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Physik der Atmosphäre I Physics of the Atmosphere I

Physik der Atmosphäre I Physics of the Atmosphere I. WS 2008/09 Ulrich Platt Institut f. Umweltphysik R. 424 Ulrich.Platt@iup.uni-heidelberg.de. Last week. Atmosphere crucial for live

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Physik der Atmosphäre I Physics of the Atmosphere I

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  1. Physik der Atmosphäre IPhysics of the Atmosphere I WS 2008/09 Ulrich Platt Institut f. Umweltphysik R. 424 Ulrich.Platt@iup.uni-heidelberg.de Physik der Atmosphäre I

  2. Last week • Atmosphere crucial for live • Atmosphere is a complex and non-linear system, interacting with the other geophysical compartments (ocean, land, ice sheet…) • The primary source of energy is solar radiation • Strongest variability (T, p, …) is in the vertical • Large range of spatial and temporal scales • Hydrostatic equation: Physik der Atmosphäre I

  3. Contents Physik der Atmosphäre I

  4. Outline for Today • Basic thermodynamic definitions • Dry-adiabatic lapse rate • Moist-adiabatic lapse rate • The potential temperature • The equivalent temperature • Vertical stability • Buoyancy oscillations Physik der Atmosphäre I

  5. The vertical structure of the atmosphere Physik der Atmosphäre I

  6. How to determine the tropospheric temperature profile • Atmosphere is heated by the Earth‘s surface • Cooling/heating rates of the air by emission/absorption of radiation are much smaller than typical transport times • Transport processes are (nearly) adiabatic • The condensation of water vapour is an additional source of heat • To determine the tropospheric temperature profile, we need • the ideal gas law • the first law of thermodynamics • the hydrostatic equation Physik der Atmosphäre I

  7. Ideal gas equation • Ideal gas: • molecules have no volume • no collisions between gas molecules • error for assuming that atmospheric gases are ideal gases is small • Ideal gas equation • p: pressure • V: volume • n: amount of gas in moles • T: absolute temperature • R: gas constant (8.314 J/mol K) • Extensive properties: • proportional to size of system, e.g. n, V • „2x size  2x property“ • Intensive property: • independent of mass: p,T, r • „intensify“ extensive property by dividing by mass or volume  “specific property”, e.g. r = m/V Physik der Atmosphäre I

  8. First law of thermodynamics • First law (1. Hauptsatz): • dQ – heat added to the system • dW – work done ON the system • dU – change in internal energy • Work done on system: compression of air • Internal energy of an ideal gas is independent of volume and proportional to temperature • Cv – heat capacity (at constant volume) Physik der Atmosphäre I

  9. First law of thermodynamics (contd.) • First law (1. Hauptsatz): • Ideal gas law: • Convert to intensive quantities by dividing by n: • q = Q/n: heat per mole • cv = Cv/n: specific heat capacity • cp = cv + R: specific heat capacity at constant pressure Physik der Atmosphäre I

  10. Dry-adiabatic lapse rate • First law (1. Hauptsatz): • Hydrostatic equation: • Movement of air parcel is assumed to be adiabatic, i.e. no heat is exchanged with the environment: dq = 0. This is justified since cooling rates in the troposphere are much smaller than typical transport times. Physik der Atmosphäre I

  11. Dry-adiabatic lapse rate (contd.) • Temperature gradient in the atmosphere: Values for air: • cp = 28.97 J/(K mole) • M = 28.97 g/mole • g = 9.81 m/s2 • Dry-adiabatic lapse rate: • The temperature gradient is given by G only if no additional heat sources (condensation, absorption of radiation) are present (dq=0) • Actual temperature gradient present in the atmosphere: Physik der Atmosphäre I

  12. Atmospheric Energy • Kinetic energy (per volume): • E=½ ρair v2, ρair = 1.293 kg m-3, v = 10 ms-1  E = 65 J m-3 • Sensible heat (per volume): • Qs = ρaircp ΔT, cp = 103 J kg-1 K-1, ΔT = 10K  Qs = 1.3x104 J m-3 • Latent heat (per volume): • QL = ρairL q, L = 2.256x106 J kg-1, q = 10 g kg-1  QL = 2.9x104 J m-3 • Phase transfer processes (e.g. convection, cloud formation) play major roles in energy balance Physik der Atmosphäre I

  13. Moisture parameters • Vapour pressure [hPa]: • partial pressure of H2O vapour: e • p=Σipi=pdry+e • assume H2O vapour to be an ideal gas: e = ρv Rv T • Saturation vapour pressure [hPa]: e* • Absolute humidity [g m-3]: a = ρv = mv / V • Specific humidity [kg/kg=1]: q = ρv / ρair, with ρair density of moist air • Relative humidity [1]: f = e / e* • Dew point: T @ e = e* (p=const) Physik der Atmosphäre I

  14. The Moist-Adiabatic Lapse Rate • Condensation of water vapour releases heat, i.e. dQ ≠ 0: • L ≈ 2250 J/g: specific evaporation heat • dmw: change in mass of gaseous water vapour • Convert to intensive quantities by dividing by n: • rw = mw/V is the saturation water vapour concentration • Re-ordering yields the moist-adiabatic lapse rate: Physik der Atmosphäre I

  15. Saturation vapour pressure Magnus formula for e* [hPa]: rule of thumb: ΔT=10K  Δe ≈ 2 e Bergeron-Findeisen process Physik der Atmosphäre I Wallace and Hobbs, 2006

  16. Moist-adiabatic lapse rate Moist-adiabatic lapse rate as a function of air temperature, with pressure as parameter (Roedel, 1994). Physik der Atmosphäre I

  17. The (Alpine) Föhn Inflow of moist air  cooling, precipitation  heating  outflow of warm, dry air Source: Roedel Physik der Atmosphäre I

  18. Potential Temperature Potential temperature Q = temperature of an air parcel if it would be adiabatically compressed to a pressure of 1013 mBar • 1st law of thermodynamics: • dq = 0 (adiabatic process) yields: • Integration yields: with k = cp/cv and the surface pressure p0 = 1013 mBar. • Q≡ T0 is the temperature of the air parcel after compression from p to p0: with (k-1)/k≈ 0.286 in air Physik der Atmosphäre I

  19. Strahlungsheizung durch O2 (UV) Strahlungskühlung durch H2O & CO2 =1900K Höhe (Km) Homosphäre Druck (mBar) Strahlungsheizung durch O3 (UV) =800K Strahlungskühlung (IR) durch H2O & CO2 =340K Konvektion Temperatur (K) Physik der Atmosphäre I

  20. Equivalent Temperature Equivalent temperature Teq = temperature of a moist air parcel if all water vapour would condense • Release of latent heat per volume... • .. leads to an increase in internal energy: • Δu = Δq Temperature increase: with water vapour mixing ratio q = rv/rair • Equivalent and equivalent-potential temperature: • Example: • L ≈ 2250 J/g • cp ≈ 1 J/(g K) • T = 15°C • Specific humidity: 70%, corresponding to q ≈ 12.410-3 • ΔT ≈ 31 K • Equivalent temperature Teq ≈ 46°C Physik der Atmosphäre I

  21. Potential temperature and vertical stability • From the hydrostatic equation, we have • Total differential of the potential temperature: • Thus, with where is the actual temperature gradient. Physik der Atmosphäre I

  22. Vertical stability • g = G, dQ/dz = 0: neutral • g < G, dQ/dz > 0: stable • g > G, dQ/dz < 0: unstable Physik der Atmosphäre I

  23. z • Auslenkung eines Luftpakets nach oben (von z2 nach z3): • ΘP=const. • ΘP< Θ(z3)  Dichte des Luftpaketes größer als Dichte der umgebenden Luft  Rücktreibende Kraft z2 z2 z (z) T(z) F z z1 z1 F  P z F • Auslenkung eines Luftpakets nach oben (von z2 nach z3): • ΘP=const. • ΘP> Θ(z3)  Dichte des Luftpaketes geringer als Dichte der umgebenden Luft  Resultierende Kraft nach oben, treibt Luftpaket weiter von der ursprünglichen Lage weg F P  Potential Temperature and Vertical Stability Physik der Atmosphäre I

  24. Dry and moist stability Physik der Atmosphäre I

  25. Stüve diagram (1) Physik der Atmosphäre I http://www.csun.edu/~hmc60533/CSUN_103/weather_exercises/soundings/smog_and_inversions/Understanding%20Stuve_v3.htm

  26. Stüve diagram (2) Wind speed and direction Air temperature Isobars Inversion Temperature [K] Temperature [°C] Pressure Altitude Isotherms Physik der Atmosphäre I

  27. Stüve diagram (3) Dew point temperature Saturation water vapour mixing ratio [g water/kg air] Physik der Atmosphäre I

  28. Yellow line: Temperature of an air parcel lifted up adiabatically from 950 mBar. Initial water vapour content: 8g/kg (inferred from dew point temperature). Air parcel is undersaturated and thus follows the dry adiabatic temperature gradient (~1K/100m) Condensation starts at 800mBar, where saturation water vapour mixing ratio equals water vapour content. Stüve diagram (4) Dry lapse rate Condensation starts Physik der Atmosphäre I

  29. Yellow line: Temperature of an air parcel lifted up adiabatically from 950 mBar. Initial water vapour content: 8g/kg (inferred from dew point temperature). Air parcel is undersaturated and thus follows the dry adiabatic temperature gradient (~1K/100m) Condensation starts at 800mBar, where saturation water vapour mixing ratio equals water vapour content. Now the air parcel follows the moist adiabat due to release of latent heat. Stüve diagram (5) Moist lapse rate Dry lapse rate Temperature of rising air parcel is always below actual temperature Stable conditions Physik der Atmosphäre I

  30. Yellow line: Temperature of an air parcel lifted up adiabatically from 950 mBar. Dew point temperature is equal to actual temperature up to 750 mBar  condensation, formation of clouds. Stüve diagram (6) Temperature of rising air parcel is above actual temperature Unstable conditions, convection Physik der Atmosphäre I

  31. Brunt-Väisälä or buoyancy oscillations How can atmospheric stability be defined quantitatively? • Equation of motion for the buoyancy of an air parcel: r: density of air parcel; r*: density of surrounding air • r proportional to 1/T: • Adiabatic and actual lapse rate: • It follows: • Potential temperature: Physik der Atmosphäre I

  32. Brunt-Väisälä or buoyancy oscillations How can atmospheric stability be defined quantitatively? • Equation of motion for the buoyancy of an air parcel: with • This is the equation of an harmonic oscillator with the Brunt-Väisälä frequency • For dQ/dz > 0 (stable conditions), this leads to buoyancy oscillations. • Typical periodic times: • 15 minutes for g = 0.8 (stable conditions) • 5 minutes for g = 0 (isotherm stratification) Physik der Atmosphäre I

  33. Lee wavesBuoyancy oscillations downwind of mountains Formation of lee waves „Lenticular clouds“ Physik der Atmosphäre I

  34. Lee waves… can propagate up to the stratosphere Polar stratospheric clouds observed in Kiruna, northern Sweden. These clouds are formed in the ascending branch of the lee waves occuring downwind of the Scandinavian mountains. (Photo courtesy of C.F. Enell) Physik der Atmosphäre I

  35. Summary • Rising air cools down due to adiabatic expansion • Dry-adiabatic lapse rate: G≈ 1K/100m • Condensation of water vapour leads to the release of latent heat • Moist-adiabatic lapse rate: (0.5 – 1)K/100m • Potential temperature Q = temperature of air parcel, if compressed adiabatically to 1013 mBar • Vertical stability of the atmosphere is determined by the actual vertical temperature gradient compared to the dry/moist lapse rate: • dQ/dz = 0: neutral • dQ/dz > 0: stable • dQ/dz < 0: unstable • Buoyancy oscillations (Brunt-Väisälä oscillations) can occur for stable conditions (dQ/dz > 0)  Formation of lee waves downwind of mountains Physik der Atmosphäre I

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