Overview of the Climate System

Lesson 1

Topic - 1

Energy & Balance

Earths Orbit

Tilt = 23.5

Inclination

Image Credit: Survey of Meteorology Online

Northern Hemisphere Winter

Image Credit: Survey of Meteorology Online

Equinoxes

Image Credit: Survey of Meteorology Online

Northern Hemisphere Summer

Image Credit: Survey of Meteorology Online

Solar Radiation

The average energy from the sun at the

mean radius of Earth is called Solar Constant S0 = 1368 Wm

-2

Total energy received by the earth per unit time = S0R

2

Earth surface Area = 4R2

What is the average amount of energy received by earth?

Albedo Not all energy incident on earth is absorbed A fraction is reflected or scattered So the average flux is actually S(1-)/4

Earths mean albedo 0.3 Oceans : 2-10% Forest : 6-18% Cities : 14-18% Grass : 7-25% Soil : 10-20% Desert (Sand) : 35-45% Cloud (thin, thick, stratus) : 30,60-70% Ice : 20-70% Snow (Old) : 40-60% Snow (Fresh) : 75-95%

Mars /2; Venus 2

Radiative Equilibrium

S

S0/4

Solar Input

SurfaceTs

S0/4

Reflected Shortwave

Radiated from

Ground

SOLAR TERRESTRIAL

Space

Radiative Equilibrium

Absorption at surface causes warming up of surface until it radiates to space as much energy as it absorbed

When surface reaches Ts , the amount of energy S radiated per unit time is given by Stefans Law S = Ts

4 where = 5.7 x 10-8 Wm-2K-4

If = 0, Incident Solar = S0/4, What is Ts?

Seasonal Distribution

Maximum in January

3.5% variation due to elliptic orbit

Black Body Radiation

Plancks Law: h = 6.62606896 x 10-34 J.s

k = 1.380 6504(24)1023 J.K-1

c = Speed of Light

Radiation IntensitySuns Temperature : 6000 KEarths Surface Temperature : 288 K

Distribution of Incident Solar Insolation

Source: PhysicalGeography.net

However..

Effective Temperature Te

4

0)1(4

1eTS =

41

0

4

)1(

= S

Te

Using = 0.3, S0 = 1368 Wm-2, and = 5.7 x 10-8 Wm-2K-4

Te = 255 K

Other Planets

S0 = 2632 Wm-2

= 0.77Te = 227 K

S0 = 1368 Wm-2

= 0.30Te = 255 K

S0 = 589 Wm-2

= 0.24Te = 211 K

Tm = 230 K Tm = 250 KTm = 220 K

In reality

Actual Radiation incident on the surface

and Plancks Law implies a lower temperature than is actually seen on Earth

This difference is due to the presence of a

fluid on Earths surface

The Fluid (atmosphere & ocean) affects things in 2 ways

1. Radiation can be absorbed by the fluid itself

2. The fluid can carry heat from one place to another thereby affecting the balance

When the atmosphere absorbs radiation:

S

S0/4

Solar Input

SurfaceTs

S0/4

Reflected Shortwave

Radiated from Ground

SOLAR TERRESTRIAL

The Greenhouse Effect

Ta Atmosphere

Space

Radiated down to Ground

A

ARadiated to Space

4

4

s

a

TS

TA

=

=( ) ASS += 01

4

1

Radiation Balance at the Surface (or) How can we alter Ts?

Change S0 Change

Change A

( ) += ASS 014

1

4

sTS =

( )

es

eaes

TT

TTTT

ASS

41

4444

0

2

2

14

1

=

=+=

+=

Radiation Balance at the Top Of the Atmosphere (TOA)

( ) = AS014

1

4

eT4

aT

KTs 30325524

1

==

TbAtmosphereLayer B

A More Opaque Greenhouse

S0/4

Solar Input

SurfaceTs

S0/4

Reflected Shortwave

SRadiated from Ground

SOLAR TERRESTRIAL

Space

Radiated down to Ground

B

ARadiated to Space

BRadiated from B to A

TaAtmosphereLayer A

ARadiated from A to B

We can extend this to an infinite number of thin layers

The Leaky Greenhouse

S

S0/4

Solar Input

SurfaceTs

S0/4

Reflected Shortwave

Radiated from Ground

SOLAR TERRESTRIAL

Ta Atmosphere

Space

Radiated down to Ground

A

ARadiated to Space

(1-)STransmitted through atmos.

( ) += ASS 014

1

( ) += SAS )1(14

10

( ) += SAS )1(14

10

TOA

( ) += ASS 014

1

Surface

At equilibrium, A = A

( ) 404)2(

21

)2(4

2es TSTS

=

==

es TT4

1

)2(

2

=

Composition of the Atmosphere

Nitrogen 78.08% Oxygen 20.95% Argon 0.93% CO2 0.0367% Neon 0.001818% Helium 0.000524% Methane 0.00017% Krypton 0.00011% Hydrogen 0.000055% Water Vapour 0-5% of total atmospheric volume Nitrous Oxide (N2O) 0.00003% Ozone (O3 ) 0 - 0.000001% Several trace gases CFCs, CO, SO2 affect radiation

Absorption in the AtmosphereShort wave Radiation

Image Credit: Wiki commons

Absorption in the AtmosphereLong wave Radiation

Image Credit: Wiki commons

Gases and what wavelengths they absorb

Image Credit: Wiki commons

Physical Properties of Air Global mean surface pressure: 1013 hPa

(millibar)

Global mean density of air at surface: 1.235 Kgm-3

Mean free path (in lower 50Km) is small enough that we can consider the atmosphere to be a continuum fluid in local thermodynamic equilibrium (LTE)

Dry air accurately obeys the perfect gas law

RTTm

Rp

a

g ==

Moist Air

v mass of water vapour per unit volume of air

d mass of dry air per unit volume of airPartial Densities

TRp

TRe

ddd

vv

=

=Partial Pressures

epp d += From Daltons Law of Partial Pressures

T

s Aee= A = 6.11 hPa = 0.067 C-1

Saturation Vapour Pressure

Moisture decreases with temperatureTropics much more moist Colder world is drier

Combination of Rotational and Vibrational states leads to a very complex and irregular absorption spectrum for water vapour

Further broadening of absorption lines occurs -Doppler and Pressure broadening

Stratospheric Ozone

MOMOO

OOO

32

2

+++

++ h Photo-dissociationM is any air molecule (Typically N2 or O2)

OOO 23 ++ h

This ozone preferentially absorbs somewhat longer wavelengths than O2

MOMOO

OOO

32

2

+++

++ h

Image credit: Dr. Jon Schrage, Department of Earth and Atmospheric Sciences, Purdue University.

Temperature Profiles Vary by Season and Location

Source: Washington & Parkinson

Three-Dimensional Climate

Modelling

Comparative Vertical Temperature Profiles

A Radiative Equilibrium Profile

Convection

Stability & Instability

Buoyancy

Same density and from hydrostatic balance have same pressures

The acceleration of the fluid parcel is

p

g

)( Ep =

p

Epgb

)( =

Not so the bottom layer!

Stability

Suppose we displace (quickly) the parcel at 1, T1 to height z2

The surroundings at z2will have density

zdz

dz

E

E

+= 12 )(

Environmental density gradient

zdz

dgb

E

=1

positivelyneutrally

negativelybuoyant if

> 0= 0< 0Edz

d

Stability (contd.)

If the parcel is positively buoyant, it will keep on rising at an accelerating rate!

positivelyneutrally

negativelybuoyant if

> 0= 0< 0Edz

d

Therefore the parcel is unstable if density increases with height!

We can rewrite the stability condition in terms of Temperature instead of density

Incompressible Only!

Hydrostatic Balance

pzp

zzppT

+=

+=

)(

)(

Assuming z to be small

zz

pp

=

zAM =

Hydrostatic Balance (contd.)

Vertical forces (upward +ve)

1. Gravitational Force

zAggMFg ==

AppFT )( +=2. Pressure Force acting on top face

ApFB =3. Pressure Force acting on bottom

0=+

gz

p

Assuming parcel is not accelerating0=++ TBg FFF

Hydrostatic Balance

Hydrostatic Balance (contd.)

0=+

gz

pDescribes how pressure decreases with height

=z

dzgzp )( Mass per unit area

earth of area Surface

atms

gMp =

Vertical Structure of Pressure and Density

RT

gpg

z

p==

p, replaced by p, T

Assuming an isothermal atmosphere (T=T0)

H

p

RT

gp

z

p==

0g

RTH 0=where scale height

=H

zpzp s exp)(

=

p

pHz slnor

Vertical Structure of Pressure and Density (contd.)

For a non-isothermal atmosphere

g

zRTzH

)()( =

)(zH

p

z

p=

)(

1ln1

zHz

p

z

p

p=

=

constant)(

ln

z

0

+

= zHzd

p

= z

0)(

exp)(zH

zdpzp s

Vertical Structure of Pressure and Density (contd.)

=H

z

RT

pz s exp)(

0

= z

0)(

exp)(

)(zH

zd

zRT

pz s

Dry Convection in a Compressible Atmosphere

Consider a parcel of ideal gas (unit mass i.e V=1) to which we add an amount of heat Q

pdVdTcQ v +=

First Law of Thermodynamics

Since

dp

pdV

dddV

2

2

11

=

=

= Using Equation of state

and simplifying

RdTdp

pdV +=

dpdTcQ p =

Dry Convection (contd.)

0==

dp

dTcQ p For adiabatic motion

dzgdp E= From Hydrostatic Equation

d

pc

g

dz

dT== Dry Adiabatic Lapse Rate

1005 JKg-1K-1

10 K/Km

Dry Convection (contd.)

zdz

dTTT

E

+= 12

2

22

RT

p=

At z2, the environmental density is

The parcel however is at

Pressure p2

And Temperature zTT dp = 1

p

pRT

p2=Therefore Density is

Dry Convection (contd.)unstable

neutralstable

buoyant if< -d= -d> -dE

dz

dT

A compressible atmosphere is unstable if temperature decreases faster than the adiabatic lapse rate

The atmosphere at most places and at most times is stable to dry convection!

Temperature

Heig

ht

dStable!

Unstable!

Add Water and things get a little more complicated.

H2O can change phase

Phase Changes are accompanied by release/absorption of energy

Ice Water Water Vapour

Energy Absorbed

Energy Released

Melting Evaporation

Freezing Condensation

Saturated Adiabatic Lapse Rate

Shallow & Deep Convection

Cumulus Cumulonimbus

Saturated Adiabatic Lapse Rate (contd.)

As the rising air parcel cools, what happens if it cools to its dew point?

At that point, any further cooling will cause the water vapour in the parcel to begin to condense, and to release latent heat.

Release of latent heat partially offsets the cooling due to expansion of the air parcel

If the parcel becomes saturated, any further lifting will cause the parcel to cool at the moist adiabatic lapse rate (also called the wet or saturated adiabatic lapse rate)

The moist adiabatic lapse rate depends on the temperature of the saturated air parcel

Warm saturated parcels contain a lot more moisture than cold saturated parcels

Temperature profile from radiative-convective calculations

Radiative Convective Equilibrium (RCE)

Radiative Convective Equilibrium (contd.)

Radiative processes cool the troposphere and warm the ground.

The primary source of tropospheric cooling is infrared emission (or radiative cooling) by water vapor and clouds.

The ground warming is due to solar heating and back radiation from atmospheric water vapor and clouds.

Such a pattern of atmospheric cooling and surface warming leads to superadiabatic lapse rates (temperature decreasing by more than 9.8 K km1) and triggers atmospheric convection.

The ensuing vertical motions transport heat from the surface to the atmosphere and restore the lapse rate to neutral (adiabatic).

The heat is released in the form of latent heating during condensation or sensible heat from turbulent eddies originating in the boundary

layer.

Temperature

Heig

ht

dStable!

Unstable!

Changing the RCE Within the troposphere:

Longwave cooling exceeds solar heating: result a net cooling. This is balanced by release of latent heating and convective

transport of sensible heat transfer from the surface.

At the surface: Solar heating far exceeds longwave cooling This radiative heating is balanced by convective transport of latent

and sensible heat from the surface to the atmosphere.

Surface radiative heating + Tropospheric radiative cooling = 0 Maintains radiation energy balance for the whole surface-

troposphere column This radiation balance is perturbed by the addition of greenhouse

gases and aerosols.

Surface Convective Cooling + Tropospheric Convective heating = 0 This balance is perturbed by land surface changes.

Source: IPCC Fifth Assessment Report

Global mean energy budget under present day climate conditions

Energy Balance

The ground warms up by incoming shortwave radiation and by the longwave radiation emitted by atmospheric absorbers. It loses heat through longwave radiation, and also through latent heat flux (evaporation)and sensible heat fluxes, both linked with the phenomenon of convection.

The vertical profile of temperature in the troposphere is determined by a combination of radiative, convective, and advectiveprocesses.