Temperature change resulting from QG

depends on:

1.Amount of heat absorbed or released

2. Thermal properties of the soilHeat capacity, C, in Jm-3K-1

Specific heat, c, in Jkg-1K-1

QS/ z = Cs Ts/ t(change in heat flux in a soil volume)

Exchange in Boundary Layers

1.Sub-surface Layer2.Laminar Boundary Layer3.Roughness Layer4.Turbulent Surface Layer5.Outer Layer

The first half of this course is concerned mainly with energy exchange in the roughness layer, turbulent surface layer and outer layer and, to a lesser extent, the sub-surface layer.

1.Sub-surface layer

Heat flows from an area of hightemperature to an area of low temperature

QG = -HsCS T/z

Hs is the soil thermal diffusivity (m2s-1)(Hs and CS refer to the ability to transferheat energy)

See definitions on page 404

Hs = ks/Cs

s = (ks Cs)1/2

s/ a = QG/ QH

2. Laminar Boundary Layer

Thin skin of air within which all non-radiative transfer is by molecular diffusion

Heat FluxQH = -cpHa T/z = -CaHa T/z

Water Vapour FluxE = - 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 energytransfer (“constant flux layer”)

Heat FluxQH = -CaKH T/z(KH is “eddy conductivity” m2s-1)

Water Vapour FluxE = -KV v/z

Latent Heat FluxQE = -LVKV v/z(LV is the “latent heat of vaporization”)

eddy diffusion coefficientfor water vapour

5.Outer Layer

The remaining 90% of the planetaryboundary layer

FREE, rather than FORCED convection

Mixed layer

convective entrainment

Lapse Profile

DAYTIME: temperature decreases with height*negative gradient (T/ z)

NIGHT: temperature usually increases with heightnear the surface “temperature inversion”

*There are some exceptions (often due to the lag time for the surface temperature wave to penetrate upward in the air after sunrise, as shown on Slide 26)

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 ºCm-1

Environmental Lapse Rate (ELR)A measure of the actual temperature structure

ABSOLUTELY UNSTABLE ABSOLUTELY STABLE

ABSOLUTELY UNSTABLE ABSOLUTELY STABLE

Moist adiabatic lapse rate:

The rate at which moist ascending air cools by expansion

m typically about -6C/1000m

Varies: -4C/1000m in warm saturated airnear -10C/1000m in cold saturated air

Latent heat of condensation liberated as parcel rises

Unstable conditionsELR > Rising parcel of air remains warmer and less dense than surrounding atmosphere 

Stable conditionsELR < m

Rising parcel of air becomes cooler and denser than surrounding air, eliminating the upward movement 

Conditionally unstable conditions > ELR > m

ELR =

Lifted parcel is theoretically cooler thanair around itafter lifting

Source: http://www.atmos.ucla.edu

Lifted parcel is theoretically warmer thanair after lifting

Lifted parcel is the same temperature asair after lifting

Note: Conditionally-unstable conditions occur for m < < d

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

‘THE LOGARITHMICWIND PROFILE’

Slope = k/u*

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.( 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 (gm-3)

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

e = vRvT

where Rv is the specific gas constant for water vapour (461.5 J g-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 reachesequilibrium 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 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)

Water Vapour FluxE = -KV v/ z

Latent Heat FluxQE = -LVKV v/ z(LV is the “latent heat of vaporization”)

Again, note that equations have same form as in laminarlayer, but with K instead of .

Eddy diffusivity for H2O(vap)

•Evaporative loss strongest during the day

•Evaporative loss may be reversed through condensation(dew formation)•Overall flux is upward (compensates for net gain from 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(a very light flow is sufficient to replenish moisture)

Ground Fog Formation

•Occurs on nights when H2O(vap) in air approaches saturation point in evening

•Surface air develops a strongly negative long-wave radiation budget (emits more than colder surface below or drier air above)

•This promotes cooling to dewpoint

•Strong flow inhibits fog formation due to turbulence

•Fog layer deepens: fog top becomes radiating surface

•May linger through day if solar heating of surface is notintense enough to promote substantial 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 soil moisture availability is highQE increases, which cools and moistens the airmass

Climates of Simple, Non-VegetatedSurfaces

So far, we have looked at bare soils:

Consider: peat (very high porosity, low albedo) vs. clay (lower porosity, higher albedo)

How would this affect diurnal patterns and vertical distribution of temperature?

Sandy Deserts

Negligibleevaporation

Q* QH + QG

Not terribly high

Instability inafternoon

Very High SurfaceTemps

(despite highalbedo)

Shallow layerof extremelyhighinstability

High winds

Strong heat flux convergence

Lower atmospherevery unstable

Mirage due to density variation

Huge diurnal air temperature range

Snow and Ice

Snow and ice permit transmission of some solar radiation

Notice the difference betweenK and Q*

Why ?

Also: Magnitudes oflongwave fluxesare small dueto low temperature

High albedo

Surface RadiationBalance forMeltingSnow

Latent heatstorage change dueto meltingor freezing(negligible QE,QM and small QS if ‘cold’ snow)

Q* can be negative for cold snow

Isothermal snow

Turbulent transfer

Raise temp

How is this measured?

Surface RadiationBalance forMeltingGlacier

High

Continual receipt ofQH and QE from atmosphere

Surface RadiationBalance for aLake

Surface EnergyBalance for Snow and Ice

Q* = QH + QE + QS + QM

Negligible QE

(sublimation possible)

Low heatconduction

Q* is negative

Q* = QH + QE + QS + QM - QR

COLD MELTING

Rainfall addsheat too

Percolation andrefreezing transfersheat

QM> QS

Condensation at surfaceis common (snow pack temperature can only riseto 0C) - QE can be important !Why ? LV>LF

QM = LF r

Next:

Surface RadiationBalance for aPlant Canopy