Adam Sobel

1. MJO Dynamics(we think it’s a moisture mode somehow destabilized by surface fluxes and moving eastward in mean westerlies) Adam Sobel With: Eric Maloney, Gilles Bellon, Dargan Frierson, Daehyun Kim RSMAS, U. Miami, March 23 2011

2. Outline • Introduction to the MJO • Argument that surface flux feedbacks (incl. radiative) are important, based on observations • Exploration of that hypothesis in several GCMs, realistic & aqua planet • Framework of a theory (if time permits)

3. The tropical atmosphere has strong, coherent variability on the intraseasonal (30-60 day) time scale Equatorial outgoing longwave radiation, a measure of deep, high cloudiness (shading) – annual cycle & ENSO removed time longitude

4. The “Madden-Julian oscillation” (MJO) propagates eastward in a belt around the equator Statistical composite MJO in outgoing longwave radiation and lower tropospheric wind (Wheeler and Hendon 2004) time longitude

5. Climate models’ simulations of intraseasonal variability are flawed, but improving (and can be improved even more today, at a cost) Lin et al. 2006 intercomparison of models used in CMIP3/IPCC AR4

6. But there is no agreement on the basic mechanisms despite ~3 ½ decades of study Surface pressure spectrum, Nauru Island, tropical Pacific Helium spectral lines wikipedia Madden and Julian 1972

7. Variance of rainfall on intraseasonal timescales shows structure on both global and regional scales Intraseasonal rain variance Northern Summer Southern Summer Sobel, Maloney, Bellon, and Frierson 2008: Nature Geosci.,1, 653-657.

8. Climatological patterns resemble variance, except that the mean doesn’t have localized minima over land Intraseasonal OLR variance (may-oct) Climatological mean OLR (may-oct)

9. Climatological patterns resemble variance, except that the mean doesn’t have localized minima over land Intraseasonal OLR variance, nov-apr Climatological mean OLR, nov-apr

10. The main difference between land and ocean is that the total surface heat flux is small over land but can be large (or small) over ocean. The fact that intraseasonal variations in rainfall are large over ocean and small over land suggests that variations in the total surface heat flux play an important role in generating the intraseasonal rainfall variations. Latent and radiative components of the total surface heat flux probably play ~comparable roles.

11. Emanuel (87) and Neelin et al. (87) proposed that the MJO is a Kelvin wave driven by wind-induced surface fluxes (“WISHE”)‏ θ=θ1+Δθ θ=θ1 cool warm Enhanced sfc flux Mean flow Perturbation flow Wave propagation

12. This idea has been somewhat abandoned because the real MJO does not look quite like the original WISHE theory Observed cloudiness and wind from TOGA COARE (Chen, Houze and Mapes 1996) Strongest winds and fluxes are in phase with or lag precipitation, and lie in westerlies Frequency-wavenumber OLR plot (Wheeler and Kiladis 1999) – MJO not a “convectively coupled” extension of any dry linear mode

13. ocean Shinoda et al. 1998 But the real MJO does have significant net surface heat flux variations, roughly in phase with convection

14. Net = 0 W/m^2 land ocean Shinoda et al. 1998 Over land, there can be no significant net flux variations on intraseasonal time scales - so if net flux were important to ISO, the observed variance maps should look as they do!

15. Note on the relevance of total surface energy flux (including shortwave) to the atmosphere It is observed that net TOA radiative influence of high clouds is small – shortwave and longwave components cancel. Thus cloud-induced shortwave reductions at the surface are accompanied by ~equal reductions in tropospheric radiative cooling (OLR reduction, ~zero sfc longwave change) Clouds heat the atmosphere and cool the ocean, just like a surface flux. So we discuss them together. Partitioning between latent and radiative components of flux changes associated with the MJO is a more subtle matter – but they appear to be of comparable magnitude.

16. In a numerical model, it is straightforward to test whether surface flux feedbacks are important to the simulated MJO. They can be disabled by replacing some component of the surface flux – e.g., latent heat flux, or the surface wind speed which controls it – by a climatology in the relevant model parameterization. If doing so eliminates (or strongly weakens) the simulated MJO, one knows that the eliminated flux variations were important. The results of such experiments vary from model to model – but for the most part support the contention that some combination of surface flux turbulent and radiative feedbacks is important.

17. In (two versions of) the Seoul National University model, though, eliminating surface wind-evaporation feedback strengthens the MJO (implying that the feedback actually inhibits the MJO) Calculations by Daehyun Kim, Columbia U. Obs lag-corr precip “good model” “bad model” control control no-WISHE no-WISHE But actually it can be shown that both versions of this model are bad – the phase relationship between wind and precipitation anomalies is wrong

18. Bad phase relationship between convection, winds & fluxes in this model obs LH flux lag-regression compared to obs (w/OLR) model obs model sfc u lag-regression compared to obs (w/OLR)

19. And in this same model, turning off radiative feedbacks on the other hand does (mostly) kill the MJO – consistent with net surface flux argument “good model” “bad model” control control no cloud-rad no cloud-rad

20. Summary of “mechanism denial” experiments incl. double & triple ones for WISHE, cloud-rad feedback, & frictional CISK Consistent results: WISHE bad for MJO (in this model, for wrong reasons), cloud-rad very good for it, frictional CISK does little either way

21. WISHE clearly important in the GFDL AM2, after tuning to amplify the MJO control GFDL AM2 Calculations by Dargan Frierson, U. Washington No-WISHE (const sfc wind speed) better model worse model

22. GCM simulation on an aqua planet with a warm pool with a modified version of the NCAR CAM3 (E. Maloney, CSU) Unfiltered precipitation (left) and winds (right) vs. longitude 5 m/s Even in unfiltered data, many salient features of the MJO apparent, including 5 m s-1 eastward propagation, and a period of 40-60 days. Maloney, Sobel, Hannah, J. Adv. Model Earth Sys.

23. Model Description NCAR Community Atmosphere Model 3 Swapped in a replacement parameterization for deep convection (we use relaxed Arakawa-Schubert, Moorthi and Suarez 1992). T42 horizontal resolution (2.8o x 2.8o), and 26 vertical levels Perpetual March 21 insolation and ozone 16-year aquaplanet simulation with idealized SST boundary condition containing zonal asymmetries and reduced meridional SST gradient

24. SST Distributions Used “Realistic” SST Zonally Symmetric Quarter Meridional Gradient

25. Mean Wind and Precipitation Variance Units: mm2 day-2 Intraseasonal variance peaks in regions of mean westerly flow at low-levels. Variance is stronger than observed.

26. Composite Precipitation and U850 (Unfiltered) From Wheeler and Hendon (2004)

27. Wavenumber-Frequency Spectra (Precip) Observations Model 90 days 30 days 90 days 30 days A strong spectral peak exists in the model at same zonal wavenumber and frequency as observations.

28. Composite PW Anomalies PW Units: mm Column precipitable water anomalies are sizeable, and in phase with precipitation anomalies, as would be expected given the strong relationship between saturation fraction and precipitation. Precipitation contour interval 4 mm day-1.

29. Composite Moisture Budget • Horizontal advection is (nearly) in quadrature with precipitation (and PW) and in phase with the humidity tendency. • Surface evaporation slightly lags the precipitation anomalies, with a strong positive covariance

30. Total • At time of peak moistening, total zonal winds are on the order of 5 m s-1. U850 Precip

31. Unfiltered Precipitation vs. Longitude,Control Versus No-WISHE Control No-WISHE • WISHE appears to destabilize the MJO in the model. 30-90 day, zonal wavenumber 1-3 variance decreases dramatically without WISHE active • Small spatial scale precipitation variability that moves slowly east is still apparent

32. In summary, evidence suggests that the MJO: • Is destabilized by surface turbulent fluxes and radiative feedbacks • Is something other than a Kelvin wave (at least over warm pool) • Needs mean low-level westerlies • Manages to go eastward despite LH fluxes strongest on west side of precip, which should drag it the other way • Is strongly influenced in its propagation by horizontal advection – wind speeds of same order as propagation speed – including by perturbation winds, so may be nonlinear • Is strongly manifest in the moisture field, and not a Matsuno mode of any type – it’s a “moisture mode”

33. Again: Kelvin wave driven by surface flux feedbacks (Emanuel 1987, Neelin et al. 1987) θ=θ1+Δθ θ=θ1 cool warm Enhanced sfc flux Mean flow Perturbation flow Wave propagation (via gravitational restoring force)

34. Instead we propose a moisture mode driven by surface flux feedbacks Warm θ=θ1+Δθ Mean + perturbation flow θ=θ1 Enhanced sfc flux humid dry Mean flow Perturbation flow (partly rotational) Disturbance propagation (via horizontal advection…)

35. So here is our idealized MJO model, thus far….(if I have lots of time left)

36. Vertically integrated equations for moisture and dry static energy, under WTG approximation ± is upper tropospheric divergence. Add to get moist static energy equation Substitute to get where is the “normalized gross moist stability”

37. Our physics is semi-empirical: The functional forms chosen are key components of the model - and hide much implicit vertical structure. We do explicitly parameterize at this point R = max(R0-rP, 0) with R0, r constants. Substituting into the MSE equation and expanding the total derivative, (for sake of argument assuming rP<R0) “effective” NGMS (including cloud-radiative feedback) u is the zonal wind at a a nominal steering level for W, presumably lower-tropospheric.

38. To compute u, rather than solve momentum equations, we assume the wind is a quasi-steady response to heating. Thus we compute it from a projection operator: For example, if we were to compute G by taking a longitudinal cut along the equator for a delta function forcing in the Matsuno-Webster-Gill problem with forcing centered on the equator, we get L depends on equivalent depth and damping rate. Sometimes, we cheat and shift G relative to forcing by a small amount. (in reality details sensitive to nonlinear advection, CMT…) Thus node between easterlies and westerlies shifts a little one way or the other.

39. Model is 1D, represents a longitude line at a single latitude, where the MJO is active. But we do not assume that the divergence = u/x. (there is implicit meridional structure, v/y ≠ 0) Relatedly, the mean state is not assumed to be in radiative-convective equilibrium. Rather it is in weak temperature gradient balance. Zonal mean precip is part of the solution. Implicitly there is a Hadley cell.

40. We parameterize precipitation on saturation fraction by an exponential (Bretherton et al. 2004): (with e.g., ad=15.6, rd=0.603), and R is the saturation fraction, R=W/W*. Here W*, the saturation column water vapor, is assumed constant as per WTG. We represent the normalized GMS either as a constant or as a specified function of W. NGMS is very sensitive to vertical structure and so the most important (implicit) assumptions about vertical structure are buried here.

41. Rather than use a bulk formula for E, we go directly to the simulations of Maloney et al. A scatter plot of E vs. U850 in the model warm pool yields the parameterization E = 100 + 7.5u With E in W/m2 and u in m/s. Note there is no dependence on W or SST. In practice it assures that simple model does not have very different wind-evaporation feedback than the GCM.

42. Model configuration details • 1D domain 40,000 km long, periodic boundaries • Background state is uniform zonal flow – eastward at 5 m/s; perturbation flow is added to it for advection and surface fluxes. • In simulations shown below NGMS=0.1; CRF=0.1; Wsat=70 mm; these factors largely control stability;

43. All linear modes are unstable due to WISHE, but westward- propagating Most unstable wavelength is ~decay length scale for stationary response to heating (c/ε, where ε is damping rate; here 1500 km)

44. Sometimes nonlinear disturbances resemble linear modes Saturation fraction Time longitude

45. Other times not! Saturation fraction Time longitude

46. With a small adjustment to the wind response to heating (westerlies a little further east) we get very nonlinear perturbation zonal wind; total is that plus mean 5m/s relative strength of easterlies and westerlies is tunable

47. This semi-empirical model is not a satisfactory theory for the MJO, • yet. It is a framework within which the consequences of several • ideas can be explored. • Key parameters: • The gross moist stability • Cloud-radiative feedback • Mean state – zonal wind and mean rainfall/divergence • The quasi-steady wind response to a delta function heating (G) – • very sensitive to small longitudinal shifts! • These can all - in principle - be derived from/tuned to diagnostics of • global models. • We see that very nonlinear • behavior can emerge.

48. Precipitation is an increasing and strongly non-linear function of saturation fraction of the troposphere

49. = 50-day mean, = deviation from 50-day mean • Zonal advection is in quadrature with moisture anomalies. Eastward zonal advection of moisture anomalies is supported by

50. Intraseasonal Vertically-Integrated MSE Budget • Horizontal advection is the leading term and is (nearly) in quadrature with PW and precipitation in the intraseasonal MSE budget • Latent heat flux slightly lags precipitation, and has a positive covariance with precipitation • 80-90% of MSE tendency due to latent heat component • Vertical advection causes anomalous MSE export during enhanced precipitation, although is overcompensated by LH and LW anomalies Precip LW LH+SH e.g. Neelin and Held (1987)