Moist formulations of the Eliassen-Palm ﬂux and their ... · Moist formulations of the...

Moist formulations of the Eliassen-Palm flux and their connection to the surface westerlies

in comprehensive and idealized GCM simulations

Paul O’Gorman, MITNovember 2016

In collaboration with John Dwyer (postdoc at MIT)

Figure: Held and Hoskins, Adv. Geophys.,1983(see also Lu et al JAS, 2010 and Donohoe et al Clim. Dyn., 2014)

12 ISAAC M. HELD AND BRIAN J. HOSKINS

150

300

mb - - -‘---W- I

I I I I

I I

I I

I ~ k A 1 1000 j-----f- - - -

45N 45N 30N 45N

DAY 1 DAY 5 DAY 8 FIG. 3. Schematic of the Eliassen-Palm flux (arrows) and divergence of this flux (contours

with plus or minus sign) at three times during the baroclinic eddy life-cycle calculation described in Section 3. The points A (45”$ 1000 mb), B (45”, 300 mb), and C (30”, 150 mb) are referred to in the text and in Fig. 4.

this stage is of quasi-horizontal propagation from mid-latitudes into the subtropics.

To add substance to this picture, estimates of particle dispersion have been computed for the three points shown in Fig. 3. For point A, near the surface at 45”N, vertical advection is negligible in the thermodynamic equation and q’ can be obtained from the temperature distribution. We define ij to be the maximum latitudinal excursion of the temperature contour centered at the latitude of interest. Curve A in Fig. 4 shows the time evolution ofijat point A. The temperature field at this level on day 6, following several days of almost exponential growth in @, is shown in Fig. 5a. The frontogenesisand occlusion process have left only a very narrow region of warm air at 45 “N. This region is eroded by the term representing sub-grid-scale mixing in the model until, by day 8, the isotherm displacement is near zero. Because of the mixing processes that have come into play, however, i j cannot be used as a measure of particle dispersion beyond day 6 .

The curves for points B and C are both obtained from the maximum latitudinal excursions on isentropic surfaces of the Ertel potential vorticity contour centered at the point of interest. At point B, the growth of ijlags that at A. It reaches a maximum soon after day 7 and declines to negligible values at day 10. Analysis shows the dynamics here to be nearly reversible, with fluid particles returning to their initial latitudes. The growth of ijat C slightly lags that at B but continues until day 8. The Ertel potential vorticity on the 3 5 0 4 isentropic surface (which passes close to C ) is illustrated in Fig. 5b. The potential vorticity field is being wrapped around a large subtropical gyre. This wrapping, or “wave breaking,” continues and generates small-scale

Schematic of baroclinic eddy lifecyleArrows: EP fluxes

Ovals: EP flux divergence

Poleward heat flux

Eliassen-Palm (EP) flux is flux of wave activity, and has been used to connect surface westerlies to

poleward heat fluxMomentum convergence

But EP fluxes typically do not account for water vaporeven though eddy latent heat fluxes important to the

general circulation…

Two approaches to including moisture in EP fluxes

Effective EP flux: Replace dry static stability with effective static stability (cf. O’Gorman, JAS, 2010)

θe EP flux: Replace potential temperature with equivalent potential temperature (cf. Stone & Salustri, JAS, 1984)

See also Yamada and Pauluis, JAS, 2016 and Chen, JAS, 2013

J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S 3

with respect to the zonal mean as denoted with an over-bar (e.g., Andrews et al. 1983). While we use this defini-tion of the EP flux when calculating our results, it is alsoconceptually helpful to consider the EP flux in the QG ap-proximation, given by

F

(f) =�acosfu0v0

F

(p) = acosf f v0q 0

qp

.(2)

The properties of EP fluxes have been discussed atlength in previous work (for example, Eliassen and Palm1961; Andrews and McIntyre 1976, 1978; Edmon, Jr. et al.1980; Tung 1986), and we summarize them here in the QGlimit for simplicity. Briefly, the EP flux is a useful diag-nostic of the propagation of waves (both magnitude anddirection) in the meridional plane. For small amplitudewaves, it represents the flux of wave activity, and its di-vergence is zero for steady conservative waves. The QGTEM momentum equation is

∂u∂ t

= f v† +F +1

acosf— ·F, (3)

where v† = v�(v0q 0/qp

)p

is the residual mean meridionalvelocity, — ·F = (acosf)�1∂f (F(f) cosf)+ ∂pF(p), andF is the zonal mean frictional force. This equation showsthat the divergence of the EP flux represents the combinedforcing of the mean zonal wind by eddy fluxes of momen-tum and heat.

The divergence of the QG EP flux is also related to theQG eddy potential vorticity flux as

— ·F = acosfv0q0, (4)

where q0 = z 0 + f (q 0/qp

)p

with z the relative vorticity.This local QG relationship assumes that the latitudinal de-pendence of the static stability and f are weak: over theeddy length scale, Dq

p

/qp

and D f/ f should be of the or-der of the Rossby number or smaller (Edmon, Jr. et al.1980). While often appropriate for the dry case awayfrom the tropopause, this assumption becomes less accu-rate when a moist static stability is used because of merid-ional humidity gradients, and this is one of the reasons weuse the full (non-QG) EP flux in all of our results.

We will see below that neither of the moist EP fluxessatisfy all of the properties that dry EP fluxes do, and onemay question whether “moist EP flux” is an appropriateterm. We follow previous authors (Yamada and Pauluis2016) in using the term “moist EP flux” because of theclose links with the dry EP flux.

a. Moist EP flux: Effective Static Stability

The first moist EP flux formulation is defined by re-placing the static stability q

p

in Eq. 1 with the effective

static stability of O’Gorman (2011). The effective staticstability approximately accounts for both the moist staticstability in regions of ascent (which are assumed to besaturated) and the dry static stability in regions of de-scent. The derivation of the effective static stability givenin O’Gorman (2011) is only valid for the eddy thermo-dynamic equation; the mean thermodynamic equation stillincludes the dry static stability and a mean latent heatingterm. Latent heat release is assumed to occur where thereis upward motion, and the resulting nonlinear dependenceof latent heating on the vertical velocity is accounted forusing an asymmetry parameter l which measures the up-down asymmetry of the vertical velocity. The parameterl is calculated as the regression of the eddy upward verti-cal velocity w"0 (a proxy for the eddy latent heating rate,where w" = w when w < 0, and w" = 0 otherwise) onthe eddy vertical velocity w 0. The regression is performedusing 6-hourly data at each latitude and level over all lon-gitudes and times, and l is found to be roughly constant inthe extratropical free troposphere with values of l ⇡ 0.6,corresponding to faster upward than downward motion.The effective static stability at a given latitude and levelis then defined as

�✓

∂q∂ p

◆

eff=�∂q

∂ p+l ∂q

∂ p

��q⇤

(5)

where q ⇤ is the saturated equivalent potential temperature,and �∂q/∂ p|q⇤ is the dry static stability for a moist adi-abatic stratification at the mean temperature and pressure.At very low temperatures, the effective static stability re-duces to the dry case since ∂q/∂ p|q⇤ tends to zero. Asthe second term on the right-hand side of Eq. 5 is neg-ative, the effective static stability is smaller than the drystatic stability, reflecting the reduced stratification that ed-dies experience in a moist atmosphere.

We define an effective QG eddy PV as q0eff = z 0 +f (q 0/(q

p

)eff)p, which leads to the same equivalence be-tween the effective QG eddy PV flux and the effective EPflux divergence as given in Eq. 4 for the dry case. Accord-ing to O’Gorman (2011), the eddy thermodynamic equa-tion written using the effective static stability has the sameform as in the dry case but without the latent heating term,and it may be combined with the eddy vorticity equation togive an evolution equation for the effective QG eddy PV.For the midlatitude beta plane and neglecting second-orderterms, this equation is ∂

t

q

0eff = �u∂xq0eff � v0(∂yq)eff + S0

where (∂y

q)eff = b + f (q y/(qp)eff)p, with b the merid-ional gradient of the Coriolis parameter, and where S0 isthe eddy tendency due to radiation and friction. The aboveequation for ∂

t

q

0eff has the same form as the dry QG eddy

PV equation, and implies a conservation equation for ef-fective wave activity (density) in the small-amplitude QGlimit: ∂

t

Aeff + — · Feff = D, where Aeff = 12 q02eff/(∂yq)eff

and D represents the tendency due to radiation and fric-tion. Similarly, the effective QG eddy potential enstrophy

Dwyer and O'Gorman, JAS, revised

Moist EP fluxes have stronger upward componentthat peaks further equatorward



200 hPa

400 hPa

600 hPa

800 hPa

2.7e+9

ERA−Interim DJF: (a) Dry

60°S 30°S 0° 30°N 60°N−5

0

5

uco

sφ [m

/s]

4.2e+9

(b) Effective

60°S 30°S 0° 30°N 60°N

6.8e+9

(c) θe

60°S 30°S 0° 30°N 60°N

200 hPa

400 hPa

600 hPa

800 hPa

3.2e+9

ERA−Interim JJA: (d) Dry

60°S 30°S 0° 30°N 60°N−5

0

5

uco

sφ [m

/s]

4.6e+9

(e) Effective

60°S 30°S 0° 30°N 60°N

8.3e+9

(f) θe

60°S 30°S 0° 30°N 60°N

FIG. 1. The time-mean EP flux (arrows) and EP flux divergence(contours) for the ERA-Interim reanalysis from 1980–2013 in DJF (toprow) and JJA (bottom row), calculated with the dry theory (a,d), with theeffective static stability (b,e) and with equivalent potential temperature(c,f). Contour intervals are 75 m2s�2 in all panels, with blue contoursindicating convergence and orange contours divergence. The horizontalarrow scale varies between panels and is given in each panel in units ofm3s�2. A vertical arrow of the same length has a flux equal to the hori-zontal arrow scale multiplied by 4.5⇥10�3 Pa m�1. Data are not plot-ted below the level at which the appropriate static stability (�∂q/∂ p,�(∂q/∂ p)eff, or �∂qe/∂ p) is smaller than 0.01 K hPa�1, as indicatedby the gray line. The red line indicates the mean level of the tropopauseusing the WMO’s lapse rate definition, and the black lines in the lowerpanels show the zonal- and time-mean surface zonal wind as measuredby ucosf at 10 m above the surface.


200 hPa

400 hPa

600 hPa

800 hPa

2.7e+9


60°S 30°S 0° 30°N 60°N−5

0

5

uco

sφ [m

/s]

4.2e+9

(b) Effective

60°S 30°S 0° 30°N 60°N

6.8e+9

(c) θe

60°S 30°S 0° 30°N 60°N

200 hPa

400 hPa

600 hPa

800 hPa

3.2e+9


60°S 30°S 0° 30°N 60°N−5

0

5

uco

sφ [m

/s]

4.6e+9

(e) Effective

60°S 30°S 0° 30°N 60°N

8.3e+9

(f) θe

60°S 30°S 0° 30°N 60°N



200 hPa

400 hPa

600 hPa

800 hPa

2.7e+9


60°S 30°S 0° 30°N 60°N−5

0

5

uco

sφ [

m/s

]

4.2e+9

(b) Effective

60°S 30°S 0° 30°N 60°N

6.8e+9

(c) θe

60°S 30°S 0° 30°N 60°N

200 hPa

400 hPa

600 hPa

800 hPa

3.2e+9


60°S 30°S 0° 30°N 60°N−5

0

5

uco

sφ [

m/s

]

4.6e+9

(e) Effective

60°S 30°S 0° 30°N 60°N

8.3e+9

(f) θe

60°S 30°S 0° 30°N 60°N


ERA-interim reanalysis 1980-2013 DJFArrows: E-P fluxes (m3/s2) Contours: convergence or divergence (75 m2/s2)

Dry Moist: Effective Moist: θe

Moist EP fluxes peak further equatorward, closer to peak in surface westerlies


Upward EP flux at 700hPaERA-interim reanalysis, annual mean

16 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S

80°S 60°S 40°S 20°S 0° 20°N 40°N 60°N 80°N

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

50.5°N54.5°S

48.3°N52.2°S

43.4°N

50.0°S

44.1°N49.7°S

Latitude

Up

wa

rd E

P F

lux

at

70

0h

Pa

[1

07 m

2s−

2P

a]

DryEffective

θe

ucosφ peak

FIG. 2. The annual mean upward EP flux at 700 hPa for ERA-Interim. The dry formulation is in blue, the effective moist formu-lation is in green, and the q

e

moist formulation is in red. The grayvertical lines represent the latitude of peak surface ucosf in each hemi-sphere. The green and red curves are only plotted where their respectivestatic stability parameters, �(∂q/∂ p)eff and �∂qe/∂ p, are larger than0.01 K hPa�1. The latitude of the peak upward EP flux is given in eachhemisphere for each formulation. In the SH, the peak was calculated forlatitudes equatorward of 70�S to avoid the peak associated with Antarc-tic topography.

Peak upward EP flux stays much closer to peak surface westerlies over seasonal cycle when moisture included


Northern or Southern HemisphereNumbers (1-12) are different monthsGFDL-CM3 historical simulation 1980-1999

Dry Moist: θe

Latitude of peak surface westerlies [u cos(lat)] Latit

ude

of p

eak

upw

ard

EP fl

ux a

t 70

0hPa


35° 40° 45° 50°35°

45°

55°

1

1

2

2

3

3

4

4

5

5

6

67

788 99

10

10

11

11

12

12

NH: r=0.97, m=0.38

SH: r=0.85, m=0.61

(a)

Dry

ER

A−

Inte

rim

35° 40° 45° 50°

1

1

2

2

3

3

4

4

5

5

6 67

7

88

9910

10

11

11

12

12

NH: r=0.99, m=0.47

SH: r=0.94, m=1.21

(b)

Effective

35° 40° 45° 50°

1

1

2

2

3

3

4

4

5

5

667

89

10

10

11

11

12

12

SH: r=0.95, m=1.14

(c)

θe

35° 40° 45° 50°35°

45°

55°

1

1

2

2

3

3

4

4

5

5

667

78

89

910

10

11

11

12

12

NH: r=0.97, m=0.49

(d)

GF

DL

−C

M3

La

titu

de

of

Pe

ak

Up

wa

rd E

P F

lux

35° 40° 45° 50°

1

1

2

2

3

3

4

4

5

5

6677 8

8 991010

11

11

12

12

NH: r=0.97, m=0.87

SH: r=0.74, m=0.50

(e)

35° 40° 45° 50°

1

1

2

2

3

3

4

4

5

5

67

89

910

10

11

11

12

12

NH: r=0.69, m=0.84

SH: r=0.81, m=0.82

(f)

2° 4° 6°

0°

4°

8°

1

1

2

2 33 44

5 5

6

6

7

7

8

8

9

91010

11 1112

12

(g)

GF

DL

−C

M3

Ch

an

ge

2° 4° 6°

1

1

2

233 4

4

5

5

6

6

7 7

8

8 99 10

1011

11

12

12

NH: r=0.65, m=1.07

(h)

Latitude of Peak ucosφ2° 4° 6°

1

1

23

3 44

5

5

678 9 10

1011

11

12

12

(i)

FIG. 4. Latitudes of peak upward EP flux at 700 hPa plot-ted against peak surface westerlies (ucosf ) for ERA-Interim over1980–2013 (a,b,c), GFDL-CM3 over 1980–1999 (d,e,f), and projectedchanges in GFDL-CM3 under the RCP8.5 scenario (g,h,i). Latitudes areshown over the seasonal cycle in the NH (blue) and SH (red) and the EPfluxes are evaluated using the dry (a,d,g), effective (b,e,h), and q

e

(c,f,i)formulations. Numbers represent the month (1 for Jan., 2 for Feb., etc.).Least-squares regression lines are plotted and the corresponding slopesm and correlation coefficients r are given in each panel, except where anull hypothesis of zero slope and independent monthly values cannot berejected at the 5% level (a two-sided t-test is used). In the q

e

panels, thelatitudes of peak upward EP flux for some months could not be foundbecause of near-zero static stabilities.


35° 40° 45° 50°35°

45°

55°

1

1

2

2

3

3

4

4

5

5

6

67

788 99

10

10

11

11

12

12

NH: r=0.97, m=0.38

SH: r=0.85, m=0.61

(a)

Dry

ER

A−

Inte

rim

35° 40° 45° 50°

1

1

2

2

3

3

4

4

5

5

6 67

7

88

9910

10

11

11

12

12

NH: r=0.99, m=0.47

SH: r=0.94, m=1.21

(b)

Effective

35° 40° 45° 50°

1

1

2

2

3

3

4

4

5

5

667

89

10

10

11

11

12

12

SH: r=0.95, m=1.14

(c)

θe

35° 40° 45° 50°35°

45°

55°

1

1

2

2

3

3

4

4

5

5

667

78

89

910

10

11

11

12

12

NH: r=0.97, m=0.49

(d)

GF

DL−

CM

3

Latit

ude o

f P

eak

Upw

ard

EP

Flu

x

35° 40° 45° 50°

1

1

2

2

3

3

4

4

5

5

6677 8

8 991010

11

11

12

12

NH: r=0.97, m=0.87

SH: r=0.74, m=0.50

(e)

35° 40° 45° 50°

1

1

2

2

3

3

4

4

5

5

67

89

910

10

11

11

12

12

NH: r=0.69, m=0.84

SH: r=0.81, m=0.82

(f)

2° 4° 6°

0°

4°

8°

1

1

2

2 33 44

5 5

6

6

7

7

8

8

9

91010

11 1112

12

(g)

GF

DL−

CM

3 C

hange

2° 4° 6°

1

1

2

233 4

4

5

5

6

6

7 7

8

8 99 10

1011

11

12

12

NH: r=0.65, m=1.07

(h)


1

1

23

3 44

5

5

678 9 10

1011

11

12

12

(i)


e


e


Dry and moist EP fluxes shift poleward by similar amount under climate change (RCP8.5 scenario)


GFDL-CM3 2080-2099 minus1980-1999Calculated for each month of the year and then averaged


Ducosf DF(p)dry DF(p)eff DF

(p)q

e

NH 2.9� 2.8� 2.4� 2.8�

SH 2.9� 1.5� 1.5 � 1.6�

TABLE 1. Poleward shifts in the latitude of peak surface westerlies asmeasured by ucosf at 10 m and upward EP fluxes in the dry, effective,and q

e

formulations at 700 hPa as projected for 21st century climatechange in GFDL-CM3. Climate change is calculated as the differencebetween 2080-2099 in the RCP8.5 scenario and 1980-1999 in the histor-ical simulation. The poleward shifts are first calculated for each monthof the year and then annually averaged.

Dry Moist θe

Shift in peak latitude of upward EP flux at 700hPa

Northern Hemisphere

Southern Hemisphere



(p)q

e

NH 2.9� 2.8� 2.4� 2.8�

SH 2.9� 1.5� 1.5 � 1.6�


e


Study moist EP fluxes over wider range of climates in idealized ‘aquaplanet’ GCM simulations

Idealized GCM simulations (see Frierson et al 2006, Frierson 2007, O’Gorman & Schneider 2008)

Idealized ‘aquaplanet’ GCM:Using moist EP fluxes weakens anomalous divergence

feature near subtropical jet


Dry Moist: θe

0.2

0.4

0.6

0.8

2.6e+9

σ

(a) Dry

30° 60°−5

05

uco

sφ [

m/s

]

5.8e+9

(b) Effective

30° 60°

1.1e+10

(c) θe

30° 60°

5.7e+9

(d) Diabatic Effective

30° 60°

FIG. 5. As in Fig. 1 but for the idealized GCM with a = 1.4 and Ds

= 1.2 (a relatively warm climate with a

global mean surface air temperature of 295 K). The EP flux formulations are (a) dry, (b) effective, (c) qe

, and

(d) diabatic effective, an alternate version of the effective formulation described in the text in Section 4. Vertical

levels are in s coordinates.

786

787

788

789

41

0.2

0.4

0.6

0.8

2.6e+9

σ

(a) Dry

30° 60°−5

05

uco

sφ [

m/s

]

5.8e+9

(b) Effective

30° 60°

1.1e+10

(c) θe

30° 60°

5.7e+9


30° 60°




, and



786

787

788

789

41

Arrows: E-P fluxes (m3/s2) Contours: convergence or divergence (75 m2/s2)Global mean surface air temperature 294K

0.2

0.4

0.6

0.8

2.6e+9

σ

(a) Dry

30° 60°−5

05

uco

sφ [

m/s

]

5.8e+9

(b) Effective

30° 60°

1.1e+10

(c) θe

30° 60°

5.7e+9


30° 60°




, and



786

787

788

789

41

0.2

0.4

0.6

0.8

2.6e+9

σ

(a) Dry

30° 60°−5

05

uco

sφ [

m/s

]

5.8e+9

(b) Effective

30° 60°

1.1e+10

(c) θe

30° 60°

5.7e+9


30° 60°




, and



786

787

788

789

41

(cf. Birner et al, 2013)

Potential enstrophy analysis: anomalous divergence is dry wave activity source due to condensational heating in this idealized GCM

Idealized ‘aquaplanet’ GCM:Using moist EP fluxes weakens anomalous divergence

feature near subtropical jet

Dry Moist: θe

0.2

0.4

0.6

0.8

2.6e+9

σ

(a) Dry

30° 60°−5

05

uco

sφ [

m/s

]

5.8e+9

(b) Effective

30° 60°

1.1e+10

(c) θe

30° 60°

5.7e+9


30° 60°




, and



786

787

788

789

41

0.2

0.4

0.6

0.8

2.6e+9

σ

(a) Dry

30° 60°−5

05

uco

sφ [

m/s

]

5.8e+9

(b) Effective

30° 60°

1.1e+10

(c) θe

30° 60°

5.7e+9


30° 60°




, and



786

787

788

789

41

0.2

0.4

0.6

0.8

2.6e+9

σ

(a) Dry

30° 60°−5

05

uco

sφ [

m/s

]

5.8e+9

(b) Effective

30° 60°

1.1e+10

(c) θe

30° 60°

5.7e+9


30° 60°




, and



786

787

788

789

41

0.2

0.4

0.6

0.8

2.6e+9

σ

(a) Dry

30° 60°−5

05

uco

sφ [

m/s

]

5.8e+9

(b) Effective

30° 60°

1.1e+10

(c) θe

30° 60°

5.7e+9


30° 60°




, and



786

787

788

789

41


25°

40°

55°(a) Δs=0.4 (b) Δs=0.8

265 280 295 310

25°

40°

55°

265 280 295 310g [K]

(d) Δs=1.6

ucosφ F(p)dry F(p)eff F

(p)θe ∇⋅Fdry

F IG . 6. Peak latitudes for various quantities as a function of globalmean surface air temperature (Tg) in the idealized GCM for differentvalues of the meridional insolation gradient parameter∆s. ucosφ is thesurface westerlies,F ( p)dry is the dry upward EP flux,F

( p)eff is the upward

EP flux in the effective formulation,F ( p)θe is the upward EP flux in theθeformulation, and� · F is the anomalous region of dry EP flux divergencenear the subtropical jet. The upward EP fluxes are evaluated atσ = 0.67.

Dwyer and O'Gorman, JAS, revisedSee also Schneider, O’Gorman & Levine, 2010

Surface westerlies shift equatorward with warmingand do not follow dry EP flux!

Global mean surface temperature (K)

Latit

ude

of p

eak

Surfacewesterlies

Upward dry EP fluxat σ=0.67


25°

40°

55°(a) Δs=0.4 (b) Δs=0.8

265 280 295 310

25°

40°

55°

265 280 295 310g [K]

(d) Δs=1.6


(p)θe ∇⋅Fdry





Dry EP flux perspective:Surface westerlies align with anomalous dry EP flux

divergence feature in hot climates


Latit

ude

of p

eak

Surfacewesterlies

Upward dry EP fluxat σ=0.67

Anomalous EPflux divergence


25°

40°

55°(a) Δs=0.4 (b) Δs=0.8

265 280 295 310

25°

40°

55°

265 280 295 310g [K]

(d) Δs=1.6


(p)θe ∇⋅Fdry





Moist EP flux perspective:Peak upward EP flux is much closer to surface westerlies

(and anomalous divergence feature unimportant)

Surfacewesterlies

Dry EP flux

Moist EP flux (θe)


Latit

ude

of p

eak


Surface westerlies can be understood with moist EP flux:Combination of broad upward EP flux and transition to

poleward wavebreaking as climate warms

Cold Moderate Hot

Arrows: E-P fluxes scaled to emphasize upper troposphereBrown hatching: area of strong upward EP fluxRed: tropopause


0.2

0.4

0.6

0.8

σ

(a) Tg=270K

30° 60°−5

05

ucos

φ [m

/s]

(b) Tg=294K

30° 60°

(c) Tg=311K

30° 60°

40°60° (d)

40°60° (e)

Latit

ude

of P

eak

ucosφ F(p)dry

265K 290K 315K

40°60° (f)

Temperature (Tg)

F(p)eff F(p)θe

F IG . 9. (a-c) EP fluxes in the θe formulation and contoured hor-izontal eddy momentum flux divergence (not EP flux divergence) forthe idealized model with∆s = 1.2 and Tg of 270 K (a), 294 K (b),and 311 K (c). To emphasize horizontal wave propagation in the up-per troposphere, the horizontal components of the EP flux vectors arefirst multiplied by a factor of 15, and then the magnitudes of the vec-tors are multiplied by− logσ and then rescaled by a constant to havethe same maximum length in each panel. Yellow contours indicate eddymomentum flux convergence and purple contours indicate eddymomen-tum flux divergence with contours every 75 m2s− 2. In the lower panels,black lines show the zonal- and time-mean surface zonal wind as mea-sured byucosφ at 10 m above the surface, and solid brown lines showthe latitude of peak upward EP flux in theθe formulation atσ = 0.67with hatching indicating the meridional range over which the upwardEP flux is at least 70% ofi ts peak value. Panels (d-f) are similar toFig. 6(c), in that they show the latitude of peak surface westerlies andpeak upward EP flux atσ = 0.67 for ∆s=1.2 in the dry (d), effective(e), and θe (f) formulations, but they also show the meridional range(hatching) over which the upward EP flux is at least 70% ofi ts peakvalue.

Conclusions

• Moist EP fluxes are stronger and peak further equatorward than conventional dry EP fluxes

• Advantages:

- Tighter connection to surface westerlies over seasonal cycle

- Make it easier to understand surface westerlies in idealized GCM

• Idealized GCM simulations illustrate how moisture can influence wave-mean flow interaction

Peak upward EP flux stays much closer to peak surface westerlies over seasonal cycle when moisture included


Northern or Southern HemisphereNumbers (1-12) are different monthsGFDL-CM3 historical simulation 1980-1999


Latitude of peak surface westerlies (u cos(lat)) Latit

ude

of p

eak

upw

ard

EP fl

ux a

t 70

0hPa


35° 40° 45° 50°35°

45°

55°

1

1

2

2

3

3

4

4

5

5

6

67

788 99

10

10

11

11

12

12

NH: r=0.97, m=0.38

SH: r=0.85, m=0.61

(a)

Dry

ER

A−

Inte

rim

35° 40° 45° 50°

1

1

2

2

3

3

4

4

5

5

6 67

7

88

9910

10

11

11

12

12

NH: r=0.99, m=0.47

SH: r=0.94, m=1.21

(b)

Effective

35° 40° 45° 50°

1

1

2

2

3

3

4

4

5

5

667

89

10

10

11

11

12

12

SH: r=0.95, m=1.14

(c)

θe

35° 40° 45° 50°35°

45°

55°

1

1

2

2

3

3

4

4

5

5

667

78

89

910

10

11

11

12

12

NH: r=0.97, m=0.49

(d)

GF

DL

−C

M3

La

titu

de

of

Pe

ak

Up

wa

rd E

P F

lux

35° 40° 45° 50°

1

1

2

2

3

3

4

4

5

5

6677 8

8 991010

11

11

12

12

NH: r=0.97, m=0.87

SH: r=0.74, m=0.50

(e)

35° 40° 45° 50°

1

1

2

2

3

3

4

4

5

5

67

89

910

10

11

11

12

12

NH: r=0.69, m=0.84

SH: r=0.81, m=0.82

(f)

2° 4° 6°

0°

4°

8°

1

1

2

2 33 44

5 5

6

6

7

7

8

8

9

91010

11 1112

12

(g)

GF

DL

−C

M3

Ch

an

ge

2° 4° 6°

1

1

2

233 4

4

5

5

6

6

7 7

8

8 99 10

1011

11

12

12

NH: r=0.65, m=1.07

(h)


1

1

23

3 44

5

5

678 9 10

1011

11

12

12

(i)


e


e


Dry and Moist EP fluxes shift poleward by similar amount under climate change (RCP8.5 scenario)


GFDL-CM3 2080-2099 minus1980-1999Calculated for each month of the year and then averaged



(p)q

e

NH 2.9� 2.8� 2.4� 2.8�

SH 2.9� 1.5� 1.5 � 1.6�


e


DryMoist:

EffectiveMoist: θe

Shift in peak latitude of upward EP flux at 700hPa

Northern Hemi.

Southern Hemi.

Idealized ‘aquaplanet’ GCM:Using moist EP fluxes weakens or removes anomalous

divergence feature near subtropical jet



0.2

0.4

0.6

0.8

2.6e+9

σ

(a) Dry

30° 60°−5

05

uco

sφ [

m/s

]

5.8e+9

(b) Effective

30° 60°

1.1e+10

(c) θe

30° 60°

5.7e+9


30° 60°




, and



786

787

788

789

41

0.2

0.4

0.6

0.8

2.6e+9

σ

(a) Dry

30° 60°−5

05

uco

sφ [

m/s

]

5.8e+9

(b) Effective

30° 60°

1.1e+10

(c) θe

30° 60°

5.7e+9


30° 60°




, and



786

787

788

789

41

Idealized GCM simulation (cf. Frierson et al 2006, Frierson 2007, O’Gorman & Schneider 2008)Arrows: E-P fluxes (m3/s2) Contours: convergence or divergence (75 m2/s2)Global mean surface air temperature 294K

(Different from what Birner et al, 2013 found for ERA-interim)


0.2

0.4

0.6

0.8

2.6e+9

σ

(a) Dry

30° 60°−5

05

uco

sφ [

m/s

]

5.8e+9

(b) Effective

30° 60°

1.1e+10

(c) θe

30° 60°

5.7e+9


30° 60°




, and



786

787

788

789

41

0.2

0.4

0.6

0.8

2.6e+9

σ

(a) Dry

30° 60°−5

05

uco

sφ [

m/s

]

5.8e+9

(b) Effective

30° 60°

1.1e+10

(c) θe

30° 60°

5.7e+9


30° 60°




, and



786

787

788

789

41

Potential enstrophy analysis suggests anomalous divergence is dry wave activity source due to condensational heating in this idealized GCM

Idealized ‘aquaplanet’ GCM:Using moist EP fluxes weakens or removes anomalous

divergence feature near subtropical jet

Moist formulations of the Eliassen-Palm ﬂux and their ... · Moist formulations of the...

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