A Stochastic Model of the

Madden-Julian Oscillation

Charles Jones

University of California

Santa Barbara

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Collaboration: Leila Carvalho (USP), A. Matthews (UK),

B. Pohl (FR)

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Outline

o Brief overview of the Madden-Julian Oscillation

o The behavior of the MJO on long time scales

o A stochastic model of the MJO

o Current research

30-60 Day OLR anomalies1958-2006

oClear Spectral

Signal

oTime Irregularity3

The Madden-Julian Oscillation

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4

* Significant case-to-case variability

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Modulate the variability of the monsoons in Asia-Australia, Africa and Americas

Teleconnections with extratropics in both hemispheres

Modulate thermocline variability in the tropical Pacific Ocean via westerly wind bursts

Influence on forecast skills in the tropics and extratropics

Lau, W. K. M., and D. E. Waliser, 2005: Intraseasonal Variability in the Atmosphere-Ocean Climate System.Zhang, C. D. 2005: Madden-Julian oscillation. Reviews of Geophysics, 43, 1-36.

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The MJO and Extreme Precipitation

Barlow et al. (2005) Jones et al. (2004)

Mo and Higgins (1998) Higgins et al (2000) Jones (2000) Bond and Vecchi (2003) Jones et al. (2004)

Carvalho et al. (2004) Liebmann et al. (2004) Jones et al. (2004)

Wheeler and Hendon (2004) Jones et al. (2004)

Jones et al. (2004)

Jones, C., D. E. Waliser, K. M. Lau, and W. Stern, 2004: Global occurrences of extreme precipitation events and the Madden-Julian Oscillation: observations and predictability. J. Climate, 17, 4575-4589.

NH winter

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Summary

oPotential Predictability Limit of the MJO: 20-30 days upper level circulation; 10-15 days precipitation (Waliser et al. 2003, BAMS)

oEl Nino (La Nina) enhances (diminishes) predictability

ObservationsoHigher frequency of extremes during active MJO phases

oOn a global scale, extreme events during active MJO are about 40% higher than in quiescent phases in locations of statistically significant signals (Jones et al. 2004)

Model Experiments

oPredictability experiments indicate higher success in the prediction of extremes during active MJO than in quiescent situations (Jones et al. 2004)

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Climate models have improved in recent years but still produce many unrealistic MJO characteristics

Lin et al. (2006) : 14 GCMs participating in IPCC-AR4

oTotal intraseasonal (2–128 day) precipitation variance is too weak.oHalf of the models have signals of convectively coupled equatorial waves. However, the variances are generally too weak for all wave modes , and the phase speeds are generally too fast.oMJO variance approaches observed value in 2/14 models; less than half of the observed value in the other 12 models.oThe ratio between eastward/westward MJO variance is too small in most models; consistent with lack of highly coherent eastward propagation of the MJO.oMJO variance (13/14 models) does not come from pronounced spectral peak, but usually comes from over-reddened spectrum; associated with too strong persistence of equatorial precipitation.

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Time scales?? ???? ?????? ????????

The behavior of the MJO

Observational knowledge about the MJO: limited to reanalysis data ~ 58 years

Does the MJO have a low-frequency mode of variability?

Will the MJO change as climate continues to warm?

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The behavior of the MJO

Jones and Carvalho (2006) J. ClimateoPositive linear trends in U200 and U850 intraseasonal anomalies in summer and winter. oPositive trends in the number of summer MJO events.oMean winter LF MJO activity: ~uniform variability from 1960s to the mid-1990soMean summer LF MJO changes: regime of high activity and low activity during 1958-2004 (~ 18.5 yr)

Current Research Objectiveso Investigate the mechanisms controlling

periods of extended MJO activity

o Develop a stochastic model capable to

reproduce the statistical properties of the

MJO including dynamical forcings of its

variability (e.g. ENSO, extratropics etc)

o This presentation: preliminary analysis of

stochastic model of the MJO

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Data preparation Wheeler and Hendon (2004) :

• Daily OLR, U200 and U850 anomalies; averaged 15S-15N; 1979-2006

• Combined EOF analysis (OLR, U200, U850)

• Use (EOF1, PC1), (EOF2, PC2)

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PC2

PC1

Phase angle between PC1 and PC2

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MJO IdentificationCriteria:oConsistent eastward propagation

at least 1--> 4 oMinimum amplitude:

A = (PC12 + PC22)1/2 > 0.35oEntire duration between 30-70 daysoMean amplitude during event > 0.9o110 MJO events in 1979-2006

Phase 1

Phase 2

Phase 3

Phase 4

Phase 5

Phase 6

Phase 7

Phase 8

OLR Anomalies

We

st. H

em. &

Afr

ica M

aritim

e Co

ntin

ent

Indian Ocean

Western Pacific

01

2 3

4

7 6

8 5

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Stochastic Model of the MJO

Time variabilityMarkov Model using time series of phases (Xt=000111222333444556677880000…)

Spatial structureDefined by mean composites

Amplitude (work in progress)Stochastic model based on observed composites (mean and standard deviation)

State 0 State 1

P01

P11

P10

P00

Xt

Xt+1

Transition Probabilities

ttttt

XXPXXXP |...,|111

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Time series Xt = 00001100010111001100001111000010011110…

Markovian property

s total # of

sg s followin#P

0

0101 10100 PP

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Xt=000111222333444556677880000111222434445556667770000222333434450…

MJO Phase Propagation

No-

MJO

Single MJOConsecutive MJOs

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We

st. H

em. &

Afr

ica M

aritim

e Co

ntin

ent

Indian Ocean

Western Pacific

01

2 3

4

7 6

8 5

0 Non-MJO

SiXSjXP tt |1

s total # of

sg s followin#P

0

0000

8,0,8,0, iSijSj

81 parameters:

s total # of

sg s followin#P

0

0101 etc

0 1 2 3 4 5 6 7 80 0.98483 0.01012 0.00206 0.00150 0.00150 0 0 0 01 0 0.80148 0.19666 0.00186 0 0 0 0 02 0 0.03609 0.78647 0.17594 0.00150 0 0 0 03 0 0 0.03888 0.78072 0.17885 0.00156 0 0 04 0.00446 0 0 0.02232 0.78571 0.18750 0 0 05 0.00311 0 0 0 0.03106 0.77950 0.18478 0.00155 06 0.00484 0 0 0 0 0.02419 0.77903 0.18710 0.004847 0.01389 0.00174 0 0 0 0 0.03125 0.77604 0.177088 0.12287 0.05293 0 0 0 0 0 0.02268 0.80151

Xt+1

Xt

Transition Probabilities

We

st. H

em. &

Afr

ica M

aritim

e Co

ntin

ent

Indian Ocean

Western Pacific

01

2 3

4

7 6

8 5

Primary MJO

We

st. H

em. &

Afr

ica M

aritim

e Co

ntin

ent

Indian Ocean

Western Pacific

01

2 3

4

7 6

8 5

Secondary MJO

We

st. H

em. &

Afr

ica M

aritim

e Co

ntin

ent

Indian Ocean

Western Pacific

01

2 3

4

7 6

8 5

MJO Ends

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Observed MJO Phase transitions

Simulated MJO Phase transitions

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Phase 0

Snapshot of 140 yrs simulation

MJO

140 yrs: 361 events

OLR Anomalies

Spatial structure and intensity same as observed composites

Simulated MJO Evolution

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Composite of simulated MJO

140 yrs: 361 events

Spatial structure and intensity same as observed composites

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OBS: 110 eventsSIM: 361 events

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Summary/Conclusions

MJO is the most important mode of tropical intraseasonal variability with a distinct role in climate variabilityKnowledge of long-term variability of the MJO is limited to ~60 yearsStochastic model of the MJO is being developed to investigate the low-frequency behavior of the oscillation and trends in climate change scenarios

Work in ProgressExtend the stochastic model to non-homogeneous Markov ModelStochastic model of intensities

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01111

1101101

1

PPr

PPP

Stationarity

Probability

Persistence Parameter

Order of Markov Model

Can be tested using log-likelihood method (minimization of Akaike information criterion –AIC – or Bayesian information criterion –BIC)

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Simulation of Two State Transitions

Uniform Random Number (r)

r < 1 Xt0 = 1 r 1 Xt0 = 0

t0

Every grid point

If Xt0 = 0 if r P01 Xt1 = 1 if r P01 Xt1 = 0

If Xt0 = 1 if r P11 Xt1 = 1 if r P11 Xt1 = 0

r t1

tn

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