Transcript Surface Exchange Processes

Surface Exchange
Processes
SOEE3410 : Lecture 3
Ian Brooks
Turbulence
• The exchange of energy and trace gases at the
surface is achieved almost entirely via turbulent
mixing.
• Wind is generated on large scales by spatial
differences in atmospheric pressure (ultimately
resulting from radiative heating/cooling)
• Kinetic energy of wind is dissipated at small
scales by friction (and ultimately as heat)
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Sources of Turblence
• Friction: mechanical
generation of turbulence
z
– Flow over rough surface /
obstacles
– Small perturbations of the
flow act as obstacles to the
surrounding flow
– Shear in the flow can result
in instability & overturning
• Turbulence results in a
wind speed profile that is
close to logarithmic
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Wind speed
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• Convection:
– heating of air near the
surface (or cooling of air
aloft) increases
(decreases) its density with
respect to the air around it,
so that it becomes buoyant.
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Large Eddy Model simulation of convective mixing
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Turbulent Fluxes
• The turbulent flux of some quantity x
(momentum, heat, CO2,…) is defined as:
Flux of x
= 1 (w′1x′1 + w′2x′2 + …w′Nx′N)
N
= w′x′
Where w′N = wN – w
And an overbar signifies an average
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• For example, the wind stress
at the surface (the vertical flux
of horizontal momentum) is
   wU '
where  is air density, and U
the wind speed. More strictly it
is

2
   wu '  wv
2

1
• The wind stress is frequently
represented by the friction
velocity
u* 

1
2

2
where u is the wind component
in the direction of the mean
wind direction and v the
component perpendicular to
the mean wind.
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Flux Parameterizations
• Measurement of turbulent fluxes is possible only on
small scales, using expensive instrumentation.
• Large-scale climate models do not include small-scale
processes such as turbulence directly; they must
parameterize the effects of turbulence in terms of largescale mean quantities:
– Mean wind speed
– Temperature difference between surface and a given altitude
– Within the surface layer turbulent fluxes are almost constant
with altitude
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u*  z 
U ( z )  ln 
k  z0 
z
U
U = mean wind speed
Z = altitude
k = von-Karman’s constant (0.4)
zo = the roughness length – a measure
of the roughness of the surface; the
altitude at which the mean wind
speed falls to zero.
u* = the friction velocity – a measure of
how variable (turbulent) the wind
speed is in the direction of the mean
wind.
Wind speed
= (w′u′)½
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Similar relationships describe the
shape of vertical profiles of scalar
quantities such as temperature,
water vapour concentration, and
gas concentrations. e.g:
T*  z 
T  Ts  ln 
k  z0 
• The sensible heat flux, QH is
given by:
QH  C pu*T*
where  is the air density and
Cp is the specific heat capacity
of air at constant pressure.
Where Ts is the surface
temperature and T* is a measure
of how variable the temperature
is.
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Bulk Transfer Schemes
The vertical flux F of any quantity,
, is assumed to be driven by its
vertical gradient, approximated by
the difference in value between
two levels – usually the surface
and z.
F  UT (  z  0 )
Where UT represents a transport
velocity.
The transport velocity is usually
parameterized as a function of
some measure of turbulence. e.g.
UT  CDU z
Where Uz is the mean wind speed
at height z, and CD is a bulk
transfer coefficient.
– Note ‘-’ sign: direction of flux is
down-gradient.
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Using u* as a measure of the
surface stress associated with
drag:
The fluxes of heat and moisture
can be similarly parameterized:
u*2  C D U z (U z  U 0 )
( w ) s  C H U z ( z   G )
2
( wq) s  C E U z (q z  qG )
For momentum transfer, CD is
often called the drag coefficient.
CH and CE are the bulk transfer
coefficients for heat and moisture.
They are often assumed to be
equal to CD, but this is not always
a valid assumption.
 CD U
(Note, CD is dimensionless. It is defined for
measurements at a specific height only)
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A note on sign conventions…
• In meteorological applications fluxes are
usually defined to be positive when
directed upwards, so that a positive
surface heat flux adds heat to the
atmosphere.
• In oceanographic applications positive is
often defined to be downwards, so a
positive surface heat flux adds heat to the
ocean.
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Sensible Heat Flux
• The flux of energy due to the movement of
parcels of air at different temperatures.
• Results from difference in temperature between
the surface and overlying air.
– Radiative warming or cooling of the surface
– Advection of air over a surface at different
temperature
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Animation of monthly sensible heat flux (W/m2)
From http://geography.uoregon.edu/envchange/clim_animations/index.html
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Latent Heat Flux
The flux of energy associated with the latent
heat of evaporation of water. Actually a flux of
water vapour.
QE  Lv wq
Lv is the latent heat of vaporisation of water, q is the
mass-mixing ratio of water vapour in air,  is the air
density.
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While the sensible heat flux is
dependent primarily on surface
temperature, the latent heat flux
depends in a much more complex
fashion on surface type:
– Rock, tarmac, etc…solid, nonporous surfaces; a source of
moisture only when surface
water present
– Water surface: ocean, lakes, etc
– Soils: can draw water up from
below surface; soil colour affects
solar heating & evaporation
– Plant cover: evapotranspiration
from leaves…dependent upon
growing conditions, season, etc.
– Ice surface: highly reflective,
does not absorb much solar
radiation. May be dry (T < 0C) or
wet (Tair  0C).
The surface energy balance
over ice is not fully understood,
and is strongly affected by
melting/freezing – while ice is
present and T near 0C, heat
exchange tends to result in
phase change of water rather
than a change in near-surface
temperature.
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Animation of monthly latent heat flux (W/m2)
From http://geography.uoregon.edu/envchange/clim_animations/index.html
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Effect of Surface Roughness
• Rougher surfaces generate more turbulence, increasing
transfer rates across the surface.
• There are three processes contributing to the effective
‘drag’ on the atmosphere:
– Frictional skin drag: related to molecular diffusion. Applies
equally to momentum, heat, & other scalars.
– Form drag: related to the dynamic pressure difference resulting
from the deceleration of air as flows around an obstacle. Applies
only to momentum flux. The effect of form drag over small
obstacles (grass, trees, etc) is usually incorporated with frictional
drag into the bulk parameterization.
– Wave drag: related to the transport of momentum by gravity
waves in statically stable air; e.g. mountain waves. Applies only
to momentum
The additional drag processes applicable to momentum suggest that there ought to be
differences between the drag coefficients for momentum and scalar quantities!
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• On the small scale, surface roughness obviously
depends upon the type of surface:
– sand, grass, low shrubs, trees,…
• The roughness length, zo, depends upon the surface
type, but the relationship is complex – it is not easy to
specify the roughness length simply from a knowledge of
the surface.
• Surface roughness values are estimated from
measurements over different surface types, and
specified for each surface grid point within numerical
models.
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Some Typical Values
Surface roughness
Drag Coefficient CDN (10m)
Flat grassland
Low crops
High crops
Parkland, bushes…
Forest, suburban
0.03 m
0.1 m
0.25 m
0.5 m
0.5 – 1.0 m
N. America
10.1 × 10-3
S. America
26.6 × 10-3
Northern Africa
2.7 × 10-3
Europe
7.9 × 10-3
Asia (north of 20ºN)
3.9 × 10-3
Asia (south of 20ºN) 27.7 × 10-3
Open ocean
0.0002 m
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Effect of Atmospheric Stability
• Unstable (convective)
conditions enhance turbulence
generation and promote mixing
– Fluxes increase
• Stable conditions suppress
turbulence.
– Fluxes decrease
• In strongly stable conditions
turbulence may cease
completely and all turbulent
fluxes reduce to zero.
• Bulk transfer coefficients are
usually derived for neutral
conditions and the bulk flux
equations modified to include
factors to account for stability
effects.
• Accounting for stability effects
greatly increases the
complexity of the
parameterizations.
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• Drag coefficient equation, including a stability correction
  z
z 

CD  k ln   M  
 L 
  z0 
2
2
Where the stability correction for stable conditions (z/L > 0) is
 z  4.7 z
M  
L
L
and for unstable conditions (z/L < 0) is


2




z
1

x
1

x

 


1
 M    2 ln 
 ln 
  2 tan x  

2
L
 2 
 2 
x  1  15z L  4 ,
1
 u*3  v
L
k w v s g
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Gas Fluxes
CO2 fluxes over land are coupled
closely to vegetation. CO2
diffuses into leaves via stomata,
where some of it takes part in
photosynthesis. ~55% returned to
atmosphere without taking part in
photosynthesis, ~45% fixed by
conversion to carbohydrates.
For a biological system in
equilibrium (no net gain/loss in
biological mass), the same
quantity of Carbon would be
returned to the environment via
decomposition, combustion, and
processing by animals.
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