Moisture modes, cloud-radiative
feedbacks and the MJOAdam Sobel
Eric Maloney, Shuguang Wang, Daehyun
Kim, also bits from Jim Benedict; thanks also
Gilles Bellon, Dargan Frierson…

FDEPS, Kyoto

The Madden-Julian oscillation – a natural fluctuation of the tropicalclimateOutgoing longwave
radiation 15S-15N

Aug 2011

Blue = rainy
Orange = clear

Oct

Sep

Dectime->Nov
Janlongitude
Source: Matt Wheeler, Centre for Australian Climate and Weather Research
cawcr.gov.au

The Madden-Julian oscillation – a natural fluctuation of the tropicalclimateOutgoing longwave
radiation 15S-15NAug 2011

Blue = rainy
Orange = clear

Oct

Sep

Dectime->Nov
Janlongitude
Source: Matt Wheeler, Centre for Australian Climate and Weather Research
cawcr.gov.au

The Madden-Julian oscillation – a natural fluctuation of the tropicalclimateOutgoing longwave
radiation 15S-15N

Aug 2011

Blue = rainy
Orange = clear

Oct

Sep

Dectime->Nov
Janlongitude
Source: Matt Wheeler, Centre for Australian Climate and Weather Research
cawcr.gov.au

The Madden-Julian oscillation – a natural fluctuation of the tropicalclimateOutgoing longwave
radiation 15S-15N

Aug 2011

Blue = rainy
Orange = clear

OctSepDectime->

Nov
Jan

longitude
Source: Matt Wheeler, Centre for Australian Climate and Weather Research
cawcr.gov.au

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

time

latitudelongitude

Statistical composite low-level flow (Wheeler and Hendon 2004)

Gill (1980) low-level flow for off-equatorial heating

Zonal/vertical circulation and temperature along equator(Zhang 2005, Rev. Geophys.)The MJO is a translation of the planetary-scale zonal
overturning (Walker) circulation

1972

Madden and Julian 1971

Humidity structure in longitude and pressure(Zhang 2005, Rev. Geophys.)The MJO is an envelope for higher-frequency disturbances

Chen et al. 1996, J. Atmos. Sci.

We now have significant forecast
skill, with dynamical models
beating statistical(Kang and Kim 2009)2012

Numerical simulations are not so bad any more… but
there is no agreement on the basic mechanisms despite~4 decades of study
Surface pressure spectrum,Nauru Island, tropical PacificHelium spectral lines

wikipedia

Madden and Julian 1972

frequency

Spectral analysis shows that the MJO is not a Kelvin wave…
so what is it?

Wheeler and Kiladis 1999

wave number

Questions• What is the MJO? What are the fundamentaldynamics?
• What sets the scales: spatial scale, and frequency orphase speed?
• Why does it go eastward?
• What is the energy source?

I will argue that cloud-radiative feedbacks are
essential to the existence of the MJO.
2001

This is not a new idea (e.g., Raymond 2000, Bony andEmanuel 2005), but is probably not broadly acceptedyet.
Historically nearly all theories of transient meteorologicalphenomena (MJO, waves, TCs…) over tropical oceans
ignore cloud-radiative feedbacks.
Presumably this is because radiative cooling variationsare << convective (condensation) heating variations.
But if conserved variables (MSE, moist entropy) are whatmatter then condensation heating is irrelevant!

Observation: Intraseasonal rainfall variance is greater overocean than land. Suggests a role for net surface heat flux.
Intraseasonal rain varianceNorthern
SummerSouthern
SummerSobel, Maloney, Bellon, and Frierson 2008: Nature Geosci., 1, 653-657.Emanuel (87) and Neelin et al. (87) proposed that the MJO
is a Kelvin wave driven by wind-induced surface fluxes(“WISHE”)
θ=θ1+Δθθ=θ1cool

Perturbation flow

warm

Enhanced
sfc flux

Wave propagation

Mean flow

This idea has been somewhat abandoned because thereal MJO does not look quite like the original WISHE theory

Observed cloudiness and wind from TOGA COARE

Strongest winds and fluxes are in phase with orlag precipitation, and lie in westerlies
Chen, Houze and Mapes 1996

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

oceanShinoda et al. 1998

But the real MJO does have significant net surface heat
flux variations, roughly in phase with convection
The shortwave surface
cooling is accompanied
by atmospheric longwave
warming of similar magnitude(so in the net, radiation acts
like a surface flux)

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 convection, weʼd expect stronger ISO over ocean

Net = 0 W/m^2oceanlandIn a number of models, surface fluxes are important to the MJO– e.g. GFDL AM2 (after Tokioka fix)

control

No-WISHE(const sfcwind speed)

Sobel et al. 2010 – calculations by Dargan Frierson

In other models, radiative feedbacks are important while
surface turbulent flux feedbacks are not – but both are MSE
sourcesradiative contribution
to maintenance of MSE
anomaly

Andersen and Kuang 2011

Moisture/convection feedback

In many models (maybe all that have been tried),a weak MJO can be strengthened by making deep
convection more sensitive to free-tropospherichumidity – that is, inhibited by dry air above the PBL.

E.g., AM3 – Donner et al. (2011), Benedict et al. (2011)
Observations

ControlModified

The improvement in intraseasonal variability comes at the cost of biases,
similar to other models (Kim et al. 2011)

So, the MJO is…
• Not a Kelvin wave
• Has convection controlled by surface
fluxes and radiation• Sensitive to moistureSo, the MJO is…
• Not a Kelvin wave
• Has convection controlled by surface
fluxes and radiation• Sensitive to moistureSounds like what we call a “moisture mode”(Neelin and Yu 1994; Sobel et al. 2001; Fuchs & Raymond,
Majda & Stechmann, Kuang, Sobel & Maloney 2012, 2013)

Aside: the MJO accelerates once it reaches the Pacific, andbecomes more Kelvin-like. If there is a pure moisture mode, it’sin the Indian ocean, & maybe western-most Pacific.

By “moisture mode” we mean (at a minimum) a dynamicalmode which depends on prognostic moisture:∂T/∂t = …
∂u/∂t = …
∂q/∂t = …
not, e.g.,∂T/∂t = …
∂u/∂t = …
q = q(T)The majority of idealized tropical dynamics models are of
the latter form, truncating out the moisture mode.

Consider a moist static energy equation of the form
dh/dt=S, where S	   is sum of advection, surface fluxes,
radiation… and h is function of (x,t)

hS

If S leads h, disturbancegoes eastward

Sh

If S leads h, disturbancegoes westwardxConsider a moist static energy equation of the form
dh/dt=S, where S	   is sum of advection, surface fluxes,
radiation… and h is function of (x,t)

h
If S is in phase withh, disturbance growshSS
If S is out of phasewith h, disturbancedecaysxA semi-empirical moisturemode theory

Sobel and Maloney 2012, 2013 (JAS)The linear model in a nutshellWʼ is perturbation column moist static energy;
U is constant background wind;Pʼ = Pʼ(Wʼ) – in linear case Wʼ/¿c;Eʼ = cuʻ; zonal wind anomaly is computed diagnosticallyfrom Pʼ using projection (Green’s) function;(I’ll explain more in a moment)Rʼ = rPʼ;
Normalized gross moist stability

is constant, <1.

A note on the dynamical role of radiation,
via the single-column limit. Our MSE equation is:

Now assume steady state and neglect advection, wecan solve for precipitation:

Now we know
, maybe << 1Remember R is radiative cooling (= minus radiative heating);
So a decrease in radiative cooling leads to an increasein precipitation. This is the opposite of what happens inradiative-convective equilibrium! Dynamics changes
everything, RCE is a bad model locally.

Gill (1980) wind and geopotential for localized heating (at 0,0)linear, damped, steady dynamics on equatorial beta plane

Equatorial zonal wind responseto equatorial delta function(in x) heating

Equatorial zonal wind response(red) to sinusoidal heating (blue)- westerlies lag heatinguu

x (Ld)x (Ld)

Compute zonal wind u from precipitation P via a projection operator:

Using Gill dynamics:

Length scale L = group velocity of free Kelvin wave * damping time scale.

Now put that all together, linearize (assuming backgroundlow-level westerly winds), and compute the growth
rates and phase speeds of the normal modes as function ofzonal wave number.
If this is a good model for the MJO, we would like to see
an unstable mode (positive growth rate), maximizing at low
wave number (long wavelength), with a slow eastward
phase speed.

Linear model: all modes are unstable due to WISHE, butwestward-propagating (in mean westerlies)
Most unstable wavelength is ~decay length scale
for stationary response to heating L (here 1500 km);at this wavelength LH flux and humidity most in phase

Wind-evaporation feedback induces growth and westward
propagation; cloud-radiative feedback induces growth andno propagation

WʼEʼ

Surface flux lags convection,
thus lags moisture, so drives westward
progagation; but lags by less than ¼/2
so also causes growthWʼ
Since radiative heating~ precipitation ~ moisture,cloud-radiative feedback
is destabilizing. No phase leador lag, so doesnʼtRʼ cause propagationx

We need an MSE source that leads convection to the east,
to produce eastward propagation.
Frictional convergence in easterlies (Wang 1988) is one
possibility. We expect this to induce shallow ascent, which
is a net source of MSE, i.e.
<0.
Zonal advection will also work, if we have a +ve mean
background zonal gradient (q increases to east). Then,easterlies are moistening. We saw this in DYNAMO.
Or…

In simulations, MJO modulation of dry air advection bysynoptic-scale transients has been found to act as anomalous
MSE source that leads convection (Maloney 2009, Andersenand Kuang 2012)

latitude

synoptic-scale eddies

Dry subtropical air

MJO westerlies

MJO easterlies

Dry subtropical air
longitude

synoptic-scale eddies
suppressed byMJO-scale easterliesWe can add any of these processes to our idealized
model very crudely as an MSE source proportional to minus
MJO (ʻ) zonal wind. E.g. if ‘’ is a synoptic-scale perturbation-∂y(vʼʼqʼʼ) = -kuʼ (k>0 gives relative moistening in easterlies)We can add any of these processes to our idealized
model very crudely as an MSE source proportional to minus
MJO (ʻ) zonal wind. E.g. if ʻʼ is a synoptic-scale perturbation-∂y(vʼʼqʼʼ) = -kuʼ (k>0 gives relative moistening in easterlies)
But also surface flux is proportional to zonal wind.
Eʼ = cuʼ, so net E - ∂y(vʼqʼ) = (c-k)uʼWe can add any of these processes to our idealized
model very crudely as an MSE source proportional to minus
MJO (ʻ) zonal wind. E.g. if ʻʼ is a synoptic-scale perturbation-∂y(vʼʼqʼʼ) = -kuʼ (k>0 gives relative moistening in easterlies)
But also surface flux is proportional to zonal wind.
Eʼ = cuʼ, so net E - ∂y(vʼqʼ) = (c-k)uʼTo cause eastward propagation, the advection has tobe stronger than the surface fluxes, (c-k)<0.
In that case it also causes damping, since uʼ and Pʼ arepositively correlated.
Thus we have to make the radiative feedback strong
enough to overcome this if the mode is to be unstable –sufficiently large feedback parameter r.

If we do all this, we get eastward propagation, and largest
growth rates at shortest and longest wavelengths

If we do all this, we get eastward propagation, and largest
growth rates at shortest and longest wavelengths
Small amount of horizontal diffusion is enough to killsmall-scale instability. Then only largest scales areselected.

XSurface fluxes always lag convection; would drive MJO westward.
Radiation must be important for growth; advection for propagation.

LW flux fromatmosphere
LH flux fromsurface

What do MSE budgets look like for the real
MJO?
Results from the tropical Indian ocean during theCINDY/DYNAMO field program, by Shuguang
Wang and Daehyun Kim

Figure 1. Hovmoeller diagram of 10oS-10oN averaged
precipitable water (mm, shaded), precipitation (mm day-1,contour 10), and 850hPa zonal wind (m s-1, arrows) during theCINDY/DYNAMO period. By Daehyun Kim

Figure 2. Area-averaged (73-80oE, Eq.-5oN) time-series of a)rainfall (mm day-1), b) precipitable water (mm), and c) column
integrated MSE (x107 J m-2) (Daehyun Kim & Shuguang Wang)

MSE budget from DYNAMO: radiation ≥ surface flux

Data: sounding
array (R. Johnson,P. Ciesielski), OAflux,CERES
analysis by Shuguang Wang

Plots by Shuguang Wang

MSE budget from DYNAMO: +ve advection (esp horizontal)
leads convection in 1 case; -ve shuts it down in the other.

Data: sounding
array (R. Johnson,P. Ciesielski), OAflux,CERES
analysis by Shuguang Wang

Weekly means from
CINDY/DYNAMO period:
Column water vapor (color, mm)
850 hPa wind vector,
Precipitation (mm/d, interval 10)

Plots by Daehyun Kim

Weekly means from
CINDY/DYNAMO period:
Column water vapor (color, mm)
850 hPa wind vector,
Precipitation (mm/d, interval 10)

Plots by Daehyun Kim

Weekly means from
CINDY/DYNAMO period:
Column water vapor (color, mm)
850 hPa wind vector,
Precipitation (mm/d, interval 10)

Plots by Daehyun Kim

Reanalysis MJO composite (not DYNAMO) moist static energy
budget: horizontal advection seems to control propagation;
radiation dominant for growth
blue=composite
MSE anomaly
black=MSE
tendency terms

Data: ERA Interim

Kim, Kug and Sobel,
J. Climate, in press

Conclusions• We argue the MJO is a moisture mode.
• This means that sources and sinks of moist static
energy control both the growth and propagation ofthe mode.
• Need moistening in easterlies for eastward
propagation – has to be advection of some kind, butseveral possibilities,• Cloud-radiative feedback is necessary to destabilize
the mode. That is, the MJO wouldn’t exist without it.
• “self-aggregation of convection on the equatorial betaplane”

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