David Stevenson Crew Building Room 314 dstevens@staffmail.ed.ac.uk

1. Next 4 weeks:Atmospheric temperature profilesStability[1-week on Fronts from Hugh Pumphrey]ThunderstormsAir Pollution David Stevenson Crew Building Room 314 dstevens@staffmail.ed.ac.uk

2. L13 Physics of Dry Air • Vertical pressure gradient through the atmosphere: • The Hydrostatic Equation (revision) • Measuring temperature profiles: radiosondes • 1st Law of Thermodynamics: conservation of energy • ‘Air parcels’ • The ‘Dry Adiabatic Lapse Rate’

3. Why are vertical profiles important? • At what height do clouds form? • Will air rise or sink? Atmospheric stability => Rain showers/thunderstorms caused by moist air rising and cooling • Inversions – e.g. fog • Pollution dispersion –e.g. Buncefield fire

4. Vertical pressure gradient • We know pressure (p) decreases as you go up through the atmosphere. • Q: So why doesn’t air flow from high p at surface to low p at altitude? (i.e. why hasn’t Earth lost its atmosphere to space?) • A: Gravity attracts it towards the centre of the Earth. • The balance of gravity and vertical pressure gradient is ‘hydrostatic balance’

5. Net upward force on slab, due to the pressure gradient= -p Downward force on airin shaded slab, due topressure of air above must balancedownwardforce due to weight of slab= gz Upward force on air inshaded slab due to pressure of air below In limit as z → 0, Hydrostatic Equation (see Lecture 8)

6. du = Change in internal energyof air parcel dw = Work doneby air parcel First law of thermodynamics Conservation of energy for a parcel of air: dq = heat added to air parcel from itssurroundings Cpis the specific heat capacity at constant pressure α is the specific volume (1/density)

7. Pumping up/letting down a tyre • Pump up tyre: air compresses, work is done on the air in the tyre (dw is –ve; the air in the tyre doesn’t do work). If we assume dq=0, then dT is +ve, the air heats up (valve gets hot). • Let down tyre: air expands, the air in the tyre does work on its surroundings (dw is +ve). If we assume dq=0, then dT is –ve, the air cools down (valve gets cold).

8. Radiosondes Temperature (and humidity, pressure) sensor, attached to weather balloon, with radio transmitter to send data back to earth.

9. How do we measure temperature and moisture in the atmosphere? Radiosonde • pressure, Temperature and moisture are all measured by sensors and the signals are transmitted to a base station by radio • Rises to between 20-30 km • then balloon bursts and radiosonde returns to surface by parachute

10. Ikarus project:http://www.youtube.com/watch?v=MCBBRRp9DOQ&NR=1

11. Wind speed and directionare not directly measuredbut inferred(radar echo, onboard radio receiver or GPS-based systems). All measurements in the profile are attributed to the nominal hour of the ascent. This is the hour at which the sonde reaches 100 mb. It takes approximately an hour for the balloon to rise to this level and thus the sondes are released one hour before the synoptic hours.

12. Automatic balloon releases

13. Radiosonde data http://weather.uwyo.edu/upperair/sounding.html Radiosonde data is reported up to four times per day at the synoptic hours of 00, 06, 12 and 18 GMT. The number of ascents varies widely between countries and stations. You can get worldwide radiosonde data from:

14. Temperature of an ascending air parcel • Start with the 1st Law of thermodynamics: • Assume the ascent is adiabatic, i.e. dq=0 • Use the hydrostatic equation: • Gives: remember: or:

15. Dry adiabatic lapse rate Acceleration due to gravity, g = 9.81 m s-2 Specific heat capacity dry air (at constant P), Cp = 1004 J K-1 kg-1 So: Check units: remember a Joule, J, can be expressed in fundamental SI units (e.g., kinetic energy = ½ m v2): 1 J = 1 kg (m s-1)2 = 1 kg m2 s-2 So units of Cp, J K-1 kg-1 = kg m2 s-2 K-1 kg-1 = m2 s-2 K-1 So the temperature gradient has units:

16. Concept: an ‘air parcel’ It’s a useful concept to imagine what will happen as a mass (‘parcel’) of air moves up or down in the atmosphere. Z p

17. Assumptions for a parcel of air • No exchange of mass with environment • No exchange of heat with surrounding • Adjusts to pressure of environment (And moves slowly enough to neglect energy of movement of air parcel)

18. Summary • Air temperature generally decreases with increasing altitude (e.g. radiosonde data) • Using some physics (hydrostatic equation, 1st Law of thermodynamics), we can derive a theoretical expression for the temperature gradient of an adiabatically ascending dry air parcel: -9.8 K/km • This is quite often a good approximation of the real atmosphere • Main complications involve moisture condensing and releasing latent heat – next lecture.

19. Current Weather Hugh Pumphrey’s web-pages: https://www.geos.ed.ac.uk/homes/hcp/currentmet.html

20. Potential Temperature (θ) • The potential temperature of an air parcel is its temperature when compressed (or expanded) adiabatically to surface pressure (p0) (defined as a standard pressure of 1000 hPa). • Again, start from the 1st Law of Thermodynamics, and make dq=0:

21. Ideal Gas Law (see Lecture 8) so: substitute in α:

22. Divide by RT: Integrate both sides, from the starting (p,T) tothe surface (p0,T0), noting cp/R is a constant: Remember integral of 1/x is natural log of x:

23. Integrating: Remember: Hence: or: Rearrange to give potential temperature, θ: