Modelling the atmosphere Hennie Kelder University of Technology Eindhoven
Content Basics of the atmosphere Atmospheric dynamics Large scale circulation Planetary waves Brewer-Dobson circulation
Some Key Processes in the Atmosphere
Temperature Troposphere T decreases with z, stratosphere T increases with z due to ozone; stratosphere very stable; stratum= layer
a) 140 b) 220 80 km 270 160 280 250 60 40 220 220 170 90S EQ 90N 220 200 210 20 90S EQ 90N Temperature (K) in stratosphere in January: a) radiative equilibrium; b) observed.
tropopause Lowermost stratosphere ( middle world ): isentropes connected with troposphere
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;
Tropopause pressure versus ozone column
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)
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
Coupling between temperature and wind Zonal wind u f u/ z ~ - g/t T/ y Temperature Zonal wind
Zonal wind in stratosphere Polar jet Subtropical jet
Polar jetstream
2002, Splitting up of the Ozone hole
Planetary waves superposed on zonal circulation Z500 5 okt 2004 (ECMWF) ECMWF
Planetary waves: -generation in troposphere (orography, convective systems) - propagating in the troposphere but also in the stratosphere - propagation in the stratosphere only possible if..
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 )
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, 1917-1981 Only large waves (k = 1,2) reach stratosphere In summer [u]<0 no waves in stratosphere atmospheric refractive index
Waves in stratosphere: Summer versus winter Zonal wind, 10 hpa 1 january 2002, waves 1 july 2002, no waves U > 0 U < 0
Winter (1 january 2002), (U > 0), different altitudes waves Φ(500 hpa), troposphere Φ(10 hpa), stratosphere
Summer (1 july 2002) (U < 0), waves in the troposphere only Φ(500 hpa), troposphere Φ(10 hpa), stratosphere
Atmospheric waves signatures in ozone
Kelvin waves velocity, temperature, pressure and ozone perturbations
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
The stratospheric meridional circulation
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)
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]
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
[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
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
[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
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
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
Monthly mean ozone column distribution, 2002 jan mar BD to the North mei jul BD to the South sep nov
Water in the stratosphere annual cycle in strength of BD circulation idem in T (tropical tropopause) idem in specific humidity tropical tropopause tape recorder
[v T ] 100 hpa: large influence on ozone transport during winter Warm NH winters Cold NH winters 2002 Antarctic stratospheric warming
Is the BD-circulation increasing? mass flux (10 8 Kg s 1 ) 80 70 60 50 40 30 20 TRANSIENT UM49L(a) UM49L(b) UM64Lchem UM64L WACCM GISS MRI GISSchem 1960 1980 2000 2020 2040 2060 2080 Year Climate model results
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