A Stochastic Model of the Madden-Julian Oscillation Charles Jones University of California Santa Barbara 1 Collaboration : Leila Carvalho (USP), A. Matthews (UK), B. Pohl (FR)

2 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 anomalies o Clear Spectral Signal o Time Irregularity 3 The Madden-Julian Oscillation

4 4 * Significant case-to-case variability

5  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.

6 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, NH winter

7 Summary o Potential Predictability Limit of the MJO: days upper level circulation; days precipitation (Waliser et al. 2003, BAMS) o El Nino (La Nina) enhances (diminishes) predictability Observations o Higher frequency of extremes during active MJO phases o On 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 o Predictability experiments indicate higher success in the prediction of extremes during active MJO than in quiescent situations (Jones et al. 2004)

8 Climate models have improved in recent years but still produce many unrealistic MJO characteristics Lin et al. (2006) : 14 GCMs participating in IPCC-AR4 o Total intraseasonal (2–128 day) precipitation variance is too weak. o Half 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. o MJO variance approaches observed value in 2/14 models; less than half of the observed value in the other 12 models. o The ratio between eastward/westward MJO variance is too small in most models; consistent with lack of highly coherent eastward propagation of the MJO. o MJO 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.

9 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?

10 The behavior of the MJO Jones and Carvalho (2006) J. Climate o Positive linear trends in U200 and U850 intraseasonal anomalies in summer and winter. o Positive trends in the number of summer MJO events. o Mean winter LF MJO activity: ~uniform variability from 1960s to the mid-1990s o Mean summer LF MJO changes: regime of high activity and low activity during (~ 18.5 yr)

Current Research Objectives o 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 11

Data preparation Wheeler and Hendon (2004) : Daily OLR, U200 and U850 anomalies; averaged 15S-15N; Combined EOF analysis (OLR, U200, U850) Use (EOF1, PC1), (EOF2, PC2) 12 PC2 PC1 Phase angle between PC1 and PC2

13 MJO Identification Criteria: o Consistent eastward propagation at least 1--> 4 o Minimum amplitude: A = (PC1 2 + PC2 2 ) 1/2 > 0.35 o Entire duration between days o Mean amplitude during event > 0.9 o 110 MJO events in Phase 1 Phase 2 Phase 3 Phase 4 Phase 5 Phase 6 Phase 7 Phase 8 OLR Anomalies West. Hem. & Africa Maritime Continent Indian Ocean Western Pacific

14 Stochastic Model of the MJO  Time variability Markov Model using time series of phases (Xt= …)  Spatial structure Defined 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 XtXt X t+1 Transition Probabilities 15 Time series Xt = … Markovian property

16 Xt= … MJO Phase Propagation No-MJO Single MJO Consecutive MJOs

17 West. Hem. & Africa Maritime Continent Indian Ocean Western Pacific Non-MJO 81 parameters: etc

West. Hem. & Africa Maritime Continent Indian Ocean Western Pacific Primary MJO West. Hem. & Africa Maritime Continent Indian Ocean Western Pacific Secondary MJO West. Hem. & Africa Maritime Continent Indian Ocean Western Pacific MJO Ends

19 Observed MJO Phase transitions Simulated MJO Phase transitions

20  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

21 Composite of simulated MJO 140 yrs: 361 events Spatial structure and intensity same as observed composites

22 OBS: 110 events SIM: 361 events

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Summary/Conclusions  MJO is the most important mode of tropical intraseasonal variability with a distinct role in climate variability  Knowledge of long-term variability of the MJO is limited to ~60 years  Stochastic model of the MJO is being developed to investigate the low-frequency behavior of the oscillation and trends in climate change scenarios Work in Progress  Extend the stochastic model to non- homogeneous Markov Model  Stochastic model of intensities 24

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) 25

Simulation of Two State Transitions Uniform Random Number (r) r <  1  X t0 = 1 r   1  X t0 = 0 t0 Every grid point If X t0 = 0 if r  P01  X t1 = 1 if r  P01  X t1 = 0 If X t0 = 1 if r  P11  X t1 = 1 if r  P11  X t1 = 0 r t1 tn 26