# Temperature change resulting from  Q G depends on: 1.Amount of heat absorbed or released 2.Thermal properties of the soil Heat capacity, C, in J  m.

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Temperature change resulting from  Q G depends on: 1.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  Q S /  z = C s   T s /  t (change in heat flux in a soil volume)

Exchange in Boundary Layers 1.Sub-surface Layer 2.Laminar Boundary Layer 3.Roughness Layer 4.Turbulent Surface Layer 5.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 high temperature to an area of low temperature Q G = -  Hs  C S   T/  z  Hs is the soil thermal diffusivity (m 2  s -1 ) (  Hs and C S refer to the ability to transfer heat energy)

 Hs = k s /C s  s = (k s C s ) 1/2  s/  a = Q G/ Q H

2.Laminar Boundary Layer Thin skin of air within which all non- radiative transfer is by molecular diffusion Heat Flux Q H = -  c p  Ha   T/  z = -C a  Ha   T/  z Water Vapour Flux E = -  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 energy transfer (“constant flux layer”)

Heat Flux Q H = -C a  K H   T/  z (K H is “eddy conductivity” m 2  s -1 ) Water Vapour Flux E = -K V    v /  z Latent Heat Flux Q E = -L V  K V    v /  z (L V is the “latent heat of vaporization”) eddy diffusion coefficient for water vapour

5.Outer Layer The remaining 90% of the planetary boundary 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 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)

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

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

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

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

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

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

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, z g 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  =  K M  (  u/  z) K M is eddy viscosity (m 2 /s) - ability of eddies to transfer 

Friction velocity, u * u * = (  /  ) 1/2 Under neutral stability, wind variation with height is as follows: u z = (u * /k) ln (z/z 0 ) where k is von Karman’s constant (~0.40m) and z 0 is the roughness length (m) – Table 2.2 ‘THE LOGARITHMIC WIND PROFILE’ Slope = k/u *

Unstable Stable

Recall: Q H = -C a  K H    /  z (  is potential temperature, accounting for atmospheric pressure changes between two altitudes) Day: negative temperature gradient, Q H is positive Night: positive temperature gradient, Q H is negative Fluctuations in Sensible Heat Flux Associated with updrafts (+) and downdrafts (-) In unstable conditions, Q H transfer occurs mainly in bursts during updrafts (Equation above gives a time- averaged value)

Diurnal Surface Temperature Wave Temperature wave migrates upward due to turbulent transfer (Q H ) 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, K H

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  R v T where R v is the specific gas constant for water vapour (0.4615 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 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) Water Vapour Flux E = -K V   v /  z Latent Heat Flux Q E = -L V  K V   v /  z (L V is the “latent heat of vaporization”) Again, note that equations have same form as in laminar layer, but with K instead of .

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 (Q H ) Calm conditions: Loss of moisture due to condensation cannot be replenished and dew formation ceases (a very light flow is sufficient to replenish moisture)

Ground Fog Formation Occurs on nights when H 2 O (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, resulting in condensation 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 of surface is not intense enough to promote substantial convection

Bowen Ratio  = Q H /Q E 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 high Q E increases, which cools and moistens the airmass

Climates of Simple, Non-Vegetated Surfaces 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 Negligible Evaporation Q*  Q H + Q G Not terribly high Instability in afternoon

Very High Surface Temps (despite high albedo) Shallow layer of extremely high instability High winds Strong heat flux convergence Lower atmosphere very 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 between K  and Q* Why ? Also: Magnitudes of longwave fluxes are small due to low temperature High albedo

Surface Radiation Balance for Melting Snow Latent heat storage change due to melting or freezing (negligible Q E, Q M and small Q S if ‘cold’ snow) Q* can be negative for cold snow Isothermal snow Turbulent transfer Raise temp How is this measured?

Surface Radiation Balance for Melting Glacier High  Continual receipt of Q H and Q E from atmosphere

Surface Radiation Balance for a Lake

Surface Energy Balance for Snow and Ice Q* = Q H + Q E +  Q S +  Q M Negligible Q E (sublimation possible) Low heat conduction Q* is negative Q* = Q H + Q E +  Q S +  Q M - Q R COLDMELTING Rainfall adds heat too Percolation and refreezing transfers heat  Q M >  Q S Condensation at surface is common (snow pack temperature can only rise to 0  C) - Q E can be important ! Why ? L V >L F  Q M = L F   r

Next: Surface Radiation Balance for a Plant Canopy

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