Chapter 5: Atmospheric Structure and Energy Balance

(I) Characteristics of the Atmosphere Thickness, air pressure, density

Air pressure and density decrease with altitude

90% of its mass (5.1 x 1018 kg) is within 16 km (10 mi) of the surface (about 0.0025 times the radius of the Earth) 97% of air in first 29 km or 18 mi; 99% 32 km (18 mi); 99.9% 47km (30mi)

Atmospheric motions can therefore be considered to occur “at” the Earth’s surface

The greatest and most important variations in its composition involve water in its various phases

Water vapor Clouds of liquid water Clouds of ice crystals Rain, snow and hail

Composition of the Atmosphere

Dry AirTRACE GASES

Argon (.93%) andCarbon Dioxide (.03%)Ozone (.000004%)

Water vapor is constantly beingadded and subtracted from the atmosphere, and varies from near0% (deserts) to 3-4% (warm, tropical oceans and jungles)

Solid particles (dust, sea salt, pollution) also exist

Vertical Structure of the Atmosphere

4 distinct layersdetermined bythe change oftemperaturewith height

Extends to 10 km in the extratropics, 16 km in the tropics

Contains 80-90% of the atmospheric mass, and 50% is contained in the lowest 5 km (3.5 miles)

It is defined as a layer of temperature decrease

The total temperature change with altitude is about 72°C (130°F), or 6.5°C per km (lapse rate)

• It is the region where all weather occurs, and it is kept well stirred by rising and descending air currents

• The transition region of no temperature change is the “tropopause”: it marks the beginning of the next layer

Vertical Structure of the Atmosphere

4 distinct layersdetermined bythe change oftemperaturewith height

Extends to about 50 km

It is defined as a layer of temperature increase and is stable with very little vertical air motion – a good place to fly!

Why does temperature increase?

The major heating is the UV of sunlight absorbed by O3.. When the sunlight travel down, the UV will become less and less available, so the temperature increase with height…

• The transition region to the next layer is the “stratopause”

Atm. vertical structure

• Air pressure p at sea level is 1 atm. = 1.013 bar = 1013 mb

• p decr. with altitude by factor of 10 every 16 km.

• T decr. with altitude in troposphere,

rises in stratosphere

drops in mesosph.

rises in thermosph.

Temperature

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(II) Radiation Energy

Objectives:

•Electromagnetic (EM) radiation & spectrum

•Energy flux

•Blackbody radiation -- Wien’s Law & Stefan-Boltzmann Law

•Planetary energy balance

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EM radiation

• EM radiation includes visible light, ultraviolet, infrared, microwaves.

• wavelength

• period T, frequency = 1/T

• wave speed or phase speed c = /T = • Speed of light in vacuum: c = 3.00108 m/s

wavelength

later t

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longer period waves => ? wavelength•c = /T => = cT = c/

longer

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Energy flux•Power = energy per unit time (watt W = J/s)

•Flux F = power per unit area (W/m2)

less flux

high lat.=> less F

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EM spectrum•EM radiation classified by their wavelength

or freq.

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•Solar flux S falls off as

Inverse-square law

S S0r0

r

2

e.g. if r = 2r0

=> S = S0/4S

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Blackbody radiation•Absolute temperature in degrees Kelvin (K)

• 0 K = -273°C (coldest possible T)

•All bodies emit EM radiation

• e.g. humans emit mainly infrared (IR)

•“Blackbody” emits (or absorbs) EM rad. with 100% efficiency.

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Wien’s LawPlanck function (blackbody rad. curve)

wavelength

Rad

. flu

x

max

max = const./TTemp. T in Kconst. = 2898 m

max refers to the Wavelength of energy radiated with greatest intensity.

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Blackbody rad. curves for Sun & Earth

max = const./TTemp. T in Kconst. = 2898 m

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Stefan-Boltzmann LawPlanck function (blackbody rad. curve)

wavelength

Rad

. flu

x

total F = area under curve

F = T4

= 5.67 x 10-8 W/m2/K4

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Planetary energy balance•Earth is at steady state: Energy emitted by Earth = Energy absorbed ..(1)

•E emitted = (area of Earth) Te4

= 4 Re2 Te

4

(Te= Earth’s effective rad. temp., Re= Earth’s radius)

•E absorbed = E intercepted - E reflected

•Solar E intercepted = S Re2 (solar flux S)

•Solar E reflected = AS Re2 (albedo A)

•E absorbed = (1-A) S Re2

•(1) => 4 Re2 Te

4 = (1-A) S Re2

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Magnitude of greenhouse effect• Te

4 = (1-A) S/4

•Te = [(1-A) S/(4 )]1/4 (i.e. fourth root)

•Te = 255K = -18°C, very cold!

•Observ. mean surf. temp. Ts = 288K = 15°C

•Earth’s atm. acts as greenhouse, trapping outgoing rad.

•Ts - Te = Tg, the greenhouse effect

•Tg = 33°C

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Greenhouse effect of a 1-layer atm.

EarthTs

Atm.Te

S/4AS/4

(1-A)S/4 Ts4

Te4

Te4

•Energy balance at Earth’s surface: Ts

4 = (1-A)S/4 + Te4 ..(1)

•Energy balance for atm.: Ts

4 = 2 Te4 .. (2)

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Subst. (2) into (1):

Te4 = (1-A)S/4 ..(3) (same eq. as in last lec.)

Divide (2) by ; take 4th root:

Ts = 21/4 Te = 1.19 Te

For Te = 255K, Ts = 303K. (Observ. Ts = 288K)

Tg = Ts - Te = 48K,

15K higher than actual value.

•Overestimation: atm. is not perfectly absorbing all IR rad. from Earth’s surface.

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(III) Modelling Energy Balance

Objectives:

•Effects of clouds

•Earth’s global energy budget

•Climate modelling

•Climate feedbacks

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Cumulus Cumulonimbus

Stratus Cirrus

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Climatic effects of clouds•Without clouds, Earths’ albedo drops from

0.3 to 0.1. By reflecting solar rad., clouds cool Earth.

•But clouds absorb IR radiation from Earth’s surface (greenhouse effect) => warms Earth.

•Cirrus clouds: ice crystals let solar rad. thru, but absorbs IR rad. from Earth’s sfc.

=> warm Earth•Low level clouds (e.g. stratus): reflects

solar rad. & absorbs IR => net cooling of Earth

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•IR rad. from clouds at T4

•High clouds has much lower T than low clouds

=> high clouds radiate much less to space than low clouds.

=> high clouds much stronger greenhouse effect.

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Earth’s global energy budget

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Climate Modelling•“General circulation models” (GCM):Divide atm./oc. into 3-D grids.Calc. variables (e.g. T, wind, water vapor, currents) at grid pts.=> expensive.

•e.g. used in double CO2 exp.

GFDL, Princeton

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•Weather forecasting also uses atm. GCMs. Assimilate observ. data into model. Advance model into future => forecasts.

•Simpler: 1-D (vertical direction) radiative-convective model (RCM):

Doubling atm. CO2 => +1.2°C in ave.sfc.T

•Need to incorporate climate feedbacks:

•water vapour feedback

•snow & ice albedo feedback

•IR flux/Temp. feedback

•cloud feedback

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Water vapour feedback• If Ts incr., more evap. => more water vapour

=> more greenhouse gas => Ts incr.

• If Ts decr., water vap. condenses out => less greenhouse gas => Ts decr.

•Feedback factor f = 2.

•From RCM: T0 = 1.2°C (without feedback)

=> Teq = f T0 = 2.4°C.

Ts

Greenhouse effect

Atm. H2O(+)

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Snow & ice albedo feedback•If Ts incr. => less snow & ice => decr.

planetary albedo => Ts incr.

•As snow & ice are in mid-high lat. => can only incorp. this effect in 3-D or 2-D models, not in 1-D RCM.

Ts

planetary albedo

snow & ice cover

(+)

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IR flux/Temp. feedback•So far only +ve feedbacks => unstable.

•Neg. feedback: If Ts incr. => more IR rad. from Earth’s sfc. => decr. Ts

Ts Outgoing IR flux(-)

•But this feedback loop can be overwhelmed if Ts is high & lots of water vap. around => water vap. blocks outgoing IR => runaway greenhouse (e.g. Venus)

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Uncertainties in cloud feedback•Incr. Ts => more evap. => more clouds

•But clouds occur when air is ascending, not when air is descending. If area of ascending/descending air stays const.

=> area of cloud cover const.•High clouds or low clouds? High clouds

warm while low clouds cool the Earth.

•GCM’s resolution too coarse to resolve clouds => need to “parameterize” (ie. approx.) clouds.

•GCM => incr. Ts => more cirrus clouds => warming => positive feedback.

=> Teq = 2 -5°C for CO2 doubling