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