Modelling the atmosphere. Hennie Kelder University of Technology Eindhoven

Transcription

1 Modelling the atmosphere Hennie Kelder University of Technology Eindhoven

2 Content Basics of the atmosphere Atmospheric dynamics Large scale circulation Planetary waves Brewer-Dobson circulation

3 Some Key Processes in the Atmosphere

4 Temperature Troposphere T decreases with z, stratosphere T increases with z due to ozone; stratosphere very stable; stratum= layer

5 a) 140 b) km S EQ 90N S EQ 90N Temperature (K) in stratosphere in January: a) radiative equilibrium; b) observed.

6 tropopause Lowermost stratosphere ( middle world ): isentropes connected with troposphere

7 Tropopause height(pressure) : geographical distribution instantaneous picture Potential Vorticity, PV: PV = (ξ θ +f) θ/ p ξ θ + f vorticity Θ potential temperature PV: small in troposphere, large in stratosphere;

8 Tropopause pressure versus ozone column

9 Dynamics of the atmosphere Equations Coordinate system on earth surface f = 2Ω sinϕ 0, Coriolis force Large scale horizontal circulation u/ t - fv + 1/ρ p/ x = F(x) v/ t + fu + 1/ρ p/ y = F(y)

10 Thermal wind Geostrophic and hydrostatic approximations f v/ z ~ g/t T/ x f u/ z ~ -g/t T/ y Coupling between temperature distribution and windstrength and wind direction T(y), dt/dy < 0, wind in x-direction v/ z = 0, v 1 =v 2, U 2 >U 1 zonal wind increases with height

11 Coupling between temperature and wind Zonal wind u f u/ z ~ - g/t T/ y Temperature Zonal wind

12 Zonal wind in stratosphere Polar jet Subtropical jet

13 Polar jetstream

14 2002, Splitting up of the Ozone hole

15 Planetary waves superposed on zonal circulation Z500 5 okt 2004 (ECMWF) ECMWF

16 Planetary waves: -generation in troposphere (orography, convective systems) - propagating in the troposphere but also in the stratosphere - propagation in the stratosphere only possible if..

17 Planetary waves, Equations, energy and momentum conservation ( / t + u 0 / x)( 2 ψ + f 02 /gb 2 ψ/ z 2 ) + β ψ/ x = 0, ψ = stream function Plane wave solution ψ = Re ψ 0 expi(ωt + kx + ly + mz) m 2 = gb/ f 02 β/(u 0 c ) - ( k 2 + l 2 ) Vertical wave propagation if m 2 > 0 u 0 c = β/( k 2 + l 2 + m 2 f 02 /gb) < U c = β/( k 2 + l 2 ) c = 0, orographic generated wave m 2 = gb/ f 02 β/u 0 -( k 2 + l 2 )

18 Charney-Drazin criterium Vertical propagation of waves only if 0 < [u] < U c = β/( k 2 + l 2 ) with U c ~ (wave length) 2 ([u] = zonal mean zonal wind) Jules Charney, Only large waves (k = 1,2) reach stratosphere In summer [u]<0 no waves in stratosphere atmospheric refractive index

19 Waves in stratosphere: Summer versus winter Zonal wind, 10 hpa 1 january 2002, waves 1 july 2002, no waves U > 0 U < 0

20 Winter (1 january 2002), (U > 0), different altitudes waves Φ(500 hpa), troposphere Φ(10 hpa), stratosphere

21 Summer (1 july 2002) (U < 0), waves in the troposphere only Φ(500 hpa), troposphere Φ(10 hpa), stratosphere

22 Atmospheric waves signatures in ozone

23 Kelvin waves velocity, temperature, pressure and ozone perturbations

24 Kelvin waves p = Pexp(-kβ/ш y 2 )expi(ш t - kx + Nk/ш z) u = Uexp(-kβ/ш y 2 )expi(ш t - kx - mz) Kelvin wind, zonal wind and pressure

25 The stratospheric meridional circulation

26 STEP 1: conservation of momentum and energy Zonal momentum equation (neglecting friction): Du/Dt fv + Φ/ x =0 Φ = geopotential = gz D/Dt = / t + u / x + v / y + w / z Thermodynamic energy equation: dt/dt + (κt/h)w = Q Details: e.g., Holton (1992)

27 STEP 2: zonal mean x=[x] + x Zonal momentum equation [u]/ t fv = - [u v ]/ y Energy equation: [T]/ t + N 2 HR -1 w = - [v T ]/ y + [Q]

28 STAP 3: TEM (Transformed Eulerian Mean) : w* [w] + RH -1 ([v T ]/N 2 )/ y, that is [T]/ t + N 2 HR -1 w*= [Q] Define v* by v*/ y+ w*/ z = 0 (continuity equation.) Zonal momentum equation: [u]/ t fv* = ρ -1 div(eliassen-palm (EP) flux) (v*,w*): Lagrangian (diabatic) circulation

29 [u]/ t fv* = ~ div(ep-flux) ~ - [u v ]/ y - [v T ]/ z By wave breaking and dissipation (especially [v T ]/ z) a meridional circulation (v*,w*) is generated, also called Brewer-Dobson circulation Brewer Dobson

30 1920 Dobson, total ozone measurements with ozone photo spectrometer Dobson eschewed all the modern methods by which distinguished scientists waste their time telephones, secretaries, meetings, committees. Instead he worked quietly and steadily at home, spending the afternoons cultivating his large and productive garden

31

32 [u]/ t fv* = div(ep-flux) = - [u v ]/ y- [v T ]/ z p/ y N u fu y y 1. Begin : [u]/ t = 0, v = 0, geostrophic equilibrium 2. Suppose div(ep-flux) < 0, hence [u]/ t< 0; 3. fu decreases, p/ y dominates fu, air moves northwards (= larger y) v* > 0 and (continuity) downwards w* > 0 Planetary waves induce Brewer-Dobson circulation

33 BD-circulation strongest in NH winter w* 0.16 mm/s (JJA) up to 0.3 mm/s (DJF), 1 km in three months 6 % atmospheric mass/year, Consequences of BD -life time of CFC s -ozone distribution -stratospheric water distribution -stratospheric temperature distribution

34 Ozone transport through Brewer-Dobson circulation Ozone production highest in the tropics Ozone column largest outside the tropics, where lower ozone production takes place; Causes: BD-circulation and tropopause height

35 Monthly mean ozone column distribution, 2002 jan mar BD to the North mei jul BD to the South sep nov

36 Water in the stratosphere annual cycle in strength of BD circulation idem in T (tropical tropopause) idem in specific humidity tropical tropopause tape recorder

37 [v T ] 100 hpa: large influence on ozone transport during winter Warm NH winters Cold NH winters 2002 Antarctic stratospheric warming

38 Is the BD-circulation increasing? mass flux (10 8 Kg s 1 ) TRANSIENT UM49L(a) UM49L(b) UM64Lchem UM64L WACCM GISS MRI GISSchem Year Climate model results

39 Summary Atmospheric dynamics and composition are strongly related The distribution of trace gases and changes in these distributions are determined by complex interaction between chemistry, dynamics and radiation