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 terms of Fahrenheit o F C=(F - 32) 5/9; K= (F - 32) 5/9 + 273.15; Temperature scale in terms of Celsius o C F=(C 9/5) + 32; K=C + 273.15; Temperature scale in terms of Kelvin K F=(K - 273.15) 9/5 + 32; C= K - 273.15;
Composition of atmosphere
Atmosphere development From From Hadean Pleistocene period to Cambrian Holocene explosion Carbon Argon 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 Definition of pressure: P 1Pa force area 10 5 F A N m bar 0.01mbar 2 Pa Atmospheric pressure: P surface 1atm 760mmHg 1atm 1. 013bar 760Torr dp dz 2 Hydrostatic equation: g g 9.81m / s : density g/cm 3 g: gravity Ideal gas equation: P V R T m V m P dp g dz R T dp m g dz P R T dz H m P R T H R T m g R: gas constant R=8.314 J/mole K m=0.029 kg/mole (for dry N 2, 0 2 air) H: scale height
Isothermal atmosphere T=const. dp P dz H H R T m g 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) P z H H P0 e or z H ln J 8.314 290K mole K kg m 0.029 9.81 2 mole s surface 8. 48 P0 P The scale height is the increase in altitude for which the atmospheric pressure decreases by a factor of e! km Barometric Formula
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 Htrop 7.31km kg m 0.029 9.81 2 mole s P trop (10km) 760 e 10km 7.31km Torr 194Torr 0.255atm 0.263bar For mapping the altitude dependence of atmospheric pressure, we define layers of atmosphere, limited by pressure conditions P 1 and P 2, 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.) z R T m g P 1 P1 ln H ln P2 P2 P 2 1 ztropospher e H ln 7.31ln km 10km P 1 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. P( z) P 0 e z dz 0 H ( z( T )) observed isothermal 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: P V R T m R P T 0 e z H m V m P R T Density scales with pressure and follows therefore the same exponential behavior with altitude z. kg 5 0.029 1.0110 Pa 10 mole 7.31 10km e J 8.314 250K mole K kg 10km 0.363 3 m N 1Pa 1 10 2 m 5 3.6310 bar 4 g cm 9.8710 1bar 1.0110 3 6 kg 0.4 3 m atm 5 Pa (kg/m 3 )
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 Tconst (isothermal)