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)
REVIEW
• 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
• 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 an
overhead projection
a
b
milk
Absorption, Scattering
ink
Radiative extinction using an overhead projection
a
Milk –scattering
Ink-absportion
b
milk
ink
Radiative extinction using an overhead projection
a
Iλ(x) = Iλ,0 exp (-βex)
b
milk
ink
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
Beer’s Law
Fig. 7.3
Extinction Over a Finite Path
Optical path
Optical depth
Optical thickness
Fig. 7.3
Extinction Over a Finite Path
Fig. 7.3
transmattance
Extinction Over a Finite Path
Fig. 7.3
Extinction Over a Finite Path
Fig. 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
• - Definition
Fig. 7.4
Plane Parallel Approximation
- Definition
Fig. 7.4
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 Atmosphere
CO2, 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
1
λ4
Fig. 7.8
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
Why?
Fig. 9
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