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
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 2
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Temperature
Troposphere T decreases with z, stratosphere T increases with z due to ozone; stratosphere very stable; stratum= ‘layer’
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 3
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
80km
60
40
20
90S EQ 90N 90S EQ 90N
Temperature (K) in stratosphere in January:a) radiative equilibrium; b) observed.
a) b)
170 210
160 250
140220
220 220
270 280
220 200
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 4
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Lowermost stratosphere (‘middle world’):isentropes connected with troposphere
tropopause
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 5
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Tropopause height(pressure) : geographical distribution instantaneouspicture
Potential Vorticity, PV:
PV = (ξθ +f)∂θ/∂p
PV: small in troposphere,large in stratosphere;
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 6
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Tropopause pressure versus ozone column
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 7
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Atmospheric dynamics
Large scale circulation
Planetary waves
Brewer-Dobson circulation
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 8
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
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)
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 9
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
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
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 10
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Coupling between temperature and wind
Zonal wind uf∂u/∂z ~ - g/T∂T/∂yTemperature
Zonal wind
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 11
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Zonal wind in stratosphere
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 12
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 13
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
2002, Splitting up of the Ozone hole
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 14
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Planetary waves
ECMWF
Z500 5 okt 2004 (ECMWF)
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 15
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Planetary waves:
- generation in troposphere (orography, convective systems)
- propagating , also in the stratosphere
- propagation only possible if…..
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 16
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
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 )⎬
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 17
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
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’
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 18
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Zonal wind, 10 hPa1 january 2002, waves 1 july 2002, no waves
Waves in stratosphere:Summer versus winter
U > 0 U < 0
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 19
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Winter (1 january 2002), (U > 0), different altitudes waves
Φ(500 hPa), troposphere Φ(10 hPa), stratosphere
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 20
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Summer (1 july 2002) (U < 0) , waves in the troposphere only
Φ(500 hPa), troposphere Φ(10 hPa), stratosphere
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 21
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
The stratospheric meridional circulation
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 22
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
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)
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 23
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
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
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 24
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
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) :
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 25
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
∂[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
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 26
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 27
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
∂[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
fuu
y
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 28
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
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
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 29
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
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
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 30
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Monthly mean ozone column distribution, 2002
jan mar
may jul
sept nov
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 31
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Water in the stratosphereannual cycle in strength of BD circulation→ idem in T (tropical tropopause)→ idem in specific humidity tropical tropopause
‘tape recorder’
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 32
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
[v’T’] 100 hPa:large influence on ozone transport during winter
Warm NH winters
Cold NH winters
2002 Antarctic stratospheric warming
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 33
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
TRANSIENT
1960 1980 2000 2020 2040 2060 2080Year
2030
40
50
60
7080
ma
ss f
lux (
10
8 K
g s
−1)
GISS GISSchem
MRIUM49L(a) UM49L(b)
UM64LUM64Lchem
WACCM
Is the BD-circulation increasing ?
Climate model results
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 34
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Global mean temperature in de stratosphere,1960-2000
Changes in stratosphereDecrease in temperature
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 35
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Decrease in temperature profile of stratosphere
1974-1994
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 36
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Decrease in temperature stratosphere 50 – 100 hPa
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 37
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Decrease in ozone
Day 4 - L4 Atmospheric modelling1 Hennie Kelder 38
DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING
Increase in water vapour