5.3. Kelvin wave in General Circulation Models

Katherine Straub

Zonal wavenumber-frequency power spectrum of tropical OLR

data, 1979-2001

This plot shows the spectral power in observed tropical OLR that exists above a smoothed red noise background spectrum.

The solid lines are dispersion curves for wave modes with equivalent depths of 8, 25, and 90 m, or Kelvin wave phase speeds of 9, 16, and 30 m s-1.

Based on Wheeler and Kiladis (1999), Journal of the Atmospheric Sciences

Kelvin

n=1 WIG

n=1 ER

MJO

Zonal wavenumber-frequency power spectrum of tropical

precipitation data, 1998-2007

This plot shows the spectral power in observed tropical precipitation (TRMM 3G68) that exists above a smoothed red noise background spectrum.

Kelvin waves are still present at the same range of shallow equivalent depths.

Kelvin

n=1 WIG

n=1 ER

MJO

Very similar to Cho et al. (2004), Journal of Climate

Do global models have Kelvin waves?

• Data: Output from 21 global models run for the World Climate Research Programme (WCRP) Coupled Model Intercomparison Project (CMIP)– “Climate of the 20th Century” model runs

(1961-2000) are analyzed for Kelvin waves– Wavenumber-frequency power spectrum of

precipitation is calculated for each model• This study is similar to Lin et al. (2006), but with the

goal of studying Kelvin waves rather than intraseasonal variability

21 models analyzed for Kelvin waves

Name Abbreviation

Model(s)

Bjerknes Center for Climate Research, Norway BCCR BCM2.0

Canadian Centre for Climate Modelling and Analysis, Canada

CCCM CGCM3.1, T63CGCM3.1, T47

CCSR/NIES/FRCGC, Japan CCSR MIROC3.2, medium resolution

CSIRO Atmospheric Research, Australia CSIRO Mk3.0Mk3.5

INGV, National Institute of Geophysics and Volcanology, Italy

INGV ECHAM4.6

Institute for Numerical Mathematics, Russia INM INMCM3.0

IPSL/LMD/LSCE, France IPSL CM4V1

LASG, Institute of Atmospheric Physics, China IAP FGOALS1.0_g

Max Planck Institute for Meteorology, Germany MPI ECHAM5/MPI

Meteo-France, Centre National de Recherches Meteorologiques, France

CNRM CM3

Meteorological Institute of the University of Bonn, Germany

MIUB ECHO-G

Meteorological Research Institute, Japan MRI CGCM2.3.2a

NASA Goddard Institute for Space Studies, USA GISS AOM C4x3E20/HYCOME20/Russell

National Center for Atmospheric Research, USA NCAR CCSM3.0PCM1

NOAA Geophysical Fluid Dynamics Laboratory, USA GFDL CM2.0CM2.1

Example: Model with strong KW variability

precipitation averaged 5S-5N

Straight lines represent equivalent depths of 8, 25, and 90 m, or KW

phase speeds of 9, 16, and 30 m s-1

Example: Model with no KW variability

Straight lines represent equivalent depths of 8, 25, and 90 m, or KW

phase speeds of 9, 16, and 30 m s-1 precipitation averaged 5S-5N

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)

Models with KW variability

• Of the 21 models analyzed, 8 have reasonable-looking KW spectra:– CCSR, Japan (MIROC)– GISS-AOM, USA– GISS-EH, USA– GISS-ER, USA– IPSL, France– MIUB, Germany (ECHO)– MPI, Germany (ECHAM5)– MRI, Japan

Models with KW variability

CCSR, Japan

GISS-AOM, USA

GISS-EH, USA

GISS-ER, USA

Models with KW variability

IPSL, France

MIUB, Germany

MPI, Germany

MRI, Japan

Models with little KW variability

BCCR, Norway

CCCM63, Canada

CCCM47, Canada

CNRM, France

Models with little KW variability

CSIRO3, Australia

CSIRO3.5, Australia

GFDL2, USA

GFDL2.1, USA

Models with little KW variability

IAP, China INGV, Italy

INM, Russia

NCAR-CCSM3, USA

Models with little KW variability

NCAR-PCM, USA

What do model KWs look like?

• How do model KWs compare to observations?

• Does the existence of a “good” KW spectral signature ensure the existence of realistic-looking waves?

Filters used to isolate KWs in precipitation datasets

Faster filter used for 3 GISS, IPSL, MRI (equivalent depths

12-150 m)

Slower filter used for CCSR, MIUB, MPI (equivalent depths

4-60 m)

Models with realistic KW distributions (MJJAS)

OLR - observations

CCSR, Japan

MIUB, Germany

MPI, Germany

Models with less realistic KW distributions

OLR - observations

GISS-AOM, USA

GISS-EH, USA

GISS-ER, USA

Models with less realistic KW distributions

OLR - observations

IPSL, France

MRI, Japan

KW structure analysis: Methodology

• Regress 40 years of daily 3-D model grids (1961-2000) onto KW filtered precipitation data at point of maximum variance during NH summer (MJJAS)

Precipitation scale and propagation speed: PAC

Observations Models

CCSR

12 m s-1

MPI

11 m s-1

MIUB

11 m s-1

14 m s-1

OLR

MRI

21 m s-1

Precipitation scale and propagation speed: PAC

Observations

Models

GISS-AOM

20 m s-1

GISS-ER

14 m s-1

GISS-EH

22 m s-1

14 m s-1

OLR

Precipitation scale and propagation speed: PAC

Models

IPSL

18 m s-1

Observations

14 m s-1

OLR

What do observed KWs look like?

• OLR centered to north of equator, along ITCZ• Dynamical signals centered on equator• Winds are primarily zonal• Convergence to east of low OLR• Westerlies in phase with low OLR

OLR (red: increased cloudiness); ECMWF 1000-hPa u, v (vectors), z (contours)

What do model KWs look like?

CCSR

MIUB

MPI

Precipitation (shading); 1000-hPa u, v (vectors); SLP (contours)

What do model KWs look like?

Precipitation (shading); 1000-hPa u, v (vectors); SLP (contours)

MRI

What do model KWs look like?

GISS-AOM

Precipitation (shading); 1000-hPa u, v (vectors); SLP (contours)

GISS-EH

GISS-ER

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)

H L

H L

Model KWs: Upper troposphere

CCSR

MIUB

MPI

Precipitation (shading); 200-hPa u, v (vectors); streamfunction (contours)

H L

L

H L

LH

H L

H L

Model KWs: Upper troposphere

Precipitation (shading); 200-hPa u, v (vectors); streamfunction (contours)

MRI

L

L

H

Model KWs: Upper troposphere

Precipitation (shading); 200-hPa u, v (vectors); streamfunction (contours)

GISS-AOM

GISS-EH

GISS-ER

LH

L H

L

LHL

Observed KWs: Vertical structure, T

Wave Motion

Temperature at Majuro (radiosonde, 7N, 171E)

Model KWs: Vertical structure, T

CCSR

MIUB

MPI

Model KWs: Vertical structure, T

GISS-AOM

GISS-EH

GISS-ER MRI

Observed KWs: Vertical structure, q

Wave Motion

Specific humidity at Majuro (radiosonde, 7N, 171E)

Model KWs: Vertical structure, q

CCSR

MIUB

MPI

Model KWs: Vertical structure, q

GISS-AOM

GISS-EH

GISS-ER MRI

Conclusions

• Of 21 models analyzed, 3 reasonably simulate convectively coupled Kelvin waves– Common features:

• Slow phase speed• Maximum wave activity in Pacific ITCZ, equatorial Indian

Ocean• Realistic amplitude of SLP anomalies relative to

precipitation• Upper-level rotational signals in both hemispheres• Second vertical mode temperature structure• Significant cooling and drying following precipitation

• The existence of a reasonable-looking precipitation spectrum does not guarantee the existence of reasonable-looking Kelvin waves

Summary and Final comments

• KWs described by shallow water theory (Matsuno, 1966).

• KWs couple the dynamical circulations to regions of enhanced tropical cloudiness and rainfall.

• Convectively coupled KWs are ubiquitous in observational data of the tropical atmosphere:

• The western Pacific (Straub and Kiladis 2002)• The Atlantic ITCZ (Wang and Fu 2007)• Africa (Mounier et al. 2007; Mekonnen et al. 2008; Nguyen and

Duvel 2008)• The Indian Ocean (Roundy 2008)• South America (Liebmann et al. 2009)

Summary and Final comments• The coupled signal of a KW moves eastward at 10-20 m/s along the

ITCZ, with a zonal wavelength of 3000-6000 km.

• Wind are primarily zonal near the equator.

• Geopotential height and zonal wind are in phase at the surface.

• Surface convergence and increased low-level moisture lead the enhanced cloudiness and precipitation in the wave by 1/8 to ¼ wavelength.

• Upper-tropospheric divergence is in phase with high cloudiness and precipitation.

• The large-scale eastward-moving envelope of cloudiness typically consists to smaller-scale, westward-moving cloud clusters.

• The predominant mode of cloudiness in the wave tends to progress from shallow to deep convective to stratiform clouds.

Summary and Final comments

• Kiladis et al. (2009) suggest the possibility of a unified theory for convectively coupled equatorial waves (CCEWs) for their dynamics and coupling mechanism.

• GCMs typically found deficient in simulating CCEWs (Lin et al. 2006).

• Given KW has the strongest spectral peak, and the importance of CCEWs in explaining the observed variability of tropical rainfall, it is of interest to fully understand and explore their representation in GCMs.

Summary and Final comments

• From 21 GCMs, less than half contain and spectral peak in precipitation in the KW band.

• From these with spectral peak, only 3 reasonably simulate the geographical distribution and 3D structure of the waves.

• The most commonality among these 3 models is the convective parameterization:

• Tiedtke (1989) modified by Nordeng (1994) in MPI and MIUB• Pan and Randall (1998) in CCSR

• Suggest that a model parameterization plays a crucial role in its ability to organize tropical convection into wave-like disturbances.