Editing Richard Lindzen (section)

==Early work (1964–1972)==
Lindzen's early work was concerned with [[ozone]] [[photochemistry]], the [[aerodynamics]] of the middle [[atmosphere]], the theory of [[atmospheric tides]], and [[planetary waves]]. His work in these areas led him to a number of fundamental scientific discoveries, including the discovery of negative equivalent depths in classical tidal theory, explanations for both the quasi-biennial oscillation of the Earth's stratosphere and the four-day period of the superrotation of the Venus atmosphere above the cloud top.

===Ozone photochemistry===
His PhD thesis of 1964 concerned the interactions of ozone photochemistry, [[radiative transfer]] and the dynamics of the middle atmosphere. This formed the basis of his seminal ''Radiative and Photochemical Processes in Mesospheric Dynamics'' that was published in four parts in the ''[[Journal of the Atmospheric Sciences]]'' between 1965 and 1966.<ref>{{cite journal | url = http://eaps.mit.edu/faculty/lindzen/raphprmdy1.pdf | last1 = Lindzen | first1 = Richard S | first2 = RM | last2 = Goody | year = 1965 | title = Radiative and photochemical processes in mesospheric dynamics: Part I. Models for radiative and photochemical processes | journal = [[J. Atmos. Sci.]] | volume = 22 | pages = 341–48 | doi = 10.1175/1520-0469(1965)022<0341:RAPPIM>2.0.CO;2 | bibcode = 1965JAtS...22..341L | issue = 4 | access-date = March 25, 2010 | archive-date = March 3, 2016 | archive-url = https://web.archive.org/web/20160303192828/http://eaps.mit.edu/faculty/lindzen/raphprmdy1.pdf | url-status = dead }}</ref><ref>{{cite journal | url = http://eaps.mit.edu/faculty/lindzen/rpremeflra.pdf | last = Lindzen | first = Richard S | year = 1965 | title = The radiative-photochemical response of the mesosphere to fluctuations in radiation | journal = J. Atmos. Sci. | doi = 10.1175/1520-0469(1965)022<0469:trprot>2.0.co;2 | pages = 469–78 | volume = 22 | issue = 5 | bibcode = 1965JAtS...22..469L | access-date = March 25, 2010 | archive-date = March 4, 2016 | archive-url = https://web.archive.org/web/20160304185609/http://eaps.mit.edu/faculty/lindzen/rpremeflra.pdf | url-status = dead }}</ref><ref>{{cite journal |url=http://eaps.mit.edu/faculty/lindzen/rpprIIpdeq.pdf |last=Lindzen |first=RS |year=1966 |title=Radiative and photochemical processes in mesospheric dynamics: Part II. Vertical propagation of long period disturbances at the equator |journal=J. Atmos. Sci. |volume=23 |pages=334–43 |doi=10.1175/1520-0469(1966)023<0334:RAPPIM>2.0.CO;2 |bibcode=1966JAtS...23..334L |issue=3 |access-date=March 25, 2010 |archive-date=March 4, 2016 |archive-url=https://web.archive.org/web/20160304190102/http://eaps.mit.edu/faculty/lindzen/rpprIIpdeq.pdf |url-status=dead }}</ref><ref>{{cite journal |url=http://eaps.mit.edu/faculty/lindzen/rpprIIIasd.pdf |last=Lindzen |first=Richard S |year=1966 |title=Radiative and photochemical processes in mesospheric dynamics. Part III. Stability of a zonal vortex at midlatitudes to axially symmetric disturbances |journal=J. Atmos. Sci. |volume=23 |pages=344–49 |doi=10.1175/1520-0469(1966)023<0344:RAPPIM>2.0.CO;2 |bibcode=1966JAtS...23..344L |issue=3 |access-date=March 25, 2010 |archive-date=May 22, 2013 |archive-url=https://web.archive.org/web/20130522082355/http://eaps.mit.edu/faculty/lindzen/rpprIIIasd.pdf |url-status=dead }}</ref><ref>{{cite journal |url=http://eaps.mit.edu/faculty/lindzen/rpprivbrwv.pdf |last=Lindzen |first=Richard S |year=1966 |title=Radiative and photochemical processes in mesospheric dynamics. Part IV. Stability of a zonal vortex at midlatitudes to baroclinic waves |journal=J. Atmos. Sci. |volume=23 |pages=350–59 |doi=10.1175/1520-0469(1966)023<0350:RAPPIM>2.0.CO;2 |bibcode=1966JAtS...23..350L |issue=3 |access-date=March 25, 2010 |archive-date=May 22, 2013 |archive-url=https://web.archive.org/web/20130522082631/http://eaps.mit.edu/faculty/lindzen/rpprivbrwv.pdf |url-status=dead }}</ref> The first of these, ''Part I: Models for Radiative and Photochemical Processes'', was co-authored with his Harvard colleague and former PhD thesis advisor, [[Richard M. Goody]], who is well known for his 1964 textbook ''Atmospheric Radiation''.<ref>{{cite book | last =Goody | first = RM |year=1964 |title=Atmospheric Radiation |publisher=Clarendon Press |place=Oxford}}</ref> The Lindzen and Goody (1965) study has been widely cited as foundational in the exact modeling of middle atmosphere ozone photochemistry. This work was extended in 1973 to include the effects of nitrogen and hydrogen reactions with his former PhD student, Donna Blake, in ''Effect of photochemical models on calculated equilibria and cooling rates in the stratosphere''.<ref>{{cite journal |url=http://docs.lib.noaa.gov/rescue/mwr/101/mwr-101-11-0783.pdf | last1 =Blake | first1 = DW | first2 = Richard Siegmund | last2 = Lindzen |year=1973 |title=Effect of photochemical models on calculated equilibria and cooling rates in the stratosphere |journal=Mon. Wea. Rev. |volume=101 | issue =11 |pages = 738–802|doi=10.1175/1520-0493(1973)101<0783:eopmoc>2.3.co;2 |bibcode = 1973MWRv..101..783B | hdl =2060/19730017658 |hdl-access =free }}</ref>

Lindzen's work on ozone photochemistry has been important in studies that look at the effects that anthropogenic [[ozone depletion]] will have on climate.<ref>See for instance the widely cited study {{cite journal |url=http://www.gfdl.gov/~gth/netscape/1980/sbf8001.pdf |last1=Fels |first1=SB |first2=JD |last2=Mahlman |first3=MD |last3=Schwarzkopf |first4=RW |last4=Sinclair |year=1980 |title=Stratospheric Sensitivity to Perturbations in Ozone and Carbon Dioxide: Radiative and Dynamical Response |journal=J. Atmos. Sci. |volume=37 |issue=10 |pages=2265–97 |doi=10.1175/1520-0469(1980)037<2265:SSTPIO>2.0.CO;2 |bibcode=1980JAtS...37.2265F |url-status=dead |archive-url=https://web.archive.org/web/20080918000835/http://www.gfdl.gov/~gth/netscape/1980/sbf8001.pdf |archive-date=September 18, 2008 |df=mdy-all }} The Lindzen and Blake formalism is used in the parameterization of radiative-photochemical damping (see Appendix A).</ref>

===Atmospheric tides===
Since the time of [[Pierre-Simon Laplace]] (1799),<ref>{{cite book | last =Laplace | first = PS |year=1799 | language = fr | title=Méchanique Céleste | url =https://archive.org/details/traitdemcaniquec04lapl |trans-title=Celestial Mechanics | place=Paris}}</ref> scientists had been puzzled as to why pressure variations measured at the Earth's surface associated with the [[atmospheric tides|semi-diurnal solar tide]] dominate those of the [[Atmospheric tides|diurnal tide]] in amplitude, when intuitively one would expect the diurnal passage of the sun to dominate. [[Lord Kelvin]] (1882) had proposed the so-called "resonance" theory, wherein the semi-diurnal tide would be "selected" over the diurnal oscillation if the atmosphere was somehow able to oscillate freely at a period of very close to 12 hours, in the same way that overtones are selected on a vibrating string. By the second half of the twentieth century, however, observations had failed to confirm this hypothesis, and an alternative hypothesis was proposed that something must instead suppress the diurnal tide. In 1961, [[Manfred Siebert]] suggested that absorption of [[insolation|solar insolation]] by tropospheric water vapour might account for the reduction of the diurnal tide.<ref>{{cite book | last = Siebert | first = M |year= 1961 |chapter= Atmospheric tides |title= Advances in Geophysics | volume = 7 | publisher = Academic Press |place=New York |pages=105–82}}</ref> However, he failed to include a role for stratospheric ozone. This was rectified in 1963 by the Australian physicist [[Stuart Thomas Butler]] and his student K.A. Small who showed that stratospheric ozone absorbs an even greater part of the solar [[insolation]].<ref>{{cite journal | last1 =Butler | first1 = Stuart Thomas | last2 = Small | first2 = KA |year=1963 |title=The excitation of atmospheric oscillations |journal= Proceedings of the Royal Society |volume=A274 |pages= 91–121}}</ref>

Nevertheless, the predictions of classical tidal theory still did not agree with observations. It was Lindzen, in his 1966 paper, ''On the theory of the diurnal tide'',<ref>{{cite journal |url=http://eaps.mit.edu/faculty/lindzen/7_diur~1.pdf | last =Lindzen | first = Richard S | year = 1966 |title=On the theory of the diurnal tide |journal=Mon. Wea. Rev. |volume=94 |pages= 295–301 | doi = 10.1175/1520-0493(1966)094<0295:OTTOTD>2.3.CO;2 | bibcode = 1966MWRv...94..295L |issue=5}}</ref> who showed that the solution set of [[Hough functions]] given by [[Bernhard Haurwitz]]<ref>{{cite journal | language = de | last = Haurwitz | first = B |year=1962a |title= Die tägliche Periode der Lufttemperatur in Bodennähe und ihre geographische Verteilung |journal=Arch. Met. Geoph. Biokl. | volume = A12 | issue = 4 |pages=426–34 |doi=10.1007/BF02249276|bibcode=1962AMGBA..12..426H | s2cid = 118241095 }}</ref> to Laplace's tidal equation was incomplete: modes with negative equivalent depths had been omitted.{{Efn | Susumu Kato had independently made the same discovery at about the same time in Japan.<ref>{{cite journal | last =Kato | first = S |year=1966 |title=Diurnal atmospheric oscillation, 1. Eigenvalues and Hough functions |journal=J. Geophys. Res. | volume = 71 | issue = 13 | pages = 3201–9 |bibcode = 1966JGR....71.3201K |doi = 10.1029/JZ071i013p03201 |url= http://www.agu.org/journals/jz/v071/i013/JZ071i013p03201/JZ071i013p03201.pdf}}</ref>}} Lindzen went on to calculate the thermal response of the diurnal tide to ozone and water vapor absorption in detail and showed that when his theoretical developments were included, the surface pressure oscillation was predicted with approximately the magnitude and phase observed, as were most of the features of the diurnal wind oscillations in the mesosphere.<ref>{{cite journal |url=http://www3.interscience.wiley.com/journal/113520655/abstract?CRETRY=1&SRETRY=0 |archive-url=https://archive.today/20130105065205/http://www3.interscience.wiley.com/journal/113520655/abstract?CRETRY=1&SRETRY=0 |url-status=dead |archive-date=2013-01-05 | last = Lindzen | first = Richard S |year=1967 |title=Thermally driven diurnal tide in the atmosphere |journal=  Quarterly Journal of the Royal Meteorological Society|volume=93 |pages=18–42 |doi = 10.1002/qj.49709339503 |bibcode = 1967QJRMS..93...18L |issue=395}}</ref> In 1967, along with his NCAR colleague, Douglas D. McKenzie, Lindzen extended the theory to include a term for [[Newton's law of cooling|Newtonian cooling]] due to emission of infrared radiation by carbon dioxide in the stratosphere along with ozone photochemical processes,<ref>{{cite journal | last1 =Lindzen | first1 = Richard Siegmund | first2 = DJ | last2 = McKenzie |year=1967 |title=Tidal theory with Newtonian cooling |journal=Pure Appl. Geophys. |volume=64 | issue =1 |pages=90–96 | doi=10.1007/BF00875315 | bibcode=1967PApGe..66...90L| s2cid = 128537347 }}</ref> and then in 1968 he showed that the theory also predicted that the semi-diurnal oscillation would be insensitive to variations in the temperature profile, which is why it is observed so much more strongly and regularly at the surface.<ref>{{cite journal | last = Lindzen | first = Richard Siegmund |year=1968 |title=The application of classical atmospheric tidal theory |journal=Proceedings of the Royal Society |volume= A303 | issue = 1474 | pages = 299–316| bibcode = 1968RSPSA.303..299L | doi = 10.1098/rspa.1968.0052 | s2cid = 97096978 }}</ref>

While holding the position of research scientist at the [[National Center for Atmospheric Research|National Center for Atmospheric Research (NCAR)]] in [[Boulder, Colorado|Boulder]], [[Colorado|CO]] Lindzen was noticed and befriended by Professor [[Sydney Chapman (mathematician)|Sydney Chapman]], who had contributed to the theory of atmospheric tides in a number of papers from the 1920s through to the 1940s. This led to their joint publication in 1969 of a 186-page monograph (republished in 1970 as a book) ''Atmospheric Tides''.<ref>{{cite journal |url=http://www-eaps.mit.edu/faculty/lindzen/29_Atmos_Tides.pdf |last1=Lindzen |first1=Richard Siegmund |first2=Sydney |last2=Chapman |year=1969 |title=Atmospheric tides |journal=Space Science Reviews |volume=10 |issue=1 |pages=3–188 |bibcode=1969SSRv...10....3L |doi=10.1007/BF00171584 |s2cid=189783807 |access-date=March 25, 2010 |archive-date=January 14, 2019 |archive-url=https://web.archive.org/web/20190114190543/http://www-eaps.mit.edu/faculty/lindzen/29_Atmos_Tides.pdf |url-status=dead }}</ref><ref>{{cite book | url= https://books.google.com/books?id=fS_TJ63wdAYC | last1 =Chapman | first1 = Sydney | first2 = Richard Siegmund | last2 = Lindzen | year = 1970 |title=Atmospheric Tides: Thermal and Gravitational |publisher=D. Reidel Press |place=Dordrecht, [[Holland|NL]] |isbn=978-90-277-0113-8}} 200 pp.</ref>

===Quasi-biennial oscillation===
Although it wasn't realized at the time, the [[quasi-biennial oscillation|quasi-biennial oscillation (QBO)]] was observed during the [[1883 eruption of Krakatoa]], when the ash from the volcano was transported around the globe from east to west by stratospheric winds in about two weeks. These winds became known as the "Krakatoa easterlies". It was observed again in 1908, by the German meteorologist [[Arthur Berson]], who saw that winds blow from the west at {{convert|15|km|2|abbr=on}} altitude in tropical Africa from his balloon experiments. These became known as the "Berson westerlies". However, it was not until the early 1960s that the ~ 26-month cycle of the QBO was first described, independently by [[Richard J. Reed]] in 1960 and Veryhard and Ebdon in 1961.

Lindzen recalls his discovery of the mechanism underlying the QBO in the semi-autobiographical review article, ''On the development of the theory of the QBO''.{{Sfn | Lindzen | 1987 | pp = 329–37}}  His interest in the phenomenon began in 1961 when his PhD advisor, Richard M. Goody, speculated that the 26-month relaxation time for stratospheric ozone at {{convert |25|km|2| abbr = on}} in the tropics might somehow be related to the 26-month period of the QBO, and suggested investigation of this idea as a thesis topic. In fact, Lindzen's, ''Radiative and photochemical processes in mesospheric dynamics, Part II: Vertical propagation of long period disturbances at the equator'', documented the failure of this attempt to explain the QBO.{{Sfn | Lindzen | 1987 | p = 329}}

Lindzen's work on atmospheric tides led him to the study of planetary waves and the general circulation of atmospheres. By 1967, he had contributed a number of papers on the theory of waves in the middle atmosphere. In ''Planetary waves on beta planes'', he developed a [[beta plane|beta plane approximation]] for simplifying the equations of classical tidal theory, whilst at the same time developing planetary wave relations. He noticed from his equations that eastward-traveling waves (known as ''Rossby waves'' since their discovery in 1939 by [[Carl-Gustav Rossby]]) and westward-traveling waves (which Lindzen himself helped in establishing as "[[kelvin waves|atmospheric Kelvin waves]]") with periods less than five days were "vertically trapped." At the same time, an important paper by Booker and [[Francis Bretherton|Bretherton]] appeared, which Lindzen read with great interest. Booker and Bretherton showed that vertically propagating gravity waves were completely absorbed at a critical level.<ref>{{Cite journal | last1 = Booker | first1 = J. R. | last2 = Bretherton | first2 = F. P. | author2-link = Francis Bretherton | doi = 10.1017/S0022112067000515 | title = The critical layer for internal gravity waves in a shear flow | journal = Journal of Fluid Mechanics | volume = 27 | issue = 3 | pages = 513 | year = 2006 |bibcode = 1967JFM....27..513B | s2cid = 120754946 }}</ref>

In his 1968 paper with [[James R. Holton]], ''A theory of the quasi-biennial oscillation'',<ref>{{cite journal |url=http://eaps.mit.edu/faculty/lindzen/qubieoscil.pdf |last1=Lindzen |first1=Richard Siegmund |first2=JR |last2=Holton |year=1968 |title=A theory of quasi-biennial oscillation |journal=J. Atmos. Sci. |volume=26 |issue=6 |pages=1095–1107 |doi=10.1175/1520-0469(1968)025<1095:atotqb>2.0.co;2 |bibcode=1968JAtS...25.1095L |access-date=March 25, 2010 |archive-date=June 13, 2010 |archive-url=https://web.archive.org/web/20100613080011/http://eaps.mit.edu/faculty/lindzen/qubieoscil.pdf |url-status=dead }}</ref> Lindzen presented his theory of the QBO after testing it in a two-dimensional (2-D) numerical model that had been developed by Holton and [[John Michael Wallace|John M. Wallace]].<ref>{{cite journal|url=http://www.atmos.washington.edu/gcg/JR_site/papers/1968_1.pdf |last1=Wallace |first1=JM |first2=JR |last2=Holton |year=1967 |title=A diagnostic numerical model of the quasi-biennial oscillation |journal=J. Atmos. Sci. |volume=25 |pages=280–92 |doi=10.1175/1520-0469(1968)025<0280:ADNMOT>2.0.CO;2 |bibcode=1968JAtS...25..280W |issue=2 |url-status=dead |archive-url=https://web.archive.org/web/20140305035436/http://www.atmos.washington.edu/gcg/JR_site/papers/1968_1.pdf |archive-date=March 5, 2014 }}</ref> They showed that the QBO could be driven by vertically propagating gravity waves with phase speeds in both westward and eastward directions and that the oscillation arose through a mechanism involving a two-way feedback between the waves and the mean flow. It was a bold conjecture, given that there was very little observational evidence available to either confirm or confute the hypothesis. In particular, there was still no observational evidence of the westward-traveling "Kelvin" waves; Lindzen postulated their existence theoretically.{{Efn | Actually, the evidence was coming in at the time, see {{cite journal | last1 =Wallace | first1 = JM | first2 = VE | last2 = Kousky |year=1967 |title=Observational evidence of Kelvin waves in the tropical stratosphere |journal=J. Atmos. Sci. |volume=25 |pages=900–7 |doi=10.1175/1520-0469(1968)025<0900:OEOKWI>2.0.CO;2 |bibcode = 1968JAtS...25..900W |issue = 5|doi-access=free }} However, Lindzen says in his 1987 recollections that he did not see this study until after the {{Harvnb | Lindzen | Holton | 1968}} paper was already submitted.{{Sfn | Lindzen | 1987 | p = 330}}}}

In the years following the publication of Lindzen and Holton (1968), more observational evidence became available, and Lindzen's fundamental insight into the mechanism driving the QBO was confirmed. However, the theory of interaction via critical level absorption was found to be incomplete and was modified to include the importance of attenuation due to radiative cooling. The revised theory was published in the Holton and Lindzen (1972) paper, ''An updated theory for the quasibiennial cycle of the tropical stratosphere''.<ref>{{cite journal |url = http://journals.ametsoc.org/doi/pdf/10.1175/1520-0469%281968%29025%3C0900%3AOEOKWI%3E2.0.CO%3B2 | last1 = Holton | first1 = JR | first2 = RS | last2 = Lindzen | year = 1972 |title=An updated theory for the quasibiennial cycle of the tropical stratosphere |journal=J. Atmos. Sci. |volume=29 |pages=1076–80 | format = PDF | doi = 10.1175/1520-0469(1972)029<1076:AUTFTQ>2.0.CO;2 |bibcode = 1972JAtS...29.1076H |issue= 6|doi-access = free }}</ref>

===Superrotation of Venus===
Since the 1960s a puzzling phenomenon has been observed in the atmosphere of Venus. The atmosphere above the cloud base is seen to travel around the planet about 50 times faster than the rotation of the planet surface, or in only four to five Earth-days.<ref>{{cite web | url = http://www.atm.ox.ac.uk/project/virtis/venus-super.html | last1 = Taylor | first1 = FW | first2 = CCC | last2 = Tsang |title= Venus super-rotation |date=February 2005 | access-date=2009-03-29 |archive-url = https://web.archive.org/web/20070706210100/http://www.atm.ox.ac.uk/project/virtis/venus-super.html |archive-date = July 6, 2007}}</ref> In 1974 a theory was proposed by [[Stephen B. Fels]] and Lindzen to explain this so-called "[[atmospheric super-rotation|superrotation]]" which held that the rotation is driven by the thermal atmospheric tide.<ref>{{cite journal | url = http://eaps.mit.edu/faculty/lindzen/60_Interac.pdf | last1 = Fels | first1 = SB | first2 = Richard S | last2 = Lindzen | year = 1974 | title = Interaction of thermally excited gravity waves with mean flows | journal = Geophys. Fluid Dyn. | volume = 6 | pages = 149–91 | doi = 10.1080/03091927409365793 | bibcode = 1974GeoFD...6..149F | issue = 2 | access-date = March 25, 2010 | archive-date = May 22, 2013 | archive-url = https://web.archive.org/web/20130522095444/http://eaps.mit.edu/faculty/lindzen/60_Interac.pdf | url-status = dead }}</ref> An alternative theory was proposed by [[Peter J. Gierasch]] in the following year which held instead that the meridional (Hadley) circulation may transport the momentum by eddy-mixing.<ref>{{cite journal |url=http://ams.allenpress.com/archive/1520-0469/32/6/pdf/i1520-0469-32-6-1038.pdf |last=Gierasch |first=PJ |year=1975 |title=Meridional circulation and the maintenance of the Venus atmospheric rotation |journal=J. Atmos. Sci. |volume=32 |pages=1038–44 |doi=10.1175/1520-0469(1975)032<1038:MCATMO>2.0.CO;2 |bibcode=1975JAtS...32.1038G |issue=6 |url-status=dead |archive-url=http://archive.wikiwix.com/cache/20100325184936/http://ams.allenpress.com/archive/1520-0469/32/6/pdf/i1520-0469-32-6-1038.pdf |archive-date=March 25, 2010 |df=mdy-all }}</ref> As of 2005, the actual cause of this phenomenon continued to be debated in the literature, with [[General Circulation Model]] experiments suggesting that both the Fels/Lindzen and Gierasch mechanisms are involved.<ref>{{cite journal | url = http://www.bu.edu/csp/uv/cp-aeronomy/Zhu_2005.pdf | last = Zhu | first = X | title = Maintenance of Equatorial Superrotation in a Planetary Atmosphere: Analytic Evaluation of the Zonal Momentum Budgets for the Stratospheres of Venus, Titan and Earth | year = 2005 | journal = SR SR A-2005-01, JHU /APL, Laurel, MD | access-date = March 25, 2010 | archive-date = March 3, 2016 | archive-url = https://web.archive.org/web/20160303235221/http://www.bu.edu/csp/uv/cp-aeronomy/Zhu_2005.pdf | url-status = dead }}</ref>