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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