ATMOSPHERIC RADIATION S.K. Satheesh Centre for Atmospheric & Oceanic Sciences

1. ATMOSPHERIC RADIATION S.K. Satheesh Centre for Atmospheric & Oceanic Sciences Indian Institute of Science Bangalore.

2. Part-1: BASIC CONCEPTS Basic introduction to electromagnetic field Dual nature of electromagnetic radiation Electromagnetic spectrum Basic radiometric quantities: energy, intensity, and flux The Lambert-Beer law Concepts of extinction (scattering + absorption) and emission Optical Depth

3. Part-2: BLACKBODY RADIATION Concepts of a blackbody and thermodynamical equilibrium Main Laws Ø Planck function Ø Stefan-Boltzmann law Ø Wien’s displacement law Ø Kirchhoff’s law

4. Part-3: Atmospheric Scattering and Absorption Rayleigh scattering, Mie scattering, Radiatively active species Why sky is blue?Why sunset sky is red? Simple aspects of Radiative Transfer through the atmosphere What happens to short wave radiation incident at the top of the atmosphere? What happens to long wave (terrestrial) radiation? Radiative Balance? RADITION BUDGET

5. Ways to label radiation • By its source • Solar radiation - originating from the Sun • Terrestrial radiation - originating from the Earth • By its proper name • ultra violet, visible, near infrared, infrared, microwave, etc…. • By its wavelength • short wave radiation  4 micrometers • long wave radiation  > 4 micrometers

6. BASIC CONCEPTS Basic introduction to electromagnetic field Dual nature of electromagnetic radiation Electromagnetic spectrum Basic radiometric quantities: energy, intensity, and flux The Lambert-Beer law Concepts of extinction (scattering + absorption) and emission Optical Depth

7. BASIC INTRODUCTION TO ELECTROMAGNETIC FIELD Electromagnetic radiation is a form of energy Electromagnetic radiationis so-named because it has electric and magnetic fields that simultaneously oscillate in planes mutually perpendicular to each other and to the direction of propagation through space Electromagnetic radiation has the dual nature: its exhibits wave properties and particulate properties

8. Wave nature of radiation The electric (E) and magnetic (H) fields oscillate in the x-y plane and perpendicular to the direction of propagation (z-direction) Waves are characterized by wavelength (or frequency) and speed.

9. WAVE NATURE OF RADIATION A schematic of a wave travelling in the z-direction

10. The speed of light in a vacuum: c = 2.9979 x 108 m/s ~ 3.0 x 108 m/s Wavelength is the distance between two consecutive peaks or troughs in a wave (symbolized by ) Frequencyis defined as the number of waves (cycles) per second that pass a given point in space (symbolized by ) Wavenumberis defined as a count of the number of wave crests (or troughs) in a given unit of length Since all types of electromagnetic radiation travel at the speed of light, short-wavelength radiation must have a high frequency Relation between  and :  = c

11. UNITS: Wavelength units: length Angstrom (A) : 1 A = 10 -10 m; Nanometer (nm): 1 nm= 10 -9 m; Micrometer (m): 1 m = 10 -6 m; Frequency units: cycles per second 1/sec (or sec -1) is called hertz (abbreviated Hz) Wavenumber units: inverse length (often in cm -1)

12. PARTICULATE NATURE OF RADIATION Radiation can be also described in terms of particles or packets of energy, called photons The energy of a photon is given by the expression: where h is Plank’s constant (h = 6.6256x10 -34 J s). This equation relates energy of each photon of the radiation to the electromagnetic wave characteristics ( and ). Ephoton = h = h c / 

13. COORDINATE SYSTEMS Both the Cartesian coordinate system and spherical coordinate system are used to characterize the propagation of electromagnetic radiation Cartesian (rectangular) coordinate system: three orthogonal unit vectors x, y, and z. Any vector A can be expressed as Ax x + Ay y + Az z and its magnitude is A= |A| =

14. Spherical coordinate system: distance r, the zenithal () and azimuthal angles (). Spherical and rectangular coordinates are related as x = r sin() cos(); y = r sin() sin(); z = r cos()

15. Solid Angle: is defined as the ratio of the area of a spherical surface intercepted by the cone to the square of the radius UNITS: of a solid angle = steradian (sr) EXAMPLE: Solid angle of a sphere = 4R2 / R2 = 4 R  = A / R2 A

16. The electromagnetic spectrum of the sun

17. Spectrum of the Sun compared with that of the Earth

18. Percent Spectral Distribution of Solar Energy

19. BASIC RADIOMETRIC QUANTITIES Flux (or irradiance)is defined as radiant energy per unit time per unit wavelength (or frequency) range per unit area perpendicular to the given direction: Thus monochromatic flux is the integration of normal component of monochromatic intensity over the all solid angles over the hemisphere. UNIT: J sec-1m-2 m = W m-2 m F = dE / dt dA d

20. Intensity (or radiance)is defined as radiant energy in a given direction per unit time per unit wavelength (or frequency) range per unit solid angle per unit area perpendicular to the given direction: Iis referred to as monochromatic intensity. Note: Monochromatic does not mean at a single wavelengths, but in a very narrow (infinitesimal) range of wavelength  centered at . UNITS: (J sec-1 m-2m-1 sr-1 ) = (W m-2m-1 sr-1 ) I = dE / d dt dA d

21. PROPERTIES OF INTENSITY In general, intensity is a function of the coordinates, direction, wavelength (or frequency), and time. Thus it depends on seven independent variables: three in space, two in angle, one in wavelength (or frequency) and one in time. Intensity, as a function of position and direction, gives a complete description of the electromagnetic field. If intensity does not depend on the direction, the electro- magnetic field is said to be isotropic. If intensity does not depend on position the field is said to be homogeneous.

22. Concept of Extinction (scattering + absorption) and Emission Electromagnetic radiation in the atmosphere interacts with gases, aerosol particles, and cloud particles. Extinction and emission are two main types of the interactions between an electromagnetic radiation field and a medium (e.g., the atmosphere). Radiation is emitted by all bodies that have a temperature above absolute zero (often referred to as thermal emission).

23. General Definition of Extinction & Emission: Extinction is a process that decreases the radiant intensity, while emission increases it. Extinction is due to absorption and scattering. Absorption is a process that removes the radiant energy from an electromagnetic field and transfers it to other forms of energy. Scattering is a process that does not remove energy from the radiation field, but redirect it.

24. More on Extinction: Scattering can be thought of as absorption of radiant energy followed by re-emission back to the electromagnetic field with negligible conversion of energy. Thus, scattering can remove radiant energy of a light beam traveling in one direction, but can be a “source” of radiant energy for the light beams traveling in other directions. The fundamental law of extinction is the Lambert-Beer law.

25. Consider a small volume V of infinitesimal length dscontaining optically active matter. Thus, the change of intensity along a path ds is proportional to the amount of matter in the path. For extinction: For emission: where eis the volume extinction coefficient(LENGTH-1) and J is the source function. dI = -e I ds ds I0 I V dI = -e J ds

26. In the most general case, the source function has emission and scattering contributions. NOTE: Volume extinction coefficient is often referred to as the extinction coefficient. Generally, the volume extinction coefficient is a function of position s. Extinction coeff. = Absorption coeff. + Scattering coeff.

27. Optical Depth Altitude E2 E1 Surface E1, E2, ….. are extinction coefficients at each altitude

28. BLACKBODY RADIATION Concepts of a blackbody and thermodynamical equilibrium Main Laws Ø Planck function Ø Stefan-Boltzmann law Ø Wien’s displacement law Ø Kirchhoff’s law Simple aspects of Radiative Transfer through the atmosphere

29. Concepts of Blackbody A hypothetical body that completely absorbs all wavelengths of radiation incident on it. Such bodies do not reflect light, and therefore appear black if their temperatures are low enough so as not to be self-luminous. All blackbodies heated to a given temperature emit thermal radiation with the same spectrum

30. PROPERTIES OF BLACKBODY RADIATION Radiation emitted by a blackbody is isotropic, homogeneous and unpolarized. Blackbody radiation at a given wavelength depends only on the temperature T. Any two blackbodies at the same temperature emit precisely the same radiation. A blackbody emits more radiation than any other type of an object at the same temperature.

31. RADIATION: Basic Laws Plank’s Law Intensity (or radiance) emitted by a blackbody having a given temperature is given by Plank’s Law.Plank’s Law can be expressed in wavelength domains as, where is the wavelength; h is the Plank’s constant; kBis the Boltzmann’s constant (kB = 1.38 x 10-23 J K -1); cis the velocity of light; and T is the absolute temperature of a blackbody. B(T) = 2hc2 / [5 (ehc/kBT-1)]

33. Stefan-Boltzmann Law The Stefan-Boltzmann law states that the total power (energy per unit time) emitted by a blackbody, per unit surface area of the blackbody, varies as the fourth power of the temperature. where is the Stefan-Boltzmann constant (= 5.671 x 10-8 W m-2 K-4), F is energy flux [W m-2], and T is blackbody temperature [K]. F =  T4

34. Wien’s Displacement Law The Wien’s displacement law states that the wavelength at which the blackbody emission spectrum is most intense varies inversely with the blackbody’s temperature. The constant of proportionality is Wien’s constant (2897 K mm): where  is the wavelength (in micrometers, m) at which the peak emission intensity occurs, and T is the temperature of the blackbody (in degrees Kelvin, K). NOTE: this law is simply derived from, NOTE: The hotter the object the shorter the wavelength of the maximum intensity emitted. max = 2897 / T B /  = 0

35. Wien’s Displacement Law

36. Kirchhoff’s Law The Kirchhoff’s law states that the emissivity, , of a medium is equal to the absorptivity, A, of this medium under thermo- dynamic equilibrium: where is defined as the ratio of the emitting intensity to the Planck function; A is defined as the ratio of the absorbed intensity to the Planck function. For a blackbody: For a non-blackbody: For a gray body:  =A  = A = 1   A < 1  = A < 1

37. Kirchoff’s Law Day • Objects that are good absorbers are also good emitters • Consider a land surface • During the day the land absorbs solar radiation and warms • At night the land emits infrared radiation and cools relative to its surroundings Warm Land (warms due to solar radiation) Night Cool Land (cools by IR radiation)

38. Emissivity of Surfaces In general, emissivity depends on the surface temperature, wavelength and some physical properties of the surface (e.g., the refractive index). In thermal IR ( > 4 m) , nearly all surfaces are efficient emitters with the emissivity > 0.8. Emissivity of some surfaces in the IR region from 10 to 12 m Water 0.993-0.998 Ice 0.98 Green grass 0.975 - 0.986 Sand 0.949 - 0.962 Granite 0.898

39. Reflection: The Albedo of Various Surfaces • Albedo: the ratio of reflected radiation to incident radiation • Surface albedo varies • Spatially • Temporally

41. Basic Properties of Radiatively Active Species (gases, aerosols, and clouds) Atmosphere is composed of: Ø Gases Ø Aerosols Ø Cloud droplets. Atmospheric Gases Constant gases: Nitrogen, Oxygen, Argon, Neon, Helium, Krypton, Xenon etc. Variable gases: Water vapor, Carbon dioxide, Methane, Hydrogen, Nitrous oxide, Carbon monoxide, Ozone.

42. Atmospheric Aerosols Atmospheric aerosols (or particulate matter) are solid or liquid particles or both suspended in air with diameters between about 0.002 mm to about 100 mm. Aerosol particles vary greatly in sources, production mechanisms, sizes, chemical composition, amount, distribution in space and time, and how long they survive in the atmosphere (i.e. lifetime). Primary atmospheric aerosols are particulates that emitted directly into the atmosphere (for instance, sea-salt, mineral aerosols (or dust), volcanic dust, smoke and black carbon, etc). Secondary atmospheric aerosols are particulates that formed in the atmosphere by gas-to-particles conversion processes (for instance, sulfates, nitrates, some organics).

43. Cloud Droplets Major characteristics are: cloud type; cloud coverage; cloud droplet concentration; cloud droplet size. Cloud droplet sizes vary from a few micrometers to hundreds of micrometers. Cloud droplet concentration varies from about 10 cm-3 to 1000 cm-3 with average droplet concentration of a few hundred cm-3 . The liquid water content of typical clouds, often abbreviated LWC, varies from approximately 0.05 to 3 g (water) m-3 , with most of the observed values in the 0.1 to 0.3 g (water) m-3. NOTE: Clouds cover approximately 50% of the Earth’s surface. Average global coverage over the oceans is about 65% and over the land is about 52%.

44. Atmospheric Scattering

45. ATMOSPHERIC SCATTERING Any type of elecromagnetic wave propagating through the atmosphere is affected by the air molecules and aerosols because of their interaction with radiation namely (i) scattering (ii) absorption and (iii) emission. Scattering occurs at all wavelengths (spectrally not selective) in the electromagnetic spectrum. Any material whose refractive index is different from that of the surrounding medium (optically inhomogeneous) scatter radiation.

46. More on Scattering: Rayleigh and Mie Scattering The amount of scattered energy depends strongly on the ratio of particle size to wavelength of the incident wave. When scatterers are very small compared to the wavelength of incident radiation (r < /10), the scattered intensity on both forward and backward directions are equal. This type of scattering is called Rayleigh scattering. For larger particles (r > ), the angular distribution of scattered intensity becomes more complex with more energy scattered in the forward direction. This type of scattering is called Mie scattering.

47. R <<  R   R >> 

48. Single Scattering  =2R/ What happens in the red box? More scattering a is like size of particle/l of light Bigger particles compared to l This graph shows the amount of scattering as a function of the relative size of the scatterers to the wavelength of light

49. Elastic Scattering, Multiple Scattering: In Rayleigh and Mie scattering, both the scattered and incident radiation have the same wavelength and hence this two scattering process are called Elastic Scattering. In the real atmosphere the particles and air molecules are randomly distributed and are separated by distances large compared to their sizes. So each particle scatter independently and there will not be any interference between the separately scattered waves. This is called Independent Scattering. In the actual case of scattering in the atmosphere there are chances that the scattered radiation from one particle may have scattered again by other particles. This is called Multiple Scattering. Multiple scattering influences are more in turbid or polluted atmospheres.

50. Difference Between Scattering and Absorption Both scattering and absorption remove flux from an incident wave. During scattering process flux is not lost from the incident beam but is redistributed over the total solid angle centered around the scatterer and it does not change the internal energy states of the molecules. Absorption changes the internal energy states of the molecules. Absorption is spectrally selective, scattering is not. Scattering depends on the ratio of particle size to wavelength of light.