Energy Balance and Greenhouse Gases - Personal...

Summer Seminar Conceptual Climate Models

Jim Walsh Oberlin College

July 23, 2013

Energy Balance and Greenhouse Gases


Global climate is determined by the radiation balance of the planet. There are three fundamental ways in which this balance can change1:

*changing the incoming solar radiation (insolation)

*changing the albedo

*altering the Outgoing Longwave Radiation (OLR)

1Intergovernmental Panel on Climate Change AR4 (2007), p. 465 (www.ipcc.ch)

2M. Wild, Institute for Atmospheric and Climate Science, ETH, Zurich.

Anthropogenic interference with climate occurs first of all through a perturbation of the radiation balance (e.g., greenhouse effect, air pollution, land use change)2


Budyko’s EBM:

M.I. Budyko, The effect of solar radiation variations on the climate of the Earth, Tellus 21 (1969)

= sine(latitude)

in E out E

insolation albedo outgoing longwave radiation (OLR)

Mikhail Budyko (20.01.1920 – 10.12.2001)

Units: W/m2 = J/(s m2)



IPCC Assessment Report 4 (2007), Working Group 1, p. 96


NASA: Earth Radiation Budget Experiment


Budyko’s EBM: = sine(latitude)

OLR


Ray Pierrehumbert University of Chicago

Principles of Planetary Climate Cambridge, 2010

(PPC)

D. Hartmann, Global Physical Climatology, Academic Press, 1994. G. Plass, Infrared radiation in the atmosphere, Amer. J. Physics 24 (1956), 303-321.

Chapter 4: Radiative transfer in temperature-stratified atmospheres

Chapter 3: Elementary models of radiation balance.


Radiation: characterized by direction of propagation and frequency

frequency (Hz) wavelength (m) wavenumber

(PPC, p. 137)

Electromagnetic spectrum

relevant in climatology

P

steradians


Solid Angles and Steradians

The measure in radians of an angle made by a collection of rays emanating from a point P is the length of the arc of the unit circle centered on P which the rays intersect. P

The measure in steradians of a solid angle made by a collection of rays emanating from a point P is the area of the patch of the unit sphere centered on P which the rays intersect.

steradians


Solid Angle Differential

Hemisphere surface area

magnitude of radiant intensity


Energy of radiation: measured by its intensity or radiance I

The amount of corresponding radiant energy is


Energy of radiation: measured by its intensity or radiance

The amount of corresponding radiant energy is

Energy per unit frequency per unit area per unit time:


Energy of radiation: Flux density

The amount of radiant energy per unit frequency per unit area per unit time:

Total energy per unit frequency passing across a unit area of a plane surface from one side to the other (integrate over the upper hemisphere):

Spectral flux density

Integrate spectral flux density over all frequencies: Flux density


Blackbody radiation: radiation reacts so strongly with matter that it achieves thermodynamic equilibrium at same temperature as the matter (“perfect absorbers and emitters”).

Planck’s Function:

k = Boltzman thermodynamic constant h = Planck’s constant c = speed of light

n

frequency (Hz) wavelength (m) wavenumber

•  spectral F.D. with T at all n


Blackbody radiation

•  isotropic: equally intense in all directions

Stefan-Boltzman Law: Total power exiting from each unit area of the surface of a blackbody:

n


Blackbody radiation

•  isotropic: equally intense in all directions

Total power exiting from each unit area of the surface of a blackbody:


Radiation balance of planets: An idealized example •  the planetary albedo is spatially uniform. •  the planet radiates like a perfect blackbody (uniform surface temp. T ) •  the planet’s atmosphere is perfectly transparent to the electromagnetic energy emitted by the surface

Planet loses energy through emission at a lower wavenumber than that at which it receives energy from the star.

(TE = 255 K)


Flux absorption: Beer’s Law

Absorption is proportional to the flux F times the mass of the absorber along the path.

absorption coefficient

density of the absorber

Assumes : (i) no scattering: a parallel beam of radiation (ii) plane-parallel approximation: atmospheric properties are functions only of the vertical coordinate


Greenhouse gas (GG):

(Figure from PPC, p. 149)

The Earth’s observed zonal-mean OLR for January, 1986 (solid curve).

(dashed curve).

Prevalence of clouds in the high, cold regions of the tropical atmosphere (condensed water small enough small enough to stay suspended for a long time.)



R. Pierrehumbert et al, On the relative humidity of the atmosphere, The Global Circulation of the Atmosphere, T. Schneider and A Sobel, eds. Princeton University Press, 2007, p. 143.



Nitrogen N2 -- 78.084% Oxygen O2 -- 20.9476% Argon Ar -- 0.934% Carbon Dioxide CO2 -- 0.0314% Neon Ne 0.001818% Methane CH4 -- 0.0002% Ozone O3 -- 0.000007% Water vapor -- highly variable; typically makes up about 1%

This is composition of air in percent by volume, at sea level at 15°C and 101325 Pa. (CRC Handbook of Chemistry and Physics, edited by David R. Lide, 1997)


Transmission spectra of major atmospheric gases

Sun Earth


Greenhouse gas: Absorption coefficient and OLR spectrum. Toy example with one (fictitious) GG

n wavenumber 600

tropopause

T Ts Tstrat

p

(Ts = 280 K, Tstrat = 200 K) (PPC, p. 218)


Greenhouse gas: Absorption coefficient and OLR spectrum. Toy example with one (fictitious) GG

tropopause

T Ts Tstrat

p

(Ts = 280 K, Tstrat = 200 K)

n wavenumber 600

(Ts = 280 K, Tstrat = 200 K)

The strength of the greenhouse effect is not so much a matter of how deep the ditch is, but how wide.

(PPC, p. 217)


Greenhouse gas: Absorption coefficient and OLR spectrum.

Absorption coefficient for pure CO2 at T = 293 K, p = 1000 mb

Infrared emission peak for Earth centered on ~ n = 670 cm-1 SUN


Greenhouse gas: Absorption coefficient and OLR spectrum.

R. Pierrehumbert, Infrared radiation and planetary temperature, Physics Today (January 2011).

T = 260 K p = 500 mb

Rather than being unquestionably lethal, the results of a doubling of CO2 may be merely catastrophic.

--R. Pierrehumbert


Greenhouse gases

R. Pierrehumbert, Infrared radiation and planetary temperature, Physics Today (January 2011).


Greenhouse gases: Logarithmic dependence of OLR on CO2

K. Caldeira and J. Kasting, Susceptibility of the early Earth to irreversible glaciation caused by carbon dioxide clouds, Nature 359 (1992), 226-228.

A(�) = �326.4 + 9.161�� 3.164�2 + 0.5468�3

B(�) = 1.953� 0.04866�+ 0.01309�2 � 0.002577�3, � = ln(pCO2/300)

OLR ⇡ �T 43< �T 4

s

�pkg

m s2· 1m2 · 1

g

s2

m· q

dF = �abs ⇢a F ds abs = (⌫, p, T ) m2/kg �p/g kg/m2

� = 2⇡5k4/(15c2h3) ⇡ 5.67 · 10�8 W m�2 K�4

F⌫ =

Z 2⇡

0

Z ⇡/2

0

B cos ✓ sin ✓ d✓ d� = ⇡B(⌫, T ) F =

Z 1

0

⇡B(⌫, T ) d⌫ = �T 4

dF⌫ = I⌫ cos ✓ d! (d! = sin ✓d✓d�) dF⌫ = I⌫ cos ✓ sin ✓ d✓ d�

Given

• frequency increment d⌫• increment of area dA

• solid angle increment d!• time increment dt

dF⌫ = I⌫ cos ✓ d! dAd⌫ dt

d! d! = sin ✓d✓d�

• A,B > 0• T % ) OLR %• CO2 $ A,B ?nu � n = ⌫/c m�1 ⌫� = c = 3⇥ 108 m/s

T = T (y, t)

R@T

@t= Qs(y)(1� ↵(y))� (A+BT )� C

✓T �

Z 1

0

Tdy

◆

1

A. McC. Hogg, Glacial cycles and carbon dioxide, Geophys. Res. Lett. 35 (2008)

H. Marshall, J. Walker and W. Kuhn, Long-term climate change and the geochemical cycle of carbon, J. Geophys. Res. 93 (D1) (1988), 791-801.

G(t) = G+ k ln⇣

C(t)C0

⌘A = �352.08 + 9.56 lnP, B = 2.053� 0.0514 lnP, P = pCO2

A(�) = �326.4 + 9.161�� 3.164�2 + 0.5468�3

B(�) = 1.953� 0.04866�+ 0.01309�2 � 0.002577�3, � = ln(pCO2/300)

OLR ⇡ �T 43< �T 4

s

�pkg

m s2· 1m2 · 1

g

s2

m· q

dF = �abs ⇢a F ds abs = (⌫, p, T ) m2/kg �p/g kg/m2

� = 2⇡5k4/(15c2h3) ⇡ 5.67 · 10�8 W m�2 K�4

F⌫ =

Z 2⇡

0

Z ⇡/2

0

B cos ✓ sin ✓ d✓ d� = ⇡B(⌫, T ) F =

Z 1

0

⇡B(⌫, T ) d⌫ = �T 4

dF⌫ = I⌫ cos ✓ d! (d! = sin ✓d✓d�) dF⌫ = I⌫ cos ✓ sin ✓ d✓ d�

Given

• frequency increment d⌫• increment of area dA

• solid angle increment d!• time increment dt

dF⌫ = I⌫ cos ✓ d! dAd⌫ dt

d! d! = sin ✓d✓d�

• A,B > 0• T % ) OLR %• CO2 $ A,B ?nu � n = ⌫/c m�1 ⌫� = c = 3⇥ 108 m/s

T = T (y, t)

R@T

@t= Qs(y)(1� ↵(y))� (A+BT )� C

✓T �

Z 1

0

Tdy

◆

1


Equilibrium solutions


Equilibrium solutions


Energy Balance and Greenhouse Gases Energy Balance and Greenhouse Gases

The Jormungand Climate Model

Geological and paleomagnetic evidence indicate that during at least two Neoproterozoic glacial periods (~630 Ma and ~715 Ma) continental ice sheets flowed into the ocean near the equator.

Positive ice-albedo feedback; snowball Earth hypothesis

Alternative theory: thin strip of open ocean about the equator.

--evidence that photosynthetic eukaryotes thrived both before and immediately after the Snowball Episodes.

--evidence that multiple lineages of sponges may have survived these glaciations

D. Abbot, A. Viogt and D. Koll, The Jormungand global climate state and implications for Neoproterozoic glaciations, J. Geophys. Res. 116 (2011) (D18103)



Abbot et al, p. 4 Henry Fuseli (1788)



Abbot et al, p. 4

Net evaporation








Summary

Lots of good science involved in the study of the atmosphere and its effects on climate. Involve physics and chemistry colleagues? Greenhouse gases and their effects on outgoing longwave radiation can be incorporated into conceptual climate models. Conceptual climate models are versatile: adjustments in the albedo function, for example, can lead to model behavior appropriate for different eras in the Earth’s past. Homework: Worksheet problems 2, 3, 4, 6, 7, 8, 13, 14

Thank You!

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