Soil Heat Flux and Soil Temperature
Heat transfer within soils is governed by:
1. Thermal conductivity
2. Heat capacity
QG = -ks (TS/ z)
Where ks is the thermal conductivity
* Notice that still air is a poor heat conductor (Table 2.1)
Three factors affect ks:
1. Conductivity of soil particles
2. Soil porosity
3. Soil moisture content
How does soil moisture affect ks ?
• Water increases thermal contact between grains
• Water expels air (air has lower thermal conductivity)
• Water has much higher heat capacity
Thermal diffusivity, Hs
Hs = ks/Cs
Hs determines the rate of heating due to a given
temperature distribution within a substance
Hs and soil moisture
Hs increases as soils dry because Cs decreases faster
than ks
Peak values occur in relatively dry soils
Very dry soils have low Hs because of the very low
thermal conductivity of air
High Hs soils have less extreme surface temperature range
(eg. saturated clay less extreme than dry peat)
Thermal admittance, s
A measure of the ease with which a surface may absorb or
release heat
s = Cs  (Hs)1/2 = (ks Cs)1/2
a = Ca  (KH)1/2
These properties are important in the transfer of sensible heat
between the ground and the atmosphere
s/ a = QG/QH
Wind (u) and Momentum ()
Surface elements provide frictional drag
Force exerted on surface by air is called shearing stress, 
(Pa)
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
Unstable
Stable
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
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)
( v in gm-3, e in Pa and T in Kelvin)
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)
Recall:
Water Vapour Flux
E = -KV  v/ z
Latent Heat Flux
QE = -LVKV  v/ z
(LV is the “latent heat of vaporization”)
•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
summer
Why ? Solar heating leads to strong temperature gradient
Low ratios occur when water is available
QE increases, which cools and moistens the airmass