Diabatic processes in the tropics - An introduction

Christian Jakob School of Earth, Atmosphere and Environment, Monash University

The Tropics

The Tropics

The Tropics

The Tropics

The Tropics

What do we mean by diabatic processes?

Let’s define the dry static energy as:s = cpT +gz

We can then rewrite the first law of thermodynamics as:dsdt

= Q

Combining this equation with the continuity equation yields the flux form as:

∂(rs)∂t

+— · (r~vs) = rQ

We write all variables as spatial averages and deviations from that average, e.g.,

Substituting in the flux form equation, neglecting density variations and taking the average again yields:

s = s+ s0

∂(rs)∂t

= �∂(rus)∂x

� ∂(rvs)∂y

� ∂(rws)∂z

� ∂(ru

0s

0)∂x

� ∂(rv

0s

0)∂y

� ∂(rw

0s

0)∂z

+rQ

resolved terms small-scale horizontal fluxes

small-scale vertical

fluxsources

Average over an area (say 100 km or so)

The small-scale horizontal fluxes are small compared to the vertical flux and usually neglected. This leaves us with:

small-scale vertical flux divergence

sources

�∂(rw0s0)∂z

and+rQ = +r(Qrad +C +E)

radiation evaporationcondensation

Similar small-scale flux terms appear in the moisture and momentum equations.

The “diabatic” terms

Tropical convection

What do diabatic processes do?

Radiation

Turbulence

PBL Turbulence

Convection

In convective regions these terms will be dominated by convection

Large-scale effects of convection - Q1 and Q2

Averaged thermodynamic equation (in dry static energy)

“large-scale” terms “small-scale” terms

∂s∂t

+~vh—s+w∂s∂z

= Qrad +L(c� e)� 1r

∂(rw0s0)∂z

Large-scale effects of convection - Q1 and Q2

This quantity can be derived from observations of the “large-scale” terms on the l.h.s. of the area-averaged equations and describe the influence of the “sub-grid”

processes on the atmosphere.

Define:

Apparent heat source

Analogous:

Apparent moisture sink

Note that:

with Moist static energy

Q1 = Qrad +L(c� e)� 1r

∂(rw0s0)∂z

Q1�Q2�Qrad = �1r

∂(rw0h0)∂z

Q2 = L(c − e)+Lρ∂ ρ ′w ′q( )

∂z

Q1 and Q2 examples

Heating and the tropical circulation

Response to idealised heating on the equator in a simple model

Gill, 1980

w and horizontal wind

Streamfunction

SLP and Wind

Stratiform processes

Organised convection

Organised convection

Convective vs stratiform processes

Equilibria

Shallow convectionThermodynamic structure of the trade-cumulus boundary layer

Emanuel, 1994

Shallow convection

Basic physics of the trade-cumulus boundary layer

Emanuel, 1994

Convective quasi-equilibrium

GARP Atlantic Tropical Experiment (1974)

Thompson et al., JAS, 1979

Wave composite vertical motion Wave composite temperature anomaly

Convective quasi-equilibrium

GARP Atlantic Tropical Experiment (1974)

Thompson et al., JAS, 1979

v (700 hPa)

−ω (700 hPa)

Precipitation

The importance of organised convection

Location of convective and stratiform precipitation

Location of organised vs “pop-corn” convection

Organised

Not organised

Contribution to rainfall

Organised Not organised All

Contribution to rainfall trendsTotal trend

(1998-2009)

Frequency of org. convection

Intensity of org. convection

All other convection

Thank you