NCAS Introduction to Atmospheric Science, November 2015
Boundary-layer meteorology
John King
British Antarctic Survey, Cambridge
Outline of Talk
• The atmospheric boundary layer – definition, importance
and contrasts with the free atmosphere
• Turbulence and its role in the ABL
• Structure of the ABL
Surface energy balance and its impact on the ABL
- Break for case study exercise • Measuring and modelling fluxes in the near-surface layer
The atmospheric boundary layer (ABL)
Definition: “… the layer of air directly above the Earth’s
surface in which the effects of the surface (friction,
heating and cooling) are felt directly on time scales less
than a day, and in which significant fluxes of momentum,
heat or matter are carried by turbulent motions on a scale
of the order of the depth of the boundary layer or less.”
J.R. Garratt, The Atmospheric Boundary Layer, CUP, 1992
Importance of the ABL
• Almost all human activity takes place within the ABL
• Dispersion of aerosols and gases (natural and
anthropogenic) emitted at the Earth’s surface is controlled
by ABL turbulence
• The ABL links the atmosphere to the other components of
the Earth System (oceans, cryosphere, land surface…) and
needs to be represented as a boundary condition in
numerical weather prediction (NWP), climate and Earth
System models
Free Atmosphere
- vertical transport
by advection
Synoptic and mesoscale systems
Boundary layer
-vertical transport
by turbulent mixing
Waves
Turbulence
Convection
-communicates
influence of
underlying surface
properties to the
free atmosphere
Turbulence
• Random, 3-d, vortical fluid motion
• Can be generated mechanically (shear flow
instability) or thermally (convection)
• Characterised by a cascade of energy from the
scales on which it is generated (typically tens to
hundreds of metres) down to the scales on which it is
dissipated by molecular viscosity (millimetres)
• Turbulence is diffusive – it acts to mix gradients of
scalars or momentum (analogous to Brownian motion
driving molecular diffusion)
z
+
→
T
Temperature gradient
+ turbulence
→
heat flux
• In the atmospheric boundary layer, turbulent diffusion
dominates over molecular diffusion at all but the very
smallest scales
Factors influencing the ABL
Turbulence can be generated Mechanically :
• Kinetic energy of sheared flow → eddy kinetic energy (eke)
(Shear production)
and can be generated or destroyed by Buoyancy:
• Potential energy of statically unstable flow → eke
(convection)
• eke → potential energy of statically stable flow
(mixing)
Factors influencing the ABL
Spectral density,
kS(k), log scale
kS(k)~k-2/3
Wavenumber, k, log scale
Turbulence:
is generated at large scales
cascades from large to small scales in the inertial subrange
is dissipated by molecular viscosity at very small scales
Factors influencing the ABL
Shear
Large-scale
flow
Surface
properties
Geostrophic wind
Baroclinicity
Roughness
Orography
Buoyancy
Subsidence
Advection
Radiation (LW & SW)
Albedo
Emissivity
Sfc. Temperature
Wetness
Statistical Theory of Turbulence
(Reynolds, 1895)
• Decompose flow into mean and fluctuating components:
u  u  u
w  w  w etc.
• Substitute into the Navier-Stokes equations and time-average:
Du
1 p

 fv
Dt
 x
(uw)

z
Equation for laminar flow Reynolds Stress term
So, to understand the effect of turbulence on the mean
flow, we only need to know the statistical properties of
the turbulent fluctuations
 xz   u 'w'
H    C w'T '
s
p
“Reynolds stress”
Turbulent heat flux
• Allows us to calculate fluxes from measurements of
turbulent fluctuations
• For this approach to be useful in modelling, we need
to be able to express the covariances (e.g. u′w′) in
terms of mean-flow (large-scale) variables – the
“turbulence closure problem”
Boussinesq: Concept of “eddy viscosity” (by analogy
with molecular diffusion)
u ' w'  K M u / z
• Still need to specify KM in terms of large-scale flow
Prandtl: Mixing-length hypothesis
• From dimensional analysis, KM=lv , where l is a
characteristic length scale of the turbulence (“mixing
length”) and v is a characteristic velocity. In a shear
flow, can write v= l du/dz, hence:
2
M
K  l u / z
• Still need to specify l !
Impact of stability on turbulence
Recall: turbulence can be generated mechanically and
generated or destroyed by buoyancy
The relative importance of these mechanisms can be
determined from the equation for turbulence kinetic
energy balance:
u
 u ' w'
z

Shear Production
g
w' T '
T0
Buoyancy
Prodn./Destrn.
 ...    0
Dissipation
Impact of stability on turbulence
Assuming that we can relate fluxes to gradients through
an eddy viscosity hypothesis and the eddy diffusivities
for momentum and heat are equal:
g  T 
 u 
SP  K   , BP  K  
T0  z 
 z 
2
Hence:
T
BP g z

 Ri
2
SP T0  u 
 
 z 
Richardson
Number
T
g z
Ri 
T0  u  2
 
 z 
Richardson number
Large and negative
Unstable
Buoyancy production
dominates (convection)
Small
Large and positive
Neutral
Stable
Mechanical production
dominates. Buoyancy
effects can be neglected
Buoyancy destruction
important.
Mixing suppressed
Unstable (convective) boundary layer
Free
atmos.
H=0
Capping inversion
• Strong turbulence
• BL depth 100s of m or greater
• Well mixed
• Top of BL well defined
• Downward (entrainment) heat
flux at top of BL – “stirring” of
free atmosphere by BL eddies
Radiative
heating
Mixed layer
Superadiabatic layer
H=Hs
θ
Growth of convective boundary layer
Surface heating only
z
θ
Surface heating
+ entrainment
Stable boundary layer
Free
atmos.
H=0
Heat flux,
H
• Weak, intermittent turbulence
• BL depth 10s -100s of m
• Typical eddy size << BL depth
• Not well mixed
• Top of BL not always
well-defined
Radiative
cooling
Surface-based
inversion
H=Hs
θ
ABL
Stable boundary layer – spot the BL top!
Temperature
Wind speed
and direction
DALR
Surface inversion
Low-level
jet
Richardson no.
CBL fits well with simple “box model”
concept for chemical modelling (SBL does
not – beware!)
Well-defined “lid”
Advective flux
Entrainment flux
Well-mixed concentration
within CBL (if reaction
timescale > eddy
turnover timescale)
Surface flux
Advective flux
Wind profiles through ABL
Free atmosphere
Coriolis
Pressure
gradient
ABL
Stress
divergence
U
Ug
Ug
Wind in ABL veers
(turns clockwise, in NH)
with height
Aircraft wind profiles through ABL
Top of ABL ~ 400 m
Wind speed
Wind direction
Surface Energy Balance
• We have seen that boundary layer structure is strongly
dependent on the strength of surface heating (unstable)
or cooling (stable)
• The surface heat flux is determined by the surface
energy balance – the net sum of all energy fluxes to and
from the surface
SURFACE ENERGY BALANCE
Fluxes towards surface
are positive
S↓ +S↑ +L↓ +L↑ +HS
RN
+HL +G = 0
An example of SEB influences on the ABL
A comparative study of the ABL at two (superficially)
similar Antarctic sites, Halley and Dome C
Reference: King, J. C., S. Argentini, and P. S. Anderson, 2006: Contrasts
between the summertime surface energy balance and boundary layer
structure at Dome C and Halley stations, Antarctica. Journal of
Geophysical Research, 111, D02105, doi:10.1029/2005JD006130.
Halley
Dome C
Halley and Dome C
Similarities and Contrasts
Halley
Dome C
Surface
Flat snowpack
Flat snowpack
Latitude
76oS
75oS
Elevation
12 m
3250 m
Distance from
coast
15 km
1100 km
Summer
temperature
0 to -10 degC
-30 to -40 degC
Typical cloud cover 4/8 to 8/8
0/8
Typical Dome C Sodar record
400 m
02
06
10
14
18
22
Typical Halley Sodar record
S↓ +S↑ +L↓ +L↑ +HS
+HL +G = 0
SHF at Dome C is ~ x3 that at Halley – consistent with observations of
convection at Dome C but not at Halley
S↓ +S↑ +L↓ +L↑ +HS
+HL +G = 0
Maybe this is because Dome C is higher, drier and less cloudy and therefore
receives more solar radiation? …
S↓ +S↑ +L↓ +L↑ +HS
+HL +G = 0
… but reduced downwelling longwave radiation at Dome C compensates
and the net radiation balance at the two sites is remarkably similar
S↓ +S↑ +L↓ +L↑ +HS
+HL +G = 0
The conductive heat flux through the snowpack, G, differs little at the two
stations, which just leaves the latent heat flux …
80
60
Halley diurnal cycle,
Dec. 1997
W m
-2
40
Rn
G
Hs(sonic)
Hl(bulk)
20
0
-20
-40
-60
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour (UT)
S↓ +S↑ +L↓ +L↑ +HS
RN + H
G=0
S + HL=+ 0
+H
+G
L
At Halley, most of Rn is partitioned into latent heat flux (sublimation) and
is not available to drive convection. Dome C is colder and drier, so most
Rn goes into sensible heat flux.
Break for case study exercise
Svalbard
Measuring fluxes in the near-surface layer
Recall: fluxes are the covariances of vertical velocity
fluctuations with those in u, T etc:
 xz   u 'w'
Momentum flux (stress)
H s    C p w'T '
Turbulent heat flux
Two possible approaches:
1.) Measure u’, w’, T’ etc directly and compute
covariances (“Eddy-correlation”)
2.) Use theory to derive fluxes from vertical profiles of
mean-flow quantities (also use this approach to
parametrise fluxes in atmospheric models)
Eddy-Correlation measurements
• Surface-layer eddies are small – need measurements with high
spatial (< 1 m) and temporal (> 10 Hz) resolution
• Need to choose an appropriate averaging time for calculating
covariances – long enough to get good statistics but short enough
so that mean flow can be regarded as steady (2-20 mins. usual)
• Conventional to remove (linear) trend as well as mean when
calculating turbulent fluctuations
• Instruments must be carefully levelled – but what does “level”
mean in complex terrain?
• Challenging to carry out these measurements from a moving
platform (aircraft, ship, etc.) – need to remove platform motion
Profile method - neutral surface layer
Fundamental parameters are:
z - height above the surface
 - surface stress
 - air density
giving a velocity scale “friction velocity”, u* 
Hence:
z u
  1
u* z
By analogy:
z T
  1
T* z
Where: T* = H/(ρCpu*)
 /
Wind profile - neutral surface layer
Wind shear in surface layer:
Integrate wrt z:
u u*

z z
u*
z
u ( z )  ln
 z0
Wind profile is logarithmic.
“Roughness length”, z0 , is a characteristic of the surface.
T*
z
For small temperature gradients: T ( z )  Ts   ln z
T
where Ts is the surface temperature. Roughness length for
heat, zT , may differ from that for momentum, z0
Wind profile over smooth snow
Halley, Antarctica, 5 Jan. 2006
Height, m
u*
z
u ( z )  ln
 z0
Slope gives
u*
Intercept gives
z0
Wind speed, m s-1
Effects of stability
ln(z/z0)
Unstable
Neutral
Stable
U(z)/u*
If conditions are non-neutral, the wind profile in the surface layer is no
longer logarithmic
Impact of stability on turbulence
In the (neutral)surface layer,
Hence:
And:
u u*

z z
u*3
SP 
z
g
 z w' T '
T0
BP
z


3
SP
u*
L
defines the Obukhov length, L.
z/L is an alternative stability parameter to
Ri, appropriate for the surface layer
Monin-Obukhov similarity theory
In the non-neutral surface layer:
z u
z

 m  
u* z
 L
z T
z
 T  
T* z
 L
Clearly, φ → 1 as z/L → 0 (neutral limit)
Otherwise, φ – functions have to be determined
from measurements (need eddy-correlation)
Once the φ – functions have been determined,
we have a framework for calculating fluxes from
gradients
The M-O similarity relationships have a sound
theoretical basis but only give implicit expressions for
the fluxes:
z T
z
 T  
T* z
 L
Both are functions of fluxes!
This means that fluxes have to be calculated iteratively.
For some applications (including parametrising fluxes
in NWP and climate models) this can be awkward, so
alternative explicit relationships, based on Richardson
number rather than z/L, have been developed.
Summary
• The ABL is central to many areas of atmospheric science
• The ABL is characterised by the presence of turbulence
• To understand the role of turbulence, we only need to know
its statistical properties (not the details of individual eddies)
• Turbulence, and hence the structure of the ABL, is strongly
influenced by the properties of the underlying surface and by
the large-scale flow
• Turbulent fluxes of momentum, heat, etc. can be measured
directly by eddy correlation or inferred indirectly from profile
measurements