1. Sensitivities of the MJO to the Shape and Strength of the Tropical Warm Pool in the Stochastic Skeleton Model [BIRS 15w5023] Stochasticity and Organization of Tropical Convection Justin P. Stachnik 1,2, Duane E. Waliser 1,2, Andrew J. Majda 3, Samuel N. Stechmann 4, and Sulian Thual 3 1. Joint Institute for Regional Earth System Science and Engineering, University of California, Los Angeles 2. Jet Propulsion Laboratory, California Institute of Technology 3. Department of Mathematics and Center for Atmosphere-Ocean Science, Courant Institute, New York University 4. Department of Mathematics and Department of Atmospheric and Oceanic Sciences, University of Wisconsin-Madison

2. Driving Questions and Goals Does the skeleton model produce a more realistic MJO structure and climatology when forced with observed SSTs? How does the climatology of MJO events change in response to natural variability of Indian and Pacific Ocean SSTs in observations and the skeleton model? -IOD may result in (1) stronger/more MJO variability with enhanced eastward propagation along the equator or (2) lower frequency MJOs and slower propagating systems near 8 °S (e.g., Kug et al. 2009; Izumo et al. 2010; Wilson et al. 2013 How does the stochasticity and variance of the MJO change as a function of the large-scale forcing?

3. The Bare Bones Equations of motion Continuity equation Energy equation Moisture equation **Wave activity** Stochastic in latest version of model Other: Variables describe anomalies from radiative- convective equilibrium for longwave approximation, linearize equations, vertically truncate at first baroclinic mode, horizontally truncate at first meridional mode, etc…

4. NOAA OI SST v2 and SSM s q, s  Observations (1970-2000)Model (Idealized Warm Pool)

5. NOAA OI SST v2 and SSM s q, s  Observations (1970-2000)“Observed” Ha from GPCP Ogrosky and Stechmann (2015)

6. NOAA OI SST v2 and SSM s q, s  Observations (1970-2000)Model (Idealized Warm Pool)

7. NOAA OI SST v2 and SSM s q, s  Observations (1970-2000)Model (ENSO SSTs)

8. NOAA OI SST v2 and SSM s q, s  Observations (1970-2000)Model (IOD SSTs)

9. Idealized Warm PoolNOAA OI SST v2 (Real Data)

10. Observed and Modeled HaNOAA OI SST v2 (Real Data) Ogrosky and Stechmann (2015)

11. Multivariate EOFs for Ha and u (Idealized WP) Idealized Warm Pool Wheeler and Hendon (2004)

12. Multivariate EOFs for Ha and u (Real SSTs) NOAA OI SST v2 (Real Data) Wheeler and Hendon (2004) (truncated)

13. (all waves) Multivariate EOFs for Ha and u (Real SSTs) NOAA OI SST v2 (Real Data) Wheeler and Hendon (2004)

14. Primary: No preceding RMM signal ≥ 1.0 Continuing: Preceded by at least 2 phases with RMM signal ≥ 1.0 Circumnavigating: Preceded by 8 phases (complete MJO cycle) with RMM signal ≥ 1.0 Terminal: RMM signal ≤ 1.0 (most common) or begins to significantly retrograde Defining MJO “Events” Stachnik et al. (2015)

15. Dataset/Event TypePrimaryContinuingCircum- navigating Terminal Observations: 1979-2012 15433015154 Skeleton Model: Idealized WP 10441428104 Skeleton Model: Real Data SSTs 904874290 Number of MJO Events, RMM Amplitude ≥ 1.0, Entire Year Increase in continuing cases and decrease in initiation events implies idealized WP and real SST event lengths exceed observations Average MJO event length of 34.8 d, 42.7 d, and 45.7 d in observations, idealized WP, and real SST simulations, respectively Average event length increase is due to the smaller increase in events with lengths of 40+ days

16. MJO Event Length in the Skeleton Model and Observations Real Data SSTs, Stochastic Model Real Data SSTs, Deterministic Model

17. MJO Climatology in Observations and SSM Observations (1979-2012)Model (Warm Pool, 34 years) [First Period] Stachnik et al. (2015)

18. MJO Climatology in Observations and SSM Observations (1979-2012)Model (Warm Pool, 34 years) [Second Period] Stachnik et al. (2015)

19. Modeled MJO event length trends are opposite to observations Observations: El Niño: 30.7 d, La Niña: 36.7 d, (Neutral: 38.7 d) Skeleton Model: La Niña: 41.8 d, El Niño: 45.1 d, (Neutral: 47.8 d)

20. Modeled MJO event length trends are opposite to observations Observations: Pos. IOD: 34.5 d, Neg. IOD 35.3 d, (Neutral: 39.9 d) Skeleton Model: Neg. IOD 41.1 d, Pos. IOD: 47.3 d, (Neutral: 51.1 d)

21. NOAA OI SST v2 and SSM s q, s  Observations (1970-2000)Model (Idealized Warm Pool)

22. SST8N (Deterministic)SST8N (Stochastic)

23. Idealized WP (Deterministic)SST8N (Stochastic) Majda and Stechmann (2011)

24. Quantifying “Stochasticity”

25. Distribution of RMM Amplitudes Case/S q,  (K day -1 ) µσ Obs1.730.458 S q,  = 0.531.800.461 S q,  = 1.001.820.460 S q,  = 2.111.760.435 S q,  = 1.00 (determin.) 1.720.370

26. Summary and Conclusions Using realistic SSTs in the skeleton model produces leading modes that are similar to Wheeler and Hendon (2004), including maximum intraseasonal variance over the warm pool and an asymmetric wavenumber-1 zonal flow MJOs are shorter during El Niño with more discrete events, while the negative phase of the IOD has more and faster MJOs that travel further to the east Skeleton model is generally insensitive to (observed) small changes in tropical SSTs (Preliminary, still in progress) The skeleton model demonstrates less variability in the RMM amplitude (i.e., reduced stochasticity within an event) for stronger radiative and moisture forcing