A Stochastic Model of the Madden-Julian Oscillation Charles Jones University of California

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

2. Outline • Brief overview of the Madden-Julian Oscillation • The behavior of the MJO on long time scales • A stochastic model of the MJO • Current research

3. The Madden-Julian Oscillation 30-60 Day OLR anomalies 1958-2006 • Clear Spectral Signal • Time Irregularity

4. * Significant case-to-case variability 4

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 Mo and Higgins (1998) Higgins et al (2000) Jones (2000) Bond and Vecchi (2003) Jones et al. (2004) Barlow et al. (2005) Jones et al. (2004) Jones et al. (2004) NH winter Carvalho et al. (2004) Liebmann et al. (2004) Jones et al. (2004) Wheeler and Hendon (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.

7. Summary • Potential Predictability Limit of the MJO: 20-30 days upper level circulation; 10-15 days precipitation (Waliser et al. 2003, BAMS) • El Nino (La Nina) enhances (diminishes) predictability • Observations • Higher frequency of extremes during active MJO phases • 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 • 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 • Total intraseasonal (2–128 day) precipitation variance is too weak. • 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. • MJO variance approaches observed value in 2/14 models; less than half of the observed value in the other 12 models. • The ratio between eastward/westward MJO variance is too small in most models; consistent with lack of highly coherent eastward propagation of the MJO. • 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. The behavior of the MJO Interannual Variations Long-term Behavior Case-to-Case Seasonal Variations Time scales ??? ???? ? ?? 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 • Positive linear trends in U200 and U850 intraseasonal anomalies in summer and winter. • Positive trends in the number of summer MJO events. • Mean winter LF MJO activity: ~uniform variability from 1960s to the mid-1990s • Mean summer LF MJO changes: regime of high activity and low activity during 1958-2004 (~ 18.5 yr)

11. Current Research Objectives • Investigate the mechanisms controlling periods of extended MJO activity • Develop a stochastic model capable to reproduce the statistical properties of the MJO including dynamical forcings of its variability (e.g. ENSO, extratropics etc) • This presentation: preliminary analysis of stochastic model of the MJO

12. 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) PC2 Phase angle between PC1 and PC2 PC1

13. OLR Anomalies • MJO Identification • Criteria: • Consistent eastward propagation • at least 1--> 4 • Minimum amplitude: • A = (PC12 + PC22)1/2> 0.35 • Entire duration between 30-70 days • Mean amplitude during event > 0.9 • 110 MJO events in 1979-2006 Phase 1 Phase 2 Phase 3 Phase 4 Phase 5 Western Pacific 7 6 Phase 6 8 5 West. Hem. & Africa 0 Phase 7 Maritime Continent 1 4 Phase 8 2 3 Indian Ocean

14. Stochastic Model of the MJO • Time variability • Markov Model using time series of phases (Xt=000111222333444556677880000…) • Spatial structure • Defined by mean composites • Amplitude (work in progress) • Stochastic model based on observed composites (mean and standard deviation)

15. Two State First Order Markov Model Time series Xt = 00001100010111001100001111000010011110… P01 P11 State 1 State 0 P00 P10 Markovian property Xt Xt+1 Transition Probabilities

16. MJO Phase Propagation No-MJO Consecutive MJOs Single MJO Xt=000111222333444556677880000111222434445556667770000222333434450…

17. Homogeneous Nine States First Order Markov Model 0 Non-MJO Western Pacific 81 parameters: 7 6 etc 8 5 West. Hem. & Africa 0 Maritime Continent 1 4 2 3 Indian Ocean

18. Western Pacific 7 6 MJO Ends 8 5 0 West. Hem. & Africa Maritime Continent 1 4 2 3 Indian Ocean Western Pacific Western Pacific 7 6 Primary MJO 7 6 Secondary MJO 8 5 8 5 0 West. Hem. & Africa West. Hem. & Africa 0 Maritime Continent Maritime Continent 1 4 1 4 2 3 2 3 Indian Ocean Indian Ocean

19. Observed MJO Phase transitions Simulated MJO Phase transitions

20. OLR Anomalies Simulated MJO Evolution Snapshot of 140 yrs simulation  MJO  Phase 0 Spatial structure and intensity same as observed composites 140 yrs: 361 events

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

22. OBS: 110 events SIM: 361 events

24. 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

25. 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)

26. Simulation of Two State Transitions r < 1 Xt0 = 1 r 1  Xt0 = 0 t0 Uniform Random Number (r) 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 t1 r tn Every grid point