1. Water Vapor Calculation
Water vapor calculation over …
Ice
Water (both above 0 Celcius and below as super cooled water)
Calculation of the dew point temperature.
Supplemental information about the atmospheric boundary layer is given at the end.

3. More Accurate Forms of Vapor Pressure over Ice and Water

5. e(T) = es(TDew)
USE
THESE
VALUES.

6. PRACTICE WITH STABILITY

7. Atmospheric Structure
From Wallace and Hobbs, 2nd ed, Atmospheric Science, chapter 9.

8. Atmospheric Boundary Layer Diurnal Variation
E.Z. refers to entrainment zone where energetic parcels from the surface overshoot and entrain and mix in air from the free atmosphere, as well as to mix boundary layer air into the free atmosphere above.
From Wallace and Hobbs, 2nd ed, Atmospheric Science, chapter 9.

9. Atmospheric Boundary Layer Diurnal Variation
Potential temperature in the U.S. standard atmosphere, and its change near the Earth’s surface due to turbulent mixing driven by sunlight.
From Wallace and Hobbs, 2nd ed, Atmospheric Science, chapter 9.

10. Example Soundings 5:00 am local time 5:00 pm local time
3 September 2010
5:00 pm local time
3 September 2010
super adiabatic
solar heated
surface
top of boundary layer in
afternoon. Mixing height.
morning inversion

11. Equation for Boundary Layer Height as a function of time during the day, and by the day of year.
T0 = surface temperature, P0 = surface pressure, 0 = adiabatic lapse rate
I = environmental lapse rate, typically of inversion and < 0,
 = latitude,  = angle of tilt of Earth’s axis = 23.5 degrees, tR = time of sunrise in hour of day,
t = time of day in hours, F is the integrated solar irradiance (W m-2) over all wavelengths at the surface, A is the surface albedo, air is the thermal diffusivity of the air, and ground= thermal diffusivity of the ground.

12. Observed Structure of the Atmospheric Boundary Layer
Many thanks to: Nolan Atkins, Chris Bretherton, Robin Hogan
Googled using presentation and Atmospheric Boundary layer.

13. Review of the last lecture
Incoming shortwave + Incoming longwave = Reflected shortwave
+ Emitted longwave + Latent heat flux + Sensible heat flux
Incoming solar radiation = (Solar constant) cos(Solar zenith angle)
Reflected solar radiation = (Incoming solar radiation) x Albedo
Longwave I=T4
Sensible heat flux Qh =  Cd Cp V (Tsurface - Tair)
Latent heat flux Qe =  Cd L V (qsurface - qair)
Bowen ratio B= Qh/Qe = Cp(Tsurface - Tair) / L(qsurface - qair) provides a simple way for estimating Qh and Qe when radiation measurements are available

14. Vertical Structure of the Atmosphere
Definition of the boundary layer: "that part of the troposphere that is directly influenced by the presence of the earth's surface and responds to surface forcings with a time scale of about an hour or less.”
Scale: variable, typically between 100 m - 3 km deep

15. Difference between boundary layer and free atmosphere
The boundary layer is:
More turbulent
With stronger friction
With more rapid dispersion of pollutants
With non-geostrophic winds while the free atmosphere is often with geostrophic winds

16. Vertical structure of the boundary layer
From bottom up:
Interfacial layer (0-1 cm): molecular transport, no turbulence
Surface layer (0-100 m): strong gradient, very vigorous turbulence
Mixed layer (100 m - 1 km): well-mixed, vigorous turbulence
Entrainment layer: inversion, intermittent turbulence

17. Turbulence inside the boundary layer
Definition of Turbulence: The apparent chaotic nature of many flows, which is manifested in the form of irregular, almost random fluctuations in velocity, temperature and scalar concentrations around their mean values in time and space.

18. Generation of turbulence in the boundary layer: Hydrodynamic instability
“Hydrodynamically unstable” means that any small perturbation would grow rapidly to large perturbation
Shear instability: caused by change of mean wind in space (i.e. mechanical forcing)
Convective instability: caused by change of mean temperature in the vertical direction (i.e. thermal forcing)

19. Shear instability
Shear: Change of wind in space

20. Example: Kelvin-Helmholtz instability
Shear instability within a fluid or between two fluids with different density
Lab experiment
Real world (K-H clouds)

21. Convective instability
Static stability – refers to atmosphere’s susceptibility to being displaced
Stability related to buoyancy  function of temperature
The rate of cooling of a parcel relative to its surrounds determines its ‘stability’ of a parcel
For dry air (with no clouds), an easy way to determine its stability is to look at the vertical profile of virtual potential temperature
v =  ( r )
Where
 = T (P0/P) is the potential temperature
r is the water vapor mixing ratio
Three cases:
(1) Stable (sub-adiabatic): v increases w/ height
(2) Neutral (adiabatic): v keeps constant w/ height
(3) Unstable (super-adiabatic): v decreases w/ height
Stable or sub-adiabatic
Neutral or adiabatic
Unstable or super-adiabatic

22. Forcings generating temperature gradience and wind shear, which affect the boundary layer depth
Heat flux at the surface and at the top of the boundary layer
Frictional drag at the surface and at the top of the boundary layer

23. Boundary layer depth: Effects of ocean and land
Over the oceans: varies more slowly in space and time because sea surface temperature varies slowly in space and time
Over the land: varies more rapidly in space and time because surface conditions vary more rapidly in space (topography, land cover) and time (diurnal variation, seasonal variation)

24. Boundary layer depth: Effect of highs and lows
Near a region of high pressure:
Over both land and oceans, the boundary layer tends to be shallower near the center of high pressure regions. This is due to the associated subsidence and divergence.
Boundary layer depth increases on the periphery of the high where the subsidence is weaker.
Near a region of low pressure:
The rising motion associated with the low transports boundary layer air up into the free troposphere.
Hence, it is often difficult to find the top of the boundary layer in this region. Cloud base is often used at the top of the boundary layer.

25. Boundary Layer depth: Effects of diurnal forcing over land
Daytime convective mixed layer + clouds (sometimes)
Nocturnal stable boundary layer + residual layer

26. Convective mixed layer (CML): Growth
The turbulence (largely the convectively driven thermals) mixes (entrains) down potentially warmer, usually drier, less turbulent air down into the mixed layer

27. Convective mixed layer (CML): Vertical profiles of state variables
Strongly stable lapse rate
Nearly adiabatic
Super-adiabatic
Well-mixed (constant profile)

28. Nocturnal boundary layer over land: Vertical structure
The residual layer is the left-over of CML, and has all the properties of the recently decayed CML. It has neutral stability.
The stable boundary layer has stable stability, weaker turbulence, and low-level (nocturnal) jet.
Weakly stable lapse rate
Nearly adiabatic
Strongly stable lapse rate

29. Boundary layer over land: Comparison between day and night
Strongly stable lapse rate
Nearly adiabatic
Super-adiabatic
Kaimal and Finnigan 1994
Weakly stable lapse rate
Nearly adiabatic
Strongly stable lapse rate
Subtle difference between convective mixed layer and residual layer: Turbulence is more vigorous in the former

30. Summary
Vertical structure of the atmosphere and definition of the boundary layer
Vertical structure of the boundary layer
Definition of turbulence and forcings generating turbulence
Static stability and vertical profile of virtual potential temperature: 3 cases
Boundary layer over ocean
Boundary layer over land: diurnal variation
Please remember to bring your calculator on Friday