1. 5.3 Observations of Convectively Coupled Kelvin Waves
5.1 Introduction
5.2 Theory
5.3 Observations of Convectively Coupled Kelvin Waves
5.3.1 Power Spectra
5.3.2 Kelvin Waves over Africa
5.3.3 Kelvin Waves and Atlantic Tropical Cyclones
5.3.4 Kelvin Waves and Other regions!

2. 1998 CLAUS Brightness Temperature 5ºS-5º N
5.1 Introduction
1998 CLAUS Brightness Temperature 5ºS-5º N

3. Atmospheric Kelvin waves are a key component of of the MJO.
5.1 Introduction
Kelvin waves were first identified by William Thomson (Lord Kelvin) in the nineteenth century.
Kelvin waves are large-scale waves whose structure "traps" them so that they propagate along a physical boundary such as a mountain range in the atmosphere or a coastline in the ocean.
In the tropics, each hemisphere can act as the barrier for a Kelvin wave in the opposite atmosphere, resulting in "equatorially-trapped" Kelvin waves.
Oceanic Kelvin waves are thought to be important for initiation of El Niño Southern Oscillation (ENSO).
Atmospheric Kelvin waves are a key component of of the MJO.

4. 5.1 Introduction
Convectively-coupled atmospheric Kelvin waves have a typical period of 6-7 days when measured at a fixed point and phase speeds of m s-1.
Dry Kelvin waves in the lower stratosphere have phase speed of m s-1.
Kelvin waves over the Indian Ocean generally propagate more slowly (12–15 m s-1) than other regions.
They are also slower, more frequent, and have higher amplitude when they occur in the active convective stage of the MJO.

5. See Notes 5.2 Theory Wind, Pressure (contours),
Divergence, blue negative

6. Frequency ω Zonal Wavenumber k
Theoretical Dispersion Relationships for Shallow Water Modes on Eq.  Plane
Frequency ω
Matsuno, 1966
Zonal Wavenumber k 6

7. Frequency ω Zonal Wavenumber k
Theoretical Dispersion Relationships for Shallow Water Modes on Eq.  Plane
Frequency ω
Westward
Eastward
Matsuno, 1966
Zonal Wavenumber k 7

8. Frequency ω Zonal Wavenumber k
Theoretical Dispersion Relationships for Shallow Water Modes on Eq.  Plane
Eastward Inertio-Gravity
Westward Inertio-Gravity
n = 4
Kelvin
n = 3
n = 2
Frequency ω
n = 1
n = 0
n = -1
Mixed Rossby-gravity (Yanai)
Equatorial Rossby
Matsuno, 1966
n = 1
n = 3
Zonal Wavenumber k 8

9. Kelvin Wave Theoretical Structure
Wind, Pressure (contours),
Divergence, blue negative 9

10. Model experiment: Gill model
Multilevel primitive atmospheric model forced by latent heating in organized convection over 2 days.
imposed heating
Vectors: 200 hPa horizontal wind anomalies
Contours: surface temperature perturbations

11. 5.3 Observations
5.3.1 Power Spectra
Important References
See: Wheeler and Kiladis (1999) Convectively Coupled Equatorial Waves: Analysis of Clouds and Temperature in the wavenumber-frequency domain, JAS, 56,
As of today cited 570 times!
See also: Kiladis et al (2009): Convectively Coupled Equatorial Waves, Rev. Geophys., 47, doi: /2008RG

12. Wave-number frequency spectrum of convectively coupled equatorial waves
CLAUS Tb
Averaged 15ºS-15ºN, 1983–2005
Symmetric component
Courtesy of G. Kiladis 12

13. Wave-number frequency spectrum of convectively coupled equatorial waves
1.25 Days
Westward Power
Eastward Power
96 Days 13

14. Wave-number frequency spectrum of convectively coupled equatorial waves
Kelvin 14

15. Outgoing Longwave Radiation (OLR) Average: 15ºS-15ºN, 1979–2001
Wave-number frequency spectrum of convectively coupled equatorial waves
Outgoing Longwave Radiation (OLR)
Average: 15ºS-15ºN, 1979–2001
Symmetric component
Background removed
Wheeler and Kiladis, 1999 15

16. Raw power spectra of OLR in 15S-15N band for years 1979-2000.
Separately for anti-symmetric and symmetric parts about the equator.
Normalized power spectra
These figures show power spectra of such observations of OLR covering all latitudes from 15S to 15N. Hence, these figures describe all the variability that occurred over this 22 year period between these latitudes.
On the figures, the planetary zonal wavenumber is on this axis, and the frequency in cycles per day is on this axis. The perios of 3 days, 6 days, and 30 days are here. Wavenumber 0 is the zonal mean, and variability that propagates to the west is on the left of each panel, while variability propagating to the east is on the right.
One thing that I did prior to this analysis was to separate the data into symmetric and antisymmetric components about the equator. The reason for this is because the theory of waves trapped in the equatorial wave guide suggest that waves should either be symmetric or antisymmetric. The antisymmetric component is here on the left and the symmetric is in these panels.
The top two panels are the raw power spectra, while the bottom two panels are the raw power normalized by an estimated red background spectrum. So the normalized spectrum shows where there are relative peaks in the raw spectrum, such as through here and here.
The MJO appears as an absolute peak here for wavenumber of about 1 to 3 and periods between 30 and 80 days. It is mostly in the symmetric component.
Elsewhere in the spectrum, however, we can see spectral peaks running along these dispersion curves that are derived from fairly simple theory. These are known as Kelvin waves, the se as equatorial rossby waves, and these as mixed-Rossby gravity waves. As well as some inertio-gravity waves at high frequencies.
Together, these waves that fall on the theoretical dispersion curves are called the convectively-coupled equatorial waves. The MJO, in contrast, does not lie on one of these theoretical curves.
Convectively-coupled equatorial waves (CCEWs)
Courtesy of NCAR, adapted from Wheeler and Kiladis (1999)
MJO

17. 5.3.2 Kelvin Waves over Africa
Some motivation for studying Kelvin Waves over Africa
2-6d filtered TB (shaded) and 700hPa  (contoured); averaged in 10-15N
From Mekonnen et al, 2006 (J. Climate).

18. Average Kelvin filtered TB variance (JAS 1984-2004)
5.3.2 Kelvin Waves over Africa
Average Kelvin filtered TB variance (JAS )
Peaks over tropical Africa, equatorial Indian Ocean, tropical Pacific
Max. over Africa near 10N, 20E

19.  5.3.2 Kelvin Waves over Africa Base point : 10N, 20E
Composites based on regression technique ….
Total fields (TB, wind, height, velocity potential, etc. ) are lag regressed onto Kelvin filtered time series at a base point.
The results are anomalies with respect to -1 standard deviation of the base point Kelvin filtered time series.

20. KTB anomalies (shaded), Velocity potential @ 200-hPa (contoured)
Winds can be separated into their contribution to the divergent and rotational flow.
The velocity potential highlights the regions where the winds are divergent and convergent.
Negative values are associated with large-scale regions or divergence.
Lag (days)

21. KTB anomalies (shaded), Velocity potential @ 200-hPa (contoured)
Lag (days)

22. Evolution from lag day -4 to day 4:
Convection, 850mb , Geopotential height anomalies
( significant > 95%)
Day -2
Day 0

23. Day 2
Day 4
Evidence, based on composite analysis, of eastward moving convective envelope associated with dynamical signals that can be tracked back to the Pacific and western Atlantic.

24. Source regions?
Kelvin convection that originate in a 10o-wide in the region between 180W-90E ( in Lat 7-12N). The Kelvin waves are  -5K and waves must propagate at least for 4-days and for 5000km from the origin

25. Summary of composite analysis:
Evidence of convectively coupled Kelvin wave that originated over central and eastern Pacific and western Atlantic that have significant impact over tropical Africa
Convectively coupled Kelvin wave characterized by an average Cph ~15m/s and  ~ km

26. Weather event: July-September 1987 (high Kelvin variance year)

27. convection (TB < 260K) and
Kelvin filtered TB < -5K (only
negatives shown).
Lat. Average: 7-12N.
Decayed
Aug. 18
Started
July 29

28. Convection (shaded TB < 260K), Kelvin TB (<-4K contoured)

29. Convection (shaded TB < 260K), Kelvin TB (<-4K contoured)

30. Convection (shaded TB < 260K), Kelvin TB (<-4K contoured)

31. Convection (shaded TB < 260K), Kelvin TB (<-4K contoured)

32. Convection (shaded TB < 260K), Kelvin TB (<-4K contoured)

33. Convection (shaded TB < 260K), Kelvin TB (<-4K contoured)

34. Convection (shaded TB < 260K), Kelvin TB (<-4K contoured)

35. Convection (shaded TB < 260K), Kelvin TB (<-4K contoured)

36. Convection (shaded TB < 260K), Kelvin TB (<-4K contoured)

37. Aug. 1987
Aug.
Aug.
Aug.

38. Kelvin waves and AEWs

39. Kelvin wave (shaded), enhanced AEWs (contoured, only one phase shown).
A series of AEWs that were initiated or enhanced in association with Kelvin wave (AEWs are labeled).
AEW-4 became TS Bret, the first tropical storm of the season.

40. Weather event (July-September 1987):
A Kelvin wave that started over east Pacific reached Africa 6-7days later had a strong impact on convection
Convective activity over tropical Africa deepens and rainfall sharply increases with the approach of the Kelvin wave
Convection weakens after the Kelvin wave passed by the region
A series of AEWs were initiated over Africa in association with enhanced Kelvin wave

41. The Berry and Thorncroft (2005) AEW formed during the passage of the convectively active phase of a CCKW
A time-longitude plot of TRMM 3B42 unfiltered rain rate anomalies (shaded) during 2000 July 20-August 10. Kelvin filtered TRMM anomalies are overlaid. The +/- 2 mm/day Kelvin filtered TRMM anomaly is only contoured. Negative Kelvin filtered TRMM anomalies are dashed.

42. Time-longitude composite of 2-10d filtered EKE averaged over each day of the CCKW index from °N. Kelvin filtered OLR anomalies are contoured (dashed if negative).

43. Kelvin waves over Central Africa

44. Kelvin-wave-filtered OLR variance90 50
Wheeler and Kiladis 1999
The Kelvin wave domain is represented by the green polygon 25 12 8
(5oS-5oN) meridional mean Kelvin wave filtered OLR variance
Peaks from the Amazon-Atlantic (AA) in March to the Pacific ocean (PO) in June.
Strongest signal over Equatorial Africa (EA) in April
Equatorial position of the ITCZ in spring. PO IO EA AA

45. Kelvin-domain-filtered symetric OLR variance in Spring (MAM)

46. Kelvin-domain-filtered symetric OLR variance in Spring (MAM)

47. Evolution of Kelvin wave Negative phase
OLR (W/m2)
Shading: min convection
max convection
Wind at 850 hPa (m/s)
Vectors, significant at the T-test 99% level
Surface Pressure (Pa)
Contours dashed: low L
continue: high H

48. Evolution of Kelvin wave Initiation phase
OLR (W/m2)
Shading: min convection
max convection
Wind at 850 hPa (m/s)
Vectors, significant at the T-test 99% level
Surface Pressure (Pa)
Contours dashed: low L
continue: high H

49. Evolution of Kelvin wave Active phase
OLR (W/m2)
Shading: min convection
max convection
Wind at 850 hPa (m/s)
Vectors, significant at the T-test 99% level
Surface Pressure (Pa)
Contours dashed: low L
continue: high H

50. Evolution of Kelvin wave Dissipation phase
OLR (W/m2)
Shading: min convection
max convection
Wind at 850 hPa (m/s)
Vectors, significant at the T-test 99% level
Surface Pressure (Pa)
Contours dashed: low L
continue: high H

51. Comparison with theoretical structure
cat3
Solution of the shallow water model
Convection is close to the theoretical convergence region but shifted slightly to the west in the region of low-level westerlies 51

52. Annual Cycle of Synoptic Weather Systems in the West African region 10W-10E
TD-filtered OLR (AEW-activity)
Peaks in summer
We know little about the nature and causes of AEW-variability
Kelvin-filtered OLR
Peaks in Spring
Key synoptic system for pre-coastal phase and possibly the coastal phase

53. High impact Kelvin waves in Ghana
Courtesy Michael Tanu

54. 5.3.3 Kelvin Waves and Tropical Cyclones

55. A convectively-coupled Kelvin wave associated with T. S
A convectively-coupled Kelvin wave associated with T.S. Debby and enhanced rainfall over tropical Africa
Total OLR – Grey Shading
Kelvin filtered active OLR – Orange Contours
650 hPa PV – Colored contours
AEJ – Red dashed lines
AEW troughs – blue solid contours
Debby – Red arrow

56. Total OLR – Grey Shading
Kelvin filtered active OLR – Orange Contours
650 hPa PV – Colored contours
AEJ – Red dashed lines
AEW troughs – blue solid contours
Debby – Red arrow

57. Total OLR – Grey Shading
Kelvin filtered active OLR – Orange Contours
650 hPa PV – Colored contours
AEJ – Red dashed lines
AEW troughs – blue solid contours
Debby – Red arrow

58. Total OLR – Grey Shading
Kelvin filtered active OLR – Orange Contours
650 hPa PV – Colored contours
AEJ – Red dashed lines
AEW troughs – blue solid contours
Debby – Red arrow

59. Total OLR – Grey Shading
Kelvin filtered active OLR – Orange Contours
650 hPa PV – Colored contours
AEJ – Red dashed lines
AEW troughs – blue solid contours
Debby – Red arrow

60. Total OLR – Grey Shading
Kelvin filtered active OLR – Orange Contours
650 hPa PV – Colored contours
AEJ – Red dashed lines
AEW troughs – blue solid contours
Debby – Red arrow

61. Total OLR – Grey Shading
Kelvin filtered active OLR – Orange Contours
650 hPa PV – Colored contours
AEJ – Red dashed lines
AEW troughs – blue solid contours
Debby – Red arrow

62. Total OLR – Grey Shading
Kelvin filtered active OLR – Orange Contours
650 hPa PV – Colored contours
AEJ – Red dashed lines
AEW troughs – blue solid contours
Debby – Red arrow

63. Total OLR – Grey Shading
Kelvin filtered active OLR – Orange Contours
650 hPa PV – Colored contours
AEJ – Red dashed lines
AEW troughs – blue solid contours
Debby – Red arrow

73. JJAS 1979-2009 Composite Unfiltered OLR anomalies (shaded)
Positive OLR anomalies statistically
different than zero at the 95% level
are within the solid contour.
Negative OLR anomalies statistically
are within dashed contour.
Tropical cyclogenesis within the MDR
(5-25°N, 15-65°W) for any given lag
is denoted by a red circle.
The genesis of Tropical Storm Debby
is highlighted by the large yellow
crossed circle.

74. -t t Tropical cyclogenesis events over the MDR
(5-25°N, 15-65°W) relative to the CCKW during
June-September
Day 0 highlights the transition to statistically significant negative unfiltered OLR anomalies, or the eastern-most side of the convectively active phase of
the CCKW.
Error bars indicate the 95% confidence interval.

75. Tropical cyclogenesis
relative to the Kelvin wave -

76. 5.3.4 Kelvin Waves in other Regions!

77. Kelvin wave over the Indian Ocean

78. Kelvin-domain-filtered symmetric OLR variance
Wheeler et al. 2000
All seasons
Peak variance at 0o, 90oE.
Broad region of variance extending across the IO and into the western PO.
KWs events can occur any time of the year.

79. Kelvin-domain-filtered symmetric OLR variance
Wheeler et al. 2000
All seasons

80. KWs over the Indian Ocean
Wheeler et al. 2000

82. Kelvin wave over the Pacific Ocean

83. Kelvin-domain-filtered total OLR variance
May to September

84. Kelvin-domain-filtered total OLR variance
May to September

85. From Kiladis et al (2009)
Minimum in OLR shifted towards low-level westerlies – a few 100km west of peak in low-level zonal convergence
While zonal winds are approximately symmetric about the Equator the convective response is strongly anti-symmetric (due to cold SSTs close to and south of the Equator).
Note 10,000km wavelength
Winds and height fields are opposite to those at low-levels consistent with theory – note significant meridional outflow

86. From Kiladis et al (2009)
Zonal wind and temperature resemble theoretical structure below 150mb.
Above 150mb the tilts are consistent with upward propagating Kelvin waves forced by a moving tropospheric heat source (see Kiladis et al 2009 for more details).

87. From Kiladis et al (2009)
2-days prior to minimum Tb humidity increases at low-levels and then increases rapidly over depth of troposphere. There is corresponding warming, first at low-levels and then aloft.
~12 hrs before, lower troposphere cools and dries, while upper troposphere is warm and moist.
Cooling in mb layer likely due to adiabatic ascent – cooling at low-levels likely due to downdrafts and cold pools.
Evolution may also highlight evolution of cloudiness:
~Day -2 shallow convection
~Day 0 deep convection
~Day +1 stratiform cloudiness and rainfall

88. Observed Kelvin wave morphology
Straub and Kiladis 2003
Wave Motion 88

89. Generalized evolution of a convectively coupled equatorial wave
Kiladis et al., 2009 89

90. Origin of KWs over South America
Courtesy of George Kiladis
Liebmann et al., 2009

91. OLR and 200 hPa Flow Regressed against Kelvin-filtered OLR (scaled -20 W m2) at eq, 60W for January-June
Day 0
Streamfunction (contours 5 X 105 m2 s-1)
Wind (vectors, largest around 5 m s-1)
OLR (shading starts at +/- 6 W s-2), negative blue 91

92. OLR and 200 hPa Flow Regressed against Kelvin-filtered OLR (scaled -20 W m2) at eq, 60W for January-June
Day-4
Streamfunction (contours 5 X 105 m2 s-1)
Wind (vectors, largest around 5 m s-1)
OLR (shading starts at +/- 6 W s-2), negative blue 92

93. OLR and 200 hPa Flow Regressed against Kelvin-filtered OLR (scaled -20 W m2) at eq, 60W for January-June
Day-3
Streamfunction (contours 5 X 105 m2 s-1)
Wind (vectors, largest around 5 m s-1)
OLR (shading starts at +/- 6 W s-2), negative blue 93

94. OLR and 200 hPa Flow Regressed against Kelvin-filtered OLR (scaled -20 W m2) at eq, 60W for January-June
Day-2
Streamfunction (contours 5 X 105 m2 s-1)
Wind (vectors, largest around 5 m s-1)
OLR (shading starts at +/- 6 W s-2), negative blue 94

95. OLR and 200 hPa Flow Regressed against Kelvin-filtered OLR (scaled -20 W m2) at eq, 60W for January-June
Day-1
Streamfunction (contours 5 X 105 m2 s-1)
Wind (vectors, largest around 5 m s-1)
OLR (shading starts at +/- 6 W s-2), negative blue 95

96. OLR and 200 hPa Flow Regressed against Kelvin-filtered OLR (scaled -20 W m2) at eq, 60W for January-June
Day 0
Streamfunction (contours 5 X 105 m2 s-1)
Wind (vectors, largest around 5 m s-1)
OLR (shading starts at +/- 6 W s-2), negative blue 96

97. OLR and 200 hPa Flow Regressed against Kelvin-filtered OLR (scaled -20 W m2) at eq, 60W for January-June
Day+1
Streamfunction (contours 5 X 105 m2 s-1)
Wind (vectors, largest around 5 m s-1)
OLR (shading starts at +/- 6 W s-2), negative blue 97

98. OLR and 200 hPa Flow Regressed against Kelvin-filtered OLR (scaled -20 W m2) at eq, 60W for January-June
Day+2
Streamfunction (contours 5 X 105 m2 s-1)
Wind (vectors, largest around 5 m s-1)
OLR (shading starts at +/- 6 W s-2), negative blue 98

99. OLR and 200 hPa Flow Regressed against Kelvin-filtered OLR (scaled -20 W m2) at eq, 60W for January-June
Day+3
Streamfunction (contours 5 X 105 m2 s-1)
Wind (vectors, largest around 5 m s-1)
OLR (shading starts at +/- 6 W s-2), negative blue 99

100. Period: Nov 1979-May 2006 53 Pacific cases 48 South America cases
Dates are found with a 1.5 standard deviations
negative OLR anomalies at 60W, Eq.
The dates are then separated by additional criteria before compositing:
“Pacific” cases: 3 days before key date Kelvin-filtered
OLR more than 16 Wm-2 below mean at 95W, 2.5N
“South America” cases: 3 days before key date, 30-day high-
pass filtered OLR more than 50 Wm-2 below mean at 60W, 20S.
Period: Nov 1979-May 2006
53 Pacific cases
48 South America cases
4 common cases
100

101. Conclusions for South America
There are at least two mechanisms that force
Kelvin waves over South America
a) upper levels disturbance propagating along the equator from the Pacific
b) lower levels cold surge from southern South America:
(e.g., Garreaud and Wallace 1998; Garreaud 2000)
Not all South American (cold) events force
Kelvin waves
Some Kelvin waves may be initiated in-situ
101

102. Eastward moving convective envelopes are ubiquitous in the tropics.
Final Comments
Eastward moving convective envelopes are ubiquitous in the tropics. L H
102

103. Eastward moving convective envelopes are ubiquitous in the tropics.
Final Comments
Eastward moving convective envelopes are ubiquitous in the tropics.
They are important – effecting rainfall locally, monsoon onset timing, TCs etc. L H
103

104. Eastward moving convective envelopes are ubiquitous in the tropics.
Final Comments
Eastward moving convective envelopes are ubiquitous in the tropics.
They are important – effecting rainfall locally, monsoon onset timing, TCs etc.
Unlike much of the field of tropical weather we have a theory for their existence! L H
104

105. Eastward moving convective envelopes are ubiquitous in the tropics.
Final Comments
Eastward moving convective envelopes are ubiquitous in the tropics.
They are important – effecting rainfall locally, monsoon onset timing, TCs etc.
Unlike much of the field of tropical weather we have a theory for their existence!
Theoretical Kelvin wave structures resemble the observed structures – e.g. winds, height. L H
105

106. Eastward moving convective envelopes are ubiquitous in the tropics.
Final Comments
Eastward moving convective envelopes are ubiquitous in the tropics.
They are important – effecting rainfall locally, monsoon onset timing, TCs etc.
Unlike much of the field of tropical weather we have a theory for their existence!
Theoretical Kelvin wave structures resemble the observed structures – e.g. winds, height.
Observed Kelvin waves in the troposphere tend to be convectively
coupled and have a coherent association with convection – that includes
an evolution of clouds that is seen in other Convectively coupled
equatorial waves (see Kiladis et al, 2009 for discussion). Research topic! L H
106

107. Eastward moving convective envelopes are ubiquitous in the tropics.
Final Comments
Eastward moving convective envelopes are ubiquitous in the tropics.
They are important – effecting rainfall locally, monsoon onset timing, TCs etc.
Unlike much of the field of tropical weather we have a theory for their existence!
Theoretical Kelvin wave structures resemble the observed structures – e.g. winds, height.
Observed Kelvin waves in the troposphere tend to be convectively
coupled and have a coherent association with convection – that includes
an evolution of clouds that is seen in other Convectively coupled
equatorial waves (see Kiladis et al, 2009 for discussion). Research topic!
There is strong motivation to monitor and predict CCKWs. L H
107

108. Eastward moving convective envelopes are ubiquitous in the tropics.
Final Comments
Eastward moving convective envelopes are ubiquitous in the tropics.
They are important – effecting rainfall locally, monsoon onset timing, TCs etc.
Unlike much of the field of tropical weather we have a theory for their existence!
Theoretical Kelvin wave structures resemble the observed structures – e.g. winds, height.
Observed Kelvin waves in the troposphere tend to be convectively
coupled and have a coherent association with convection – that includes
an evolution of clouds that is seen in other Convectively coupled
equatorial waves (see Kiladis et al, 2009 for discussion). Research topic!
There is strong motivation to monitor and predict CCKWs.
Models have a hard time doing this (not shown). L H
108

109. Eastward moving convective envelopes are ubiquitous in the tropics.
Final Comments
Eastward moving convective envelopes are ubiquitous in the tropics.
They are important – effecting rainfall locally, monsoon onset timing, TCs etc.
Unlike much of the field of tropical weather we have a theory for their existence!
Theoretical Kelvin wave structures resemble the observed structures – e.g. winds, height.
Observed Kelvin waves in the troposphere tend to be convectively
coupled and have a coherent association with convection – that includes
an evolution of clouds that is seen in other Convectively coupled
equatorial waves (see Kiladis et al, 2009 for discussion). Research topic!
There is strong motivation to monitor and predict CCKWs.
Models have a hard time doing this (not shown).
Remains a challenge to get the operational forecasting world on board. L H
109