# Search Results

## You are looking at 1 - 10 of 35 items for

- Author or Editor: Kenneth P. Bowman x

- Refine by Access: All Content x

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## Abstract

A quantitative climatological analysis of regional-scale atmospheric transport in Texas is developed using previously described Lagrangian (kinematic) trajectory methods. The trajectories are computed using resolved winds from 1979 to 2001 from the National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis project dataset. The wind data do not include small-scale turbulent atmospheric motion. The probability distributions of particle trajectories can be used to estimate the climatological (ensemble mean) Green's function for the mass conservation equation for a passive trace substance. A discrete approximation of the Green's function is computed for low-level summertime atmospheric flow over Texas. Examples are provided of the use of the Green's function to estimate both forward and backward transport properties. The Green's function can be used to evaluate the climatological probability of transport by the resolved flow to or from a given location.

## Abstract

A quantitative climatological analysis of regional-scale atmospheric transport in Texas is developed using previously described Lagrangian (kinematic) trajectory methods. The trajectories are computed using resolved winds from 1979 to 2001 from the National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis project dataset. The wind data do not include small-scale turbulent atmospheric motion. The probability distributions of particle trajectories can be used to estimate the climatological (ensemble mean) Green's function for the mass conservation equation for a passive trace substance. A discrete approximation of the Green's function is computed for low-level summertime atmospheric flow over Texas. Examples are provided of the use of the Green's function to estimate both forward and backward transport properties. The Green's function can be used to evaluate the climatological probability of transport by the resolved flow to or from a given location.

## Abstract

During the first three-and-a-half years of the Tropical Rainfall Measuring Mission (TRMM), the TRMM satellite operated at a nominal altitude of 350 km. To reduce drag, save maneuvering fuel, and prolong the mission lifetime, the orbit was boosted to 403 km in August 2001. The change in orbit altitude produced small changes in a wide range of observing parameters, including field-of-view size and viewing angles. Due to natural variability in rainfall and sampling error, it is not possible to evaluate possible changes in rainfall estimates from the satellite data alone. Changes in TRMM Microwave Imager (TMI) and the precipitation radar (PR) precipitation observations due to the orbit boost are estimated by comparing them with surface rain gauges on ocean buoys operated by the NOAA/Pacific Marine Environment Laboratory (PMEL). For each rain gauge, the bias between the satellite and the gauge for pre- and postboost time periods is computed. For the TMI, the satellite is biased ∼12% low relative to the gauges during the preboost period and ∼1% low during the postboost period. The mean change in bias relative to the gauges is approximately 0.4 mm day^{−1}. The change in TMI bias is rain-rate-dependent, with larger changes in areas with higher mean precipitation rates. The PR is biased significantly low relative to the gauges during both boost periods, but the change in bias from the pre- to postboost period is not statistically significant.

## Abstract

During the first three-and-a-half years of the Tropical Rainfall Measuring Mission (TRMM), the TRMM satellite operated at a nominal altitude of 350 km. To reduce drag, save maneuvering fuel, and prolong the mission lifetime, the orbit was boosted to 403 km in August 2001. The change in orbit altitude produced small changes in a wide range of observing parameters, including field-of-view size and viewing angles. Due to natural variability in rainfall and sampling error, it is not possible to evaluate possible changes in rainfall estimates from the satellite data alone. Changes in TRMM Microwave Imager (TMI) and the precipitation radar (PR) precipitation observations due to the orbit boost are estimated by comparing them with surface rain gauges on ocean buoys operated by the NOAA/Pacific Marine Environment Laboratory (PMEL). For each rain gauge, the bias between the satellite and the gauge for pre- and postboost time periods is computed. For the TMI, the satellite is biased ∼12% low relative to the gauges during the preboost period and ∼1% low during the postboost period. The mean change in bias relative to the gauges is approximately 0.4 mm day^{−1}. The change in TMI bias is rain-rate-dependent, with larger changes in areas with higher mean precipitation rates. The PR is biased significantly low relative to the gauges during both boost periods, but the change in bias from the pre- to postboost period is not statistically significant.

## 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.

## 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.