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METSWN Organisation, 2 nd half

METSWN Organisation, 2 nd half. Transfer of Energy. Conduction between objects having direct physical contact Convection within one fluid (gas, liquid) individual particles containing heat rise Radiation needs no medium. Literature.

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METSWN Organisation, 2 nd half

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  1. METSWN Organisation, 2nd half

  2. Transfer of Energy • Conduction between objects having direct physical contact • Convection within one fluid (gas, liquid) individual particles containing heat rise • Radiation needs no medium

  3. Literature Early studies of the transfer of EM radiation were primarily carried out by astronomers and astrophysicists • Petty, G., 2006: “A first course in Atmospheric Radiation”, 2nd Edition, Sundog Publishing, 458 S., $ 48,- http://www.sundogpublishing.com/AtmosRad/ • Bohren, Craig F. , und Eugene Clothiaux, 2006: „Fundamentals of Atmospheric Radiation: An Introduction with 400 Problems“, Wiley-VCH, 1st edition, 490 Seiten. • Liou, K.-N.,1992: „An Introduction to Atmospheric Radiation, Volume 84, Second Edition, $102 • Liou, K.-N.,1992: „Radiation and cloud processes in the atmosphere“. Oxford Univ. Press, Oxford, 487 Seiten • Goody, R.M. and Y.L. Young, 1995: „Atmospheric Radiation“. Oxford Univ. Press., 2nd Edition, 544 Seiten, $117,- prices from Amazon Web-Seite, 17.3.08

  4. Content 1. Introduction 2. Properties of electromagnetic radiation 2.1 Electromagnetic waves 2.2 Frequency 2.3 Polarization 2.4 Energy 2.5 Mathematical description 2.6 Quantum properties of radiation 2.7 Radiation measures • Electromagnetic Spectrum • Reflection and Refraction • Radiative properties of natural surfaces • Thermal emission • Atmospheric transmission • Atmospheric emission • Absorption atmospheric gases • Broadband fluxes and heating rates (cloud free) • Radiative transfer with scattering • Scattering and absorption by particels • Radiative transfer with multiple scattering

  5. Motivation • Most of the energy exchange within the universe is realized by electromagnetic (EM) radiation • Solar radiation at top of the atmosphere (TOA) – is the only significant energy source for the Earth – drives atmospheric photochemistry, weather regimes and climate – is the basis for all biologic life • Globally and over long time periods the climate system is in radiative energy equilibrium – on small spatial and short time scales there may be no radiative equilibrium – thermal gradients lead to hydro- & thermodynamic processes – all interactions with solar radiation in the atmosphere are of importance for the radiative budget and climate • Radiation is a diabatic process, which acts continuously and over long distances (non local)

  6. What would happen if the sun were suddenly switched off? Electromagnetic Spectrum Solar spectrum

  7. Terrestrial Spectrum thermal emission by Earth surface, gases and hydrometeors

  8. Sources of Radiation • Solar radiation- 99 % of energy between 0.23 and 5 μm- maximum at 0.501 μmPhotosphere has an effective temperature of 5778 K (Corona: ~5×106 K)  1366 W/m2orthogonal to sun direction at TOA •  total solar irradiance (TSI) – „solar constant“ • Terrestrial radiation - 99 % of energy between 3 - 80 μm- maximum at ~10 μm Wikipedia: During a total solar eclipse, the solar corona can be seen with the naked eye. • Earth surface with about 300 K emits continuous spectrum • atmospheric gases (temperatures between 200 and 300 K) have distinct spectral characteristics due to rotational, vibrational and electronic transitions • hydrometeors and aerosols with temperatures between 200 – 300 K show continuous spectra

  9. Solar and Terrestrial Spectrum at Top of theatmosphere (TOA)! UV VIS Infrared

  10. Total Solar Irradiance (TSI) Perihel (January) ~1420 W/m2 Aphel (July) ~1328 W/m2 σT4 rS Ik rS-E The total solar irradiance Ik is the radiative flux density arriving at a distance of 1 astronomical unit (AU) at a surface perpendicular to the solar rays. 1 AU is the mean Earth–Sun distance, i.e. about 149 597 871 km Irradiance (flux density) is the total radiative energy per time per unit through a horizontal unit plane in Wm−2. Ik=1366±5 W/m² Under the assumption that the sun emits like a black body it is possible to calculate the sun‘s radiative temperature Ts from Ik using the Stefan-Boltzmann law:

  11. Effective Emission Temperature of the Earth/Atmosphere System Ik /4 TE σTE4 α • Globally and over long time periods the climate system is in energetic equilibrium (balanced net radiation, i.e., downward – upward = 0). Terrestrial emission compensates uptake of solar energy • Terrestrial emission into space can be related to a radiative equilibrium temperatureTE via the Stefan-Boltzmann-law • Not all solar radiation is absorbed  part reflected back to space from surface and clouds (planetary Albedo α)

  12. Summary σTE4 , TE=255 K Photosphere TS~6000K ~240 W/m² absorbed α=30% TS~106K 1366 W/m² 1373 W/m² 6x107W/m² 343 W/m²

  13. Energy Balance of the Atmosphere solar terrestrial shortwave longwave Atmosphere has a radiation deficitcompensated by turbulent fluxes of sensible and latent heat Phase transitions couple energy and water cycle KIEHL J., and K. TRENBERTH, 1997: Earth´s annual global mean budget. Bull. Am. Met. Soc., 78, 197-208.

  14. The Atmosphere as a Heat Engine Meridional temperature gradient

  15. Radiation: Importance for Remote Sensing!

  16. Meteosat’s 12 “Eyes” VIS 0.6 VIS 0.8 NIR 1.6 NIR 3.9 WV 6.2 WV 7.3 IR 8.7 IR 9.7 IR 10.8 IR 12.0 IR 13.4 HRVIS

  17. Properties ofElectromagnetic (EM) Radiation 2.1 Electromagnetic Waves 2.2 Polarization 2.3 Energy 2.4 Maxwell Equations 2.7 Quantum Properties of Radiation 2.8 Radiation Measures

  18. 2.1 Electromagnetic (EM) Radiation • Electric and magnetic fields are detectable in some distance from the source,e.g. hairs on balloons, refrigerator magnets • Quantitatively static electric and magnetic fields are described by • a) The electric field vector E (Coulomb–law) in units of V m−1: • with: ε0 = 8.854210−12 A s V−1 m−1 (= F m−1) representing the dielectricity, or also called the electric permittivity in vacuum, q electric charge [A s = C], Δr the radial distance [m], and the radial unit vector b) The magnetic field vector H (Faraday–law) in units of V s−1 = T (Tesla).Magnetic fields are determined by the distribution of electric current near by • Because both E and H are vectors they are described by their magnitude and direction (and phase, therefore complex).

  19. 2.1 Electromagnetic Radiation • The superposition of all oscillating electromagnetic waves in the atmosphere is called atmospheric radiation • Maxwell Equations  changingelectrical fields induce magnetic fieldschangingmagnetic fields induce electrical fields • EM radiation has both electric E and magnetic H field components, which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation • EM waves are transversal waves propagating with the speed of light c=co/n (co=2.997x108 m/s the speed of light in vacuum) and refractive index n. • In vacuum EM waves transport energy infinitely far; within matter, energy is ultimately converted to heat, kinetic or chemical energy. • Different waves do not effect each other, however, local interference of waves can lead to enhancement (constructive interference) or reduction (negative interference)

  20. Basic Properties • Frequency ν – oscillation rate determines the interaction with matter: • Amplitude of oscillation Eodetermines the amount of energy carried by the EM wave (Entropy); energy is proportional to Eo2 • Polarization of radiationthe direction of polarization is defined as the direction of the electric field vector. It does not directly influence the oscillation but partly the interaction with surfaces or particles The faster the oscillations, (e.g. UV wavelengths) the stronger they influence “light” matter (i.e. electrons); slow oscillations (IR, micro waves) effect heavier constituents (molecules) Here the energy transported by waves, interaction effects with matter and their frequency interaction is most interesting.

  21. Oscillations • Oscillations can be described by their • Wavelength the distance an EM travels within one cycle; = distance between two individual maxima, e.g. =0.7 m • Frequency  (= c/ ; number of oscillations within a certain time span (1 s), e.g. =0.7 m  4.3 x 1014 cycles per second = Hz. • Wavenumber (= 1/ ; number of maxima (minima) within a certain length (1 cm), e.g.=0.7 m  14286 cm-1 Depending on application the exchangable quantities wavelength, frequency or wave number are used

  22. Frequencies • Monochromatic radiation EM radiation of a single frequency (only one color) often only an ideal case  reality: quasi-monochromatic (e.g. receiver bandpass) • Broadband radiation Mixture over a broad frequency range in the atmosphere i.e. solar and terrestrial region • Frequency decomposition Every EM time series can be decomposed into its single periodic oscillations (Fourier decomposition) • individual EM perturbations propagate independently radiative transfer can be regarded separately for each frequency α amplitude ω angular frequency Φ phase shift

  23. Coherence • Coherence describes a fixed phase difference between two superimposed waves, e.g. laser, microwave oven, applause • Incoherent radiation consists of randomly superimposed finite single monochromatic wave packets (black body radiation) • Multiple waves of the same quasi-monochromatic frequency (ν±Δν) also lead to incoherent radiation • Coherence length Δl: propagation distance from a coherent source to a point where an electromagnetic wave maintains a specified degree of coherence (1/e reduction); Δl=c/nΔν (c: phase velocity of light in medium, n: refractive index, Δν=band width) • Coherence time: τ= 1/nΔν

  24. 2.2 Polarization • Orientation of the oscillating EM field is perpendicular to the direction of propagation • linear polarization: EM wave oscillates in a constant direction • An unpolarized wave oscillates in no preferred direction – product of superposition of multiple single waves • Superposition of two waves: summation of EM field vectors • If two waves are linearly polarized and are superimposed without phase delay, the product is again is a linearly polarized vertically horizontally 45 deg linear

  25. 2.2 Polarization • If a phase difference between two single EM-waves exist, the resulting wave will be elliptically polarized. If the phase difference is 90° (Δφ = λ/4) and the amplitude of both waves is equal the wave will be … ???

  26. 2.2 Polarization • If a phase difference between two single EM-waves exist, the resulting wave will be elliptically polarized. If the phase difference is 90° (Δφ = λ/4) and the amplitude of both waves is equal the wave will be circularly polarized • Natural radiation, as emitted by inhomogeneous media, is unpolarized (e.g. solar radiation); coherent radiation from active sources is mostly linearly polarized • Interaction with homogeneous media leads to polarization (e.g. reflection of solar radiation on water surfaces  horizontal component is reflected stronger than vertical component); scattering on ice particles

  27. 2.3 Energy • Waves convey energye.g. solar energy is transported to the Earth surface (hot beach sand …) • Natural radiation is continuous, so that the rate of energy transfer is of interest • radiated power [W=J/s] over a unit surface = radiation flux density F [W/m2] (irradiance, radiant exitance) • Problem 1 • In the tropics sunrise is at 6 LST and sunset at 18 LST. Assuming the netto flux density of solar energy is immediately absorbed by the dry vegetation and transferred to the atmospheric layer above: t in hours, Fo = 500 W/m2 • How much solar energy [J/m2] is added to the boundary layer (BL) within 24 h? • How high is the temperature rise in the BL (thickness dz=1 km, air density 1kg/m3 und heat capacity cp=1004 J/(K kg)) in the course of the day? • And how high if the BL is only 10 m thick?

  28. 2.3 Energy • Problem 1 • In the tropics sunrise is at 6 LST and sunset at 18 LST. Assuming the netto flux density of solar energy is immediately absorbed by the dry vegetation and transferred to the atmospheric layer above: • t in hours, Fo = 500 W/m2 • How much solar energy [J/m2] is added to the boundary layer (BL) within 24 h? • How high is the temperature rise in the BL (thickness dz=1 km, air density 1kg/m3 und heat capacity cp=1004 J/(K kg)) in the course of the day? • And how high if the BL is only 10 m thick? • 137 K convection leads to a quick expansion of the BL

  29. 2.4 Maxwell-equations Assumptions homogeneous medium: dielectrical properties isotropic & linear free of charge electric displacement [C m-2=As m-2] magnetic induction [Vs m-2 = Tesla] electric field [V m-1] magnetic field [A m-1] electric current [A m-2] density electric charge [C m-3] εo 8.85410-12 F / m permittivity of free space χ electric susceptibility μ magnetic permeability σ conductivity [S m-1]  determine the relationship between E and H of a medium

  30. Plane harmonic wave amplitude phase • k‘ is perpendicular to surfaces of constant phase  propagation direction • k‘‘ is perpendicular to surfaces of constant amplitude •  if both are parallel or k‘‘=0  homogeneous wave non-absorbing medium complex wave vector radial velocity [rad s-1] phase velocity (homogeneous) insert into homogeneous time-dependent Maxwell-Equations

  31. Wave number Homogeneous, time-dependent Maxwell-Equations in a dielectricum propagation direction normal to oscillation N complex refractive index μ relative permeability (~1) ε relative permittivity between 1 and 80 (=dielectric constant) c speed of light in medium

  32. Refractiveindex N In a vacuum k‘‘= 0ε = εo= 8.85410-12 F / m permittivity of free spaceμ = μo = 410-7 Vs / (A m) permeability In a non-vacuum N complex refractive index μ relative permeability (~1) ε relative permittivity between 1 and 80 (=dielectric constant) c speed of light in medium If N is only real (non-absorbing medium) c is the phase speed of the wave … in most media N>1  c<co

  33. Poynting vector • Instantaneous direction and magnitude of the transported energy is given by the Poynting-Vector (John Henry Pointing, 1852-1914) • All three vectors are perpendicular • Average over a complete cycle for a harmonic EM-wave: • The flux density is proportional to |E|2

  34. Absorption • Scalar amplitude of a harmonic wave at location x • Radiation flux density for a plane wave with Foat location x=0 • Energy of wave has reduced to 1/e = 37 % at 1/βa βa absorption coefficient [m-1] N complex refractive index

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