High Arctic Observations of Strato-mesospheric Temperatures and Gravity Wave Activity
Thomas James Duck
A thesis submitted to the Faculty of Graduate Studies in partial hlfilment of the requirements for the degree of
Doctor of Philosophy
Graduate Programme in Physics and Astronomy York University North York, Ontario
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DOCTOR OF PHILOSOPHY
01999 Permission has been granted to the LIBRARY OF YORK UNIVERSITY to lend or sell copies of this dissertation, to the NATIONAL LIBRARY OF CANADA to microfilm this dissertation and to lend or sell copies of the film. and to UNIVERSITY MICROFILMS to publish an abstract of this dissertation. The author reserves other publication rights, and neither the dissedation nor extensive extracts from it may be printed or otherwise reproduced without the author's written permission. Abstract
Over four hundred nights of temperature and internal gravity wave measurements were obtained in the middle atmosphere by a lidar (laser radar) stationed in the Canadian
High Arctic at Eureka (80 ON, 86 OW) during the winters of 1992/93 to 1997/98. These observations are particularly interesting due to the influence over Eureka of the Arctic stratospheric vortex, an enormous cyclone that dominates the wintertime stratospheric circulation. It is within the lower stratosphere of the vortex core that (temperature sensitive) ozone depletions are found. Movements of the vortex have allowed measurements from
Eureka to be obtained inside the vortex core, within the vortex jet, and outside of the vortex altogether.
The observations have shown that temperatures in the lower (upper) stratosphere of the vortex core are very cold (warm), and vice versa for measurements obtained outside of the vortex altogether. By examining temperature measurements inside the vortex core only, an unexpected strong annual warming of the upper stratosphere was found. The warming commenced on average in late December and propagated down to levels below 30 krn in altitude. A smaller but significant cooling was apparent in the lower mesosphere at the same time.
The measurements of gravity wave activity revealed low gravity wave energies both inside the vortex core and outside of the vortex altogether. Episodes of high gravity wave activity were only seen in the vortex jet after late December and ended with the vortex breakdown in late March / early April. It is proposed, and supported by simple calculations, that the late December elevation in gravity wave activity within the vortex jet drove the concurrent intra-vortex stratospheric warming; i.e, that increased turbulent gravity wave dissipation near the stratopause forced flow into the vortex centre which compressed and adiabatically warmed the stratospheric airmass. The variations in gravity wave activity with respect to vortex position and time of year are related to stratospheric wind speeds and critical level filtering. These observations have implications for our understanding of sudden stratospheric warming events and the ozone depletion problem. Acknowledgements
1 would like to express my sincerest thanks to my supervisor, Professor Allan
Carswell. I am very fortunate to be have been part of such a dynamic and interesting research programme. The advice, independence and responsibility that Dr. Carswell gave me were all important factors in the completion of this work.
I am also indebted to my colleague Prof. James Whiteway. The many discussions we have had regarding this thesis and other collaborations have been of tremendous value.
Several others have also made notable contributions to this study. 1 should thank the following members of the York University / CRESTech lidar group for their participation in the Eureka measurement programme: J. Bird, D. Donovan, D. Hlaing, S. Pal, W.
Steinbrecht, and D. Velkov. The advice of Prof. Gary Klaassen was extremely helpful. I wish to also thank Jeannette Wild of the NDSCMCEP for providing the atmospheric analyses, and AES for operating the stratospheric observatory at Eureka and for providing the radiosonde measurements. Financial support by NSERC is gratefidly acknowledged.
I deeply appreciate the encouragement of my parents, Prof. Thomas A. and Wendy
Duck. I would also like to express my gratitude to my brothers and sister, Ken, Brad and
Teresa, and to my "new7' family members, Warren, Gail, Edna, Jim and Robert Turner.
Finally, I wish to thank my wife, Louisa; her love and patience have been tremendously important to me throughout my graduate student career, and especially in the preparation of this thesis. Contents
Abstract i v Acknowledgements vi List offigures ix List of tables xii
Chapter One Introduction
Chapter Two Background
2.1 The Static Structure of the Earth's Atmosphere 2.2 The Dynarnical Structure of the Earth's Atmosphere 2.3 The Mean Meridional Circulation of the S trato-mesosphere 2.4 Atmospheric Internal Gravity Waves
Chapter Three Measurement and Analysis Technique
3.1 The UV Lidar System at Eureka 3.2 Rayleigh Lidar Temperature Retrieval 3 -3 Gravity Wave Extraction Procedure 3 -4 NCEP Meteorological Analyses
Chapter Four The Northern Hemisphere Winter Circulation: 1992193 - 1997f98
4.1 Introduction 4.2 Sudden Stratospheric Warrnings 4.3 Zonal Mean Circulation Diagnostics 4.4 Stratospheric Variability over Eureka 4.5 The Vortex Relative Position 4.6 Horizontal Winds above Eureka
vii Chapter Five Observations of Strato-mesospheric TherrnaI Structure
5.1 Introduction 5-2 Night-average Temperature Measurements 5 -3 Evolution of Temperatures within the Vortex Core 5.4 Discussion
Chapter Six Observations of Stratospheric Gravity Wave Activity
6 1 Introduction 6 -2 Night-average Gravity Wave Measurements 6.3 Factors Affecting the Upward Propagation of Gravity Waves 6.4 Implications of Changes in Gravity Wave Activity within the Vortex Jet 6.5 Discussion
Chapter Seven Observations of Gravity Waves during a Final Warming
7.1 Introduction 7.2 Observations of Gravity Waves during Vortex Breakdown 7.3 Discussion
Chapter Eight Conclusions
References List of Figures
2.1.1 Average profiles of pressure and temperature for the Northern Hemisphere in January from CIRA86 2.1.2 Average profile of the Brunt-Vaisala frequency for the NH in January 2.2.1 CIRA86 zonal mean zonal wind speeds and temperatures for January 2.3.1 Radiatively determined zonal mean temperatures for January 15 23.2 Mean rneridional circuiation streamlines during January 1979 2.3.3 The zonal mean absolute angular momentum per unit mass for January 2.3.4 Diagram depicting the effects of gravity wave drag on the wintertime strato- mesospheric circulation 2.4.1 Sample measurements of wind and temperature showing wave-like perturbations 2.4.2 Diagram illustrating the structure of an internal gravity wave 2.4.3 Diagram showing the relationship between phase progression and group propagation for an internal gravity wave 3.1.1 Schematic for the UV Iidar system at Eureka 3.1.2 Sample signal profiles from the lidar at Eureka 3.2.1 A simdated lidar signal profile and the retrieved temperature profile 3.2.2 Sample temperature profiles measured at Eureka 3.3.1 Response profile for the gravity wave extraction procedure obtained fiom a simulation 3.3.2 Sample gravity wave analysis from temperature profiles obtained at Eureka 3.4.1 Maps of height and wind showing the Arctic stratospheric vortex 3.4.2 Comparison of wind profiles obtained from radiosonde measurements and NCEP data 4.2.1 Height maps showing the evolution of a sudden stratospheric warming 4.2.2 Stratospheric maps of height and potential vorticity showing a breaking 69 planetary wave
4.3.1 Daily difference between zonal mean temperatures at 90 and 60 ON during 75 the winters of 1992193 to 1997198 (30 hPa) 4.3.2 Daily zonal mean winds and the daily difference between zonal mean 79 temperatures at 90 and 60 ON during the winter of 1995196 (30 hPa)
4.4.1 Maps of height and wind showing the positional variability of the 80 stratospheric vortex 4.5.1 Illustration showing how the vortex relative position index is determined 83 4.5.2 The daily vortex relative position index during the winters of 1992193- 85 1997/98 4.6.1 Geostrophic winds above Eureka during the winters of 1992/93- 1997198 89 5.2.1 Temperature measurements obtained by the lidar at Eureka during the 93 winters of 1992193- l997I98 5.2.2 Representative temperature profiles obtained in the vortex core and outside 97 of the vortex altogether 5.23 Average temperature profiles obtained in the vortex core and outside of the 97 vortex altogether 5.3.1 Intra-vortex temperature profiles measured during 1996197 showing an 100 upper stratospheric warming 5.3.2 Composite time series of intra-vortex temperatures measured above Eureka 102 showing an annual upper stratospheric warming 5.3.3 Contours showing the altitude dependence of the annual intra-vortex 102 stratospheric warming 5.3.4 NCEP intra-vortex temperature data during the winters of l992/93-1996/97 104 that show an annual upper stratospheric warming 5.3.5 NCEP intra-vortex temperatures showing the evolution of upper 104 stratospheric temperatures during 1997198 6.2.1 Nightly measurements of stratospheric gravity wave activity at Eureka 115 during 1992193 to 1997/98 Composite time series of gravity wave energies measured in the vortex jet Gravity wave energy distributions depending on the vortex position Gravity wave energy distributions for measurements obtained in the vortex jet in different altitude ranges Gravity wave energy distributions for different stratospheric wind speed ranges A time series of stratospheric wind speeds in the vortex jet as seen from Eureka Gravity wave energy distributions for different transmission ranges Distributions of gravity wave transmission values for pre- and post- warming dates A comparison between measured intra-vortex temperature anomalies and vortex jet gravity wave energies showing simultaneous increases Comparison of NCEP intra-vortex temperatures with gravity wave energies measured at Eureka during 1997/98 Map showing the locations of four northern weather stations Gravity wave energies measured by radiosondes at four northern weather stations during the final warming of 1 996 Maps of height showing the evolution of the final warming of 1996 Evolution of stratospheric winds measured by radiosondes above Eureka during the final warming event of 1996 List of Tabfes
3.1.1 Lidar transmitter specifications 41 3.1.2 Lidar receiver specifications 41
6.2.1 Gravity wave energy distribution statistics depending on vortex position 119
7.2.1 Radiosonde measurement statistics taken before and after the final 159 warming of 1996
xii Chapter One
Introduction
The discovery of the springtime hole in the ozone layer above Antarctica [Furman et al., 19851 has motivated an international effort toward studies of polar stratospheric dynamics and chemistry. It is now established that chlorine chemistry, by way of heterogeneous reactions on the surfaces of polar stratospheric cloud (P SC) aerosols, is largely responsible for high-iatitude ozone depletions [Solomon, 19901. The critical step in this process, i.e., the heterogeneous conversion of anthropogenic chlorine compounds from inert species into reactive (ozone-destroying) forms, is particularly sensitive to temperature:
PSCs can only form below about 195 K (see Donovan el ai. [I9971 and references therein).
The conditions necessary for chlorine activation are limited to over the poles, where the wintertime s~atospherescan become extremely cold due to the lack of solar insolation
[Fels, 1985; Shine, 19871. It is interesting, however, that polar strato-mesospheric temperatures are often found to be far fiom radiative equilibrium. For example, the mesospheric meridional temperature gradient is "reversed" at the solstices so that the highest temperatures occur over the winter pole (in total darkness) and the lowest temperatures occur over the summer pole (in Ml sunlight). A diabatic circulation induced by the turbulent drag of dissipating internal gravity (buoyancy) waves is thought to be the source of this incongruity [Lindzen, 198 1; Holtoon, 19831. Similarly, that there should be o (warm) stratopause over either pole during winter at all is attributed to gravity wave driving [Holton,
1983; Kanzawa, 1989; Hitchman et al., 1989; Garcia and Boville, 19941. Lower down in the stratosphere, the relatively warm high-latitude conditions during winter coupled with cool equatorial temperatures are often ascribed to forcing by planetary waves [Mchfyre,19921.
That gravity waves can propagate from low level sources to great heights, and so provide an appreciable contribution to the momentum balance there, was first recognized by
Hines [I9601 in his interpretation of ionospheric wind irregularities. Atmospheric internal gravity waves, akin to waves on the surface of water, generally become unstable by the time they reach the mesosphere [Hodges, 19671, where they break down into turbulence (like water waves breaking on a beach) and exert a drag on the flow [Jones and Houghton, 197 11.
In the mean, this gravity wave drag acts to drive a small meridional diabatic circulation with compressional warming and descent at the end of the forward branch, and decornpressional cooling and rising toward the rear [Haynes et al., 199 11. Thus, the effects of gravity waves are of considerable importance in determining strato-mesospheric temperatures.
A quantitative description of the global gravity wave field and associated physical processes remains distant due largely to the dearth of measurements, and at present there is little consensus as to how gravity wave effects should be parameterized in atmospheric models [Hamilton, 19961. In particular, the lack of observations within the polar stratospheres is particularly significant due to the dominance of enormous and nearly circumpolar vortices found during winter above both regions. There is no equivalent perturbation to the flow at mid- or tropical latitudes, where observations are somewhat more abundant. Further, it is within the cores of these polar stratospheric vortices that the low temperatures leading to ozone depletions are observed [Schoeberl and Hartmann, 19911.
Clearly, if long term predictions regarding the state of the ozone layer and stratospheric circulation are to be made, the effects of gravity waves on temperatures in the polar vortices must be understood.
In early 1993, a new stratospheric observatory was established at Eureka (80 ON,
86 OW) in order to help address the need for increased observation of the Arctic middle atmosphere. The observatory is perched atop a mountain ridge (600 m elevation) on
Ellesmere Island, and houses a multitude of instruments for measurements of atmospheric properties and constituents. For the purposes of this study, a lidar (laser radar) was used to obtain over 400 nights of strato-mesospheric temperature measurements during the winter months of 1992/93 to 1997/98. The small-scale perturbations apparent in each temperature profile were extracted and used to provide a measure of gravity wave activity. The observations were interpreted in the context of the large-scale circulation, and have revealed previously unidentified characteristics of the High Arctic strato-mesospheric thermal and dynamical evolution.
Chapter Two begins with a survey of the observed atmospheric static and dynamical structure, supported with the relevant theory. In particular, the theory of internal gravity waves is developed, and equations relating the effects of wave drag on the general circulation are presented. Chapter Three follows with a description of the lidar at Eureka and the temperature retrieval algorithm. A procedure for extracting gravity wave induced perturbations fiom stratospheric temperature profiles is related and tested. The treatment of global atmospheric analyses, used to gauge the circulation in the vicinity of Eureka, is also provided.
A description of the stratospheric flow during each winter of observations is given in Chapter Four. The circulation is interpreted 2t first in terms of zonal mean diagnostics. and discussed in light of "sudden stratospheric warmings" (i-e., the planetary-wave driven synoptic events that lead to warm stratospheric temperatures over the pole). The description of the circulation during each wintertime campaign is furthered by focussing on the dynamics of the flow near Eureka A diagnostic is advanced that indicates when Eureka is located below the vortex core, beneath the vortex jet, and outside of the vortex altogether. A time series of the column wind vectors above Eureka is given Last.
Chapter Five presents the observations of large-scale strato-mesospheric thermal structure obtained by the lidar at Eureka. It is demonstrated that temperature changes in the stratosphere are associated primarily with movements of the polar vortex, an observation that contrasts with some past studies. Most importantly, a strong annual warming in the upper stratosphere of the vortex core was detected. The warming commenced in late December and propagated downward to levels below 30 km in altitude. A smaller but significant cooling was observed in the mesosphere at the same time. This annual intra-vortex stratospheric warming has not previously been discussed in the literature, and represents an event distinctly different fiom planetary-wave driven sudden stratospheric warmings and the seasonal march of temperatures due to changing solar insolation. The question of what could have caused such a warming is addressed late in the following chapter (and here, presently).
The observations of gravity waves above Eureka are reported in Chapter Six. The gravity wave activity was found to be consistently low during November and until mid- to late December. Thereafter, while low gravity wave potential energy densities continued within the vortex core and outside of the vortex altogether, episodes of elevated gravity wave activity were detected in the vortex jet. This rise in gravity wave activity was unanticipated. and correlates with the onset of the intra-vortex warming discussed in Chapter Five. The variations in gravity wave activity with respect to vortex position and time of year are shown to be related to the strength of the stratospheric winds and the amount of critical level filtering.
With observations of gravity waves that differ fiom what was expected, a new theory is advanced: it is proposed that the increased levels of gravity wave activity within the vortex jet in late December and thereafter drove the annual intra-vortex stratospheric warming. The elevated levels of gravity wave activity are thought to have induced increased turbulent drag near the stratopause, thereby forcing a flow into the vortex centre that acted to compress and adiabatically warm the underlying airmass. Simple calculations based on the equations presented in Chapter Two are used to support this idea. Finally, observations of gravity waves during a late-March / early-April "final warming" event are given in Chapter Seven. Since lidar measurements were not possible during this interval, radiosonde measurements from four northern weather stations were used instead. These observations showed a striking drop in gravity wave activity in the lower stratosphere upon vortex breakdown. The radiosonde measurements conf rm that the strength of stratospheric winds and critical level filtering are important factors with respect to gravity wave propagation into the stratosphere, and so strongly support the observations reported in Chapter Six.
A summary of the main results of this thesis is presented in Chapter Eight. Chapter Two
Background
2.1 The Static Structure of the Earth's Atmosphere
Global observations of the Earth's neutral atmosphere (fiom the grot
- 100 krn) indicate that its large scale vertical structure is rather consistent fiom place to place. Some average atmospheric properties compiled fiom radiosonde and satellite data for the Northern Hemisphere in January are presented in Figure 2.1.1.
As is shown in Figure 2.1.lq atmospheric pressure falls off exponentially with altitude from its value of about 1000 hPa at sea level with an e-folding height of roughly
7 krn. The reasons for this exponential decrease can be understood fiom simple theory.
Consider a parcel of air that is an ided gas so that
where p is the parcel pressure, T is its temperature, and p is its density. In the absence of atmospheric motions, the forces that act on the parcel are the up& pressure gmdient force ( -dp/d~) and the downward force of gravity (pg), which balance to give the hydrostatic equation,
where z is the geometric altitude and g(z) is the acceleration due to gravity. Substituting the
7 Pressure (hPa)
Scale Height (km) 6 7 8
180 200 220 240 260 280 300 Temperature (K)
Figure 2.1.1. a, The pressure, and b, the area weighted average temperature (or scale height H=RTig) for the Northern Hemisphere in January. In b, the dotted lines represent the maximum and minimum values, and the different layers of the atmosphere based on the thermal structure are marked. The data are from the COSPAR International Reference Atmosphere [Fleming et al., 1 9901, heredter referred to as CIRA86. ideal gas law (eq. 2.1.1) for p in the hydrostatic equation (eq. 2.1.2) and integrating gives the variation of pressure with height for an isothermal atmospheric layer bounded between altitudes z, and z2 as
where H=RTfg is referred to as the atmospheric scale height For a temperature of T = 230 K
(roughly the average temperature of the neutral atmosphere) the scale height is H = 6.7 km, and so equation 2.1.3 well describes the observed exponential pressure decrease with height.
Integrating the hydrostatic equation (eq. 2.1.2) from the top of the atmosphere downward yields
and so the pressure at any given level in a hydrostatic atmosphere is simply the weight per unit area of the overlying atmospheric column.
An average temperature profile for the Northern Hemisphere atmosphere in January is given in Figure 2.1.1 b. As is shown, the atmosphere can be separated into four distinct layers based upon changes in the vertical thermal gradients. Both the troposphere
(0 - 15 km) and the mesosphere (50 - 95 krn) are characterized by temperature decreasing with height, whereas the stratosphere (15-50 km) and thermosphere (95+ krn) have positive vertical temperature gradients'. The interfaces between these layers are designated the
tropopause (- 15 km), stratopause (-50 km), and mesopause (-95 km), and each separates
layers of different average stability with respect to vertical displacements. 'The static stability
of each layer can be determined by considering that the ideal parcel described before obeys
the thermodynamic equation,
where Tdq is the heat exchanged with the environment, dq is the entropy change, c, is the
specific heat of air at constant pressure, and v, (=pi)is the specific volume. Consider a
displacement of the parcel in the vertical by an infinitesimal amount dz. If no heat is
exchanged between the parcel and its surroundings, then ~dq=O and the motion is said to
be adiabatic or isentropic. Substituting the hydrostatic equation (eq. 2.1.2) into the
thermodynamic equation (eq. 2.1.5) with Tdq =O yields
where r=g/cpis referred to as the dry adiabatic lapse rate. According to equation 2.1.6, a
parcel that moves upward (downward) adiabatically will cool (warm) at a rate of
r = 9.77 Kkm.
Now, consider the change in environment that the parcel experiences. If the parcel
' The stratosphere and mesosphere are often referred to colIectively as the middle atmosphere or strato-mesosphere. automatically adjusts to the pressure po(z) of its new surroundings (which have temperature
To@) and density po(z)), then its density must change by an amount
where the ideal gas law (eq. 2. I. I), the hydrostatic equation (eq. 2.1.2), and the equation for dry adiabatic vertical motions (eq. 2.1.6) have been used. Here, the subscripts T and p are used to indicate that the temperature and pressure are held constant in their respective derivatives. The density change in the parcel's surroundings over the interval dz is given similarly by
The tiactional density difference between the parcel and its surroundings as the parcel rises or sinks is then
where If the background temperatures decrease with altitude at a rate no less than the lapse rate r,
then equation 2.1.7 shows that a parcel displaced upward (downward) will be heavier
(lighter) than its surroundings and so will experience a stabilizing downward (upward)
restoring force. The quantity N is referred to as the Brunt-Vaisala frequency, and may be
used to define the atmospheric stability. Figure 2.1.2 shows a vertical profile of N for the
temperature profile of Figure 2.1.1 b. As can be deduced fkom Figure 2.1.2, on average the
troposphere has relatively low stability, the stratosphere is strongly stratified, and the
mesosphere has intermediate stability.
2.2 The Dynamical Structure of the Earth's Atmosphere
As a first approximation, the temperature and wind fields of the Earth's atmosphere may be treated as zonally (i-e., longitudinally) symmetric. Figure 2.2.1 depicts zonally averaged temperature and wind measurements for January, which were compiled From radiosonde and satellite data. The layered temperature structure discussed in 92.1 is evident in Figure 2.2.la. Figure 2.2.lb presents the zonal average zonal winds: in the Northern
Hemisphere, two jets of "westerly" (i.e., eastward travelling) wind are centred at 30 ON and
35 ON, and at 10 km and 65 km in altitude respectively, and in the Southern Hemisphere the jets are positioned at 45 "S and 40 "S and at 10 km and 70 km respectively. Notice that meridional (i.e., latitudinal) temperature gradients underlie each of the jets. Horizontal thermal gradients act to drive the atmospheric winds, as will be demonstrated shortly. Buoyancy Period (min)
0.01 0.02 0.03 Brunt-Vaisala Frequency (s-I)
Figurc 2.1.2. The average Brunt-Vaisala frequency N for the Northern Hemisphere in January, calculated from the CIRA86 data. apwe1 08 09 OP 02 0 02- OP- 09- 08-
aPnWe1 08 09 OP 02 0 02- OP- 09- 08- The equation of motion for a parcel moving in Earth's rotating frame of reference is
where rr is the parcel velocity, t is he,L1 is Earth's rotation rate, and F, is a fictional term
that accounts for molecular viscosity. The total derivative (DIDt) gives the change in the
property being considered (here, the velocity) following the motion of the parcel. By
transforming equation 2.2.1 into tangent plane coordinates and retaining only the significant terms, the horizontal momentum equations reduce to
and
where x and y are the zonal (eastward) and meridional (northward) distances respectively, u and v are the velocities in the x and y directions, and f=2Qsin@ is the Coriolis parameter
(4 is the parcel's latitude). For steady-state atmospheric motions the horizontal momentum equations reduce to the "geostrophic" wind equations
and where u,(x~,z)and v&xy,z) are the zonal and meridional components of the geostrophic wind respectively, and the subscript z has been used as a reminder that the derivat-LIV~S are evaluated on surfaces of constant altitude. Since pressure decreases monotonically with height (see eq. 2.1.3), the geostrophic wind equations can be recast using pressure as the vertical coordinate such that U~=U~(X,Y,P)and vg=V,(X,Y,P) . By employing the differential definition for the "geopotential height" 2,
(where go = 9.8 1 m/s 2, the transformation to pressure coordinates gives
and
Global meteorological analyses are usually given as height values on a constant pressure surface, and so equations 2.2.5 and 2.2.6 are the variants of the geostrophic wind equations that shall be used hereafter. The geopotential height Z (or just hew)is closely related to the geometric altitude
(or just altitude), as can be seen by inspection of equation 2.2.4. Substituting the hydrostatic
equation (eq. 2.1.2) and the ideal gas law (eq. 2.1.1) into equation 2.2.4 and integrating with
the temperature held constant gives
as the height between pressure surfaces p,(z,) and p2(z2).Clearly, a height gradient between two pressure surfaces can only exist in the presence of horizontal temperature gradients.
Substitution of equation 2.2.7 into the geostrophic wind relations (eqs. 2.2.5 and 2.2.6) give the equations for the "thermal wind", i-e., the change in the geostrophic wind between the two pressure surfaces due to the horizontal temperature gradients. Temperatures decreasing toward the pole, then, will "open" an overlying jet of wind, and temperatures increasing toward the pole at higher levels will cause the jet to '%lose". This arrangement of temperatures and winds is evident in the zonal mean contours of Figure 2.2.1.
2.3 The Mean Meridional Circulation of the Strato-mesosphere
The starting point for many studies of atmospheric dynamics is an examination of the temperature structure that would result if the atmosphere were in radiative equilibrium.
Obsenred deviations from the radiatively determined state can then be attributed to dynarnical effects. Figure 2.3.1 shows the results of such a calculation. obtained for January Figure 23.1'. The zodmean temperatures for IS [mumy calculated with a time-marched radiative-convective- photochemical model (after Fels [I 9851). 15 from a radiative-convective-photochemical model that was time-marched through an annual cycle. As is shown in Figure 2.3.1, the high-latitude equilibrium temperatures in the winter hemisphere are extremely cold, with no apparent stratopause. This is a result of the fact that the high-latitude winter is mostiy sunless, and so there is little solar heating of the middle atmosphere. However, toward the midlatitudes and southward, the temperature structure is much more familiar, with the usual stratospheric increase in temperatures up to 55 km and decreasing temperatures above there. This structure is due primarily to the solar heating of ozone, which is at its highest mixing ratio near the stratopause.
By comparing the observed meridional temperature distribution (Fig. 2.2.1) with the radiative equilibrium temperatures (Fig. 2.3. I), several features become immediately apparent. The temperatures at the stratopause are close to radiative equilibrium throughout the Southern Hemisphere and into the rnidlatitudes. However, the stratospheric temperatures at the winter pole are much warmer than are expected from the radiative calculations. The
Arctic stratopause is particularly warm, and so is often referred to as the "separated polar winter stratopause", presumably because it sometimes appears at a different altitude and is necessarily caused by a separate means fiom its more southern counterpart [Hitchmanet a[.,
19891. In the Tropics, the lower stratosphere is cooler than anticipated. Perhaps most remarkably, the observed thermal gradient in the mesosphere is reversed so that the warmest mesospheric temperatures are found in the winter hemisphere and the coolest temperatures occur in the summer hemisphere. To understand how the temperatures are driven from radiative equilibrium by dynamics, consider again the parcel approach used earlier. Dynamically, a parcel initially in radiative equilibrium may be caused to warm (cool) by a compression (decompression), as can be deduced from the thermodynamic equation (eq. 2.1.5) for adiabatic motions,
If the atmosphere is to remain hydrostatic, the increased (decreased) parcel pressure must be due to the addition (removal) of mass to (from) the overlying column of air (see eq. 2.1.4).
Since the volume of a compressed (decompressed) parcel decreases (increases), its centre of mass moves downward (upward) in response to the compression (decompression) from above. Continuity demands that the mass added to (removed fiom) the overlying column be supplied by a meridional flow.
Now, since the compressed (decompressed) parcel is no longer in radiative equilibrium, it will radiate away (absorb) its excess (deficit) in internal energy, which must be compensated for by increased compression (decompression) from above if the parcel's temperature is to remain constant. The net result is a persistent downward (upward) mass transport though the warm (cool) region, forced by the continual addition (removal) of mass above by the meridional flow. The zonal mean meridional circulation of the middle atmosphere inferred in this way is shown in Figure 2.3.2. ( sense of mesospheric \ 1 cr'rcuLarion(schematic) \
Latitude
Figure 2.3.2. The mass-weighted zonal mean meridional streomlines for the stratospheric flow during January 1979, estimated from satellite data (after Solomon el al. [1986]). The meridionai velocities between 50 and 60 km in altitude are on the order of a few dsand the vertical veIocities are less than 1 cm/s. The sense of the mesospheric circulntion has been added as a schematic by Mchtyre [I 9921. It should be noted, however, that the law of angular momentum conservation implies
that frictionless rotating atmospheres resist rneridional flow. As is shown in Figure 2.3 -3,
there exists a strong meridional gradient in the zonal mean absolute angular momentum
distribution of the Earth's atmosphere. This distribution arises mainly from the rotation of
the Earth and is only slightly distorted by atmospheric motions. As such, angular momentum
conservation requires that parcels displaced meridionally experience an apparent restoring
force in the Earth's rotating fnme of reference. A significant torque (i.e., frictional dissipation) on the zonal flow is required to induce a persistent meridional flow, as was demonstrated by Leovy El9641 for the mesospheric circulation. That friction can drive a meridional circulation is most easily understood through the use of the free body diagrams utilized in Figure 2.3.4. Assuming the initial conditions of purely zonal flow, the dominant force balance in the horizontal plane is between the pressure gradient and Coriolis forces.
If a drag force operating in the opposite direction to the fluid flow is applied, the balance of forces can only be such that a small meridional flow exists in addition to the basic-state zonal flow.
The meridional circulation can be diagnosed mathematically by considering the zonal mean (or Eulerian mean) equations for the atmosphere, --SO -60 -40 -20 0 Latitude (deg.)
Figurc 233. The zonal average absolute angular momentum per unit mass of the atmosphere (km2/s)calculated from the CIRA86 data. Figurc 2.3.4 a, The Northern Hemisphere ninter steady state circulation resulting from differentia1 solar heating only. The northward pressure gradient- hrce F, and the southward Coriolis force F,,, balance so that the flow velocity V is purely zonal (i.e. rV[ = u ). The atmosphere is in radiative equilibrium and so the net diabatic heating rate 3 is zero everywhere. b. The Northern Hemisphere winter steady state circulation in the presence of eddy-induced drag. The balance of forces is now between the pressure gradient force, the Coriolis force and the wave drag force F,, which leads to a small meridional velocity ;' in addition to the zonal tlow . The mass piled up over the North Pole po~verfdlycompresses the underlying air, causing it to wm. In the steady state, this compressional heating is balanced by radiative cooling ( 74 since the temperature is away from equilibrium). and the net mass flus p,;' in the warm region is downward. and
which are the zonal mean momentum, conservation of heat, and mass continuity equations
respectively (see, for example, Holton [ 19921). Variables with overbars denote zonal mean
quantities while primed variables represent large scale perturbations to the mean state. The
quantity2 is the drag due to unresolved small scale eddies, and 7 is the diabatic heating rate.
The equations are to be evaluated on constant pressure surfaces, and so z is a vertical
coordinate defined by equation 2.1.3 for a fixed scale height H = RTs/g (i.e.,
z+ -H lnCp/ps] ), where T, is the constant scale temperature andp, is the surface pressure. The
reference density p, is defined by p,(z) = p,(O)exp( -zlH). and the squared Brunt-Vaisala
frequency is
in this formulation.
Care must be taken in the interpretation of the zonal mean equations, since the mean meridional circulation does not correspond to the mean rneridional mass circulation. The true meridional mass flow depends upon the small difference between the eddy inflow to and the mean outflow from the region considered. A non-zero mass flux into a region will result
in compressional heating or cooling of the underlying air mass, and an associated vertical mass transport. With this in mind, the zonal mean equations are usually transformed by the substitutions
and
which yields
and
The quantity Facts as a drag on the zonal flow and is given by - s = p;'~~-po~tvj.+ pof~~r~f~(~2~~)+ X where j and k are unit vectors in the meridional and vertical directions respectively. Here
the quantities F ' and G ' clearly represent the eddy driven "diabatic" circulation, and the
circulation they describe is illustrated schematically in Figure 2.3.4. Equations 2 -3.1 - 2.3 -3
are popularly referred to as the residual circuiation or transformed Eulerian mean (TEM)
equations [Andrews and McIrztyre, 19761. The term in parentheses pertaining to the large
scale eddies is referred to as the Eliassen-Palm flux, and results from the nonlinear growth
of planetary scale waves, as will be discussed in $4.2.
Returning to Figure 2.3.2, which depicts the mean meridional mass circulation, two
hemispheric cells in the seatosphere and one large circulation in the mesosphere (schematic
only) are evident. The lower set of cells is often attributed to forcing by large scale eddies
(see, for example, the review by Mclntyre [1992]), whereas the mesospheric circulation is
thought to be due to the effects of atmospheric internal gravity waves, i-e., the small scale
eddies [Linden, 198 1; Holton, 19831. The measurements obtained for the purposes of this
study will be used to show how =avity waves also play an important role in the stratospheric
circulation.
2.4 Atmospheric Internal Gravity Waves
Small scale eddies are observed in wind profiles obtained throughout the atmosphere, as can be seen kom the sample measurements shown in Figure 2.4.1. Figure 2.4.1 also shows a temperature measurement that is likewise irregularly disturbed. The temperature Temperature (K) 200 220 240 260
L I 1 19 January 1995,1 1:00 z
0 20 40 60 80. 100 120 Wind Speed (mls)
Figure 2.4.1. a, Radiosonde measurements of temperature and wind in the' troposphere and stratosphere above Eureka (80 "N, 86 " W), and b, wind measurements in the thermosphere fkom meteor trd data (after Liller and Whippk [I 9541). Srnd eddies in the wind fields are apparent on scales of 1-5 lun in a and 5-1 5 Lim in b . Wnve- like perturbations can du, be seen in the temperature profile of a. The wind and temperature perturbations arc interpreted ns evidence of atmospheric internal gravity waves. and wind oscillations are interpreted as being due to atmospheric internal gravity waves, and can be shown to be related by using the parcel approach empioyed earlier.
Consider several rows of parcels in an incompressible and stratified fluid that overlie each other in a slantwise fashion and are alternately dispIaced so that a wave results, as is illustrated in Figure 2.4.2. Since the parcels conserve density, rows that are displaced slantwise upward (downward) are heavier (lighter) than the mounding fluid (see eq. 2.1.7).
For adiabatic motions in the atmosphere, the parcels displaced upward (downward) are also colder (warmer) than the surrounding environment (see eq. 2.1.6), and so a slantwise wave in temperature results. For hydrostatic perturbations, the pressure at any given level is due to the mass of the overlying fluid column (see eq. 2.1.4), and therefore the heavier (lighter) parcels displaced in the slantwise upward (downward) direction overlie slantwise isopleths of high (low) pressure. The force of gravity (or buoyancy) acts to restore the parcels to their original position in the vertical, and lateral pressure gradients restore them in the horizontal.
For phase progressing waves, the slantwise parcel velocities are in phase with the pressure perturbations. Since horizontal velocity components are affected by the Coriolis force, the parcels trace cyclonic (anticyclonic) paths in the Northern (Southern) Hemisphere for downward phase progression.
Disturbances of this type have been historically referred to as "gravity waves", because gravity is ultimately the source of the restoring forces in both the vertical and horizontal directions. Gravity wave perturbations are realized in each of the density, Background Pressure & Density Increasing
Background Pressure + - & Density Constant
Figure 2-42, A schematic ihstrating the structure of an atmospheric internal gravity wave. The parcels are displaced in a wavelike fashion from equilibrium, and are assumed to instantly adjust to the pressure of their surroundincps. Those parcels displaced slanhvise upward are more dense than the surrounding air, and are coder due to adiabatic decompression. The air beneath the slantwise dense layer is compressed to a higher pressure. SimiIarly, parcels displaced dow=nward are less dense, wmer, and overlie low pressure perturbations. The phase progression is perpendicular to the wave Fronts, and so the points of masimum parcel speed are at the nodes of the oscillation. The group velocity is in a direction perpendicuIar to the wavevector. pressure, temperature, and wind fields. A few sources of gravity waves in the atmosphere
include topography [Nastrom and Fritts, 19921, convection [Fovell et al. , 1992; Dewan et
al., L 9981, fronts [Fritts and Nastrorn, 1992; Fairlie et ul., 19901 and adjustment processes
[O'Sullivan and Dunkerton, 19951. A quantitative understanding of the relation between the
perturbation variables can be understood through a detailed theoretical analysis.
Consider the perturbation equations of motion in an incompressible, Boussinesq and windless fluid,
and
auldx + avidy + &laz = o ,
which are the three perturbation momentum equations, the perturbation form of the
31 incompressibility statement
and the mass continuity perturbation equation respectively. Here, the five perturbation
quantities in the five perturbation equations are the three wind components u, v and w, the
pressure p', and the density p', and the background quantities are the pressure p&),
temperature To@),and density pdz). Equations 2.4.1 - 2.4.5 may combined to yield the wave
equation
where the squared Brunt-Vaisala frequency for incompressible motions is given by
N~ = -(g/po)ap,,/a~
and the horizontal and total gradient operators are given by OH2= a2/& 2+a2/ay2and
= a2/& +a2& +#/a= respectively*. Equation 2.4.6 can be solved for w to give
with the dispersion relation
A fully compressible treatment (see, for example, Gill [1982]) gives the same value forN as in equation 2. I .8. The value quoted here is only applicabte to incompressible fluids (such as water). where o is the intrinsic frequency, k,2,k2+Z2 is the horizontal wavenumber, k,'=k2+12+m ' is the total wavenumber, and k, 1 and m are the wavenumbers in the x, y and z directions respectively. By defining @, as the angle between the horizontal and the wavevector k,the dispersion relation (eq. 2.4.8) may be rewritten as
The polarization relations for the remaining variables are then
u = -tan@,w ,
and
Equations 2.4.7 - 2.4.13 describe in rigorous mathematical detail what was illustrated in
Figure 2.4.2 and described earlier in this section (with the one basic difference being that the perturbations are no longer required to be hydrostatic).
Within this theoretical framework, some of the other properties of gravity waves may be identified. From the dispersion relation (eq. 2.4.9), it is clear that gravity waves can have a maximum frequency of N and a minimum frequency ofJ comesponding to periods in the
atmosphere of about five minutes and 12.2 hours (at 80 ON) respectively. Also, since the intrinsic frequency of any gravity wave is dependent upon only the wavevector inclination and not the wavevector magnitude, the group velocity of the wave (defined as the gradient of o in wavenumber space) is perpendicular to its direction of propagation, i-e., the group velocity is parallel to the phase fronts and so downward phase propagation implies upward group propagation. This surprising fact can be understood physically by realizing that waves with wavevectors inclined more toward the horizontal wilI have phase speeds c given by
that are faster than waves with wavevectors inclined more in the vertical for constant k,. If two waves with wavevectors separated by an infinitesimal angle d& are allowed to interfere, then the patterns of constructive and destructive interference propagate at right angles to the phase fronts, as is illustrated in Figure 2.4.3.
The perturbation energy conservation equation may be obtained by adding equations
2.4.1 - 2.4.3, multiplied by p,u, p,v and pow respectively, and equation 2.4.4 multiplied by
$(p'lpo)N2 to get Figurc 2.43. The relationship between phase progression and group propagation for internal graviq waves. In a, two waves progress slantwise downward so that they will soon interfere (pamllel lines denote phase front ma.-xima). The wave directed at o shallower angle to the horizontal travels faster than the wave with the steeper inclination. In 6,c and d, the zone of constructive interference between the two waves (denoted by the dotted line) propagates slantwise upward as the fater wave progresses through the slower one. In d, the net phase progression is shown to be in the average direction the phase fronts are progressing, and the group propagation is in the direction the intefierence pattern moves. where the perturbation kinetic energy can be identified as
EK = !4pO(u2 + v2 + w2)
and the perturbation potential energy as
From equations 2.4.14 and 2.4.15, energy conservation dictates that as gravity waves
propagate vertically, the perturbed quantities u',3, $ and (pf/p,)' must grow exponentially
in response to the decreasing background density.
The fractional density perturbations may be related to fractional temperature
perturbations in the atmosphere by returning to the parcel approach used earlier. If a parcel
displaced in the vertical cools adiabatically, then its perturbation temperature will be given
by
Substituting this for I? in the equation for the corresponding density perturbation (eq. 2.1.7) yields as the relation between density a temperature hctional perturbations. Equation 2.4.16 will be used to replace p'lp, in all of the gravity wave perturbation energy calculations that follow hereafter'.
* The fully incompressible treatment of the perturbation energy equation (see Gill 119821) yields E, = '/ip,{(g/~z(p'/po -c~~~~~/~~)~+c~~~@~/~~)~),where c, is the speed of sound. The same approximation leads to both E,, = ~/;p,(~~/~~)(p~/p~~and E, = K~,($/N 2)(r'/~o)2,and so using either density or temperature perturbations to provide a measure of gravity wave activity is permissible. Chapter Three
Measurement and Analysis Technique
3.1 The W Lidar System at Eureka
The primary instrument used in this study to probe the atmosphere above Eureka was a laser radar, or lidar system. The principle of operation for lidars is similar to the more common radar (microwave) and sonar (acoustic) systems. A pulse of laser light is transmitted into the atmosphere, and the backscatter from atmospheric constituents is measured as a function of time (or equivalently distance). The received signal intensity is proportional to the total molecular and aerosol backscattering cross-sections, and so the rangecorrected signal intensity in an aerosol-fiee atmosphere is proportional to the density
(which decreases exponentially with increasing dtitude). Various wavelengths may be employed to take advantage of different molecular absorption and fluorescence features, and spectroscopic analysis techniques may also be used. Lidars using these principles are employed to measure relative densities [Hauchecorne and Chanin, 19801, temperatures
[Hauchecorne and Chanin, 1980; Nedeljkovic et al., 1993; She ei al., I 990, 19921 and winds
[Chanin et al., L 989; Bilk et al., 199 1a, 199 1b], as well as the abundances of trace species such as ozone [Carswell et al., 1991; McGee el al., 19931, sodium [Bills et al., 199 1b], hydroxyl [Brinksma et al., 1 9981 and water vapour [Me@ et al., 19891. Larger particulates such as sulphate aerosols [Anrmann et a/., 1997; Donovan et al., 19981, tropospheric clouds [Smsen et at., 19951, polar stratospheric clouds [Donovanet a[, 1996, 19971, and noctilucent clouds [Germurd et a[., 19981 may also be characterized.
The lidar system used in this study is illustrated schematically in Figure 3.1.1, and a description of its construction and operation follows. As is shown in Figure 3.1.1, the components of the lidar can be divided into two subsections: the transmitter and the receiver.
The primary component of the transmitter is an XeCl "Excimer" laser, which emits pulses in the near ultraviolet at a wavelength of 308 m. Stimulated Rarnan (inelastic) scattering in hydrogen gas is used to convert part of the laser radiation into a secondary wavelength at 353 nrn (first order vibrational Stokes shift). Outgoing pulses are expanded and collimated in order to minimize divergence, and are directed into the night sky by a steerable mirror. Specifications for the lidar transmitter components are given in Table 3.1.1.
Immediately adjacent to the transmitter is a 1 rn Newtonian telescope, which is used to collect the laser light backscattered fiom atmospheric constituents. The outgoing pulse stream is aligned so that it may be viewed within the telescope's narrow field of view.
Photons collected by the telescope are directed into the optics module, where they are separated by dichroic beam splitters into four different channels. The wavelengths of interest are the elastic (or Rayleigh) backscatter at 308 and 353 nm and the Rarnan backscatter from nitrogen gas at 332 and 385 nm. Interference filters are used to reduce the amount of background light away fYom these wavelengths. Signal detection is achieved via photomultiplier tubes (PMTs) operated in photon counting mode so that the extremely low 1z1 332 nrn Rotating Chopper I
Figurc 3.1.1. Schematic for the UV lidar system housed in the stratospheric observatory at Eureka- The sjmhols used to identi@ components are as follows: A=Aperture, BS=Dichroic Beam Splitter, IF=Interfcrence Filter, L=Lens, LED=Light Emitting Diode and detector, M=Mirror, NDF=Neutral Density Filter wheel, and PMT=PhotoMuldplicr Tube. The transmitter and receiver are cnclosed by separatc boscs. S pccificat ion
I Laser pulse energy I Laser pulse duration Laser pulse repetition rate
Laser divergence 65% of enera within a 0.4 mrad cone
Transmitter output wavelengths 308.0 nm (XeC! fundamental) I1 353.3 rim (1st Stokes vibrational Raman shift in Hz) Output linewidths (308.0 nrn. 353.3 nm) 0.3 nrn, 0.3 nm 1 -- Output pulse energies (308.0 nm, 353.3 urn)
Transmitter pulse stream divergence
Tablc 3.1.1 : Lidnr transmitter specifications
Parameter Specification
Telescope type I rn Newtonian, f = 2.5 m
Aperture field of view 0.2 to 1 mrad
Neutral density filters transmittances T = 1 0-05, 1 O*',10" and 10-3
IF bandwidths (@. 308.0,33 1.9, 353.3 & 385.0 nrn) 2.0,2.0,2.0 & 0.5 nm FWHM
PMT model EM1 9893/350
PMT gain and rise time 83s106 and 2.5 ns
Amplifier model Phillips model 770
Amplifier gain 10s
Discriminator model Phillips model 704
Discriminator threshold - 50 mV Counter board model Optech model FDC-700M
Countcr board maximum counting rate 700 MHZ
Receiver range and resolution 120 hand300 m
Tablc 3.1.2: Lidar receiver specifications signal levels received fiom the highest altitudes can be accurately measured. The intense elastic backscatter fiom low altitudes is removed via the use of a rotating chopper in order to eliminate signal induced noise and to avoid damaging the PMTs. Alternatively, a series of neutral density filters may be employed to reduce the signal levels, which allows the signal from low altitudes to be collected (although the high altitude photons are lost). A light-emitting diode and detector are used to monitor the chopper rotation and thereby synchronize the transmission of the outgoing laser pulse with the mechanical shutter.
The signal from each PMT is amplified, and pulses above a certain threshold
(corresponding to collected photons as opposed to spurious noise) are converted into digital logic pulses by a discriminator circuit. These pulses are accumulated by a counting circuit in successive bins of fixed duration, corresponding to intervals at an increasing range fiom the lidar. The commencement of photon counting for each shot is triggered by a photodiode that responds to the transmission of each outgoing laser pulse. The return signal is measured in this way for a fixed duration and then stored offline for later processing. Specifications for the receiver components are given in Table 3.1.2.
The need for routine data acquisition at Eureka led to a standard cycle of measurements that was repeated through the course of a night of observations. In each cycle, three consecutive high altitude profiles were obtained for ten minutes in duration with the chopper set to remove the elastic backscatter below 15 krn in altitude. A sample measurement of this type is given in Figure 3.1.2. Two subsequent low dtitudc I 10 100 lo3 104 lo5 lo6 lo7 lo8 Photon Counts
100 103 lo4 lo5 lo6 lo7 lo8 lo9 Photon Counts
Figurc 3.1.2 a, A ten-minute average sipaI profile (06:lS - 06:28 z), and b, the night-average signal protiIe (05:37 - 12:26 z, hm3 1 ten-minute averaged profiles) obtained by the lidar at Eureka on 14 February 1996. The signal from the 353 nrn channel is in solid black, 305 nm is in soIid grey, 385 nm is in dashed bIack, and 332 nrn is in dashed grey. measurements of five minute in duration each were acquired with the chopper set at 7 km and
0 km, and the neutral density filters set at T=10 " and T=1O5 respectively (where T is the transmission). An average of 8 cycles of measurements, or approximately 25 high altitude observations, were obtained in a typical night of observations. The high altitude signal at
353 nm, which is unaffected by ozone absorption, was used in this study to measure temperatures in the middle atmosphere. The remaining wavelengths and low altitude measurements can be used to measure atmospheric ozone (via differential absorption at 308 and 353, or 332 and 385 nm) and aerosol content, from about five to fifty km in altitude [Pal et al., 19961; they will not be considered further in this study.
3.2 Rayleigh Lidar Temperature Retrieval
In an aerosol-f?ee atmosphere, the Rayleigh backscatter collected by the lidar system may be used to derive an absolute measure of temperature, as will now be shown. Consider a measurement that collects N(z,) photons fkom an interval Az centred at altitude z, , where the altitude bins enumerate from i=O at the transmitter base to i=N at the top of the profile.
The amount of signal measured in each altitude bin is related to the average density p(zJ in that interval by where No is the number of transmitted photons, E is the optical efficiency of the system, TZ is the two way atmospheric optical trmsmission, A is the telescope area (and so ~lz:is the solid angle it subtends), axRis the Rayleigh backscattering differential cross section at the wavelength of interest, and M is the mean molecular mass. This can be rearranged to give the measure of atmospheric density at altitude z, as
where C is a normalization constant that incorporates several different instrumental parameters, and the atmospheric transmission. The two-way atmospheric transmission is given by
where a is the atmospheric extinction coefficient at the wavelength of interest. The transmission at 353 nm is essentially constant above 30 km in altitude, and will be treated as such hereafter; however, it may be calculated from equation 3.2.3 with the use of a model density profile in order to provide an altitude dependent correction to the constant C in equation 3.2.2 and so extend the measurement to somewhat Lower altitudes. The uncertainty in the density is given by where the error estimate for Poisson (random) statistics, which is appropriate for photon counting, has been used.
The instrumental constant C is difficult to determine in practice, and so Rayleigh lidars are said to only measure a relative density profile. The measurement can, however, be used to obtain an absolute profile of temperature. Equation 2.1 A, which relates the variation of pressure with altitude in a hydrostatic atmosphere, may be modified to become
where z, is the top observational altitude. Using the abbreviations p -(z,) = p(z, -LL/2) and p &) = p(zi+Ad2), this can be expressed in the discrete form applicable to binned lidar data as
or equivalently as the recursion relation
Psq = P+@J + p(z,)g& -
With the use of equation 3.2.2, equation 3.2.5 may be written as which demonstrates that the lidar also obtains a relative measure of pressure. The pressure
uncertainty is given by
where equation 3.2.4 for the signal error has been used. Notice that below about a scale
height fiom the top of the profile, the model pressure p+(z,) and pressure uncertainty 6p+(zN)
become smdl in equations 3.2.7 and 3.2.8 respectively.
Now, equation 2.1.3 (which assumes the atmosphere is ideal and hydrostatic) can be
rearranged to give
as the equation relating temperature to pressure. This has the error equation
which, afier using equation 3.2.6 to help evaluate 8@-(r,)/p+(z,)),becomes
47 where equations 3 -2.2 and 3.2.4 have again been employed.
The equations required to obtain a temperature measurement from lidar signals are now completely specified. An atmospheric model is used to determine the parametersp+(z,) and C (with the aid of equation 3.2.2). Equation 3.2.7 may then be used to obtain a relative pressure profile , and equation 3.2.9 to give the absolute measure of temperature. Equations
3.2.8 and 3.2.10 give the pressure and temperature uncertainties respectively. Note that since p+(z,) and Gp+(z,Jbecome small in equations 3.2.7 and 3.2.8 respectively below about a scale height from the top of the profile, the constant C divides out wherever it appears in both equations 3 -2.9 and 3.2.10.
Routine processing of the lidar data Leads to a few additional caveats. The first task in processing red lidar signals is to remove the constant noise levels due to background light and PMT dark counts (the background noise levels are evident in the sample signal profiles of Figure 3.1.2). In this study, the background is approximated as the average signal retrieved from above 1 10 krn. The uncertainty in the remaining "true" signal profile is then estimated as where B is the number of background photon counts. The top of the profile is taken as the altitude where the noise level is 15% of the signal. The night-average temperature profile is calculated fm using model temperatures to set the pressure value at the top of the profile.
The ten-minute average profiles are then obtained by using the night-average profile to constrain the top-level temperatures. In each case, the pressure error at the profile top is taken as 10%.
The temperature retrieval algorithm described above may be tested by constructing simulated lidar signal profiles from model data. The simulated signal profiles may then be processed, and the results compared with the known temperatures. Accordingly, a series of
30 ten-minute average signal profiles were created from a model hydrostatic density profile through the use of equation 3.2.2, normalized using the measured signal at 40 km from the data of Figure 3.1.2a. A realistic background noise level (again, obtained from the data given in Figure 3.1.2a) was added to the signal, as well as a measure of Gaussian distributed white noise corresponding to both the signal and background levels. The signals simulated in this way are shown in Figure 3.2. la.
A temperature profile derived i?om the night-average simulated signal is given in
Figure 3.2.1 b. Note that the profiles agree well with the original model temperature data, as expected. Figure 3.2.2 shows the temperature profiles obtained from the real Iidar signals given in Figure 3.1.2 by using the identical retrieval algorithm. Wave-like perturbations are evident in the ten-minute average temperature profile of Figure 3.2.2a. These disturbances 1 10 100 lo3 lo4 lo5 lo6 lo7 lo8 109 Photon Counts
180 200 220 240 260 280 Temperature (K)
Figure 3.2.1. 11, Lidar profiles simulated from hydrostatic CIRA86 density data. The ten-minute average protile is given in black, and the night-average protile is in grey. b, The calcuiated night-average temperature profik from the simulated signal given in a. The temperature vaIues are given in black, and the one sips standard deviation \ralues are in grey. The original temperature profile from CIRA86 is given as the dashed line. 180 200 220 240 260 280 Temperature (K)
180 200 220 240 260 280 Temperature (K)
Figurc 3.2.2. Temperature profiles obtained kom the lidar signals given in Figure 3.1.2. a, A ten-minute average profde (06: 18 - 06:28 z), and b, the night-average temperature profile measured above Eureka (05137 - 12:26 z) on 14 February 1996. The solid black line is the measured temperature profile, and the grey lines represent the measurement uncertainty. The dashed line is the CERAS6 temperature profile for January at 80 "N. are interpreted as evidence of atmospheric internal gravity waves. The characterization of
these waves will form a major component of this study.
3.3 Gravity Wave Extraction Procedure
In order to quantitatively study the gravity waves evident in measured temperature
profiles, they must be distin,&shed fiom the background atmospheric conditions. Consider
the disturbances apparent in the temperature profiles of Figures 2.4.1 a and 3.2.2a The waves
have wavelengths that vary from a few kilometres to over ten kilometres and have amplitudes
from a few Kelvin to greater than ten Kelvin, with the longer vertical wavelengths
corresponding to larger wave amplitudes. The observed waveforms show growth with
height, as would be expected &om the energy conservation considerations discussed in $2.4.
The basic state thermal structure itself varies on a scale of about 30 krn and greater, which adds a significant complication. Any usell gravity wave extraction procedure must be able to reliably remove the background state under a wide range of conditions.
In this study, the background for each ten-minute average temperature profile is approximated by a series of overlapping least squares cubic polynomials fits. Each of the fits are 25 krn in length and are centred in 1.5 km intervals. In creating the average background profile, only the middle third of each fit is retained in full; the end portions
(which may wag considerably) are smoothly removed from the average by decreasing their contribution exponentially with distance fiom the centre portion (an e-folding factor of about 3 lun is used). The final result is smoothed with a 1.5 km running mean.
The night-average fractional temperature variance [T'(z)/T,,(z)]~is then calculated from the series of ten-minute average perturbation profiles. The fractional noise variance o:, due to the uncertainty in photon counting over N, perturbation profiles, is estimated as
and is subtracted fiom the hctional temperature variance profile to yield the "true7' gravity wave variance profile. The uncertainty in the gravity wave fractional variance profile is taken as o:/& [Whiteway and Carswell, 19951. The potential energy density profile for the wave field may then be determined by using equation 2.4.15 (with eq. 2.4.161, where the buoyancy frequency is determined using equation 2.1.8 and the background fit to the night's mean temperature profile. The top of the potential energy profile is taken as 2.5 krn below the altitude where the noise variance overwhelms the gravity wave variance. Although the variance profile can extend down to the bottom of the temperature profile, only potential energy data above 30 km in altitude are considered so that no end effects, due to either aerosol contamination of the original temperature profiles or wag in the background fits, affect the analysis.
In order to demonstrate the utility of this procedure, several simulations were conducted. Eighteen sets of ten-minute average signal profiles were created following the method outlined in $3.2. Each set of signals was perturbed by a single propagating
sinusoidal wave; the waves were scaled to reflect the range of wavelengths and amplitudes
appropriate to the disturbances observed above Eureka. Temperature profiles were then
produced from the simulated signals and the wave variances extracted. The perturbation
energies were calculated and compared to the known input values in order to create the
response curve shown in Figure 3.3.1.
As is shorn in Figure 3.3.1, the gravity wave extraction procedure described above yields the correct potential energy densities to within about 20% for vertical wavelengths between 2 and 15 km. For vertical wavelengths shorter than 2 km, the input wave energies were extremely small, and so they could not be measured accurately. Vertical wavelengths larger than 25 krn, corresponding to background variability, are essentially invisible to the extraction procedure and only account for energy densities of a few Jouleskg at most.
Vertical wavelengths between 15 and 25 km correspond to the transition region from waves to background variability, and are only partly extracted by the background fitting procedure.
Disturbances of this type are rarely seen in the stratospheric temperature profiles measured above Eureka. The background fit to the temperature profile presented in Figure 3.2.2 and the average gravity wave potential energy profile for that night is given in Figure 3.3.2.
3-4 NCEP Meteorological Analyses
An important dynarnical field not measured by the lidar at Eureka is the atmospheric Vertical Wavelength (km)
I I I 1 I I 200 E \ : \, lnput Energy - 180 \ 9--o - \ \ - 160 \
- 100
I1I1l11 0 o4 1 o'~ 1 o-~ Vertical Wavenumber ( rn")
Figurc 3.3.1. The response of the gravity wave extraction procedure described in the test to waves of various wavetengths and energies. The dashed line gives the input energy as a function of the vertical wavelength, and the solid line gives the retrieved energy. The response is the fraction of the input energy retrieved by the ex~action procedure, and is given by the dotted line. The wave energies are retrieved to an acceptable degree of accuracy for vertical wavelengths between 2 and 15 h. 14 February 1996
180 210 240 270 -8 -4 0 4 8 1 10 100 100 Temperature (K) Perturbation (9%) Potential Energy (J/kg)
Figurc 3.3.2. The gravity wave analysis for 14 February 1996. a, The ten-minute average temperature profiIe previously shown in Figure 3.2.2a, and the estimated background fit (dashed he). b, The perturbation profile that results after the background fit has been removed. c, The night-average potential energy dens@ profile from the full night of observations (3 1 ten-minute average profiles). wind. A low resolution wind field can be obtained, however, through the use of atmospheric meteorological maps or "analyses", as was suggested in $2.2. Atmospheric analyses are global gridded maps of height and temperature, provided for this study by NCEP' on eighteen pressure surfaces ranging from 1000 to 0.4 hPa (i-e., from the ground to about 55 km in altitude). A sample height map for the Northern Hemisphere stratosphere is given in
Figure 3.4. la. The maps are constructed by combining or "assimilating" radiosonde and satellite temperature measurements with the use of a numerical model. Height fields are derived from the temperature data by stacking the thicknesses at each level produced by using equation 2.2.7. The radiosonde data are obtained fiom over 200 stations worldwide, and the satellite data are supplied by the TiROS Operational Vertical Sounder (TOVS) radiometer system. In the troposphere only radiosonde data are used, whereas both radiosonde and satellite data are employed in the lower stratosphere; analyses above 10 Wa are based on satellite data only. The NCEP gridded data products are described and used by
Finger et a!. [1993], Trenberth and Olson [I 9881, and GeNer et al. [1983], amongst others.
In this study, the height analyses are used to determine the geostrophic wind through the use of equations 2.2.5 and 2.2.6. Wind maps are calculated for the Northern Hemisphere
@oleward of 15 ON) in the following way: The height grids are interpolated to 23 constant latitude circles between 17.2 and 86.4 ON, spaced in accordance with the data- Each latitude circle, comprised of 64 equispaced points, is smooihed by applying a Fourier transform and
' The National Centers for Environmental Prediction (NCEP) were formerly collectively referred to as the National Meteorological Center (NMC). Wind Speed (m/s)
Figure 3.4.1. a, The Northern Hemisphere height map (epm) at the 10 hPa pressure level for I S January 1994. The height isohes are separated by 250 gpm and decrease monotonically down to the low (marked by an L), cscept for in the region of the Aleutian High (marked by the H). b, The map of geostrophic wind poleward of 15 "Ncalculated tiom the height data in a. Vectors are used to indicate the direction of the wind wherc its speed exceeds I5 mls. The dark ring of strong cyclonic tlow (counter-clochxise rotation) is the Arctic stratospheric vortex. A weak anticyclone (clockwise rotation) can be seen over the Aleutian Islands. In each map, the inner circles are at the constant latitudes of 30,60,and 80°N respectively. Eureka is denoted by the white dot. truncating at zonal wavenumber 6, as suggested by Randel [I 9871. Derivatives are evaluated in both the zonal and meridional directions through the use of cubic spline interpolation, which has the property of producing both smooth interpolations and smooth derivatives
[Elson, 19861. The derivatives are then scaled by the latitude dependent Coriolis parameter in order to yield the geostrophic wind.
A sample wind map for the Northern Hemisphere stratosphere is given in Figure
3.4.1 b. It should be noted that the flow circulates in the counter-clockwise direction around the stratospheric low apparent in Figure 3.4.la, and so is referred to as a cyclone.
Conversely, the flow around a stratospheric high is in the clochvise direction, and is consequently referred to as an anticyclone (cf. equations 2.2.5 and 2.2.6). In what follows, height and wind maps will be used interchangeably to characterize the atmospheric circulation.
The wind values calculated from the analyses may be compared to the measurements obtained from balloon borne radiosondes launched at Eureka. A few comparisons of this type are given in Figure 3.4.2. Note that the calculated and measured winds are in good agreement in both magnitude and direction at almost all altitudes. As can be seen in Figure
3.4.2, the geostrophic winds tend to underestimate the strength of tropospheric jets, and are often incorrect near the ground since boundary layer frictional effects have not been taken into account. When the winds are low (say, below five mk), the measured wind direction may vary enormously due to the influence of gravity waves, and so a comparison under these -120-60 0 60 120 Wind Speed (Ws) Direction (deg. clockwise from N)
b 60
40 z5 -- 2 20
0 0 20 40 60 80 -120 -60 0 60 120 Wind Speed (Ws) Direction (deg. clockwise from N)
-120 -60 0 60 120 Wind Speed (rnls) Direction (deg. clockwise from N)
Figure 3.4.2. Representative compYisons of radiosonde mememenb at Eureka (solid lines) with the geostrophic ~vindscalculntfd torn NCEP analyses (clear circles). a. 28 December 1994. b, 7 Fsbruar). 1995, and c, 6 March 1995- conditions is not possible. Higher order balance approximations to the wind field (see, for example, Randel [1987]) were tested, but were not found to provide an appreciable improvement over the comparisons shown in Figure 3.4.2. The geostrophic winds, which are much less expensive (in computation time) to calculate than higher order balance approximations, are sufficiently accurate in both the troposphere and stratosphere for the purposes of this work. Chapter Four
The Northern Hemisphere Winter Circulation: 1992/93 - 1997198
4.1 Introduction
The interpretation of ground-based measurements benefits greatly &om comparisons with large-scale meteorological maps, i.e., the atmospheric "analyses" described in $3.4.
This is especially true for observations obtained in the High Arctic stratosphere, a region dominated during winter by a pervasive meteorological feature: the Arctic stratospheric vortex. The vortex is an enormous cyclone that develops during winter in response to the stratospheric meridional heating gradient (see 52.2 and 52.3). It spans a diameter of roughly
4000 km between wind speed maxima that may be in excess of 80 ds. Example maps of height and stratospheric winds, used equivalently hereafter to infer the vortex state (see
§3.4), were given in Figure 3.4.1; the vortex is apparent in Figure 3.4. la as a deep stratospheric low and in Figure 3.4.lb as the closed cyclonic circulation. That the vortex dominates the wintertime strato-mesospheric circulation is evident in the zonal mean zonal wind contours for January given in Figure 2.2.1 b.
An important point, however, is that the vortex itself is not usually zonally symmetric in form; it may be displaced far fiom its quiescent position over the pole, and so may significantly modulate any measurements of dynamical properties in the Arctic region. With this in mind, daily analyses of height and temperature were obtained fiom NCEP for each
62 year &om 1992193 to 1997/98 for November through March. The analyses will be used in the following sections to describe in detail the circulation during the six wintertime observational campaigns at Eureka, and will be referred to extensively in the following chapters. Before proceeding, however, it will be necessary to discuss a particular large-scale phenomenon observed during winter at high latitudes: the b'sudden stratospheric warming".
4.2 Sudden Stratospheric Warmings
The discovery of stratospheric wamings is usually attributed to Scherhag [1952], who fust observed a sudden stratospheric temperature increase in wintertime radiosonde measurements over Berlin The term "sudden stratospheric warming" has since evolved to imply a large-scale midwinter synoptic event that rearranges the zonal mean thermal structure of the high-latitude stratosphere so that the stratospheric temperatures over the pole warm relative to midlatitudes and the zonal mean zonal winds decelerate. The "suddemess" of these events is spectacular, with the relevant changes observed to occur within only a few weeks. Reviews of midwinter warming observations and theory are given by Andrews ef al.
[1987], McIntyre [l982], Labitzke 1198 11, and Schoeberl 119781.
Sudden stratospheric warrnings are of interest because they represent changes in the atmosphere in a direction opposite to what would be expected from radiative considerations alone (see $2.3). Somewhat arbitrarily, a sudden stratospheric warming is referred to as a
"major warming" if at 10 hPa (-30 km) or below the zonal mean stratospheric temperatures increase and the zonal mean circulation is reversed poleward of 60 ON; such an event usually resdts in the complete breakdown of the vortex. The term "minor warming" is used to imply a strong reduction in the zonal mean meridional thermal gradient poleward of 60 ONy but not a circulation reversal. A "fmd warming" is simply the event that leads to the anticyclonic circulation dominant in the stratosphere during summer. Defined in this way, minor warmings are observed annually whereas major warmings are seen only every few years.
Final warmings usually occur in late March or early April.
Although the definitions given above are expressed in terms of zonal mean phenomena, sudden stratospheric warmings are intrinsically asymmetric synoptic events.
To illustrate this point, a series of height and temperature maps for Decernber/January
1984/85 are presented in Figure 4.2.1; the evolution of the dynamical fields during that period are typical of what is observed during a major stratospheric warming. As is shown in Figure 4.2. la, the circulation in mid-December of 1984 was characterized by a strong and cold vortex low that was slightly displaced from its quiescent position over the pole by a warm "Aleutian High"' located over the dateline. Within a week, another high developed over the Greenwich Meridian and acted in tandem with the Aleutian High to pinch the vortex into a "dumbbell" shape (Figure 4.2.1b). In early January of 1985 this pinching caused the vortex to split in half as the warm anticyclones merged over the pole (Figure 4.2.lc), resulting in a reversal of the high-latitude stratospheric meridional temperature gradient and
A high is regularly observed in the stratosphere over the Aleutian Islands, and so it has been given this special name. See Harvey and Hilchrnan [I 9961 for a c1imatoIogy of Aleutian High observations. Figure 4.2.1. Mnps of height (dam) adtemperature (K) on the 10 hPa pressure surface in the Northern Hemisphere for a, 20 December 1 984, b, 28 December 1984, and c, 2 January 1985 (after Fairfie and O %dl [1988]). (Continued on next page) Figurc 4.2-1. (Continued from previous page) zonal mean zonal circulation, i-e., a major stratospheric warming. Sudden warmings produced by a single stratospheric high (as in Figure 4.2. la) and by pinching of the vortex
(as in Figure 4.2.lb) are both observed [Labirzke, 19771'. Note that neither of these configurations is zonally symmetric, and that the perturbation fields are observed to rotate clockwise around the pole with height.
Now, imagine that for a configuration that is zonally symmetric, the parcels along any constant latitude circle form a ring or "materid contour". It is of some interest to examine how these material contours distort when the flow becomes asymmetric, i.e., during a warming like the one described above. To this end, a suitable tracer of contour parcels must be defmed. Consider fmt that if radiative effects are negligible then the parcels are restricted to travel along isentropic surfaces. By integrating the isentropic form of the thermodynamic equation (eq. 2.1.5) with respect to pressure, it is straight-forward to show that these surfaces have a constant "potential temperature" 0 given by
which represents the temperature a parcel at pressure p and temperature T would obtain if it was adiabatically compressed to some reference pressure p, (usually taken as the average surface pressure). Now, on isentropic surfaces, there is a quantity referred to as Ertel's
Equivalently, if the spectrum of height perturbations from the zonal mean is evaluated around a constant latitude circle (say 60 ON) and the dominant wavenumber used to characterize the degree of asymmetry, then the events in Figures 4.2.la and 4.2.lb can be referred to as "wave 1" and "wave 2" phenomena respectivety. potential vorticity and defined by
which is analogous to angular momentum and so is conserved for adiabatic frictionless flow'.
Here, the term re =(aV/ax4u/av>, is the relative vorticity (or curl) evaluated on the isentropic
surface. Now, since the Coriolis parameterf increases from equator to pole and the curl is
greatest around the vortex axis, it can be seen that the potential vorticity should increase from the equator to the vortex centre (aB/ap is always negative). The material contours mentioned above, then, can be taken as the rings of constant potential vorticity that circle the vortex centre.
The distortion of material contours that accompanies a sudden stratospheric warming was f~stshown by McIntyre and Palmer [I 983, 19841 in a study of the events leading to a major warming in February 1979. Maps of height and potential vorticity in the stratosphere are given for two January days of that year in Figure 4.2.2. As is shown by the height map in Figure 4.2.2a, the circulation in mid-January was roughly symmetric around a deep polar vortex. However, Figure 4.2.2b indicates that only ten days later a strong Aleutian High had developed and acted to displace the vortex away from the pole (which is similar to the situation illustrated in Figure 4.2. la). The potential vorticity maps that correspond to each of these days are given in Figures 4.2.2~and 4.2.2d respectively. As is confirmed by Figure
The development of the potential vorticity equation and a good supplementary discussion is given by Holton [1992]. Figure 4.2.2, Maps of Northern Hemisphere height on the 10 hPa pressure surface for a, I7 and b, 27 January 1979 (contour interval 24 dam). The corresponding mops of potentid vorticity Q (x lo4 Km-Is-')are given in c and d for the 850 K isentropic dace(near 10 hPa)- The contour interval in the potential vorticity maps is 2 units, with values greater than 2 shaded lightly and vdues greater than 4 shaded darkly. (After Meinye and Palmer [ 1983, 19841) 4.2.2c, potential vorticity is highest within the vortex and lowest in the tropics. Furthermore,
it is apparent that steep gradients in potential vorticity are associated with the vortex jet, and
so these gradients are often used to define the vortex "edge7'. Figure 4.2.2d demonstrates that
the emergence of the Aleutian High over the dateline is associated with a poleward intrusion
of subtropical air coupled with erosion of the vortex edge so that a long "tongue7' of high
potential vorticity extends equatorward. This "buckling7' of potential vorticity contours gives
rise to a well mixed region referred to as the rnidlatitude "surf zone", and acts to further
sharpen the potential vorticity gradient at the vortex edge. During a final warming, maps of
potential vorticity (not shown) reveal that the remnants of the vortex airmass are mixed into the midlatitude surf zone and are replaced over the pole by air from the subtropics.
With respect to the distribution of temperatures during a sudden stratospheric warming, the region of largest dynarnical warming associated with the large scale eddies is found in the intense jet between a stratospheric high and the vortex low [Fairlie and 0 'NeiZZ,
1988; Manney et a!. , 1 9941. Certain observations during the development stages of a sudden warming have revealed a stratopause descended to about 40 km with temperatures as high as 40 "C [Labitzke, 1972; von Zahn et al., 19981. After a major warming is llly developed, high-latitude measurements have shown relatively cool temperatures in the upper stratosphere, and warm temperatures in the lower stratosphere [Labitzke, l972].
With the synoptic description of sudden stratospheric warmings now complete, an examination of causal mechanisms seems appropriate. In $2.3, it was shown that zonal mean flows are resistant to meridional circulation- To see how this is manifested in the three
dimensional flow, consider the response of a parcel with initially zero relative vorticity that is displaced toward the pole. This movement will result in an increased Coriolis parameter
(f) for the parcel, and so the relative vorticity (co)in equation 4.2.2 must become negative if potential vorticity is to be conserved. Negative relative vorticity implies an equatorward curl of the parcel, and so the parcel is stabilized against poleward displacement. Similarly, movement of the parcel toward the equator will result in a curl back toward the pole, and so the flow in general is stable against meridional displacement. The atmosphere, then, supports horizontal waves in the dynamical quantities (potential vorticity, height, wind and temperature) along constant latitude circles; these waves are commonly referred to as planetary waves. Generally only planetary waves with global zonal wavenumbers I to 3 are allowed in the winter stratosphere due to filtering by the background winds [Charney and
Drain, 196 11.
Now, similar to gravity waves, planetary waves that propagate upward fiom tropospheric sources grow with height in response to the decreasing background density.
Usually this has little effect in the Arctic stratosphere because for small amplitudes the waves are generally ccdefocussed" fiom the pole; i.e., their wavevectors follow great circle trajectories that lead to the tropics and oblivion. However, if the forcing from below is strong or the waves encounter critical lines (i-e., where the wave phase speeds equal the background wind speeds), then the planetary waves may become strongly nonlinear right within the stratosphere. It is this nonlinear stage of development that leads to contour
buckling' (or wave breaking) and sudden stratospheric warmings, as was first shown by the
mechanistic model of Matsuno [I97 11".
In mechanistic models like the one used by Matsuno [ 197 11, the height on some level
associated with the top of the troposphere (say, 300 hPa) is prescribed, and its effects on the
dynamics of the stratosphere are determined numerically by solving the primitive equations.
Experiments with mechanistic models ace usually performed by perturbing the tropospheric
boundary so that planetary waves are generated (see, for example, 0 'Neill and Pope [1988]).
When strong forcing is prescribed at the tropospheric boundary, planetary wave breaking and
sudden stratospheric warmings are produced. Impressively, numerical experiments using
atmospheric analyses to prescribe the tropospheric boundary develop warmings in tandem
with the observations (see, for example, Fairlie et al. [1990]).
The interactions of planetary wave breaking with the zonal mean circulation can be
diagnosed through the diabatic circulation equations given in $2.3. It is found that the eddies
associated with contour buckling lead to a convergence of the Eliassen-Palm flux at high
At this stage, the planetary-scale circulation is better described by interacting vortices instead of planetary wave disturbances, as was discussed byO'Neill and Pope [1988]. A case in point: the Aleutian High is the product of a contour buckling event and so is associated with wave breaking and not the wave itself per se. The strengths of the "wave 1" and "wave 2" perturbations footnoted earlier, then, should not be associated with the amplitudes of planetary waves, but rather just used to characterize the nonlinear flow (although this fact is often ignored).
" it is interesting to note that when the Quasi-Biennial Oscillation (QBO), i,e., the 27 month oscillation of tropical winds from easterlies to westerlies and back, is in its easterly phase, more sudden stratospheric warmings are observed; this is thought to be due to the criticai line filtering imposed by the QBO at low latitudes [Holfon and Tan, 1982; Hamilton, 19981. latitudes, and thus the drag force that must accompany the deceleration of the zonal mean
zonal winds and warming over the pole [Palmer, 19811. It is often said that this phenomenon
represents the focussing of the planetary wave activity into high latitudes, although this
seemingly ignores the fact that the eddy fluxes are a result of planetary wave breaking and
not the linear propagation of the waves per se. 0 'Neill and Pope [I9881 and Juckes and
0 'Neill [I9881 alternatively argue that the poleward focussing of the Eliassen-Palm flux is
symptomatic of a widening surf zone and cannot be justified as the cause of stratospheric
warmings as suggested in the earlier (zonal mean) studies.
Returning to the synoptic analysis, it is of interest that mechanistic models such as
those of 0 'Neil1 and Pope [I9881 and Fairlie et al. [1990], and high resolution models such
as the one layer barotropic model of Juckes and Mclnwe [I9871 and the "domain-filling"
trajectory model of 0 'Neill et al. [1994] indicate that the vortex is impervious to transport
through its edge, even during stratospheric warmings. Observationally, this impenetrability
is realized by sharp gradients in tracer concentrations across the vortex edge (see, for
example, Donovan et al. [1995, 19961). The models of Juckes and Mclntyre [I9871 and
0 'Neill et al. [ 19941 also showed that material contours in the surf zone are stretched into
long filaments and are sometimes advected around the vortex edge or a stratospheric high;
these filaments may be observed as perturbations in ground-based measurements of ozone
profiles [Manney et al., 19981. Last, the model of Fairlie el al. [I9901 confirmed observations that the region of greatest dynarnical warming associated with the large scale eddies is in the region between a stratospheric high and the vortex low.
It is important to make one final note regarding the interpretation of ground-based observations during sudden stratospheric warmings. It should be obvious that, due to the asymmetries evident during sudden warmings, any measurements will need to be examined with reference to the synoptic maps. Some zonal mean quantities will be described next, but will only be used as a guide to place the measurements at Eureka in the context of previous studies. Following that, the meteorological conditions local to Eureka during the course of each observational campaign will be described.
4.3 Zonal Mean Circulation Diagnostics
The sense of the high-latitude zonal mean meridional temperature gradient, used to infer periods of stratospheric warming, is most easily determined by taking the difference of the zonal mean temperatures between 90 and 60 ON. The variations in this quantity are shown for the wintertime measurement campaigns of 1992/93 to l997/98 in Figure 4.3.1.
As is shown in Figure 4.3.1, the high-latitude zonal mean temperatures were quite variable during the course of each winter. The temperature differences between 90 and
60 ON varied from between -25 K and +20 Ky with periods of difference approaching or greater than 0 K representing significant stratospheric warming. Some winters were more variable than others; during the winters of l992/93, 1993/94, 1994/95 and 1997/98, many episodes of significant sudden warming were apparent, whereas the 1995/96 and l996/97 -60 -30 0 30 60 90 Time (days since January 1 )
h - 20 - 51994195 -30 I I 1 ,#I I I I -60 -30 0 30 60 90 Time (days since January 1)
Figure 43.1. The daily merence between the zonal mean temperatures at 90 and 60 " N on the 30 hPa pressure surface. Tick marks on the upper ordinate of each graph indicate measurement dates for the lidar at Eureka. (Continued on nest page) -60 -30 0 30 60 90 Time (days since January 1)
30 IMl,llUl UIII I 1111 1 11111. 1 1 I-11 II h 20 - 1996197 - s. -
-60 -30 0 30 60 90 Time (days since January 1 )
11- 11- I If 1 ll !I-~IUI - 1997198 - - -
I i Iltlll I I III. I I -60 -30 0 30 60 90 Time (days since January 1)
Figurc 4.3.1. (Continued from previous page) seasons were relatively undisturbed "cold" years. In particular, the 1996/97 season was
peculiar in that, after a warming that peaked in early December, the stratosphere remained
practically undisturbed through the end of March. For each winter, the lower stratospheric
meridional eddy heat fluxes (not shown) correlated reasonably well with episodes of zonal
mean warming, which is consistent with the view that the warmings were generally forced
by planetary-scale disturbances propagating upward £kom below. Coy ei al. [I9971 have
shown that the Lower stratospheric meridional eddy heat fluxes during the February and
March of 1997 were significantly lower than during any of the previous 18 winters, which explains in part why the stratosphere at the higher levels during that time was so undisturbed.
It is interesting that none of the warrnings apparent in Figure 4.3.1 can be considered a major warming since the zonal mean circulation did not reverse everywhere poleward of
60 ON, and a vortex breakdown never occurred'. To be sure, some warnings did see significant high-latitude circulation reversal (e.g., as far south as 67.5 ON in early-March
1993 and 65.5 ON in late-Januaqdearly-February 1995), but not all the way south to the
(arbitrarily) defined latitude of 60 ON". An example of a final warming with a full circulation reversal, constructed by extending the data set for the winter of 1995/96, is given
After the cornpietion of this work, a major warming / early final warming occurred in early March 1999.
" Manney et al. [ 1994) incorrectly reported that the early-March 1993 sudden warming was major. In fact, their own maps of zonal mean zonal wind (their Fig. 1) show that this was not the case. in Figure 4.3.2. Since major warmings had previously been detected every few winters (see,
for example, any of the review papers discussed in §4.2), it is surprising that one did not
occur during any of the six winters described here. The reasons for this remain an open
question in the literature.
4.4 Stratospheric Variability over Eureka
As discussed in $4.2, the utility of zonal mean diagnostics in interpreting
measurements obtained in the High Arctic are limited because the stratospheric flow there
is far from zonally symmetric, especially during sudden warmings. For measurements at
Eureka it is of more immediate interest to determine where the vortex was positioned each
day reIative to the observatory. To this end, a few maps of height and wind, representative
of the range of conditions encountered during the wintertime measurement campaigns of
l992/93 to 1997198, are given in Figure 4.4.1 ; the corresponding wind profiles over Eureka were given previously in Figure 3.4.2.
As is shown in Figure 4.4.1, the vortex dominates the stratospheric circulation around
Eureka during winter, as was related earlier. Furthermore, the maps of wind reveal that different regions of the vortex may be clearly identified, and so the position of Eureka in the vortex Gamework may be determined. In what follows, the region of relatively low wind speeds in the eye of the vortex is referred to as the "vortex core" or as being "intra-vortex", whereas the cyclonic ring of relatively high wind speeds is referred to as the "vortex jet". -60 -30 0 30 60 90 1 20 1 50 Time (days since January 1 )
Figure 43.2. The time progression of two stratospheric warming diagnostics on the 30 Papressure surface for the winter of 1995196. a, The di£Faence in zonal mean temperatures between 90 and 60 " N, and b, the zonal mean zonal winds (ds)for latitudes poleward of 20 " N. In b, the zero dswind contour is in bold, and the intervals of anticyclonic zonal mean circulation are shaded. Note that the strong find warming in early April is accompanied by a reversal of the zonal mean circulation direction. Figure 4.4.1. Maps of Northern Hemisphere height and wind speed on the 10 hPa pressure level for three days during the 1994/95 winter season: a, 28 December 1994, b, 7 February 1995, and c, 6 March 1995. The same contour interval md shading scheme has been used as in Figure 3.4.1. The corresponding wlnd profiles over Eureka are given in Figure 3 -4.2. Locations away from either of these regions are said to be "outside of the vortex altogether7' or as being "extra-vortexy7.An examination of the maps in Figure 4.4.1, then, show that the vortex was at times positioned so that Eureka was beneath its core, below its jet, or outside of the vortex altogether. The choice of Eureka as the site for a stratospheric observatory was rather fortuitous since Eureka lies directly beneath the region of maximum wintertime stratospheric variability in this regard [Harvey and Hitchman, 19961.
Due to the large number of observations at Eureka, however, it is unsuitable to compare each measurement to the corresponding maps of height or wind. Instead. it is best to define indices that determine the state of the vortex in a way that leads to simple interpretation. For example, the temperature differences between 90 and 60 ON were used in 54.3 to infer periods of stratospheric warming. Likewise, the position of the Arctic stratospheric vortex with respect to Eureka can be simply described through the use of a quantitative index specified for use here: the vortex relative position.
4.5 The Vortex Relative Position
The structure and dynamics of the polar stratospheric vortex can be defined in any number of ways; for example, the vortex may be visuaIized by using maps of wind or equivalently height (see Fig. 4.4. I), and potential vorticity (see Fig. 4.2.2). For the purposes of studies aiming to interpret ground based measurements of dynarnical properties within the context of the large-scale circulation, it is easiest to ascertain the influence of the vortex through maps of wind, and so this approach will be followed hereafter. Investigations of tracer transport typically use potential vorticity to define the vortex edge because potential vorticity is a conserved quantity for frictionless adiabatic flow (see, for example, Donovan et al. [1995, 1996, 1997, 19981).
The vortex relative position index is used to determine when Eureka is beneath the vortex core, jet, and outside of the vortex altogether, and its calculation is demonstrated in
Figure 4.5.1. To begin, a great circle contour is drawn on a map so that it passes through
Eureka and is taken in a direction perpendicular to the wind at 30 km in altitude above there.
The 30 krn height level is selected because it represents the usual height of the vortex jet maximum when it passes over Eureka (see Figure 3.4.2). The absolute wind speeds normal to the contour at 30 km in height are determined, and the positions of the vortex core wind speed minimum and vortex jet wind speed maximum are found; they are assigned index values of 0 and 1 respectively. These locations are also used to defrne a linear distance scale along the contour so that the vortex relative position of Eureka can be determined.
In what follows hereafter, vortex relative position index values less than 0.4 will be used to indicate when Eureka is beneath the vortex core, values from 0.4 to 1.6 to imply when Eureka is below the vortex jet, and values greater than 1.6 to indicate measurements taken outside the vortex altogether. The inner boundary is chosen as a compromise between two competing factors: the region defined as the vortex core needs to be narrow enough so that the winds within there are always low (as one would expect in the "eye" of any vortex), -4000 -2000 0 2000 4000 6000 8000 Distance from Eureka (krn)
Figurc 4.5.1. Determination of the vortes relative position index (usi~gthe data fiom 18 December 1994, shown in Figure 3.4.1 a, as an esample): a, A great circle contour "AB" is drawn (in black), taken perpendicular to the wind at 30 h in height above Eureka; b, The magnitude of the wind normal to AB at 30 km in height is examined, and the position of the vortes core wind minimum and vortex jet wind maximum are marked with index values of 0 and 1 respectively. On this particular day, then, Eureka is at a vortes relative position of 0.936. but broad enough so that a good number of measurements are also captured. The outer boundary was chosen to be an equal distance away from the jet maximum as the inner boundary. Note that vortex tilting is smali enough that it does not appreciably affect the categorization described above when looking at other levels in the stratosphere.
Furthermore, the results that follow in later chapters are not significantly affected if the index values for each boundary are changed (say, by *O. I).
An alternative index based on potential vorticity could have been used to gauge the position of the vortex relative to Eureka. However, the potential vorticity "edge" does not reliably trace the vortex jet maximum, its gradient is highly variable, and a diagnostic index based on this quantity would need to consider potential vorticity across the entire vortex. An emphasis on local dynamics is desired here, and so the definition of the vortex relative position is given. Regardless, measurements said to be inside the vortex core here are unquestionably within the region of high potential vorticity associated with the polar vortex, as may be seen from an inspection of Figure 4.2.2.
Continuing, graphs displaying the vortex relative position for Eureka during each measurement campaign (1 992193 to 1997198) are given in Figure 4.5.2. A comparison of the vortex relative positions given in Figure 4.5.2~ for the 1994/95 season with the corresponding maps of wind in Figure 4.4.1 shows how the new index relates the position of the vortex with respect to Eureka; i.e., measurements in the vortex core are clearly represented by the lowest index values, and measurements outside of the vortex altogether -60 -30 0 30 60 90 Time (Days since Jan 1 )
-60 -30 0 30 60 90 Time (Days since Jan 1)
-60 -30 0 30 60 90 Time (Days since Jan 1 )
Figurc 45.2. The vortes relative position indices for the six winter measurement seasons at Eureka. Indes values behveen 0 and 0.4 indicate periods when Eureka is beneath the vortes core, values between 0.4 and 1.6 are t&en to be in the vortex jet, and values greater than 1 .G represent measurements obtained outside of the vortes altogether (dotted lines separate each of the regions). Tick marks on the upper ordinate of each graph indicate measurement dates for the lidar at Eureka. (Continued on nel9 page) -60 -30 0 30 60 90 Time (Days since Jan 1)
-60 -30 0 30 60 90 Time (Days since Jan I)
I-I1 I-I1 I 11 l~l111IlI IlUlllllUIllLlllllll Ill II 1- llll[ 1997198 2 -
II, -60 -30 0 30 60 90 Time (Days since Jan 1)
Figurc 4.5.2. (Continued from previous page) are identified by the highest index values.
As can be seen in Figure 4.5.2, the variability in the position of the vortex with respect to Eureka may change significantly from year to year. For example, during the l992/93 and 1994/95 seasons, the vortex moved so that Eureka was positioned beneath its core, jet, and outside of the vortex altogether during different periods of time. In contrast,
Eureka was located mostly beneath the vortex core during the winter of 1996/97, and largely below the jet during the 1993/94 and t997/98 seasons.
It is of interest to note the high degree of correlation between the vortex relative position index values of Figure 4.5.2 and their corresponding sudden stratospheric warming diagnostics given in Figure 4.3.1. This implies that periods of time when Eureka was positioned beneath the vortex core were not intervals of signiticant sudden stratospheric warming. Conversely, episodes of sudden stratospheric warming were most apparent when
Eureka was outside of the vortex altogether. This is an important point, and will be referred to in Chapter Five when interpreting temperature profiles measured by the lidar at Eureka.
4.6 Horizontal Winds above Eureka
The description of iarge-scale meteorological variability may be completed by presenting profiles of the background winds above Eureka. A measure of the winds above
Eureka is important for the interpretation of gravity wave measurements, since the background winds can affect gravity waves through Doppler shifting. Consider, by defining Ow(-.) as the angle between the background wind and north and Q as the (constant) angle between a gravity wave's wavevector and north, that the projection of the background wind in the direction of the wavevector is given by u0cos[OW(z) -0,]. A gravity wave with intrinsic frequency o=k, c, ,then, is Doppler shifted by the background wind to the new fkequency o, = k, {c, -uo cos [8&) -€I,]1. The Doppler shifting of gravity waves with small horizontal phase speeds c, will prove to be important in the gravity wave analysis of
Chapter Six.
The horizontal winds above Eureka were obtained fkom the NCEP height analyses
(see §3.4), and are given for each measurement campaign in Figure 4.6.1. As is apparent in
Figure 4.6.1, the wind field above Eureka was highly variable. Wind speeds ranged from calm conditions at all levels to over 100 m/s in the upper stratosphere. The wind direction at ail levels was highly variable, and most often ranged between northerly and westerly flow.
By comparing Figure 4.6.1 with Figure 4.5.2, it is clear that periods of high wind speed in the stratosphere corresponded to times when Eureka was located beneath the vortex jet, as would be expected. Low stratospheric wind speeds occurred when Eureka was inside the vortex core, and also when Eureka was outside of the vortex altogether and beneath a stratospheric high. Time (days since Jan 1)
-30 0 30 Time (days since January 1)
Time (days since January 'I)
Figurc 4.6.1. Geostrophic winds above Eureka calculated from NCEP analyses for each winter from I99293 to 1997198. The shading gives the wind speed and the scale given in a is used for each plot. The vectors indicate the direction of the wind: up indicates flow toward the north, left is to the west, right is to the east, and down is to the south. Tick marks on the upper ordinate of each graph indicate measurement dates for the lids at Eureka. (Continued on nest page) 0 30 60 Time (dayssince January 1)
0 30 60 Time (days since January 1)
U I I I I I -60 -30 0 30 60 Time (days since January 1)
Figure 46.1. (Continued from prcvious page) Chapter Five
Observations of Strato-mesospheric Thermal Structure
5.1 Introduction
The discovery of the springtime ozone hole over Antarctica [Fmmanet al., 19851 has motivated increased observational investigation of the Arctic stratosphere. The Arctic studies have revealed somewhat lower levels of chemical ozone depletion (see, for example,
Donovan et al. [1995, 1996, 19971 and Newman et al. [I 9971) than over Antarctica, which is consistent with the notion that temperatures in the stratosphere of the Northern Hemisphere only fall below the chlorine activation threshold on an occasional basis [Scchoeberl and
Hiwtmann, 19911. It is anticipated, however, that this situation could change due to the cooling effect of anthropogenic CO, emissions on strato-mesospheric temperatures [Rindet al., 19901. For example, Shindell et al. [I9981 used chlorine and greenhouse gas emission projections as input into a general circulation model to predict that there should be continued and increased ozone depletion until after the year 2010. Recovery of the ozone layer to levels found in the early 1980s is not expected until after 2050.
General circulation models like the one used by Shindell et al. [1998], however, have certain difficulties predicting the detailed circulation of the middle atmosphere, and in particular often suffer f?om a ''cold pole" problem with associated overly strong vortex winds [Hamilton, 19961. These deficiencies make the utility of ozone depletion predictions unclear at present, especially when considering the sensitivity of the ozone depletion process to polar stratospheric temperatures. A goal in this observational study, then, is to identify aspects of the circulation that are not well understood, in the hope that progress can be made toward a more comprehensive description of polar strato-mesospheric dynamics.
In this chapter, night-average temperature profiles measured by the lidar at Eureka during the winters of 1992/93 to 1997/98 are presented, and variations in the profiles on vertical scales greater than 25 km and on time scales longer than a few days are discussed.
Observations of the smaller scale fluctuations due to atmospheric internal gravity waves will be considered in Chapter Six.
5.2 Night-average Temperature Measurements
Four hundred and forty-five nights of temperature measurements were obtained by the lidar at Eureka for the purposes of this study. Due to the large number of observations, it is inconvenient to present this data as a series of night-average temperature profiles.
Instead, the data for each campaign are presented in Figure 5.2.1 as season-mean temperature profiles and contour plots showing the daily temperature anomalies.
Figure 5.2.1 was constructed by using the mean temperature profile for each night with the effects of gravity waves removed (as is described in 53.3). Lidar data were used above 25 krn, and radiosonde data were employed at the lower altitudes. Gaps between the Averaae
180 210 240 270 40 60 Temperature (K) Time (days since Jan. 1)
180 210 240 270 -30 0 30 60 Temperature (K) Time (days since January 1)
180 210 240 270 0 30 60 Temperature (K) Time (days since January 1)
Figure 5.2.1. Wintertime temperature measurements at Eureka by lidar (25 - 60 km) and radiosonde (10 - 25 knl) during 199293 to 1997/98. The seasonmean temperature pro6Ie (solid line) and the daily temperature diEerences from that profiIe (contours) are given separately for each year. The error bars on each profile represent one standard deviation of the corresponding anomalies, and the dashed temperature profile is an average at 80 " N for November to March chom the CIRA86 data. The legend for each contour plot is given in a, and tick marks on the upper ordinate of each contour plot denote the measurement dates. (Continued on nest page) Averaae d - 1995196
180 210 240 270 -30 0 30 60 Temperature (K) Time (days since January 1)
180 210 240 270 -30 0 30 60 Temperature (K) Time (days since January 1)
Averaae Anomalies
180 210 240 270 -30 0 30 60 Temperature (K) Time (days since January 1)
Figurc 5.2.1. (Continued from previous page) radiosonde and lidar measurements were interpolated through the use of a cubic polynomial fit. No data smoothing was used so that the variations seen in the contour plots of Figure
5.2.1 reflect the large-scale changes observed each day in the stratospheric temperatures.
The error bars on each season-mean temperature profile represent one standard deviation of the corresponding anomalies, with the variance due to the noise in each night-average profile removed via a procedure analogous to that outlined for gravity waves in $3 -3.
The profiles given in Figure 5.2.1 show that the average wintertime stratospheric temperatures differed from year to year. The 1992/93, 1993/94, 1994/95, and 1997/98 measurement campaigns were characterized by a relatively warm lower stratosphere above
Eureka, whereas the 1995/96 and 1996/97 seasons were significantly colder. The contour plots of Figure 5.2.1, however, indicate that a tremendous amount of variability around each season-mean profile was observed. At 40 krn in altitude, the average standard deviation was roughly 13.5 K, which is larger than for stations at Lower latitudes; for example, Leblanc et a[. [I9981 indicate that the standard deviation at 40 km between November and March is roughly 12 K at midlatitudes, and decreases dramatically toward the subtropics*.
The vertical structure of the midwinter temperature anomalies presented in Figure
5.2.1 is of considerable interest. Inspection of the anomalies reveals that warm temperatures
*~eblatrcel af. [I9981 give their temperature standard deviations for 33 day running means with the effects of gravity waves and intra-seasonal variations included. The study here has excluded both effects, but instead has included the seasonal variations. The intra-seasonal and seasonal variations turn out to be roughly equal for the time period considered, and the effects of gravity waves are relatively small. and so this direct comparison can be made. in the upper stratosphere are often accompanied by cold temperatures in the lower stratosphere, and vice versa. By comparing the contours in Figure 5.2.1 with the vortex relative position indices of Figure 4.5.2, the strong dependence of stratospheric temperatures on the vortex position is immediately apparent. When the vortex moved so that Eureka was situated beneath the vortex core, the temperatures in the upper stratosphere became warm and the lower stratospheric temperatures became cold, and vice versa for movements that placed
Eureka outside the vortex altogethe<.
Figure 5.2.2 shows two representative profiles of temperature that demonstrate these coupled changes in the stratosphere, one obtained when Eureka was in the core of the polar vortex and one taken outside of the vortex altogether. The profile measured in the vortex core shows a very warm upper stratosphere, and an extremely cold lower stratosphere.
Conversely, the observation taken outside of the vortex shows a cool upper stratosphere and a warm lower stratosphere, and is nearly isothermal throughout the entire middle atmosphere.
The measurement outside of the vortex altogether was obtained within a stratospheric high
(the usual case for extra-vortex measurements at Eureka), as is revealed by the corresponding maps of height and wind given in Figure 4.4.1 b.
Average profiles of intra-vortex and extra-vortex temperatures, given in Figure 5.2.3, yield similar results. The average profiles were constructed by using all of the available Iidar measurements with vortex relative position indices less than 0.4 and greater than 1.6
.. - . --
Definitions for the various vortex relative positions were given previously in $4.5.
96 Profiles InsideIOutside of Vortex
180 200 220 240 260 280 Temperature (K)
Figurc 5.2.2. Representative profiles of temperature obtained in the vortes core (solid Iine) and outside of the vortex altogether (dotted Line). The profiles were measured at Eureka by the tidar (above 25 h)and by radiosonde (below 25 km).
Averaae Profiles Inside/Outside of Vortex 1'1'1'1"'1
180 200 220 240 260 280 Temperature (K)
Figurc 5.2.3. Average profiles of temperature inside the vortes core (solid line) and outside of the vortex altogether (dotted line) as obtained by the lidar at Eureka. The error bars represent one standard deviation for the respective set of measurements. Note that the verticaI scale used here is different than that in Figure 5.2.2. respectively. A total of 83 measurements obtained in the vortex core and 22 observations
taken outside of the vortex altogether were used in the averages.
There are a few other features in the contour plots of Figure 5.2.1 that warrant
comment. First, temperature anomalies in mid- to late March are often positive throughout
the stratosphere, especially for observations obtained within the vortex core. This late-winter stratospheric temperature rise is to be expected because of the increased solar heating available at high latitudes at that time [Shine, 19871. However, a few other episodes of strong positive temperature anomalies throughout the stratosphere are apparent; for example, the entire stratosphere was warm in late January 1995 and late December 1997. These events corresponded to periods of significant sudden stratospheric warming (cf. Fig. 4.3.1) and when Eureka was positioned in the outer regions of the vortex jet (cf. Fig. 4.5.2); that temperatures throughout the stratosphere are warm with the vortex in such a configuration is consistent with studies that have showed the maximum dynarnical warming due to large- scale eddies occurs in the jet between the vortex low and a stratospheric high [Fairlie and
0 'Neill, 198 8; Fairlie et al., 19901. In both cases, when the vortex moved so that Eureka was positioned outside of the vortex altogether, the anomalies returned to their regular pattern of coupled higMow level temperature changes.
5.3 Evolution of Temperatures within the Vortex Core
The temperatures obtained during the 1996/97 measurement campaign are of particular interest because, as was discussed in 54.5 and shown in Figure 4.5.2e, the vortex
was positioned so that Eureka was largely within or near the vortex core for the entire winter.
The contours of Figure 5.2. le, then, represent the quasi-evoiution of temperatures within the
vortex core during the 1996/97 winter season. By examining these contours from late
December onward, an interesting feature emerges: the temperatures measured in the upper
stratosphere warmed significantly relative to the seasonmean profile, a warming that was
sustained through the end of that campaign. Figure 5.3.1 shows a series of temperature
profiles obtained during the warming onset, a progression that emphasizes that the
disturbance enhances already warm temperatures in the upper stratosphere of the vortex core.
That a warming of the vortex core occurred during the winter of 1996/97 is of considerable
interest because the stratosphere was particularly unaffected by sudden stratospheric
warming disturbances from late December through March of that measurement campaign (cf.
Fig. 4.3.1e).
The temperatures measured during 1996/97, however, were not obtained entirely
£kom within the core of the vortex (as defined by the vortex relative position index of $4.5);
some were taken on the "inside edge" of the jet. Regardless, a view of the thermal evolution
of the vortex core can be constructed by averaging all of the intra-vortex measurements taken
fkom 1992/93 to 1997/98. Even though the evolution of the circulation was different for each year, all of the intra-vortex measurements were obtained in conditions unaffected by sudden stratospheric warmings (see §4.5), and so a "composite" view of the intra-vortex thermal l996/97 Intra-vortex Tern ~eratureProfiles
180 210 240 270 Temperature (K)
Figure 5.3.1. A series of temperature profiles obtained by the lid= a Eureka from 27 December 1996 to 13 January 1997. The solid black lines ore the measurements with uncertainties bounded by the lines in solid grey. The CM86 temperature profile for January is given as the dashed line for reference. Note the strong warming that begins in the upper stratosphere and propagates downward. evolution in relatively consistent conditions can be developed.
The average evolution of temperatures in the intra-vortex composite confirms that a
significant and persistent wintertime warming occurred annually in the upper stratosphere
of the vortex core. Figure 5.3.2 shows a time series of all of the intra-vortex temperature
measurements at 45 km in altitude (representative of the upper stratosphere); January 1 of
each year is taken as day zero. As is shown in Figure 5.3.2, on average the temperatures in
the upper stratosphere of the vortex core were fairly constant (or perhaps slowly decreasing) through November until mid-December. A remarkably strong upper stratospheric warming of 2S&Z K' commenced in late December. The warming developed over a period of roughly three weeks and persisted through the end of March.
The vertical structure of the observed intra-vortex warming can be understood from
Figure 5.3.3, which shows the evolution of temperatures in the vortex core at each altitude with the prewarrning (average for November and December) temperatures having been subtracted. An average version of the data given in Figure 5.3.2 is contained in Figure 5.3.3 at 45 km in altitude. As is shown in Figure 5.3.3, the annual intra-vortex warming peaked at this level and propagated downward at a speed of roughly 1 km/day. The warming penetrated deep into the stratosphere, and can be seen at altitudes lower than 30 km. A small but significant cooling developed in the mesosphere during the same period of time.
Here, the average prewarming temperature was 233 * 1.5 K and the average postwarming temperature was 258 & 1 K, where the uncertainties represent one standard deviation of the mean. The pre- and postwarming temperatures represent averages before December 27 and after January 10 respectively. -60 -30 0 30 60 90 Time (days since January 1)
Figurc 53.2. Temperatures obtained within the vortex core at 35 hin altitude by the lidar at Eureka during sis measurement campaigns from 199293 to 1997198. January 1 of each year is taken as day zero. Note the strong stratospheric warming that commenced on average in late December..
Pre-warmina mean Anomalies (K)
180 200 220 240 260 -30 0 30 60 Temperature (K) Tin:e (days since January 1)
Figurc 5.3.3. A composite presentation of all of the intra-vortex temperature profiles obtained by lidar and radiosonde during winter at Eureka fiom 1992/93 to 1997198- The profile gives the mean intra-vortex temperature profile for measurements taken prior to December 27, and the contours show the average deviation of intra-vortex temperatures kom that profile as a bction of time. The zero Kelvin anomaly is denoted by a thick black line, and temperatures over 5 K warmer than the profile are shaded. Note that on average a strong stratospheric warming (coupled with a mesospheric cooling) commenced in late December. The lidar observations of a signifkant intra-vortex warming in late December may be confirmed by examining temperatures fiom the NCEP global analyses. Figure 5.3 -4 gives a series of temperatures fiom the analyses, sampled at a height of 40 krn and at a location directly above the I0 hPa height minimum (which corresponds to the vortex axis); data is presented for each winter fiom 1992/93 to 1996/97 (the 1997198 data will be considered separately). As is confirmed by Figure 5.3.4, the average intra-vortex temperatures of the upper stratosphere were relatively constant £?om November until mid-December during those years. An intra-vortex warming of roughly 20 K commenced on average in mid-December and developed over a period of about four weeks. In contrast with the lidar observations was the additional LO K warming apparent in the analyses over the final 2% months. It should be noted, however, that the temperatures presented in Figure 5.3.4 were sampled with the vortex in a variety of ~o~gurations,and not just in the undisturbed state within which the corresponding lidar measurements of Figure 5.3.2 were obtained. Thus, differences in the development of the warming can be expected (including, say, the peak in the 1994/95 data in late January).
With respect to the winter of 1997/98, the temperatures in the upper stratosphere of the vortex core evolved in a somewhat different fashion for that year than during the preceding five measurement campaigns. As is shown in Figure 5.3 -5, the upper stratospheric temperatures held a relatively low and constant value during November of 1997, which is similar to the previous five winters. However, a strong intra-vortex warming peaked in late - - - - - Height: 40 km 1 -60 -30 0 30 60 90 Time (days since January 1)
Figurc 5.3.4. Temperatures sampled at a height of 40 hon the vortes axis during the winters of 1992193 to 1996197 from NCEP analyses.
Height: 40 km 220 I"I"1" 1"I"l -60 -30 0 30 60 90 Time (days since January 1)
Figurc 5.3.5. Temperatures sampled at a height of 40 km on the vortex a-sduring the winter of 1997198 from NCEP analyses. December and completely disappeared by mid-January, when the temperatures returned to their pre-warming mean. By early March the temperatures in the vortex core returned to their climatological values (given previously in Figure 5.3.4), where they remained until the end of the measurement season. The unusual evolution of intra-vortex temperatures during the winter of l997/98 will be addressed in $6.5.
5.4 Discussion
An analysis of temperature profiles obtained by the lidar at Eureka has revealed that the strato-mesospheric thermal structure depends strongiy on the position of the wintertime vortex. Inside the vortex core, temperatures in the lower stratosphere were found to be relatively cold, whereas in the upper stratosphere they were seen to be relatively warm. For measurements obtained outside of the vortex altogether the reverse was true, and so at times an almost isothermal temperature profile was apparent there. The observed distribution of temperatures is consistent with the notion that horizontal temperature gradients are required to force the vortex winds, i-e., that temperatures decreasing (increasing) toward the vortex axis in the lower (upper) stratosphere created the horizontal height (or pressure) gradients needed to open (close) the vortex jets (see $2.2 and 53.4).
The coupled low level coolings with high level warmings (and vice versa) observed in the stratosphere above Eureka, then, are clearly linked to vortex movements. When the vortex moved so that Eureka was closer to its centre, temperatures in the lower stratosphere became colder than the mean, and temperatures in the upper stratosphere warmed. As the
vortex moved away from Eureka, the opposite was seen to occur. The persistently cold
temperatures observed in the lower stratosphere during the 1995196 and 1996/97
measurement campaigns can be attributed to the fact that the balance of measurements during
those years were obtained in the vortex core (see 84.5).
The interpretation of the coupled temperature changes described above contrasts with
some earlier works that regarded the progression of warm temperatures in the upper
stratosphere to the lower stratosphere as representative of an evolving sudden stratospheric
warming (see, for example, Labitzke [ 198 1I). The fnst measurements at Eureka during
February and March of 1993 were discussed in this framework by Whiteway and Carswell
[1994], and the interpretation is fbrthered here by considering the measurements in a more
global context. For example, it is now clear that warm intra-vortex temperatures in the upper
stratosphere are a persistent feature: they cannot be uniquely identified with classical sudden
stratospheric warming because the vortex core is positioned above Eureka only when the
stratosphere is relatively undisturbed (see 84.5). Conversely, measurements taken outside of the vortex altogether are only obtained during periods of sudden stratospheric warming
(see 54.5); significant warming in extra-vortex temperature profiles is apparent below 30 km
(- 10 hPa) only, which is consistent with the discussion of $4.2.
Regardless, that the upper stratosphere of the vortex core is warm at all is surprising, since there is little solar heating in the High Arctic during the mostly sunless winter and also because extra-vortex air is not observed to be mixed into the vortex centre (see 54.2). In the absence of any dynamical effects, then, the temperatures should be expected to appear more like those at 80 ON in Figure 2.3.1, i.e., perhaps LOO K colder than the intra-vortex stratopause temperature seen in Figure 5.2.3.
The additional strong and sustained warming of the intra-vortex upper stratosphere in late December was a completely unanticipated phenomenon. It represents an event distinctly different from the sudden stratospheric warmings discussed in 54.2. Sudden stratospheric warmings are characterized by a disruption of the vortex by stratospheric highs, and by the synoptic rearrangement of temperatures over the entire Arctic region; a well developed sudden stratospheric warming yields warm temperatures over the poie below 10 hPa only (in general), and usually dissipates within a month (except for final warmings). The warming observed here occurs at the vortex centre; Eureka is very close to the pole, and so clearly this warming does not represent a "disruption" of the vortex. Further, the well developed stage of the observed intra-vortex warming is sustained over several months and maximizes in the upper stratosphere, i-e., much higher than for classical sudden stratospheric warming events. Evidently we have observed a new class of "sudden warming", but will refer to it separately as an "intra-vortex warming" so as to avoid confusion with the more widely known synoptic-scde event.
The onset of the intra-vortex warming near the winter solstice suggests a dynamical origin, since radiative calculations indicate that high latitude upper stratospheric temperatures should not increase until late February [Shine, 19871. The theory presented in $2.3 suggests
that there are two principal candidates that may be used to explain such warmings: large
scale eddy (planetary wave) and small scale eddy (gravity wave) drag. The study of Garcia
and Boville 119941 indicated that the amount of gravity wave activity in the Northern
Hemisphere should decrease in late December, which suggests that gravity waves cannot be
responsible for this warming.
However, it is no more clear that planetary wave driving can be used to explain an
annual warming of the vortex core. Consider that all of the intra-vortex temperature
measurements presented here were obtained in non- sudden stratospheric warming conditions
(see 54.5), which implies a relatively undisturbed stratosphere. A case in point is the season
of 1996/97, which saw a significant and sustained intra-vortex warming even though upward
propagating large-scale disturbances fiom the troposphere were at a twenty year low during
February and March of that year [Coy et a[., 19971. Furthermore, Hol&on [I9831 demonstrated that the drag due to planetary waves in the upper stratosphere is relatively small, and so it is unlikely that they could force such a strong warming. Moreover, the studies of Fairlie and 0 'Neil1 [ 1 9 881 and Fairlie e t al. [ 19901 show that the majority of dynamical warming induced the by large-scale eddies is found in the jet between the vortex and an impinging stratospheric high, and not at the vortex centre.
Finally, consider that near the stratopause, temperatures are warmer in the vortex core than outside of the vortex altogether, and so eddy exchanges of material between the vortex and midlatitudes must transport heat equatorward. The vertical component of the Eliassen-
Palm (EP) flux (the term in brackets in eq. 2.3.4), then, must point downward at high altitudes. Since there is no known strong source of downward propagating disturbances in the mesosphere, it is unlikely that a strong EP flux convergence (which accompanies warmings) could occur in the upper stratosphere. With this in mind, it is of interest that the winter stratopause over Antarctica is warmer than over the Arctic (by roughly 17 K), where planetary wave activity is substantially greater [Kanzuwa, 19891.
It would seem, then, that the forcing of an annual intra-vortex warming is no more likely to be produced by planetary waves than gravity waves; this issue will be revisited in
S6.4. Chapter Six
Observations of Stratospheric Gravity Wave Activity
6.1 Introduction
It is now known that the circulation of the middle atmosphere is strongly coupled to the troposphere by way of vertically propagating waves. This was first appreciated for the case of g1obaI scale planetary waves, described in Chapter Four within the context of the stratospheric flow. With the advent of lidar systems and advances in other instruments, small scale internal gravity waves are now receiving an increased amount of attention.
Gravity waves are observed by the Iidar at Eureka as perturbations to ten-minute average temperature profiles, and are examined using the techniques described in $3 -3. A few case studies showing temperature and gravity wave perturbation profiles are given by
Whiteway and Carswell [I9941 and Whiteway et aZ. [1997]. The vertical wavelengths considered here are less than 15 krn (see 53.3), which is much smaller than the perhubation scales observed for planetary waves (the effects of vortex movements on temperature profiles are described in 55.2).
That gravity waves are able to transport energy (and therefore momentum) from tropospheric sources to high altitudes was fust realized by Hines 119601, in his interpretation of ionospheric wind irregularities. Gravity waves do not proceed to such heights unaffected, however, since their propagation is impeded by at least two important mechanisms. First,
110 since gravity waves grow with height in response to the decreasing background atmospheric
density, gravity waves that propagate upward become strongly unstable when superadiabatic
lapse rates are eventually induced (or the gradient Richardson number Ri=N 2/(a daz) falls
below % [Miles,19611). This issue was first discussed by Hodges 119671 and was later used
to develop an initial theory on the form of gravity wave vertical wavenumber energy spectra
[Vmandt, 1982; Dewan and Good, 1986; Smith et al., 19871'. Second, gravity waves may
be prevented from propagating vertically if they are Doppler shifted to small vertical
wavelengths kZ,since this also produces convective and dynamic instabilities. Consider that
for gravity waves with Doppler shifted frequencies given by
(see §4.6), the dispersion relation (eq. 2.4.8) reduces to
for waves with m )) k,. Equation 6.1.1 shows that Doppler shifting to small vertical
wavelengths occurs whenever the projection of the background wind in the direction of the gravity wave wavevector, ~~~os[B,(z)-€Ik], approaches the gravity wave horizontal phase speed c,,. The obstruction of vertically propagating gravity waves in this way is referred to as cccriticallevel filteringy', and is discussed in detail by Brerherton [I9661 and Booker and
A review of the leading gravity wave saturation theories is given by Gardner [ 19961.
11 1 Brerherton [ i 9671.
Gravity waves that become unstable are said to "break" or undergo "turbulent
dissipation" and so deposit momentum into the background flow [Jones and Houghion,
19711. This momentum deposition is often referred to as "gravity wave drag7',since its effect
is to drag the background wind toward the phase speed and direction of the original gravity
wave wavevector [Lindzen, 198 11. That momentum deposition by gravity waves might be
the source of drag required to cause the reversed mesospheric meridional temperature
gradient (see 92.3) was frrst considered theoretically by Linciien [I9811 and later numerically
by Holton [ 19831 and others. Linhen [I9811 developed a parameterization scheme based
on the linear instability theory of gravity waves [Hodges, 19671 that suggested gravity wave
drag could induce a significant meridional flow. When this scheme was incorporated into
the model of Holton [1983], the observed reversed wintertime mesospheric rneridional
temperature gradient resulted.
Lindzen 's [I9811 parameterization was later used by Hitchman et ul. [I9891 and
Garcia and Boville [1994] to explain the existence of the separated wintertime polar
stratopause (see 92.3). Their zonal mean models showed that gravity wave drag was required to produce the warm temperatures observed in the polar upper stratosphere during winter, a time during which there is no solar insolation. These works built upon the two dimensional model of Holton [1983],who obtained a stratopause in the vortex core with the gravity wave parameterization tuned in order to produce a realistic mesospheric temperature distribution and without any planetary wave parameterization at all; his model demonstrated that the
effects of planetary waves in the upper stratosphere and mesosphere are likely small.
Curiously, the study of Garcia and Boville [I9941 predicted that gravity wave
activity should decrease in late December due to the critical level filtering associated with
increased planetary wave activity and an emerging surf zone. It is one of the main results
of this study that the amount of gravity wave activity in the vortex jet actuaIIy increases in
late December. This increase is associated with a strengthening of the vortex jet and a
decreased amount of critical level filtering, and is proposed as the source of the strong intra- vortex warming described in 55.3.
6.2 Night-average Gravity Wave Measurements
A total of 445 nights of gravity wave potential energy density measurements were obtained by the lidar at Eureka during the winters of 1992/93 to 1997/98. The data were found to be of excellent quality between 30 and 45 km in altitude. Below 30 km, end effects affect the gravity wave extraction procedure, and above 45 km the gravity wave temperature perturbations were not often of sufficient amplitude to be detected above fluctuations due to noise (see 53.3). For the purposes of this study, night-averaged gravity wave energies in the
30-35,35-40, and 40-45 km altitude ranges were used. The measurements were separated a priori according to whether they were obtained in the vortex core, jet, or outside of the vortex altogether (see $43, in anticipation that the vortex winds might modulate the observed gravity wave activity via Doppler shifting (see $4.6 and $6.1).
Figure 6.2.1 gives the measurements of gravity wave energy density obtained in the
30-35 km altitude range during each season at Eureka. As is shown in Figure 6.2.1, the
gravity wave activity observed in the stratosphere above Eureka was highly variable. Where
there was some consistency i~ the large scale stratospheric thermal structure each night (cf.
§5.2), the gravity wave energy densities were seen to change dramatically between
measurements. Since interpolations between observations are clearly not possible, changes
in the gravity wave field are best described by changes in the distribution of energy
measurements averaged over different periods of time, and will be treated as such hereafter.
Further examination of Figure 6.2.1 shows that the gravity wave energy densities
obtained in the vortex core and outside the vortex altogether were generally Low. In the
vortex jet, episodes of high gravity wave activity were evident in addition to some lower
values. Moreover, these episodes of high gravity wave activity were only observed at times
later than mid-December. To illustrate this point more clearly, a scatter plot showing a11 of
the gravity wave measurements obtained in the vortex jet, with January 1 of each year taken as day zero, is given in Figure 6.2.2. Figure 6.2.2 reveals a remarkable phenomenon: during
November and much of December, the gravity wave energies within the vortex jet were relatively low; however, in mid- to late December episodes of high wave activity were apparent and were observed through the end of measurements in late March. In what follows, measurements in the vortex jet will be separated into two different time periods: -60 -30 0 30 60 90 Time (days since January 1 )
-60 -30 0 30 60 90 Time (days since January 1 )
-60 -30 0 30 60 90 Time (days since January 1)
Figure 6.2-1. Gravity wave potential energy densities measured during the winters of 1 992/93 to 1 997198 by thc lidar at Eureka (averages between 30-35 km in altitude). The measurements are marked according to where they were obtained with respect to the vortex as follows: 0 I vortex core, A E vortex jet, 0 - outside of thc vortcs altogether. (Continued on nest page) -60 -30 0 30 60 90 Time (days since January 1 )
-60 -30 0 30 60 90 Time (days since January 1 )
-60 -30 0 30 60 90 Time (days since January 1 )
Figurc 6.2.1. (Continued fiom last page) I. I..I I.. I *
-30 0 30 60 Time (days since January 1 )
Figure 6.2.2.. The wintertime evolution of gravity wave potential energy density measurements (30-35 km) in the vortesjet Symbols correspond to measurements in a particular winter: + 5 1992193, '1 s 1993194, 0 =- 1994195, 0 - 1995196, A = I996/97, 0 = l99?/98. those obtained before mid-December and those taken in Iate December or thereafter. No such divisions in time will be made for measurements taken in the vortex core or outside of the vortex altogether, since the gravity wave potential energies seen there were generally
low, and also because the quantity of data obtained in those regions before mid-December does not allow for a good statistical analysis.
Table 6.2.1 lists the average and standard deviation for the gravity wave energy distributions obtained in each vortex region (and for different time periods, where applicable). In the vortex core, the gravity wave energies are generally low. In the vortex jet, the average gravity wave energy is low during November to mid-December and increases by about 5%10% for measurements taken after late December, a change that is separated by almost 9 standard deviations of the mean. The standard deviation of the distribution taken after late December is much larger than for before mid-December, which reflects that the gravity wave energies are spread to higher values at that time. Outside of the vortex altogether, the average wave energy appears to be high, but the large standard deviation of the mean reflects the fact that a few outliers have significantly affected the statistics there.
A more appropriate way to compare changes in the gravity wave field when this is the case is to view potential energy density histograms and accumulated probability distributions.
Figure 6.2.3a presents separate histograms for the gravity wave energies obtained in the vortex core and in the vortex jet after late December. The use of histograms removes any biases that might be perceived when viewing scatter plots (such as the one in Figure 6.2.2) Region N E, average Standard deviation I Vortex core 84 6.7 *0.6 5.7
Vortex jet (t c Dec. 17) 6 1 5.9 k 0.4 3 -4
Vortex jet (t > Dec. 26) 235 9.4 * 0.4 6-8 Outside of vortex 22 9.4 * 2.7 12.8
Tabic 6.2.1. Gravity wave potential energy distribution statistics for the vortes core, vortes jet (for dam earlier than December 17 and Iater than December 26), and outside of the vortes altogether. The number of measurements (N), average potential energy, and standard deviation of the distribution are given for each region. ------Vortex core Vortex jet (t>Dec. 26)
0 5 10 15 20 25 Potential Energy (Jlkg)
Vortex Jet (tcDec. ' \/nrtnv let It>nnr ' " "I .&A Yk. 1.- YIY. 26)
,-- Outside Vortex
0 5 10 15 20 25 Potential Energy (Jlkg)
Figure 6.2.3. a, Potential energy histograms for gravity wave measurements at Eureka in the 30 - 35 km altitude range, each smoothed with a 2 Jkg windowed mean. Calculations were performed separately for observations in the vortex core, in the vortex jet (before December I7 and after December 26 separately), and outside the vortex altogether, dthough only two histograms are shown in a for clarity. b, Accumulated probability distributions for the measurements of gravity wave potential enerey density. The distributions in a and b are bused on 84 measurements in the vortex core, 6 1 and 235 measurements within the vortex jet (berore December 17 and after December 26 respectivety), and 22 observations outside of the vortex dtogether. The accumulated probability distribution for outside the vortes altogether is truncated at high energy values duc to a lack of data there. by eye due to an uneven data spacing or density. As is shown in Figure 6.2.3q the
distribution for measurements obtained in the vortex core is markedly different from the
distribution for measurements taken in the vortex jet after late December. The vortex core
distribution is sharply peaked near 4 Jlkg, whereas the vortex jet distribution is broadly
peaked near 4 or 5 J/ kg and is spread so that higher energy values have a significant
occurrence probability. Although the displacement between these maxima is small, the
sharpness of the vortex core peak ensures that many more of the measurements there have
energies less than 6.5 Jkg than for measurements in the vortex jet. Curiously, at the highest
wave energies, the distributions seem to converge, although the low number of observations at those levels allows for very little certainty in this respect.
Figure 6.2.3b shows accumulated probability distributions for the gravity wave energy distribution observed in each vortex region (and time periods, where applicable). For a distribution across any variable x with probability densities @(x), the accumulated probability P(xra) is given by
For these measurements, the accumulated probability is simply the fiaction of measurements that yield energy values E, less than a chosen gravity wave potential energy value L,i.e.,
P(E,rE,). Graphs of accumulated probability present the same information as histograms, except that the significant smoothing required to produce histograms for continuous data is not required. In this way, distributions that are similar in nature may be more easily compared.
As is shown in Figure 6.2.3b, the distributions for gravity wave potential energy densities obtained in the vortex core, within the jet before mid-December, and outside of the vortex altogether are very similar for a broad range of energy values. This suggests that the conditions regulating the propagation of gravity waves in each case are likely similar. For measurements obtained in the vortex jet after late December, the accumulated probability distribution is significantly different from the others, and so the relevant gravity wave propagation conditions are likely to have changed as well. The characterization of propagation conditions in each of the different vortex regions, and especially the changes that occur in the vortex jet in early winter, are the topic of 86.3.
Finally, Figure 6.2.4 shows accumulated probability distributions for the gravity wave energy measurements obtained in the vortex jet after late December for the three different altitude ranges. Figure 6.2.4 illustrates that there is a shift with altitude to gravity waves with higher potential energy densities, which is consistent with energy conservation considerations (see 52.4). The distributions taken in the other vortex regions show similar increases with height. 0 5 10 15 20 25 30 35 40 45 50 Potential Energy (Jikg)
Figure 6.24. Accumulated probability for measurements of gravity wave potential energy density in the vortex jet after December 26 for three different altitude ranges. The other accumulated probabilities given in Figure 6.2.3b show a similar growth with altitude. 6.3 Factors Affecting the Upward Propagation of Gravity Waves
That the highest levels of gravity wave activity are observed in the vortex jet suggests
that gravity waves are affected significantly by the winds through which they propagate.
Figure 6.3. la gives a scatter plot of all gravity wave potential energy density measurements
as a function of the wind speed at 30 km in height. The winds were taken from the data presented previously in 54.6. Figure 6.3.1 a demonstrates that the majority of gravity wave measurements obtained when the stratospheric wind speeds were low gave low energy densities. For high stratospheric winds, the distribution of gravity wave energies is spread to much higher values. Again, these features are most easily seen by viewing histograms and accumulated probabilities for measurements in different wind speed regimes, and so these are given in Figures 6.3.1 b and 6.3.1 c respectively. For stratospheric wind speeds less than
25 ds,the histogram of wave energies is sharply peaked near 4 J/kg. For stratospheric wind speeds greater than 50 ds,the distribution of gravity wave energies is broad and peaked somewhere between 4 and 5 Jkg. Although the displacement between these maxima is small, the sharpness of the peak for low stratospheric wind speeds ensures many more measurements there with energies less than 6.5 Jkg than when the stratospheric wind speeds are high. This is reinforced by the accumulated distributions given in Figure 6.3.1 c, which show that for any given gravity wave potential energy value, there are more measurements in high winds with energies greater than the chosen value than there are for low wind speeds.
Because gravity wave energies clearly vary with the background stratospheric wind o 20 40 60 80 loo Wind speed (mls)
0 5 10 15 20 25 Potential Energy (Jlkg)
0 5 10 15 20 25 Potential Energy (Jlkg)
Figurc 63.1. a, A scatter plot of gravity wave potential energy density measurements (30-35 km) versus the wind speed at 30 km in altitude. The measurements arc marked according to where they were obtained with respect to the vortes as foIlows: 0 5 vortes core, A r vortes jet, 0 5 outside of the vortex altogether. b, Potential enera Iustogams for measurements in different wind speed ranges, each smoothed with a 2 Jkg running mean. c. The corresponding (unsmoothed) graphs of accumuIated probability for the histopams given in b. speed, and since gravity wave energy densities in the vortex jet were observed to increase in late December, it is of interest to examine how the vortex jet winds evolved during that time. A scatter plot showing the wind speed at two stratospheric levels for every day that the vortex jet was over Eureka during the winters of 1992/93 to 1997/98 is given in Figure 6.3.2; a 21 point running average for those data is given by the thick black line. As is shown in
Figure 6.3.2, the stratospheric vortex jet strengthened significantly during November and much of December, and then levelled off in late December. The evolution of the stratospheric winds, then, appears to contribute to the concurrent increase in gravity wave activity. A mechanism relating these two phenomena is discussed in $6.5.
Another factor thought to affect the upward propagation of gravity waves is critical level filtering, which was described in $6.1. At locations where the horizontal projections of the background wind and a particular gravity wave's wavevector are equal (or at least close), an instability develops and the gravity wave is removed from the atmosphere via turbulent dissipation. In general, the atmosphere is thought to contain a large number of gravity waves at a variety of phase speeds at any given time. Gravity waves generated by orographic sources are generally locked to the topography and so have low phase speeds relative to the ground, whereas waves generated by convection or other internal mechanisms in the atmosphere may have higher phase speeds. The distribution of wavevectors in space is often treated as isotropic (see, for example, Hincs 1199I]), although some recent studies have suggested the spectrum is anisotropic (e.g., Medvedev et al. [I 9981). -60 -30 0 30 60 90 Time (days since January 1 )
-60 -30 0 30 60 90 Time (days since January 1)
Figurc 6.3.2- Scatter plots of the wind speed in the vortes jet, sampled above Eureka from NCEP analyses for each season from I992/93 to 1997198. &ch symbol correspond to a particular winter: + = 1 992/93, C =- 1993194,
CI= 1994195,O 5 1995196, A = 1996197, V = 1997198. The solid line in each plot represents a 2 1 point running mean. The data presented were sampled at a, 20 krn in aItitude (lower stratosphere) and b 30 km in altitude (middIe stratosphere). Note that when the wind speed at 30 km (which corresponds to the height of the jet maximum over Eureka) increases, similar changes penetrate downward into the lower stratosphere. Since the lidar measurements at Eureka contain no information regarding gravity
wave horizontal phase speeds or directions, some approximations must be made in this
regard. First, since there is surely little convective gravity wave generation during the dark
months of the High Arctic winter, orographic generation is likely the dominant contributor
to the gravity wave field there. Observations at Eureka during winter often find stationary
or very slowly progressing waves [Whttewqy and Carswell, 19941, a fact that supports this
assumption. Second, for simplicity the horizontal distribution of gravity wave wavevectors
will be taken as isotropic.
For gravity waves with zero phase speed, critical level filtering occurs when
u,cos[0,(z)-0~ = 0, i.e., when either u0=O or 0y(~)-0k=*900.At any level, then, gravity
waves propagating in a direction perpendicular to the background wind are not allowed. If
the background wind turns, a whole range of propagation directions are prohibited.
Following Dunkerfon and Butchart [1984], this can be used to define an average transmission
where
I, if cos[€Iw(z) -€Ik] *0 at all altitudes z, < z < z2. 0, if COS[~~(Z)-~,]=Oat aN altitudes z, < z < z2.
128 The gravity wave transmission was calculated between z,=5 krn and rz=30 krn from the winds presented in $4.5 for each gravity wave potential energy measurement obtained at Eureka Only days where the winds exceeded 4 rn/s between z, and z2are considered, because the direction for winds less than that value are uncertain (see $3.4). This also loosens the restriction regarding gravity wave phase speeds: any waves with phase speeds less than 4 m/s will be removed by a turning of the background wind. The two levels used for the calculations correspond to mid-tropospheric and mid-stratospheric levels respectively.
Approximately l/3 of the measurements were excluded using these restrictions. Note that by lowering z, an increasing number of measurements are disallowed, since the winds are observed to decrease rapidly toward the ground.
Figure 6.3.3a gives a scatter plot of the measured gravity wave energy densities as a function of the calculated transmission. As is shown in Figure 6.3.3a, the gravity wave potential energy densities for low transmission values are generally small. For higher transmission, the gravity wave potential energy distribution is spread to greater values. Note that when the transmission is high, a broad spectrum of energies is still expected because of the uncertain and variable source strength at lower levels, and also since the gravity waves may have travelled significant distances before reaching the mid-stratosphere above Eureka
[Dunkerfonand Butchart, 19841'.
A study by Whiteway and Duck [I9961 showed that in the absence of critical level filterins, the amount of gravity wave activity in the lower stratosphere generally increased with the wind speed near the ground (the study used radiosonde data, and so both temperature and wind measurements were available). This supports the assumption that the gravity wave fietd above Eureka is generally forced by topography. 0.0 0.2 0.4 0.6 0.8 1.0 Transmission
0 5 10 15 20 25 Poten~IalEnergy (J/kg)
0 5 10 15 20 25 Potential Energy (Jlkg)
Figurc 63.3. a, Scatter plot for measurements of gravity wave potential energy density (30-35km) versus the transmission coefficient due to critical level filtering between heights of 5 and 30 km- The measurements are marked according to where they were obtained with respect to the vortes as follows: 0 = vones core, A z vortcs jet, = outside of the vortex altogether. b, Potential energy histograms for the data in hvo different transmission ranges, each smoothed with a 3 Jkg windowed mean. c, The corresponding (unsmoothed) graphs of accumulated probability for the histograms given in b. Figure 6-3-31, and 6.3.3~give gravity wave energy histograms and accumulated
probability distributions respectively for two different transmission ranges. As can be seen
in Figure 6.3.3b, for low transmission the distribution is sharply peaked at low energies,
whereas for high transmission the wave energies are spread to higher values, in much the
same fashion as were the measurements for high winds described in $6.2. Following the
analysis there, it is of interest to examine the wintertime evolution of critical level filterins.
The transmission was calculated for each day at Eureka during the 1992/93 to 1997198
seasons between the same levels as before. No restrictions on wind speed were used here,
however, so as to avoid biasing the results toward high values of transmission. A histogram
for transmission values in the vortex core and vortex jet (before mid-December and after late
December separately) are given in Figure 6.3.4.
As is shown in Figure 6.3.4a, the histogram for the atmospheric gravity wave transmission in the vortex jet before mid-December formed an essentially white noise spectrum; i.e., there were approximately equal probabilities for conditions providing high and low transmission values. However, after late December, the transmission distribution in the vortex jet is seen to be sharply peaked toward high values. This implies that after late
December there is significantly less critical level filtering in the vortex jet than before mid-
December, which is consistent with the observed late December increase in gravity wave activity. Further, Figure 6.3.4b shows that the accumulated probability distributions for measurements obtained in the vortex core and vortex jet before mid-December are very 0.0 0.2 0.4 0.6 0.8 1-0 Transmission
Figure 63.4. a, Histograms for transmission vdues over Eureka during November throu@ March of the 1992193 to 1997/98 winters. b, The corresponding (unsmoothed) graphs of accumulated probability for the histograms given in a. A vortex core histopam is not shown in a for reasons of clarity. similar in form. The offset seen between the two is due to the fact that there are more occasions of 100% critical level filtering in the vortex core than in the vortex jet before mid-
December.
6.4 Implications of Changes in Gravity Wave Activity within the Vortex Jet
The observations presented in section 56.2 show a late December increase in stratospheric gravity wave activity within the vortex jet that persists through the end of
March. The increases were related to a strengthening of the stratospheric vortex jet and statistical changes in the transmission of gravity waves. Since the vortex affects the propagation of gravity waves through the stratosphere, it is of interest to contemplate how increases in gravity wave activity might affect the vortex in turn.
Consider that, consistent with the discussion in $6.1, a rise in stratospheric gravity wave activity with the vortex jet should result in increased momentum deposition and gravity wave drag at some higher level. As was described in $2.3 and diagrammed in Figure 2.3.4? the effect of drag on the stratospheric momentum balance is to force flow into the vortex core which compresses and adiabatically wmsthe intra-vortex airrnass at lower levels. By using the theory described in 92.3, the magnitude of warming induced by changes in gravity wave activity can be estimated.
The chief assumptions in the calculation are as follows: 1) The gravity wave field observed at Eureka is representative of other locations within the High Arctic; 2) Increases in stratospheric gravity wave potential energy densities result in proportional increases in the
gravity wave drag at the gravity wave breaking level; 3) The gravity wave breaking level
is near the stratopause; and 4) Temperatures warmer than radiative equilibrium in the vofiex
core are caused strictly by gravity wave drag in the vortex jet. Surely, the first assumption
must be verified by further observation; it does, however, seem plausible when considering
that the changes in gravity wave activity observed at Eureka depend strongly on the vortex
evolution in general (see 46.3). The second assumption is also reasonable - Linken 's
[I98 11 gravity wave parameterization, which has been used so successfdly in models of the
middle atmosphere circulation, has the gravity wave drag proportional to the energy below
the altitude where gravity wave breaking first occurs*. Next, although gravity waves are observed to produce patches of instability in the stratosphere f Whitewayand Carswell, 1994;
Sicn and Thorsley, 19961, strong gravity wave breaking is likely to begin near the stratopause, since it is just above there that the background atmospheric stability is at its
lowest in the middle atmosphere (see Fig. 2.1.2). The final assumption seems appropriate
fi-om the work of Ho Iton [ 1 9831, Hitchman er al- [I 9891 and Garcia and Boville [ 1 9941, who showed that the separated winter stratopause in the High Arctic owes its existence to gravity wave driving; Holton [1983] achieved a warm intra-vortex stratopause without any planetary
Linken S [I98 11 equation 24 has the gravity wave drag expressed as -p;'(dldz)pO
Now, consider that the vortex can be treated approximately as a symmetric flow centred over the pole, so that the diabatic circulation equations discussed in $2.3 are applicable. Gravity wave drag in the vortex jet must be balanced by a meridional flow (i.e., flow toward the vortex centre) so that
Substituting equation 6.4.1 into the mass continuity equation (eq. 2-33)gives
as the relation that determines the vertical descent in the vortex core comesponding to the rneridional flow. Following similar arguments in Hqvnes et al. [1991], suppose that the meridional flow velocities decrease over the length L and the vertical mass
-0 flux powo develops in a layer of depth D, so that equation 6.4.2 gives as a scale for the vertical velocity in the vortex core immediately below the gravity wave
breaking altitude 4.' Below the gravity wave breaking layer the induced drag is taken as
zero, and so equation 6.4.2 indicates that the vertical mass flux pow 'there must be constant.
Taking the density to decrease exponentially with height according to equation 2.1.3, this
gives
as the variation of the vertical velocity with height be!ow the wave breaking Iayer.
Now, in the steady state, the thermodynamic equation (eq. 2.3.2) implies that descent in the vortex core is accompanied by an amount of radiative cooling given by
where the scale height N is constant (with scale temperature T,) and the squared Brunt-
Vaisala frequency is given by N * =(R/fJ) [dTldz +(?/T~)T~. The radiative term in equation
6.4.5 is frequently approximated by Newtonian cooling,
where the aimass at temperature T cools to the equilibrium temperature T, on a temperature
' The length scale L can be treated as the radius of the vortex, and the width scale D as the depth of the layer within which the waves break. Note, however, that these parameters divide out in the caIculation, and so assigning values to them now is unnecessary. The impiicit assumption here is that they do not change as the warming develops. dependent time scale rr(T). Substituting equation 6.4.6 into equation 6.4.5 and differentiating yields
where 6 represents a small change in any of the given variables.
The first two terms on the left hand side of equation 6.4.7 can be estimated for temperature perturbations 6T through the use of scaling arguments. The first term scales as
where D,is the depth to which the warming penetrates and where T=T~has been taken in the denominator. The scaling for the second term can be determined by consulting Shine 's
[I9871 Figure I 1, which shows that the variation of the radiative relaxation time with temperature for polar night perturbations in the upper stratosphere is approximately
near the temperatures of interest, where C = 1500 Wday . The second term on the left hand side of equation 6.4.7 can then be reduced to A scale for the third term on the left hand side of equation 6.4.7 can be found for the upper stratosphere by differentiating equation 6.4.3, which gives
With the scales for each term on the lefi hand side of 6.4.7 determined, the strength of the intra-vortex warming driven by changes in the gravity wave drag can be estimated.
Substituting equations 6.4.8 - 6.4.10 into equation 6.4.7 yields
where the warming temperature scale T, is defined by
For an infinitely deep warming in the absence of radiative effects, the warming temperature scale is simply given by the difference between the actual and radiatively determined temperatures (T-T 1. The radiative term in equation 6.4.12 acts to suppress the warming,
as would be expected since the radiative relaxation rate decreases quadratically with
temperature in this formulation. The depth term acts to enhance the warming as D,v decreases.
Equation 6.4.1 1 (with eq. 6.4.12) expresses, in an extremely simple and compact form, the intra-vortex temperature changes expected to accompany a change in gravity wave momentum deposition in the vortex jet during the polar night in terms of measurable quantities. Using the mean intra-vortex temperature profile in Figure 5.2.3, the pammeters relating to temperature can be estimated as 7'' = 26W10 K, T-T~= 100315 K and
dT/dr = 3kO -5 Wkm for the upper stratosphere. From Shine [I 9871, the radiative timescale in the upper stratosphere is r, = 20h5 days. The warming depth scale is likely within the range of a few scale heights to the depth of increasing temperatures in the stratosphere, i.e.,
D, = 20k10 krn. Substituting these values into equation 6.4.12 gives the warming temperature scale as T, = 61*15 K, where all of the uncertainties have been added in quadrature. The fractional change in gravity wave drag within the vortex jet can be -- estimated from the data given in Table 6.2.1 as 6979 = 59*10%. The predicted warming magnitude in the upper stratosphere of the vortex core following a change in the average gravity wave energy in the vortex jet of 59*10%, then, is 6T = 36*11 K. 6.5 Discussion
In 86.2, the observations of gravity wave activity in the stratosphere above Eureka
were used to show that the most energetic gravity waves occurred in the jet of the Arctic
stratospheric vortex. Lower gravity wave energies were found in the vortex core and outside
of the vortex altogether. These results are consistent with the study of Wu and Waters
[1996], which observed a similar distribution of gravity wave activity from temperature
variances measured by the Microwave Limb Sounder (MLS) on the Upper Atmosphere
Research Satellite (UARS). It is of interest to note that the MLS measures temperature variances in the horizontal whereas the lidar at Eureka obtains them in the vertical, and so these two independent studies strongly support each other.
In $6.3,the gravity wave activity at Eureka was shown to depend on the strength of the stratospheric winds. The study of Whiteway et al. [I9971 interpreted this as evidence of the background winds Doppler shifting gravity waves away ftom instability. Consider that equation 6.1.1 implies that the vertical wavelength of a monochromatic gravity wave varies linearly with the background wind speed, and so high winds Doppler shift gravity waves with low phase speeds to long vertical wavelengths. Since the longer vertical wavelengths are observed to saturate at higher energies than those with shorter vertical wavelengths
[VanZandf,19821, it follows that Doppler shifting in high stratospheric winds should lead to increased gravity wave activity'. The gravity wave potential energy spectra presented by
This is rigorously true for monochromatic waves only, so that linear instability theory [Dewan and Good, 1986; Smith et al., 19871 appiies. Whiteway et al. [1997], which showed that the increases in gravity wave energies for high
stratospheric winds occurred at the long vertical wavelengths, were used to support this
interpretation.
Gravity wave activity was also shown to depend on the amount of critical level
filtering. It seems likely, however, that the critical level filtering of gravity waves is strongly tied to the strength of the stratospheric winds. Consider that when wind speeds in the middle atmosphere are high, the vortex jet is observed to penetrate to lower altitudes (this is seen. for example, in Fig. 6.3.2). As the vortex jet strengthens, it will gradually begin to organize the flow at increasingly lower altitudes, thereby reducing any turning of the wind and so the amount of critical level filtering. Clearly, critical level filtering and Doppler shifting effects are two important but inseparable factors that regulate the propagation of gravity waves through the stratosphere.
In $6.2 it was shown that the distribution of gravity wave activity in the vortex jet before mid-December was similar to the distribution for measurements in the vortex jet; the gravity wave transmission characteristics for those distributions were also seen to be similar.
However, it was also shown that the gravity wave activity in the vortex jet during 1992/93-
1997198 increased on average around mid- to late December, a change that was sustained through the end of measurements in late March. This increase was unanticipated, and contrasts with the study of Garcia and Boville [1994], which predicted a general late-
December decrease in gravity wave activity. The model of Garcia and Boville [1994], however, examined the propagation of waves through a zonal mean flow with parameterized
planetary wave drag; the gravity wave activity in their model was reduced in late December
due to the increasing planetary wave activity at that time. While it may be true that gravity
wave activity in general is reduced due to planetary waves, it is cleat- fiom the observations
here that this is not necessarily the case everywhere. Moreover, the study of Dunkerron and
Butchart 11 9841 demonstrated that calculations of critical level filtering by the zonal mean
winds produce much lower gravity wave transmissions than when the three dimensional
winds are used, and that significant regions of gravity wave transmission associated with the
vortex jet exist even during a sudden stratospheric warming. The late-December rise in
gravity wave activity observed at Eureka was associated with a strengthening of the vortex
jet and a corresponding decrease in the amount of critical level filtering calculated fiom the
actual wind fieId.
The effects of the increases in gravity wave activity within the vortex jet were
explored in $6.4. The theory there, although admittedly crude, revealed that an intra-vortex
warming on the order of several tens of degrees should accompany the increases in gravity
wave activity described above. Consider, then, that an upper stratospheric warming of
25 & 2 K was observed to occur in the vortex core in late December (see 55.3 and Duck et
al. [I 99 81). For illustrative purposes, the average intra-vortex temperature anomalies shown
in Figure 5.3.3 and the compilation of gravity wave energy densities obtained in the vortex jet given in Figure 6.2.2 are presented together in Figure 6.5.1. As is shown in Figure 6.5.1, Anomalies (K)
-30 0 30 60 Time (days since January 1)
Figure 6.5.1. a, The average evolution of intra-vortex temperature anomalies (from Figure 5.3-31, and b, measurements of gravity wave activity in the vortes jet (fiom Figure 6.2.2). Symbols correspond to measurements in a particular winter: + l992/93, 0 1993/94, = I994/95, o z l995/96, A = l996/9?, v z I997/9S. the onset of intra-vortex warming and increased gravity wave activity in the vortex jet occurred simultaneously.
It was dso noted in 55.3 that the upper stratospheric temperatures in the vortex core developed somewhat differently during 1997198 than in previous years. As was shown in
Figure 5.3.5, the intra-vortex temperatures during November and early December were low as usual; however, a strong intra-vortex warming was observed to peak in late December and then diminish by mid January, with temperatures only returning to their climatological values by early February. The temperatures presented in Figure 5.3.5 are repeated in Figure 6.5.2, with the corresponding measurements of gravity wave activity in 6.2. Ifoverlaid (note that most of the gravity wave observations during 1997/98 were obtained in the vortex jet). As is shown in Figure 6.5.2, there was a strong relation between upper stratospheric temperatures at the vortex centre and gravity wave activity in the vortex jet during the winter of 1997/98. During November and early December, both the temperatures and gravity wave activity were low. However, the distribution of gravity wave activity during the strong
December warming was clearly spread to higher energy values. Remarkably, the low gravity wave energies detected during most of January were accompanied by a significant intra- vortex cooling. The return of the vortex centre to climatological temperatures was accompanied by a renewed spread of the gravity wave potential energy distribution to higher values.
It was previously asserted in $5.4 that planetary waves are not likely able to produce -60 -30 0 30 60 90 Time (days since January 1)
Figure 6.5.2. Gravity wave potentid energy densities measured by the lidar at Eureka in the 30-35 Ian aItitude range (symbols) and the temperature above the vortes axis at a height of 40 km from NCEP andyses (sold Iine) during the winter of 1997/98. The symbols for the gravity wave measurements are sorted according to where they were obtained with respect to the vortex: 0 r vortex core, A vortex jet, 0 = outside of the vortex altogether. significant and sustained intra-vortex warming in the upper stratosphere. The tandem development of increased gravity wave activity in the vortex jet and intra-vortex warming, along with the calculations performed in $6.4., suppa the following theory: warmings in the upper stratosphere of the wintertime Arctic vortex core are largely forced by gravity wave drag in the vortex jet near the stratopause. This statement appears to be true not only in a climatological sense, as was shown in Figure 6.5.!, but also during particular seasons as well, as was illustrated in Figure 6.5.2.
The measurements and calculations presented in this chapter suggest a rather fascinating description for the dynamics of the stratospheric vortex. During November and
December, temperatures in the vortex core decrease in response to radiative cooling during the dark High Arctic winter months. Decreasing temperatures in the vortex core lead to a strengthening of the vortex jet. Stronger vortex winds lead to the increased transmission of gravity waves, since they are less likely to saturate or approach critical levels as they propagate through the stratosphere. When gravity waves propagating through the vortex jet dissipate near the stratopause due to instabilities brought on by wave growth, a drag is exerted that forces flow into the vortex core. The ensuing intra-vortex mass pileup near the stratopause compresses the underlying airmass and a large adiabatic warming results. This warming initially acts to dose the vortex jet. However, as the vortex continues to strengthen, increasing gravity wave activity forces the warming to progress increasingly deeper into the stratosphere. This continues until a balance between radiative cooling and compressional warming is achieved in the lower stratosphere, and so the vortex can strengthen no longer.
This balance occurs on average, it seems, around the end of December (see Figure 6.3.2).
The effect of gravity waves, then, is to provide a feedback loop whereby the vortex strength is regulated.
The feedback mechanism regulating the strength of the vortex has significant implications for studies of chemical ozone depletion. As was discussed in Chapter One, the processes leading to the chemical depletion of ozone are strongly temperature dependent; significant ozone depletions are only observed in the vortex core, where temperatures may drop below the chlorine activation threshold of roughly 195 K. However, a balance of radiative cooling and gravity wave driving are apparently required to determine temperatures in the vortex core. Since both radiative and gravity wave effects are parameterized in general circulation models, this balance will be sensitive to the details of each parameterization. The production of realistic gravity wave energy distributions and intra-vortex warrning will be necessary for general circulation models in any effort to predict the future state of the ozone layer and stratospheric circulation in general. Chapter Seven
Observations of Gravity Waves during a Final Warming
7.1 Introduction
In previous chapters, the evolution of gravity wave activity above Eureka was
examined during the development of the Arctic stratospheric vortex and throughout the
winter months (see Chapter Six). It is therefore natural to complete this study by presenting
observations of the gravity wave field during the springtime vortex breakdown, or "final
warming". Unfortunately, observations by the lidar at Eureka during the vortex breakdown
interval, i.e., during late March and early April, are not available because the strong
background light at that time overwhelms the measurement signal. BaIloon borne radiosondes, however, have been found effective for gravity wave studies [Allen and Vincent,
1995; Whiteway and Duck, 19961. They will be employed here to examine the final warming of Spring 1996 and also to test some of the ideas presented in the previous chapter.
Radiosonde measurements of temperature and wind are obtained twice daily by a network of over twenty-five weather stations across Canada, eleven of which are found north of 60" latitude. The radiosonde system currently in use (Vaisala RS80) records data every ten seconds, corresponding to a height interval of approximately 50 m. The measurements often reach altitudes in excess of 25 km,except for when the conditions are extremely cold (which causes the balloons to rupture). Measurements fiom a subset of four northern stations
were chosen on the basis of location and data availability: Alert (82.3 1 ON, 62.18 OW),
Eureka (80.00 ON, 86.00 OW), Cambridge Bay (69.06 ON, 105.08 OW) and Baker Lake
(63.40 ON, 96.08 "W). The position of each of these stations is shown on the map provided
in Figure 7.1.1.
Perturbations due to internal gravity waves are evident in both the temperature and
wind profiles at each station (see, for example, the sample profiles given for Eureka in Figure
2.4. la), and generally have much shorter vertical wavelengths and smaller amplitudes than
for the gravity waves seen at higher altitudes by the lidar measurements (cf. Figure 3.3.2).
Gravity wave potential energy densities are calculated from the temperature perturbations
using the same technique employed by Whiteway and Duck [1996]: a single cubic
polynomial fit of seven kilometres in length is used to extract temperature perturbations in
the 15 - 22 km altitude range, which corresponds to measurements in the lower stratosphere.
The gravity wave perturbation potential energy is then calculated using equation 2.4.15 (with
the use of eq. 2.4.16).
Maps of height were obtained for the Northern Hemisphere during the period of vortex breakdown so that the gravity wave measurements can be interpreted in the broader context of the general circulation. It should be noted, however, that where horizontal wind values are required, the actual sonde measurements are used instead of geostrophic values calculated from the height maps. For example, the transmission of gravity waves into the Figurc 7.1.1. The locations of four of the northern stations in the Canadian radiosonde network. lower stratosphere due to critical level filtering (see $6.3) is calculated from the radiosonde wind profiles alone. Following Whiteway and Duck [1996], critical level filtering was calculated beginning at a height of 1 km for gravity waves with zero horizontal phase speed relative to the ground. The top altitude is taken as 15 km, which corresponds to the lower bound of the gravity wave measurement.
7.2 Observations
The gravity wave potential energy densities measured in the 15-22 km altitude region between days 45 and 145 are given for each station in Figure 7.2.1. As is shown in Figure
7.2.1, the gravity wave energies in the lower stratosphere through late February and March were spread fiom small values to about 5 Jkg. These energies are significantly smaller than those observed in the 30 to 35 km altitude range by the lidar at Eureka (cf. §6.2), which is consistent with the notion that gravity waves grow with altitude due to the decreasing background density (see $2.4). Of particular interest, however, is that the gravity wave activity decreased sharply at the end of March and remained low through May (and into the summer, not shown).
The cause of the gravity wave decrease is associated with the breakdown of the stratospheric vortex, as may be seen by viewing Figure 4.3.2, which shows the evolution of the zonal mean zonal winds and meridional temperature difference between 90 and 60 ON during the period of interest. As is shown in Figure 4.3.2b, the lower stratospheric zonal Potential Energy (Jlkg) Potential Energy (J/kg) Potential Energy (Jlkg) Potential Energy (Jlkg) -L -L A 4 ONPaOoO ONPCnmO ONPOmQ ONP00oO
IZ, 0 mean winds at high latitudes rapidly decelerated in late March and permanently reversed during the first week of May. Figure 4.3.2a illustrates that the wind reversal was accompanied by a strong warming above the pole; the warming never dissipated, and so this was the "final" warming of spring 1996.
A view of the vortex breakdown that accompanied the find warming may be obtained from maps of height in the Northern Hemisphere during the period of interest. Height contours are also streamlines of the geostrophic wind, with cyclonic (counter-clockwise) rotation around a low and anticyclonic (clockwise) rotation around a high (see §3.4), and so the height maps can be equally well viewed as wind maps. Figure 7.2.2 shows a series of height maps on the 300 hPa, 70 hPa, and 30 hPa pressure levels, which correspond to the levels of the tropospheric jet stream, the radiosonde gravity wave measurements, and the vortex jet respectively. Maps are provided for every five days and are representative of the flow during the period of vortex breakdown.
As is shown in the series of 30 hPa maps given in Figure 7.2.2, a strong vortex dominated the stratosphere during March of 1996. The vortex was positioned over northern
Canada and moved so that the two northernmost stations (Alert and Eureka) were positioned largely below the vortex core or under the vortex jet. The two southernmost stations
(Cambridge Bay and Baker Lake) were located mostly under the vortex jet, except for in late
March when the vortex moved rapidly from over northern Canada to northern Russia. In early April the vortex jet rapidly decelerated in the presence of several transient highs, and March 17 (day 76)
March 27 (day 86)
Figurc 7.2.2. Maps ofheight hr a series of dates in 1996 at the 300 hPa (-8.5 km), 70 hPa (-. IS km) :mi4 30 hPa (-23 km) pressure levels. The contour interval for each map is 200 rn. Lows and highs arc marked wllh an L and H respectively. (Continued on nest page) April 2 (day 92)
April 7 (day 97)
April 12 (day 102)
April 17 (day 107)
April 22 (day I 12)
Figure 7.2.2. (Continued from previous page) was eventually replaced in mid-April by a permanent anticyclone over the pole.
At the 300 hPa (i.e., upper tropospheric) level, the circdation during both March and
April was governed by the midlatitude jet stream. Occasionally, this jet stream or its
offshoots swept over the Arctic landmass; the general sense of the circulation during these
episodes was toward eastward flow, although periods of flow toward the north or south were
evident.
The 70 hPa level, then, represents the region of transition between the dominance of
the stratospheric vortex and tropospheric jet stream. During March, the lower extent of the
stratospheric vortex jet was apparent at 70 Ma. This situation began to change in early
April, when the vortex jet rapidly decelerated. By mid-April, the dominance of the vortex
at 70 hPa began to wane; the vortex was replaced by a much broader low centred over the
pole shortly thereafter. The circulation at the 70 hPa level around April 22 and thereafter
was cyclonic and so in opposition to the flow at higher levels, but now in accordance with
the tropospheric jet stream. During the vortex breakdown, then, there was a rapid transition
at 70 hPa between control by the overlying stratospheric vortex to the underlying midlatitude jet stream.
A view of the winds above each station during the vortex breakdown may be seen by
examining the radiosonde measurements. The wind speeds measured at the 20 krn height
level are given in Figure 7.2.3. As is shown in Figure 7.2.3, the lower stratospheric winds at each station during late February and March were spread through generally high values, a Cambridge Bay 0 Baker Lake
60 90 120 150 Time (days since January 1)
Figure 7.2.3. The wind speed measured by radiosondes at 20 hin height above the four different stations considered during 1996. which reflects influence of the vortex jet. However, in late March the winds above
Cambridge Bay and Baker Lake quickly dropped, which may be identified with the
movement of the vortex from over northern Canada to northern Russia. Similarly, the
stratospheric winds above Alert and Eureka dropped in early May, a decrease that is
associated with the final destruction of the wintertime stratospheric vortex. As seen by the
radiosonde measurements at the four northern stations, the changes in circulation associated
with the final warming occurred between about days 90 and 100. In what follows,
measurements obtained before this interval are taken as "prewarming" and after the interval
as "postwarming".
Measurements of several important parameters with respect to gravity wave
propagation into the lower stratosphere (see 56.3) are given in Table 7.2.1 for each of the
four stations. As is shown in Table 7.2.1, the average gravity wave potential energy densities at each station were decreased dramatically after the final warming. The average wind
speeds at 1 krn and 20 krn in height were both seen to decrease as well. At the northernmost stations (Alert and Eureka) the gravity wave transmission remained essentially constant, whereas for the southernmost stations (Cambridge Bay and Baker Lake) the transmission decreased markedly. Paramctcr Alert Eureka Cambridge Bay Baker Lakc
(82.3 1ON) (80.00 ON) (69.06"N) (63.40" N)
E, (Jlkg) - before 1-4k 0.3 (1 9%) 1.0 0.1 (10%) 1.7 * 0.2 (10%) 1.5 h 0.2 (12%) E, (Jtkg) - aftcr 0.48 0.03 (7%) 0-51 * 0.03 (5%) 0.62 k 0.03 (5%) 0.72 k 0.04 (6%) U, (mls) - before 7.3 * 0.8 5.7 0.5 10.1 k0.6 10.2 k 0.G U, (mls) - after 6.3 * 0.4 5.4 * 0.4 7.6 * 0.3 8.2 * 0.6 1 U,, (mls) - before 29 * 2 37k2 34 * 2 27 * 3 U,, (mls) - aftcr 2.5 * 0.2 3.5 * 0.2 5.6 * 0.3 4.8 * 0.2
T - bcforc 0.25 tt 0.05 0.29 6 0.04 0.68 0.03 0.53 0.04
T - after 0.26 * 0.03 0.3 1 i 0.03 0.42 * 0.03 0.37 C 0.03
Table 7.2.1. Average radiosonde measurements at four northern weather stations for various parameters taken before (days 45 to 90) and after (days 100 to 145) the final warming of 1996. The measurement parameters considered are the gravity wave potential energy density E, ( 15-22 km), the wind speed at I km in altitude U,, the wind speed at 20 h in altitude U,,, and the transmission for gravity waves with zero phase speed T. The error estimates in each case are given by the standard deviation of the mean. In the potential enera rows, the errors in parentheses were calculated before any data roundoffs- 7.3 Discussion
Prior to the vortex breakdown, the average gravity wave activity for each station
ranged fkom 1.0 to 1.7 Jkg, as is shown in Table 7.2.1. The prewarrning data from Alert will
be disregarded (for now), since the large emor estimate for tile gravity wave energy is mostly
due to the small number of measurements obtained there at that time; the gravity wave
energy measured at Alert before the fmal warming is consistent with both the highest and
lowest values obtained eisewhere.
Comparing the remaining three stations, it is apparent that prior to the final warming the gravity wave energy at Eureka was substantially lower than at either Cambridge Bay or
Baker Lake, the two southernmost stations. Referring to the wind data, it is clear that the stratospheric winds were high in each case. However, at 1 km in height, the wind at Eureka was only half that at the more southern stations. Whiteway and Duck [I9961 showed that the wind speed at the 1 krn level corresponds to the forcing strength for topographic waves, and so the prewming gravity wave forcing at Eureka was significantly lower than at the two southernmost stations. The higher source level winds at the southernmost stations reflects the fact that they were affected more frequently by the midlatitude jet stream, as one might expect. Further, the critical level filtering at Eureka (and indeed at Alert) was substantially greater than that at either Cambridge Bay or Baker Lake. The higher amount of critical level filtering found above Eureka was due to the fact that before the final warming Eureka was often either below the vortex core (see $6.3)or under a westward stratospheric jet that was directed opposite to the general sense of the tropospheric flow (see Fig. 7.2.2). The relatively low level of gravity wave activity found at Eureka before the final warming, then, was likely due to the lower levels of source forcing and gravity wave transmission found there.
After the ha1 warming, the gravity wave energies at each station were dramatically reduced. An important reason for this decrease was that the stratospheric wind speeds dropped sharply, thereby reducing the amount of Doppler shifting to the (more energetic) long vertical wavelengths (see $6.2). Furthermore, significant critical level filtering was observed at each station after the final warming. That the source level winds for only the southernmost stations were significantly lowered emphasizes that the winds at higher levels are of some importance for determining the Lower stratospheric gravity wave activity.
It is interesting that in a comparison between postwarrning measurements at the northernmost and southernmost pair of stations, the winds at both the source and stratospheric levels decreased with increasing latitude (on average), as did the gravity wave activity. The postwarrning meridional wind speed gradient at both of these levels is due to the influence of the midlatitude tropospheric jet stream, which dominates the tropospheric flow always and the circulation in the lower stratosphere only after the final warming.
Furthennore, the poleward decrease in gravity wave transmission is associated with this meridional wind speed gradient. That these gravity wave propagation parameters all imply decreasing gravity wave propagation into the lower stratosphere with increasing latitude agrees with the measured latitudinal decrease in gravity wave activity observed on average after the final warming. That Doppler shifting and critical level filtering are important factors determining the propagation of gravity waves into the stratosphere is confirmed. Chapter Eight
Conclusions
Measurements of thermal structure and gravity wave activity in the middle
atmosphere were obtained in the Canadian High Arctic at Eureka (80 ON, 86 " W) during the
winters of 1992/93 to l997/98 by the use of a Rayleigh Lidar and radiosondes, and compared
with the general circulation. The main results of this study are as follows:
1) The wintertime strato-mesospheric thermal structure observed above Eureka was
strongly tied to the position of the Arctic stratospheric vortex. Temperatures inside the vortex were very cold in the lower stratosphere and warm in the upper stratosphere. Outside of the vortex, the temperatures were relatively waxm in the lower stratosphere and cool in the upper stratosphere. Because Eureka was only under the vortex core when the stratosphere was relatively undisturbed, the warm temperatures found in the upper stratosphere cannot be uniquely associated with sudden stratospheric warming events.
2) A strong warming was observed to occur annually in the upper stratosphere of the vortex core and was sustained through the end of observations in late March. The warming commenced in late December and propagated downward to levels below 30 krn. This
"climatological" intra-vortex warming had not previously been identified in the literature, and is not associated with classical sudden stratospheric warming. Further, it is not clear that forcing by planetary waves is able to explain such a strong warming in the vortex core. 3) Gravity wave activity was observed to be generally low in the vortex core and
outside of the vortex altogether, and was spread to higher values in the vortex jet. The
differences in gravity wave activity between these separate regions are largely due to the
effects of critical level filtering and Doppler shifting.
4) Measurements of gravity wave activity within the vortex jet show late-December
increases that are sustained through the end of observations in late March. The increases
were unanticipated and were associated with a strengthening of the vortex jet and a
corresponding decrease in the amount of critical level filtering.
5) That the increased level of gravity wave activity in the vortex jet correlated with
a warming in the upper stratosphere of the vortex core suggests that the two events were
related. It was proposed that increases in wintertime gravity wave activity within the vortex jet force midwinter warmings of the vortex core; i.e., that the extra gravity wave drag exerted near the stratopause after late December forces flow into the vortex core that compresses the underlying airmass and so causes adiabatic warming. A simple calculation using the diabatic circulation equations was used to support this argument.
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