General Meteorology. Part II. I Introduction and Terminology. II Earth s Atmosphere and Sun

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1 Part II General Meteorology I Introduction and Terminology II Earth s Atmosphere and Sun III Thermodynamics of the Atmosphere (Stability of atmosphere) IV Meteorological Dynamics (atmospheric motion) II/1

2 II Earth s atmosphere and sun II.1 Chemical composition of dry atmosphere II.2 Physical units for trace gas amounts II.3 Layering of the atmosphere II.4 Hydrostatic Equation II.5 Temperature profile of the atmosphere II.6 Moisture water vapour in the air II.7 Earth s radiation budget II/2

3 chemical composition II.1 Chemical composition of dry atmosphere Molecule partial volume/ partial pressure Molar mass [10-3 kg/mole] Boiling point [ C] Nitrogen N Oxygen O Argon Ar Carbon dioxide CO Major components (air) (-193) Neon Ne 18 X Helium He 5.2 X Methane CH4 1-2 X Crypton Kr 1.0 X Hydrogen H2 0.5 X Nitrous oxide N2O X Xenon Xe 0.08 X Carbon monoxide CO Ozone O3 (*) X X 10-6 (*) surface value, stratosphere: 2-8 X other minor components (note: chemical active species are in minority!!) CH2O (formaldehyde), NO2 (nitric oxide), NH3 (ammonia), SO2(sulfur dioxide), I2 (jodine), Cl2 (chlorine), Rn (radon) II/3 water vapour: very variable 0-4%

4 Trace gas amounts II.2 Physical units for trace gas amounts ideal gas law pv = nrt (Eq. II.1) p pressure V volume n amount in units of mole R =8.31 J/(mole K), gas constant T temperature in K trace gas amount: 1 mole is the amount of a substance which has the same number of molecules as 12g of 12 C isotope 1 mole contains x molecules N A =6.022 x molecules/mole Avogadro number II/4

5 Trace gas amounts molecular density: molar density ρ n mol = = V p RT units: mole/m 3 (Eq. II.2) number density ρ n N p N p V RT kt = A = A = units: molec./m 3 (Eq. II.3) k=1.38x10-23 J/K Boltzmann constant mass density ρ m = n m = V m p RT units: kg/m 3 (Eq. II.4) m: molar mass in g/mole (air ~29 g/mole) II/5

6 Trace gas amounts volume mixing ratio of i-th trace gas: P i, V i : partial pressure and partial volume of i-th trace gas p air pressure; r, r mol air density (molar or number density) volume mixing ratio units: volume parts per million=ppmv=10-6 or ppbv=10-9 ρ = ρ = ρ + ρ + m i, m N2, m O2, m i ρ = ρ = ρ + ρ + i ξ i i N2 O2 p= p = p + p + i ρ p ρ V ξ = i ρ = p = ρ = V i N2 O2 ρ = ρ = ρ + ρ + mol i, mol N 2, mol O2, mol i i i imol, i mol other units used are ppmm (mass parts per million) or ppbm according to partial mass density Note: if neither volume or mass units are given, then most likely: 1 ppm=1 ppmv or 1 ppb =1 ppbv II/6

7 II.3 Layering of the atmosphere atmospheric layering dissociation molecular diffusion mixing II/7 glossary: Luftdruck=pressure, Luftdichte =air density, Ozonschicht=ozone layer, Höhe=height, Ozonschicht=ozone layer, B- E-, F-Schicht=B-,E-,F-layer (ionic layers), kosmische Strahlung=(galactic) cosmic ray, Polarlicht=aurora, Meteore=meteorites, leuchtende Nachtwolken=noctilucent clouds, Perlmutterwolken=polar stratospheric clouds (mother of pearl clouds)

8 atmospheric layering Criterium life forms composition temperature middle atmosphere upper atmosphere radio physics term biosphere homosphere homopause heterosphere troposphere tropopause stratosphere stratopause mesosphere mesopause thermosphere exosphere ionosphere magnetosphere altitude 0-20 km km km >120 km 0-12 km ~12 km km ~50 km km ~85 km km >500 km km >300 km II/8

9 atmospheric layering and temperature seasonal variation in NH January & July (Valley 1965) WMO standard atmosphere 1962 (global) atmospheric mass: troposphere 90% stratosphere 9.5% mesosphere 0.5% stratospheric warming in winter 75 N (Valley 1965) II/9

10 atmospheric layering other criteria: aerodynamical state (planetary boundary layer) Prandtl layer 0-50 m Ekman layer m free atmosphere (above boundary layer > 1000 m) fractions homosphere molecular weight [g/mole] II/10 O O 2, N 2

11 The sun and ionosphere solar surface view (photosphere) cross-section II/11 glossary: Sonnenfleckengruppe=sun spot group, Rotationsachse=rotation axis

12 The sun and ionosphere glossary: Sonne=sun, magnetische Feldlinien=magnetic field lines, Sonnenwind=solar wind, Magnetschweif der Erde=magnetic tail, shaded area=van Allen belt (ion plasma) II/12

13 The sun and ionosphere Photochemical process wavelength [Å] layer glossary: Nachtseite= night side, sporadische E-Schicht=sporadic E-layer, photochemischer process=photochemical reaction, Wellenlänge =wavelength II/13

14 The sun and ionosphere el. density particle density λ 1 <λ 2 P ρ F λ P : ion production rate ρ : density of ionisable trace gases F λ : solar flux density at wavelength λ layer altitude radiation ions el.density max e- [km] [cm -3 ] [km] glossary: Röntgen=x-ray, weiche Röntgen= soft x-ray, Dichte=density, Flußdichte=flux density, Ionenproduktionsrate=ion production rate II/14

15 hydrostatic equation II.4 Hydrostatic equation II/15

16 hydrostatic equation (cont d) (Eq. II.5) integration on the left from p(h) to p( ) and from height h to top-ofathmosphere (h= ) (Eq. II.6) partial mass density of air column above height h in units of kg/m 2 II/16 that means that the pressure at altitude h is proportional to the weight of air column above that altitude

17 hydrostatic equation (cont d) (Eq. II.7) Now we have separated variables, pressure terms to the left and height dependent terms to the right This is an important relationship that will allow us to estimate temperature from geopotential height maps at two pressure levels II/17 (Eq. II.8)

18 hydrostatic equation (cont d) This way the relationship between atmospheric pressure and temperature can be well approximated at any altitude II/18 (Eq. II.9)

19 atmospheric scale height ) km Ahrens 1999 if our atmosphere is compressed to normal sea level pressure the atmosphere would be 8 km thick at about 5.5 km altitude the pressure is half the value at sea level (~500 hpa) air number density and pressure decrease exponentially with altitude II/19

20 atmospheric scale height W is called the air vertical (total) column density usually given in molec./cm 2 Ahrens 1999 (Eq. II.10) II/20

21 trace gas column density m II/21 global ozone total column average about 300 DU ozone layer is extremely thin (3 mm) but still very important since O 3 is a very strong absorber (per molecule) of UV radiation

22 ozone Seinfeld 1986 DU II/22 global ozone total column average about 300 DU ozone layer is extremely thin (3 mm) but still very important since O 3 is a very strong absorber (per molecule) of UV radiation

23 geopotential height geopotential φ at any point of the atmosphere is defined as the work to be done to bring a 1 kg mass against gravity to that point from sea level [ φ J m ] = m 2 kg = s energy per unit mass=path acceleration dφ = g dh h φ( h) = gh ( ') dh' (Eq. II.11) h' = 0 g is not constant and its value depends on latitude and height g g g ϕ h ϕ ϕ ( ϕ, ) [ = = cos(2 ϕ ) cos (2 ϕ )] aaaaaaaaaaaaaaaaaaaaaaaaaaaaa 7 [ h] Boguer formula with h in meter and g in m/s 2 g [m/s 2 ] j=0 j= 45 j= 90 h=0 km h=30 km II/23

24 geopotential height Definition of geopotential height z (GPH): h 1 φ( h) z = g( ϕ, h') dh' g g h' = 0 o (Eq. II.12) go 9.8 m/ s 2 dφ = g dh = go dz φ=45 : h=5 km z=4.996 km h=50 km z= km h=500 km z= km at lower altitudes geopotential height z is almost identical to geometric height h. at surfaces of equal geopotential heights the gravity force remains the same. this is important for energy considerations in large-scale motion (see atmospheric dynamics) II/24

25 geopotential height hypsometric equation is an important tool for weather charts: starting from Eq. II.8 φ = g h= g z o This is the hypsometric equation difference in geoptential heights (z 2 -z 1 ) from two pressure levels (p 1 and p 2 ) is called relative topography and is proportional to the mean temperature between these two layers II/25

26 relative topography: cold droplet T low H high K cold W warm surface pressure [hpa] GPH difference between 500 and 1000hPa [dm] hpa C cold droplet GPH at 500hPa[dm] II/26 Malberg 1997

27 relative topography: cold droplet dry condition (clouds dissolving) high convection (clouds, thunderstorm) temperature anomaly in C relative humidity in % Malberg 1997 II/27