modelling the atmosphere • basics of the atmosphere ... · day 4 - l4 atmospheric modelling1...

Day 4 - L4 Atmospheric modelling1 Hennie Kelder 1

DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING

• Modelling the atmosphere

• Basics of the atmosphere• Atmospheric dynamics

Temperature

Troposphere T decreases with z, stratosphere T increases with z due to ozone; stratosphere very stable; stratum= ‘layer’

90S EQ 90N 90S EQ 90N

Temperature (K) in stratosphere in January:a) radiative equilibrium; b) observed.

170 210

160 250

140220

220 220

270 280

220 200

Lowermost stratosphere (‘middle world’):isentropes connected with troposphere

tropopause

Tropopause height(pressure) : geographical distribution instantaneouspicture

Potential Vorticity, PV:

PV = (ξθ +f)∂θ/∂p

PV: small in troposphere,large in stratosphere;

Tropopause pressure versus ozone column

Atmospheric dynamics

Large scale circulation

Planetary waves

Brewer-Dobson circulation

Equations

Coordinate system on earth surface

f = 2Ω sinϕ0 , Coriolis forces

Large scale horizontal circulation

∂u/∂t - fv + 1/ρ∂p/∂x = F(x)

∂v/∂t + fu + 1/ρ∂p/∂y = F(y)

Thermal windGeostrophic approximation fv = RT/p ∂p/∂x = RT∂lnp/∂xHydrostatic approximation - g/RT = ∂lnp/∂z∂T/∂z << ∂T/∂x, ∂T/∂y

f∂v/∂z ~ g/T ∂T/∂xf∂u/∂z ~ -g/T ∂T/∂yCoupling between temperature distributionand windstrength and wind direction

T(y), dT/Dy < 0, wind in x-direction∂v/∂z= 0, v1=v2,U2>U1

Coupling between temperature and wind

Zonal wind uf∂u/∂z ~ - g/T∂T/∂yTemperature

Zonal wind

Zonal wind in stratosphere

2002, Splitting up of the Ozone hole

Planetary waves

Z500 5 okt 2004 (ECMWF)

Planetary waves:

- generation in troposphere (orography, convective systems)

- propagating , also in the stratosphere

- propagation only possible if…..

Planetary waves, Equations, energy and momentum conservation(∂/∂t + u0∂/∂x)(∇2 ψ + f0

2/gB∂2ψ/∂z2) + β∂ψ/∂x = 0, ψ = stream function

Plane wave solutionψ = Re⎨ψ0expi(ωt + kx + ly + mz)⎬m2 = gB/ f0

2⎨β/(u0 –c ) - ( k2 + l2 )⎬

Vertical wave propagation if m2 > 0u0 – c = β/( k2 + l2 + m2f0

2/gB) < Uc= β/( k2 + l2)c = 0, orographic generated wavem2 = gB/ f0

2⎨β/u0 - ( k2 + l2 )⎬

Charney-Drazin criterium

Jule Charney, 1917-1981

Vertical propagation of waves only if

0 < [u] < Uc= β/( k2 + l2)

with Uc ~ (wave length)**2

([u] = zonal mean zonal wind)

Only large waves (k=1,2) reach stratosphereIn summer [u]<0 → no waves in stratosphere

‘atmospheric refractive index’

Zonal wind, 10 hPa1 january 2002, waves 1 july 2002, no waves

Waves in stratosphere:Summer versus winter

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

The stratospheric meridional circulation

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

STEP 1: conservation of momentum and energy

Details: e.g., Holton (1992)

x=[x] + x’

Zonal momentum equation

∂[u]/∂t –fv = - ∂[u’v’]/∂y

Energy equation:

∂[T]/∂t+ N2HR-1w= -∂[v’T’]/∂y + [Q]

STEP 2: zonal mean

w*≡[w]+RH-1∂([v’T’]/N2)/∂y, that is

∂[T]/∂t+ N2HR-1w*= [Q]

Define v* z.d.d. ∂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

STEP 3: TEM (Transformed Eulerian Mean) :

∂[u]/∂t –fv* = ~div(EP-flux) ~ -∂[u’v’]/∂y-∂[v’T’]/∂z

By wave breaking and dissipation (especially ∂[v’T’]/∂z) ameridional circulation (v*,w*) is generated, also calledBrewer-Dobson circulation

Brewer Dobson

∂[u]/∂t –fv* = div(EP-flux) = -∂ [u’v’]/∂y-∂[v’T’]/∂z

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

y∂p/∂yN

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

Ozone production highest in the tropics

Ozone column largest outside the tropics, where lower ozone production takes place;Causes: BD-circulation and tropopause height

Ozone transport throughBrewer-Dobson circulation

Monthly mean ozone column distribution, 2002

jan mar

may jul

sept nov

Water in the stratosphereannual 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

TRANSIENT

1960 1980 2000 2020 2040 2060 2080Year

GISS GISSchem

MRIUM49L(a) UM49L(b)

UM64LUM64Lchem

Is the BD-circulation increasing ?

Climate model results

Global mean temperature in de stratosphere,1960-2000

Changes in stratosphereDecrease in temperature

Decrease in temperature profile of stratosphere

1974-1994

Decrease in temperature stratosphere 50 – 100 hPa

Decrease in ozone

Increase in water vapour

Summary

Overview of the basics of the atmosphereSome aspects of atmospheric dynamicsTemperature and ozone distributionStratospheric characteristics

modelling the atmosphere • basics of the atmosphere ... · day 4 - l4 atmospheric modelling1...

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