large-scale tropical atmospheric dynamics: asymptotic nondivergence & self-organization
DESCRIPTION
Large-Scale Tropical Atmospheric Dynamics: Asymptotic Nondivergence & Self-Organization. (& Self-Organization). by Jun-Ichi Yano. With Sandrine Mulet, Marine Bonazzola, Kevin Delayen, S . Hagos, C. Zhang, Changhai Liu, M. Moncrieff. Large-Scale Tropical Atmospheric Dynamics:. - PowerPoint PPT PresentationTRANSCRIPT
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Large-Scale Tropical Atmospheric Dynamics:
Asymptotic Nondivergence & Self-Organization
by Jun-Ichi Yano
With Sandrine Mulet, Marine Bonazzola, Kevin Delayen, S. Hagos, C. Zhang, Changhai Liu, M. Moncrieff
(& Self-Organization)
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Large-Scale Tropical Atmospheric Dynamics:
Strongly Divergent ?
or Asymptotically Nondivergent
?
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Strongly Divergent?: Global Satellite Image (IR)
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Madden-Julian Oscillation (MJO) :Madden & Julian (1972) 30-60 days
Dominantly Divergent-FlowCirculations?
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MJO is Vorticity Dominant? (e.g., Yanai et al., 2000)
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(TOGA-COARE IFA Observation)Heat Budget
Con
vective H
eating(K
/day)
Vertical Advection+Radiation
Con
den
sation(K
/d
ay)Balanced?(Free-Ride,Fraedrich & McBride 1989):Vertical Advection=Diabatic Heating
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Scale Analysis (Charney 1963)
Thermodynamic equaton:
i.e., the vertical velocity vanishes to leading orderi.e., the horizontal divergence vanishes to leading order of asymptotic expansion
i.e., Asymptotic Nondivergence
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Observatinoal Evidences?
TOGA-COARE LSA data set
(Yano, Mulet, Bonazzola 2009, Tellus)
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Vorticity >> Divergence with MJO:
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Temporal Evolution of Longitude-Height Section:
Divergence vorticity
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Scatter Plotsbetween Vorticity and Divergencevorticity
vorticity
vorticity
divergence
divergence
divergence
850hPa
500hPa
250hPa
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Cumulative Probabilityfor |divergence/vorticity| :
i.e.,
at majority of points:
Divergence < Vorticity
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Quantification:Measure of a Variability (RMS of a Moving Average):
where
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Asymptotic Tendency for Non-Divergence:
Divergence/Vorticity(Total)
Time scale (days)
ho
rizon
tal scale (km
)
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Asymptotic Tendency for Non-Divergence:
Divergence/Vorticity(Transient)
Time scale (days)
ho
rizon
tal scale (km
)
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(TOGA-COARE IFA Observation)Heat Budget
Con
vective H
eating(K
/day)
Vertical Advection+Radiation
Con
den
sation(K
/d
ay)Balanced?(Free-Ride,Fraedrich & McBride 1989):1. Vertical Advection=Diabatic Heating
Effectively Neutral Stratification:hE=0 :
:No Waves (Gravity)!
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Waves ?
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Dry Equatorial Waves with hE=25 mOLR Spectrum:
(Wheeler & Kiladis 1999)Equatoriallyasymmetric
Equatoriallysymmetric
Zonal Wavenumber Zonal Wavenumber
Freq
uen
cy
Freq
uen
cy
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•Equivalent depth: hE
•Vertical Scale of the wave: D
•Gravity-Wave Speed: cg=(ghE)1/2~ND
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Scale Analysis (Summary):Yano and Bonazzola (2009, JAS)•L~3000km, U~3m/s (cf., Gill 1980): Wave Dynamics (Linear)
•L~1000km, U~10m/s (Charney 1963): Balanced Dynamics (Nonlinear)
R.1. Nondimensional: =2L2/aUR.2. VerticalAdvection:
(Simple)
(Asymptotic)
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Question:
Are the Equatorial Wave Theories consistent with the Asymptotic Nondivergence?
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A simple theoretical analysis:
RMS Ratio between the Vorticity and the Divergence for Linear Equaotorial Wave Modes:
<(divergence)2>1/2/<(vorticity)2>1/2
(Delayen and Yano, 2009, Tellus)
?
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cg=50m/s cg=12m/s
Linear Free Wave Solutions: RMS of divergence/vorticity
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Forced Problem
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Linear Forced Wave Solutions(cg=50m/s): RMS of divergence/vorticityn=0 n=1
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Asymptotically Nondivergent
but Asymptotic Nondivergence is much weaker than those expected from
linear wave theories (free and forced)
Nonlinearity defines the divergence/vorticity ratio(Strongly Nonlinear)
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Asymptotically Nondivergent Dynamics (Formulation):
•Leading-Order Dynamics: Conservation of Absolute Vorticity
•Higher-Order: Perturbation“Catalytic” Effect of Deep ConvectionSlow Modulation of the Amplitude of the Vorticity
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Balanced Dynamics (Asymptotic: Charney)
•vorticity equation (prognostic)
•thermodynamic balance: w~Q:(free ride)
Q w
•continuity: w weak divergence
•hydrostatic balance:
•dynamic balance: non-divergent •divergence equation (diagnostic)
barotropics -plane vorticity equation Rossby waves (without geostrophy): vH
(0)
•moisture equation (prognostic): q
Q=Q(q,… )
}weak forcing on vorticity (slow time-scale)
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Asymptotically Nondivergent Dynamics (Formulation):
•Leading-Order Dynamics: Conservation of Absolute Vorticity:
:Modon Solution?
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Is MJO a Modon?:
Streamfunction
Absolute Vorticity
?
A snap shot from TOGA-COARE (Indian Ocean):40-140E, 20S-20N
(Yano, S. Hagos, C. Zhang)
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Last Theorem
“Asymptotic nondivergence” is equivalent to “Longwave approximation” to the linear limit.
Last RemarkHowever, “Asymptotic nondivergence” provides a qualitatively different dynamical regime under Strong Nonlinearity.
Reference: Wedi and Smarkowiscz (2010, JAS)
(man. rejected by Tellus 2010, JAS 2011)
Last Question: What is wrong with this theorem?
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Convective Organizaton?:(Yano, Liu, Moncrieff 2012 JAS)(Yano, Liu, Moncrieff 2012 JAS)
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Convective Organizaton?:Point of view of Water BudgetPoint of view of Water Budget
PrecipitationRate, P
Column-Integrated Water, I
?
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Convective Organizaton?:(Yano, Liu, Moncrieff 2012 JAS)(Yano, Liu, Moncrieff 2012 JAS)
Self-Organized CriticalityHomeistasis(Self-Regulation)
?
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Convective Organizaton?:(Yano, Liu, Moncrieff 2012 JAS)(Yano, Liu, Moncrieff 2012 JAS)
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Convective organization?:(Yano, Liu, Moncrieff, 2012, JAS)
with spatial averaging for 4-128km:
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Convective organization?:(Yano, Liu, Moncrieff, 2012, JAS)
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Convective organization?:(Yano, Liu, Moncrieff, 2012, JAS):dI/dt = F - P
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Convective organization?:(Yano, Liu, Moncrieff, 2012, JAS)
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Self-Organized CriticalityandHomeostasis:Backgrounds
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Self-Organized Criticality:
•Bak et al (1987, 1996)•Criticality (Stanley 1972)
•Dissipative Structure (Gladsdorff and Prigogine 1971)
•Butterfly effect (Lorenz 1963)
•Synergetics (Haken 1983)
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Homeostasis:•etimology: homeo (like)+stasis(standstill)•Psyology: Cannon (1929, 1932)•Quasi-Equilibrium (Arakawa andSchubert 1974)•Gaia (Lovelock and Margulis 1974)•Self-Regulation (Raymond 2000)•cybernetics (Wiener 1948)•Buffering (Stevens and Feingold 2009)•Lesiliance (Morrison et al., 2011)