Boundary-Layer Dynamics
(mostly from an observational point of view)
Margaret (Peggy) LeMone
EOL/ASP Colloquium
1 June 2009
REFERENCES: Numerous field programs
2 types: Focus on PBL structure/dynamics/turbulence (AHATS)
PBL component of more comprehensive experiment (GATE, hurricanes)
EARLY:
O’Neill, Nebraska (“Exploring the Atmosphere’s First Mile”, Lettau and Davidson (1957)
The “Kansas Experiment” (1968, SW Kansas)
MORE RECENT
Puerto Rico (1972)
AMTEX (1975)
GARP Atlantic Tropical Experiment (GATE, E Tropical Atlantic Ocean, Summer 1974)
STORM Fronts Experiment Systems Test (NE Kansas, Spring1992)
CASES-97 (SE Kansas, Spring 1997)
CASES-99 (SE Kansas, Fall 1999)
ACE (Atmospheric Chemistry Experiment (West of Tasmania, Dec. 1995)
IHOP_2002 (Southern Great Plains, late Spring 2002)
WKY-TV Tower (Oklahoma, year round, until 1980s)
CCOPE (Cooperative Convective Precipitation Experiment, Montana, 1981)
T-REX (Terrain-Induced Rotor Experiment, Owens Valley, California, 2006)
STAAARTE (Switzerland, 1999)
AND – modeling studies as well.
Definition of “Boundary Layer”
When you take off or land in an airplane, the air is
“bumpy” near the ground but gets smooth higher
up. The “bumpy” layer near the ground is the
daytime planetary boundary layer (convective
boundary layer)
Which leads to the AMS Glossary of Meteorology
Definition (paraphrased), the layer of air near the
ground that is directly affected by friction from the
ground and possibly by transport of heat from the
surface.
Different “Views” of the Convective Boundary Layer
= 10 km horizontally
64 km along perimeter of
60-km circle
Lidar aerosol backscatter
over the Pacific, west of Tasmania
(Donald Lenschow)
23 km N-S
WCR radar reflectivity
(insects) in dry CBL
29 May 2002, OK,
(Bart Geerts).
49 km E-W
DIAL Lidar water vapor and
vertical velocity in dry CBL
IHOP_2002, 7 June 2002, OK
(Chris Kiemle et al., 2007,
JTech)
Vertical Distribution of Turbulence in CBL
Turbulence kinetic energy = u2+ v2+ w2, where the lower-case letters indicate a departure
from the mean, is elevated through the CBL..
u2 and v2 maximum near the surface; w2 maximum within PBL.
1/3
U, V = horizontal wind; W = vertical wind, w* is a scaling velocity: w*   gzi w v 
zi = PBL depth.
 v 
Lenschow et al. (1980, AMTEX, JAS
Idealized PBL (1960s, pre-LES)
H
Force balance above CBL
(Northern Hemisphere)
PGF
wind vector
Coriolis + centrifugal
L
Force balance in CBL
(Northern Hemisphere)
Friction
Coriolis + centrifugal
Wind at top of PBL along
isobars (normal to pressure
gradient).
Wind at surface is
•slower,
•toward low pressure
Wind hodograph in neutral PBL
(Moeng and Sullivan, JAS, 1994)
Slowdown by friction reduces Coriolis
and centrifugal effects.
Potential temperature and mixing ratio well-mixed
Vertical Structure – Idealized CBL
(strong convective heating from the bottom, supported by LES)
Force balance above CBL
(Northern Hemisphere)
PGF
Coriolis + centrifugal
PGF
Force balance in CBL
(Northern Hemisphere)
Friction
Coriolis + centrifugal
Change in force balance with height, leads to wind turning takes place in the
entrainment layer
Surface Layer
(blue=log profile)
(red=stability correction)
(M-O theory, Paulson 1970, updated)
Sh 

u*   zh 
ln


  
sh  ,
k   z0 

1  x 2 

1  x 
1
 sh  2 ln 

ln

2
tan
x

 2 
2
 2 



T*   zh 
Th  ln     th  ,
k   zt 

1  x 2 
 th  2 ln 

 2 
Figure from Fleagle and Businger, 1963,
Adapted from Lettau and Davidson, 1957,
Exploring the Atmosphere’s Lowest Mile)
 z
x  1  
L

1
4
u*3Tv
L
kg  w ' Tv '
Semi-Idealized Equations for Wind and Virtual
Potential Temperature
Virtual potential temperature v
P
0
Horizontal wind components U and V aligned such that
x
 u ' w '
U
1 P

 fV  V U 
t
 x
z
 v ' w '
V
1 P

 fU  V V 
t
 y
z
 w ' 'v 

v
 S
 V v  
t
z
u  U  u ', etc.
Overbars and capital letters indicate averages
Assuming horizontal heterogeneity and no change in wind…
CONVECTIVE BOUNDARY LAYER
Assume horizontal heterogeneity
wind steady state
U, V and v well-mixed vertically
no sources/sinks for v
 u ' w '
U
1 P

 fV  V U 
t
 x
z
 v ' w '
V
1 P

 fU  V V 
t
 y
z
 w ' 'v 

v
 S
 V v  
t
z
Convective Boundary Layer
  u ' w ' 
z
1 P

 fV
 x
Similarly
 u ' w '    1 P 
V
 
f
2

z
z   x 
z
2
≈0
 2 u ' w ' 
z
2
0
or
=0
  u ' w ' 
z
 Fluxes vary linearly with height.
 C1
  v ' w ' 
z
 C2
and
  v' w ' 

 C
3
z
C1, C2, and C3 are constants
TOP: Idealized
LEFT: LES (shading)
with observations
10 Sept 1974 (GATE)1
-0.04 0.0
1Nicholls
0.08 0.16
RIGHT: Observed
vertical flux of alongwind component of
0.24 momentum2
et al. (GATE, 1982, QJRMS); 2Pennell and LeMone (Puerto Rico,1974, JAS)
For fair weather, light winds, w’v‘ at h ≈-0.2 w’v‘ at surface
CAUTION:
The “-0.2” rule
applies to
w’ v’ not w’ v’
h
Normalized virtual temperature flux
for four fair-weather days in GATE.2
Note that mixing-ratio and humidity-flux
profiles remain linear, but with varying
slopes.
1Nicholls
et al. (1982, QJRMS)
2Nicholls and LeMone (1980, JAS)
10 Sept 1974 (Day 253, GATE)
temperature-flux
profile, tropical East Atlantic1
Exception: growing PBL with strong shear at PBL
top (Conzemius and Fedorovich, 2006)
w ' Tv '
 w ' Tv '

0
How well does wind fit mixed-layer model?
OVER LAND (Oklahoma example)
Less shear daytime
Low-shear occur local noon
to early afternoon
OVER OCEAN (Tropical BL)
Six-month average:
2 m/s increase with height
6° veering with height (Gray 1972)
An exception: rapidly-growing PBL
Nice mixed layer for 10 March, but not
for 27 February.
Horizontal advection and wind
above PBL similar.
Shear on 27 Feb from
rapid engulfment of strong
northerly momentum
as PBL grew in bottom example.
LeMone et al. (1998, BLM,
STORM-FEST)
IMPACT OF SURFACE HETEROGENEITY:
DATA SOURCE: 50-km flight track +
surface array SE of Wichita, Kansas
Winter Wheat
(brown)
1 May 97 (CASES)
Grassland
(tan, light green)
1 May 97 (CASES)
8
+
+
G
7
+
9
WW
7-9 on grassland
A
28 May 02 (IHOP)
16 May 02 (IHOP)
A’
12 June 02 (IHOP)
14 June 02 (IHOP)
Winter Wheat Harvested ~ 15 June
Impact of Surface Heterogeneity IHOP_2002 (Summer)
A’
Land-use map
Red line = flight track
Oranges, pinks: crops
Light green: grassland
A
Summer (IHOP)
Wheat dormant (warm)
Grass green (cool)
H larger
over/downstream of
winter wheat
Fluxes are
4-km running averages
plotted every kilometer.
Longitude
Impact of Surface Heterogeneity for CASES-97 (spring)
37.5
37.4
37.3
A’
A
A and A’ – green winter wheat (brown in map)
Green and Tan – Grass (mixed dormant
and green)
H larger over/downstream of winter wheat
Also – with super-adiabatic lapse rate, higher elevations have
higher temperatures than surrounding air at same height.
Heterogeneous surface effect on horizontal winds
RWP 1-hour “Consensus” winds
Whitewater
Beaumont
Oxford
Wind (SSW 5-6 m s-1)
LeMone et al. BLM 2002
IMPACT on BL STRUCTURE:
Mesoscale Circulations in CASES-97
Large-scale subsidence
 for Eastern Track
and “Triangle Legs”
Aircraft conv/div patterns
ABLE
Radar wind
profiles
Green fetch 
cool air
Dormant fetch +
elevated heat source (fetch along ridge) 
Warm air
Heterogeneity at the top of the PBL – Clouds
heterogeneous cloud distribution
Wind + stability conditions imply
horizontal roll vortices over region to
right
Clouds streets visible only over land
(LCL high enough for clouds to form).
Similarly
Over Ocean, clouds reveal islands
1
Over land
Differences in land cover affect cloud
distribution1
•First clouds over harvested winter
wheat field in Oklahoma
•Suppressed clouds over and around
lakes
Clouds/storms form preferentially over
elevated terrain
1Rabin
et al (BAMS, 1990)
Gemini image of cloud streets over Georgia
coast.
Heterogeneity at the top of the PBL – Clouds
heterogeneous cloud distribution
1
Over land
Differences in land cover affect cloud
distribution1
•First clouds over harvested winter
wheat field in Oklahoma
•Suppressed clouds over and around
lakes
Clouds/storms form preferentially over
elevated terrain
Cumulus clouds forming over foothills
west of Boulder – there were no clouds
anywhere else.
1Rabin
et al (BAMS, 1990)
Low shear
Cumulus draw air from beneath
via buoyancy-generated pressure
forces (solenoidal circulation)
Large vertical shear at cloud base
Pressure forces generated by interaction
of updraft with shear (as well as buoyancy).
 e Lw0 dU
p0 
 dz
2 p
B

2
z
z
Where
p’ = p0sin(2/L)
w’ = -w0cos(2/L)
p’ and w’ are
departures from
layer means.
Complete Equation:
(Rotunno and Klemp,
MWR, 1982)
2
 p '   u   v   w 
 u   v 
 u   w 
 v   w  B
2          
  2    2 
  2 
  z
p

x

y

z

y

x

z

x

z

y

 

 
  

 0     
2
2
Cumulus increase subcloud vertical-velocity variance
(relative to clear-sky values)
AMTEX data and formula from Lenschow et al. (JAS)
Latitude (Degrees North)
Modulation of PBL by
waves (local origin)
a. Cu generate waves
b. Waves assume characteristics
determined by lowertropospheric environment
c. Waves modulate PBL behavior
9.4
Waves generated from other sources
can also modulate PBL motions.
8.4
23.4
23.0
22.6
Longitude (Degrees West)
Schematic: Based on Clark et al. (1986)
Data: LeMone and Meitin (1984)
The Growing PBL (14 June 2002, Oklahoma Panhandle)
Figure 8, Bennett et al., to be submitted to MWR.
The Growing PBL
PBL top growth change:
zi
 we  W
t
results from heating from below,
entrainment of air from above the boundary
layer, represented by entrainment velocity we
we 
w' s '
s
in response to buoyancy flux
and mechanical mixing
BL grows against subsiding air, represented
by mean vertical velocity W
Bennett et al. (MWR, submitted, IHOP_2002)
Surface virtual temperature flux
VERY idealized growth rate, for little shear at PBL top, no advection
v v h  w 'v 'h   w 'v 'h


t
h t
h
Where

z=h
h is PBL depth
v ≡  is the gradient above h
h
h 1  2  w 'v '0   w 'v 'h  w 'v '0
h 
h 


t 2 t


Thus, for constant flux, h ~ t1/2.
Note that here there is no entrainment
Growth by “encroachment”
(no heat mixed in from
above PBL, i.e., no
entrainment)
Entraining PBLs (still no shear) from Garratt (1992)
Start with two relationships:
vm  w ' v '0   w ' v 'h

t
h

 h
 
    wh   m
t
 t
 t
v
 h
 (1   )  w 'v '0 h
    wh  
t
h
 t

No entrainment (=v=0)
Obtain:
 w ' v '0

2
h   
2t
vm
With entrainment:
v
w ' v 'h
w '  v '0
 w '  v '0

2
 h   (1  2 ) 
2t
(same as previous slide)
Conzemius and Fedorovich (2006, JAS) discuss importance of shear; and
note that a value less than -0.2 for the ratio of buoyancy flux at h to that at
the surface is an indication of the importance of shear.
18
0
6
12
4:00 8:00 12:00 16:00 20:00
18
Signal-to-Noise Ratio
T.L.
h
super-adiabatic layer top
6:30
7:59
9:29
10:59
12:29
14:00
stable layer
top
15:30 17:00 18:33 20:22 21:30
CASES-97
Data: CASES-99, from S. Burns
Nocturnal PBL
1200
LST
2000
LST
(Schematic from Garratt (1992)
At night, cooling due to
IR radiation. Surface cools
most rapidly.
Nocturnal PBL:
Turbulence not necessarily
decrease with height
“upside-down” BL
“z-less” BL
Poulos et al. (BAMS, 2003, CASES-99)

z
Ri 
2
 U 
v 

 z 
g
Airflow at night can decouple from mean flow if sufficiently stable, or
sufficiently large.
Clear nights with light wind:
Air at low levels decoupled from synoptic
flow. Cooling  negative buoyancy
and downhill flow.
Air current flowing downhill
continues to cool, creating a
linear dependence of temperature
with elevation in the descending current.
Windy Nights
Near-surface air coupled to synoptic flow
(constant potential temperature)
Intermediate: Near-surface air
intermittently decoupled from synoptic
flow.
Top (Mahrt et al. BLM, 2001, CASES-99), Bottom (LeMone et al. JAS, 2002,
CASES-97). Also see Acevedo and Fitzjarrald, JAS, 2001)
Complex Terrain: ABL affected by the presence of terrain-forced
and diurnal flows at many spatial and temporal scales
Example of conceptual model of fair
weather evolution of ABL in mountains:
NIGHT
DAY
35
Whiteman, 2000, after Fiedler, from de Wekker
Daytime PBL – Complex Terrain (aerosols as tracers)
AL height
CBL height
1: mountain venting (elevated heat source)
2: cloud venting (clouds draw in air from below)
3: advection (local and from elsewhere)
(De Wekker)
De Wekker et al, 2004 36
Outstanding Research Problems for PBL (only a subset)
•
•
•
•
•
•
•
•
•
•
•
•
•
How to measure (at the surface): Surface energy budget, transfer of trace gases
How to measure (at the PBL top): PBL top, entrainment rate, vertical velocity
Interaction of PBL with cumulus and stratiform clouds
Anything to do with nocturnal/stable PBLs
Behavior of turbulence at small scales
Surface energy budget in complex terrain (on a slope)
Effects of surface heterogeneity
(surface properties, terrain, ocean waves, cities, wind farms, solar farms)
Dispersion of aerosols, trace gases (especially for complex terrain, stable conditions)
Interaction of mesoscale phenomena (waves, PBL mesoscale circulations)
with PBL turbulence and fluxes
Effects of chemical reactions on PBL flux and concentration profiles
Representation in models of
• surface layer (over land and ocean, especially in strong winds
• PBL
• Sub-grid turbulence
The role of PBL in the evolution of precipitation convection
(onset of convection through “recovery” of boundary layer)
Behavior of the PBL during the “evening transition”
References
Carson, D.J., 1973: The development of a dry inversion-capped convectively
unstable boundary layer. Q. J. Roy. Meteor. Soc., 99, 450-467.
Conzemius, R.G., and E. Fedorovich, 2006: Dynamics of sheared convective
boundary layer entrainment, Part I: Methodological background and largeeddy simulation. J. Atmos. Sci., 63, 1151-1178.
Garratt, J. The Atmospheric Boundary Layer, Cambridge University Press,
1992.
And articles referred to on the individual pages.