MJO Evolution as Revealed by Multivariate Principal Oscillation Analysis Leslie M. Hartten 1, 2 , Cécile Penland 2 , and Rosa M. Vargas 3, 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
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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
! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection3
! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection4
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
! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection5
Results – An MJO-Like Mode • 55-day period, 15-day decay time, propagates like MJO
! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection6
Results – An MJO-Like Mode
• Peak power at 30-80 days - no Fourier filtering!
! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection7
unpublished data, 12 June 2015: L.M. Hartten and C. Penland, CIRES &/or NOAA/ESRL/Physical Sciences Division
0
2000
4000
6000
8000
10000
10 100 1000
MJO Mode(mode3 & mode4)
Re(mode3)Im(mode3)
Nor
mal
ized
Pow
er
Period (days)
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)
0
2000
4000
6000
8000
10000
40 50 60
MJO Mode(mode3 & mode4)
Re(mode3)Im(mode3)
Nor
mal
ized
Pow
er
Period (days)
43 52
Results – An MJO-Like Mode
• Minimally wet
! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection8
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
! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection9
Methods – Event Selection • event lists in Straub (2013) and from Ling et al. (2013) - October-April 1998-2009, start dates ±10d
! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection10
! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection11
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
! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection12
Lingetal.
StraubFull
StraubCirc
StraubConv
Lingetal.
StraubFull
StraubCirc
StraubConv
Results – January 1999 “Primary” MJO Event
• Suppressed convection can be a dominant characteristic
! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection13
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
! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection15
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.
! NOAA CVP 2016 Webinar Series - Understanding & Improving Prediction of Tropical Convection16
“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
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.
0
2000
4000
6000
8000
10000
10 100 1000
MJO Mode(mode3 & mode4)
Re(mode3)Im(mode3)
Nor
mal
ized
Pow
er
Period (days)
0
2000
4000
6000
8000
10000
40 50 60
MJO Mode(mode3 & mode4)
Re(mode3)Im(mode3)
Nor
mal
ized
Pow
er
Period (days)
43 52
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
-25
0
25
50
-20
-10
0
10
20Re_z3Im_z3 Re(xsi3)
Im(xsi3)
z3
!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
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
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.
0
2000
4000
6000
8000
10000
10 100 1000
MJO Mode(mode3 & mode4)
Re(mode3)Im(mode3)
Nor
mal
ized
Pow
er
Period (days)
0
2000
4000
6000
8000
10000
40 50 60
MJO Mode(mode3 & mode4)
Re(mode3)Im(mode3)
Nor
mal
ized
Pow
er
Period (days)
43 52
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
-25
0
25
50
-20
-10
0
10
20Re_z3Im_z3 Re(xsi3)
Im(xsi3)
z3
!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 • 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
! 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
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
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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10 100 1000
MJO Mode(mode3 & mode4)
Re(mode3)Im(mode3)
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mal
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Pow
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Period (days)
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MJO Mode(mode3 & mode4)
Re(mode3)Im(mode3)
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Period (days)
43 52
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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20Re_z3Im_z3 Re(xsi3)
Im(xsi3)
z3
!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 – 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