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1. Convection in the tropics and its role in wave dynamics and climate feedbacks.

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1. Convection in the tropics and its role in wave dynamics and climate feedbacks.

Richard S. Lindzen

Massachusetts Institute of Technology

Aosta

June 2007

- Some general thoughts on convection
- The role of convection in tropical waves
- The role of convection in determining tropical cloudiness and humidity

Topic 1 will be dealt with briefly, and I’ll move on to the next topic immediately.

Convection, generally refers to motion resulting from buoyancy of lighter fluid. Buoyancy, in meteorology, results from combination of humidity and temperature. The most dramatic form of atmospheric convection consists in cumulonimbi, which mostly occur in clusters, are too small to be resolved in GCMs and play major roles in carrying heat into the atmosphere, in moisturizing and drying the atmosphere, and in producing high cirrus.

Cumulus towers almost always occur in organized patterns.

With the development of serious GCMs, it was recognized that some account had to be taken of cumulus convection – especially in the tropics. The study of Riehl, H and J. S. Malkus (1958: On the heat balance in the equatorial trough zone, Geophysica, 6, 503-538) led to an accepted picture of the role of these clouds. The standard approach was to parameterize the role of the clouds. One of the most important results of Riehl and Malkus was that active cumulus towers occupy only a small percentage of the tropical area while carrying the bulk of the tropical atmosphere’s ascent.

Manabe, S., J. Smagorinsky, and R.F. Strickler, 1965: Simulated climatology of a general circulation model with a hydrologic cycle. Mon. Wea. Rev., 93, 769-798.

Kuo, H.L., 1974: Further studies of the parameterization of the influence of cumulus convection on large-scale flow. J. Atmos. Sci., 31, 1232-1240.

Arakawa, A. and W. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large-scale environment. J. Atmos. Sci., 31, 674-701.

Tiedke, M. (1989), A comprehensive mass flux scheme for cumulus parameterization in large-scale models, Mon. Weather Rev., 117, 1779–1800.

These remain the basis for most GCM parameterizations. Their emphasis was almost exclusively on replicating the role of cumulus in carrying heat into the atmosphere. However, with the current emphasis on climate, the role of convection in determining feedbacks is receiving somewhat more attention.

Lindzen, R.S., 1990. Some coolness concerning global warming. Bull. Amer. Met. Soc., 71, 288-299.

Emanuel, K. and M. Zivkovic-Rothman, 1999. Development and Evaluation of a Convection Scheme for Use in Climate Models. J. Atmos. Sci., 56, 1766-1782.

Lindzen, R.S., M.-D. Chou and A.Y. Hou, 2001. Does the Earth have an adaptive infrared iris? Bull. Amer. Met. Soc.82, 417-432.

Note, however, that even current cloud resolving models still use the primitive microphysics of Kessler or Bowen.

How should one think about atmospheric convection?

Through the 1960’s, the paradigm for most work on astro and geophysical convection was Rayleigh-Benard convection.

The basic state consisted in a constant ‘unstable’ lapse rate; however, convection was inhibited by conduction and viscosity.

Convection required that a certain Rayleigh Number be exceeded. The precise number dependend on the stress boundary conditions at the top and bottom of the domain.

Critical Rayleigh Numbers are typically around 1700, while astrophysical and meteorological values are many orders of magnitude greater. Thus, all relevant convection is essentially turbulent. The turbulence led to near neutral lapse rates in the interior, and this observation led to the notion of convective adustment: ie, one basically assumed that convection wiped out unstable lapse rates. This notion was introduced in the early 20th Century. However, the use of this approach in meteorology largely follows the work of

Manabe, Smagorinsky and Strickler (1965) and more recently of Arakawa and Schubert (1974), both of which involve determining convection on the basis of achieving equilibrated stabilities (essentially convective adjustment).

By contrast, the approaches of Kuo (1974) and Tiedke (1988) (as well as Lindzen, 1981, 1988) are based on moisture convergence driving convection.

Is the Rayleigh-Benard paradigm actually appropriate to meteorology (or astrophysics)?

Thermal convection, in these fields, tends to arise from thermal anomalies at the bottom giving rise to buoyant plumes rising into stably stratified air.

Also, in the case of cumulus convection, the convective plumes are typically concentrated in area, and accompanied by broad areas of subsidence.

This gave rise to the notion of penetrative convection.

In a number of ways, the most elegant implementation of this notion was in the work on the diurnal boundary layer over land and its role in pollution:

Tennekes, H., 1973: A model for the dynamics of the inversion above a convective boundary layer, J. Atmos. Sci., 30, 558-567.

Sarachik (1975, 1985) attempted to apply Tennekes’ ideas to tropical convection.

a again taken as 0.2

Sarachik’s picture provided a useful framework for looking at tropical convection:

1. It quantitatively predicts the height and magnitude of the trade inversion:

2. It provides a rationale for the relative independence of dynamics above and below the trade inversion as invoked by Lindzen and Nigam (1987. On the role of sea surface temperature gradients in forcing low level winds and convergence in the tropics. J. Atmos. Sci., 44, 2418-2436) among many others.

The interaction of the trade wind boundary layer with deep convection through the influence of subsidence from deep convection on the trade wind inversion remains a relatively unexplored approach to a unified theory of tropical convection. However, there are reasons for supposing that trade cumuli and deep cumulus can profitably be treated separately.

The physics of the mixed layer, the trade cumulus layer and deep cumulus are meaningfully different.

This brings us to the matter of deep cumulus convection. As noted, there are a number of approaches – mostly developed 30 years ago. Some, such as convective adjustment (Manabe, et al) and Arakawa and Schubert (1974) involve equilibrating adjustments of the convection and the mean stratification. Others such as Kuo, Tiedke, and Lindzen involve moisture budgets. Such choices, while important, are mostly irrelevant to the following discussion.

Note that s is essentially linear in p.

The gross earlier picture tends to disguise the details of the trade inversion structure.

The primary task of cumulonimbus parameterization is the determination of the cumulus mass flux, Mc.

Some important relations:

The above defines s convection.

This term is essentially zero by definition

This term is the cumulus heating

Interpretation of cumulus heating:

Part of w comes from ascent in cumulus towers which does not contribute to adiabatic cooling, and hence, represents effective heating in the energy equation.

= LP

- In terms of modeling heating distributions, the preceding was reasonably successful. However, there are serious shortcomings:
- It is not clear what gives rise to low level convergence. Convection, itself, could provide this.
- No serious attention was devoted to cloud microphysics. As a result, this, like most traditional parameterizations, was relatively useless for modeling the impact of cumulus convection on cirrus outflow or the moisture budget. (Emanuel and Zivkovic, 1999)
- There are numerous additional problems. In particular, parameterizations like those of Arakawa and Schubert suggest that Mc is strongly influenced by convergence above the boundary layer.

However, the first two items above, will be central to my next two lectures.

Some observational considerations:

Let the precipitation in ITCZ = P. This is then roughly the amplitude of the oscillations in P associated with tropical waves and even squalls (or clusters). Most of P in the ITCZ is associated with convergence which appears to be driven by relatively steady surface temperature gradients. However, the waves often do not seem to provide the convergence needed to reorganize all of P. This suggests that for transients, triggering may be occurring for which the convection, itself provides the requisite convergence.

In recent years, the notion of convective inhibition energy (CIN) has become popular. Mapes (2000) Convective Inhibition, Subgrid-Scale Triggering Energy, and Stratiform Instability in a Toy Tropical Wave Model, J. Atmos. Sci., 57, 1515-1535.

- The situation is not so different from the laboratory observation for Benard convection: one can determine any plan form for convection (triangles, squares, hexagons, etc.) by placing almost imperceptible dents in the bottom plate. The dents do nothing to the overall convection, but they profoundly alter its organization.
- With respect to tropical convection, the situation is somewhat similar. Ultimately, convection is determined by evaporation, but the organization of the convection responds to both large scale convergence (via the return flow of the Hadley-Walker circulations) and triggering in connection with waves.
- Numerous questions remain:
- Why does cumulonimbus convection seem to be organized by large scale steady convergence, but triggered by waves. Here, the answer may be trivial: namely, any amount of convergence might trigger convection, but if the convergence is sufficient, the clouds don’t have to provide more.
- Why is spectrum bimodal in many regions but not others?
- How do microphysical processes influence the structure and role of convection?
- Cumulonimbus convection is usually organized into clusters; is this intrinsic to their behavior and function?

As will be seen in the next two lectures, applications are helpful in presenting insights into the basic issues of cumulus parameterization.