MJO Evolution as Revealed by Multivariate Principal ...cpo.noaa.gov › sites › cpo › ESS › Hartten.MJOlikeMode_slides.final.pdf · MJO Evolution as Revealed by Multivariate

MJO Evolution as Revealed by

Multivariate Principal Oscillation Analysis

Leslie M. Hartten1, 2, Cécile Penland2, and Rosa M. Vargas3, 4

1 Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado - Boulder 2 NOAA/Earth Science Research Laboratory (ESRL), Physical Sciences Division 3 Significant Opportunities in Atmospheric Research and Science (SOARS®) Program, UCAR 4 Dept. of Physics, University of Puerto Rico - Mayagüez

NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection 25 October 2016

The Conundrum:

Madden and Julian (1972)

Our Approach:

MJO = a Linear System with Stochastic Forcing as per Newman et al. (2009, J. Climate)

! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection2

MJO

Part 1 - Multivariate Principal Oscillation Analysis

Part 2 - Event Evolution


Methods – Data

• daily 2.5° × 2.5° gridded analyses, 30°S to 30°N, 1974-2013: - OLR , u850, u200, SLP, T400 (from NCEP/NCAR Reanalyses & NOAA Interpolated OLR) - removed longterm annual cycle & longterm mean - computed pentads


Methods – Analysis Technique

1) EOF analysis with the pentad data - normalized each variable set by σPC1 - retained leading 9-24 EOFs from each variable 2) Multivariate EOF analysis with those timeseries - retained timerseries of 15 leading multivariate eigenvalues 3) Principal Oscillation Pattern (POP) analysis with retained multivariate PCs - yielded 15 dynamical modes

⇒ The least-damped oscillating mode looks like the MJO


Results – An MJO-Like Mode • 55-day period, 15-day decay time, propagates like MJO


Results – An MJO-Like Mode

• Peak power at 30-80 days - no Fourier filtering!


unpublished data, 12 June 2015: L.M. Hartten and C. Penland, CIRES &/or NOAA/ESRL/Physical Sciences Division

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MJO Mode(mode3 & mode4)

Re(mode3)Im(mode3)

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Periodogram of MJO ModeObtained from POP Analysis

The POP analysis employed:OLR, SLP, T

400mb, u

850mb, and u

200mb

pentads, June 1974 - December 2013, (30°S-30°N, 0.0-357.5°E)

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Re(mode3)Im(mode3)

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Results – An MJO-Like Mode

• Minimally wet


OLR

u850

u200

SLP

T400

0% 5% 10% 15% 20% 25% 30%

Contribution to Modal Variance

Part 1 - Multivariate Principal Oscillation Analysis

Part 2 - Event Evolution


Methods – Event Selection • event lists in Straub (2013) and from Ling et al. (2013) - October-April 1998-2009, start dates ±10d


Lower-levelwind (u850)

Upper-levelwind (u200)

Convec3on

(OLR)

Precipita3on (TRMMsatellite)

RMM*

Dates

Straub-Circ.Only ✓ ✓ ✓ 1979-2010

Straub-Full ✓ ✓ ✓ ✓ 1979-2010

Straub-Conv.Only ✓ ✓ 1979-2010

Lingetal. ✓ Oct-Apr1998-2009

*Real-4meMul4variateMJOindex(WheelerandHendon2004)

Methods – Event Selection • examined 8 of 12 identified events


Primary

Intensifying

Non-MJO

Jan1999

Nov 2009

Jan2006

Dec 2006

Jan2002

Apr 2003

Oct2002

Nov 2006

Straub-Circ.Only ✓ ✓ ✓ ✓ ✓ ✓

Straub-Full ✓ ✓ ✓ ✓ ✓

Straub-Conv.Only ✓ ✓ ✓ ✓

Lingetal. ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

Results – November 2009 “Primary” MJO Event • A textbook-like case of OLR evolution


Lingetal.

StraubFull

StraubCirc

StraubConv

Lingetal.

StraubFull

StraubCirc

StraubConv

Results – January 1999 “Primary” MJO Event

• Suppressed convection can be a dominant characteristic


Lingetal.

StraubFull

StraubCirc

StraubConv

Lingetal.

StraubFull

StraubCirc

StraubConv

Lingetal.

StraubFull

StraubCirc

StraubConv

Takeaway Points • Isolated an MJO-like mode (without bandpass filtering)

• MJO-like mode is “minimally wet” - OLR contributes ~50% as much variance as other fields - OLR doesn’t dominate forcing

• Estimated timeseries of MJO-like mode’s stochastic forcing - appears unpredictable on daily timescale - may maintain MJO events, rather than cause them

• MJO-like mode can depict Primary, Intensifying, & non-MJO - Dry phase sometimes ≥ enhanced convection phase - Precursor patterns (Ling et al. 2013) sometimes seen ! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection14

Future Work

• Stochastic forcing - maintaining instead of initiating events? - subdaily forcing?

• Midlatitude effects

• Examine other dynamical modes - “Missing” enhanced convection (Jan 1999 event)?


Acknowledgements

• Chidong Zhang (U. Miami) provided us with an event list from Ling et al. (2013).

• NOAA Interpolated OLR and NCEP/NCAR Reanalysis data provided by the NOAA/ OAR/ESRL Physical Sciences Division, Boulder, Colorado, USA. (http:// www.esrl.noaa.gov/psd/)

• Map & plot colors from www.ColorBrewer.org by Cynthia A. Brewer (Penn State).

• Brian Bevirt & Eileen Carpenter (NCAR) and Katie McCaffrey (CIRES) offered many suggestions that improved the visual presentation of results.

• Co-Investigator Chris Fairall (NOAA/ESRL/PSD) has been a supportive presence for many years.

• Funding provided by grants from NOAA’s Office of Global Programs to the NOAA/ESRL/Physical Sciences Division.


“A linear Markov process driven by Gaussian white noise”

"

- X(t) contains 5-day mean gridded analyses - L is estimated from X(t) using Linear Inverse Modeling (not shown) - x(t) contains daily gridded analyses - ξ(t) can be estimated from x(t) and L

"

see Penland and Sardeshmukh (1995, J. Climate) and Newman et al. (2009, J. Climate)

dX(t)dt

= LX(t)+ ξ(t)

ξ(t) ≈ x(t +δ )− x(t −δ )2δ

− LX(t)

! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convectioni

Stochastic Forcing Fields • Field in geographical space in terms of modal patterns uα and amplitudes zα:

"

• Evolution equations for zαr and zαi:

"

"

xi(t)= uiαα∑ zα (t)

dzαr

dt= (βα

r zαr − βα

i zαi )+ ξα

r

dzαi

dt= (βα

i zαr + βα

r zαi )+ ξα

i

! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convectionii

EOF Analyses

! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convectioniii

presented at the AGU Fall Meeting, San Francisco CA, 14 - 18 December 2015

Investigating MJO Precursors and Initial Stages with Multivariate Principal Oscillation AnalysisLeslie M. Hartten1, 2, Cécile Penland 2, and Rosa M. Vargas3, 4

1 Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado 2 Physical Sciences Division, NOAA/Earth System Research Laboratory (ESRL)3 Significant Opportunities in Atmospheric Research and Science (SOARS®) Program, UCAR, Boulder, Colorado 4 Dept. of Physics, University of Puerto Rico, Mayagüez, Puerto Rico

email addresses:[email protected] & [email protected] & [email protected]

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Introduction Global models do a poor job of simulating the Madden Julian Oscillation (MJO). The research community’s current focus is on better understanding the “initiation phase”; recent studies have shown that there is considerable variability in this regard. Here, we view the MJO as a fundamentally linear system which is forced stochastically. We are initially employing an event-based approach, so as not to assume similarity where it might not exist. Our ultimate goal is to determine the temporal and spatial characteristics of the stochastic forcing required to support MJO initiation.

Selecting MJO Events We focus on three methods for identifying MJO events presented by Straub (2013) and one presented by Ling et al. (2013). Their key characteristics and the dates over which the authors used them to identify MJO initiation events are summarized in the table below.

u850 u200 OLR Precip† RMM* Dates

StraubCirculation Only ✓ ✓ ✓ 1979-2010

StraubFull RMM ✓ ✓ ✓ ✓ 1979-2010

StraubConvection Only ✓ ✓ 1979-2010

Ling et al. ✓ Oct-Apr 1998-2009

† from TRMM* Real-time Multivariate MJO index (Wheeler and Hendon 2004)

Working from event lists provided in Straub (2013) and by Zhang (2014, personal communication) we identified 12 events in October-April 1998-2009 with start dates within 10 days of each other. They spanned three types of event initiations (Primary, Intensifying, and Non-MJO) and had varying levels of agreement among the four methods. We focussed on the 4 events listed below.

Type(s) Ling et al. StraubConvection

StraubFull RMM

StraubCirculation

Non-MJO† vs. Intensifying* 2 Oct 2002 5 Oct 2002 5 Oct 2002

Non-MJO† vs. Intensifying*

17 Nov 2006 10 Nov 2006

Intensifying* 8 Jan 2002 8 Jan 2002 12 Jan 2002 13 Jan 2002

Intensifying* 22 Apr 2003 27 Apr 2003 25 Apr 2003

† Non-MJO convection doesn’t propagate out of Indian Ocean * Intensifying events “evolve from a pre-existing lower-amplitude MJO signal” in the RMM

Analysis Technique We started with daily 2.5° x 2.5° gridded analyses, 30°S to 30°N during 1974-2013, of the following variables: u850, u200, SLP, T400, and OLR. For each variable we removed the longterm annual cycle and the longterm mean; computed pentads; and performed an EOF analysis with the pentad data. We retained 9 to 24 eigenvalues for each variable, which we combined for a multivariate EOF analysis.

We retained 15 multivariate eigenvalues and next used them in a Principal Oscillation Pattern (POP, von Storch et al. 1988) analysis. Of the 15 resulting dynamical modes, one is MJO-like, with an 11-pentad (55-day) period, a 3-pentad (15-day) decay time, and a pattern that propagates from the Indian Ocean across the Maritime Continent to the western Pacific (Fig. A). The mode’s power is concentrated in the 30-80 day range, with the largest peaks in the 40-60 day band (Fig. B).

Figure A. Idealized evolution of the MJO-like dynamical mode, as seen in the contribution from OLR, u200, and u850. All fields are anomalies.

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Figure B. Normalized power of the real and imaginary portions of the MJO-like mode. The 40-60 day band is shaded green in both the full range (top) and the close-up view (bottom).

UnivariateEOF Analysis

MultivariateEOF Analysis

Field EigenvaluesRetained

Variance Retained

Variance Retainedafter Combining Fields

u850 16 45.3% 33%

u200 11 41.2% 30%

T400 18 58.7% 35%

SLP 24 78.3% 53%

OLR 9 23.0% 12%

Total 78 n/a n/a

Evolution and Forcing of the MJO-like Mode The actual evolution of the mode during any event (Fig. C) differs from the theoretical to the extent that the real and imaginary amplitudes vary from perfectly in-quadrature sine waves. The timing of the mode’s convection sometimes differs from various estimates of “Intensifying” initiation events. Our MJO-like mode picks up one “Non-MJO” event but not the other (not shown).

We standardized all variables to their RMS (averaged over all locations and all times), then calculated the contribution of each to the MJO-like mode’s variance. The OLR contribution to the variance is about half that of each of the other fields.

Figure E. The loading of QMJO’s eigenvectors in terms of the EOFs of

u850, u200, T400, SLP, and OLR. QMJOEOF1 contains 61% of the variance of

ξMJO, and QMJOEOF2 contains 39%.

Figure D. Evolution of the MJO-like mode (heavy lines) and its stochastic forcing ξ (light lines) during the January 2002 Intensifying MJO event. Real part in red; imaginary part in blue.-50

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!3

Nov'01 Dec Jan'02 Feb

intensifying MJO

Some Key ReferencesLing, J., C. Zhang, and P. Bechtold, 2013: Large-scale distinctions between MJO and non-MJO convective initiation over the tropical Indian Ocean. J. Atmos. Sci., 70, 2696-2712.

Penland, C., and L. M. Hartten, 2014: Stochastic forcing of north tropical Atlantic sea surface temperatures by the North Atlantic Oscillation. Geophys. Res. Lett., 4.

Straub, K. H., 2012: MJO initiation in the real-time multivariate MJO index. J. Climate, 26, 1130-1151.

von Storch, H., T. Bruns, I. Fischer-Bruns, and K. Hasselmann, 1988: Principal oscillation pattern analysis of the 30- to 60-day oscillation in general circulation model equatorial troposphere. J. Geophys. Res., 93, 11022-11036.

Acknowledgments This work was supported by grants from NOAA’s Climate Program Office to the NOAA/ESRL/Physical Sciences Division. We thank Chidong Zhang (U. Miami) for providing us with an event list, and Brian Bevirt and Eileen Carpenter (NCAR) for presentation suggestions.NOAA Interpolated OLR and NCEP/NCAR Reanalysis data provided by the NOAA/OAR/ESRL Physical Sciences Division, Boulder, Colorado, USA (http://www.esrl.noaa.gov/psd/). Map colors from www.ColorBrewer.org by Cynthia A. Brewer, Dept. of Geography, Penn State.

Takeaway Points! We have isolated an MJO-like dynamical mode without bandpass filtering the underpinning data; its Fourier spectrum is naturally concentrated in the 40-60 day band.

! We have objectively estimated the time series this mode’s stochastic forcing. Unfortunately for prediction, this forcing does indeed appear to be unpredictable on the daily timescale.

! It is not clear that extrema of this forcing initiate MJO events as much as they play a role in maintaining it. (c.f. Fig. D)

! The OLR contributes about half as much to the variance of the MJO mode as do each of the other fields. Similarly, while the OLR contribution to the stochastic forcing is significant, it does not dominate.

! We need to examine both midlatitude effects and forcing at sub-daily timescales (c.f. T400 and SLP in Fig. C).

In order to evaluate the contributions of each field to !, we estimated the covariance matrix QMJO of that mode's stochastic forcing in field space. Since the MJO mode consists of one complex conjugate pair, QMJO has a rank of two and therefore has two eigenvectors, QMJOEOF1 and QMJOEOF2 (Fig. E). While the OLR contribution to the stochastic forcing is significant, it does not dominate.

Figure C. Evolution of the u850, u200, T400, SLP, and OLR contributions of the MJO-like mode during the the January 2002 “Intensifying” MJO event. Arrows indicate the initiation times according to different identification methods.

Straub Full

Straub Conv Ling et al.

dz!r

dt= (!"

r z"r ! !"

i z"i )+ !"

r dz!i

dt= (!"

r z"i + !"

i z"r )+ !"

i

We used daily u850, u200, T400, SLP, and OLR to calculate the stochastic forcing fields (c.f. Penland and Hartten 2014): • Field in geographical space in terms of modal patterns u! and amplitudes z!:

• Evolution equations for z!r and z!i:

The real and imaginary parts of modal amplitudes (Fig. D) affect each other's evolution, but the real (imaginary) part of the forcing " affects only the real (imaginary) modal amplitude. Unlike the modes, the real and imaginary parts of ! do not appear in a set sequence. Extremes of ! in some fields (e.g. OLR) look like the modes themselves, while others bear little resemblance to the modal patterns.

xi = ui!!! z! (t)

FieldContribution

to ModalVariance

u850 19.6%

u200 20.6%

T400 23.5%

SLP 26.1%

OLR 10.2%

Total 100%

Results – An MJO-Like Mode • 55-day period, 15-day decay time, propagates like MJO

OLR u200 u850

! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convectioniv





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StraubFull RMM

StraubCirculation



17 Nov 2006 10 Nov 2006







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Variance Retained


u850 16 45.3% 33%

u200 11 41.2% 30%

T400 18 58.7% 35%

SLP 24 78.3% 53%

OLR 9 23.0% 12%

Total 78 n/a n/a







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Straub Full


dz!r

dt= (!"

r z"r ! !"

i z"i )+ !"

r dz!i

dt= (!"

r z"i + !"

i z"r )+ !"

i




xi = ui!!! z! (t)

FieldContribution

to ModalVariance

u850 19.6%

u200 20.6%

T400 23.5%

SLP 26.1%

OLR 10.2%

Total 100%

Results – An MJO-Like Mode • Minimally wet

FieldContribution to Modal Variance

OLR 10.2%

u850 19.6%

u200 20.6%

SLP 26.1%

T400 23.5%

Total 100%

! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convectionv

Methods – Event Selection • examined 8 of 12 identified events

! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convectionvi

Primary

Intensifying

Non-MJO

Jan1999

Nov 2009

Jan2006

Dec 2006

Jan2002

Apr 2003

Oct2002

Nov 2006

Straub-Circ.Only

P11Jan

I10Jan

I18Dec

I13Jan

I25Apr

I5Oct

Straub-Full

P10Jan

I18Dec

I12Jan

I5Oct

I10Nov

Straub-Conv.Only

P28Oct

P19Dec

I8Jan

I27Apr

Lingetal. P17Jan

P30Oct

P9Jan

P15Dec

I8Jan

I22Apr

N2Oct

N17Nov

Results – January 2002 “Intensifying” MJO Event • Actual evolution based on modal amplitudes (zα) - differs from theoretical & from other ID systems

T400 SLP OLR

! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convectionvii





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StraubFull RMM

StraubCirculation



17 Nov 2006 10 Nov 2006







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Variance Retained


u850 16 45.3% 33%

u200 11 41.2% 30%

T400 18 58.7% 35%

SLP 24 78.3% 53%

OLR 9 23.0% 12%

Total 78 n/a n/a







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Straub Full


dz!r

dt= (!"

r z"r ! !"

i z"i )+ !"

r dz!i

dt= (!"

r z"i + !"

i z"r )+ !"

i




xi = ui!!! z! (t)

FieldContribution

to ModalVariance

u850 19.6%

u200 20.6%

T400 23.5%

SLP 26.1%

OLR 10.2%

Total 100%

Results – January 2002 “Intensifying” MJO Event • Used daily data to calculate stochastic forcing ξα - two-day correlation is highly insignificant

• Equations (not shown) - real & imaginary parts of zα affect each other’s evolution - real (imaginary) parts of ξα only affect real (imaginary) zα

! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convectionviii

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Documents

MJO Evolution as Revealed by Multivariate Principal ...cpo.noaa.gov › sites › cpo › ESS › Hartten.MJOlikeMode_slides.final.pdf · MJO Evolution as Revealed by Multivariate