lecture 8: atmosphere transmission petty chapter 7
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Lecture 8: Atmosphere Transmission
Petty Chapter 7
Atmospheric Transmission
• EM wave propagating through a homogeneous medium whose index of refraction N included a nonzero imaginary part.– ñ = n-ik
Here, the real part of the refractive index n indicates the phase speed (snell’s law), while the imaginary part κ indicates the amount of absorption loss when the electromagnetic wave propagates through the material.
• Intensity I falls off exponentially with distance:Iλ(x) = Iλ,0 exp (-βax)
where βa is an absorption coefficient that depend on the physical medium and wavelength.
• n= sin i / sin r. (i: incident angle, r: the angle of refraction)
• Refractive index is also equal to the velocity c of light of a given wavelength in empty space divided by its velocity v in a substance, or n = c/v.
REVIEW
Review
• refractive indexdepend strongly upon the frequency of light. Standard refractive index measurements are taken at yellow doublet sodium D line, with a wavelength of 589 nanometres.
• There are also weaker dependencies on temperature, pressure/stress,
• In general, an index of refraction is a complex number with both a real and imaginary part, where the latter indicates the strength of absorption loss at a particular wavelength—thus, the imaginary part is sometimes called the extinction coefficient k. Such losses become particularly significant, for example, in metals at short (e.g. visible) wavelengths, and must be included in any description of the refractive index.
Review
• Some typical refractive indices for yellow light (wavelength equal to 589 nanometres [10-9 metre]) are the following: air, 1.0002; water, 1.333
• The refractive index of X-rays is slightly less than 1.0, which means that an X-ray entering a piece of glass from air will be bent away from the normal, unlike a ray of light, which will be bent toward the normal.
Snell’s Law Review
• Ni * Sin(Ai) = Nr * Sin(Ar), • where:
Ni is the refractive index of the medium the light is leaving,Ai is the incident angle between the light ray and the normal to the meduim to medium interface,Nr is the refractive index of the medium the light is entering,Ar is the refractive angle between the light ray and the normal to the meduim to medium interface.
Apply to atmosphere
Fig. 7.1
Apply to atmosphere
Interpretation of physical meaning of (7.1)
Apply to atmosphere
Radiative extinction using anoverhead projection
a b
milkink
Absorption, Scattering
Radiative extinction using an overhead projection
a bmilk ink
Milk –scatteringInk-absportion
Radiative extinction using an overhead projection
a bmilk inkIλ(x) = Iλ,0 exp (-βex)
Extinction, Scattering and Absorption Coefficients
Extinction, Scattering and Absorption Coefficients
Single scattering albedo
Extinction Over a Finite Path
Fig. 7.3
Extinction Over a Finite Path Fig. 7.3
Beer’s Law
Extinction Over a Finite Path Fig. 7.3
Optical pathOptical depthOptical thickness
What is the dimension of Tao What is the range of Tao
Extinction Over a Finite Path Fig. 7.3
transmattance
Extinction Over a Finite PathFig. 7.3
Extinction Over a Finite PathFig. 7.3
Answer:
Ans (cont.)
Mass Extinction Coefficient
Mass Extinction Coefficient
Answer:
Mass Extinction Coefficient
Mass Extinction Coefficient
Mass Extinction Coefficient
Extinction Cross-Section
What is unit for δe?
Extinction Cross-Section
? 7.24
Generalization to Scattering and Absorption
Single scattering albedo
Generalization to Arbitrary Mixtures of Components
Plane Parallel Approximation
Fig. 7.4
Clouds?
Plane Parallel Approximation
Fig. 7.4
Clouds?
Plane Parallel Approximation
Fig. 7.4
• - Definition
Plane Parallel Approximation
Fig. 7.4
- Definition
Answer:
Optical Depth as Vertical Coordinate
Optical Depth as Vertical Coordinate
Application to Meteorology, Climatology and Remote Sensing
- The Transmission Spectrum of the Atmosphere
Application to Meteorology, Climatology and Remote Sensing
- The Transmission Spectrum of the AtmosphereCO2, Mauna Loa Observatory, Hawaii
The “Keeling curve,” a long-term record of atmospheric CO2 concentration measured at the Mauna Loa Observatory (Keeling et al.). Although the annual oscillations represent natural, seasonal variations, the long-term increase means that concentrations are higher than they have been in 400,000 years.
Application to Meteorology, Climatology and Remote Sensing
- The Transmission Spectrum of the Atmosphere
• Fig. 7.6
Fig. 7.7
Scattering by Clear Air
Fig. 7.8
1
λ4
Extinction and Scattering by Aerosols and Clouds
Extinction and Scattering by Aerosols and Clouds
Extinction and Scattering by Aerosols and Clouds
Measuring Solar Intensity from the Ground
Fig. 9
Why?
Transmittance in an Exponential Atmosphere
Transmittance in an Exponential Atmosphere_
Transmittance in an Exponential Atmosphere
Transmittance in an Exponential Atmosphere
Fig. 7.10
Transmittance in an Exponential Atmosphere
Fig. 7.10
Transmittance in an Exponential Atmosphere
Transmittance in an Exponential Atmosphere
Optical thickness and Transmittance of a Cloud Layer
Optical thickness and Transmittance of a Cloud Layer
Optical thickness and Transmittance of a Cloud Layer
Optical thickness and Transmittance of a Cloud Layer
Monodisperse Cloud
Fig. 7.11
Optical thickness and Transmittance of a Cloud Layer
Monodisperse Cloud
Optical thickness and Transmittance of a Cloud Layer
Monodisperse Cloud
Optical thickness and Transmittance of a Cloud Layer
Monodisperse Cloud
Optical thickness and Transmittance of a Cloud Layer
Monodisperse Cloud
Optical thickness and Transmittance of a Cloud Layer
Cloud Condensation Nuclei and Cloud Optical Depth
Optical thickness and Transmittance of a Cloud Layer
Cloud Condensation Nuclei and Cloud Optical Depth
Optical thickness and Transmittance of a Cloud Layer
Cloud Condensation Nuclei and Cloud Optical Depth
Optical thickness and Transmittance of a Cloud Layer
Cloud Condensation Nuclei and Cloud Optical Depth
Optical thickness and Transmittance of a Cloud Layer
• Polydisperse Cloud
Polydisperse Cloud