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Global Energy Balance: The Greenhouse Effect. Geos 110 Lectures: Earth System Science Chapter 3: Kump et al 3 rd ed. Dr. Tark Hamilton, Camosun College. 3 Inner Rocky Planets with Atmospheres. Venus -------------Earth----------------Mars

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Global energy balance the greenhouse effect

Global Energy Balance:The Greenhouse Effect

Geos 110 Lectures: Earth System Science

Chapter 3: Kump et al 3rd ed.

Dr. Tark Hamilton, Camosun College


3 inner rocky planets with atmospheres
3 Inner Rocky Planets with Atmospheres

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

The Goldilocks Zone



Venus south pole 460 c co 2 so 2 uv image pioneer venus orbiter feb 5 1979
Venus: South Pole > 460°C, CO right, so she ate it all up!2 SO2UV 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: The Blue Planet (Ice, Water, Steam) right, so she ate it all up!

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

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


Mars 55 c co 2 millibar atmosphere
Mars: -55°C, CO right, so she ate it all up!2millibar atmosphere

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

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


Electromagnetic radiation waves
Electromagnetic Radiation - Waves right, so she ate it all up!

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

  • E-field interacts with matter through its electrons


Energy frequency wavelength
Energy, Frequency & Wavelength right, so she ate it all up!

  • E = h ν, Higher Frequency  Higher Energy

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

  • Whats nu? ……. ν = c/ λ

  • Or

  • λν = c , c = 3x108 m/s


400 nm visible light 700 nm
400 nm < Visible Light < 700 nm right, so she ate it all up!

  • 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 time normal incidence minimizes area
Flux: Energy per unit area per unit time right, so she ate it all up!Normal 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 footprint maximum flux
Normal Incidence = Circular Footprint right, so she ate it all up!Maximum Flux!


Inclined Incidence Increases Area but Decreases Heating right, so she ate it all up! Decreased Flux


Inverse square law
Inverse Square Law right, so she ate it all up!

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
Temperatures of Water Phase Changes right, so she ate it all up!

Celsius based on freezing & boiling or H2O

Kelvins Absolute (no offset), same size as Celsius

Farenheit Freezing & Coagulation of Human Blood…eeew!


Temperature scales
Temperature Scales right, so she ate it all up!

  • 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
A Cold Black Body absorbs at all wavelengths right, so she ate it all up!

Cold = Black Hot = emits Red Hotter = emits White


The planck function
The Planck Function right, so she ate it all up!

  • 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 wavelength
The Planck Function: variation of blackbody radiation & right, so she ate it all up!λ (wavelength)


Wein s law max 2898 t kelvins
Wein’s Law: right, so she ate it all up!λ max ~ 2898/T (Kelvins)

  • The Sun’s Photosphere is ~ 5780 Kelvins


Stefan boltzmann law sum of all flux t 4 emission goes up as temperature to the 4th power
Stefan-Boltzmann Law: Sum of All Flux ~ right, so she ate it all up!σ T4Emission goes up as temperature to the 4th power!


Blackbody emission spectra for sun earth
Blackbody Emission Spectra for Sun & Earth right, so she ate it all up!

  • 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 flux stefan boltzmann law
Solar Energy Flux right, so she ate it all up!Stefan 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
Earth’s Global Energy Balance right, so she ate it all up!

  • For Earth’s Energy Budget to Balance

  • Flux inmust = 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
A Closer Look at Global Energy Balance right, so she ate it all up!


Earth s energy balance
Earth’s Energy Balance right, so she ate it all up!

Energy emitted = Energy absorbed :

  • Energy emitted = 4π REarth2 x σTEarth4

    • This follows from Stefan-Boltzmann & Spherical Shape

      E absorbed = E intercepted – E reflected:

  • E absorbed = πREarth2S - πREarth2SA = πREarth2 S(1-A)

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

      Therefore: 4π REarth2 x σTEarth4 = πREarth2 S(1-A)

      or: σTEarth4 = S(1-A)/4


The greenhouse effect one layer atmosphere
The Greenhouse Effect right, so she ate it all up!One-Layer Atmosphere

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

  • Atmosphere radiates IR down & absorbs IR up


The greenhouse effect one layer atmosphere1
The Greenhouse Effect right, so she ate it all up!One-Layer Atmosphere

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 Air4

    For Earth’s Air: atmosphere radiates 2 ways

  • σTSurface4 = 2σTEarth’s Air4

    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


Was 387 co 2 now 390 02 ppm august 2011 increasing 2 ppm yr n 2 o 2 ar are inert

Was 387, CO right, so she ate it all up!2 now = 390.02 ppm August 2011

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


Trace greenhouse gases
Trace Greenhouse Gases right, so she ate it all up!

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 atmosphere dominate the atmospheric structure
Thermal Layers in Earth’s Atmosphere right, so she ate it all up!Dominate 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
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 layering troposphere stratosphere mesosphere thermosphere exosphere
Atmospheric Thermal Layering 100 kmTroposphere, Stratosphere, Mesosphere, Thermosphere, Exosphere

  • Earth’s surface & Stratopause are warmest

  • The Tropopause and Mesopause are coldest


Atmospheric thermal layering
Atmospheric Thermal Layering 100 km

  • 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
Modes of Heat Transport & Storage 100 km

  • 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
Heat Storage and Transfer 100 km

  • 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 transfer1
Heat Storage and Transfer 100 km

  • 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
Heat Storage & Transfer: Troposphere 100 km

  • 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 o 3 ozone is in the stratosphere
Most of the O 100 km3Ozone is in the Stratosphere

  • < 5ppm H2O vapour, usually no clouds, stratified

    Exception is Antarctic Winter, thin Stratospheric Clouds


Why is there such a wavy t profile
Why is there such a wavy T° Profile 100 km

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 moment makes it rotate when it absorbs ir
Water’s Big Dipole Moment 100 kmMakes 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
Molecular Absorption Spectrum: GHG’s 100 km

  • 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


Co 2 s bending mode of vibration
CO 100 km2’s bending mode of vibration

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


Other greenhouse gases reduce outgoing ir
Other Greenhouse Gases 100 kmReduce 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 n 2 o 2
So 100 kmWazzup 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 Have Variable Effects on IR 100 km

  • Clouds & lower concentration aerosols block heat

  • Different types: Stratus, Cumulus, Cirrus

  • Can raise albedo blocking Sun or hold heat in




Tall Cumulonimbus have all 3 Phases 100 km

  • Vertical Convection, Thunderstorms

  • Water-Ice (sleet/hail)-Steam


Radiation flux versus cloud type
Radiation Flux versus Cloud Type 100 km

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

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


General circulation model climate
General Circulation Model 100 km 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
Global Energy Balance 100 km

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
Radiative Convective 1D Model 100 km 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 s1
Radiative Convective 1D Model 100 km 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
Water Vapour Feedback: Hothouse 1D RCM’s 100 km

  • 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
Radiative Convective 1D Model 100 km 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 100 kmVapour 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
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
Uncertain effects of Cloud Types oscillations

  • 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
Uncertainties in Climate Models oscillations

  • 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?


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