Buoyancy driven turbulence in the
atmosphere
Stephan de Roode (TU Delft)
Applied Physics Department
Clouds, Climate and Air Quality
s.r.deroode@tudelft.nl
1
Clouds, Climate and Air Quality
Harm Jonker, Pier Siebesma and Stephan de Roode
cloud-climate feedback
detailed numerical simulation
N2O
atmospheric boundary layer in the laboratory
Multi-Scale Physics
CH4
new methods for measuring emission rates
Faculty of Applied Sciences
Length scales in the atmosphere
Earth 103 km
~1mm-100mm
Landsat 60 km
65km
~mm
LES 10 km
~100m
3
courtesy: Harm Jonker
Global mean turbulent heat fluxes
4
source: Ruddiman, 2000
No single model can encompass all relevant processes
mm
10 m
100 m
1 km
Cloud
microphysics
 turbulence
Cumulus
clouds
DNS
10 km
100 km
1000 km
Cumulonimbus Mesoscale
Extratropical
clouds
Convective systems Cyclones
10000 km
Planetary
waves
Large Eddy Simulation (LES) Model
Cloud System Resolving Model (CSRM)
Numerical Weather Prediction (NWP) Model
Global Climate Model
5
DALES: Dutch Atmospheric Large-Eddy Simulation Model
Dry LES code (prognostic subgrid TKE, stability dependent length scale)
Frans Nieuwstadt (KNMI) and R. A. Brost (NOAA/NCAR, USA)
Radiation and moist thermodynamics
Hans Cuijpers and Peter Duynkerke (KNMI/TU Delft, Utrecht University)
Parallellisation and Poisson solver
Matthieu Pourquie and Bendiks Jan Boersma (TU Delft)
Drizzle
Margreet Van Zanten and Pier Siebesma (UCLA/KNMI)
Atmospheric Chemistry
Jordi Vila (Wageningen University)
Land-surface interaction, advection schemes
Chiel van Heerwaarden (Wageningen University)
Particle dispersion, numerics
Thijs Heus and Harm Jonker (TU Delft)
Contents
Governing equations & static stability
Observations, large-eddy simulations and parameterizations:
- Clear convection
- Latent heat release & shallow cumulus
- Longwave radiative cooling & stratocumulus
7
measured
vertical
temperature profile
Static stability
Q: what will happen with the air
parcel if it is vertically displaced?
z
Temperature
8
First law of thermodynamics: Conservation of energy
dq

added heat
1 
c vdT  pd  
 
internal
energy
work
cv = specific heat of dry air at constant volume (718 J kg-1K-1 at 0 oC)
T = temperature
p = air pressure
 = air density
9
Equation of state for dry air: gas law
p  R d T
Combine gas law and energy conservation
dp
dq  c pdT 

cp = specific heat of dry air at constant pressure (1005 J kg-1K-1 at 0 oC)
Rd = gas constant for dry air (287 J kg-1K-1 )
10
Hydrostatic equilibrium
dp
 - g
dz
Gas law, energy conservation and hydrostatic equilibrium
dq  c pdT gdz
Adiabatic process dq=0  dry adiabatic lapse rate
dT
g
 = - d  -9.8 K/km
dz
cp
11
measured
vertical
temperature profile
Atmospheric stability: dry air
dry adiabatic
lapse rate:
–10K/km
F
z
A dry air parcel, moved
upwards, cools according to
the dry adiabatic lapse rate.
But now it is warmer than
the environmental air, and
experiences an upward
force.
unstable
situation
for dry air
A dry air parcel, moved downwards,
warms according to the dry
adiabatic lapse rate. But now it is
cooler than the environmental air,
and experiences a downward force.
F
T
12
A dry air parcel, moved upwards,
cools according to the dry adiabatic lapse rate.
But now it is cooler than the environmental air,
and experiences a downward force.
F
F
Atmospheric stability: dry air
A dry air parcel, moved
downwards, warms
according to the dry
adiabatic lapse rate.
But now it is warmer
than the environmental
air, and experiences an
upward force.
z
stable
situation
for dry air
dry adiabatic
lapse rate:
–10K/km
measured
environmental
temperature profile
unstable
situation
for dry air
T
13
Harm Jonker's saline convective water tank
Initial state:
tank is filled with salt water
Convection driven by
a fresh water flux at the surface
14
Schematic by Daniel Abrahams
Convective water tank
15
Movie by Phillia Lijdsman
Adiabatic process dq=0  dry adiabatic lapse rate (2)
dp
dp
dq  c pdT   c pdT  RT  0

p
R d / c p
p(z) 
(z) = T(z) 

 p 0 
 cst
The potential temperature  is the temperature if a parcel would be
brought adiabatically to a reference pressure p0
16
Balloon observations at Cabauw during daytime
17
Q: what makes this case challlenging for modeling?
LES results of a convective boundary layer: Buoyancy flux
warm air going down
g
g
w' v '   w''
v

entrainment of
warm air

warm air going up
w' 
w' w'
g
w' w' w' 2 p'
 2 w'  v ' 
 w'
 2 
t
v
z
 z
x j 
2
18
Q: what is sign of the mean tendency for v?

LES results
Buoyancy flux and vertical velocity variance
w' 
w' w'
g
w' w' w' 2 p'
 2 w'  v ' 
 w'
 2 
t
v
z
 z
x j 
2
19

LES results of a convective boundary layer resolved TKE budget
E g
U
V w' w' w' 1 w' p'
 w'  v '  u' w'
 v' w'



t  v
z
z
z
 z
20

LES results
Humidity flux
Flux-jump relation:
w'q'T = -weDq
Dq
H
q
w' q'

t
z


H
 w e + w ls
t

q w eDq  w' q' z0

t
H
we and wls are of the order 1 cm s-1
21
Entrainment scaling
Large-scale subsidence
Entrainment
atmospheric
boundary layer
w'  v ' top  w e D v  Aw'  v ' sfc

we  A
w'  v ' sfc
D v
, A  0.2
H
 w e + w ls
t
22
Photograph: Adriaan Schuitmaker

Conservation of energy: saturated case
L vdq l

heat released
by condensation
c vdT
internal
energy

1 
pd  
 
work
ql = liquid water content
Lv = enthalpy of vaporization of water (2.5x106 J kg-1 at 0 oC)
23
For a moist adiabatic process, the liquid water static
energy (sl) is a conserved variable
cp T  gz  L v q l = sl  constant
sl
meteorologists
dT
g
L v dq l
 
 - s
dz
cp
c p dz
24
Atmospheric stability: conditional instability
measured
environmental
temperature profile
F
F
z
A dry air parcel, moved
upwards, cools according
to the dry adiabatic lapse
rate. But now it is cooler
than the environmental air,
and experiences a
downward force.
A moist air parcel, moved
upwards, cools according
to the wet adiabatic lapse
rate. But now it is warmer
than the environmental
air, and experiences an
upward force.
dry adiabatic
lapse rate
F
wet adiabatic
lapse rate
T
25
Atmospheric stability: conditional instability
stable
for dry and
moist air
stable
for dry air
z
possibly
unstable
for moist
air
T
26
Q: why possibly unstable for moist air?
Convective transport in Shallow Cumulus: Characteristics
Courtesy Bjorn Stevens
LES
Heus
TU Delft
27
28
Shallow cumulus movie by Thijs Heus
Stratocumulus
29
Longwave radiative flux (FL) profile in cloud

F

 1
,
net

 L


8
K
/
hr
!
!
!

t 
c

z
p
Cloud top cooling!
Turbulence in stratocumulus: LES results and observations
Nighttime
Daytime
Standard transport parameterization approach:




w
K

z
 

w

M
(

)
u








w

S

t 
z
This unwanted situation can lead
to:
•Double counting of
processes
•Inconsistencies
•Problems with transitions
between different regimes:
dry pbl  shallow cu
scu  shallow cu
shallow cu deep cu
32
How to estimate updraft fields and mass flux?
The old working horse:
Betts
1974 JAS
Arakawa&Schubert
1974 JAS
Tiedtke
1988 MWR
Gregory & Rowntree
1990 MWR
Kain & Fritsch
1990 JAS
And many more……..
Entraining plume model:
c
  (c   ) for    l , qt 
z
1 M
  
M z
1 wc2
g
 v   v 
 b wc2  aB, B 
2 z
0


M
Plus boundary conditions
at cloud base.
Downgradient-diffusion models
w' '  K 


z
K   c l E1/ 2


E
U
U  g

 u' w'
 v' w'

w'

'

w' E'  w' p' /


v
t
z
z   v
z


34
Downgradient-diffusion models

E
U
U  g

 u' w'
 v' w'

w'

'

w' E'  w' p' /


v
t
z
z   v
z

2
2 







U
U
U
V
2


u' w'
 v' w'

K


K
S





m
m
z
z 
z
z










g
g  v
w'  v '  K H
 K H N 2
  v
 v z
E 3/2
  cd
l
 l  c m,h


E
w'
E'

w'
p'
/

2K

 m z
z
E 1/ 2
N
for stable stratification
35


Analytical solutions for stable stratifications see Baas et al. (2008)
Stable boundary layer solutions
36
Turbulence and clouds:
do we care?
37
Climate Model Sensistivity estimates of GCM’s participating in IPCC AR4
Source: IPCC Chapter 8 2007
• Spread in climate sensitivity:
concern for many aspects of climate
change research, assesment of climate
extremes, design of mitigation scenarios.
What is the origin of this spread?
Radiative Forcing, Climate feedbacks,
Relative Contributions to the uncertainty in climate feedbacks
Cloud feedback
Surface albedo feedback
Water vapor feedback
Radiative effects only
Source: Dufresne & Bony, Journal of Climate 2008
Uncertainty in climate sensitivity mainly due to
(low) cloud feedbacks