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What controls the location and intensity of the ITCZs? Thermodynamic factors acting in a single column: SST, fluxes, temperature & humidity, etc.? Or momentum dynamics of the boundary layer, by which SST gradients control low-level convergence? (Lindzen & Nigam 1987; Tomas & Webster 1997, etc.)
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Axisymmetric QTCM2 prototype – a survey of recent results
Adam Sobel, Gilles Bellon, David Neelin
Convection Workshop, Oct 16 2009Harvard, Cambridge MA
1. QTCM2 development, mean ITCZ
Nieto Ferreira & Schubert 1997
What controls the location and intensity of the ITCZs?
Thermodynamic factors acting in a single column: SST, fluxes, temperature & humidity, etc.?
Or momentum dynamics of the boundary layer, by which SST gradients control low-level convergence?(Lindzen & Nigam 1987; Tomas & Webster 1997, etc.)
We designed a model to study the interaction of boundary layer dynamics and tropospheric thermodynamics, based on the Neelin-Zeng (2000) quasi-equilibrium tropical circulation model (QTCM).
The first QTCM had a baroclinic and barotropic mode,v(x,y,p,t) = v1(x,y,t)V1(p) + v0(x,y,p,t)V0(p)
No boundary layer.
We added an explicit boundary layer, fully prognosticin temperature, humidity, momentum. This allows allthe boundary layer momentum mechanisms to operate.
At this point we only have an axisymmetric version fully developed. (3D underway: B. Lintner, G. Bellon)
Vertical structure:
pt
pb
00 q
bb(z)
b1(z)
0 Tab(z)
a1(z)
0 vVb(z)
V0(z)V1(z)
v(t,y,z) = v0 (t,y)V0(z) + v1(t,y)V1(z) + vb(t,y)Vb(z) T(t,y,z) = Tref(z) + T1(t,y)a1(z) + sb (t,y)ab(z) q(t,y,z) = qref(z) + q1(t,y)b1(z) + qb (t,y)bb(z)
pt
pb
0
Mass conservation: (pt-pb) ∂yv0(t,y) =- pb ∂yvb(t,y)
Vertical structures: QTCM1-like, but chopped at bottom and placed on top of slab atmospheric BL. “Barotropic” & baroclinic modes orthogonal in free troposphere.
ps
pe
pt
b
01
The baroclinic mode is top-heavy and has weakly positive gross moist stability, the ABL/barotropic mode is bottom-heavy and has very negative GMS.
vertical modestructures forverticalvelocity
The ITCZ precipitation is very sensitive to the horizontal diffusivity of free-tropospheric humidity.
These are calculations over an idealized SST distributionon a beta plane, Newtonian cooling for radiation, no WISHE (Sobel & Neelin 2006)
MSE budget over the whole troposphere shows a local balance in the ITCZ between diffusion and ABL import
ABL momentum budget shows a balance near the ITCZbetween Lindzen-Nigam forcing and friction
In this model, the ABL momentum dynamics, driven by SST gradients a la Lindzen-Nigam, pushes moist static energy into the ITCZ, where deep convection (and the associated circulation) tries to get rid of it, resulting in large rainfall. The circulation is ineffective at getting rid of the energy, so an horizontal diffusion of moisture is needed to keep rainfall at reasonable values.
Important parameters are horiz. moisture diffusivity, and those related to vertical structure function profiles (these strongly influence GMS), incl. PBL depth and assumed depth of convection (level to which temp. perturbations are assumed moist adiabatic)
Some observational (& other) support for this model
• Negative (or near-zero) GMS in ITCZ (Back & Bretherton 2006)• Lindzen-Nigam picture relevant to time mean E. Pac ITCZ
(Raymond et al. 2006)• Thermodynamic influence of SST & dynamic influence of SST
gradient appear to be independent (Back & Bretherton 2009 semi-empirical models)
• Existence of “shallow circulation” shows that LN w/o some form of convective instability doesn’t lead to precip (Zhang, Nolan)
• Diffusive behavior of transient tropical eddies, with magnitude in ballpark of what we use in the model (Peters et al. 2008)
Sikka and Gadgil 1980Time
latitude
2. Intraseasonal oscillations
29
-2
SST
y (thousands of km)y0
-7-9 9
Gilles Bellon had the idea of using the axisymmetric QTCM2 to simulate the northern summer ISO – Indian monsoon active and break periods
The model is similar in some respects (but not all) to some others that have been used on this problem (B. Wang & colleagues)
The model produces a nice intraseasonal northward propagating oscillation, robustly to parameters – remarkably easy (by MJO standards)
time
Latitude (1000’s km)
Precipitation (mm/d)
Bellon & Sobel 2008a,b
obl dynamics is essential to northward propagation
growth rate period
Mixed layer depth
Wind-induced sfc fluxes are crucial to the model instability, hence dependence on ocean mixed layer depth is as we expect (e.g. S&Gildor 2003, S&Maloney 2004)
3. Multiple equilibria
SST = SSTEq - ΔSST [(1-k) sin2(lat) + k sin4(lat) ]
k = 0.6
k = 0
k = 1
We consider the axisymmetric model again on the equatorial ¯ plane, now with equatorially symmetric SST field of varying flatness, described by parameter k
k = 1
k = 0
k = 0.2
k = 0.4
k = 0.6
latitude (1000s of km)
For sufficiently flat SST profiles, there are multiple stable equilibria: one symmetric, two asymmetric (mirror images)
k = 0.6
Latit
ude
of m
axim
umpr
ecip
itatio
n
Sensitivity of the convection to free-tropospheric humidity
asymmetric equilibrium
symmetric equilibrium
control case
The multiple equilibria arise as long as convective parameterization is sufficiently sensitive to free-tropospheric humidity (large parameter ¸)
λ = 0.73
WTG SCM for the same forcing
Latitude
Subtropical minimum of precipitation in the axisymmetric model
The bifurcation in the axisymmetric model corresponds to the emergence of multiple equilibria in the SCM
Summary• In our simple model, PBL momentum dynamics
driven by SST gradients pump MSE into the ITCZ; horiz diffusion is necessary to vent it if we want a nice-looking solution
• If we allow WISHE, this model produces northward-propagating intraseasonal disturbances very robustly
• For sufficiently flat SST profiles symmetric about the equator, we get multiple equilibria, either symmetric or asymmetric ITCZ/Hadley cells
• These multiple equilibria map fairly directly onto SCM multiple equilibria
The diffusivity may represent transient eddies?
Nieto Ferreira & Schubert 1997
Peters et al. 2008
Multiple equilibria in the General Circulation Models
Hysteresis in the seasonal cycle [Chao, 2000; Chao and Chen, 2001]
Multiple regimes of the Hadley circulation for uniform, constant forcing[Chao and Chen, 2004; Barsugli et al., 2005]
[Barsugli et al. ,2005]
Solar forcing (Wm-2)
20°S
Eq
310 300 290
Latit
ude
of IT
CZ
Equatorial ITCZOff-equatorial ITCZ
Multiple equilibria in the tropical atmosphere
Is there a link between SCM and GCM multiple equilibria?
Do we find them in models of intermediate complexity?
Wang et al. 2006
There is both northward and eastward propagation
Mean states
Results: two limit cycles
CMAP July, 80E-90E
Limit Cycle 2
Limit Cycle 1