Download - Lecture 5: Radiative transfer theory where light comes from and how it gets to where it’s going
Lecture 5: Radiative transfer theory
where light comes from and how it gets to where it’s going
Tuesday, 19 January 2010
Ch 1.2 review, 1.3, 1.4http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html (scattering)http://id.mind.net/~zona/mstm/physics/light/rayOptics/refraction/refraction1.html (refraction)http://id.mind.net/~zona/mstm/physics/light/rayOptics/refraction/snellsLaw/snellsLaw1.html (Snell’s Law)Review On Solid Angles, (class website -- Ancillary folder: Steradian.ppt)
Last lecture: color theorydata spaces color mixturesabsorption
Reading
The Electromagnetic Spectrum (review)
Units:Micrometer = 10-6 mNanometer = 10-9 m
Light emitted by the sun
The Sun
Light from Sun – Light Reflected and Emitted by Earth
Wavelength, μm
W m
-2 μ
m -1
W m
-2 μ
m-1 sr
-1
The sun is not an ideal blackbody – the 5800 K figure and graph are simplifications
Atmospheric Constituents
10
50
90
Troposphere
Stratosphere
Mesosphere
Thermosphere
Almost allH2O
Hei
ght (
km)
Temperature (K)
280200
Ozone
Constant Nitrogen (78.1%) Oxygen (21%) Argon (0.94%) Carbon Dioxide (0.033%) Neon Helium Krypton Xenon Hydrogen Methane Nitrous Oxide
Variable Water Vapor (0 - 0.04%) Ozone (0 – 12x10-4%) Sulfur Dioxide Nitrogen Dioxide Ammonia Nitric Oxide
All contribute to scatteringFor absorption, O2, O3, and N2 are important in the UVCO2 and H2O are important in the IR (NIR, MIR, TIR)
Solar spectra before and after passage through the atmosphere
Atmospheric transmission
Modeling the atmosphere
dz
e
To calculate we need to know how k in the Beer-Lambert-Bouguer Law (called here) varies with altitude. Modtran models the atmosphere as thin homogeneous layers.
L
L ze
L
LsL ze
)(
Modtran calculates k or for each layer using the vertical profile of temperature, pressure, and composition (like water vapor).
This profile can be measured made using a balloon, or a standard atmosphere can be assumed.
o is the incoming flux
Radiosonde dataA
ltitu
de (k
m)
Alti
tude
(km
)
Relative Humidity (%) Temperature (oC)
20
15
10
5
0
20
15
10
5
00 20 40 60 80 100 -80 -40 0 40
Mt Everest
Mt Rainier
Radiant energy – Q (J) - electromagnetic energy
Solar Irradiance – Itoa(W m-2) - Incoming radiation (quasi directional) from the sun at the top of the atmosphere.
Irradiance – Ig (W m-2) - Incoming hemispheric radiation at ground. Comes from: 1) direct sunlight and 2) diffuse skylight (scattered by atmosphere).
Downwelling sky irradiance – Is↓(W m-2) – hemispheric radiation at ground
Path Radiance - Ls↑ (W m-2 sr-1 ) (Lp in text) - directional radiation scattered into the camera from the atmosphere without touching the ground
Transmissivity – - the % of incident energy that passes through the atmosphere
Radiance – L (W m-2 sr-1) – directional energy density from an object.
Reflectance – r -The % of irradiance reflected by a body in all directions (hemispheric: r·I) or in a given direction (directional: r·I·-1)
Note: reflectance is sometimes considered to be the reflected radiance. In this class, its use is restricted to the % energy reflected.
Ig
Ls↑
Itoa
0.5º
Is↓
L
Terms and units used in radiative transfer calculations
DN = a·Ig·r + b
Radiative transfer equation
Ig is the irradiance on the groundr is the surface reflectancea & b are parameters that relate to instrument and atmospheric characteristics
This is what we want
Parameters that relate to instrument and atmospheric characteristics
DN = g·(e·r · i·Itoa·cos(i)/ + e· r·Is↓/ + Ls↑) + o
g amplifier gainatmospheric transmissivitye emergent anglei incident angler reflectanceItoa solar irradiance at top of atmosphereIg solar irradiance at ground Is↓ down-welling sky irradianceLs↑ up-welling sky (path) radianceo amplifier bias or offset
Radiative transfer equation
DN = a·Ig·r + b
The factor of Consider a perfectly reflective (r=100%) diffuse “Lambertian” surface that
reflects equally in all directions.
Lambert
The factor of Consider a perfectly reflective (r=100%) diffuse “Lambertian” surface that
reflects equally in all directions.
If irradiance on the surface is Ig, then the irradiance from the surface is r·Ig = Ig W m-2.
The radiance intercepted by a camera would be r·Ig/ W m-2 sr-1.
The factor is the ratio between the hemispheric radiance (irradiance) and the directional radiance. The area of the sky hemisphere is 2 sr (for a unit radius).So – why don’t we divide by 2 instead of ?
∫ ∫ L sin cos ddL2
0 0
•Incoming directional radiance L at elevation angle is isotropic
•Reflected directional radiance L cos is isotropic
•Area of a unit hemisphere:
∫ ∫ sin dd 2
0 0
The factor of Consider a perfectly reflective (r=100%) diffuse “Lambertian” surface that
reflects equally in all directions.
i Itoa cos(i)
Itoa
gi Itoa cos(i)
i
r reflectance
r (i Itoa cos(i)) / reflected light
“Lambertian” surface
e
e
Ls↑ (Lp)Highlighted terms relate to the surface
i
i Itoa cos(i)
Itoa
gi Itoa cos(i)
i
r reflectance
r (i Itoa cos(i)) / reflected light
“Lambertian” surface
e
e
Measured Ltoa
DN(Itoa) = a Itoa + b
Ltoae r (i Itoa cos(i)) / +
e r Is↓ / + Ls↑
Ls↑ (Lp)Highlighted terms relate to the surface
Is↓
Ls↑=r Is↓ / i
Lambert
Next lecture: Atmospheric scattering and other effects
Mauna Loa, Hawaii