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Temperature change resulting from QG
depends on:
1. Amount of heat absorbed or
2. Thermal properties of the soil
Heat capacity, C, in Jm-3K-1
Specific heat, c, in Jkg-1K-1
QS/ z = Cs  Ts/ t
(change in heat flux in a soil volume)
Exchange in Boundary Layers
1. Sub-surface Layer
2. Laminar Boundary Layer
3. Roughness Layer
4. Turbulent Surface Layer
5. Outer Layer
The first half of this course is concerned mainly
with energy exchange in the roughness layer,
turbulent surface layer and outer layer
1. Sub-surface layer
Heat flows from an area of high
temperature to an area of low temperature
QG = -HsCS T/z
Hs is the soil thermal diffusivity (m2s-1)
(Hs and CS refer to the ability to transfer
heat energy)
s = (ks Cs)1/2
Hs = ks/Cs
s/ a = QG/ QH
2. Laminar Boundary Layer
Thin skin of air within which all nonradiative transfer is by molecular diffusion
Heat Flux
QH = -cpHa  T/z = -CaHa  T/z
Water Vapour Flux
E = - Va  v/z
Gradients are steep because  is small (insulation barrier)
3. Roughness Layer
Surface roughness elements cause
eddies and vortices (more later)
4. Turbulent Surface Layer
Small scale turbulence dominates energy
transfer (“constant flux layer”)
Heat Flux
QH = -CaKH  T/z
(KH is “eddy conductivity,” m2s-1)
Water Vapour Flux
E = -KV  v/ z
Latent Heat Flux
QE = -LVKV  v/ z
(LV is the “latent heat of vaporization”)
5. Outer Layer
The remaining 90% of the planetary
boundary layer
FREE, rather than FORCED convection
Mixed layer
convective entrainment
Lapse Profile
temperature usually decreases with height*
negative gradient (T/ z)
temperature usually increases with height
near the surface “temperature inversion”
*There are some exceptions and there is a lag time for the
surface temperature wave to penetrate upward in the air.
Dry Adiabatic Lapse Rate ()
A parcel of air cools by expansion or warms by compression
with a change in altitude
-9.8 x 10-3 ºCm-1
Environmental Lapse Rate (ELR)
A measure of the actual temperature structure
Moist adiabatic lapse rate:
The rate at which moist ascending air cools by
 m typically about 6C/1000m
4C/1000m in warm air
near 10C/1000m in cold air
Latent heat of condensation liberated as parcel rises
Unstable conditions
ELR > 
Rising parcel of air remains warmer and less dense than
surrounding atmosphere
Stable conditions
ELR <  m
Rising parcel of air becomes cooler and denser than
surrounding air, eliminating the upward movement
Conditionally unstable conditions
 >ELR> m
Lifted parcel
is theoretically
cooler than
air around it
after lifting
ELR = 
DALR = 
Lifted parcel
is theoretically
warmer than
air after lifting
ELR = 
DALR = 
Lifted parcel
is the same
temperature as
air after lifting
Note: Conditionally-unstable conditions
occur for m <  < d
Wind (u) and Momentum ()
Surface elements provide frictional drag
Force exerted on surface by air is called shearing stress, 
Air acts as a fluid – sharp decrease in horizontal wind
speed, u, near the surface
Drag of larger surface elements (eg. trees, buildings)
increases depth of boundary layer, zg
Vertical gradient of mean wind speed (u/z) greatest
over smooth terrain
Density of air is ‘constant’ within the surface layer
Horizontal momentum increases with height
Why ? Windspeeds are higher (momentum  u)
Examine Figure 2.10b
Eddy from above increases velocity ( momentum)
Eddy from below decreases velocity ( momentum)
Because wind at higher altitudes is faster, there is a
net downward flux of momentum
 = KM(u/z)
KM is eddy viscosity (m2/s) - ability of eddies to transfer 
Friction velocity, u*
u* = (/)1/2
Under neutral stability, wind variation with height is
as follows:
uz = (u*/k) ln (z/z0)
where k is von Karman’s constant (~0.40m) and
z0 is the roughness length (m) – Table 2.2
Recall: QH = -CaKH  /z
( is potential temperature, accounting for atmospheric
pressure changes between two altitudes)
Day: negative temperature gradient, QH is positive
Night: positive temperature gradient, QH is negative
Fluctuations in Sensible Heat Flux
•Associated with updrafts (+) and downdrafts (-)
•In unstable conditions, QH transfer occurs mainly in
bursts during updrafts (Equation above gives a timeaveraged value)
Diurnal Surface Temperature Wave
Temperature wave migrates upward due to turbulent
transfer (QH)
Time lag and reduced amplitude at higher elevations
The average temperature is also shifted downward.
( is not shifted downward)
Rate of migration dependent on eddy conductivity, KH
Water Vapour in the Boundary Layer
Vapour Density or Absolute Humidity, v
The mass of water vapour in a volume of air (gm-3)
Vapour Pressure, e
The partial pressure exerted by water vapour
molecules in air (0e<5 kPa)
e = vRvT
where Rv is the specific gas constant for water
vapour (461.5 J kg-1 K-1)
Alternatively, v=2.17(e/T)
Saturation Vapour Pressure, e*
•Air is saturated with water vapour
•Air in a closed system over a pan of water reaches
equilibrium where molecules escaping to air are balanced
by molecules entering the liquid
•Air can hold more water vapour at higher temperatures
(See Figure 2.15)
•Most of the time, air is not saturated
•Vapour Pressure Deficit
VPD = e* - e
Dew Point / Frost Point
The temperature to which a parcel of air must be cooled
for saturation to occur (if pressure and e are constant)
Water Vapour Flux
E = -KV  v/ z
Latent Heat Flux
QE = -LVKV  v/ z
(LV is the “latent heat of vaporization”)
Again, note that equations have same form as in laminar
layer, but with K instead of .
•Evaporative loss strongest during the day
•Evaporative loss may be reversed through condensation
(dew formation)
•Overall flux is upward (compensates for precipitation)
Critical Range of Windspeed for Dewfall
Wind too strong: Surface radiative cooling (L*) offset by
turbulent warming (QH)
Calm conditions: Loss of moisture due to condensation
cannot be replenished and dew formation ceases
Ground Fog Formation
•Occurs on nights when air approaches saturation point
in evening
•Surface air develops a strongly negative long-wave radiation
budget (emits more than colder surface or air above)
•This promotes cooling to dewpoint (fog droplet formation)
•Strong flow inhibits fog formation due to turbulent mixing
•Fog layer deepens as fog top becomes radiating surface
•May linger through day if solar heating insufficient for
promotion of convection
Bowen Ratio
= QH/QE
High ratios where water is limited (eg. deserts) or when
abnormally cool and moist airmass settles over a region in
Why ? Solar heating leads to strong temperature gradient
Low ratios occur when soil moisture availability is high
QE increases, which cools and moistens the airmass
Climates of Simple, Non-Vegetated
So far, we have looked at bare soils:
peat (very high , low ) vs.
clay (lower , higher )
How would this affect diurnal patterns and
vertical distribution of temperature?
Sandy Deserts
Q* QH + QG
Not terribly high
Instability in
Very High
Strong heat flux convergence
Lower atmosphere
very unstable
Mirage due to density variation
(despite high
Shallow layer
of extremely
High winds
Huge diurnal air
temperature range
Snow and Ice
Snow and ice permit
transmission of some
solar radiation
Notice the
K and Q*
Why ?
High albedo
Also: Magnitudes of
longwave fluxes
are small due
to low temperature
Latent heat
change due
to melting
or freezing
(negligible QE,
QM and small
QS if ‘cold’
Q* can be
negative for
cold snow
Isothermal snow
Raise temp
Turbulent transfer
How is this
High 
receipt of
QH and QE
for a
Q* = QH + QE + QS + QM
Q* = QH + QE + QS + QM - QR
Rainfall adds
heat too
Negligible QE
(sublimation possible)
Surface Energy
Balance for
Snow and Ice
Q* is negative
Low heat
 QM>  QS
QM = LF  r
Percolation and
refreezing transfers
Condensation at surface
is common (snow pack
temperature can only rise
to 0C) - QE can be important !
Why ? LV>LF
for a
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