Axisymmetric QTCM2 prototype – a survey of recent results Adam Sobel, Gilles Bellon, David Neelin Convection Workshop, Oct Harvard, 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) = v 1 (x,y,t)V 1 (p) + v 0 (x,y,p,t)V 0 (p) No boundary layer. We added an explicit boundary layer, fully prognostic in temperature, humidity, momentum. This allows all the 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: ptpt pbpb 0 0 q b b (z) b 1 (z) 0 T a b (z) a 1 (z) 0 v V b (z) V 0 (z) V 1 (z) v(t,y,z) = v 0 (t,y)V 0 (z) + v 1 (t,y)V 1 (z) + v b (t,y)V b (z) T(t,y,z) = T ref (z) + T 1 (t,y)a 1 (z) + s b (t,y)a b (z) q(t,y,z) = q ref (z) + q 1 (t,y)b 1 (z) + q b (t,y)b b (z) ptpt pbpb 0 Mass conservation: ( p t - p b ) ∂ y v 0 (t,y) =- p b ∂ y v b (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.

psps pepe ptpt  b b 00 11 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 mode structures for vertical velocity

The ITCZ precipitation is very sensitive to the horizontal diffusivity of free-tropospheric humidity. These are calculations over an idealized SST distribution on 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 ITCZ between 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 1980 Time latitude 2. Intraseasonal oscillations

29 -2 SST y (thousands of km) y0y 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 = SST Eq - Δ SST [(1-k) sin 2 (lat) + k sin 4 (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 Latitude of maximum precipitation 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 Latitude of ITCZ 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 There is both northward and eastward propagation

Mean states Results: two limit cycles CMAP July, 80E-90E Limit Cycle 2 Limit Cycle 1