Global Energy Balance:The Greenhouse Effect

Geos 110 Lectures: Earth System ScienceChapter 3: Kump et al 3rd ed.

Dr. Tark Hamilton, Camosun College

3 Inner Rocky Planets with Atmospheres

Venus -------------Earth----------------Mars

The Goldilocks Zone

Then Goldilocks tried Baby Bear’s

porridge and it was just right, so she ate it all up!

Venus: South Pole > 460°C, CO2 SO2

UV Image: Pioneer Venus Orbiter, Feb, 5, 1979

Greenschist Facies Metamorphism, No Clays

Supercritical Fluids, No Liquid Water

Earth: The Blue Planet (Ice, Water, Steam)

Earth ~ 15°C average, Seasons, abundant liquid water

Transparent N2 – O2 – Ar Atmosphere, minor GHS’s

Mars: -55°C, CO2 millibar atmosphere

Colder than a Polar winter, hydrated minerals, no H2O(l)

• Less atmosphere than a Bar in Nanaimo, Dry Ice Caps

Electromagnetic Radiation - Waves

• E and B vary as wave passes at speed of light

• E-field interacts with matter through its electrons

Energy, Frequency & Wavelength

• E = h ν , Higher Frequency Higher Energy

• E = h c/λ , Lower energy Longer Wave

• Whats nu? ……. ν = c/ λ

• Or

• λ ν = c , c = 3x108 m/s

400 nm < Visible Light < 700 nm

• Longer wave infra-red and microwaves are “heat” for greenhouse• Shorter wavelength hard UV & X-rays are ionizing radiation

Flux: Energy per unit area per unit timeNormal Incidence Minimizes Area

• Heat or Light per unit area decreases w/ Sun Angle• The Sun heats less at Dawn, Dusk & Winter than 12pm

Normal Incidence = Circular FootprintMaximum Flux!

Inclined Incidence Increases Area but Decreases Heating Decreased Flux

Inverse Square Law

Intensity of light/heat decreases w/ square of distance

e.g. 2X distance = ¼ power, 1/3 distance = 9 x power

Temperatures of Water Phase Changes

Celsius based on freezing & boiling or H2O

Kelvins Absolute (no offset), same size as Celsius

Farenheit Freezing & Coagulation of Human Blood…eeew!

Temperature Scales

• Celsius: 0° Freezing, 100° Boiling

• T°F = [T°C + 1.8] + 32° or

• T°C = [T°F – 32] / 1.8 where 1.8 = 9/5

• T K = T°C + 273.15 (Kelvins, not degrees K)

A Cold Black Body absorbs at all wavelengths

Cold = Black Hot = emits Red Hotter = emits White

The Planck Function

• The Planck Function: variation of blackbody radiation & λ• Wein’s Law: λmax ~ 2898/T (Kelvins)• Stefan-Boltzmann Law: Sum of All Flux ~ σ T4

The Planck Function: variation of blackbody radiation & λ (wavelength)

Wein’s Law: λ max ~ 2898/T (Kelvins)

• The Sun’s Photosphere is ~ 5780 Kelvins

Stefan-Boltzmann Law: Sum of All Flux ~ σ T4

Emission goes up as temperature to the 4th power!

Blackbody Emission Spectra for Sun & Earth

• Ultraviolet.…Visible………………………..Infrared• The Sun emits more at all wavelengths λ (energies)• The Earth absorbs in visible light (0.4-0.7) μm & emits in infrared ( λ > 1μm)

Solar Energy FluxStefan Boltzmann Law

• Fsun = σ (5780 K)4 ~ 6.3 x 107 W/m2

• If some other star were twice as hot:

• Fstar = σ (2 x 5780 K)4 • = (2)4 x σ (5780 K)4 = 16 Fsun !

• Sooo… this must be a real rock star?

Earth’s Global Energy Balance

• For Earth’s Energy Budget to Balance

• Flux in must = Flux out

• if true T°C = Constant, One climate, No weather

• but Flux in > Flux out so Earth is Warming

• 3 Factors Control Earth’s Energy Budget & Climate:– Solar Flux at any particular distance– Earth’s reflectivity (albedo)– Greenhouse Gas Effects

A Closer Look at Global Energy Balance

Earth’s Energy Balance

Energy emitted = Energy absorbed :

• Energy emitted = 4π REarth2 x σTEarth

4

– This follows from Stefan-Boltzmann & Spherical Shape

E absorbed = E intercepted – E reflected:

• E absorbed = πREarth2 S - πREarth

2 SA = πREarth2 S(1-A)

– Where : S = Solar Flux & SA = Earth’s Projected Area

Therefore: 4π REarth2 x σTEarth

4 = πREarth2 S(1-A)

or: σTEarth4 = S(1-A)/4

The Greenhouse EffectOne-Layer Atmosphere

• ~33°C net surface warming = Tmean sT - Tradiating

• Atmosphere radiates IR down & absorbs IR up

Flux up from ground = Net Solar input + Flux down from air

For Earth’s Surface: solar input + atmospheric heat

• σTSurface4 = S(1-A)/4 + σTEarth’s Air

4

For Earth’s Air: atmosphere radiates 2 ways

• σTSurface4 = 2σTEarth’s Air

4

Equate, subtract σTEarth’s Air4 & divide by σ to obtain:

• TS = 2 ¼ TEA this is hotter with Air by 1.19

• or ΔTg = TS – TEA = 303 – 255 = 48K, Really ~15 K

The Greenhouse EffectOne-Layer Atmosphere

Was 387, CO2 now = 390.02 ppm August 2011

Increasing ~ 2 ppm/yr, N2, O2 & Ar are “inert”

Trace Greenhouse Gases

CFC’s from blowing gas, refrigerants & burned plastic H2O 4% = 40,000 ppm, 1.7 ppm CH4 ~ 63 ppm CO2

Thermal Layers in Earth’s AtmosphereDominate the Atmospheric Structure

• The Pressure gradient is log-linear, decreasing 6 orders of magnitude over the 1st 100 km

• Earth’s surface & Stratopause are warmest

• The Tropopause and Mesopause are coldest

The Log-Linear Pressure Gradient Decreases by 6 orders in 100 km

• Barometric Law: Pressure decreases with altitude by a factor of 10 for each 16 km altitude -0.625 bar/km

• Deviation from Log-Linearity is due to temperature gradients within layers

• At Jet airplane heights ~11 km the pressure 618 mb

Atmospheric Thermal LayeringTroposphere, Stratosphere, Mesosphere, Thermosphere, Exosphere

• Earth’s surface & Stratopause are warmest

• The Tropopause and Mesopause are coldest

Atmospheric Thermal Layering• Exosphere: gas rarely collides, can escape to space

• Thermosphere: (85 to 120 - 500 km) > Δ~1.3°/km– Mesopause = minimum in thermal profile ~ -95°C

• Mesosphere: (50 to 60 – 85 to 120 km) Δ-2.3°/km– Stratopause = maximum in thermal profile ~ 0°C

• Stratosphere: (8 to 15 – 50 to 60 km), Δ~1.4°/km– Tropopause = minimum in thermal profile ~ -65°C

• Troposphere: (0- 8 or 15 km), densest, warmest, lowest layer, thick in Tropics, thin at Poles, Δ-6°/km– Clouds, Rain, Snow; well mixed by convection– Earth & Ocean surface is base of Troposphere

Modes of Heat Transport & Storage

• How is each one of these important in the Atmosphere and at Earth’s Surface?

• Where and when is each of these important?

Heat Storage and Transfer

• Sensible Heat cal/g°C is proportional to density– You can stand hot or cold air better than water of same T

• Latent Heat depends on condensable H2O

• Radiation = emission of photons by excited electons

• Convection = Heat, Mass & Momentum transfer in a fluid, via fluid motion w/ density currents/gradients

• Conduction = Heat transfer by direct contact of molecules (significant only in solids, not fluid or gas). Hot rocks, sand, hot asphalt, hot tin roof

Heat Storage and Transfer

• Sensible Heat You can stand hot or cold air better than water of same T, more mass or density, more heat capacity

• Latent Heat Evaporated H2O carries heat to atmosphere, condensed/crystallized H2O leaves heat

• Radiation = The hotter the atmosphere, the more radiation to the air, ground and space

• Convection = Heating unevenly or from below in gravity field drives convection

Heat Storage & Transfer: Troposphere

• Earth & Ocean are heated ~ equally by sun’s radiation

• The Earth’s surface re-radiates in IR

• This IR and that of the Sun, heats GHG’s in the Troposphere or is reflected downwards by clouds, especially near the Earth’s surface unstable lower density air rises & convects, thus we get weather

• Troposphere re-radiates IR up into less dense atmosphere layers where it can be lost to space

• There is also sensible, latent and convected heat

Most of the O3 Ozone is in the Stratosphere

• < 5ppm H2O vapour, usually no clouds, stratifiedException is Antarctic Winter, thin Stratospheric Clouds

Why is there such a wavy T° Profile

Earth’s surface heats lower Troposphere which convects

O3 in Stratosphere is heated above by UV, stable stratification

O2 absorbs short wave UV in Thermosphere for uppermost atmospheric heating

Water’s Big Dipole MomentMakes it rotate when it absorbs IR

• IR λ > 12 μm is virtually all absorbed by water’s rotation band

• CO2 has 2 perpendicular π bonds which also absorb

Molecular Absorption Spectrum: GHG’s

• Molecules can: rotate, or vibrate atoms changing bond lengths and bend changing dipole moments

• CO2 at λ > 15 μm is a bending mode for O=C=O

CO2’s bending mode of vibration

• Alternating planes of π bonds C=O and lone pairs on end oxygens experience polarizations & bending

Other Greenhouse GasesReduce Outgoing IR

• N2O Nitrous Oxide - several bands between 530-760/cm & between 1585-4000/cm

• O3 Ozone – 9.6 μm in window between H20 & CO2

• CH4 Methane = 37x the value of 1 CO2 for GHG, many absorption bands in 1.16 μm region

• Freons – CHClF2 , CCl2F2 , substituted lopsided polar methanes absorb in 8-12 μm window! More GHC power than a CO2 molecule

So Wazzup with N2 & O2 ?

• N2 & O2 are highly symmetric w/ short strong bonds

• They absorb in UV & don’t affect IR heating

Clouds Have Variable Effects on IR

• Clouds & lower concentration aerosols block heat

• Different types: Stratus, Cumulus, Cirrus

• Can raise albedo blocking Sun or hold heat in

Low Level Stratus are Water Droplets

High Level Cirrus are Ice Crystals

Tall Cumulonimbus have all 3 Phases

• Vertical Convection, Thunderstorms

• Water-Ice (sleet/hail)-Steam

Radiation Flux versus Cloud Type

• Cirrus are high thin, pass more light, lower IR flux

• Stratus-Cumulus: low dense, reflect more, high IR

General Circulation Model Climate

• OK, so quantify this, match it to the Earth System• Now build a Computer model-change it-see an effect,

conclude, change something else, map it out

Global Energy Balance

At the top of the Atmosphere:

• 100 Solar in = 25 Air refl + 5 Earth refl + 70 IR out

Near the Ground

• 100 Solar in = 45 Earth abs + 55 Air refl + abs

• 53%, 45 Solar in = Water evap

• 133 Earth in = 45 Solar in + 88 GHG IR

The Multiple IR paths increase flux to surface & heat

Radiative Convective 1D Model Climate (RCM’s)

• Ignore lateral variations of clouds, oceans, land

• Put in Atmospheric layers with average values (no poles or tropics)

• Just deal with Radiation in and out & Convection

• Easier to compute but how relevant is it to the real Earth System?

• You should still get the major effects of increased GHG (compared to our 1 layer Atmosphere model)

• How far can you trust the predictions, feedbacks?

Radiative Convective 1D Model Climate (RCM’s)

• RCM’s correctly predict a GHG warming +33°C

• for ΔTg = Ts + Te where g = GHG, s = surface and e = atmospheric layer.

• This match is not so trivial!

• RCM’s predict GHG effects for doubling GHG’s

• Like CO2 from 300 ppm to 600 ppm ΔTg = 1.2°C

• This doesn’t sound like so much but ignores:– Lateral variations, deserts, polar regions get most change– Ignores feedback or interaction effects

Water Vapour Feedback: Hothouse 1D RCM’s

• Positive feedback loop in the short term esp. heating

• H2O (g) is close to rain or ice/snow, condensation –

• More Heat more steam, less heat way less steam

Radiative Convective 1D Model Climate (RCM’s) & Relative Humidity• Relative Humidity is %H2O/Saturation% f(T°C)\

– Steam Rooms & tropics hold way more H2O and heat

• for ΔTeq = T0 + Tf where eq = equilibrium, 0 = equil w/no feedback and f = feedback offset Daisyworld

• The feedback for more CO2 and more H20 is double!

• ΔTg = 2.4°C so f = (2.4°/1.2°) = 2

• This doesn’t sound like so much but is a really strong positive feedback.

• In Earth History Cretaceous & Devonian Hothouse Earth Times

Water Vapour Feedback: Ice Ages need 2-3D models, Regional variations

• Positive feedback loop in long term, ice age effects

• H2O (g) is close to rain or ice/snow, condensation –

• Less heat way less steam, way more ice ages!

Earth’s Climate Tends to be Stable despite changes and oscillations

• Negative feedback due to outgoing IR’s strong dependence on surface temperature: short time scale

• Tropospheric heating from below

• Runaway GHG like Venus can break this stablity

Uncertain effects of Cloud Types

• Cirrus causes net Warming!

• Low Stratus-Cumulus can cause net coolingThe real uncertainty here is does increased Albedo outweigh GHG IR effects or not, Aerosols are knotty buggers!

Uncertainties in Climate Models

• How good is a climate modeller’s prediction?

• How meaningful is average temperature to how you dress yourself hour to hour or day to day?