MJO Dynamics(we think it’s a moisture mode somehow destabilized by surface fluxes and moving eastward in mean westerlies)

With: Eric Maloney, Gilles Bellon, Dargan Frierson, Daehyun Kim

Adam Sobel

RSMAS, U. Miami, March 23 2011

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)

The tropical atmosphere has strong, coherent variability onthe intraseasonal (30-60 day) time scale

time

longitude

Equatorial outgoing longwave radiation, a measureof deep, high cloudiness (shading) – annual cycle & ENSO removed

The “Madden-Julian oscillation” (MJO) propagates eastwardin a belt around the equator

Statistical composite MJO in outgoing longwave radiation and lower tropospheric wind (Wheeler and Hendon 2004)

time

longitude

Climate models’ simulations of intraseasonal variability are flawed, but improving (and can be improved even more today, at a cost)

Lin et al. 2006intercomparison of modelsused in CMIP3/IPCC AR4

But there is no agreement on the basic mechanisms despite ~3 ½ decades of study

Surface pressure spectrum,Nauru Island, tropical Pacific

Madden and Julian 1972

Helium spectral lines

wikipedia

Intraseasonal rain variance

NorthernSummer

SouthernSummer

Variance of rainfall on intraseasonal timescales shows structure on both global and regional scales

Sobel, Maloney, Bellon, and Frierson 2008: Nature Geosci., 1, 653-657.

Intraseasonal OLR variance (may-oct)

Climatological mean OLR (may-oct)

Climatological patterns resemble variance, exceptthat the mean doesn’t have localized minima over land

Intraseasonal OLR variance, nov-apr

Climatological mean OLR, nov-apr

Climatological patterns resemble variance, exceptthat the mean doesn’t have localized minima over land

The main difference between land and ocean is thatthe total surface heat flux is small over land but can belarge (or small) over ocean.

The fact that intraseasonal variations in rainfallare large over ocean and small over land suggeststhat variations in the total surface heat flux play an important role in generating the intraseasonal rainfallvariations.

Latent and radiative components of the total surfaceheat flux probably play ~comparable roles.

Wave propagation

Mean flowPerturbation flow

Enhanced sfc flux

Emanuel (87) and Neelin et al. (87) proposed that the MJOis a Kelvin wave driven by wind-induced surface fluxes (“WISHE”)

θ=θ1+Δθ

θ=θ1

cool warm

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 orlag precipitation, and lie in westerlies

Frequency-wavenumber OLR plot (Wheeler and Kiladis 1999) – MJO not a “convectively coupled” extension of any dry linear mode

Shinoda et al. 1998

ocean

But the real MJO does have significant net surface heat flux variations, roughly in phase with convection

Shinoda et al. 1998

ocean land

Net = 0 W/m^2

Over land, there can be no significant net flux variationson intraseasonal time scales - so if net flux were importantto ISO, the observed variance maps should look as they do!

It is observed that net TOA radiative influence of high cloudsis small – shortwave and longwave components cancel.

Thus cloud-induced shortwave reductions at the surface areaccompanied by ~equal reductions in tropospheric radiativecooling (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 fluxchanges associated with the MJO is a more subtle matter – butthey appear to be of comparable magnitude.

Note on the relevance of total surface energy flux (includingshortwave) to the atmosphere

In a numerical model, it is straightforward to test whethersurface flux feedbacks are important to the simulated MJO.They can be disabled by replacing some component of thesurface flux – e.g., latent heat flux, or the surface wind speedwhich controls it – by a climatology in the relevant modelparameterization. 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 feedbacksis important.

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)

“bad model”“good model”

But actually it can be shown that both versions of this model are bad – thephase relationship between wind and precipitation anomalies is wrong

Calculations by Daehyun Kim,Columbia U.

control

no-WISHE no-WISHE

control

Obs lag-corrprecip

Bad phase relationship betweenconvection, winds & fluxes in this model

LH flux lag-regressioncompared to obs(w/OLR)

sfc u lag-regressioncompared to obs(w/OLR)

obs model

obs

model

And in this same model, turning off radiative feedbacks on the other hand does (mostly) kill the MJO – consistent with net surface flux argument

“bad model”“good model”

controlcontrol

no cloud-rad no cloud-rad

Summary of “mechanism denial” experiments incl. double & triple onesfor WISHE, cloud-rad feedback, & frictional CISK

Consistent results: WISHE bad for MJO (in this model, for wrongreasons), cloud-rad very good for it, frictional CISK does little either way

GFDL AM2

WISHE clearly important in the GFDL AM2, after tuning to amplify the MJO

better model worse model

control

No-WISHE(const sfcwind speed)

Calculations by Dargan Frierson,U. Washington

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.

5 m/s

Maloney, Sobel, Hannah, J. Adv. Model Earth Sys.

Unfiltered precipitation (left) and winds (right) vs. longitude

GCM simulation on an aqua planet with a warm pool with amodified version of the NCAR CAM3 (E. Maloney, CSU)

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

SST Distributions Used

Zonally Symmetric

“Realistic” SST

Quarter Meridional Gradient

Mean Wind and Precipitation Variance

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Units: mm2 day-2

Intraseasonal variance peaks in regions of mean westerly flow at low-levels. Variance is stronger than observed.

Composite Precipitation and U850 (Unfiltered)

From Wheeler and Hendon (2004)

Wavenumber-Frequency Spectra (Precip)

27

30 days90 days30 days90 days

A strong spectral peak exists in the model at same zonal wavenumber and frequency as observations.

Model Observations

Composite PW Anomalies

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PW Units: mmColumn 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.

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

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

Total

PrecipU850

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

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”

Wave propagation (via gravitational restoring force)

Mean flowPerturbation flow

Enhanced sfc flux

Again: Kelvin wave driven by surface flux feedbacks (Emanuel 1987, Neelin et al. 1987)

θ=θ1+Δθ

θ=θ1

cool warm

Disturbance propagation (via horizontal advection…)

Mean flowPerturbation flow(partly rotational)

Enhanced sfc flux

Instead we propose a moisture mode driven by surface flux feedbacks

θ=θ1+Δθ

θ=θ1

Warm

Mean + perturbation flow

humid dry

So here is our idealized MJO model, thus far….

(if I have lots of time left)

Vertically integrated equations for moistureand dry static energy, under WTG approximation

± is upper tropospheric divergence. Add to getmoist static energy equation

Substitute to get

where

is the “normalized gross moist stability”

Our physics is semi-empirical:

The functional forms chosen are key components of the model - and hidemuch 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)

u is the zonal wind at a a nominal steering level for W, presumablylower-tropospheric.

“effective” NGMS (including cloud-radiative feedback)

To compute u, rather than solve momentum equations, we assumethe 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 cutalong 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.

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 weaktemperature gradient balance. Zonal mean precip is part ofthe solution. Implicitly there is a Hadley cell.

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 assumedconstant 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 structureand so the most important (implicit) assumptions about verticalstructure are buried here.

Rather than use a bulk formula for E, we go directlyto 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 onW or SST. In practice it assures that simple model does not have very different wind-evaporation feedback than the GCM.

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;

All linear modes are unstable due to WISHE, but westward-propagating

Most unstable wavelength is ~decay length scalefor stationary response to heating (c/ε, where ε isdamping rate; here 1500 km)

longitude

Tim

e

Sometimes nonlinear disturbances resemble linear modes

Saturation fraction

longitude

Tim

e

Other times not!

Saturation fraction

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/srelative strength of easterlies and westerlies is tunable

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 ofglobal models.

We see that very nonlinear behavior can emerge.

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

• = 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

• 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

hv

t

h

Precip

LH+SHvh

LW

50

SWLWSHLHhvvht

h

Intraseasonal Vertically-Integrated MSE Budget

e.g. Neelin and Held (1987)

Figure 10. Phase-longitude diagram of OLR (contour, interval-5, green-positive/purple-negative) and evaporation (shaded). a) OAflux/AVHRR, b) Tok=0, c) Tok=0/noWISHE, d) Tok=0.1,and e) Tok=0.1/noWISHE. Phases are from MJO life-cycle composite and values are 10oS-10oN averaged. The unit of OLR and evaporation is W m-2.

Figure 11. Phase-longitude diagram of OLR (contour, interval-5, green-positive/purple-negative) and 1000hPa zonal wind anomaly (shaded). a) NCEP/AVHRR, b) Tok=0, c) Tok=0/noWISHE, d) Tok=0.1,and e) Tok=0.1/noWISHE. Phases are from MJO life-cycle composite and values are 10oS-10oN averaged. The units are W m-2 and m s-1 for OLR and zonal wind, respectively.

Northward propagating intraseasonal rainbandsover India in NH summer (Nanjundiah et al. 1992)

The surface flux argument is attractive because it appears likely to work in both hemispheres and seasons

latit

ude

time

We have a “simple” axisymmetric model which produces an intraseasonal northward-propagating oscillation, robustly to parameters (like in Asian monsoon)

time

Latitude (1000’s km)

Precipitation anomaly (mm/d)

Bellon and Sobel 2008, J. Atmos. Sci., 65, 470-489.

Wind-induced sfc fluxes are crucial to the model instability.

Eq

ua

tor