Presentation on theme: "Dr. Mathias (Mat) Disney UCL Geography Office: 113, Pearson Building"— Presentation transcript:
1 GEOGG141/ GEOG3051 Principles & Practice of Remote Sensing EM Radiation (ii) Dr. Mathias (Mat) DisneyUCL GeographyOffice: 113, Pearson BuildingTel:
2 EMR arriving at Earth We now know how EMR spectrum is distributed Radiant energy arriving at Earth’s surfaceNOT 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 = 4r2x1373 = 3.88x1026WIncidentally we can now calculate Tsun (radius=6.69x108m) from SB LawT4sun = 3.88x1026/4 r2 so T = ~5800K
3 Departure from blackbody assumption Interaction with gases in the atmosphereattenuation of solar radiation
4 Radiation Geometry: spatial relations Now cover what happens when radiation interacts with Earth SystemAtmosphereOn the way down AND way upSurfaceMultiple interactions between surface and atmosphereAbsorption/scattering of radiation in the atmosphere
5 Radiation passing through media Various interactions, with different resultsFrom
6 Radiation Geometry: spatial relations Definitions of radiometric quantitiesFor parallel beam, flux density defined in terms of plane perpendicular to beam. What about from a point?Schaepman-Strub et al. (2006)see
7 Radiation Geometry: point source dAPoint sourcerConsider flux dϕ emitted from point source into solid angle d, where dF and d very smallIntensity I defined as flux per unit solid angle i.e. I = dϕ/d (Wsr-1)Solid angle d = dA/r2 (steradians, sr)
8 Radiation Geometry: plane source dϕPlane source dSdS cos What about when we have a plane source rather than a point?Element of surface with area dS emits flux dϕ in direction at angle to normalRadiant exitance, M = dϕ / dS (Wm-2)Radiance L is intensity in a particular direction (dI = dϕ/) 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 is dS cos , so…..Radiance L = (dϕ/) / dS cos = dI/dS cos (Wm-2sr-1)
9 Radiation Geometry: radiance So, radiance equivalent to:intensity of radiant flux observed in a particular direction divided by apparent area of source in same directionNote 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 4 steradians at its centre.
10 Radiation Geometry: solid angle Cone of solid angle = 1sr from sphere = area of surface A / radius2Radiant intensityFrom
11 Radiation Geometry: cosine law Emission and absorptionRadiance linked to law describing spatial distn of radiation emitted by Bbody with uniform surface temp. T (total emitted flux = T4)Surface of Bbody then has same T from whatever angle viewedSo intensity of radiation from point on surface, and areal element of surface MUST be independent of , angle to surface normalOTOH flux per unit solid angle divided by true area of surface must be proportional to cos
12 Radiation Geometry: cosine law XRadiometerdAYXRadiometerYdA/cos Case 1: radiometer ‘sees’ dA, flux proportional to dACase 2: radiometer ‘sees’ dA/cos (larger) BUT T same, so emittance of surface same and hence radiometer measures sameSo flux emitted per unit area at angle to cos so that product of emittance ( cos ) and area emitting ( 1/ cos ) is same for all This is basis of Lambert’s Cosine LawAdapted from Monteith and Unsworth, Principles of Environmental Physics
13 Radiation Geometry: Lambert’s cosine law Observed intensity (W/cm2·sr)) for a normal and off-normal observer; dA0 is the area of the observing aperture and dΩ is the solid angle subtended by the aperture from the viewpoint of the emitting area element.Emission rate (photons/s) in a normal and off-normal direction. The number of photons/sec directed into any wedge is proportional to the area of the wedge.Radiant intensity observed from a ideal diffusely reflecting surface (Lambertian surface) surface directly proportional to cosine of angle between view angle and surface normal
14 Radiation Geometry: Lambert’s Cosine Law When radiation emitted from Bbody at angle to normal, then flux per unit solid angle emitted by surface is cos Corollary of this:if Bbody exposed to beam of radiant energy at an angle to normal, the flux density of absorbed radiation is cos In remote sensing we generally need to consider directions of both incident AND reflected radiation, then reflectivity is described as bi-directionalAdapted from Monteith and Unsworth, Principles of Environmental Physics
15 Recap: radiance Radiance, L L = d2ϕ / (d dS cos ) (in Wm-2sr-1) Projected surface dS cos Radiance, Lpower emitted (dϕ) per unit of solid angle (d) and per unit of the projected surface (dS cos) of an extended widespread source in a given direction, ( = zenith angle, = azimuth angle)L = d2ϕ / (d dS cos ) (in Wm-2sr-1)If radiance is not dependent on i.e. if same in all directions, the source is said to be Lambertian. Ordinary surfaces rarely found to be Lambertian.Ad. From
16 Recap: emittance Emittance, M (exitance) For Lambertian surface 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 i.e. if same in all directions, the source is said to be Lambertian.For Lambertian surfaceRemember L = d2ϕ / (d dS cos ) = constant, so M = dϕ/dS =M = LAd. From
17 Recap: irradianceRadiance, L, defined as directional (function of angle)from source dS along viewing angle of sensor ( in this 2D case, but more generally (, ) in 3D case)Emittance, M, hemisphericWhy??Solar radiation scattered by atmosphereSo we have direct AND diffuse componentsDirectDiffuseAd. From
18 ReflectanceSpectral reflectance, (), defined as ratio of incident flux to reflected flux at same wavelength() = L()/I()Extreme cases:Perfectly specular: radiation incident at angle reflected away from surface at angle -Perfectly diffuse (Lambertian): radiation incident at angle reflected equally in all angles
20 Interactions with the atmosphere 1targetR4targetR2targetR3targetNotice that target reflectance is a function ofAtmospheric irradiancereflectance outside target scattered into pathdiffuse atmospheric irradiancemultiple-scattered surface-atmosphere interactionsFrom:
21 Interactions with the atmosphere: refraction Caused by atmosphere at different T having different density, hence refractionpath of radiation alters (different velocity)Towards normal moving from lower to higher densityAway from normal moving from higher to lower densityindex 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/cnnote that n always >= 1 i.e. cn <= cExamplesnair =nwater = 1.33
22 Refraction: Snell’s Law Optically less denseOptically more denseIncident radiation 2 3 1Path affected by atmospherePath unaffected by atmosphereRefraction described by Snell’s LawFor given freq. f, n1 sin 1 = n2 sin 2where 1 and 2 are the angles from the normal of the incident and refracted waves respectively(non-turbulent) atmosphere can be considered as layers of gases, each with a different density (hence n)Displacement of path - BUT knowing Snell’s Law can be removedAfter: Jensen, J. (2000) Remote sensing of the environment: an Earth Resources Perspective.
23 Interactions with the atmosphere: scattering Caused by presence of particles (soot, salt, etc.) and/or large gas molecules present in the atmosphereInteract with EMR anc cause to be redirected from original path.Scattering amount depends on: of radiationabundance of particles or gasesdistance the radiation travels through the atmosphere (path length)After:
24 Atmospheric scattering 1: Rayleigh Particle size << of radiatione.g. very fine soot and dust or N2, O2 moleculesRayleigh scattering dominates shorter and in upper atmos.i.e. Longer scattered less (visible red scattered less than blue )Hence during day, visible blue tend to dominate (shorter path length)Longer path length at sunrise/sunset so proportionally more visible blue scattered out of path so sky tends to look more redEven more so if dust in upper atmosphereAfter:
25 Atmospheric scattering 1: Rayleigh So, scattering -4 so scattering of blue light (400nm) > scattering of red light (700nm) by (700/400)4 or ~ 9.4From
26 Atmospheric scattering 2: Mie Particle size of radiatione.g. dust, pollen, smoke and water vapourAffects longer than Rayleigh, BUT weak dependence on Mostly in the lower portions of the atmospherelarger particles are more abundantdominates when cloud conditions are overcasti.e. large amount of water vapour (mist, cloud, fog) results in almost totally diffuse illuminationAfter:
27 Atmospheric scattering 3: Non-selective Particle size >> of radiatione.g. Water droplets and larger dust particles,All affected about equally (hence name!)Hence results in fog, mist, clouds etc. appearing whitewhite = equal scattering of red, green and blue sAfter:
28 Atmospheric absorption Other major interaction with signalGaseous molecules in atmosphere can absorb photons at various depends on vibrational modes of moleculesVery dependent on Main components are:CO2, water vapour and ozone (O3)Also CH4 ....O3 absorbs shorter i.e. protects us from UV radiation
29 Atmospheric absorption CO2 as a “greenhouse” gasstrong absorber in longer (thermal) part of EM spectrumi.e m where Earth radiatesRemember peak of Planck function for T = 300KSo shortwave solar energy (UV, vis, SW and NIR) is absorbed at surface and re-radiates in thermalCO2 absorbs re-radiated energy and keeps warm$64M question!Does increasing CO2 increasing T??Anthropogenic global warming??Aside....
30 Atmospheric CO2 trends Antarctic ice core records Keeling et al. Annual variation + trendSmoking gun for anthropogenic change, or natural variation??Antarctic ice core records
31 Atmospheric “windows” As a result of strong dependence of absorptionSome totally unsuitable for remote sensing as most radiation absorbed
32 Atmospheric “windows” If you want to look at surfaceLook in atmospheric windows where transmissions highIf you want to look at atmosphere however....pick gapsVery important when selecting instrument channelsNote atmosphere nearly transparent in wave i.e. can see through clouds!V. Important consideration....
33 Atmospheric “windows” Vivisble + NIR part of the spectrumwindows, roughly: , , , , nm
34 Summary Measured signal is a function of target reflectance plus atmospheric component (scattering, absorption)Need to choose appropriate regions (atmospheric windows)μ-wave region largely transparent i.e. can see through clouds in this regionone of THE major advantages of μ-wave remote sensingTop-of-atmosphere (TOA) signal is NOT target signalTo isolate target signal need to...Remove/correct for effects of atmosphereA major part component of RS pre-processing chainAtmospheric models, ground observations, multiple views of surface through different path lengths and/or combinations of above
35 Summary Generally, solar radiation reaching the surface composed of <= 75% direct and >=25 % diffuseattentuation even in clearest possible conditionsminimum loss of 25% due to molecular scattering and absorption about equallyNormally, aerosols responsible for significant increase in attenuation over 25%HENCE ratio of diffuse to total also changesAND spectral composition changes
36 Natural surfaces somewhere in between ReflectanceWhen EMR hits target (surface)Range of surface reflectance behaviourperfect specular (mirror-like) - incidence angle = exitance angleperfectly diffuse (Lambertian) - same reflectance in all directions independent of illumination angle)Natural surfaces somewhere in betweenFrom
37 Surface energy budgetTotal amount of radiant flux per wavelength incident on surface, () Wm-1 is summation of:reflected r, transmitted t, and absorbed, ai.e. () = r + t + aSo need to know about surface reflectance, transmittance and absorptanceMeasured RS signal is combination of all 3 componentsAfter: Jensen, J. (2000) Remote sensing of the environment: an Earth Resources Perspective.
38 Reflectance: angular distribution Figure 2.1 Four examples of surface reflectance: (a) Lambertian reflectance (b) non-Lambertian (directional) reflectance (c) specular (mirror-like) reflectance (d) retro-reflection peak (hotspot).(a)(b)(c)(d)Real surfaces usually display some degree of reflectance ANISOTROPYLambertian surface is isotropic by definitionMost surfaces have some level of anisotropyFrom:
39 Directional reflectance: BRDF Reflectance of most real surfaces is a function of not only λ, but viewing and illumination anglesDescribed by the Bi-Directional Reflectance Distribution Function (BRDF)BRDF of area A defined as: ratio of incremental radiance, dLe, leaving surface through an infinitesimal solid angle in direction (v, v), to incremental irradiance, dEi, from illumination direction ’(i, i) i.e. is viewing vector (v, v) are view zenith and azimuth angles; ’ is illum. vector (i, i) are illum. zenith and azimuth anglesSo in sun-sensor example, is position of sensor and ’ is position of sunAfter: Jensen, J. (2000) Remote sensing of the environment: an Earth Resources Perspective.
40 Directional reflectance: BRDF Note that BRDF defined over infinitesimally small solid angles , ’ and interval, so cannot measure directlyIn practice measure over some finite angle and and assume validsurface area Asurface tangent vectori2-vviincident solid angle incident diffuse radiationdirect irradiance (Ei) vector exitant solid angle viewerConfiguration of viewing and illumination vectors in the viewing hemisphere, with respect to an element of surface area, A.From:
41 Directional reflectance: BRDF Spectral behaviour depends on illuminated/viewed amounts of materialChange view/illum. angles, change these proportions so change reflectanceInformation contained in angular signal related to size, shape and distribution of objects on surface (structure of surface)Typically CANNOT assume surfaces are Lambertian (isotropic)Modelled barley reflectance, v from –50o to 0o (left to right, top to bottom).From:
52 Measuring BRDF via RSNeed multi-angle observations. Can do three ways:multiple cameras on same platform (e.g. MISR, POLDER, POLDER 2). BUT quite complex technically.Broad swath with large overlap so multiple orbits build up multiple view angles e.g. MODIS, SPOT-VGT, AVHRR. BUT surface can change from day to day.Pointing capability e.g. CHRIS-PROBA, SPOT-HRV. BUT again technically difficult
53 AlbedoTotal irradiant energy (both direct and diffuse) reflected in all directions from the surface i.e. ratio of total outgoing to total incomingDefines lower boundary condition of surface energy budget hence v. imp. for climate studies - determines how much incident solar radiation is absorbedAlbedo is BRDF integrated over whole viewing/illumination hemisphereDefine directional hemispherical refl (DHR) - reflectance integrated over whole viewing hemisphere resulting from directional illuminationand bi-hemispherical reflectance (BHR) - integral of DHR with respect to hemispherical (diffuse) illuminationDHR =BHR =
54 Albedo Actual albedo lies somewhere between DHR and BHR Broadband albedo, , can be approximated aswhere p() is proportion of solar irradiance at ; and () is spectral albedoso p() is function of direct and diffuse components of solar radiation and so is dependent on atmospheric stateHence albedo NOT intrinsic surface property (although BRDF is)
56 Surface spectral information Causes of spectral variation in reflectance?(bio)chemical & structural propertiese.g. In vegetation, phytoplankton: chlorophyll concentrationsoil - minerals/ water/ organic matterCan consider spectral properties as continuouse.g. mapping leaf area index or canopy coveror discrete variablee.g. spectrum representative of cover type (classification)
61 SummaryLast weekIntroduction to EM radiation, the EM spectrum, properties of wave / particle model of EMRBlackbody radiation, Stefan-Boltmann Law, Wien’s Law and Planck functionThis weekradiation geometryinteraction of EMR with atmosphereatmospheric windowsinteraction of EMR with surface (BRDF, albedo)angular and spectral reflectance properties