UCL DEPARTMENT DEPARTMENT OF GEOGRAPHYOF GEOGRAPHY GEOGG141/ GEOG3051 Principles & Practice of Remote Sensing EM Radiation (ii) Dr. Mathias (Mat) Disney UCL Geography Office: 113, Pearson Building Tel: 7679 0592 Email: [email protected] http://www2.geog.ucl.ac.uk/~mdisney/teaching/GEOGG141/GEOGG141.html http://www2.geog.ucl.ac.uk/~mdisney/teaching/3051/GEOG3051.html UCL DEPARTMENT OF GEOGRAPHY EMR arriving at Earth • We now know how EMR spectrum is distributed • Radiant energy arriving at Earth’s surface • NOT blackbody, but close • “Solar constant” • solar energy irradiating surface perpendicular to solar beam • ~1373Wm-2 at top of atmosphere (TOA) • Mean distance of sun ~1.5x108km so total solar energy emitted = 4πr2x1373 = 3.88x1026W 8 • Incidentally we can now calculate Tsun (radius=6.69x10 m) from SB Law 4 26 2 •σ T sun = 3.88x10 /4π r so T = ~5800K 2 UCL DEPARTMENT OF GEOGRAPHY Departure from blackbody assumption • Interaction with gases in the atmosphere – attenuation of solar radiation 3 UCL DEPARTMENT OF GEOGRAPHY Radiation Geometry: spatial relations • Now cover what happens when radiation interacts with Earth System • Atmosphere • On the way down AND way up • Surface • Multiple interactions between surface and atmosphere • Absorption/scattering of radiation in the atmosphere 4 UCL DEPARTMENT OF GEOGRAPHY Radiation passing through media • Various interactions, with different results From http://rst.gsfc.nasa.gov/Intro/Part2_3html.html 5 UCL DEPARTMENT OF GEOGRAPHY Radiation Geometry: spatial relations • Definitions of radiometric quantities • Radiant energy emitted, transmitted of received per unit time is radiant flux (usually Watts, or Js-1) • Radiant flux density is flux per unit area (Wm-2) • Irradiance is radiant flux density incident on a surface (Wm-2) e.g. Solar radiation arriving at surface • Emittance (radiance or radiant exitance) (Wm-2) is radiant flux density emitted by a surface • For parallel beam, flux density defined in terms of plane perpendicular to beam. What about from a point? 6 UCL DEPARTMENT OF GEOGRAPHY Radiation Geometry: point source Point source dω dF dA r • Consider flux dF emitted from point source into solid angle dω, where dF and dω very small • Intensity I defined as flux per unit solid angle i.e. I = dF/dω (Wsr-1) • Solid angle dω = dA/r2 (steradians, sr) 7 UCL DEPARTMENT OF GEOGRAPHY Radiation Geometry: plane source dF ψ ω Plane source dS dS cos ψ • What about when we have a plane source rather than a point? • Element of surface with area dS emits flux dF in direction at angle ψ to normal • Radiant emittance, M = dF / dS (Wm-2) • Radiance L is intensity in a particular direction (dI = dF/ω) divided by the apparent area of source in that direction i.e. flux per unit area per solid angle (Wm-2sr-1) • Projected area of dS is direction ψ is dS cos ψ, so….. • Radiance L = (dF/ω) / dS cos ψ = dI/dS cos ψ (Wm-2sr-1) 8 UCL DEPARTMENT OF GEOGRAPHY Radiation Geometry: radiance • So, radiance equivalent to: • intensity of radiant flux observed in a particular direction divided by apparent area of source in same direction • Note on solid angle (steradians): • 3D analog of ordinary angle (radians) • 1 steradian = angle subtended at the centre of a sphere by an area of surface equal to the square of the radius. The surface of a sphere subtends an angle of 4π steradians at its centre. 9 UCL DEPARTMENT OF GEOGRAPHY Radiation Geometry: solid angle • Cone of solid angle Ω = 1sr • Radiant intensity from sphere •Ω = area of surface A / radius2 From http://www.intl-light.com/handbook/ch07.html 10 UCL DEPARTMENT OF GEOGRAPHY Radiation Geometry: terms and units 11 UCL DEPARTMENT OF GEOGRAPHY Radiation Geometry: cosine law • Emission and absorption • Radiance linked to law describing spatial distn of radiation emitted by Bbody with uniform surface temp. T (total emitted flux = σT4) • Surface of Bbody then has same T from whatever angle viewed • So intensity of radiation from point on surface, and areal element of surface MUST be independent of ψ, angle to surface normal • OTOH flux per unit solid angle divided by true area of surface must be proportional to cos ψ 12 UCL DEPARTMENT OF GEOGRAPHY Radiation Geometry: cosine law X Radiometer dA Y X Radiometer ψ Y dA/cos ψ • Case 1: radiometer ‘sees’ dA, flux proportional to dA • Case 2: radiometer ‘sees’ dA/cos ψ (larger) BUT T same, so emittance of surface same and hence radiometer measures same • So flux emitted per unit area at angle ψ ∝ to cos ψ so that product of emittance (∝ cos ψ ) and area emitting (∝ 1/ cos ψ) is same for all ψ • This is basis of Lambert’s Cosine Law Adapted from Monteith and Unsworth, Principles of Environmental Physics 13 UCL DEPARTMENT OF GEOGRAPHY Radiation Geometry: Lambert’s Cosine Law • When radiation emitted from Bbody at angle ψ to normal, then flux per unit solid angle emitted by surface is ∝ cos ψ • Corollary of this: • if Bbody exposed to beam of radiant energy at an angle ψ to normal, the flux density of absorbed radiation is ∝ cos ψ • In remote sensing we generally need to consider directions of both incident AND reflected radiation, then reflectivity is described as bi-directional Adapted from Monteith and Unsworth, Principles of Environmental Physics 14 UCL DEPARTMENT OF GEOGRAPHY Recap: radiance • Radiance, L dω • power emitted (dF) per unit of solid angle (d ) and per unit of the projected ω ψ surface (dS cosψ) of an extended widespread source in a given direction, ψ (ψ = zenith angle, ϕ= azimuth angle) Projected surface dS cos ψ • L = d2F / (dω dS cos ψ) (in Wm-2sr-1) • If radiance is not dependent on ψ i.e. if same in all directions, the source is said to be Lambertian. Ordinary surfaces rarely found to be Lambertian. Ad. From http://ceos.cnes.fr:8100/cdrom-97/ceos1/science/baphygb/chap2/chap2.htm 15 UCL DEPARTMENT OF GEOGRAPHY Recap: emittance • Emittance, M (exitance) • emittance (M) is the power emitted (dW) per surface unit of an extended widespread source, throughout an hemisphere. Radiance is therefore integrated over an hemisphere. If radiance independent of ψ i.e. if same in all directions, the source is said to be Lambertian. • For Lambertian surface • Remember L = d2F / (dω dS cos ψ) = constant, so M = dF/dS = • M = L π 2 π 2 π Lcosψdω = 2πL cosψ sinψdψ = πL ∫0 ∫0 16 Ad. From http://ceos.cnes.fr:8100/cdrom-97/ceos1/science/baphygb/chap2/chap2.htm € UCL DEPARTMENT OF GEOGRAPHY Recap: irradiance • Radiance, L, defined as directional (function of angle) • from source dS along viewing Direct angle of sensor (θ in this 2D case, but more generally (θ, ϕ) in 3D case) • Emittance, M, hemispheric • Why?? Diffuse • Solar radiation scattered by atmosphere • So we have direct AND diffuse components Ad. From http://ceos.cnes.fr:8100/cdrom-97/ceos1/science/baphygb/chap2/chap2.htm 17 UCL DEPARTMENT OF GEOGRAPHY Reflectance • Spectral reflectance, ρ(λ), defined as ratio of incident flux to reflected flux at same wavelength •ρ (λ) = L(λ)/I(λ) • Extreme cases: • Perfectly specular: radiation incident at angle ψ reflected away from surface at angle -ψ • Perfectly diffuse (Lambertian): radiation incident at angle ψ reflected equally in all angles 18 UCL DEPARTMENT OF GEOGRAPHY Interactions with the atmosphere From http://rst.gsfc.nasa.gov/Intro/Part2_4.html 19 UCL DEPARTMENT OF GEOGRAPHY Interactions with the atmosphere R4 R1 R2 R3 target target target target • Notice that target reflectance is a function of • Atmospheric irradiance • reflectance outside target scattered into path • diffuse atmospheric irradiance • multiple-scattered surface-atmosphere interactions 20 From: http://www.geog.ucl.ac.uk/~mdisney/phd.bak/final_version/final_pdf/chapter2a.pdf UCL DEPARTMENT OF GEOGRAPHY Interactions with the atmosphere: refraction • Caused by atmosphere at different T having different density, hence refraction • path of radiation alters moving from medium of one density to another (different velocity) • index of refraction (n) is ratio of speed of light in a vacuum (c) to speed cn in another medium (e.g. Air) i.e. n = c/cn • note that n always >= 1 i.e. cn <= c • Examples • nair = 1.0002926 • nwater = 1.33 21 UCL DEPARTMENT OF GEOGRAPHY Refraction: Snell’s Law Incident • Refraction described by Snell’s Law radiation • For given freq. f, n1 sin θ1 = n2 sin θ2 n1 •where and are the angles from the θ 1 θ1 θ2 Optically normal of the incident and refracted waves less dense respectively Optically more • (non-turbulent) atmosphere can be θ 2 n2 dense considered as layers of gases, each with a Path Optically θ 3 unaffected different density (hence n) less dense by n • Displacement of path - BUT knowing 3 atmosphere Path affected by Snell’s Law can be removed atmosphere 22 After: Jensen, J. (2000) Remote sensing of the environment: an Earth Resources Perspective. UCL DEPARTMENT OF GEOGRAPHY Interactions with the atmosphere: scattering • Caused by presence of particles (soot, salt, etc.) and/or large gas molecules present in the atmosphere • Interact with EMR anc cause to be redirected from original path. • Scattering amount depends on: •λ of radiation • abundance of particles or gases • distance the radiation travels through the atmosphere (path length) 23 After: http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/fundam/chapter1/chapter1_4_e.html UCL DEPARTMENT OF GEOGRAPHY Atmospheric scattering 1: Rayleigh • Particle size << λ of radiation • e.g. very fine soot and dust or N2, O2 molecules • Rayleigh scattering dominates shorter λ and in upper atmos. • i.e. Longer λ scattered less (visible red λ scattered less than blue λ) • Hence