Spectral signatures, VNIR/SWIR, MWIR/LWIR
Radiation models

Jin: We failed to show this one on class, you can access it from the link above

Much of the previous discussion centered around the selection of the specific spectral bands for a given theme

In the solar reflective part of the spectrum (350-2500 nm), the shape of the spectral reflectance of a material of interest drives the band selection

Recall the spectral reflectance of vegetation

Select bands based on an absorbing or reflecting feature in the material

In the TIR it will be the emissivity that is studied

The key will be that different materials have different spectral reflectances

As an example, consider the spectral reflectance curves of three different materials shown in the graph

These divisions are not precise and can vary depending on the publication
1) Visible-Near IR (0.4 - 2.5);
2) Mid-IR (3 - 5);
3) Thermal IR (8 - 14);
4) Microwave (1 - 30 centimeters)
VNIR - visible and near-infrared ~0.4 and 1.4 micrometer (µm)
Near-infrared (NIR, IR-A DIN ): 0.75-1.4
µm in wavelength, defined by the water absorption
Short-wavelength infrared (SWIR , IR-B DIN): 1.4-3 µm, water absorption increases significantly at 1,450 nm.
The 1,530 to 1,560 nm range is the dominant spectral region for long-distance telecommunications.
Mid-wavelength infrared (MWIR , IR-C DIN) also called intermediate infrared (IIR): 3-8 µm
Long-wavelength infrared (LWIR , IR-C DIN): 8–15 µm
Far infrared (FIR): 15-1,000 µm

Spectral signature is the idea that a given material has a spectral reflectance/emissivity which distinguishes it from other materials
 Spectral reflectance is the efficiency by which a material reflects energy as a function of wavelength
 The success of our differentiation depends heavily on the sensor we use and the materials we are distinguishing
 Unfortunately, the problem is not as simple as it may appear since other factors beside the sensor play a role, such as
• Solar angle
• View angle
• Surface wetness
• Background and surrounding material
 Also have to deal with the fact that often the energy measured by the sensor will be from a mixture of many different materials
 This discussion will focus on the solar reflective for the time being

Minerals and rocks can have distinctive spectral shapes based on their chemical makeup and water content
 For example, chemically bound water can cause a similar feature to show up in several diverse sample types
 However, the specific spectral location of the features and their shape depends on the actual sample 1

Samples shown here are for a variety of vegetation types
 All samples are of the leaves only
 That is, no effects due to the branches and stems is included

Note that many of the themes for Landsat TM were based on the spectral reflectance of vegetation
 Show a typical vegetation spectra KNOW THIS CURVE
 Also show the spectral bands of TM in the VNIR and SWIR as well as some of the basic physical process in each part of the spectrum

Recall the graph presented earlier showing the transmittance of the atmosphere

Can see that there are absorption features in the atmosphere that could be used for atmospheric remote sensing

Also clues us in to portions of the spectrum to avoid so that the ground is visible

Have to keep in mind that a spectral signature is not always enough
 Signature of a water absorption feature in vegetation may not indicate the desired parameter
 Vegetation stress and health

Vegetation amount
 Signatures are typically derived in the laboratory

Field measurements can verify the laboratory data

Laboratory measurements may not simulate what the satellite sensor would see
 Good example is the difficult nature of measuring the relationship between water content and plant health

Once the plant material is removed from the plant to allow measurement it begins to dry out

Using field-based measurements only is limited by the quality of the sensors

The next question then becomes how many samples are needed to determine what signatures allow for a thematic measurement

This is a black spruce forest in the BOREAS experimental region in Canada.
Left: backscattering (sun behind observer), note the bright region (hotspot) where all shadows are hidden. Right: forwardscattering (sun opposite observer), note the shadowed centers of trees and transmission of light through the edges of the canopies. Photograph by Don Deering. http://www-modis.bu.edu/brdf/brdfexpl.html

A soybean field. Left: backscattering (sun behind observer). Right: forwardscattering
(sun opposite observer), note the specular reflection of the leaves.
Photograph by Don Deering. http://www-modis.bu.edu/brdf/brdfexpl.html

The next thing to be concerned about is the fact that we will not fully sample the entire spectrum but rather use fewer bands
In this case, all four bands will allow us to differentiate clay and grass
Using bands 1, 3, and
4 would also be sufficient to do this
Even using just bands 3 and 4 would allow us to separate clay and grass

Band selection and resolution for spectral signatures should be chosen first based on the shapes of the spectra

That is, it is not recommended to rely on the absolute difference between two reflectance spectra for discrimination
 Numerous factors can alter the brightness of the sample while not impacting the spectral shape
 Shadow effects and illumination conditions
 Absolute calibration
 Sample purity

Bands showngive

Gypsum
- Low, high, lower
 Montmorillonite
- High, high, low

Quartz
- high, high, not so high

It is necessary to understand the energy quantities that are typically used in remote sensing
 Radiant energy (Q in joules) is a measure of the capacity of an EM wave to do work by moving an object, heating, or changing its state.
 Radiant flux (Φ in watts) is the time rate (flow) of energy passing through a certain location.
 Radiant flux density (watts/m 2 ) is the flux intercepted by a planar
 Irradiance (E) is flux density incident upon a surface.
 Exitance (M) or emittance is flux density leaving a surface.
 The solid angle (Ω in steradians) subtended by an area A on a
 Radiant intensity (I in watts/sr) is the flux per unit solid angle in a
 Radiance (L in watts/m 2 /sr) is the intensity per unit projected area.
 Radiance from source to object is conserved

Radiant flux, irradiance (radiant exitance), radiance
The three major energy quantities are related to each other logically by examining their units
In this course, we will deal with the special case
Object of interest is located far from the sensor (factor of five)
Change in radiance from object is small over the view of the sensor
Then
Φ
Φ detector detector
E detector
= L object
= E object
= L object
× Area collector
× Area collector
× Ω
GIFOV
× Ω
GIFOV
Ω
GIFOV
= Area
Ω
GIFOV
= Area
GIFOV
/H 2 detector
/f 2

Emissivity, absorptance, and reflectance
All three of these quantities are unitless ratios of energy quanities
Emissivity, ε, is the ratio of the amount of energy emitted by an object to the maximum that could possibly emitted at that temperature
Absorptance, α, is the ratio of the amount of energy absorbed by an object to the amount that is incident on it
Reflectance, ρ, is the ratio of the amount of energy reflected by an object to the is incident on it
All three can be written in terms of the emitted, reflected, incident, and absorbed radiance, irradiance, radiant exitance, or radiant flux (but since above three quantities are unitless, numerator and denominator must be identical units)
In terms of radiant flux we would have

Cosine Law - Irradiance on surface is proportional to cosine of the angle between normal to the surface and incident radiance
E = E
0 cosθ
In figures below, if E
0
(or L
0 converted to irradiance using the solid angle) is normal to the surface, we have a maximum incident irradiance
For E
0 that is tangent to surface, the incident irradiance is zero

Graph on this page shows the downwelling total irradiance as a function of time for a single day as measured from a pyranometer

2
or 1/R 2 states that the irradiance from a point source is inversely proportional to the square of the distance from the source
Only true for a point source, but for cases when the distance from the source is large relative to the size of the source (factor of five gives accuracy of 1%)
Sun can be considered a point source at the earth
Satellite in terrestrial orbit does not see the earth as a point source
Can understand how this law works by remembering that irradiance has a
1/area unit and looking at the cases below
In both cases, the radiant flux through the entire circle is same
Area of larger sphere is 4 times that of the smaller sphere and irradiance for a point on the sphere is ¼ that of the smaller sphere

Lambertian surface is one for which the surface-leaving radiance is constant with angle

It is the angle leaving the surface for which the radiance is invariant

Lambertian surface says nothing about the dependence of the surfaceleaving radiance on the angle of incidence

In fact, from the cosine law, we know that the incident irradiance will decrease with sun angle

If the incident irradiance decreases, the reflected radiance decreases as well

The radiance can decrease, as long as it does so in all directions equally 2

Using the integral form of the relationship between radiance and irradiance we can show that
E lambertian
=¶L lambertian
To obtain the irradiance we have to consider the radiance through an entire Hemisphere
Because of the large range of angles, we cannot simply use E=LΩ

States that the spectral radiant exitance from a blackbody depends only on wavelength and the temperature of the blackbody
A blackbody is an object that absorbs all energy incident on it, α=1
Corrollary is that a blackbody emits the maximum of energy possible for an object a given temperature and wavelength

Once you are given the temperature and wavelength you can develop a Planck curve
Planck curves never cross
Curves of warmer bodies are above those of cooler bodies

Peaks of Planck Curves get lower and move to longer wavelengths as temperature decreases
Maximum wavelength of emission is defined by Wien’s Law
λ max
=2898/T [μm]

Sun is the primary source of energy in the VNIR and SWIR
Peak of solar curve at approximately 0.45 μm
Distance to sun varies from 0.983 to 1.0167 AU
Irradiance (not spectral irradiance) at the top of the earth’s atmosphere for normal incidence is 1367 W/m 2 at 1 AU

Energy radiated by the earth peaks in the TIR
Effective temperature of the earth-atmosphere system is 255 K
Planck curves below relate to typical terrestrial temperatures

When taking into account the earth-sun distance it can be shown that solar energy dominates in VNIR/SWIR and emitted terrestrial dominates in the TIR
Sun emits more energy than the earth at ALL wavelengths
It is a geometry effect that allows us to treat the wavelength regions separately

Plots here show the energy from the sun at the sun and at the top of the earth’s atmosphere
Also show the emitted energy from the earth

Understanding the vertical structure of the atmosphere allows one to understand better the effects of the atmosphere
 Atmosphere is divided into layers based on the change in temperature with height in that layer
 Troposphere is nearest the surface with temperature decreasing with height
 Stratosphere is next layer and temperature increases with height temperatures

Atmosphere is composed of dust and molecules which vary spatially and in concentration
 Dust also referred to as aerosols
 Also applies to liquid water, particulate matter, airplanes, etc.
 Primary source of aerosols is the earth's surface
 Size of most aerosols is between 0.2 and 5.0 micrometers
 Smaller aerosols coagulate with other aerosols to make larger particles
 Both aerosols and molecules scatter light more efficiently at short


Molecules scatter very strongly with wavelength (blue sky)
Aerosols typically scatter with 1/(wavelength)
 Both aerosols and molecules absorb
 Molecular (or gaseous absorption is more wavelength dependent
 Depends on concentration of material

MODTRAN3 output for US Standard Atmosphere, 2.54 cm column water vapor, default ozone 60-degree zenith angle and no scattering

Same curve as previous page but includes molecular scatter

Changing the angle of the path through the atmosphere effectively changes the concentration

More material, lower transmittance

Longer path, lower transmittance

At longer wavelengths, absorption plays a stronger role with some spectral regions having complete absorption

The MWIR is dominated by water vapor and carbon dioxide absorption

In the TIR there is the “atmospheric window” from 8-12 μm with a strong ozone band to consider

Easier to consider the specific problem of the radiance at a sensor at the top of the atmosphere viewing the surface

There will be three components of greatest interest in the solar reflective part of the spectrum
 Unscattered, surface reflected radiation L
λ su
 Down scattered, surface reflected L
λ sd skylight
 Up scattered path L
λ sp radiance
 Radiance at the sensor is the sum of these three

Radiative transfer is basis for understanding how sunlight and emitted surface radiation interact with the atmosphere

For the atmospheric scientist, radiative transfer is critical for understanding the atmosphere itself

For everyone else, it is what atmospheric scientists use to allow others to get rid of atmospheric effects

Discussion here will be to understand the effects the atmosphere will have on remote sensing data
 Start with some definitions
 Zenith Angle

Elevation Angle
 Nadir Angle

Airmass is 1/cos(zenith)

Azimuth angle describes the angle about the vertical similar to cardinal directions

Optical depth describes the attenuation along a path in the atmosphere

Depends on the amount of material in the atmosphere and the type of material and wavelength of interest

Soot is a stronger absorber (higher optical depth) than salt
 Molecules scatter better (higher optical depth) at shorter wavelengths

Aerosol optical depth is typically higher in Los Angeles than Tucson
 Total optical depth is less on Mt. Lemmon than Tucson due to fewer molecules and lower aerosol loading

Optical depth can be divided into absorption and scattering components which sum together to give the total optical depth
δ total
= δ scatter
+ δ absorption

Scattering optical depth can be broken into molecular and aerosol
δ scatter
= δ molec
+ δ aerosol

Absorption can be written as sum of individual gaseous components
δ absorption
= δ
H
2
O
+ δ
O
3
+ δ
CO
2
+ .........

Beer’s Law relates optical depth to transmittance

Increase in optical depth means decrease in transmittance

Assuming that optical depth does not vary horizontally in the atmosphere allows us to write Beer’s Law in terms of the vertical optical depth

1/cosθ=m for airmass is valid up to about θ=60 (at larger values must include refractive corrections)
 Recalling that optical depth is the sum of component optical depths
 Beer’s Law also relates an incident energy to the transmitted energy

First consider the directly transmitted solar beam, reflected from the ground, and transmitted to the sensor the unscattered surface-reflected radiation, L
λ su

Can also write the transmittance as an exponential in terms of optical dept
 Beer’s law

Need to account for the path length of the sun due to solar zenith
 angle of the sun in computing transmittance
Account for the cosine incident term to get the irradiance on the surface
Recall m=1/cosθ solar
E
λ ground, solar is the solar irradiance at the bottom of the atmosphere normal to the ground surface
(shown here to be horizontal)
Requires a 1/r 2 to account for earth-sun distance

The surface topography will play a critical role in determining the incident irradiance
 Two effects to consider

Slope of the surface

Lower optical depth because of higher elevation

Good example of the usefulness of a digital elevation model (DEM) and assumption of a vertical atmospheric model

Surface elevation model can be used to predict energy at sensor

Given

Solar elevation angle
 local topography
(slope, aspect) from DEM
 Simulate incident angle effect on irradiance
 Calculate incident angle for every pixel

Determine cos[θ(x,y)]
 Creates a “shadedrelief” image
TM: Landsat thematic mapper

Reflect the transmitted solar energy from the surface within the field of view of the sensor

Once the solar irradiance is determined at the ground in the direction normal to the surface it is reflected by the surface

The irradiance is converted to a radiance

Conversion from irradiance to radiance is needed because we want to use the nice features of radiance

Recall the relationship between irradiance and radiance derived earlier for a lambertian surface - E=¶L

There is a similar relationship between incident irradiance and reflected radiance from a Lambertian surface

Last step is to transmit the radiance from the surface to the sensor along the view path
 Simply Beer’s law again, except now we use the view path instead of the solar path

Atmosphere scatters light towards the surface and this scattered light is reflected at the surface to the sensor

Compute an incident irradiance from the incident radiance due to atmospheric scattering

This incident irradiance is reflected from our lambertian surface to give

Still need to transmit this through the atmosphere to get the at-sensor radiance

Image below is three-band mix of ETM+ bands 1, 4, and 7
 Note that there is still energy coming from the shadows
 Scattered skylight - which will have a blue dominance to it

Path radiance describes the amount of energy scattered by the atmosphere into the sensor’s view
 Basically, any photon for which the last photon scattering event occurred in the atmosphere is a path radiance term
 Can include or exclude an interaction with the ground
 If it includes a surface interaction then this can be affected by atmospheric adjacency effects
 The intrinsic path radiance is the radiance at the sensor that would be measured if there were zero surface reflectance
 Contribution only from the atmosphere
 Depends only on atmospheric parameters
 No simple formulation
 Requires radiative transfer code
 Use L
λ sp

A similar effect can be seen over water

Images here are also bands 3, 4, and 7 of ETM+ (LANDSAT)
 Water is highly absorbing at these wavelengths thus almost all of the signal is due to atmospheric scattering

Summing the previous three at-sensor radiances will give the total radiance at the sensor

There is a huge amount of buried information in the above
 This is a simplified way of looking at the problem

Phase function effects from scattering and single scatter albedo are contained in
E down and the path radiance

Optical depths due to scattering and absorption are combined in the transmittance terms
 Also assumes lambertian surface!!!

Model output shows the spectral dependence of the atsensor radiance for path radiance and reflected radiance

MISR data showing the effect of view angle on TOA radiance with brightening and blue dominance at large views

Comparison between measured spectra of RRV Playa using AVIRIS and predicted radiance based on ground measurements
The airborne visible/infrared imaging spectrometer (AVIRIS)

Results below model the at-sensor radiance compared to the sensor output
A raw AVIRIS spectrum (measured in digital numbers or. DN's)

There will also be three components of greatest interest in the emissive part of the spectrum (or TIR)

Unattenuated, surface emitted radiation L
Downward emitted, surface reflected skylight L

Upward emitted path radiance L

Radiance at the sensor is the sum of these three
λ eu
λ ed
λ ep
L
λ e = L
λ eu + L
λ ed + L
λ ep

In the TIR, the problem is similar in philosophy as the reflective

Still have a path radiance, and reflected downwelling

Direct reflected term in reflective is analogous to the surface emitted term in the TIR

Difference is that we are now dealing primarily with emission and absorption rather than scattering

Reflective we are most concerned with how much stuff is in the atmosphere and what it is

Aerosol loading (Gives aerosol optical depth)

Atmospheric pressure (Gives molecular optical depth)

Types of aerosols (Phase function and absorption properties)

Amount of gaseous absorbers (Water vapor, ozone, carbon dioxide)

In the TIR we must also worry about where these things are vertically

Temperature depends on altitude

Emission depends on temperature

Need vertical profile of termperature, pressure, and amounts of absorbers

Surface emitted term will depend upon the emissivity and temperature of the surface attenuated along the view path

Easiest assumption is to assume that the surface is a blackbody but then the temperature obtained will not correspond to the actual temperature

Better assumption is to assume the emissivity and temperature are known and use Planck’s law to obtain the emitted radiance

Transmitting this through the atmosphere gives

Here, the equations are identical to the reflective case

The downwelling radiance depends on atmospheric temperature and composition

Equations are the same

Path radiance term is same as in reflective

Must be computed from radiative transfer
 Depends heavily on atmospheric ,

Use
L
λ sp

Sum is same approach as reflective

Concepts work in the other direction as well

Radiance at the sensor will depend mostly upon where the layer is that is emitting the energy seen by the sensor

Location of the layer affects the temperature
 The warmer the layer, the higher the radiance that is emitted

ETM+ Band 6 of Tucson showing temperature effects

This image is from July

Note the hot roads and cool vegetation

Water is dark in reflective bands but can be bright in LWIR

Warm water relative to surround

Water is also high emissivity (nearly unity)

Example of
New Orleans shown here points out the
High temperatures of the urban area

Water in this case is much colder than the land
 Little contrast in the reflective

the LANSSAT TM consists of 7 bands that have these characteristics:
Band No.
Wavelength
Interval (µm)
Spectral
Response
Resolution (m)
4
5
6
1
2
3
7
0.45 - 0.52
Blue-Green
0.52 - 0.60
Green
0.63 - 0.69
2.08 - 2.35
Red
0.76 - 0.90
Near IR
1.55 - 1.75
Mid-IR
10.40 - 12.50 Thermal IR
Mid-IR
30
30
30
30
30
120
30

CLASS Part.: WHY?
Clouds seen in the TIR (band 6 left) and visible (band 3 right) of ETM+ from July

TIR “Shadows” seen in the ETM+ band 6 image left are of far different nature than those of the band 3 shadows

Canyons act as blackbody as well as have higher temperatures due to lower elevations
 GOES image here shows low radiance as bright

Note the Grand
Canyon is plainly
Visible

Also evident are landwater boundaries (and not just because of the lines drawn to show them)