1. Atmospheric
Analysis
Lecture 2

3. REVIEW Q* - positive in daytime - almost always negative at night
Any Q* imbalance is accounted for by
convective exchange or conduction
Q* = QH + QE + QG + S
where QH = sensible heat flux
QE = latent heat flux
QG = conduction to or from ground

4. Recall the First Law of Thermodynamics
ENERGY IN = ENERGY OUT
Qin > Qout (flux convergence)
Net storage gain leads to warming
Qout > Qin (flux divergence)
Net storage energy loss leads to cooling
Qin = Qout
No net change in energy storage

6. DAYTIME:
Both sides of equation are positive:
surface radiative surplus
Surplus partitioned into ground and atmosphere
Convection is the most important means of
daytime heat transport from surface
QE is greater when soil moisture is high
QH is greater when water is more restricted

7. NIGHT:
Both sides of equation are negative:
surface radiative deficit
Deficit partitioned into heat gain from ground
and atmosphere
Q* loss is partially replenished by QG
QE and QH of less importance as convective
exchange is dampened by the night-time
temperature stratification

8. Temperature change resulting from QG depends on:
Amount of heat absorbed or
released
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)

10. Sample Question
It is a hot, sunny day in the Sahara desert. Over a one hour period,
the temperature of the top 0.1 m of the dry, sandy soil increased by
2.3 ºC. Calculate the energy flux density that went into storage via
soil heating.

11. Exchange in Boundary Layers
Sub-surface Layer
Laminar Boundary Layer
Roughness Layer
Turbulent Surface Layer
Outer Layer
The first half of this course is concerned with
energy exchange in the roughness layer, turbulent
surface layer and outer layer

12. 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)

16. 2. Laminar Boundary Layer
Thin skin of air within which all non-
radiative 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

18. Roughness Layer
Surface roughness elements cause
eddies and vortices (more later)
Turbulent Surface Layer
Small scale turbulence dominates energy
transfer (“constant flux layer”)

19. (LV is the “latent heat of vaporization”)
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”)

20. Outer Layer
The remaining 90% of the planetary
boundary layer
FREE, rather than FORCED convection
Mixed layer

21. convective entrainment

22. Lapse Profile DAYTIME: temperature usually decreases with height*
negative gradient (T/ z)
NIGHT: 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.

23. 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
If ELR> , the atmosphere is unstable
If ELR< , the atmosphere is stable
If ELR= , the atmosphere is neutral
Can you think of conditions likely to support each of these
three cases ?

25. Moist adiabatic lapse rate:
The rate at which moist ascending air cools by
expansion
 m typically about 6C/1000m
Varies: 4C/1000m in warm air
near 10C/1000m in cold air
Latent heat of condensation liberated as parcel rises

26. Conditionally 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

27. ELR =  DALR =  Lifted parcel is theoretically cooler than
air around it
after lifting
ELR = 
DALR = 
Source:

28. ELR =  DALR =  Lifted parcel is theoretically warmer than
air after lifting
ELR = 
DALR = 

29. Lifted parcel
is the same
temperature as
air after lifting
Note: Conditionally-unstable conditions
occur for m <  < d