5.3. Kelvin wave in General Circulation Models

Katherine Straub

Zonal wavenumber-frequency power spectrum of tropical OLR data, 1979-2001This 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

Zonal wavenumber-frequency power spectrum of tropical precipitation data, 1998-2007This 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.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 wavesWavenumber-frequency power spectrum of precipitation is calculated for each modelThis 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

Example: Model with strong KW variability

Example: Model with no KW variability

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

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., 2006Observations

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

Models with KW variabilityOf the 21 models analyzed, 8 have reasonable-looking KW spectra:CCSR, Japan (MIROC)GISS-AOM, USAGISS-EH, USAGISS-ER, USAIPSL, FranceMIUB, Germany (ECHO)MPI, Germany (ECHAM5)MRI, Japan

Models with KW variability

Models with KW variability

Models with little KW variabilityBCCR, NorwayCCCM63, CanadaCCCM47, CanadaCNRM, France

Models with little KW variabilityCSIRO3, AustraliaCSIRO3.5, AustraliaGFDL2, USAGFDL2.1, USA

Models with little KW variabilityIAP, ChinaINGV, ItalyINM, RussiaNCAR-CCSM3, USA

Models with little KW variabilityNCAR-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 datasetsFaster 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 - observationsCCSR, JapanMIUB, GermanyMPI, Germany

Models with less realistic KW distributionsOLR - observationsGISS-AOM, USAGISS-EH, USAGISS-ER, USA

Models with less realistic KW distributionsOLR - observationsIPSL, FranceMRI, Japan

KW structure analysis: MethodologyRegress 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: PACObservationsModels

Precipitation scale and propagation speed: PACObservationsModels

Precipitation scale and propagation speed: PACModelsObservations

What do observed KWs look like?OLR centered to north of equator, along ITCZDynamical signals centered on equatorWinds are primarily zonalConvergence to east of low OLRWesterlies in phase with low OLR

What do model KWs look like?CCSRMIUBMPIPrecipitation (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-AOMPrecipitation (shading); 1000-hPa u, v (vectors); SLP (contours)GISS-EHGISS-ER

Observed KWs: Upper troposphereDivergence collocated with/to the west of lowest OLRZonal winds near equatorRotational circulations off of equatorOLR (shading); ECMWF 200-hPa u, v (vectors), streamfunction (contours)HLHL

Model KWs: Upper troposphereCCSRMIUBMPIPrecipitation (shading); 200-hPa u, v (vectors); streamfunction (contours)HLLHLLHHLHL

Model KWs: Upper tropospherePrecipitation (shading); 200-hPa u, v (vectors); streamfunction (contours)MRIH

Model KWs: Upper tropospherePrecipitation (shading); 200-hPa u, v (vectors); streamfunction (contours)GISS-AOMGISS-EHGISS-ERLHLHLLHL

Observed KWs: Vertical structure, TWave MotionTemperature at Majuro (radiosonde, 7N, 171E)

Model KWs: Vertical structure, TCCSRMIUBMPI

Model KWs: Vertical structure, TGISS-AOMGISS-EHGISS-ERMRI

Observed KWs: Vertical structure, qWave MotionSpecific humidity at Majuro (radiosonde, 7N, 171E)

Model KWs: Vertical structure, qCCSRMIUBMPI

Model KWs: Vertical structure, qGISS-AOMGISS-EHGISS-ERMRI

ConclusionsOf 21 models analyzed, 3 reasonably simulate convectively coupled Kelvin wavesCommon features: Slow phase speedMaximum wave activity in Pacific ITCZ, equatorial Indian OceanRealistic amplitude of SLP anomalies relative to precipitationUpper-level rotational signals in both hemispheresSecond vertical mode temperature structureSignificant cooling and drying following precipitationThe existence of a reasonable-looking precipitation spectrum does not guarantee the existence of reasonable-looking Kelvin waves

Summary and Final commentsKWs 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 commentsThe 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 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 commentsKiladis 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 commentsFrom 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 MIUBPan 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.

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