in summer 2012 with a research aircraft during the Diabatic Influences on Mesoscale Structures in Extratropical Storms (DIAMET) field campaign. The first cyclone deepened only down to 995 hPa; the second cyclone deepened down to 978 hPa and formed a potential vorticity (PV) tower, a frequent signature of intense cyclones. The objectives of this article are to quantify the effects of diabatic processes and their parameterizations on cyclone dynamics. The cyclones were analyzed through numerical simulations incorporating tracers for the effects of diabatic processes on potential temperature and PV. The simulations were compared with radar rainfall observations and dropsonde measurements. It was found that the observed maximum vapor flux in the stronger cyclone was twice as strong as in the weaker cyclone; the water vapor mass flow along the warm conveyor belt of the stronger cyclone was over half that typical in winter. The model overestimated water vapor mass flow by approximately a factor of 2 as a result of deeper structure in the rearward flow and humidity in the weaker case. An integral tracer interpretation is introduced, relating the tracers with cross-isentropic mass transport and circulation. It is shown that the circulation around the cyclone increases much more slowly than the amplitude of the diabatically generated PV tower. This effect is explained using the PV impermeability theorem.

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Ben Harvey, John Methven, Chloe Eagle, and Humphrey Lean

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In situ aircraft observations are used to interrogate the ability of a numerical weather prediction model to represent flow structure and turbulence at a narrow cold front. Simulations are performed at a range of nested resolutions with grid spacings of 12 km down to 100 m, and the convergence with resolution is investigated. The observations include the novel feature of a low-altitude circuit around the front that is closed in the frame of reference of the front, thus allowing the direct evaluation of area-average vorticity and divergence values from circuit integrals. As such, the observational strategy enables a comparison of flow structures over a broad range of spatial scales, from the size of the circuit itself (100 km) to small-scale turbulent fluctuations (10 m). It is found that many aspects of the resolved flow converge successfully toward the observations with resolution if sampling uncertainty is accounted for, including the area-average vorticity and divergence measures and the narrowest observed cross-frontal width. In addition, there is a gradual handover from parameterized to resolved turbulent fluxes of moisture and momentum as motions in the convective boundary layer behind the front become partially resolved in the highest-resolution simulations. In contrast, the parameterized turbulent fluxes associated with subgrid-scale shear-driven turbulence ahead of the front do not converge on the observations. The structure of frontal rainbands associated with a shear instability along the front also does not converge with resolution, indicating that the mechanism of the frontal instability may not be well represented in the simulations.

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Simon C. Peatman, John Methven, and Steven J. Woolnough

Abstract

The rate of humidity entrainment in the convective parameterization scheme in a general circulation model affects the simulation of convectively coupled waves. However, it is unclear whether this is caused directly by the effects of entrainment on waves or indirectly through associated impacts such as on the basic state. Therefore, using an aquaplanet model, we employ a novel framework in which we entrain a weighted average of the resolved humidity field and a prescribed zonally symmetric field, with the weighting controlled by a decoupling parameter. Hence, we can vary the entrainment rate of basic-state humidity independently of the entrainment of humidity perturbations, simultaneously minimizing changes in the basic state. Thus, we isolate the effect of moisture entrainment on the waves. Enhancing the entrainment rate increases spectral power over all zonal wavenumbers and frequencies, with an increase in the ratio of eastward-to-westward power. The Kelvin wave speed decreases as entrainment increases, which can be partially accounted for by an associated change in basic-state humidity. Increasing the decoupling parameter reduces spectral power in Kelvin waves relative to the background, with only long waves still prominent when entrainment is almost fully decoupled from the resolved moisture field, suggesting the wave structure in humidity is required for convection to organize into short-wave structures. For long waves, the increase in the ratio of eastward-to-westward power as entrainment rate increases cannot be explained by the changes in the coupling with the wave structure in humidity but is consistent with the changes in the basic state.

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