chapter 3: Radiative transfer Flashcards
Define remote sensing
- The science of acquiring information about the earth’s surface without actually being in contact with it
How is remote sensing done?
- Sensing and recording reflected and emitted energy and
- Processing
- Analyzing
- Applying that information
Information received from remote sensing comes in the form of
- Electromagnetic radiation
Electromagnetic radiation consist of:
- Alternating
- Electric field and
- Magnetic field
- The electric field vector is perpendicular to the magnetic field vector
- The direction of propagation is perpendicular to both
Radiation is often specified by:
- Its wavelength
- It is the distance between crests of the electric or magnetic field
Alternate way to describe radiation
- Give its frequency
- It is the rate at which the electric or magnetic field oscillates when observed at a point
What is the unit of frequency?
- Hz or
- One cycle per second
Give the equation of finding the frequency
- V=c/lamda
- C is the speed with which electromagnetic radiation travels and is known as the speed of light
- In vacume c is 299,792 km s-1
- In the atmosphere c is slower 299,703 km s-1 due to interaction with air molecules
Radiation is specified by
- Wavenumber k
- The recoprical of the wavelength
- Inversely proportional to wavelength
- Directly proportional to frequency
Property of electromagnetic radiation:
- Can transport energy
- Many of the units used to quantify EM radiation are based on energy
Unit of radiant energy
- Joule
Radiant flux
- Radiant energy per unit time
Radiant flux unit:
- Watts
- Joules per second
Radiant flux depend on
- Area
- It is usually normalized by surface area
Define radiant flux density
- Radiant flux crossing a unit area
Radiant flux density unit:
- Watts per square meter
Why is radiant flux density subdivided?
- To indicate which way the energy is traveling
Radiant flux density is subdivided to
- Irradiance (E)
- Radiant flux density incident on an area
- Radiant exitance
- Radiant flux density emerging from an area
In nature radiation is a function of
- Direction
- The direction dependence is taken into account by employing the solid angle
Solid angle:
- If one draws lines from the center of the unit sphere to every point on the surface of an object, the area of the projection on the unit sphere is the solid angle
Unit of solid angle:
- Steradians (sr)
Equation of solid angle:
- Ω = A/r2
- Object with cross sectional area
- A << r2
- R is the radius of the sphere
In a sphere of one foot radius a steradian would correspond to a solid angle that
- Subtended an area of one square foot on the surface of the sphere. Since the total area of a sphere is 2pi r2 there are 4 pi steradians in a sphere
Define radiance
- Radiant flux density per unit solid angle leaving (or incident on) the surface perpendicular to the beam
Radiance represents
- The radiation leaving (or incident on) an area perpendicular to the beam,
- For other directions, we must
- Weight the radiance by cos ©(where © is the zenith angle, i.e., the angle measured from the normal to the surface).
Radiance (in certain wavelength) can be expressed as:
Monochromatic radiance (L)
- The most fundamental radiation unit for satellite meteorology
- The energy per unit time per unit wavelength per unit solid angle crossing a unit area perpendicular to the beam.
Radiance has the useful property that it is
- Independent of distance from an object as long as the viewing angle and the amount of intervening matter are not changed.
Consider a satellite viewing a small object. The irradiance reaching the satellite from the object will
- Will decrease inversely as the square of the distance of the satellite.
- The solid angle of the object subtended at the satellite will also decrease inversely as the square of the distance of the satellite
The radiance of the object as viewed by the satellite
- Which is simply the irradiance divided by the solid angle, is, therefore, independent of distance.
The radiance of an object measured at the Earth’s surface would ………………………….at the satellite, due to
- Be different from that measured
- To the intervening atmosphere
All matter with a temperature greater than absolute zero (0 Kelvin) emits
- Thermal radiation.
For a given material, the amount of radiation emitted depends upon
- Wavelength of the radiation and
- The temperature of the material.
Different materials at the same temperature emit
- Different amounts of radiation.
Blackbody
- Called a perfect radiator
- A material which emits the maximum possible radiance at a given temperature is
- Black body cannot exist
Black body radiation mainly depends on
- Temperature and
- Wavelength
As the temperature increases,
- The amount of energy emitted at any wavelength increases (Stefan Boltzmann’s law)
- The wavelength of maximum emission decreases (Wien’s displacement law)
The characteristic temperatures of the Sun and of the Earth lie at around
- 6000 K
- And 300 K respectively.
The solar radiation peaks at around
- 0.5 microns (i.e., in the visible region of the EM spectrum)
Radiation emitted from the Earth peaks at
- 10 microns
Wavelengths most frequently observed by remote sensing satellites
- 0.5 and 10 microns
The radiance being emitted by a blackbody is given by
- The Planck’s function
Planck’s constant
- 6.6261x10‐34 J.s
Boltzmann’s constant
- 1.3801x10‐23 JK‐1
C1 =
- 3.74 x 10-16 W/m2
C2 =
- 1.44 x 10-2 mk
What do c1 and c2 stand for
- First and second radiation constants
Brightness temperature:
- If radiance in a narrow wavelength band is measured, the Planck function can be used to calculate the temperature of the black body that emitted it.
- For most purposes the radiance measured by the satellite sensor are converted to this quantity.
Since real material is not perfectly black, its radiation is quantified using
- Black body radiation
Emittance is a function of
- Temperature
- Viewing geometry
- Wavelength
For a blackbody € is
- Identically one
The incident radiation undergoes
- Absorption,
- Reflection and
- Transmission.
- These three processes are the only possibilities for the incident radiation. Therefore, by energy conservation, each quantity must be between 0 and 1, a+p+t =1
Radiative transfer
- Describes the processes which affect a radiation beam as it travels through a continuous medium.
Radiative transfer effect
- All types of electromagnetic radiation and
- all media
The precise effect of radiative transfer processes
Vary depending on
- the nature of the radiation and
- the medium.
Radiative transfer relevant to almost all remote sensing application
- Within the atmosphere
For a radiation travelling along a specified path through the medium, there are a number of possible outcomes:
- It can be transmitted through the medium
- It can be scattered by particles in the medium
- It can be absorbed by the medium
Extinction Processes (explanation)
- Consider the radiation stream along a specified direction through a slab of medium of a particular thickness
- We can define the radiation (in a specific wavelength) entering the slab along the chosen path as L and that leaving the slab as L + dl .Thus the change due to the various processes occurring within the slab is dl
Radiation entering the slab may be
- Absorbed,
- Scattered or
- Transmitted.
Definition of extinction process
- The radiation entering the slab may be absorbed, scattered or transmitted. The first two cases will cause a reduction in the radiation stream along the path.
- In the third case (transmission), the radiation stream is unaffected
- Dl will always be negative
Augmentation processes
- Add radiation to the stream
Augmentation processes (explanation)
- Firstly, the material in the slab will be emitting thermal radiation according to its temperature and emission spectrum. As thermal emission occurs in all directions, some of it will be added to the path being considered.
- Secondly, some of the radiation travelling in other directions through the slab will be scattered into the path
The terms in the radiative transfer equation are determined by a number of factors
- The nature of the medium, which will determine its absorption, emission and scattering properties
- The temperature of the medium
- The distribution of wavelengths in the incident radiation
Radiative Transfer Equation
Absorbtion
- Beer’s Law states that The rate of decrease in the intensity of radiation as it passes through a medium is proportional to the intensity of the radiation.
Volume absorption coefficient units
- Same as volume scattering coefficient
- M-1
Radiative Transfer Equation
emision
- By Kirchhoff’s law, we can state that the material in the medium will Emit radiation with the same efficiency as it absorbs. In other words, at a given wavelength: emissivity = absorptivity
The radiative transfer properties of a material are dependent upon its
- Temperature
Radiative Transfer Equation
scattering out of the radiation path
- Beer’s law applies to Extinction via scattering
Radiative Transfer Equation
Scattering into the Radiation Path
- The final term in the radiative transfer equation is made up of photons which have been scattered from their original path into the stream under consideration.
- This will be a complicated function, as radiation travelling in any direction through the medium may be scattered and so all directions must be accounted for
Radiative transfer is dependent on
- Wavelength
- Temperature
- Scattering
- Absorption properties of the medium
Radiometers
- Found in weather satellites
- Passively measure upwelling electromagnetic radiation from the Earth and atmosphere.
Infrared (IR, long‐wave)and microwave radiation are emitted by
- Earth
- Atmosphere
- Clouds
Visible light (short‐wave or solar radiation)
- Emitted by the sun and reflected and absorbed by the Earth system.
What the satellite can “see” in any one wavelength depends on
- The transparency of the air at that wavelength
A perfectly transparent atmosphere allows
- The upwelling radiation from the Earth’s surface or highest cloud top to reach the satellite.
- Wavelengths for which the air is transparent are good for observing clouds and land use.
If air molecules strongly absorb upwelling radiation at another wavelength, then
- None of the signal at that wavelength from the Earth and clouds will reach the satellite (i.e., an opaque atmosphere).
According to Kirchhoff’s law, ……………….. Equal ……………………….
- Absorptivity equals the emissivity at that wavelength. This atmosphere will emit its own spectrum of radiation according to Planck’s law.
- Wavelengths with this characteristic are good for observing the top of the atmosphere, but are not suitable for remote sensing of the Earth and clouds.
Transmittance
- of the electromagnetic energy that is upwelling through any height, the percentage of it that comes out the top of the atmosphere.
- Transmittance varies with wavelength.
Windows
- Portions of the spectrum where transmittances are large
Shoulder regions
- Wavelengths near the window
- Transmittance rapidly changes
Dirty windows
- Portions of the spectrum having partial transmittance
Transmittance at different wavelengths (0 – 6 um)
- Transmittance curves are not constant
- Can change slightly with atmospheric conditions
- Windows are regions with transmittance of about 80% or higher
Absorption lines
- Different gases in the atmosphere have different molecular vibration and rotation modes, causing them to absorb at discrete wavelengths
Absorption bands
- (i.e., non‐window regions) shift wavelength very slightly with temperature and pressure.
The amount of absorption and transmission depend strongly on
- The concentration of absorbing gas along the path length of the radiation.
Water vapor is a major
- Absorber, so
- More humid conditions and deeper moist layers cause greater absorption.
- Transmittance is weakest in the tropics (high humidity and deep troposphere) and
- Strongest near the poles (low absolute humidity and shallow troposphere)
- At mid latitudes, transmittance is
- Greatest in winter (low humidity, shallow troposphere) and
- Weakest in summer (higher humidity and deeper troposphere).
- More humid conditions and deeper moist layers cause greater absorption.
The Radiative Transfer Equation (RTE)
- Deals with the change in radiance, as the radiation passes through the atmosphere.
The radiance received at the satellite would consist of:
- The radiation emitted at the earth’s surface
- The radiation emitted by the intervening atmosphere and
- The atmospheric emission, which is reflected back by the earth’s surface
Molecular scattering can be neglected in
- IR and
- MW regions
- The third contribution i.e., the radiation emitted downwards by the atmosphere and reflected back in the direction of the satellite neglected by assuming that the earth’s surface is black
Transmission (τ) is a function of
- Temperature and
- The mixing ratio of the absorbing gas.
For well‐mixed gases such as ……………………….. We assume that
- O2 and CO2
- The mixing ratio is known and independent of height
- Wavelengths that are sensitive to these gases are used to retrieve the atmospheric temperature
Weighting function
- Weights the Planck’s function in the atmospheric component of the emitted radiation
Weighting function at a given wavelength represents
- Contributions from various atmospheric layers to the radiance reaching the top of the atmosphere.
Weighting function at a given wavelength specifies / determines
- The layer from which the radiation emitted to space originates
- The region of the atmosphere, which can be sensed from space at this wavelength.
Since the transmission of atmospheric gases varies with wavelength …………………… varies
- The altitude of the peak of the weighting function
In the spectral regions of high absorption ( …………) , the weighting function
- (absorption bands)
- Peaks high in the atmosphere and thus most of the radiation observed is emitted from high levels.
In spectral regions of low absorption (…………………), the weighting function
- (windows)
- Peak at low altitudes and thus most of the radiation comes from deep levels.
Retrieval of temperature profile
- Using radiation at different frequencies for which the absorption strength is different
- we can build a family of weighting function, which provide information on the mean temperature of many such layers
- leading to the idea that we might be able to RETRIEVE information on the atmospheric temperature profile from a set of multi‐frequency measurements.
