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A Homogeneous Stochastic Model of the Madden-Julian Oscillation Charles Jones

A Homogeneous Stochastic Model of the Madden-Julian Oscillation Charles Jones University of California Santa Barbara. Collaboration : Leila Carvalho (USP ) , A. Matthews (UK) B. Pohl (Fr). Motivations to develop stochastic MJO models.

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A Homogeneous Stochastic Model of the Madden-Julian Oscillation Charles Jones

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  1. A Homogeneous 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. Motivations to develop stochastic MJO models • MJO discovered ~38 years ago; great deal has been learned about the oscillation • However, there are many unresolved issues • Temporal Variability of the MJO Observational knowledge about the MJO is limited to reanalysis data ~60 yrs MJO Weather Climate

  3. Positive trends in MJO intensity (winter and summer) Positive trends in number of MJOs (winter and summer) Jones and Carvalho (2006)

  4. Jones and Carvalho (2006) • 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)

  5. Long-term changes in MJO activity • what is real signal? • what is data sampling problem? • satellite data • number of raobs

  6. Our Goal: develop stochastic MJO models: • Able to simulate statistical properties of the MJO • Potential to test hypotheses and develop probabilistic approaches to some outstanding MJO issues • Provide additional tools to improve MJO representation in CGCM • Done so far: • homogeneous model • (no seasonal, interannual dependencies)

  7. Typical MJO: 12 34 5 67 8 • Data • Daily U200 and U850 (1948-2006), OLR (1979-2006) • Subtract daily climatology; band-pass filtered (20-200 days) • Average 15S-15N • Combined EOF analysis (U200, U850) • Use (EOF1, PC1), (EOF2, PC2) • Phase angle (PC1,PC2) normalized Wheeler and Hendon (2004)

  8. OLR Anomalies • MJO Identification • Criteria: • Systematic 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 • 210 MJO events in 1948-2006 Western Pacific 7 6 8 5 West. Hem. & Africa Maritime Continent 1 4 2 3 Indian Ocean

  9. Observed MJO Periods Mean ~46 days Sdv ~10 days Observed MJO Amplitudes A = (PC12 + PC2) 1/2 Mean ~1.50 Sdv ~0.66

  10. A Homogeneous Stochastic MJO Model

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

  12. Transition Matrix

  13. Western Pacific MJO starts Eastward propagation 7 6 8 5 Westward propagation 0 Maritime Continent West. Hem. & Africa MJO ends 1 4 Consecutive MJO starts 2 3 Persistence Indian Ocean

  14. Model Simulation • Initial condition S = 0 (non-MJO) • Uniform random number r [0,1]  transition probabilities • non-MJO: S=0  MJO: S = [1,2,3,4] • draw random duration Tk days (Gamma PDF fitted to observed MJO durations) • r [0,1]: MJO propagates through phases 1-8 for Tk days • at end of event: S=0 (non-MJO) or S=1 (consecutive MJO) • Given temporal distribution: • phases [1-8]  observed composites  spatial structure • Intensity: • Amplitude factor: A = 1 + 0.1 R, where R Gaussian number N[0, 1] • Testing: 100 members, each run 59 years

  15. Example of Observed MJO Phase Evolution Example of simulated MJO Phase Evolution

  16. Amplitude factors Simulated MJO Phase Evolution (Example)  MJO  Phase 0

  17. MJO Simulation Simulation Periods 100 members, 59 years each, 16990 MJOs Mean ~48 days Sdv ~9.3 days Simulation Amplitude Factor 59 year run: 200 MJOs Up to ± 30% weaker/stronger

  18. Number of MJOs per year Observed MJO Ensemble mean

  19. Observations Md ~52 days Sdv ~47.7 days   Duration of MJO episodes Simulations Md ~55 days Sdv ~53 days 100 members, 59 years each, 10424 episodes

  20. Observations  Md ~60 days Sdv ~85 days Interval between MJO episodes Simulations Md ~90 days Sdv ~125 days 100 members, 59 years each, 10524 intervals

  21. Ratio = 100 x # MJOs simulation # MJOs observations in 59 years (x100)

  22. Wavenumber x Period Spectrum Observations Model

  23. Summary/Conclusions • Homogeneous stochastic model provides a realistic, first order approximation to simulate the main characteristics of the MJO • Model deficiencies: • underestimates total occurrences of MJOs (~20%) • overestimates ratio primary/successive MJOs (x2) • Computation of transition matrix in subsamples: • changes in MJO activity  non-homogeneity

  24. Future Work • Non-homogeneous Empirical Model •  Time varying transition matrix: • Seasonal variations • Interannual variations (e.g. ENSO state) • Decadal changes (Indian Ocean SSTs ?) • Stochastic model of MJO periods: (Pohl & Matthews 2007) • Interannual variations (ENSO state) • Stochastic model of MJO intensities:(Pohl & Matthews 2007) • Interannual variations (ENSO state) • Decadal changes (before/after ~1977) • Linear trends • www.icess.ucsb.edu/asr

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