Transcript Lecture 5:
Tuesday, 20 January Lecture 5: Radiative transfer theory where light comes from and how it gets to where it’s going http://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 theory, data spaces, color mixtures, absorption, photogrammetry The Electromagnetic Spectrum (review) Units: Micrometer = 10-6 m Nanometer = 10-9 m Light emitted by the sun W m-2 μm-1 sr-1 W m-2 μm -1 Light from Sun – Light Reflected and Emitted by Earth Wavelength, μm Atmospheric Constituents 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 Thermosphere 90 Height (km) Constant Mesosphere 50 Stratosphere Ozone 10 All contribute to scattering For absorption, O2, O3, and N2 are important in the UV CO2 and H2O are important in the IR (NIR, MIR, TIR) Almost all H2O Troposphere 200 Temperature (K) 280 Atmospheric transmission Modeling the atmosphere To calculate we need to know how k in the Beer-LambertBouguer Law (called here) varies with altitude. Modtran models the atmosphere as thin homogeneous layers. Modtran calculates k or for each layer using the vertical profile of temperature, pressure, and composition (like water vapor). e dz e Fo is the incoming flux e L z L ( sL L ) z L This profile can be measured made using a balloon, or a standard atmosphere can be assumed. 20 20 15 15 Altitude (km) Altitude (km) Radiosonde data 10 5 0 0 20 40 60 80 100 Relative Humidity (%) 10 Mt Everest 5 Mt Rainier 0 -80 -40 0 40 Temperature (oC) Terms and units used in radiative transfer calculations 0.5º 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 Itoa L Ls↑ 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·p-1) Is↓ Ig Note: reflectance is sometimes considered to be the reflected radiance. In this class, its use is restricted to the % energy reflected. Radiative transfer equation Parameters that relate to instrument and atmospheric characteristics DN = a·Ig·r + b This is what we want Ig is the irradiance on the ground r is the surface reflectance a & b are parameters that relate to instrument and atmospheric characteristics Radiative transfer equation DN = a·Ig·r + b DN = g·(e·r · i·Itoa·cos(i)/p + e· r·Is↓/p + Ls↑) + o g e i r Itoa Ig Is↓ Ls↑ o amplifier gain atmospheric transmissivity emergent angle incident angle reflectance solar irradiance at top of atmosphere solar irradiance at ground down-welling sky irradiance up-welling sky (path) radiance amplifier bias or offset The factor of p Consider a perfectly reflective (r=100%) diffuse “Lambertian” surface that reflects equally in all directions. 2p p/2 ∫ ∫ L sin then cos irradiance d dwpL If irradiance on the surface is I , the from the surface is g 0 0 r·Ig = Ig W m-2. •Incoming directional radiance L at elevation angle is isotropic The radiance intercepted by a camera would be r·Ig/p W m-2 sr-1. •Reflected directional radiance L cos is isotropic The factor p is the ratio between the hemispheric radiance (irradiance) and the directional The area of the sky hemisphere is 2p sr (for a unit •Area radiance. of a unit hemisphere: radius). So – why don’t we divide2pbyp/22p instead of p? ∫ ∫ sin Lambert d dw2p 0 0 Measured Ltoa DN(Itoa) = a Itoa + b Itoa Ltoae r (i Itoa cos(i)) /p + e r Is↓ /p + Ls↑ Itoa cos(i) i Highlighted terms relate to the surface i Ls↑=r Is↓ /p Ls↑ (Lp) e i e Igi Itoa cos(i) Lambert Is↓ r reflectance r (i Itoa cos(i)) /p reflected light “Lambertian” surface Next lecture: Atmospheric scattering and other effects Rayleigh Scattering l>>d Mauna Loa, Hawaii