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Kenneth P. Bowman

Abstract

Theory and observations suggest that the Antarctic polar vortex is relatively isolated from midlatitudes, although others have interpreted the observations to indicate that there is substantial mixing from the interior of the vortex into middle latitudes. The equivalent barotropic model of Salby et al. is used to study quasi-horizontal mixing by the large-scale flow in the lower stratosphere during Southern Hemisphere spring, which is when the Antarctic ozone hole appears and disappears. The model is forced by relaxation to observed climatological monthly mean zonal-mean winds and by an idealized wave 1 or 2 forcing at the lower boundary. Mixing and transport are diagnosed primarily through Lagrangian tracer trajectories. For September, October, and November basic states, there is little or no mixing in the interior of the vortex. Mixing occurs near the critical lines for the waves: in the tropics and subtropics for a stationary wave 1, and in midlatitudes on the equatorward flank of the jet for an eastward-moving wave 2. For the December basic state, the wave 2 forcing rapidly mixes the interior of the vortex. Mixing of Lagrangian tracer particles can be significant even when the waves do not “break,” as evidenced by the potential vorticity field. In the model there does not appear to be any significant transport of air out of the interior of the polar vortex prior to the vortex breakdown. The principal factor that leads to the vortex breakdown and mixing of the vortex interior is the deceleration of the jet to the point where winds in the interior of the vortex are close to the phase velocity of the wavenumber 2 forcing. The tracer transport is very similar to many aspects of the behavior of the total ozone field during the spring season.

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Kenneth P. Bowman

Abstract

A simple conceptual model of the relationship between advective transport by breaking waves and diffusive transport is derived. line model postulates that the displacement of fluid parcels by a breaking wave is analogous to molecular diffusion (in a manner similar to conventional mixing length theory). Unlike molecular diffusion, in which the fluctuations of nearby particles are independent, in fluid flow the motion of nearby parcels can be coherent. The effectively random phase of wavebreaking events with respect to an individual particle, however, results in a macroscopic “random walk” of the parcel with a step size related to the width of the breaking wave and a timescale related to the frequency of wave breaking events. As in the case of molecular diffusion, the motion of individual molecules or fluid parcels is unpredictable (chaotic, in fact), but averaging over a large ensemble of parcels results in an ensemble variance that increases linearly with time, formally equivalent to molecular diffusion of a gas.

Examples are shown of isentropic parcel dispersion in the stratosphere. Lagrangian trajectory calculations indicate that the latitudinal dispersion of air parcels increases linearly with time in wavebreaking regions, but first increases and then levels off in regions where little or no wavebreaking occurs. A simple model for barriers to mixing is also proposed.

These results suggest a new approach to parameterization of mixing in numerical models. The required parameters are the distributions of the frequency, width, and location of wavebreaking events. These in turn be related to the frequency, phase speed, and amplitude of the breaking waves, and the locations of critical lines in the fluid.

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Kenneth P. Bowman

Abstract

Nine years of total ozone measurements from the Total Ozone Mapping Spectrometer (TOMS) on Nimbus 7 are used to study the global structure of the quasi-biennial oscillation (QBO) in total ozone. Interannual variability of total ozone near the equator (10°S to 10°N) is dominated by the QBO. The equatorial ozone anomalies are independent of season and are well correlated (r > 0.8) with the equatorial zonal wind. In both hemispheres midlatitude anomalies are two to three times larger in winter than in summer. Global patterns of the ozone QBO are identified by computing lagged correlations between the zonal-mean equatorial ozone and ozone elsewhere on the globe. Correlations between equatorial and extratropical ozone are weak during the summer season (r ∼ 0) and large and negative during the winter (r < − 0.8 in the Southern Hemisphere and r − 0.6 in the Northern Hemisphere). There are nodes or phase shifts in the correlation patterns at ±10° latitude, at 60°S, and at 50°N. Large negative correlations extend to the poles in both winter hemisphere There are indications of a correlation between wave activity, as measured by the eddy variance of the total ozone field, and the QBO, although the variability of the eddy activity is large and the sample size is small. The correlations support the accepted view that equatorial ozone anomalies result from vertical transport by the QBO circulation. The correlation patterns do not support the theory that extratropical ozone anomalies on the QBO time scale are the result of either advection of equatorial ozone anomalies by the climatological circulation or quasi-horizontal mixing of the equatorial anomalies by planetary waves. Instead, the ozone anomalies resemble a seasonally modulated standing oscillation, possibly resulting from quasi-biennial wave forcing of the planetary-scale mean meridional circulation and the associated vertical advection of ozone.

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Kenneth P. Bowman

Abstract

Lagrangian trajectories are used to calculate isentropic mixing properties for unfiltered and filtered Southern Hemisphere stratospheric winds. In wintertime significant mixing is confined to the surf zone between the Tropics and the edge of the polar vortex. The mixing barrier at the edge of the vortex is located near the core of the polar jet stream (where the maximum wind speeds occur), which is also approximately where the meridional potential vorticity gradient is largest. In summer there is significant mixing throughout the hemisphere, and no high-latitude mixing barrier exists.

When the winds are filtered by zonal wavenumber to retain either the planetary-scale waves (1–3) or the smaller-scale waves (4–12), mixing in the surf zone is generally reduced but not eliminated. When the winds are filtered by phase speed, however, mixing is significantly reduced in restricted latitude zones where the phase speeds of the filtered waves are close to the speed of the local zonal-mean zonal wind. These results indicate that mixing primarily occurs near the critical lines for Rossby waves, where the waves would be expected to break. The presence of the mixing barrier around the polar vortex can be interpreted as a result of the lack of waves with fast phase speeds comparable to the speed of the jet. Artificially amplifying the fast-moving waves can destroy the mixing barrier around the vortex. In summer, when winds are weaker, waves break throughout the hemisphere and the mixing barrier disappears.

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Kenneth P. Bowman

Abstract

Four years of precipitation retrievals from the Tropical Rainfall Measuring Mission (TRMM) satellite are compared with data from 25 surface rain gauges on the National Oceanic and Atmospheric Administration/Pacific Marine Environment Laboratory (NOAA/PMEL) Tropical Atmosphere–Ocean Array/Triangle Trans-Ocean Buoy Network TAO/TRITON buoy array in the tropical Pacific. The buoy gauges have a significant advantage over island-based gauges for this purpose because they represent open-ocean conditions and are not affected by island orography or surface heating. Because precipitation is correlated with itself in both space and time, comparisons between the two data sources can be improved by properly averaging in space and/or time. When comparing gauges with individual satellite overpasses, the optimal averaging time for the gauge (centered on the satellite overpass time) depends on the area over which the satellite data are averaged. For 1° × 1° areas there is a broad maximum in the correlation for gauge-averaging periods of ∼2 to 10 h. Maximum correlations r are in the range 0.6 to 0.7. For larger satellite averaging areas, correlations with the gauges are smaller (because a single gauge becomes less representative of the precipitation in the box) and the optimum gauge-averaging time is longer. For individual satellite overpasses averaged over a 1° × 1° box, the relative rms difference with respect to a rain gauge centered in the box is ∼200% to 300%. For 32-day time means over 1° × 1° boxes, the relative rms difference between the satellite data and a gauge is in the range of 40% to 70%. The bias between the gauges and the satellite retrievals is estimated by correlating the long-term time-mean precipitation estimates across the set of gauges. The TRMM Microwave Imager (TMI) gives an r 2 of 0.97 and a slope of 0.970, indicating very little bias with respect to the gauges. For the Precipitation Radar (PR) the comparable numbers are 0.92 and 0.699. The results of this study are consistent with the sampling error estimates from the statistical model of Bell and Kundu.

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Kenneth P. Bowman
and
Tatiana Erukhimova

Abstract

The global-scale transport properties of the NCEP reanalysis winds for the period from 1979 to 1997 are compared to a standard simulation with version 3 of the NCAR Community Climate Model (CCM3) forced by observed sea surface temperatures for the same period. The transport properties of each dataset are defined by the climatological Green's function for the mass conservation equation for a conserved, passive tracer. Characterizing the atmospheric circulation in terms of material transport provides a very different view of the circulation than standard Eulerian-mean statistics. The Green's functions are estimated from large numbers of Lagrangian (kinematic) particle trajectories computed by using the NCEP and CCM3 resolved winds. Generally the Green's functions computed from the two datasets agree well. The transport circulation is dominated by two thermally direct cells, one in each hemisphere. There is a substantial seasonal cycle in the transport, particularly in the Tropics. From a transport point of view, the atmosphere can be divided into three regions: the Southern Hemisphere extratropics, the Tropics, and the Northern Hemisphere extratropics. Particle dispersion within each region is relatively rapid, while exchange between the regions is slower. There are partial barriers to transport between the Tropics and extratropics. Differences between the transport characteristics of NCEP and CCM3 are most noticeable in the Tropics, where CCM3 has stronger subsidence in the ITCZ compared to NCEP. The transport circulation is slightly faster in NCEP than in CCM3. Interhemispheric transport rates computed from the Green's functions are compared with measurements of long-lived trace species from the Atmospheric Lifetime Experiment/Global Atmospheric Gases Experiment (ALE/GAGE) network. The ALE/GAGE station data for the northern and southern extratropics give an interhemispheric time lag of ∼1.8 yr for long-lived tracers such as CFCs. Fitting the transport data to a three-box model gives interhemispheric time lags of ∼1.8 and ∼2 yr, respectively, for NCEP and CCM3.

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Kenneth P. Bowman
and
Ping Chen

Abstract

A global, nonlinear, equivalent barotropic model is used to study the isentropic mixing of passive tracers by barotropic instability. Basic states are analytical zonal-mean jets representative of the zonal-mean flow in the upper stratosphere, where the observed 4-day wave is thought to be a result of barotropic, and possibly baroclinic, instability. As is known from previous studies, the phase speed and growth rate of the unstable waves is fairly sensitive to the shape of the zonal-mean jet; and the dominant wave mode at saturation is not necessarily the fastest growing mode; but the unstable modes share many features of the observed 4-day wave. Lagrangian trajectories computed from model winds are used to characterize the mixing by the flow. For profiles with both midlatitude and polar modes, mixing is stronger in midlatitudes than inside the vortex; but there is little exchange of air across the vortex boundary. There is a minimum in the Lyapunov exponents of the flow and the particle dispersion at the jet maximum. For profiles with only polar unstable modes, there is weak mixing inside the vortex, no mixing outside the vortex, and no exchange of air across the vortex boundary. These results support the theoretical arguments that, whether wave disturbances are generated by local instability or propagate from other regions, the mixing properties of the total flow are determined by the locations of the wave critical lines and that strong gradients of potential vorticity are very resistant to mixing.

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Kenneth P. Bowman
and
Jin Huang

Abstract

A multigrid finite-difference solver is developed for the Helmholtz equation on the sphere. The finite-difference grid resolution is constant in the latitudinal direction and variable in the longitudinal direction so as to keep the physical gridpoint spacing approximately uniform over the sphere. The cpu time per grid point required to reduce the residual by a given amount is independent of grid resolution. The discretization error is slightly worse than second order as a result of the variable grid spacing. The method should be applicable to general elliptic equations on the sphere and should be useful for problems where uniform grid spacing is disadvantageous.

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Kenneth P. Bowman
and
Thomas L. Bell

Abstract

The eddy variance of a meteorological field must tend to zero at high latitudes due solely to the nature of spherical polar coordinates. The zonal averaging operator defines a length scale: the circumference of the latitude circle. When the circumference of the latitude circle is greater than the correlation length of the field, the eddy variance from transient eddies is the result of differences between statistically independent regions. When the circumference is less than the correlation length, the eddy variance is computed from points that are well correlated with each other, and so is reduced. The expansion of a field into zonal Fourier components is also influenced by the use of spherical coordinates. As is well known, a phenomenon of fixed wavelength will have different zonal wavenumbers at different latitudes. Simple analytical examples of these effects are presented along with an observational example from satellite ozone data. It is found that geometrical effects can be important even in middle latitudes.

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Cameron R. Homeyer
and
Kenneth P. Bowman

Abstract

Rossby wave breaking is an important mechanism for the two-way exchange of air between the tropical upper troposphere and lower stratosphere and the extratropical lower stratosphere. The authors present a 30-yr climatology (1981–2010) of anticyclonically and cyclonically sheared wave-breaking events along the boundary of the tropics in the 350–500-K potential temperature range from ECMWF Interim Re-Analysis (ERA-Interim). Lagrangian transport analyses show net equatorward transport from wave breaking near 380 K and poleward transport at altitudes below and above the 370–390-K layer. The finding of poleward transport at lower levels is in disagreement with previous studies and is shown to largely depend on the choice of tropical boundary. In addition, three distinct modes of transport for anticyclonic wave-breaking events are found near the tropical tropopause (380 K): poleward, equatorward, and symmetric. Transport associated with cyclonic wave-breaking events, however, is predominantly poleward. The three transport modes for anticyclonic wave breaking are associated with specific characteristics of the geometry of the mean flow. In particular, composite averages show that poleward transport is associated with a “split” subtropical jet where the jet on the upstream side of the breaking wave extends eastward and lies poleward and at lower altitudes of the subtropical jet on the downstream side, producing a substantial longitudinal overlap between the two jets. Equatorward transport is not associated with a split subtropical jet and is found immediately downstream of stationary anticyclones in the tropics, often associated with monsoon circulations. It is further shown that, in general, the transport direction of breaking waves is determined primarily by the relative positions of the jets.

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