ATMO 551aHomework 6Due 11/12/08

Use the skew T figure below to do the following problems

Assume the actual surface dew point is 10oC.

  1. At approximately what pressure level and altitude above sea level is cloud base? (900 mb ~ 1 km, 800 mb ~ 2 km, 700 mb ~ 3 km)
  2. Calculate e at cloud base
  3. Using the figure, assuming the air parcel rises along a moist adiabat, what is the approximate pressure and altitude above sea level to which the air parcel will rise & become neutrally buoyant? (Help: 300 mb ~ 9 km, 200 mb ~ 12 km, 100 mb ~ 16 km)
  4. Reading from the figure, what is potential temperature of the air parcel at that altitude?
  5. How close is this to your answer for (3)?
  6. Approximately what is the CAPE of the air parcel (in J/kg)? (by eye, estimate the average temperature difference between the moist adiabat and environmental air temperature and multiply that by the height interval over which the air parcel is warmer than the environment).
  7. What will the air parcel’s vertical velocity be when it reaches this neutral buoyancy altitude? (same as the midterm)
  8. By how much will the air parcel overshoot the neutral buoyancy level altitude? (set the kinetic energy of the air parcel at the neutral buoyancy level equal to the work/mass done by the negative acceleration on the air parcel above the altitude where it is neutrally buoyant and solve for the height above neutral buoyancy. Remember the acceleration is proportional to the Brunt Vaisala frequency squared: Eq’s 37 & 38 from adiabatic lapse rate notes.)
  9. Assuming all the water that condenses out falls out as rain, approximately how much rain in mm per square meter will fall out of each 1 m3 air parcel as it rises?
  10. Diffusion? Into the core?
  11. Eddy correlation
  12. Given the diffusivity of air, determine the collisional crosssectional area of molecules of air
  13. When the mean free path equals a scale height, molecules can potentially overcome earth’s gravity and escape to space.
  14. Determine the approximate pressure level at which this occurs in Earth’s atmosphere?
  15. Determine the approximate height of the exobase for N2. Assume the average temperature of the atmosphere up to 90 km is 230K and the air is sufficiently mixed that the mean molecular mass is 28.96 g/mole. Above 90 km, assume the average temperature is 500 K and the scale height depends on the selected molecule, in this N2.
  16. Is the kinetic energy of the N2 molecules sufficient to overcome the binding energy of gravity?

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