Atmospheric Physics @ TU Delft

Stephan de Roode, Harm Jonker

clouds, climate and weather air quality in the urban environment energy

Conservation equations

€

dρdt

+ρ∂u j

∂x j

= 0Mass

€

du i

dt= −δ i3g −

1ρ

∂p∂x i

+ ν∂2u i

∂x j2

+Sother forcesMomentum"Navier Stokes"

€

dq

dt= ν q

∂2q

∂x j2

+Sevap/cond rainWater

Heat

€

dθdt

= ν θ∂2θ

∂x j2

+Sradiation +Sevap/cond

Clouds & ClimateLandsat satellite 65 km

10 kmLarge Eddy Model

~mm ~100m~1mm-100mm

Earth ~13000 km

Cloud dynamics

10 m 100 m 1 km 10 km 100 km 1000 km 10000 km

turbulence Cumulus

clouds

Cumulonimbus

clouds

Mesoscale

Convective systems

Extratropical

Cyclones

Planetary

waves

Large Eddy Simulation (LES) Model

Limited Area Weather Model (LAM)

Numerical Weather Prediction (NWP) Model

Global Climate Model

The Zoo of Atmospheric Models

DNS

mm

Cloud microphysics

Fundamental Engineering

Cloud dynamics

10 m 100 m 1 km 10 km 100 km 1000 km 10000 km

turbulence Cumulus

clouds

Cumulonimbus

clouds

Mesoscale

Convective systems

Extratropical

Cyclones

Planetary

waves

Large Eddy Simulation (LES) Model

Current developments

DNS

mm

Cloud microphysics

Limited Area Weather Model (LAM)

Global Climate Model

Numerical Weather Prediction (NWP) Model

Fundamental Engineering

Cloud dynamics

10 m 100 m 1 km 10 km 100 km 1000 km 10000 km

turbulence Cumulus

clouds

Cumulonimbus

clouds

Mesoscale

Convective systems

Extratropical

Cyclones

Planetary

waves

Large Eddy Simulation (LES) Model

The Zoo of Atmospheric Models

DNS

mm

Cloud microphysics

Limited Area Weather Model (LAM)

Global Climate Model

Numerical Weather Prediction (NWP) Model

Harm Jonker

Stephan de Roode

Pier Siebesma (KNMI/TUD)

Computing the weather

Wien’s law:

)(I

Stefan-Boltzmann

4

0

Td)(I

4T

1e

1ch2)(I

kT/hc5

2

Km10898.2T 3max

Planck:

K/J1038.1k

Js10625.6h

s/m103c

23

34

8

€

=5.67⋅10−8 Wm-2K -4

Solar radiation

UV image of the sun source: SOHO EIT

The sun

Surface temperature Tsun = 5778 KRadius Rsun = 6.96342×105 km

Total energy production:

Q = sTsun4 x 4pRsun

2 = 3.85×1026 W

energy emitted (W/m2)

total surface area (m2)

Solar constant S0 : flux of solar energy at the top of the Earth's atmosphere

Distance RE-S= 1.496×1011 m

Energy conservation: Flux integrated over the imaginairy surface area of a sphere centered around the sun is constant

=>

Q = sTsun4 x 4pRsun

2 = S0 x 4pRE-S2

€

S0 = σTsun4 Rsun

RE−S

⎛

⎝ ⎜

⎞

⎠ ⎟

2

= 1367 W/m2

Radiative equilibrium for an Earth without an atmosphere

Radiative equilibrium temperature

€

a2 1−α p( ) S0 = 4πa2 σTe4

ap = Earth surface albedo

€

Te =1−α p( ) S0

4σ

⎡

⎣ ⎢

⎤

⎦ ⎥

1/4

Fraction of solar radiation absorbed by the Earth = Radiation emitted by the Earth

Radiative Earth equilibrium temperature (no atmosphere)

sea

land

ice

snow

mea

n al

bed

o E

arth

real mean Tearth = 288 K

€

Te =1−α p( ) S0

4σ

⎡

⎣ ⎢

⎤

⎦ ⎥

1/4

Scattering and absorption

absorption cross section sa:

effective area of the molecule for removing energy from the incident beam

shortwave longwave

scattering cross section ssca

absorption cross section sa

Apply energy balance

4eT

€

S0 / 4

€

asS0 /4

€

Te

€

1−ε( ) σTe4

€

Ta

€

1−α( )σTe4

4aT

4aT

Energy conservation of the system4aT

€

S0 1−as( )/4 = εσTa4 + 1−ε( ) σTe

4

Apply energy balance

4eT

€

S0 / 4

€

asS0 /4

€

Te

€

1−ε( ) σTe4

€

Ta

€

1−α( )σTe4

4aT

4aT

Energy conservation of the system4aT

€

S0 1−as( )/4 = εσTa4 + 1−ε( ) σTe

4

Radiative energy balance of the atmosphere

4e

4a T T 2

Apply energy balance

4eT

€

S0 / 4

€

asS0 /4

€

Te

€

1−ε( ) σTe4

€

Ta

€

1−α( )σTe4

4aT

4aT

Energy conservation of the system4aT

€

S0 1−as( )/4 = εσTa4 + 1−ε( ) σTe

4

Radiative energy balance of the atmosphere

4e

4a T T 2

Radiative equilibrium temperature of the Earth surface

€

Te4 =

S0 1− as( )

4σ 1− ε /2( )

Radiative equilibrium temperature for an Earth with an atmosphere

€

Te =1−as( ) S0

4σ 1−ε /2( )

⎡

⎣ ⎢

⎤

⎦ ⎥

1/4

mea

n em

issi

vity

atm

osph

ere

16°C

enhanced greenhouse effect

Stephens et al., 2012

Clouds in a future climate

Dufresne & Bony, Journal of Climate 2008

Radiative effects only

Water vapor feedback

Surface albedo feedback

Cloud feedback

The playground for cloud physicists: Hadley circulation

deep convection shallow cumulus stratocumulus

Study the evolution of a low cloud deck during its

advection towards the tropics

deep convection shallow cumulus stratocumulus

Study the effects of clouds on the radiation budget with a

high-resolution turbulence model

Clouds are strong reflectors of solar radiation

0

0. 2

0. 4

0. 6

0. 8

1

0 10 20 30 40 50 60

clo

ud

alb

ed

o

c l o u d o p ti c a l d e p th

100 200 300 400 500 c lo u d la y e r th i c k n e s scloud layer geometric thickness [m]

A total amount of about 0.1 mm of liquid water in an atmospheric column is sufficient to reflect 50% of the downward solar radiation

courtesy Kees Floor

stratocumulus

The Eddington (E) Index

Arthur Eddington

(Einstein and Eddington, HBO-BBC co-production, 2008 )

Chandrasekhar (Nobel prize for physics 1983)

(E-Index 84!)

Navier Stokes in DWDD

http://dewerelddraaitdoor.vara.nl/media/308806

Journal papers

writing a paper, how to deal with citations, co-authors?

H-index

peer review

journal impact factor

open access journals

Exercises

22 October: Paper discussions

Stephens et al., 2012: An update on Earth's energy balance in light of the latest global observations, Nature

Geosciences. (group 1 presents, group 2 asks questions)

Stevens and Bony, 2013: Water in the atmosphere, Physics Today. (group 3 presents, group 4 asks questions)

29 October?: One paper, one exercise

Dufresne and Bony, 2008: An assessment of the primary sources of spread of global warming estimates from

coupled atmosphere-ocean models, J. Climate. (group 2 presents, group 1 asks questions)

Exercise on equilibrium state solutions of low clouds. (group 3 presents, group 4 asks questions)