Vertical Structure of
the Atmospheric Boundary Layer
in Trade Winds
Yumin Moon
MPO 551
September 26, 2005
Papers to Present
• Riehl, H., Yeh T. C., Malkus J. S., and La Seur,
N. E., 1951: “The Northeast Trade of the Pacific
Ocean”. Quarterly Journal of the Royal
Meteorological Society. 77, 598-626.
• Augstein E., Schmidt, H., and Ostapoff, F., 1974:
“The Vertical Structure of the Atmospheric
Planetary Boundary Layer in Undisturbed Trade
Winds over the Atlantic Ocean”. Boundary Layer
Meteorology, 6, 129-150.
Riehl 1951
• Analyzed observations in
the Northeast Pacific
Ocean during the dry
season (July to October).
• Three weather ships, Pearl
Harbor, Hickam Field, both
in Honolulu, HI.
• Hourly surface
observations, two
radiosonde observations
per day.
Riehl 1951
• Wind Steadiness
• Air above the
Inversion Top
• Inversion Layer
• Cloud Layer
S

V
Vm
• Subcloud layer
100
• Vm = mean speed
Riehl 1951
Vertical Cross-Section of Wind Speed
Mean Vertical Distribution
of Wind Speed
Riehl 1951


0 z ( w)dz  0 s ( v)dz
z
z
Equation of Continuity,
assuming steady state
Vertical Distribution of Divergence
Riehl 1951
• “Whereas the inversion
ascends downstream,
individual columns
descend, shrink
vertically and spread
horizontally. Large
masses of air, located
above the inversion at
32N have become a
part of the cloud layer
when they reach
Honolulu, HI”.
Riehl 1951
• The air that has been
incorporated in the
inversion layer
• The air that has been
incorporated in the
cloud layer
• The air that has been
below the inversion
throughout the journey
from 32N.
Riehl 1951
Riehl 1951
Riehl 1951
Riehl 1951
Equation of Continuity for Latent Heat in a layer of unit thickness and cross-section
and extending over the distance ds
L


 A q
( qv)ds  L  ( qw)ds  L   (
)ds  L  ( E  P)ds  0
s
z
z  z
Horizontal
Vertical
Turbulent
Exchange
Source/Sink
•
Steady-state is assumed.
•
Lateral mixing is neglected compared to vertical mixing.
•
The vertical coordinate is attached to the trajectory of the mean
motion  w vanishes everywhere thus the second term (vertical) is
dropped out, except at the top where the boundary is a horizontal
surface.
Riehl 1951
Riehl 1951
• Rise of the inversion is
accomplished through the pickup of
latent heat by the trade in the
course of its passage over the
tropical ocean.
• The bases of cumulus clouds are
nearly uniform height, but the tops
are very irregular.
• The tops of the cumulus clouds
break off and evaporate quickly.
• Moisture is introduced into the
lower portions of the inversion
layer.
• Then the air in the inversion layer
becomes gradually similar to the
characteristics of the cloud layer.
Riehl 1951
 1 p

dv
Equation of momentum
 
 f 
dt
  s


 ( v)
p
 div ( vv )    f
t
s
  v 
f   
z  z 
Integrating over a volume bounded by ds, dz,
and of unit thickness in the direction normal to s


 p


vdsdz

div
(

v
v
)
dsdz



f

dsdz



t
 s



 vvdz  vvdz   vwds  vwds   ( pu  pd )dz   (
u
d
Inflow term
upstream,
downstream
t
b
Inflow term
top, bottom
Pressure
Term
v
v 
)t  (  )b ds  0
z
z 
Turbulent term
top, bottom
Riehl 1951
In units of 10^8 G CM SEC^-2
Layer
(mb)
Inflow
Outflow
Net
Upstream Downstream
Inflow Outflow Net
Top
Bottom
Pressure Turbulent
Term
Term Bottom
Turbulent
Term Top
1020960
-0.3
-0.2
-0.1 0
0
0
-2.7
4.4
-1.6
960880
-0.4
-0.4
0
-0.1
0
-0.1 -2.6
1.6
1.1
880800
-0.4
-0.4
0
-0.1
-0.1
0
-1.2
-1.1
2.3
800720
-0.4
-0.3
-0.1 -0.1
-0.1
0
0
-2.3
2.4
Augstein 1974
• Analyzed observations
collected during the Atlantic
Expedition 1965 Sep 12 to
Oct 11 and the Atlantic
Tradewind Experiment
(ATEX) 1969 Feb 6-21.
• Three ships, Planet at the
northeast, Discoverer at
the northwest, and Meteor
at the south.
• 8 radiosondes observations
per day, radar wind
measurements.
Augstein 1974
• Surface Layer – adiabatic temperature gradient, decrease
of specific humidity with height, slight statical instability.
• Mixed Layer – adiabatic temperature lapse rate, nearly
constant vertical specific humidity.
• Transition Layer – nearly isothermal temperature
distribution, strong upward decrease of moisture.
• Cloud Layer – temperature gradient slightly higher than the
moist adiabatic lapse rate, upward weak decrease of
specific humidity, conditionally unstable.
• Trade Inversion – increasing temperature, steep decrease
of moisture.
Augstein 1974
Augstein 1974
 Increasing cumulus
convection causes an
increase of downward
flux of inversion air into
the cloud layer, thus
pushing the inversion
upward. This process is
combined with downward
heat flux which effects a
diabatic warming of the
cloud layer.
• Strong convective activity
destroys the trade
inversion; the organized
cloud circulation then
transports air parcels with
relatively low potential
temperature upward and
with high potential
temperature downward.
This process results in a
diabatic warming of the
lower part of the cloud
region and in a diabatic
cooling of the upper part
Augstein 1974
Augstein 1974
Augstein 1974