1. REMOTE SENSING EM Radiation Interactions with the Atmosphere
Professor Ke-Sheng Cheng
Department of Bioenvironmental Systems Engineering
National Taiwan University

2. Propagation of EM radiation in the atmosphere
Once the electromagnetic radiation emitted by the Sun enters into and propagates through the Earth’s atmosphere, the atmosphere may affect its properties including the speed and direction of propagation, the wavelength, the intensity, and the spectral distribution.
5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

3. These effects arise due to absorption, refraction, and scattering by the atmosphere.
Most remote sensing image analysts are not concerned about refraction, and thus we will focus our discussion on details of absorption and scattering by the atmosphere.
5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

4. Absorption
Absorption is the process by which radiant energy is absorbed and converted into other forms of energy. An absorption band is a range of wavelengths (or frequencies) in the electromagnetic spectrum within which radiant energy is absorbed by substances such as water (H2O), carbon dioxide (CO2), oxygen (O2), ozone (O3), and nitrous oxide (N2O).
Ozone, carbon dioxide, and water vapor are the three main atmospheric constituents which absorb radiation.
5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

5. Ozone serves to absorb the harmful (to most living things) ultraviolet radiation from the sun. Without this protective layer in the atmosphere our skin would burn when exposed to sunlight.
Carbon dioxide is referred to as a greenhouse gas. This is because it tends to absorb radiation strongly in the far infrared portion of the spectrum - that area associated with thermal heating - which serves to trap this heat inside the atmosphere.
5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

6. Water vapor in the atmosphere absorbs much of the incoming longwave infrared and shortwave microwave radiation (between 22 m and 1mm ). The presence of water vapor in the lower atmosphere varies greatly from location to location and at different times of the year. For example, the air mass above a desert would have very little water vapor to absorb energy, while the tropics would have high concentrations of water vapor (i.e. high humidity).
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

7. Absorption is limited to radiation in certain wavelength regions only
Absorption is limited to radiation in certain wavelength regions only. The wavelength ranges in which the atmosphere is particularly transmissive of energy are referred to as atmospheric windows.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

8. Atmospheric Windows 5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

9. Note also that heat energy emitted by the Earth corresponds to a window around 10 m in the thermal IR portion of the spectrum, while the large window at wavelengths beyond 1 mm is associated with the microwave region.
5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

10. Absorption of the Sun's Incident Electromagnetic Energy in the
Region from 0.1 to 30 m by Various Atmospheric Gases
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

11. 5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

12. Major Atmospheric Windows
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

13. Atmospheric absorption
Absorption is the process by which radiant energy is absorbed and converted into other forms of energy. When propagating through the earth atmosphere, photons of solar radiation may be absorbed by constituent molecules in the atmosphere.
The molecular absorption involves three major mechanisms including electron orbital transition, molecular vibration, and molecular rotation.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

14. The energy required for electron orbit transitions typically corresponds to energy carried by photons of shortest wavelength radiation in the ultraviolet and visible regions of the electromagnetic spectrum.
Energy change due to molecule vibration motion is associated with absorption in the near and middle infrared wavelength regions.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

15. Energy change due to molecular rotation motion is associated with absorption in the thermal infrared and microwave wavelength regions.
Since a molecule possesses energy at certain energy levels, it can only absorb energy of certain incremental amount. Thus, we expect atmospheric absorption to occur in selective discrete wavelengths associated with those photons having exact energy needed to induce an allowable energy transition.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

16. In fact, a few factors including the Heisenberg uncertainty principle, the Doppler broadening effect, and the pressure (or collision) broadening effect contribute to the broadening of these discrete absorption lines.
The broadening effects result in spectral absorption bands in the electromagnetic spectrum.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

17. Many near-by and overlapped absorption bands can form a continuous wavelength range in which radiant energy is significantly absorbed by various atmospheric constituents. Table 1.3 lists the main absorption lines of the earth’s atmosphere.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

18. Table 1.3 Principal molecular absorption lines of the earth’s atmosphere.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

19. Propagation of electromagnetic radiation in the atmosphere can be conceived of as a beam of photons bombarding a volumetric sample of atmospheric particles.
Most of the incoming photons pass through the volume without colliding with atmospheric particles, while a few photons do collide with and are absorbed by particles in the volume.
5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

20. Modeling the atmospheric absorption - Absorption cross section
The absorption cross section is a measure for the probability of an absorption process. In other words, absorption cross section indicates the ability of an atmospheric molecule to absorb a photon of a particular wavelength.
5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

21. It is expressed as a fraction of the geometric cross section Cg that absorption by the molecule takes place, i.e.,
where  is a wavelength-dependent efficient factor that is proportional to the molecule’s ability to absorb incoming photons.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

22. A beam of photons of a particular wavelength  coming into contact with a set of m molecules of radius r in a volumetric element of cross section area dA and length dx. A fraction of these photons are absorbed by these molecules.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

23. Let N(x) and N(x+dx) respectively represent the number of photons of the same wavelength  entering and leaving the volumetric element per unit of time. The number of photons absorbed by molecules in the volumetric element per unit of time is thus expressed as
5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

24. The amount of m/(dAdx) in the above equation represents the number of molecules per unit volume, i.e. the number density  of molecules. Thus,
is termed the volumetric absorption coefficient . It is worthy to note that, although the absorption cross section C has a unit of area, it does not refer to an actual area size.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

25. The effect of atmospheric absorption can also be expressed in terms of the radiant flux absorbed by the volumetric element per unit of time, i.e.,
5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

26. 5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

27. 5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

28. Layered atmosphere
Consider the atmosphere as having N homogeneous layers.
Fig A stratified atmosphere with N homogeneous layers.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

29. Considering all constituents present in the atmosphere, the optical depth of the i-th layer is calculated by
where n is the number of different constituents in that layer of the atmosphere.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

30. Transmittance of the whole atmosphere with respect to irradiance of wavelength  is given by
where and respectively represent the transmittance of the i-th homogeneous layer and the absorption optical depth of the atmosphere as a whole.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

31. If the irradiance has an incident angle , then the optical depth of the entire atmosphere due to absorption becomes
5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

32. Table 1.4 Spectral regions commonly used in earth remote sensing.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

33. Atmospheric scattering
Atmospheric particles: gas molecules, dust, smoke, pollen, cloud droplets, raindrops, etc.
These particles vary in their geometric shapes and sizes.
When propagating through the atmosphere, solar radiation may be unpredictably redirected (scattered) into various directions by these atmospheric particles.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

34. Major types of atmospheric scattering
Rayleigh scattering
Mie scattering
Non-selective scattering
The size of atmospheric particles relative to wavelength of incident radiation affects the occurrence of different scattering types.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

35. The degree of scattering effect depends on several factors
the wavelength of radiant energy,
the abundance of particles or gases, and
the distance the radiant flux travels through the atmosphere.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

36. Table 1.5 Types of atmospheric particles and their associated scattering regimes with respect to visible, thermal infrared and microwave radiation.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

37. Since the type of scattering that may occur is dependent on the size of atmospheric particles relative to the wavelength of incident radiation, a size parameter  is defined as
where r is the radius of an atmospheric particle and  is the wavelength of the incident radiation.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

38. Fig. 1. 12 Scattering regimes classified by the size parameter
Fig Scattering regimes classified by the size parameter. VIS: visible, NIR: near infrared, TIR: thermal infrared, MW: microwave.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

39. Rayleigh scattering
Rayleigh scattering occurs when the diameter of atmospheric particles (usually gas molecules such as oxygen and nitrogen) are much smaller than the wavelength of the incident EM radiation.
Similar to the absorption coefficient in the atmospheric absorption process, scattering coefficient of the atmospheric scattering can also be defined.
5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

40. The fractional amount of energy of spectral wavelength  scattered into a direction defined by  and  per unit solid angle per unit length is defined as the Rayleigh angular scattering coefficient and can be written as
where is the wavelength-dependent index of refraction of the atmosphere and m is the number of gas molecules per unit volume. It is noteworthy that Rayleigh angular scattering coefficient does not depend on .
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

41. Fig. 1.13 Radiation scattered into a direction defined by  and .
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

42. The total fractional amount of energy scattered by gas molecules per unit length can thus be calculated by integrating over all angular directions, i.e.
5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

43. The amount of scattered energy by Rayleigh scattering is inversely proportional to the fourth power of wavelength of radiation.
Rayleigh scattering causes shorter wavelengths of radiation to be scattered much more than longer wavelengths.
The blue sky and red sunset are typical examples of Rayleigh scattering.
Rayleigh scattering is the dominant scattering mechanism in the upper atmosphere.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

44. The effect of Rayleigh scattering varies with the angle .
The maximum amount of energy is scattered into the incident ray direction.
A phase function p() defined by
is used to characterize such angular variation of the Rayleigh scattering.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

45. The term in the above equation represents the average scattered fraction of incident radiation per unit solid angle per unit length.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

46. Fig Phase function of the Rayleigh angular scattering coefficient. (Particle radius r=0.5nm, incident radiation wave length  = 0.45m (blue), 0.55m (green), 0.65m (red), unpolarized). The amount of scattered radiation is linearly proportional to the distance from the center.
Energy scattered into the direction perpendicular to the incident radiation is the lowest and equals half of the energy scattered into the incident direction.
5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

47. Mie scattering
Mie scattering occurs when the size of atmospheric particles such as smoke, haze, pollen and dust is about the same order as the wavelength of incident radiation. Mie scattering occurs mostly in the lower portions of the atmosphere where larger particles are more abundant, and dominates when cloud conditions are overcast.
5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

48. 5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

49. Fig. 1. 15 Phase function of the Mie angular scattering coefficient
Fig Phase function of the Mie angular scattering coefficient. (Particle radius r=0.5m, incident radiation wave length  = 0.45m (blue), 0.55m (green), 0.65m (red), unpolarized). The amount of scattered radiation is linearly proportional to the distance from the center.
5/8/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

50. Non-selective scattering
Nonselective scattering occurs when the particles are large compared to the wavelength of solar radiation. The effect of nonselective scattering is approximately the same in all scattering directions and is almost independent of wavelength. This is why fog and clouds appear white.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

51. Geometric scattering
Geometric scattering occurs when the size of atmospheric particles is much larger than the wavelength of radiation. For geometric scattering, ray tracing techniques can be applied to describe the reflection and refraction of solar radiation by these particles.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

52. Similar to the Rayleigh scattering, we can also define angular scattering coefficient for the Mie scattering and nonselective scattering.
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

53. Estimating the exoatmospheric irradiance by Langley plot
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

54. Langley Plot
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.