Water Vapor Calculation

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 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 Heightas 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 fluxQh =  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 =  (1 + 0.61 r ) • Where •  = T (P0/P)0.286 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 Well-mixed (constant profile) Strongly stable lapse rate Nearly adiabatic Super-adiabatic

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 Subtle difference between convective mixed layer and residual layer: Turbulence is more vigorous in the former Strongly stable lapse rate Nearly adiabatic Super-adiabatic Kaimal and Finnigan 1994 Weakly stable lapse rate Nearly adiabatic Strongly stable lapse rate

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