Detection of Equatorial Waves in Data

OLR power spectrum, 1979–2001 (Symmetric) from Wheeler and Kiladis, 1999

Space-Time Spectrum of JJA Symmetric OLR, 15  S-15  N Wheeler and Kiladis, 1999 Kelvin MJO “TD” band Eq. Rossby

Space-Time Spectrum of JJA Antisymmetric OLR, 15  S-15  N Wheeler and Kiladis, 1999 Inertio- Gravity MJO “TD” band

Space-Time Spectrum of JJA Antisymmetric OLR, 15  S-15  N Wheeler and Kiladis, 1999

2002 CLAUS Brightness Temperature 5ºS-5º N

2005 CLAUS Brightness Temperature 5ºS-5º N

1987 CLAUS Brightness Temperature 5ºS-5º N

2001 CLAUS Brightness Temperature 5ºS-5º N

Vertical Structure of Equatorial Waves

CWC W Direction of Motion Temperature Structure of a Dry Kelvin Wave

CWC W Direction of Motion Temperature Structure of a Dry Kelvin Wave

Temperature at Majuro (7  N, 171  E) Regressed against Kelvin-filtered OLR (scaled -40 W m 2 ) for OLR (top, Wm -2 ) Temperature (contours,.1 °C), red positive from Straub and Kiladis 2002

Temperature at Majuro (7  N, 171  E) Regressed against Kelvin-filtered OLR (scaled -40 W m 2 ) for OLR (top, Wm -2 ) Temperature (contours,.1 °C), red positive from Straub and Kiladis 2002 Wave Motion

is the equivalent depth whereis the vertical wavenumber is the vertical wavelength is the scale height Linear Theory Predicts:

Using Representative Numbers for the Tropical Stratosphere: for h=200 m, c=45 m/s, Lz=12.0 km “Peak Projection Response”

for h=30 m, c=15 m/s, Lz=4.0 km Using Representative Numbers for the Tropical Stratosphere: for h=200 m, c=45 m/s, Lz=12.0 km “Peak Projection Response” Convectively coupled Kelvin

for h=30 m, c=15 m/s, Lz=4.0 km for c=5 m/s, Lz=1.2 km Using Representative Numbers for the Tropical Stratosphere: for h=200 m, c=45 m/s, Lz=12.0 km “Peak Projection Response” Convectively coupled Kelvin MJO

Zonal Wind at Majuro (7  N, 171  E) Regressed against Kelvin-filtered OLR (scaled -40 W m 2 ) for OLR (top, Wm -2 ) Zonal Wind (contours,.25 m s -1 ), red positive from Straub and Kiladis 2002

Temperature at Majuro (7  N, 171  E) Regressed against Kelvin-filtered OLR (scaled -40 W m 2 ) for OLR (top, Wm -2 ) Temperature (contours,.1 °C), red positive from Straub and Kiladis 2002 Wave Motion

Specific Humidity at Majuro (7  N, 171  E) Regressed against Kelvin-filtered OLR (scaled -40 W m 2 ) for from Straub and Kiladis 2002 OLR (top, Wm -2 ) Specific Humidity (contours, 1 X g kg -1 ), red positive Wave Motion

Haertel and Kiladis 2004 TOGA COARE Temperature (2  S, 155  E) Regressed against Westward Inertio Gravity-filtered OLR (scaled -40 W m 2 ) Temperature (contours,.1 °C), red positive Wave Motion

Haertel and Kiladis 2004 TOGA COARE Specific Humidity (2  S, 155  E) Regressed against Westward Inertio Gravity-filtered OLR (scaled -40 W m 2 ) Specific Humidity (contours, 1 X g kg -1 ), red + Wave Motion

OLR and 850 hPa Flow Regressed against MJO-filtered OLR (scaled -40 W m 2 ) at eq, 155  E, Day 0 Streamfunction (contours 4 X 10 5 m 2 s -1 ) Wind (vectors, largest around 2 m s -1 ) OLR (shading starts at +/- 6 W s -2 ), negative blue from Kiladis et al. 2005

OLR and 850 hPa Flow Regressed against MJO-filtered OLR (scaled -40 W m 2 ) at eq, 155  E, Day-16 Streamfunction (contours 4 X 10 5 m 2 s -1 ) Wind (vectors, largest around 2 m s -1 ) OLR (shading starts at +/- 6 W s -2 ), negative blue

OLR and 850 hPa Flow Regressed against MJO-filtered OLR (scaled -40 W m 2 ) at eq, 155  E, Day-12 Streamfunction (contours 4 X 10 5 m 2 s -1 ) Wind (vectors, largest around 2 m s -1 ) OLR (shading starts at +/- 6 W s -2 ), negative blue

OLR and 850 hPa Flow Regressed against MJO-filtered OLR (scaled -40 W m 2 ) at eq, 155  E, Day-8 Streamfunction (contours 4 X 10 5 m 2 s -1 ) Wind (vectors, largest around 2 m s -1 ) OLR (shading starts at +/- 6 W s -2 ), negative blue

OLR and 850 hPa Flow Regressed against MJO-filtered OLR (scaled -40 W m 2 ) at eq, 155  E, Day-4 Streamfunction (contours 4 X 10 5 m 2 s -1 ) Wind (vectors, largest around 2 m s -1 ) OLR (shading starts at +/- 6 W s -2 ), negative blue

OLR and 850 hPa Flow Regressed against MJO-filtered OLR (scaled -40 W m 2 ) at eq, 155  E, Day 0 Streamfunction (contours 4 X 10 5 m 2 s -1 ) Wind (vectors, largest around 2 m s -1 ) OLR (shading starts at +/- 6 W s -2 ), negative blue

OLR and 850 hPa Flow Regressed against MJO-filtered OLR (scaled -40 W m 2 ) at eq, 155  E, Day+4 Streamfunction (contours 4 X 10 5 m 2 s -1 ) Wind (vectors, largest around 2 m s -1 ) OLR (shading starts at +/- 6 W s -2 ), negative blue

OLR and 850 hPa Flow Regressed against MJO-filtered OLR (scaled -40 W m 2 ) at eq, 155  E, Day+8 Streamfunction (contours 4 X 10 5 m 2 s -1 ) Wind (vectors, largest around 2 m s -1 ) OLR (shading starts at +/- 6 W s -2 ), negative blue

OLR and 850 hPa Flow Regressed against MJO-filtered OLR (scaled -40 W m 2 ) at eq, 155  E, Day+12 Streamfunction (contours 4 X 10 5 m 2 s -1 ) Wind (vectors, largest around 2 m s -1 ) OLR (shading starts at +/- 6 W s -2 ), negative blue

Zonal Wind at Honiara (10  S, 160  E) Regressed against MJO-filtered OLR (scaled -40 W m 2 ) for OLR (top, Wm -2 ) U Wind (contours,.5 m s -1 ), red positive OLR Pressure (hPa) from Kiladis et al Wave Motion

Temperature at Honiara (10  S,  E) Regressed against MJO-filtered OLR (scaled -40 W m 2 ) for OLR (top, Wm -2 ) Temperature (contours,.1 °C), red positive OLR Pressure (hPa) from Kiladis et al Wave Motion

Specific Humidity at Truk (7.5  N,  E) Regressed against MJO- filtered OLR (scaled -40 W m 2 ) for OLR (top, Wm -2 ) Specific Humidity (contours, 1 X g kg -1 ), red positive OLR Pressure (hPa) from Kiladis et al Wave Motion

from Mapes et al Lag-height regressions of OSA specific humidity vs. moisture budget-derived rainrate. The data are progressively regridded to coarser time intervals ((a) 6 h, (b) 1 day, and (c) 4 days), and a light high-pass filter is used for each panel (cutoff period six times the lag window width). (d) The original unfiltered 6 h data are used, with a very wide lag window. Contour unit is 0.1 g/kg per mm/h.

Conclusion 2: A portion of tropical convective activity is organized by equatorially trapped waves of Matsuno’s shallow water theory Conclusion 1: Large scale atmospheric waves modulate waves and convection (along with the diurnal cycle) on smaller scales

Conclusion 2: A portion of tropical convective activity is organized by equatorially trapped waves of Matsuno’s shallow water theory Conclusion 3: Equatorial waves have a warm lower troposphere ahead of the wave, with cooling behind. The mid-troposphere is warm within the convective region Conclusion 1: Large scale atmospheric waves modulate waves and convection (along with the diurnal cycle) on smaller scales

Conclusion 2: A portion of tropical convective activity is organized by equatorially trapped waves of Matsuno’s shallow water theory Conclusion 3: Equatorial waves have a warm lower troposphere ahead of the wave, with cooling behind. The mid-troposphere is warm within the convective region Conclusion 1: Large scale atmospheric waves modulate waves and convection (along with the diurnal cycle) on smaller scales Conclusion 4: Low level moisture is high ahead of the waves (high CAPE) and is lofted rapidly into the mid-troposphere as deep convection develops, with drying occurring at low levels first while it is still moist aloft behind the waves

Haertel and Kiladis 2004 TOGA COARE Diabatic Heating Q1 (2  S, 155  E) Regressed against Westward Inertio Gravity-filtered OLR (scaled -40 W m 2 ) Diabatic Heating (contours, °K/day), red + Wave Motion

Radar Derived Divergence and Omega Regressed against Rain Rate from Mapes et al Regression composite of the MCS life cycle in divergence and vertical motion. Plotted are averages of regression sections from seven tropical radar deployments (see Mapes and Lin, 2005 for details). (a) VAD divergence regressed against rainrate for a circular area of 96 km diameter, contour unit 10−6 s−1 per mm/h. (b) The corresponding mass flux (pressure units, but with positive sign indicating upward motion), contour unit 10 h Pa/day per mm/h.

Q1 Regressed against MJO-filtered OLR over the IFA during COARE from Kiladis et al. 2005

Morphology of a Tropical Mesoscale Convective Complex in the eastern Atlantic during GATE (from Zipser et al. 1981) Storm Motion

Observed Kelvin wave morphology (from Straub and Kiladis 2003) Wave Motion

Two day (WIG) wave cloud morphology (from Takayabu et al. 1996) Wave Motion

from Benedict and Randall, 2007 MJO Propagation

from Kiladis et al., 2009 Generalized Evolution of a Convectively Coupled Equatorial Wave

Conclusion 2: A portion of tropical convective activity is organized by equatorially trapped waves of Matsuno’s shallow water theory Conclusion 3: Equatorial waves have a warm lower troposphere ahead of the wave, with cooling behind. The mid-troposphere is warm within the convective region Conclusion 1: Large scale atmospheric waves modulate waves and convection (along with the diurnal cycle) on smaller scales Conclusion 4: Low level moisture is high ahead of the waves (high CAPE) and is lofted rapidly into the mid-troposphere as deep convection develops, with drying occurring at low levels first while it is still moist aloft behind the waves

Conclusion 2: A portion of tropical convective activity is organized by equatorially trapped waves of Matsuno’s shallow water theory Conclusion 3: Equatorial waves have a warm lower troposphere ahead of the wave, with cooling behind. The mid-troposphere is warm within the convective region Conclusion 1: Large scale atmospheric waves modulate waves and convection (along with the diurnal cycle) on smaller scales Conclusion 4: Low level moisture is high ahead of the waves (high CAPE) and is lofted rapidly into the mid-troposphere as deep convection develops, with drying occurring at low levels first while it is still moist aloft behind the waves Conclusion 5: Equatorial wave cloud morphology is consistent with a progression from shallow to deep convection, followed by stratiform rain during the passage of the wave

Summary and Question All waves examined have broadly self-similar vertical structures in terms of their dynamical fields (temperature, wind, pressure, diabatic heating, cloud morphology) This is consistent with a progression of shallow to deep convection, followed by stratiform precipitation from the mesoscale on up to the MJO Suggests a fundamental interaction between wave dynamics and convection across a wide range of scales All waves examined have broadly self-similar vertical structures in terms of their dynamical fields (temperature, wind, pressure, diabatic heating, cloud morphology) This is consistent with a progression of shallow to deep convection, followed by stratiform precipitation from the mesoscale on up to the MJO Suggests a fundamental interaction between wave dynamics and convection across a wide range of scales

All waves examined have broadly self-similar vertical structures in terms of their dynamical fields (temperature, wind, pressure, diabatic heating, cloud morphology) This is consistent with a progression of shallow to congestus and then deep convection, followed by stratiform precipitation from the mesoscale on up to the MJO Suggests a fundamental interaction between wave dynamics and convection across a wide range of scales Is a systematic cascade of energy from the mesoscale on up to the planetary scale crucial for the maintenance of equatorial waves? All waves examined have broadly self-similar vertical structures in terms of their dynamical fields (temperature, wind, pressure, diabatic heating, cloud morphology) This is consistent with a progression of shallow to congestus and then deep convection, followed by stratiform precipitation from the mesoscale on up to the MJO Suggests a fundamental interaction between wave dynamics and convection across a wide range of scales Is a systematic cascade of energy from the mesoscale on up to the planetary scale crucial for the maintenance of equatorial waves? Summary and Question

Convection in General Circulation Models Question: How well do GCMs do in characterizing intraseasonal tropical convective variability? Jialin Lin et al. (2006) applied identical space-time spectral techniques to observed and modeled tropical precipitation Models used are the 14 coupled ocean-atmosphere GCMs used for intercomparison in the 4th Assessment Report of the Intergovernmental Panel on Climate Change (IPCC)

Rainfall Power Spectra, IPCC AR4 Intercomparison 15S-15N, (Symmetric) from Lin et al., 2006 Observations

Rainfall Power Spectra, IPCC AR4 Intercomparison 15S-15N, (Symmetric) from Lin et al., 2006

Rainfall Spectra/Backgr, IPCC AR4 Intercomparison 15S-15N, (Symmetric) from Lin et al., 2006 Observations

from Lin et al., 2006 Rainfall Spectra/Backgr, IPCC AR4 Intercomparison 15S-15N, (Symmetric)

Rainfall Spectra/Backgr., IPCC AR4 Intercomparison 15S-15N, (Antisymm.) from Lin et al., 2006 Observations

Rainfall Spectra/Backgr., IPCC AR4 Intercomparison 15S-15N, (Antisymm.) from Lin et al., 2006

Rainfall Spectra at 5S-5N, 85E from IPCC AR4 Intercomparison

Models with good KW variability CCSR, Japan GISS-AOM, USA GISS-EH, USA GISS-ER, USA

Observed KWs: Upper troposphere Divergence collocated with/to the west of lowest OLR Zonal winds near equator Rotational circulations off of equator OLR (shading); ECMWF 200-hPa u, v (vectors), streamfunction (contours)

Model KWs: Upper troposphere MIUB MPI MRI Precipitation (shading); 200-hPa u, v (vectors); streamfunction (contours)

Temperature at Majuro (7  N, 171  E) Regressed against Kelvin-filtered OLR (scaled -40 W m 2 ) for OLR (top, Wm -2 ) Temperature (contours,.1 °C), red positive from Straub and Kiladis 2002 Wave Motion

Model KWs: Vertical structure, T MIUB MPI MRI

Specific Humidity at Majuro (7  N, 171  E) Regressed against Kelvin-filtered OLR (scaled -40 W m 2 ) for from Straub and Kiladis 2002 OLR (top, Wm -2 ) Specific Humidity (contours, 1 X g kg -1 ), red positive Wave Motion

Model KWs: Vertical structure, q MIUB MPI MRI

Outstanding Issues General Circulation Models do a relatively poor job in correctly simulating variability in tropical convection (but not necessarily its mean state) Is this due to the misrepresentation of convection itself, or its coupling to the large scale (or both)? Is convection even parameterizable in models? Improvements in the representation of tropical convection will lead to improvements in medium-range weather forecasts in mid-latitudes (and perhaps to ENSO) What is the impact of poor tropical variability in GCMs on climate change scenarios?