what drives the brewer-dobson circulation? · is +~k~pw(i -sin 45’) writing r=6,ooo km and w=50...

What drives the Brewer-Dobson Circulation?

Edwin Gerber and Naftali Cohen*Center for Atmosphere Ocean ScienceCourant Institute of Mathematical Sciences, New York University!!!!*Now at Yale University!Special thanks to the U.S. National Science Foundation

Recent Ozone

Recent Ozone: the Brewer-Dobson Circulation

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Dobson, Harrison, and Lawrence [1929]



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on November 24, 2010rspa.royalsocietypublishing.orgDownloaded from


5 5 I ..5 I 0. .5 EVIDENCE F O R A W O R L D CIRCULATION PROVIDED BY THE MEASUREMENTS OF HELIUM AND WATEK

V.4POUR DISTRIBUTION IN T H E STRATOSPHERE By A. W. BREWER, M.Sc. , A.1nst.P.

(Manuscript received 23 February 1949)

SUMMARY Information is now available regarding the vertical distribution

of water vapour and helium in the lower stratosphere over southern England. The helium content of the air is found to be remarkably constant up to 2 0 km but the water content is found to fall very rapidly just above the tropopause, and in the lowest I km of the stratosphere the humidity mixing ratio falls through a ratio of 10-1.

The helium distribution is not compatible with the view of a quiescent stratosphere free from turbulence or vertical motions. The water-vapour distribution is incompatible with a turbulent stratosphere unless some dynamic process maintains the dryness of the stratosphere. In view of the large wind shear which is normally found just above the tropopause it is unlikely that this region is free from turbulence.

The observed distributions can be explained by the existence of a circulation in which air enters the stratosphere a t the equator, where it is dried by condensation, travels in the stratosphere to temperate and polar regions, and sinks into the troposphere. The sinking, however, will warm the air unless it is being cooled by radiation and the idea of a stratosphere in radiative equilibrium must be abandoned. The cooling rate must lie between about 0 . 1 and I . I " C per day but a value near o.g°C per day seems most probablc. At the equator the ascending air must be subject to heating by radiation.

The circulation is quite reasonable on energy considerations. I t is consistent with the existence of lower temperatures in the equatorial stratosphere than in polar and temperate regions, and if the flow can carry ozone from the equator to the poles then it gives a reasonable explanation of the high ozone values observed a t high latitudes. The dynamic consequences of the circulation are not considered. I t should however be noted that there is considerable difficulty to account for the smallness of the westerly winds in the stratosphere, as the rotation of the earth should convert the slow poleward movement into strong westerly winds.

I. INTRODUCTION Between 1943 and 194s the writer made some 16 ascents into

the stratosphere over Southern England during which humidity measurements were made by means of a frost-point hygrometer. On some of the ascents the carbon dioxide (CO,) content of the air of the stratosphere was measured by using the hygrometer at the CO, point. The hygrometer has been described by Brewer, Dobson and

36 1

360 A. W. BREWER

tropopause rather than in the stratosphere as is suggested here. Shaw calculates the energy released by the circulation to be 23.7 x 1 0 7 ergs per gram and the thermodynatnic efficiency of the cycle is 0 . 2 3 . ‘The large amount of energy liberated and the high efficiency makes the circulation \ ery probable. Shaw suggests that this circulation may provide the energy necessary to maintain the general circulation of the atmosphere, hut he notes that “ The evidence for a direct descent of air through the layers beneath is not bery strong ”. It is suggested that evidence is now available.

lsotherms over the Globe F I G . 5 . A SUPPIY of dry air is maintained by a slow mean circulation from

the equatorial tropopause.

\Ye may use this to calculate the total energ) released by the circulation. Let H be the radius of the earth and ZPI the mean rate of sinking through the tropopause which is presumed to occur in all latitudes higher than 45’. Let p be the density of the air at the tropopause, then the weight of air circulated in both hemispheres is + ~ K ~ p w ( i -sin 45’) writing R=6,ooo km and w=50 m/day we obtain 2 . 5 x IO’* gm per day as the weight of air circulated. ‘This, by Shaw’s data, would release 23’7 x lo7 ergs per g m or 6 x 1oZ6 ergs per day. T h i s would be increased to about loz7 i f w= IOO ni /day.

The energy required to maintain the general circulation has hem variously estimated by different workers. Sverdrup (1918) estimates the requirement at 2 per cent of the solar energy which equals 1.4 x 102’ ergs/day, Brunt (1926) estimates the requirements at 5 watts/m’ which is equal to 2 x 102’ ergs/d;iy. I t will be seen

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Obituary Professor G. O. P. ObasiObituary Prof. Alan Brewer

Prof. Alan Brewer (1915–2007) was an out-standing meteorologist and an innovative designer of instruments for observation of the structure and composition of the stratosphere. Interpreting data from these observations enabled him to make original and seminal contributions to knowledge of the physics, chemistry and dynamics of the stratosphere.

Alan Brewer was born in 1915, in Montreal, Canada, where his parents were living for a short period. His real home, though, was in Derby, where his father’s family had lived for generations; and indeed two of his forbears were famed painters of Crown Derby porcelain. His father was a craftsman and from him, perhaps, Brewer acquired his lifelong love of craftsmanship. His mother was a schoolmistress, later headmistress and was widowed quite young. However, this did not mean he always excelled at school. Until the age of 15 he was consistently near the bottom of the class. He then decided, or was persuaded by his mother, that results mattered and thereafter was consistently top. It has been said of Brewer that he was good at things he wished to be good at – and he decided what those were.

From school he gained a scholarship to University College, London where he read Physics (BSc 1936, MSc 1937) after which he joined the Meteorological Office as a scientist. The outbreak of war found him as a weather forecaster at an RAF station near Oxford.

Brewer’s scientific career began in 1942, in the dark days of the Second World War, when he was taken off the rota of weather forecasters and asked urgently to investigate how aircraft could avoid making condensation trails. Because these trails

are so visible, scores of aircraft were being shot down. Together with Gordon Dobson, Professor of Meteorology at Oxford, he built new instruments to measure temperature and humidity from high-flying aircraft and was soon getting a handle on the problem of condensation trails. In 1944 he was awarded a King’s Commendation for service in the air. In the course of this work, he made the remarkable discovery that the stratosphere is uniformly and exceptionally dry.

After the war, for a short time Brewer joined Elliott Brothers, a scientific instrument firm before he was appointed lecturer in meteorology in Dobson’s department at Oxford University in 1949.

Since his discovery of the very dry stratosphere, Brewer reflected on how it could be so dry and realized that the only known source of such dry air was the region of the tropopause in tropical regions. Another discovery from Dobson’s ozone observations around that time was that there was more ozone in the stratosphere over the polar regions than over the Equator even though ozone is made through the action of sunlight. Brewer put these discoveries together and in 1949 wrote a seminal paper for the Quarterly Journal of the Royal Meteorological Society describing how air enters the stratosphere over the Equator and leaves it at higher latitudes in what became known as the Brewer-Dobson circulation (Brewer, 1949). This paper and his subsequent work investigating this circulation created a lot of scepticism and some disbelief (it cut across established thinking at the time – typical of Brewer’s style!) but it created an essential framework on which subsequent research has been built. Its lasting value was recognized in 1999 when a symposium held at Oxford celebrating the fiftieth anniversary of the 1949 paper attracted some of the world leaders in stratospheric research. Brewer’s name will forever live on in the Brewer-Dobson circulation.

Brewer not only provided this valuable conceptual framework, he also designed and constructed innovative and elegant instruments that provided the means for much observational research to be pursued. The Brewer ozone sonde and the Brewer spectrophotometer for ozone measurement (a modern development of the original Dobson spectrophotometer) both still today widely in use all over the world are prime examples.

Brewer’s influence also permeated through his colleagues and his students. I became his first research student in 1951. The task I was given was to make measurements of the flux of infrared radiation in the

lower stratosphere from which it might be possible to infer the size of the vertical motion that was maintaining the dry stratosphere. He was a wonderfully patient teacher and mentor. As we worked together on a radiometer for a Mosquito aircraft, he passed on his exceptional knowledge of experimental techniques, his skill as an instrument designer, his remarkable feel for the way the atmosphere works, and his deep enthusiasm for science. I could not have had a more inspiring start as a research scientist – even though the radiation measurements we were able to make proved not to be sufficiently accurate to infer the amount of vertical motion. Those of us who had the privilege of working in the rather cramped quarters of Room 256 in Oxford’s Clarendon Laboratory gained a great deal from interactions with him and also had enormous fun as we pursued our different projects in atmospheric science.

In 1957, when Gordon Dobson retired, Brewer took over as Reader in Meteorology. He was a Vice-President of the Royal Meteorological Society from 1957 to 1959 and also a member of the Research Committee of the Meteorological Office during this period. In 1962 he moved from Oxford to found a department of meteorology at Toronto University in Canada where he continued to work on the design of improved instruments for stratospheric observation and to contribute to understanding of chemical and physical processes in the stratosphere, especially those that could shed light on the characteristics of the Brewer-Dobson circulation he had postulated in 1949. Jointly with two of his students, he was awarded the Royal Meteorological Society’s Darton Prize for novel instrumentation twice – in 1954 and in 1965. While in Canada, the Canadian Meteorological Society was founded under his leadership and he became its first president.

He was elected to Honorary Membership of the Royal Meteorological Society in 1982, from which he resigned in 2000 characteristically because he wanted a younger person to take over a membership that he felt he no longer needed.

In 1976 aged 60, Brewer returned to the UK and bought a farm in Devon (being a farmer had always been one of his ambitions) and began work on restoring a very old, derelict farmhouse. In 1994, he retired from there to East Garston, a village south of Oxford. From there he would travel regularly to Oxford to attend seminars at his old department at the Clarendon Laboratory. He lived there until 2007 when he moved to a nursing home in Bristol where he died on 21 November 2007.











36 1

Wea

ther

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ctob

er 20

08, V

ol. 6

3, N

o. 10

312

Obituary Professor G. O. P. ObasiObituary Prof. Alan Brewer

Prof. Alan Brewer (1915–2007) was an out-standing meteorologist and an innovative designer of instruments for observation of the structure and composition of the stratosphere. Interpreting data from these observations enabled him to make original and seminal contributions to knowledge of the physics, chemistry and dynamics of the stratosphere.

Alan Brewer was born in 1915, in Montreal, Canada, where his parents were living for a short period. His real home, though, was in Derby, where his father’s family had lived for generations; and indeed two of his forbears were famed painters of Crown Derby porcelain. His father was a craftsman and from him, perhaps, Brewer acquired his lifelong love of craftsmanship. His mother was a schoolmistress, later headmistress and was widowed quite young. However, this did not mean he always excelled at school. Until the age of 15 he was consistently near the bottom of the class. He then decided, or was persuaded by his mother, that results mattered and thereafter was consistently top. It has been said of Brewer that he was good at things he wished to be good at – and he decided what those were.

From school he gained a scholarship to University College, London where he read Physics (BSc 1936, MSc 1937) after which he joined the Meteorological Office as a scientist. The outbreak of war found him as a weather forecaster at an RAF station near Oxford.

Brewer’s scientific career began in 1942, in the dark days of the Second World War, when he was taken off the rota of weather forecasters and asked urgently to investigate how aircraft could avoid making condensation trails. Because these trails

are so visible, scores of aircraft were being shot down. Together with Gordon Dobson, Professor of Meteorology at Oxford, he built new instruments to measure temperature and humidity from high-flying aircraft and was soon getting a handle on the problem of condensation trails. In 1944 he was awarded a King’s Commendation for service in the air. In the course of this work, he made the remarkable discovery that the stratosphere is uniformly and exceptionally dry.

After the war, for a short time Brewer joined Elliott Brothers, a scientific instrument firm before he was appointed lecturer in meteorology in Dobson’s department at Oxford University in 1949.

Since his discovery of the very dry stratosphere, Brewer reflected on how it could be so dry and realized that the only known source of such dry air was the region of the tropopause in tropical regions. Another discovery from Dobson’s ozone observations around that time was that there was more ozone in the stratosphere over the polar regions than over the Equator even though ozone is made through the action of sunlight. Brewer put these discoveries together and in 1949 wrote a seminal paper for the Quarterly Journal of the Royal Meteorological Society describing how air enters the stratosphere over the Equator and leaves it at higher latitudes in what became known as the Brewer-Dobson circulation (Brewer, 1949). This paper and his subsequent work investigating this circulation created a lot of scepticism and some disbelief (it cut across established thinking at the time – typical of Brewer’s style!) but it created an essential framework on which subsequent research has been built. Its lasting value was recognized in 1999 when a symposium held at Oxford celebrating the fiftieth anniversary of the 1949 paper attracted some of the world leaders in stratospheric research. Brewer’s name will forever live on in the Brewer-Dobson circulation.

Brewer not only provided this valuable conceptual framework, he also designed and constructed innovative and elegant instruments that provided the means for much observational research to be pursued. The Brewer ozone sonde and the Brewer spectrophotometer for ozone measurement (a modern development of the original Dobson spectrophotometer) both still today widely in use all over the world are prime examples.

Brewer’s influence also permeated through his colleagues and his students. I became his first research student in 1951. The task I was given was to make measurements of the flux of infrared radiation in the

lower stratosphere from which it might be possible to infer the size of the vertical motion that was maintaining the dry stratosphere. He was a wonderfully patient teacher and mentor. As we worked together on a radiometer for a Mosquito aircraft, he passed on his exceptional knowledge of experimental techniques, his skill as an instrument designer, his remarkable feel for the way the atmosphere works, and his deep enthusiasm for science. I could not have had a more inspiring start as a research scientist – even though the radiation measurements we were able to make proved not to be sufficiently accurate to infer the amount of vertical motion. Those of us who had the privilege of working in the rather cramped quarters of Room 256 in Oxford’s Clarendon Laboratory gained a great deal from interactions with him and also had enormous fun as we pursued our different projects in atmospheric science.

In 1957, when Gordon Dobson retired, Brewer took over as Reader in Meteorology. He was a Vice-President of the Royal Meteorological Society from 1957 to 1959 and also a member of the Research Committee of the Meteorological Office during this period. In 1962 he moved from Oxford to found a department of meteorology at Toronto University in Canada where he continued to work on the design of improved instruments for stratospheric observation and to contribute to understanding of chemical and physical processes in the stratosphere, especially those that could shed light on the characteristics of the Brewer-Dobson circulation he had postulated in 1949. Jointly with two of his students, he was awarded the Royal Meteorological Society’s Darton Prize for novel instrumentation twice – in 1954 and in 1965. While in Canada, the Canadian Meteorological Society was founded under his leadership and he became its first president.

He was elected to Honorary Membership of the Royal Meteorological Society in 1982, from which he resigned in 2000 characteristically because he wanted a younger person to take over a membership that he felt he no longer needed.

In 1976 aged 60, Brewer returned to the UK and bought a farm in Devon (being a farmer had always been one of his ambitions) and began work on restoring a very old, derelict farmhouse. In 1994, he retired from there to East Garston, a village south of Oxford. From there he would travel regularly to Oxford to attend seminars at his old department at the Clarendon Laboratory. He lived there until 2007 when he moved to a nursing home in Bristol where he died on 21 November 2007.

HELIUM .4ND WATER V m U R DISTRIBUTION 363

loss of heat is necessary in the polar and temperate stratosphere if subsidence occurs without disturbing the isothermal state.

The ratio of the mean subsidence rate to the mean value of the diffusion constant just above the tropopause can be fixed by the water vapour profiles fairly closely to 3 x I O - ~ cgs units. In the absence of data of the rate of radiative cooling or of the degree of turbulence of the lower stratosphere actual values for w and K cannot be fixed. The values can probably be said to lie within the limits 300 and 4,000 cgs units and 8 and IOO mlday.

The matter can only be decided by measurements of K or of the radiative conditions of the stratosphere and both are possible.

The writer considers that K will prove to be of the order of I o r 2 x 103/cm2 sec-’ and w about 50 m/day. If the circulation is as rapid as this it will make a significant contribution to the energy of the general circulation.

The dynamic consequences of the circulation have not been discussed. There are considerable difficulties in this respect.

-%CKNOWLE DGMBNTS

The humidity measurements were carried out a s part of the programme of the Meteorological Research Flight and a re quoted by permisison of the Director, Meteorological Office, Air Ministry.

Particular thanks are due to Sir Nelson Johnson for his personal interest in these problems, and to members of the Meteorological Research Committee amongst whom special thanks a re due to Professor G. M. B. Dobson, F.R.S., Professor Sidney Chapman, F.R.S., and Assistant Professor P. A. Sheppard for their helpful comments and discussions.

Bamford, C. H.

Brewer, A. W . , Dohson, G . M. B., and Cwilong, B.

Brunt, D. Brunt, D, and

Kapur, A. K. Cwilong, B. Dobson, G . M. B.,

Brewer, A. W. and Cwilong, B.

Ihbson, G. M. B. Hamson, D. N. and Lawrence, J.

E l s a s w , W. M.

Jaumotte. J. Paneth. F. A, , and

Gluckauf, E. Pettemsen, S., and

Swinbank, W. C. Priestley, C. H. B..

and Swinbank, W. Taylor, G. I. Richard,wn, L. F. shaw, N.

Sverdmp, H. U

1943

1948

1926 1938

1947 1946

1929

1942

1936 1945 1947

1947

1915 1420 1923

1918

C.

REFERENCES Reports on Progress in Physics, London, IX,

Proc.Phys.Soc., London, 60, p. 52. p. 75.

Phil.Mag., London. 7th Series, 1, p. 523. Quart.J.R.Met.Soc., Liondon, 64, p. 510.

Pm.Roy.Soc. , London, A., 190, p. 157. [bid., 185, p. 144.

[hid. . 122, p. 484.

Harvard Meteorological Studies, Milton, Mass.,

Mern.R.Inst.Met., Bruxelles, 5. Pmc.Roy.Soc., London, A, 185, p. 89.

Quart.J.R.Met.Soc., London, 73, p. 335.

Nature, London, 159, p. 61. Phil.Yrans.Roy.Sac., London, A, 215, p. 1. Proc.Roy.Scc., London, A, 97, p. 354. Dictionary lof Applied Physics (London), 3,

Veroffentlich Geophys.Inst., Leipzig, 2nd Series

6. p. 97.

p. 84. 2, p. 190.











36 1







-%CKNOWLE DGMBNTS



Bamford, C. H.






E l s a s w , W. M.





Sverdmp, H. U

1943

1948

1926 1938

1947 1946

1929

1942

1936 1945 1947

1947

1915 1420 1923

1918

C.





[hid. . 122, p. 484.






6. p. 97.

p. 84. 2, p. 190.

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Bamford, C. H.






E l s a s w , W. M.





Sverdmp, H. U

1943

1948

1926 1938

1947 1946

1929

1942

1936 1945 1947

1947

1915 1420 1923

1918

C.





[hid. . 122, p. 484.






6. p. 97.

p. 84. 2, p. 190.

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Bamford, C. H.






E l s a s w , W. M.





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1943

1948

1926 1938

1947 1946

1929

1942

1936 1945 1947

1947

1915 1420 1923

1918

C.





[hid. . 122, p. 484.






6. p. 97.

p. 84. 2, p. 190.

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Bamford, C. H.






E l s a s w , W. M.





Sverdmp, H. U

1943

1948

1926 1938

1947 1946

1929

1942

1936 1945 1947

1947

1915 1420 1923

1918

C.





[hid. . 122, p. 484.






6. p. 97.

p. 84. 2, p. 190.

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Bamford, C. H.






E l s a s w , W. M.





Sverdmp, H. U

1943

1948

1926 1938

1947 1946

1929

1942

1936 1945 1947

1947

1915 1420 1923

1918

C.





[hid. . 122, p. 484.






6. p. 97.

p. 84. 2, p. 190.

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Questions • What drives the Brewer-Dobson Circulation?

!

!

• How will the Brewer-Dobson Circulation respond to anthropogenic forcing?


(Which waves are responsible for balancing the Coriolis torque?)!

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Gravity wave momentum fluxesRossby wave momentum and heat fluxes


(Which waves are responsible for balancing the Coriolis torque?)

Chapter 4: Stratospheric Dynamics 117

of the )turn-around latitudes3 where�w* is zero (i.e., the latitudes where the tropical upwelling changes to extra-tropical downwelling 6 Figure 4.9b). The annual cycle in the integrated upward mass ux between these turn-around latitudes was also generally well reproduced, though again the SOCOL and ULAQ models did not perform as well as the other models (Figure 4.9c). In the REF-B2 simula-tions, the turn-around latitudes are, on average, the same as in the REF-B1 simulations to within 0.5°. The multi-model mean REF-B2 upwelling is 0.1-0.2 mm/s greater in DJF and SON and 0.1-0.2mm/s less in March-April-May (MAM) and June-July-August (JJA) than that for REF-B1, though the annual mean upwelling is the same in both sets of simulations to within 1%.

On average the annual-mean tropical upwelling mass uxes in the REF-B1 simulations, calculated between the turn-around latitudes at 70 hPa and following the seasonal movement of those latitudes, agrees with the mass uxes derived from the UKMO analysis (Figure 4.10a, black bars). The standard error in the multi-model mean is less than the interannual variability in the analysed mass uxes (not shown). The contributions of resolved and parameter-ised wave drag in driving this upward mass ux can be es-

timated using the Haynes et al. (1991) Downward Control Principle (e.g., Butchart et al., 2010). These contributions are shown by the grey bars in Figure 4.10a. With the ex-ception of the UMUKCA-METO there is a signi cant con-tribution from the parameterised orographic gravity wave drag (OGWD) (for those models that supplied OGWD data), which on average accounts for 21.1% of the driving of the upwelling at 70 hPa decreasing to 4.7% at 10 hPa (Figure 4.10b). At 70 hPa the resolved waves accounted for 70.7% (71.6% at 10 hPa) and non-orographic gravity wave drag (NOGWD) 7.1% (10.9% at 10 hPa) of the driving again averaged over those models which provided these diagnostics. In general, however, there was a wide spread between the models in the contributions from the wave drags. At 70 hPa, the contributions from the resolved waves ranged from 31.4 % (ULAQ) to 102.1% (UMUKCA-METO), while the range for OGWD and NOGWD was 2.0 (UMUKCA-METO) to 40.9% (CCSRNIES) and -3.4 (CMAM) to 16.8% (SOCOL), respectively. It is also worth noting that the models generally overestimate the 100 hPa heat ux (~vertical component of the EP-Flux) between 20°S and 40°S (Section 4.3.4, Figure 4.12), which includes the southern latitude (i.e., the turn-around latitude, c.f.,

(a) Annual mean upward mass flux at 70 hPa (b) Annual mean upward mass flux at 10 hPa

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Figure 4.10: Annual mean upward mass ux averaged from 1980 to 1999 for the REF-B1 simulations and from 1992 to 2001 for the UKMO analyses. Averaging the modelled upwelling from 1992-2001 gives very similar values to those shown for 1980-1999. Upwelling calculated from�w * is shown by black bars. Upwelling calculated by downward control is split into contributions from: resolved waves (dark grey), orographic gravity wave drag (OGWD) (grey), and non-orographic gravity wave drag (NOGWD) (light grey). OGWD and NOGWD are shown combined for the GEOSCCM and MRI model. For some models only the resolved wave contribu-tions are shown due to the unavailability of gravity wave drag diagnostics. In the CMAM, NOGWD produces a negative upwelling and so cancels some of the upwelling produced by the OGWD and the resolved waves. This cancellation is shown by diagonal lines. The black horizontal lines show the multi-model mean and the inter-model standard error. The 95% con dence interval for the UKMO analyses is shown by the unshaded part of the bar with the horizontal line at the mid-point being the multi-year (10-year) mean. Values shown at (a) 70 hPa, and (b) 10 hPa. The numbers above the bars in (b) are the ratio for that model of the upwelling mass ux (normalised by the multi-model mean) at 10 hPa to upwelling mass ux (normalised by the multi-model mean) at 70 hPa.

Rossby wavesorographic GW

total

non-orographic GW

[CCMVal2 Report, Butchart et al. 2011]

Questions • How will the Brewer-Dobson Circulation respond to anthropogenic forcing?

• Models uniformly predict that it will increase [e.g. Butchart et al. 2010], but can’t be validated w/ available measurements [e.g. Garcia et al. 2011].

Questions • How will the Brewer-Dobson Circulation respond to anthropogenic forcing?

• Models uniformly predict that it will increase [e.g. Butchart et al. 2010], but can’t be validated w/ available measurements [e.g. Garcia et al. 2011].

• Do we understand why?

Chapter 4: Stratospheric Dynamics118

Figure 4.9b) at which the downward control integral is per-formed, though it is unclear what impact this would have on the upwelling estimated from the EP- ux divergence.

Similar results were obtained for the REF-B2 simu-lations (not shown) with the multi-model mean upwelling within 3% of that in the REF-B1 simulations. The largest differences occurred for the CNRM-ACM which had over 15% less upwelling for the REF-B2 than for the REF-B1 simulation.

In REF-B1 simulation, the ratio of the upwelling (as calculated from�w*) at 10 hPa to that at 70 hPa (weighted by the multi-model means) gives some indication of the relative leakiness of the tropical pipe in the lower strato-sphere with respect to the multi-model mean (Neu and Plumb, 1999; see also Chapter 5, Section 5.2.1.2). This ratio is shown in Figure 4.10b (see gure caption for de-tails). The UMUKCA and GEOSCCM simulations show too little upwelling at 70 hPa and too much upwelling at

10hPa, with the ratio of upwelling at 10 hPa to that at 70 hPa being around 115% of that of the multi-model average. Conversely, the CCSRNIES model, and the CMAM show too much upwelling at 70 hPa and too little upwelling at 10 hPa, with a ratio of 90% or less of that of the multi-model average.

For all the models the annual mean upward mass ux at 70 hPa increased from the start (1960) to the end of the REF-B2 simulations (see Figure 4.11). On average the trend in the upward mass ux was about 2% per decade (Figure 4.11b, c, d) with the largest trends occurring in JJA (not shown). With the exception of the SOCOL model, in-terannual variability in the annual mean upward mass ux is less than the multi-model spread (Figure 4.11a). For the end of the 20th century (1980-1999) the trends predicted by the REF-B2 simulations (Figure 4.11) were very similar to those for the REF-B1 simulations (not shown). The largest difference was found for the CCSRNIES model, which had

(a) (b) Annual mean mass flux trend at 70 hPa, 1980-1999

(c) Annual mean mass flux trend at 70 hPa, 2000-2049 (d) Annual mean mass flux trend at 70 hPa, 2050-2099

CC

SRN

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CM

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GEO

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s Fl

ux tr

end

(% p

er d

ecad

e) 4

3

2

1

0M

ass

Flux

tren

d (%

per

dec

ade) 4

3

2

1

0

Mas

s Fl

ux tr

end

(% p

er d

ecad

e)

4

3

2

1

0

5

6

Mas

s Fl

ux (1

09kg

s-1

)

Year1960 1980 2000 2020 2040 2060 2080 2100

10

9

8

7

6

5

4

CMAM

MRI

ULAQ

UMUKCA-UCAMWACCM

CNRM-ACMGEOSCCM

CCSRNIES

UMUKCA-METO

SOCOL

Figure 4.11: For the REF-B2 simulations. (a) Annual mean upward mass ux at 70 hPa, calculated from�w* . Also shown is the annual mean mass ux trend at 70 hPa from (b) 1980-1999, (c) 2000-2049 and (d) 2050-2099. The grey shading and diagonal lines are as in Figure 4.10. The values are calculated from a linear t to the annual mean mass ux from (b) 1980-1999 shown as a percentage of 1980 mass ux values, (c) 2000-2049 and (d) 2050-2099 shown as a percentage of 2000 mass ux values. The horizontal lines show the multi-model mean and the inter-model standard error.


total

non-orographic GW

[CCMVal2 Report]


!

!

• How will the Brewer-Dobson Circulation respond to anthropogenic forcing?

Interaction between Rossby and gravity wave driving complicates

the answers… !

(Did we ask the right question in the first place?)

What drives the Brewer-Dobson Circulation?

�u

�t� v�(f � �u

�y) + w� �u

�z= F zonal mean

torque

Downward Control [Haynes et al. 1991]

(Transformed Eulerian Mean momentum equation)

�u

�t� v�(f � �u

�y) + w� �u

�z= F zonal mean

torque


steady state

�u

�t� v�(f � �u

�y) + w� �u

�z= F zonal mean

torque


QG (neglect relative vorticity)

�u

�t� v�(f � �u

�y) + w� �u

�z= F zonal mean

torque

Coriolis force must balance torque

v� = �Ff


�u

�t� v�(f � �u

�y) + w� �u

�z= F zonal mean

torquestreamfunction ψ

Coriolis force must balance torque

v� = �Ff


Which waves contribute to the zonal mean torque?

latitude

pres

sure

(hPa

)

u (m s−1)

−80 −40 0 40 80

1

3

10

30

100

300

950 −100

−50

0

50

100

JJA zonal mean zonal wind

ECHAM6 (MPI-ESM-MR) (courtesy of Felix Bunzel)

F = � · F + GOGW + GNOGW


latitude

pres

sure

(hPa

)

u (m s−1)

−80 −40 0 40 80

1

3

10

30

100

300

950 −100

−50

0

50

100



Eliassen-Palm flux divergence: Rossby waves,

planetary and synoptic;

fairly well observed, resolved in models.


latitude

pres

sure

(hPa

)

u (m s−1)

−80 −40 0 40 80

1

3

10

30

100

300

950 −100

−50

0

50

100



orographic gravity waves, of scale 10-1000 km,

generated in stratified flow over topography;

marginally observed, parameterized in models


latitude

pres

sure

(hPa

)

u (m s−1)

−80 −40 0 40 80

1

3

10

30

100

300

950 −100

−50

0

50

100



non-orographic gravity waves: generated via

convection, frontal instabilities (thus have

non-zero phase speed), less well observed,

parameterized in models


latitude

pres

sure

(hPa

)

u (m s−1)

−80 −40 0 40 80

1

3

10

30

100

300

950 −100

−50

0

50

100



� = �EPFD + �OGW + �NOGW

using downward control, partition the

circulation


latitude

pres

sure

(hPa

)

u (m s−1)

−80 −40 0 40 80

1

3

10

30

100

300

950 −100

−50

0

50

100




using downward control, partition the

circulation

implicit assumption: the wave forcings are independent

The JJA Residual Circulation in ECHAM6

latitude

pres

sure

(hPa

)

residual mean mass streamfunction (kg s−1)

−80 −40 0 40 80

1

3

10

30

100−8

−6

−4

−2

0

2

4

6

8

x 109

The JJA Residual Circulation in ECHAM6

latitude

pres

sure

(hPa

)

residual mean streamfunction (kg s−1)

−80 −60 −40 −20

1

3

10

30

100−8

−6

−4

−2

0

2

4

6

8

x 109

Breaking down the streamfunction

latitude

pres

sure

(hPa

)

EPFD (m s−1 day−1)

−80 −60 −40 −20

1

3

10

30

100 −6

−4

−2

0

2

4

6

latitude

pres

sure

(hPa

)


−80 −60 −40 −20

1

3

10

30

100−8

−6

−4

−2

0

2

4

6

8

x 109

Breaking down the streamfunction

latitude

pres

sure

(hPa

)

EPFD (m s−1 day−1)

−80 −60 −40 −20

1

3

10

30

100 −6

−4

−2

0

2

4

6

latitude

pres

sure

(hPa

)

EPFD streamfunction (kg s−1)

−80 −60 −40 −20

1

3

10

30

100 −8

−6

−4

−2

0

2

4

6

8x 109

latitude

pres

sure

(hPa

)


−80 −60 −40 −20

1

3

10

30

100−8

−6

−4

−2

0

2

4

6

8

x 109

latitude

pres

sure

(hPa

)

EPFD, OGWD (m s−1 day−1)

−80 −60 −40 −20

1

3

10

30

100 −6

−4

−2

0

2

4

6Breaking down the streamfunction

latitude

pres

sure

(hPa

)

EPFD, OGWD streamfunction (kg s−1)

−80 −60 −40 −20

1

3

10

30

100 −8

−6

−4

−2

0

2

4

6

8x 109

latitude

pres

sure

(hPa

)


−80 −60 −40 −20

1

3

10

30

100−8

−6

−4

−2

0

2

4

6

8

x 109

OGWD

latitude

pres

sure

(hPa

)


−80 −60 −40 −20

1

3

10

30

100 −6

−4

−2

0

2

4


latitude

pres

sure

(hPa

)

EPFD, OGWD, NOGWD s (kg s−1)

−80 −60 −40 −20

1

3

10

30

100 −8

−6

−4

−2

0

2

4

6

8x 109

latitude

pres

sure

(hPa

)


−80 −60 −40 −20

1

3

10

30

100−8

−6

−4

−2

0

2

4

6

8

x 109

NOGWDOGWD

Puzzle pieces fit together to provide a smooth circulation!

−80 −60 −40 −20 0 20 40 60 80

−6

−4

−2

0

2

latitude

109 k

g s−

170 hPa residual streamfunction

DirectEPFD+GWDEPFDNOGWDOGWD

This decomposition of the BDC is used to assess the roles of each type of wave driving.

−80 −60 −40 −20 0 20 40 60 80

−6

−4

−2

0

2

latitude

109 k

g s−

170 hPa residual streamfunction


What drives the Brewer-Dobson Circulation? Chapter 4: Stratospheric Dynamics 117





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0.95

0.91

0.90

1.02

0.71

1.03

1.16

0.95

0.95

1.07

1.02

1.14

1.17

1.09



total

non-orographic GW

[CCMVal2 Report, Chpt 4]

Why do the models agree more on the total circulation than on

the components? !

How do the components fit together so nicely to produce a smooth circulation?

An idealized Atmospheric GCM

negative-correlation integration (Fig. 3b), the parame-terized wave driving is trapped in the lower strato-sphere, and the wave driving above 70 hPa is extremelyweak. In the positive-correlation integration (Fig. 3a),however, there is a substantial drag on the upperstratosphere.

The difference between the OGWD in the positiveand negative integrations is shown in Fig. 4a. The am-plitude of the zonally integrated perturbation is quitesignificant, on the order of 109N, and can be put intocontext by considering the residual-mean mass circula-tion implied by downward control, as shown in Fig. 4b.

FIG. 1. A comparison between model configurations with Rayleigh friction, the ‘‘old’’ model used in Gerber andPolvani (2009), and the Alexander and Dunkerton (1999) NOGW parameterization, the ‘‘new’’ model used in thisstudy: (a),(b) the time- and zonal-mean zonal winds (m s21), (c),(d) the time- and zonal-mean parameterized gravitywave driving (109N), and (e),(f) the residual-mean mass streamfunction (109 kg s21).

3784 JOURNAL OF THE ATMOSPHER IC SC IENCES VOLUME 70

• dry primitive equations on the sphere

• Newtonian relaxation of temperature to radiative-convective equilibrium profile [Held and Suarez 1994; Polvani and Kushner 2002]

• Simple large scale topography [Gerber and Polvani, 2009]

• Alexander and Dunkerton [1999] non-orographic gravity wave drag

• Pierrehumbert [1987] orographic gravity wave drag

[Cohen et al. 2013]

Two experiments: Perturb the Orographic Gravity Wave Drag

Model A: positive correlationlon (deg)

pres

sure

(hPa

)

positive correlation

0 100 200 300

0.1

0.3

1

3

10

30

100

300

950 −10

0

10

20

30

40

lon (deg)pr

essu

re (h

Pa)

negative correlation

0 100 200 300

0.1

0.3

1

3

10

30

100

300

950 −10

0

10

20

30

40

Model B: negative correlation

ms-1 ms-1

zonal wind OGW drag

[Cohen et al. 2013]

Impact of differences in OGW configuration

latitude

pres

sure

(hPa

)

OGWD positive correlation

20 40 60 80

0.1

0.3

1

3

10

30

100 −20

−15

−10

−5

0

5

10

15

20

latitude

pres

sure

(hPa

)

OGWD negative correlation

20 40 60 80

0.1

0.3

1

3

10

30

100 −20

−15

−10

−5

0

5

10

15

20

OGW driving (109 N) “positive correlation”

OGW driving (109 N) “negative correlation”

[Cohen et al. 2013]

Impact on BDC

latitude

pres

sure

(hPa

)

diff OGWD

20 40 60 80

0.1

0.3

1

3

10

30

100 −20

−15

−10

−5

0

5

10

15

20

difference in OGW driving (109 N)

[Cohen et al. 2013]

Impact on BDC

latitude

pres

sure

(hPa

)

diff OGWD

20 40 60 80

0.1

0.3

1

3

10

30

100 −20

−15

−10

−5

0

5

10

15

20

latitude

pres

sure

(hPa

)

diff OGW streamfunction

20 40 60 80

0.1

0.3

1

3

10

30

100 −3

−2

−1

0

1

2

3


difference ψ*, downward control (109 kg/s)

[Cohen et al. 2013]

latitude

pres

sure

(hPa

)

diff OGW streamfunction

20 40 60 80

0.1

0.3

1

3

10

30

100 −3

−2

−1

0

1

2

3

Impact on BDC

latitude

pres

sure

(hPa

)

diff OGWD

20 40 60 80

0.1

0.3

1

3

10

30

100 −20

−15

−10

−5

0

5

10

15

20

latitude

pres

sure

(hPa

)

diff BDC

20 40 60 80

0.1

0.3

1

3

10

30

100 −3

−2

−1

0

1

2

3



actual difference ψ* (109 kg/s)

latitude

pres

sure

(hPa

)

diff EPFD streamfunction

20 40 60 80

0.1

0.3

1

3

10

30

100 −3

−2

−1

0

1

2

3

latitude

pres

sure

(hPa

)

diff EPFD

20 40 60 80

0.1

0.3

1

3

10

30

100 −20

−15

−10

−5

0

5

10

15

20

Compensation by the resolved waves

latitude

pres

sure

(hPa

)

diff BDC

20 40 60 80

0.1

0.3

1

3

10

30

100 −3

−2

−1

0

1

2

3

difference EP flux divergence (109 N)


actual difference ψ* (109 kg/s)

OGWD

−80 −60 −40 −20 0 20 40 60 80−1

−0.5

0

0.5

1

1.5

2

2.5

3

latitude

mas

s st

ream

func

tion

(109 k

g s−

1 )


−80 −60 −40 −20 0 20 40 60 80−1

−0.5

0

0.5

1

1.5

2

2.5

3

latitude

mas

s st

ream

func

tion

(109 k

g s−

1 )


What “drives” the BDC?

Residual Mean Streamfunction at 70 hPa

Model A Model B[Cohen et al. 2013]

Implication of compensation for BDC driving…

p.c. n.c.0

0.5

1

1.5

2

2.5

3

3.5

mas

s up

ward

mas

s flu

x (1

09 kg

s−1 )

BDCEPFD+GWDEPFDNOGWDOGWD

Chapter 4: Stratospheric Dynamics 117





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1.09


mod

el A

mod

el B

What is going on here?


When I find myself in times of trouble, Father Hoskins comes to me, speaking words of wisdom …

!

PV … PV!


When I find myself in times of trouble, Father Hoskins comes to me, speaking words of wisdom …

!

PV … PV!

(That is, how do the wave forcings affect the potential vorticity.)

Back to Basics: Haynes et al. 1991 (Near) steady response to a localized torque

zonal wind streamfunction ψ

For what torques is the circulation reasonable?

zonal wind

QG Potential Vorticity

qy = � � uyy + f⇥y

⇥p

zonal wind

For what torques is the circulation reasonable?

For what torques is the circulation reasonable? Stability depends critically on meridional scale


qy = � � uyy + f⇥y

⇥p

Lu � A

L2

zonal wind

amplitude A, meridional scale L

For what torques is the circulation reasonable? Stability depends critically on meridional scale


qy = � � uyy + f⇥y

⇥p

For

perturbation to PV gradient

Lu � A

L2

L << LR

� A

L4

zonal wind

amplitude A, meridional scale L

Stability of the circulation for a compact torqueam

plitu

de o

f wav

e dr

iving

meridional length scale

gradient in the relative vorticity 2u1yy and vortexstretching 2(!u1p)p.

d For L ! Ld, when L is large compared to the Rossbyradius of deformation, the vertical gradient in u1,associated with the vortex stretching, dominates thePV gradient and (11) yields a simple condition on thenecessary condition for instability:

A.QyL

2

tr. (12)

In this limit the amplitude must be fairly large tosatisfy the necessary condition for instability.

d For L " Ld, when L is small compared to Ld, therelative vorticity gradient dominates and (11) yieldsthe following necessary condition for instability:

A.QyL

4

trL2d

H2r

H2. (13)

Here, the critical amplitude for instability decreasesrapidly with the meridional scale of the perturbation,and so is extremely sensitive to L. In addition, thecritical amplitude is inversely proportional to the squareof the wave forcing height scale: the larger the verticalextent, the smaller the critical amplitude for instability.

d If L 5 Ld and H 5 Hr, the condition is

A[Ac5QyL

2d

tr. (14)

If we suppose that Qy scales as b, then we get a roughestimate of the critical amplitudeAc’ 83 1026m s22’1ms21 day 21, based on the parameters consistent withour model,N5

ffiffiffi5

p3 1022 s21,H5 7km, tr5 40 days,

and where the torque is centered around f 5 508N.

WhenA and L are such that q0y 1q1y , 0, as in (7a), theonly way that a stable equilibrated limit can be achievedis if a resolved wave driving is generated such that

q0y1 (q1y1 qRy). 0, (15)

where qR stands for the contribution of a perturbed re-solved Rossby wave to the QG-PV meridional gradient.In an OGW parameterization, L is set primarily by thespatial extent of the subgrid-scale mountain height andsurface winds. In practice, both tend to vary on a muchshorter scale than the deformation radius Ld of thestratosphere, which is about 50% larger than in the tro-posphere because of increased stratification. Typical am-plitudes for the OGWDare on the order of 1ms21 day 21

(Alexander et al. 2010), thus the necessary condition forinstability is quite likely to be satisfied.

As discussed above, Haynes et al. (1991) denotedLd/L as Hr/HR, because Ld/L5NHr/f0L5Hr/HR. In-spection of (8) and (11) reveals that the necessary con-dition for instability depends on the second and fourthmeridional derivatives of the wave forcing, hence we be-lieve that Ld/L is a better instability measure thenHr/HR.Figure 9 sketches out where the necessary condition

for instability in (11) is satisfied as a function of the wavedriving amplitude and length, using Qy 5 0.1b, b, and2b, where tr 5 40 days, N5

ffiffiffi5

p3 1022 s21, H 5 29 km,

and the forcing is centered at f0 5 508 such that Ld ’138. Clearly, Qy has a stabilizing effect; the larger it is,the more stable the flow is. The nonlinear shaded grayindicates the region where the Rossby number exceeds 1,hence the QG approximation breaks down and the QGdownward control limit is no longer applicable. Note,however, that the flow is likely to go unstable before itreaches this limit. The boldface cross in the figure denotesthe amplitude and meridional scale of the perturbationgenerated by the GFDLOGW scheme, shown in Fig. 3a.Clearly, this wave forcing had to be compensated to yielda sensible mean state.

b. Verification of the theory in the model

We next test the hypothesis that compensation is re-lated to instability in our AGCM, where we can explore

FIG. 9. The necessary condition for instability, as in (11), asa function of the wave driving’s amplitude A, meridional extentL, and background PV gradient Qy, where tr 5 40 days,N5

ffiffiffi5

p3 1022 s21,H5 29 km, centered atf05 508. The solid lines

correspond to instability thresholds for Qy 5 0.1b, b, and 2b. Tothe lower-right, the flow is likely to be stable and to the upperleft, the flow is likely to be unstable. The shaded gray area indicatesthe nonlinear region where the downward control limit is no longerapplicable. The open circles indicate the different A and L valuesthat we explored in our AGCM. The thick cross denotes the am-plitude and meridional scale of the perturbation generated by theGFDL OGW scheme, shown in Figure 3a.

DECEMBER 2013 COHEN ET AL . 3793

Stability of the circulation for a compact torqueam

plitu

de o

f wav

e dr

iving




A.QyL

2

tr. (12)



A.QyL

4

trL2d

H2r

H2. (13)



A[Ac5QyL

2d

tr. (14)


ffiffiffi5

p3 1022 s21,H5 7km, tr5 40 days,



q0y1 (q1y1 qRy). 0, (15)





ffiffiffi5

p3 1022 s21, H 5 29 km,





ffiffiffi5




stable

ampl

itude

of w

ave

drivi

ng


unstable

stable



A.QyL

2

tr. (12)



A.QyL

4

trL2d

H2r

H2. (13)



A[Ac5QyL

2d

tr. (14)


ffiffiffi5

p3 1022 s21,H5 7km, tr5 40 days,



q0y1 (q1y1 qRy). 0, (15)





ffiffiffi5

p3 1022 s21, H 5 29 km,





ffiffiffi5



DECEMBER 2013 COHEN ET AL . 3793Stability of the circulation for a compact torque

ampl

itude

of w

ave

drivi

ng




A.QyL

2

tr. (12)



A.QyL

4

trL2d

H2r

H2. (13)



A[Ac5QyL

2d

tr. (14)


ffiffiffi5

p3 1022 s21,H5 7km, tr5 40 days,



q0y1 (q1y1 qRy). 0, (15)





ffiffiffi5

p3 1022 s21, H 5 29 km,





ffiffiffi5




k 5 R/cp ’ 2/7, where cp is the specific heat at constantpressure, and R is the dry gas constant.Following the downward control derivation, using

(3a) in (3b) we get

y*52G

f00

v*(y,p)51

f0

ðp

p1

Gy(y, s) ds1v*(y,p1) . (4)

Taking the y derivative of (3c) and using (4) yields

(ur 2 u)y5 trvy*up

5trupf0

ðp

p1

Gyy(y, s) ds1 trupvy* (y, p1) . (5)

Multiplying (5) by f0/up and taking the p derivative gives

trGyy5 f0

"(ur 2 u)y

up

#

p

5 [!(u2 ur)p]p , (6)

where the equality on the right follows using (3d).Equation (6) provides the essence of the downwardcontrol: the mean flow fields u and u are solely de-termined by thewave forcingG (up to a boundary term).In a stable dynamically equilibrated stratosphere, the

background qy is positive (e.g., in regions with no shearflow, qy 5b. 0) and so we write the necessary condi-tion for instability as qy , 0. Let us consider a meanwave driving G0 that determines the zonal-mean fieldsu0 and u0 such that qy 5 q0y $ 0, where q0 denotes thezonal-mean QG-PV of the mean state. For example,Fig. 8 shows q0y over the Northern Hemispheric strato-sphere for the default integration with the NOGW (sim-ulation 1 in Table 1); q0y is strictly positive and its overallamplitude is on the order of b. Now, consider a pertur-bation to the stable system. We denote the perturbedwave driving as G1 and the resultant flow as u1 and u1.Under the assumption that the wave forcing is linearlyadditive, with no interactions between the wave forcings,G5G0 1G1, the necessary condition for instability in (2)becomes

qy5 q0y1 q1y, 00q0y, u1yy1 (!u1p)p , (7)

where q1y is defined to be

q1y [ 2 u1yy 2 (!u1p)p . (8)

In words, the necessary condition for instability is thatthe perturbed QG-PV meridional gradient overwhelms

the existing meridional gradient. Equation (6) can be sep-arated for a basic-state balance governed byG0 and a bal-ance due to the perturbationG1, where the latter balance is

trG1yy5 (!u1p)p . (9)

Using standard dimensional analysis technics (e.g.,Barenblatt 1996), let the perturbed wave driving G1

scale with amplitude A, let L and H be the meridionaland vertical scales on which the wave driving varies,respectively, and let u1 scale with U. The scale of thebackground QG-PV gradient q0y is denoted as Qy. Tomake analytical progress, we simplify ! by assuming con-stant stratification N2 52g2rup/u and that the tempera-ture is equal to the reference temperature T5T0. Thus,! simplifies to ( f0gp/RT0N)2 5 (p/Ld)

2, whereLd5NHr/f0 is the Rossby radius of deformation and Hr 5 RT0/g isthe density height scale. It follows from (9) thatu1 scales as

u1 }U } trAL2d

L2

H2

H2r

. (10)

The same scaling analysis can be found in Garcia (1987)and Haynes et al. (1991), though in the latter they denoteLd/L asHr/HR, whereHR5 f0L/N is the ‘‘Rossby height’’for the problem. Using (9) and (10), we scale each term inthe necessary condition for instability [(7b)] to get

Qy ,trA

L2max

(L2d

L2

H2

H2r

, 1

). (11)

Note that the factorL2dH

2/L2H2r is the ratio between the

amplitude of the QG-PV associated with meridional

FIG. 8. The time and zonal mean of the meridional gradient oftheQG-PV q0y (m

21 s21) in the default integrationwith theNOGWand g 5 6Kkm21. The black contours denote the location andstrength of the wave forcing G1 discussed in section 4.


Test the predictionunstable

stable

PV Gradient

Test the prediction

waves in the mesosphere. Even though the wave drivingis determined separately for each column, the structureof the subgrid-scale mountain height parameter givesthe resulting drag significant zonal structure relative tothe climatological stationary planetary waves as seen—for example, in our integrations in Figs. 2c and 2d. Theparameterized wave forcing can thus be a source ofplanetary waves, providing a resolved Eliassen–Palm fluxdivergence that could compensate the parameterizedtorque. McLandress andMcFarlane (1993) found furtherevidence for the generation of planetary waves by theOGWD, although their analysis suggested a differentmechanism than initially proposed by Holton (1984).

To assess the significance of the spatial and temporalstructure of the parameterized wave driving, we turnedoff the OGW parameterization and ran simulations us-ing a steady specified torque derived from the OGWforcing of the positive-correlation (with k 5 2) simula-tion. Specifically, we ran three simulations with specifiedforcing by applying (i) the time mean and (ii) the timeand zonal mean, and by (iii) using the time-mean forcingbut shifting its phase by 1808. Note that the latter ex-periment is similar, in structure, to the sensitivity case Din McLandress and McFarlane (1993), except that theyinstead shift the resolved waves. Figure 7 (see labels‘‘time-mean forcing,’’ ‘‘time- and zonal-mean forcing,’’

FIG. 6. The residual-mean streamfunction at 70 hPa, as a function of latitude, for the (a) positive-correlation and(b) negative-correlation integrations (109 kg s21). ‘‘Direct’’ refers to the total residual-mean streamfunction com-puted directly from the definition of the residual-mean velocities. ‘‘EPFD1GWD’’ refers to the total residual-meanmass streamfunction computed by downward control, while ‘‘EPFD,’’ ‘‘NOGWD,’’ and ‘‘OGWD’’ refer to theresidual-mean streamfunctions associated with each of the wave components: resolved, nonorographic, and oro-graphic gravity wave driving (the thick black curve is thus the sum of the blue, green, and red curves).

FIG. 7. (a) The compensation metric C for the various integrations. Each bar corresponds to a difference between twointegrations as listed inTable 1. For example, the control run is the difference between integrations 3 and 4 in Table 1. Theerror bars correspond to one standard deviation in C. (b) The bootstrap kernel density estimate for the integrationslabeled by ‘‘L 5 2.5,’’ ‘‘L 5 5.0,’’ . . . , ‘‘L 5 25.0.’’ The colored bars in (a) and the colored curves in (b) match.


waves in the mesosphere. Even though the wave drivingis determined separately for each column, the structureof the subgrid-scale mountain height parameter givesthe resulting drag significant zonal structure relative tothe climatological stationary planetary waves as seen—for example, in our integrations in Figs. 2c and 2d. Theparameterized wave forcing can thus be a source ofplanetary waves, providing a resolved Eliassen–Palm fluxdivergence that could compensate the parameterizedtorque. McLandress andMcFarlane (1993) found furtherevidence for the generation of planetary waves by theOGWD, although their analysis suggested a differentmechanism than initially proposed by Holton (1984).

To assess the significance of the spatial and temporalstructure of the parameterized wave driving, we turnedoff the OGW parameterization and ran simulations us-ing a steady specified torque derived from the OGWforcing of the positive-correlation (with k 5 2) simula-tion. Specifically, we ran three simulations with specifiedforcing by applying (i) the time mean and (ii) the timeand zonal mean, and by (iii) using the time-mean forcingbut shifting its phase by 1808. Note that the latter ex-periment is similar, in structure, to the sensitivity case Din McLandress and McFarlane (1993), except that theyinstead shift the resolved waves. Figure 7 (see labels‘‘time-mean forcing,’’ ‘‘time- and zonal-mean forcing,’’

FIG. 6. The residual-mean streamfunction at 70 hPa, as a function of latitude, for the (a) positive-correlation and(b) negative-correlation integrations (109 kg s21). ‘‘Direct’’ refers to the total residual-mean streamfunction com-puted directly from the definition of the residual-mean velocities. ‘‘EPFD1GWD’’ refers to the total residual-meanmass streamfunction computed by downward control, while ‘‘EPFD,’’ ‘‘NOGWD,’’ and ‘‘OGWD’’ refer to theresidual-mean streamfunctions associated with each of the wave components: resolved, nonorographic, and oro-graphic gravity wave driving (the thick black curve is thus the sum of the blue, green, and red curves).

FIG. 7. (a) The compensation metric C for the various integrations. Each bar corresponds to a difference between twointegrations as listed inTable 1. For example, the control run is the difference between integrations 3 and 4 in Table 1. Theerror bars correspond to one standard deviation in C. (b) The bootstrap kernel density estimate for the integrationslabeled by ‘‘L 5 2.5,’’ ‘‘L 5 5.0,’’ . . . , ‘‘L 5 25.0.’’ The colored bars in (a) and the colored curves in (b) match.


k 5 R/cp ’ 2/7, where cp is the specific heat at constantpressure, and R is the dry gas constant.Following the downward control derivation, using

(3a) in (3b) we get

y*52G

f00

v*(y,p)51

f0

ðp

p1

Gy(y, s) ds1v*(y,p1) . (4)

Taking the y derivative of (3c) and using (4) yields

(ur 2 u)y5 trvy*up

5trupf0

ðp

p1

Gyy(y, s) ds1 trupvy* (y, p1) . (5)

Multiplying (5) by f0/up and taking the p derivative gives

trGyy5 f0

"(ur 2 u)y

up

#

p

5 [!(u2 ur)p]p , (6)

where the equality on the right follows using (3d).Equation (6) provides the essence of the downwardcontrol: the mean flow fields u and u are solely de-termined by thewave forcingG (up to a boundary term).In a stable dynamically equilibrated stratosphere, the

background qy is positive (e.g., in regions with no shearflow, qy 5b. 0) and so we write the necessary condi-tion for instability as qy , 0. Let us consider a meanwave driving G0 that determines the zonal-mean fieldsu0 and u0 such that qy 5 q0y $ 0, where q0 denotes thezonal-mean QG-PV of the mean state. For example,Fig. 8 shows q0y over the Northern Hemispheric strato-sphere for the default integration with the NOGW (sim-ulation 1 in Table 1); q0y is strictly positive and its overallamplitude is on the order of b. Now, consider a pertur-bation to the stable system. We denote the perturbedwave driving as G1 and the resultant flow as u1 and u1.Under the assumption that the wave forcing is linearlyadditive, with no interactions between the wave forcings,G5G0 1G1, the necessary condition for instability in (2)becomes

qy5 q0y1 q1y, 00q0y, u1yy1 (!u1p)p , (7)

where q1y is defined to be

q1y [ 2 u1yy 2 (!u1p)p . (8)

In words, the necessary condition for instability is thatthe perturbed QG-PV meridional gradient overwhelms

the existing meridional gradient. Equation (6) can be sep-arated for a basic-state balance governed byG0 and a bal-ance due to the perturbationG1, where the latter balance is

trG1yy5 (!u1p)p . (9)

Using standard dimensional analysis technics (e.g.,Barenblatt 1996), let the perturbed wave driving G1

scale with amplitude A, let L and H be the meridionaland vertical scales on which the wave driving varies,respectively, and let u1 scale with U. The scale of thebackground QG-PV gradient q0y is denoted as Qy. Tomake analytical progress, we simplify ! by assuming con-stant stratification N2 52g2rup/u and that the tempera-ture is equal to the reference temperature T5T0. Thus,! simplifies to ( f0gp/RT0N)2 5 (p/Ld)

2, whereLd5NHr/f0 is the Rossby radius of deformation and Hr 5 RT0/g isthe density height scale. It follows from (9) thatu1 scales as

u1 }U } trAL2d

L2

H2

H2r

. (10)

The same scaling analysis can be found in Garcia (1987)and Haynes et al. (1991), though in the latter they denoteLd/L asHr/HR, whereHR5 f0L/N is the ‘‘Rossby height’’for the problem. Using (9) and (10), we scale each term inthe necessary condition for instability [(7b)] to get

Qy ,trA

L2max

(L2d

L2

H2

H2r

, 1

). (11)

Note that the factorL2dH

2/L2H2r is the ratio between the

amplitude of the QG-PV associated with meridional

FIG. 8. The time and zonal mean of the meridional gradient oftheQG-PV q0y (m

21 s21) in the default integrationwith theNOGWand g 5 6Kkm21. The black contours denote the location andstrength of the wave forcing G1 discussed in section 4.


narrow

wide

PV Gradient

latitude

pres

sure

(hPa

)


−80 −60 −40 −20

1

3

10

30

100 −6

−4

−2

0

2

4


latitude

pres

sure

(hPa

)

EPFD, OGWD streamfunction (kg s−1)

−80 −60 −40 −20

1

3

10

30

100 −8

−6

−4

−2

0

2

4

6

8x 109

latitude

pres

sure

(hPa

)


−80 −60 −40 −20

1

3

10

30

100−8

−6

−4

−2

0

2

4

6

8

x 109

OGWD

Interaction between wave driving suggest that the “forcings” are somewhat fungible.



0 0.25 0.5 0.75 10

50

100

150

200

250

TURN

1xCO

2(k

g m−1

s−1

)

(a)DirectOGW+EP

OGWEP

0 0.25 0.5 0.75 10

20406080

100120

Ψ 70 hPaTURN−52N

(b)

0 0.25 0.5 0.75 1−10

0

10

20

30

40

50

G

2xCO

2−1xCO

2(k

g m−1

s−1

)

(c)

0 0.25 0.5 0.75 1−10−5

05

10152025

G

(d)

Fig. 4. The mass stream function Ψ at 70 hPa for NH winter (DJF) as a function of G(first column) at the turnaround latitude and (second column) the difference between Ψ atthe turnaround latitude and 52◦N for (first row) 1×CO2 and (second row) the response toclimate change.

24

intensity of parameterized wave driving (parameter G)

Compensation makes total circulation more robust than components [Sigmond and Shepherd, 2014]

Uncertainty in “forcing” increases with future trends

resolved wavesorographic GW

total

non-orographic GW









CC

SRN

IES

CM

AM

GEO

SCC

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A-U

CAM

WAC

CM

Mas

s Fl

ux tr

end

(% p

er d

ecad

e) 4

3

2

1

0

Mas

s Fl

ux tr

end

(% p

er d

ecad

e) 4

3

2

1

0

Mas

s Fl

ux tr

end

(% p

er d

ecad

e)

4

3

2

1

0

5

6

Mas

s Fl

ux (1

09kg

s-1

)

Year1960 1980 2000 2020 2040 2060 2080 2100

10

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8

7

6

5

4

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MRI

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… but compensation may affect response to CO2

37

Streamfunction DJF (Past)

-90 -60 -30 0 30 60 90Latitude (deg)

-50

0

50

100

150

200

Psi (

kg m

-1 s

-1)

70 hPa

(a)

DirectEPFD+GWDOGWDEPFD (stat)EPFD (trans k=1-3)EPFD (trans k=4-32)

Difference (Future-Past)

-90 -60 -30 0 30 60 90Latitude (deg)

-20

-10

0

10

20

30

40

50(b)

70 hPa

DirectEPFD+GWDOGWDEPFD (stat)EPFD (trans k=1-3)EPFD (trans k=4-32)

FIG 2. Downward control mass streamfunction for DJF at 70 hPa for (a) past and (b) future minus past: combined resolved and parameterized wave drag (thick black); resolved stationary wave drag (solid blue); transient planetary-scale wave (k=1-3) drag (dash-dotted); transient synoptic-scale wave (k=4-32) drag (dotted); and parameterized orographic gravity-wave drag (red). The thin black line denotes the streamfunction computed directly from the vertical residual velocity. The downward control streamfunctions cannot be computed in the tropics.

[Shepherd and McLandress 2011]

Impact of GW depends on basic state of the model [Sigmond and Shepherd, 2014]

0 0.25 0.5 0.75 10

50

100

150

200

250

TURN

1xCO

2(k

g m−1

s−1

)

(a)DirectOGW+EP

OGWEP

0 0.25 0.5 0.75 10

20406080

100120

Ψ 70 hPaTURN−52N

(b)

0 0.25 0.5 0.75 1−10

0

10

20

30

40

50

G

2xCO

2−1xCO

2(k

g m−1

s−1

)

(c)

0 0.25 0.5 0.75 1−10−5

05

10152025

G

(d)


24


0 0.25 0.5 0.75 10

50

100

150

200

250

TURN

1xCO

2(k

g m−1

s−1

)

(a)DirectOGW+EP

OGWEP

0 0.25 0.5 0.75 10

20406080

100120

Ψ 70 hPaTURN−52N

(b)

0 0.25 0.5 0.75 1−10

0

10

20

30

40

50

G

2xCO

2−1xCO

2(k

g m−1

s−1

)

(c)

0 0.25 0.5 0.75 1−10−5

05

10152025

G

(d)


24

0 0.25 0.5 0.75 10

50

100

150

200

250

TURN

1xCO

2(k

g m−1

s−1

)

(a)DirectOGW+EP

OGWEP

0 0.25 0.5 0.75 10

20406080

100120

Ψ 70 hPaTURN−52N

(b)

0 0.25 0.5 0.75 1−10

0

10

20

30

40

50

G

2xCO

2−1xCO

2(k

g m−1

s−1

)

(c)

0 0.25 0.5 0.75 1−10−5

05

10152025

G

(d)


24


G

Impact of GW depends on basic state of the model [Sigmond and Shepherd, 2014]

Tuning of the basic state influences the relative role of wave forcings in climate response Chapter 4: Stratospheric Dynamics 117





UKM

O

CAM

3.5

CC

SRN

IES

CM

AM

CN

RM

-AC

M

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A

EMAC

GEO

SCC

M

MR

I

Niw

aSO

CO

L

SOC

OL

ULA

Q

UM

UKC

A-M

ETO

UM

UKC

A-U

CAM

WAC

CM

8

6

4

2

0

Mas

s Fl

ux (1

09 kg

s-1)

UKM

O

CAM

3.5

CC

SRN

IES

CM

AM

CN

RM

-AC

M

E39C

A

EMAC

GEO

SCC

M

MR

I

Niw

aSO

CO

L

SOC

OL

ULA

Q

UM

UKC

A-M

ETO

UM

UKC

A-U

CAM

WAC

CM

4

3

2

1

0

Mas

s Fl

ux (1

09 kg

s-1)

0.95

0.91

0.90

1.02

0.71

1.03

1.16

0.95

0.95

1.07

1.02

1.14

1.17

1.09











CC

SRN

IES

CM

AM

GEO

SCC

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UKC

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CAM

WAC

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CN

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-AC

M

CC

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AM

GEO

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CAM

WAC

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CC

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CM

AM MR

I

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Q

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A-M

ETO

UM

UKC

A-U

CAM

WAC

CM

Mas

s Fl

ux tr

end

(% p

er d

ecad

e) 4

3

2

1

0

Mas

s Fl

ux tr

end

(% p

er d

ecad

e) 4

3

2

1

0

Mas

s Fl

ux tr

end

(% p

er d

ecad

e)

4

3

2

1

0

5

6

Mas

s Fl

ux (1

09kg

s-1

)

Year1960 1980 2000 2020 2040 2060 2080 2100

10

9

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7

6

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4

CMAM

MRI

ULAQ

UMUKCA-UCAMWACCM

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A potential vorticity, surf zone perspective

latitude

pres

sure

(hPa

)

u (m s−1)

−80 −40 0 40 80

1

3

10

30

100

300

950 −100

−50

0

50

100


Action of Rossby waves is to mix potential vorticity in the surf zone between the polar vortex and tropical stratosphere.

[McIntyre and Palmer, 1983]


latitude

pres

sure

(hPa

)

u (m s−1)

−80 −40 0 40 80

1

3

10

30

100

300

950 −100

−50

0

50

100


Gravity wave driving inside surf zone will have limited impact on the BDC. !

More likely for stationary OGW, which break at same critical levels as stationary Rossby waves

[Cohen et al. 2014]


latitude

pres

sure

(hPa

)

u (m s−1)

−80 −40 0 40 80

1

3

10

30

100

300

950 −100

−50

0

50

100

JJA zonal mean zonal windGravity wave driving outside surf zone likely to have large impact on the BDC. !

More likely for NOGW, which can modify polar vortex.

[Cohen et al. 2014]

Anthropogenic forcing modifies surf zone [Shepherd and McLandress 2011]

C(v, k)dv 5 C(c, k)dc, where c 5 va cosu/k, a is theearth’s radius, and u is latitude. Although Rossby wavesconserve angular phase velocity rather than regular phasevelocity during propagation through a zonally homoge-neous flow on the sphere, as in Randel and Held (1991)we plot regular phase velocity to allow a direct compar-ison with the zonal-mean zonal wind. A phase-velocitygrid of resolution Dc 5 1 m s21 was used. Cospectra foreach year were averaged over the appropriate time periodsand over the three simulations. The plotted cospectraldensities in (c, k) space have been divided by Dc andtherefore have units of the physical quantities. We havechecked that the integrated EPFD across all phase speedsclosely matches the transient EPFD computed directlyfrom the physical fields.

Note that the wavenumber–frequency analysis re-quires daily 3D data, which are not available on theCCMVal archive. Thus, it is not possible to extend thisanalysis to other models using the existing archive.

3. Analysis

We start by showing the predicted changes in tem-perature and zonal wind arising from climate change inthe CMAM. Although this is not a new scientific result,it sets the context for the subsequent analysis. Figure 1shows the differences between the past (1960–79) andfuture (2080–99) of the annual- and zonal-mean tem-perature and zonal wind from the ensemble mean ofthe three simulations, along with the westerly jets for thepast. The strengthening of the upper flank of the sub-tropical jets in both hemispheres is readily apparent.Note that this cannot possibly be the response to astrengthened BDC, because a strengthened BDC wouldcool the tropics and warm the extratropics and thus actto weaken rather than to strengthen the upper flank ofthe jets. At middle and high latitudes, the zonal-windchanges differ substantially between the two hemi-spheres and their interpretation is less straightforwardbecause the zonal winds respond in a first-order way tothe dynamical changes (MS09). Our focus here howeveris on the subtropical changes, because it is the wave dragat subtropical latitudes that is determinative of the nettropical upwelling and thus of the BDC as usually un-derstood (Butchart et al. 2006; MS09).

Because the wavenumber–frequency analysis can onlybe performed for waves with a nonzero phase velocity,stationary waves are necessarily excluded. It is thereforeimportant to determine how much of the resolved wavedrag is missed by this procedure. Although it is oftentacitly assumed that planetary waves, especially in theNH, are primarily stationary, the contribution of sta-tionary waves to the driving of the BDC has not been

quantitatively assessed. Figure 2 shows the mass stream-function for DJF at 70 hPa inferred from downwardcontrol for the past (left) and the difference between thefuture and past (right). This is a revised version of Fig. 18of MS09, but with the resolved wave drag now separatedinto its stationary (monthly mean) and transient (de-viations from monthly mean) components. Because thenet downward mass flux in each hemisphere is pro-portional to the mass streamfunction evaluated at the

FIG. 1. Difference between the past (1960–79) and the future(2080–99) of the annual- and zonal-mean (a) temperature (K) and(b) zonal wind (m s21), from the ensemble mean of the three CMAMsimulations. The thin dashed–dotted lines in (b) denote the sub-tropical westerly jet for the past using a contour interval of 10 m s21;for clarity, the zero line and easterlies are not plotted. The subtropicaljet maximum is located near 408N and 408S.

788 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 68

Expansion of subtropical jets raises critical level for wave breaking. !

(Stratosphere is shrinking, lifting the surf zone!)

Anthropogenic forcing modifies surf zone [Shepherd and McLandress 2011]

C(v, k)dv 5 C(c, k)dc, where c 5 va cosu/k, a is theearth’s radius, and u is latitude. Although Rossby wavesconserve angular phase velocity rather than regular phasevelocity during propagation through a zonally homoge-neous flow on the sphere, as in Randel and Held (1991)we plot regular phase velocity to allow a direct compar-ison with the zonal-mean zonal wind. A phase-velocitygrid of resolution Dc 5 1 m s21 was used. Cospectra foreach year were averaged over the appropriate time periodsand over the three simulations. The plotted cospectraldensities in (c, k) space have been divided by Dc andtherefore have units of the physical quantities. We havechecked that the integrated EPFD across all phase speedsclosely matches the transient EPFD computed directlyfrom the physical fields.

Note that the wavenumber–frequency analysis re-quires daily 3D data, which are not available on theCCMVal archive. Thus, it is not possible to extend thisanalysis to other models using the existing archive.

3. Analysis

We start by showing the predicted changes in tem-perature and zonal wind arising from climate change inthe CMAM. Although this is not a new scientific result,it sets the context for the subsequent analysis. Figure 1shows the differences between the past (1960–79) andfuture (2080–99) of the annual- and zonal-mean tem-perature and zonal wind from the ensemble mean ofthe three simulations, along with the westerly jets for thepast. The strengthening of the upper flank of the sub-tropical jets in both hemispheres is readily apparent.Note that this cannot possibly be the response to astrengthened BDC, because a strengthened BDC wouldcool the tropics and warm the extratropics and thus actto weaken rather than to strengthen the upper flank ofthe jets. At middle and high latitudes, the zonal-windchanges differ substantially between the two hemi-spheres and their interpretation is less straightforwardbecause the zonal winds respond in a first-order way tothe dynamical changes (MS09). Our focus here howeveris on the subtropical changes, because it is the wave dragat subtropical latitudes that is determinative of the nettropical upwelling and thus of the BDC as usually un-derstood (Butchart et al. 2006; MS09).

Because the wavenumber–frequency analysis can onlybe performed for waves with a nonzero phase velocity,stationary waves are necessarily excluded. It is thereforeimportant to determine how much of the resolved wavedrag is missed by this procedure. Although it is oftentacitly assumed that planetary waves, especially in theNH, are primarily stationary, the contribution of sta-tionary waves to the driving of the BDC has not been

quantitatively assessed. Figure 2 shows the mass stream-function for DJF at 70 hPa inferred from downwardcontrol for the past (left) and the difference between thefuture and past (right). This is a revised version of Fig. 18of MS09, but with the resolved wave drag now separatedinto its stationary (monthly mean) and transient (de-viations from monthly mean) components. Because thenet downward mass flux in each hemisphere is pro-portional to the mass streamfunction evaluated at the

FIG. 1. Difference between the past (1960–79) and the future(2080–99) of the annual- and zonal-mean (a) temperature (K) and(b) zonal wind (m s21), from the ensemble mean of the three CMAMsimulations. The thin dashed–dotted lines in (b) denote the sub-tropical westerly jet for the past using a contour interval of 10 m s21;for clarity, the zero line and easterlies are not plotted. The subtropicaljet maximum is located near 408N and 408S.

788 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 68

key to differences in downward control

diagnostics is in GW forcing here

Expansion of subtropical jets raises critical level for wave breaking. !

(Stratosphere is shrinking, lifting the surf zone!)

Conclusions• The Brewer-Dobson Circulation is wave driven, but defining the precise role of

Rossby vs. gravity waves is problematic.• resolved waves dominant in the stratosphere: mixing PV• impact of gravity waves, particularly non-orographic waves, may largely

be indirect, by shaping the Rossby wave forcing• intermodel differences in wave driving likely reflect tuning, not

fundamental limitations in our understanding

• Models accurately simulate the current BDC (albeit with tuning), and robustly predict an increase in the future

• differences in role of GW vs. resolved waves may be a red herring• mechanism of rising critical latitudes (i.e. a shrinking of the

stratosphere) is robust

• Idealized GCMs provide a bridge to connect theoretical insights with the observed and modeled Brewer-Dobson Circulation

Why might we care about the Brewer-Dobson Circulation and stratospheric ozone?

(bonus slides)

Latitude

80S 60S 40S 20S EQ 20N 40N 60N 80N

20

50

200

500

8501000 −20

−15−10−50510152025303540455055

ERA40 DJF zonal mean zonal wind [u]

20 km

pres

sure

(hPa

)

10 km

0 km

=120 mph

The jet streams in austral summer (Dec.-Feb.)

m/s

The jet streams in austral summer (Dec.-Feb.) Recent trends

2000–2079 in the CCMVal‐2 REF‐B2 and AR4 A1B sce-nario integrations. An exception is section 3.1, where trendsare calculated for the period 1979–1999 to be comparedwith reanalysis data, and for the period 2001–2050 to becompared with the previous CCMVal activity (CCMVal‐1).Past climate changes are analyzed for a relatively longperiod of 40 years, mainly because O3 depletion beganbefore 1979; observations have shown that O3 concentrationstarted to decrease in the late 1960s, although early trendsare quite weak [e.g., Solomon, 1999, Figure 1]. The longerperiod also allows us to obtain better statistics and compareour results with previous studies. The analysis length forfuture climate change is twice as long as that for past climatechange because O3 recovery is predicted to be slower thanits depletion in the past. The CCMVal‐2 models predict thattotal column O3 over the Antarctic will likely reach its 1980value around 2060 [Austin et al., 2010]. Although the

analysis period is somewhat subjective, results are onlyweakly sensitive to the choice of time period. It is found thattrends over 2000–2049 are quantitatively similar to thoseover 2000–2079, although the intermodel standard deviationis somewhat larger.[13] Stratospheric O3 has strong seasonality and its long‐

term trend is largest in the late spring. Its impact on the tro-pospheric circulation, however, is delayed by a few monthsand reaches a maximum in the summer, December–February(DJF) [Gillett and Thompson, 2003; Shindell and Schmidt,2004; Perlwitz et al., 2008; Son et al., 2008]. Hence, mostanalyses in this study are carried out for the SH summer.

3. Results

[14] We first evaluate the CCMVal‐2 models by com-paring the spatial and temporal structure of the zonal mean

Figure 1. The long‐term mean (thick orange) and linear trend (thin black contour) of DJF [u] over1979–1999: (a) CCMVal‐2 REF‐B1 multimodel mean, (b) ERA40, and (c) NCEP‐NCAR reanalysisdata. (d) Future trends over 2000–2079 as simulated by the CCMVal‐2 REF‐B2 models. Contour intervalsof climatological wind and trend are 10 m s−1 starting from 10 m s−1 and 0.4 m s−1/decade, respectively. InFigures 1a and 1d, multimodel mean values exceeding 1 standard deviation are shaded. In Figures 1b and1c, trends which are statistically significant at the 95% confidence level are shaded. Zero contours are omit-ted in all plots.

SON ET AL.: OZONE AND SOUTHERN HEMISPHERE CLIMATE D00M07D00M07

4 of 18

[Son et al. 2010]

20 km

pres

sure

(hPa

)

10 km

0 km

DJF Trends in zonal mean zonal wind

late 20th century

[Son et al. 2008; Gerber et al. 2011]

reanalysis


reanalysis

late 20th century

models w/GHGs models w/ GHGs+O3



late 20th century

predictions 2000-2079

?


reanalysis models w/GHGs models w/ GHGs+O3

hPa (a)

Temperature change, 1960−1999

Mod

els

with

fixe

d oz

one 200

400

600

800

1000

(b)

Temperature change, 2000−2079

hPa

latitude

(c)

Mod

els

with

var

ying

ozo

ne

60S 30S 0 30N 60N

200

400

600

800

1000

latitude

°C

(d)

60S 30S 0 30N 60N

−10 −8 −6 −4 −2 0 2 4 6 8

Temperature Signature of Anthropogenic Forcing

21st century Southern Hemisphere jet stream trends in summer (DJF)

jet s

hift (

o /dec

ade)

0 0.4 0.8 1.2 1.6

−0.6

−0.4

−0.2

0

0.2

all, R=−0.45**CCMVal2, R=−0.18CMIP3, R=−0.52CMIP5(4.5), R=−0.18CMIP5(8.5), R=−0.53**

a) ∆ Ulat vs. ∆ Ttrop

∆ Ttropical (K/decade)

∆ U

lat (°

/dec

ade)

0 0.4 0.8 1.2 1.6

all, R=0.62**CCMVal2, R=0.62CMIP3, R=0.81**CMIP5(4.5), R=0.70**CMIP5(8.5), R=0.40*

b) ∆ Ulat vs. ∆ Tpolar

∆ Tpolar (K/decade)

Fig. 10. The relationship between the 21st century shift in the austral jet stream ∆Ulat and(a) tropical upper tropospheric temperatures ∆Ttrop or (b) polar stratospheric temperatures∆Tpolar. Circles, squares, triangles, and diamonds mark CCMVal2 REF-B2, CMIP3 A1B,CMIP5 RCP4.5, and CMIP RCP8.5 model integrations, respectively. The correlation isstatistically significant at the 95 or 99% confidence level if marked by one or two asterisks,respectively.

52

tropical warming (K/decade)

polar stratospheric temp. trends (K/decade)

CO2 signal Stratospheric O3 signal

[Gerber and Son 2014]

jet s

hift (

o /dec

ade)

0 0.4 0.8 1.2 1.6

−0.6

−0.4

−0.2

0

0.2

all, R=−0.45**CCMVal2, R=−0.18CMIP3, R=−0.52CMIP5(4.5), R=−0.18CMIP5(8.5), R=−0.53**

a) ∆ Ulat vs. ∆ Ttrop

∆ Ttropical (K/decade)

∆ U

lat (°

/dec

ade)

0 0.4 0.8 1.2 1.6

all, R=0.62**CCMVal2, R=0.62CMIP3, R=0.81**CMIP5(4.5), R=0.70**CMIP5(8.5), R=0.40*

b) ∆ Ulat vs. ∆ Tpolar

∆ Tpolar (K/decade)

Fig. 10. The relationship between the 21st century shift in the austral jet stream ∆Ulat and(a) tropical upper tropospheric temperatures ∆Ttrop or (b) polar stratospheric temperatures∆Tpolar. Circles, squares, triangles, and diamonds mark CCMVal2 REF-B2, CMIP3 A1B,CMIP5 RCP4.5, and CMIP RCP8.5 model integrations, respectively. The correlation isstatistically significant at the 95 or 99% confidence level if marked by one or two asterisks,respectively.

52

polar stratospheric warming (K/decade)

CO2 signal Stratospheric O3 signal

tropical warming (K/decade)

[Gerber and Son 2014]

21st century Southern Hemisphere jet stream trends in summer (DJF)

what drives the brewer-dobson circulation? · is +~k~pw(i -sin 45’) writing r=6,ooo km and w=50...

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