Atmosphere and Climate

The atmosphere is a complex hydrodynamical system, driven by radiative, convective, gravitational, and rotational forces, which can cause frequent dynamic fluctuations in temperature and pressure conditions. These can translate into short time local “weather” conditions. Long term, general climate considerations are based on approximate equilibrium assumptions necessary for developing appropriate models for atmosphere simulation. Approximations

One dimensional models describing the vertical structure of the atmosphere as a sequence of different atmospheric layers with altitude dependent density, temperature, pressure, composition profile.

For more complex global simulations, two-dimensional or even three-dimensional atmosphere models are necessary! Physical structure of atmosphere Temperature at high altitudes Temperature scale in Temperature scale in Temperature scale in terms of Fahrenheit oF terms of Celsius oC terms of Kelvin K C=(F - 32) ·5/9; F=(C · 9/5) + 32; F=(K - 273.15) · 9/5 + 32; K= (F - 32) · 5/9 + 273.15; K=C + 273.15; C= K - 273.15; Composition of atmosphere Atmosphere development

From FromHadean Pleistocene period to toCambrian Holocene explosion CarbonArgon Molecule Growth Content in Earth’s of Earth’s Atmosphere Atmosphere

Variation with time Composition and altitude Vertical structure of pressure conditions in the atmosphere

force F  N  P     Pa Definition of pressure: area A m2  1Pa  105bar  0.01mbar

P  1atm  760mmHg  760Torr Atmospheric pressure: surface 1atm  1.013bar

dP : density g/cm3 Hydrostatic equation:    g g  9.81m / s2 dz g: gravity

m m  P Ideal gas equation: P V  R T    R: gas constant V R T R=8.314 J/mole K m  P m=0.029 kg/mole dP    g  dz R T (for dry N2, 02 air) dP m  g dz R T   dz   H  H: scale height P R T H m  g Isothermal atmosphere T=const. J 8.314 290K dP dz R T mole K   H  H   8.48km surface kg m P H m  g 0.029 9.81 mole s2 Differential equation which is solved by an exponential equation for pressure depending on height (Note: the scale height H is temperature dependent and the temperature T varies with altitude z between 200K and 300K.) Assuming an isothermal atmosphere (T=const) z  H  P0  P  P0 e or z  H ln   P  Barometric Formula The scale height is the increase in altitude for which the atmospheric pressure decreases by a factor of e! For the troposphere – the lowest layer of the atmosphere – a representative average temperature value of T=250K is adopted. J 8.314  250K mole K H   7.31km trop kg m 0.029 9.81 mole s2 10km  7.31km Ptrop(10km)  760 e Torr  194Torr  0.255atm  0.263bar For mapping the altitude dependence of atmospheric pressure, we define layers of atmosphere, limited by pressure conditions

P1 and P2, which correspond to a layer thickness z with a mean temperature T (mass/mole m depends also on the humidity and the chemical composition of the atmospheric layer.)

R T  P1   P1  z   ln   H ln  m g  P2   P2 

 P   1   2  ztroposphere  H ln   7.31ln  km 10km  P1   0.255  Non-isothermal atmosphere T=const

Scaled height H depends linearly on temperature T and mass/mole m, which both change with altitude z. To determine pressure at a certain altitude z requires integration over the atmospheric layer.

z dz observed  isothermal 0 H (z(T )) P(z)  P0 e

Deviations are negligible (for the purpose of this class) and are mostly associated with temperature variations at certain atmosphere levels above T=240K as observed for the stratopause located at altitudes between stratosphere and mesosphere as well as the altitude range above the mesosphere such as the thermosphere and ionosphere. Density in an isothermal atmosphere Ideal gas law applies over the entire atmosphere: m m  P P V  R T    V R T  z    m  P0  H    e 1bar 1.01105 Pa R T Density scales with pressure and follows therefore the same exponential behavior with altitude z. (kg/m3) kg 5  10  0.029 1.0110 Pa     mole e  7.31  10km J 8.314 250K mole K kg g kg   0.363  3.63104  0.4 10km m3 cm3 m3 N 1Pa 1 105 bar  9.87106 atm m2 Vertical temperature structure of atmosphere

Temperature structure is not homogeneous with altitude because of different energy (heat) transport modes as well as radiation absorption processes at different altitudes.

Troposphere: convective heat transport mode  T declines with z Stratosphere: radiative heat transport mode  Tconst (isothermal)