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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
http://www.uni-graz.at/~foelsche/
Textbooks
Atmo II 01
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
Atmo II 02
Exams
Atmo II 03
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
Atmo II 04
UF
(1) Electromagnetic Waves
NASA
Physics of the Atmosphere II
Atmo II 05
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)
Atmo II 06
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.
Atmo II 07
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.
Atmo II 08
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).
Atmo II 09
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:
Atmo II 10
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:
Atmo II 11
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:
Atmo II 12
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:
Atmo II 13
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:
Atmo II 14
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
Atmo II 15
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
Atmo II 16
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
Atmo II 17
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
Atmo II 18
Electromagnetic Waves
James N. Imamura, Univ. Oregon
Atmo II 19
Electromagnetic Waves
ESA
Gamma Rays
NASA/DOE/Swift
Atmo II 20
A gamma-ray blast 12.8 billion light years away, Supernova Cassiopeia A, Cygnus region.
X Rays
JAXA/NASA/POLAR
Atmo II 21
The Sun and the Earth’s northern Aurora-Oval in X-Rays.
Ultraviolet
NASA/SDO
Atmo II 22
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
Atmo II 23
Visible
Jenny Mottar SOHO/Jeannie Allen
Atmo II 24
Color temperatures of stars and spectral signatures on Earth.
Near–Infrared
Jeff Carns/NASA
Atmo II 25
Vegetation and different Soil types from reflected near–infrared.
Infrared
NASA/Jeff Schmaltz MODIS
Atmo II 26
Saturn’s strange aurora and forest fires in California.
Microwaves
NASA
Atmo II 27
Hurricane Katrina.
Corresponding Wavelengths: 1m to 1 mm
Radio Waves
Michael L. Kaiser, Ian Sutton, Farhad Yusef-Zedeh NASA
Atmo II 28
Radio Waves
Atmo II 29
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
Atmo II 30
For processes in the lower atmosphere wavelengths from 0.2 to 100 µm are most important
Wiki