Atmospheric Circulation (WAPE: General Circulation of the Atmosphere and Variability) François Lott, flott@lmd.ens.fr http://web.lmd.jussieu.fr/~flott 1) Mean climatologies and equations of motion a)thermal, chemical and dynamical climatologies b)equations of motion 1
Vertical structure of the atmosphere: Température as a function of the geometrical altitude z* CIRA data (1988): Rockets, rasiosondes, satellites above 110km. Troposphere: T decreases with z*, the heating comes from the surface, whereas the wator vapor and clouds cool thye atmosphere above via infrared emission (IR). The middle atmosphere: contain 2 of the 3 layers of the neutral atmosphere: the stratosphere and the mesosphere. Les chemical major constituant are still well mixed There is a Max in T at 50km due to 03. This defines the stratopause separating the stratosphere and the mesosphere Above 90km lies the thermosphere, a layer highly exposed to sun radiation and the X-rays ionised the constituents. It contains the ionosphere (80-500km) where Aurora Borealis occur. Extremely thin in mass, T can vary from 600K to 1800K in one day. The atmosphere there is no longer neutral, is no longer well mixed: the composition varies according to the mass of the molecules because of the large distance between them. 2
Static relations: P, ρ, θ et Φ as a function of T(z*) Perfect gas law + hydrostatic relation: Pressure and Temperature: Log-pressure altitude: H = R T s g =7km T s ~240K,( mean characteristic Temperature) z=z* si T=T s Characteristic height: Potential Temperature: Geopotential: =T p s p =T exp z H Hydrostatic relation: 3
Static stability: Parcel method: we displace adiabatically a volume V of air and consider that the pressure P adjust to the environment (P p =P(z*+ z*))!! F= g (ρ(z )V ρ(z +δ z )V d )= g m( 1 ρ( z +δ z ) = gm( 1 Vertical acceleration: T p )) T (z +δ z Brunt Vaisala Frequency: = gm ( 1 θ(z ) d 2 δ z = F dt 2 m = g θ N 2 = g θ d θ dz ρ p ) θ( z +δ z )) d θ dz δ z 4
Major trace species (1): CO 2 et H 2 O CO2 : Uniformly mixed and very active in the infrared Satellite measurements in the stratosphere Vapeur d'eau (H 2 O): Rapid decay with altitude, very weak values (almost uniform) in the stratosphere. Strong greenhouse impact in the troposphere. Note the minimum value at the equatorial tropopause Balloon measurements in the troposphere: 5 5
Major trace species (2), Ozone: O3 Absorption of Uv-b's by 0 3 is the main driver of the middle atmosphere (stratosphere + mesosphere) circulation. Ozone protects us from the UV-b Maximum at 30-40km, in the stratosphere. Ozone profile in the midlatitudes and penetration of the UV-a, UV-b, UV-c 6
The Ozone heating makes up the stratosphere above the stratosphere. Vertical distribution of the heating due to absorption of the solar radiation and of the cooling due to emission of Infrared radiation. 7
Seasonal cycle of the solar flux O3 re-emit almost instantaneously producing a chemical heating, the UV it absorbs The solar flux is maximum at the poles in summer, in part because the length of the day is 24h there Averaged over the year, the solar flux is maximum at the equator 8
The heat capacity of the ocean is very large, it allows the oceans to integrate the solar cycle. The thermal forcing is then in the IR, and absorbed by H2O and CO2 before reaching the middle atmosphere (greenhouse effect) The SST is always warmer in the equatorial regions It maintains a large humidity in the tropical regions, yielding a large greenhouse effect there. The troposphere is essentially forced from below, and will experience a less dramatic annual cycle than the middle atmosphere 9
A striking illustration of the differences in circulation between the troposphere and the stratosphere ECMWF (93-97) horizontal wind January at z=12km (tropopause) Winter time mean climatologies: The winds in the troposphere are eastward in both hemisphere and in the mid-latitudes. In the stratosphere the winds are eastward in the winter hemisphere and westward in the summer hemisphere. 10
Solstices Zonal mean zonal wind climatologies (CIRA dataset) U (m/s) Equinoxes In all seasons there are two westerly jets near below the subtropical tropopause. These westerlies extent almost down to the surface (0-16km) and characterize the midlatitude circulations. Still in troposphere, the winds tend to be slightly westward (easterly) in the tropics. In the middle atmosphere (20-90km), the winds are eastward (westerlies) in the winter hemisphere and westward in the summer hemisphere. In spring and fall the middle atmosphere jets are eastward in both hemisphere (equinox). Note, that during the winters, the jets in the southern hemisphere (July) are stronger than in the northern hemisphere (January). 11
Zonal mean temperature climatologies (CIRA dataset) Solstices T(K)-230 Equinoxes Temperature decay with altitude in the troposphere. There is a minimum at the tropical tropopause (a greenhouse effect due to the presence of water vapour). In the stratosphere (20km<z<50km), T decreases from the summer pole to the winter pole. At the stratopause (50km) in the summer hemisphere, there is a max in T. During solstices and in the upper mesosphere (70-90km) T increases from the summer pole to the winter pole! Still in the solstices and at the mesopause, (90km) there are pronounced minima in T (~180K) over the summer pole!! 12
b) Equations of motion Newton law applied to hydrodynamic over a rotating sphere: Frictional forces pressure Gravitation with a correction to include the centrifugal acceleration Acceleration in spherical coordinates: r=a+z* Material derivative Wind components: 13
b) Equations of motion Approximate form for the and for a thin atmosphere (z*<<a, w<<u,v) Still in this approximation, the vertical component of the Newtown law reduce to the hydrostatic balance: We can therefore use the Log pressure altitude as a vertical coordinate: Material derivatives become: With vertical velocity : 14
b) Equations of motion Pressure force expressed using the log-altitude z: For a very small variation on a surface with λ=cte and for a surface z=cte, δp=0: δ p=0 ( p ϕ ) ϕ, z δ ϕ 1 ρ δφ Mass conservation: Bilan de chaleur: 15
Newton law: Primitive equations in log pressure coordinate (summary): Du Dt uv a Dv Dt u² a b) Equations of motion tan 2 sin v= 1 tan 2 sin u= 1 a a cos Y X z = R T H (Hydrostatic) Mass conservation: 0 u a cos v cos 0 w =0 z Thermodynamics: or: Material derivatives: Wind components: 16
Newton law: Du Dt uv a Dv Dt u² a Dw Dt tan 2 sin v= 1 tan 2 sin u= 1 a = Φ z + b+z, b) Equations of motion Boussinesq approximation (not detailed here) θ=θ s + θ( x,t ), p=p s + p( x,t ), b a cos Y X is the buoyancy: Φ= p ρ s b=g T T s =g θ θ s = g ρ ρ s Mass conservation: Thermodynamics: Material derivatives: 1 u acos v cos w z =0 D b D t =Q or D b Dt +N 2 w=q where b( x,t )=b ( x,t)+b 0 (z) The Buoyancy frequency: N 2 = g θ s dθ 0 d z Et z=z* Wind components: 17