Potential Vorticity Aspects of the MJO

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POTENTIAL VORTICITY AND ENERGY ASPECTS OF THE MJO
THROUGH EQUATORIAL WAVE THEORY
Masters Thesis Defense Matthew T. Masarik
Colorado State University
Atmospheric Science Department
Advisor Prof. Wayne
Schubert - CSU Atmospheric Science Department
Co-advisor Prof. Tom Vonder
Haar - CSU Atmospheric Science Department
Committee Member Prof. David Randall -
CSU Atmospheric Science Department
Committee Member Prof. Richard Eykholt -
CSU Physics Department
Wednesday, November 15th 2006
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ACKNOWLEDGEMENTS

• Friends

• Family

• Schubert Research Group,

• Brian McNoldy, Jonathan Vigh, Paul Ciesielski,
  and Rick Taft

• Funding Sponsor

DoD Center for Geosciences/Atmospheric Research
at Colorado State University under Cooperative
Agreements DAAD19-02-2-0005, and
W911NF-06-2-0015, with the
Army Research Laboratory.
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OVERVIEW

• Motivation

• Madden-Julian Oscillation (MJO) phenomena

• Conclusions

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MOTIVATION

• MJO not satisfactorily explained
• Complex phenomena
• multi-scale structure,
• intra-seasonal time scale
• ? Look at one piece of the puzzle.
• Inspired by mid-latitude balanced theory (QG,
  SG)
• PV in the tropics?
• New approach

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MJO PHENOMENA

• A composite, mean MJO lifecycle seen in OLR
  (W/m²) anomalies.

enhanced convection
supressed convection
Animation credit Dr. Adrian Matthews
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MJO PHENOMENA

• A composite, mean MJO lifecycle seen in OLR
  (W/m²) anomalies.

enhanced convection
supressed convection
Animation credit Dr. Adrian Matthews
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MULTI-SCALE STRUCTURE
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HORIZONTAL STRUCTURE

• Anomalous MJO-filtered OLR and circulation from
  ERA-15 reanalysis, 1979-93. (Kiladis et al. 2005)

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VERTICAL STRUCTURE

• MJO-filtered OLR and zonal wind anomalies at the
  equator (ERA-15 reanalysis). (Kiladis et
  al. 2005)

E
W
W
E
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PRIMITIVE EQUATION MODEL

• Governing equations, vertical struture
• Forcing function
• Frame of reference, solutions

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SEPARATION OF VERTICAL STRUCTURE

• Vertical structure functions Z1(z) Z(z) and
  Z1'(z) Z'(z).
• The curve labeled Q/cp is the 120-day mean
  vertical profile of heating rate for the western
  Pacific warm pool during
  TOGA-COARE. Adapted from (Johnson and
  Ciesielski, 2000).

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DIABATIC FORCING STRUCTURE

• Eastward propagating deep convection

• ? x ct
• c 5 m/s

• Q0/cp 12 K/day
• a0 1250 km
• b0 450 km
• y0 0, 450 km

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ZONAL COORDINATE TRANSFORM

• Zonal distance variable, ? x - ct
• Steady state translating at constant speed c

• Reference frame propagating with convective
  forcing

• Primitive equation generalization of the
  simplest MJO model involving the 1st baroclinic
  mode response to a large-scale moving heat source
  under the long-wave approximation. (Chao, 1987)

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SOLUTIONS / WAVE COMPONENTS FOR Y0 0
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SOLUTIONS / WAVE COMPONENTS FOR Y0 450
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POTENTIAL VORTICITY ASPECTS

• PV principle
• Idealized PV principle (analytical solution)
• Invertibility principle

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DIABATIC PV GENERATION
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PV VIEW OF THE KELVIN WAVE
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PV WAKE Y0 0 AND Y0 450
6 10-6s-1
-6 10-6s-1
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IDEALIZED PV PRINCIPLE

• Insight into (1) ßv term, (2) PV wake magnitude.

• PV principle

• Consider only dissipation and convective forcing
• Assume translating steady state.

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WAKE MAGNITUDE PARAMETER

• Large PV anomaly Zonally long
• Slow
  moving
  
  
• Highly
  convective

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ßV INFLUENCE
? ßv tends to make PV anomaly stronger, broader
in westward, north-south extent.

• Idealized PV 68 of correct strength, does not
  extend far enough westward or poleward.

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EQUATORIAL BALANCE RELATIONSHIP
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INVERTIBILITY PRINCIPLE
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CIRCULATION FROM INVERTED PV
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ENERGY ASPECTS

• Total energy principle
• Parseval Relation
• Energy dependence on forcing parameters

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PARSEVAL RELATION

• PARSEVALS THEOREM - The energy contained in a
  waveform f(x) integrated over all physical space
  (x) is equal to the energy contained in the
  spectrally transformed waveform F(k) integrated
  over all of its wavenumber components.

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NORMALIZED ENERGY VS. LAT. DISPLACEMENT
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NORMALIZED ENERGY VS. PHASE SPEED

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NORMALIZED ENERGY VS. ZONAL WAVENUMBER
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TOTAL RESPONSE PER ZONAL WAVENUMBER
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CONCLUSIONS
New contributions -
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CONCLUSIONS
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CONCLUSIONS
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CITED WORK

• MJO animation Dr. Adrian Matthews, School of
  Environmental Sciences, University of East
  Anglia, http//envam1.env.uea.ac.uk/e058/
• Kiladis, G. N., K. H. Straub, and P. T. Haertel,
  2005 Zonal and vertical structure of the
  Madden-Julian Oscillation. J. Atmos. Sci., 62,
  2790-2809.
• Johnson, R. H., and Ciesielski, P. E., 2000
  Rainfall and radiative heating rates from the
  TOGA-COARE atmospheric budgets. J. Atmos. Sci.,
  57, 1497-1514.
• Schubert, W. H., and Masarik, M. T., 2006
  Potential vorticity aspects of the MJO. Dynamics
  of Atmospheres and Oceans, 42, 127-151.

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MASTERS PRESENTATION
v EXTRA SLIDES v