Physics of the Atmosphere 2 Radiation and Energy Balance

Lecture, Summer Term 2015

Ulrich Foelsche Institute of Physics, Institute for Geophysics, Astrophysics, and Meteorology (IGAM)

University of Grazund

Wegener Center for Climate and Global Change

ulrich.foelsche@uni-graz.at

http://www.uni-graz.at/~foelsche/

Textbooks

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C. Donald Ahrens, Meteorology Today: An Introduction to Weather, Climate, and the Environment, Brooks/Cole, 9. Ed., ISBN: 0495555746 (also paperback) UB-Semesterhandapparat, IGAM-Library

K.N. Liou, (Ed.), An Introduction to Atmospheric Radiation, Academic Press, 2nd Ed., ISBN: 978-0-12-451451-5, 2002<http://books.google.at/books?id=mQ1DiDpX34UC> (partial)

Murry L. Salby, Physics of the Atmosphere and Climate, Cambridge Univ. Press, 2nd Ed., ISBN: 978-0-521-76718-7, 2012<http://books.google.at/books?id=CeMdwj7J48QC> (partial)

Lehrbücher

Helmut Kraus, Die Atmosphäre der Erde - Eine Einführung in die Meteorologie, Springer, Berlin, 3. Auflage, ISBN: 978-3-540-20656-9 (auch paperback) UB-Semesterhandapparat, IGAM-Bibliothek

Gösta H. Liljequist & Konrad Cehak, Allgemeine Meteorologie, Springer, Berlin, 3. Auflage ISBN: 3540415653 (nützliches deutsch-englisches Register) UB-Semesterhandapparat, IGAM-Bibliothek

Ludwig Bergmann & Clemens Schaefer, Lehrbuch der Experimentalphysik, Band 7, Erde und Planeten, (Kapitel 3 – Meteorologie, Kapitel 4 – Klimatologie), de Gruyter, Berlin, ISBN: 978-3-11-016837-2 UB-Semesterhandapparat, IGAM-Bibliothek

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Exams

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No, it will be the other way round – you will be forced to answer questions – in my office & IGAM

Exam dates and registration viaUNIGRAZonline: online.uni-graz.at

Picture credit: Gary Larson

Different Aspects of Atmospheric Radiation

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UF

(1) Electromagnetic Waves

NASA

Physics of the Atmosphere II

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The Electromagnetic Field

Basic Properties of the Electromagnetic Field

Within the framework of classical electrodynamic theory, it is represented by the vector fields:Electric field E [V/m]Magnetic field B [Vs/m2] = [T] (Tesla)

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To describe the effect of the field on material objects, it is necessary to introduce a second set of vectors: the Electric current density j [A/m2]Electric displacement field D [As/m2]Magnetizing field H [A/m]

The space and time derivatives of the vectors field are related by Maxwell's equations – we will focus on the differential form.

The Electromagnetic Field

The electric field E and the electric displacement field D are related by

where ε0 is the electric constant 8.854 187 817 · 10-12 AsV-1m-1 (exact)[NIST Reference: http://physics.nist.gov/cuu/Constants/index.html], and P is the electric polarization – the mean electric dipole moment per volume.

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PED 0ε

The magnetic field B and the magnetizing field H are related by

where µ0 is the magnetic constant 4π·10-7 VsA-1m-1 (exact), andM is the magnetic polarization – the mean magnetic dipole moment per volume.

MHB 0μ

Maxwell's Equations in Matter

The First Maxwell Equation, also known as Gauss’s Law:

relates the divergence of the displacement field to the (scalar) free charge density: Positive electric charges are sources of the displacement field (negative electric charges are sinks). Closed field lines can be caused by induction.

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f reeρ D

The Second Maxwell Equation or Gauss’s Law for Magnetism:

states that there are no magnetic charges (magnetic monopoles). The magnetic field has no sources or sinks – its field lines can only form closed loops.

0 B

Maxwell's Equations in Matter

The Third Maxwell Equation, or Faraday’s Law of Induction:

describes how a time-varying magnetic field causes an electric field (induction).

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t

B

E

The Fourth Maxwell Equation:

shows that magnetic (magnetizing) fields can be caused by electric currents (Ampère’s Law), but also by changing electric (displacement) fields (Maxwell’s Correction – which is very important, since it “allows” for electromagnetic waves – also in vacuum).

t

D

jH

The previous formulations are known as Maxwell’s Macroscopic Equations or Maxwell’s Equations in Matter. Under specific conditions the relations on slide 07 can be simplified.

The Earth's atmosphere is a linear medium – the induced polarization P is a linear function of the imposed electric field E. The Earth’s atmosphere is also an isotropic medium – P is parallel to E:

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ED ε

Maxwell's Equations in Gas

EP e0εThe electric susceptibility χe degenerates to a simple scalar (in general it would be a tensor of second rank) and we get:

EEED εεεε re1 00 where ε is the permittivity (or dielectric constant in a homogenous medium) and εr = 1 + χe is the dimensionless relative permittivity, which depends on the material and is unity for vacuum.

Similar considerations for M and H yield:

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Maxwell's Equations in Gas

HM m0μ

where χm is the (scalar) magnetic susceptibility (in general it would be again a tensor of second rank), µ is the permeability and µr = 1 + χm is the dimensionless relative permeability (which is also unity in vacuum).

HHHB μμμμ rm1 00

The electric current density j is related to the electric field E via the electric conductivity σ [Ω-1m-1] (a scalar for isotropic media, but in general again a tensor) through the differential form of Ohm’s Law:

Ej σ

The lower atmosphere (troposphere and stratosphere, at least up to ~ 50 km) is a neutral (ρfree = 0), and isotropic medium, and has a negligible electric conductivity (σ = 0) yielding j = 0.

Maxwell’s equations can therefore be written as:

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Maxwell's Equations in Neutral Gas

0 E

0 B

t

B

E

tεμ

E

B

Maxwell's equations relate the vector fields by means of simultaneous differential equations. On elimination we can obtain differential equations, which each of the vectors must separately satisfy. Applying the curl operator on Faraday’s law, interchanging the order of differentiation with respect to space and time (which can be done for a slowly varying medium like the atmosphere is one at frequencies of practical interest) and inserting the fourth Maxwell equation yields:

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Electromagnetic Waves

2

2

t

E

BE εμt

with EEE 0 E 2

we get2

2

tεμ

E

E2

2

tεμ

B

B

These partial differential equations are standard wave equations. Considering plane waves, the solutions have the form:

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Electromagnetic Waves

exp, ωtit rkErE 0)(

and2ω

where ν is the frequency (Hz) and λ is the wavelength [m]. Inserting the above solutions into Maxwell’s equations yields:

exp, ωtit rkBrB 0)(

where k is the wave number vector, pointing in the direction of wave propagation. The angular frequency, ω [rad/s] and the angular wave number, k [rad/m], are defined as (with k = |k|):

2

k

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Electromagnetic Waves

which shows that the field vectors E and B are perpendicular to each other and that both are perpendicular to k. Electromagnetic waves are thus transverse waves.

0Eki 0Bki BEk ii EBk ii

micro.magnet.fsu.edu wikimedia

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Electromagnetic Waves

Inserting the first equation of slide 14 in to the wave equation using the vector identity:

EkkkEkEkk and the orthogonality

0Ek yields

22 k With the definition of the phase velocity:k

c

we see that monochromatic electromagnetic waves propagate in a medium with the phase velocity:

rr

11

00

c

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Electromagnetic Waves

And in vacuum we get:

001

0 c C0 = 299 792 458 m s-1 which is nothing else than the speed of light in vacuum

In geometric optics the refractive index of a medium (n) is defined as the ratio of the speed of light in vacuum (c0) to that in the medium (c):

rr0

c

cn which is known as the Maxwell Relation.

In the Earth’s atmosphere the relative permeability is almost exactly = 1, thus we get (in a general, frequency-dependent form):

)( r)( n

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Electromagnetic Waves

James N. Imamura, Univ. Oregon

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Electromagnetic Waves

ESA

Gamma Rays

NASA/DOE/Swift

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A gamma-ray blast 12.8 billion light years away, Supernova Cassiopeia A, Cygnus region.

X Rays

JAXA/NASA/POLAR

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The Sun and the Earth’s northern Aurora-Oval in X-Rays.

Ultraviolet

NASA/SDO

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The Sun in UV and the “Ozone Hole” above Antarctica.

Visible

The visible part of the solar spectrum – including Fraunhofer lines

(US) National Optical Astronomy Observatory

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Visible

Jenny Mottar SOHO/Jeannie Allen

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Color temperatures of stars and spectral signatures on Earth.

Near–Infrared

Jeff Carns/NASA

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Vegetation and different Soil types from reflected near–infrared.

Infrared

NASA/Jeff Schmaltz MODIS

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Saturn’s strange aurora and forest fires in California.

Microwaves

NASA

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Hurricane Katrina.

Corresponding Wavelengths: 1m to 1 mm

Radio Waves

Michael L. Kaiser, Ian Sutton, Farhad Yusef-Zedeh NASA

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Radio Waves

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In German:

LW – Langwelle

MW – Mittelwelle

KW – Kurzwelle

UKW – Ultrakurzwelle

Microwaves – 1m to 1 mm

Military Radar Nomenclature: L (1 – 2 GHz), S, C, X (8 – 12 GHz), Ku, K (18 – 27 GHz) and Ka bandsPhysics Hypertextbook

Solar EM Waves

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For processes in the lower atmosphere wavelengths from 0.2 to 100 µm are most important

Wiki