Chap 4.
Equatorial trapped waves
and tropical large-scale oscillations
Which relevance for forecasters ?

Provide some predictability to the tropical
atmosphere beyond the diurnal cycle.

Equatorial waves modulate deep convection
inside the ITCZ ans the SCPZ (South
Convergence Pacific Zone)
general contents
Chap 4.
Equatorial trapped waves
and tropical large-scale oscillations
4.1 The equatorial trapped waves
4.2 The tropical large-scale oscillations
4.2.1 The Madden-Julian Oscillation (MJO)
4.2.2 The Quasi-Biennial Oscillation (QBO)
4.3 A review of ‘synoptic to intraseasonnal’
tropical waves with relevance to
forecasting
general contents
4.1 The equatorial trapped waves

This course stress only on waves coupled with
deep convection (indeed, it exist some waves which
don’t modulate convection)

They initiate between 12°N/12°S and they vanish
beyond 20° (whence the name ‘trapped waves’).

A valid proxy for deep convection is the
Outgoing Longwave Radiation (OLR);
The OLR behave about as the Infrared Red
radiation and so, anomalies of OLR are negative
when deep convection occur.
general contents
4.1 The equatorial trapped waves :
OLR variance for all equatorial waves
Figure showing the OLR variance for all equatorial wave
(included MJO) beyond the diurnal cycle
Reminder : the variance show the modulation of deep
convection through waves
Source : Wheeler et Kiladis, 99
• Maximum of variance ‣ in the summer hemisphere
‣ especially over Indian Ocean
and West Pacific
general contents
4.1 The equatorial trapped waves :
The Kelvin wave

Modulate deep convection between 7°N/7°S

Explain 10% of the total of OLR variance along
the Equator, especially from february to august

Period : 15-20 days

Speed phase = + 15 to 20 m/s
Source : Wheeler et Kiladis, 99
general contents
4.1 The equatorial trapped waves :
Equatorial Rossby (ER)

Modulate deep convection between 7 and 15° of latitude

Explain 7% of the total of OLR variance at 10° of latitude
from the Indian Ocean to the West Pacific (ITCZ an SCPZ
affected), particularly from november to march

Period = 15-20 m/s

Speed phase = -5 m/S
general contents
Source : Wheeler et Kiladis, 99
4.1 The equatorial trapped waves :
Mixed Rossby-Gravity (MRG)

Modulate deep convection between 3 and 10° of latitude

Explain 4% of the total of OLR variance at 7.5° of latitude
near dateline (ITCZ and SCPZ affected), particularly from
september to november

Period =4-5 days

Speed phase = -23m/s
general contents
Source : Wheeler et Kiladis, 99
4.1 The equatorial trapped waves:
The gravity waves

Which moves eastwards (Eastwards Inertial
Gravity, EIG) ; EIG explain 4% of the total of
OLR variance at 7.5° near date line

Which moves westwards (westwards Inertial
Gravity, WIG) : WIG1 explain 6% of the total of
OLR variance at the Equator over eastern
hemisphere

Which moves westwards : WIG2 explain 2% of
the total of OLR variance at 5° of latitude over
eastern hemisphere
general contents
Chap 4.
Equatorial trapped waves
and tropical large-scale oscillations
4.1 The equatorial trapped waves
4.2 The tropical large-scale oscillations
4.2.1 The Madden-Julian Oscillation (MJO)
4.2.2 The Quasi-Biennial Oscillation (QBO)
4.3 A review of ‘synoptic to intraseasonnal’
tropical waves with relevance to
forecasting
general contents
Chap. 4
Equatorial trapped waves
and tropical large-scale oscillations
4.1 The equatorial trapped waves
4.2 The tropical large-scale oscillations
4.2.1 The Madden-Julian Oscillation (MJO)
4.2.2 The Quasi-Biennial Oscillation (QBO)
4.3 A review of ‘synoptic to intraseasonnal’
tropical waves with relevance to forecasting
sommaire
general contents
4.2.1 The Madden-Julian Oscillation (MJO)
Main features of the MJO :

It is firstly mentionned by Madden and Julian in 1971
as being a fluctuation of zonal wind at surface of 2-3
m/s and a fluctuation of mean sea-level pressure (0.7
hPa) over Canton Island (West Equatorial Pacific)

Finally, this fluctuaction is an intraseasonal oscillation
with a period of 40 to 50 days, called ‘Madden-Julian
Oscillation’, which modulate deep convection in tropics
from Indian Ocean to Western Pacific.
general contents
4.2.1 : The MJO cycle
Source : Madden
et Julian,1971.
Westerly speed Phase
time :days
5 m/s (Equatorial
Africa)
1
5
6
10
5 m/s (Indian Ocean)
5 m/s (Indonésia)
11
15
5m/s (Western Pacific)
16
20
5 m/s (dateline)
21
25
10 to 15 m/s
(eastern
Pacific)
26
30
10 to 15 m/s
(America)
31
35
10 to 15 m/s
(Atlantic)
36
40
Italic = inactive MJO
general contents
4.2.1 The OLR variance linked to MJO
 The
MJO explain 10 to 15% of the total of OLR variance
at 10° of latitude (latitude of the maximum)
 The
MJO behaves like an equatorially-trapped wave :
no signal beyond 20°; the MJO could be a mixture between
an Equatorial Rossby (ER=) wave and a Kelvin wave

Seasonal variability of the MJO : maximum in january
and february
Source : Wheeler et Kiladis, 99
general contents
4.2.1 The MJO : 3D conceptual model
Source : Rui et Wang, 1990
Top figure show
active MJO at 90°E :
Over India and
Central Indian
Ocean
The deep convection
phase is coupled
with westerly
anomalies (+ 3 m/s)
and fall of MSLP
at surface and
upper easterlies
(- 6 m/s)
Bottom figure
(10 days after the
top figure) :
enhanced convection
over 150°E
(West Pacific) and
suppressed
convection over
Indian monsoon
(90°E)
general contents
Chap 4.
Equatorial trapped waves
and tropical large-scale oscillations
4.1 The equatorial trapped waves
4.2 The tropical large-scale oscillations
4.2.1 The Madden-Julian Oscillation (MJO)
4.2.2 The Quasi-Biennial Oscillation (QBO)
4.3 A review of ‘synoptic to intraseasonnal’
tropical waves with relevance to forecasting
general contents
4.2.2 The Quasi-Biennial Oscillation (QBO)
: Main Features
Source : d’après Coy, 1979, 1980

Described as an approximately 26-month
alternation between easterlies ans westerlies in the
equatorial stratosphere (between 23 and 30 km).

The amplitude is as large as 20 m/s between 10 and
40 hPa and decrease towards adjacent layers and
higher latitudes.
general contents
4.2.2 The Quasi-Biennial Oscillation (QBO)
: Main Features

Impact of the QBO on tropical storm intensity and
frequency

Hypothesis of the QBO : Equatorial region is
favourable for vertical propagation of equatorial
gravity waves energy (group velocity) from midtroposphere towards low stratosphere; then
combined action of Kelvin/MRG waves propagate
energy towards mid-stratosphere where we observe
the QBO peak intensity.
general contents
Chap 4.
Equatorial trapped waves
and tropical large-scale oscillations
4.1 The equatorial trapped waves
4.2 The tropical large-scale oscillations
4.2.1 The Madden-Julian Oscillation (MJO)
4.2.2 The Quasi-Biennial Oscillation (QBO)
4.3 A review of ‘synoptic to intraseasonnal’
tropical waves with relevance to forecasting
general contents
4.3 A review of ‘synoptic to
intraseasonnal’ tropical waves with
relevance to forecasting
• In Australia, real time filtering of MJO OLR has
already been implemented in an semi-operationnal
setting, and has shown some success for both
monitoring and forecasting beyond the medium range
(i.e. beyond several days)
• And real time filtering of others waves is also used,
especially for monitoring, not very useful for
forecasting (ER, Kelvin, MRG)
• Finally, we have animation OLR for MJO, ER,
Kelvin, MRG on this web site :
general contents
And if you want to know more about waves you
can visit the UFR (Unity Teaching-Research Department)
website
:
http://intraufr.enm.meteo.fr/pages/ufr/ressources/ressour_rec
h/biblio/biblio_index.htm
general contents
OLR variance linked to EIG wave
Source : Wheeler et Kiladis, 99
general contents
OLR variance linked to WIG1 wave
Source : Wheeler et Kiladis, 99
general contents
OLR variance linked to WIG2 wave
Source : Wheeler et Kiladis, 99
general contents
References
- Coy, L., 1979 : ‘An unusually large westerly amplitude of the quasibiennial oscillation’. J. Atmos. Sci., Vol.36, p.174-176.
- Coy, L., 1980 : ‘Corrigendum’. J. Atmos. Sci., Vol.37, p.912-913
-Madden, R. A. et P. R. Julian, 1971 : Detection of a 40-50 day oscillation
in the zonal wind in the tropical Pacific. Journal of the Atmospheric
Sciences, Vol.28, p. 702-708
- Rui, H., Wang, B., 1990 : ‘Development characteristics and dynamic
strcuture of tropical intraseasonal convcetion anomalies’. J. Atmos. Sci.,
Vol.47, p.357-379
- Wheeler, M., Kiladis, G., N., 1999: ‘Convectively coupled equatorial
waves : analysis of clouds and temperature int the wavenumber-frequency
domain’. J. Atmos. Sci., Vol.56, p.374-399