SOILS AND THE

1. SOILS AND THE SOIL-ATMOSPHERE INTERFACE

2. 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)

3. 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 mainly with energy exchange in the roughness layer, turbulent surface layer and outer layer and, to a lesser extent, the sub-surface layer.

4. 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) See definitions on page 404

6. s = (ks Cs)1/2 s/ a = QG/ QH Hs = ks/Cs

8. 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 (insulation barrier)

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

12. ENERGY EXCHANGE IN THE CONSTANT FLUX LAYER

13. 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”) eddy diffusion coefficient for water vapour

14. TEMPERATURE PROFILE OF THE BOUNDARY LAYER

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

16. convective entrainment

17. STABILITY AND INSTABILITY

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

19. Dry Adiabatic Lapse Rate () A parcel of air cools by expansion or warms by compression with a change in altitude -9.8 x 10-3ºCm-1 Environmental Lapse Rate (ELR) A measure of the actual temperature structure ABSOLUTELY UNSTABLE ABSOLUTELY STABLE

20. ABSOLUTELY UNSTABLE ABSOLUTELY STABLE

21. 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 saturated air near -10C/1000m in cold saturated air Latent heat of condensation liberated as parcel rises

22. 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

23. Lifted parcel is theoretically cooler than air around it after lifting ELR =  Source: http://www.atmos.ucla.edu

24. Lifted parcel is theoretically warmer than air after lifting

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

27. WIND AND MOMENTUM

29. 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

30. 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 

31. 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 Slope = k/u* ‘THE LOGARITHMIC WIND PROFILE’

33. AERODYNAMIC PROPERTIES OF NATURAL SURFACES

35. EFFECT OF STABILITY ON ENERGY FLUXES

36. Unstable Stable

38. 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 time- • averaged value)

39. DIURNAL TEMPERATURE PATTERNS

40. 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

42. VAPOUR PRESSURE

43. 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 g-1 K-1) Alternatively, v = 2.17  (e / T)

44. 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 vapourat higher temperatures • (See Figure 2.15) • Most of the time, air is not saturated • Vapour Pressure Deficit • VPD = e* - e

47. 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 . Eddy diffusivity for H2O(vap)

48. 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 condensation • cannot be replenished and dew formation ceases • (a very light flow is sufficient to replenish moisture)

50. 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 not • intense enough to promote substantial convection