Soil Heat Flux and Soil Temperature

Heat transfer within soils is governed by:

1. Thermal conductivity2. 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 particles2. Soil porosity3. 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 fasterthan ks

Peak values occur in relatively dry soils

Very dry soils have low Hs because of the very lowthermal 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 orrelease heat

s = Cs (Hs)1/2 = (ks Cs)1/2

a = Ca (KH)1/2

These properties are important in the transfer of sensible heatbetween the ground and the atmosphere

s/ a = QG/QH

Wind (u) and Momentum ()

Surface elements provide frictional dragForce exerted on surface by air is called shearing stress, (Pa)

Air acts as a fluid – sharp decrease in horizontal windspeed, 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 2.10bEddy 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 isas follows:

uz = (u*/k) ln (z/z0)

where k is von Karman’s constant (~0.40m) andz0 is the roughness length (m) – Table 2.2

Unstable

Stable

Recall: QH = -CaKH /z( is potential temperature, accounting for atmosphericpressure changes between two altitudes)

Day: negative temperature gradient, QH is positiveNight: positive temperature gradient, QH is negative

Fluctuations in Sensible Heat Flux•Associated with updrafts (+) and downdrafts (-)

•In unstable conditions, QH transfer occurs mainly inbursts during updrafts (Equation above gives a time-averaged value)

Diurnal Surface Temperature Wave

Temperature wave migrates upward due to turbulent transfer (QH)

Time lag and reduced amplitude at higher elevationsThe 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 (gm-3)

Vapour Pressure, eThe partial pressure exerted by water vapour molecules in air (0e<5 kPa)

e = vRvT

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 gm-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 reachesequilibrium where molecules escaping to air are balancedby 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 DeficitVPD = e* - e

Dew Point / Frost Point

The temperature to which a parcel of air must be cooledfor saturation to occur (if pressure and e are constant)

Recall:

Water Vapour FluxE = -KV v/ z

Latent Heat FluxQE = -LVKV 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 condensationCannot 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 radiationbudget (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 availableQE increases, which cools and moistens the airmass