# Dr. Mathias (Mat) Disney UCL Geography Office: 113, Pearson Building

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GEOGG141/ GEOG3051 Principles & Practice of Remote Sensing EM Radiation (ii)
Dr. Mathias (Mat) Disney UCL Geography Office: 113, Pearson Building Tel:

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 = 4r2x1373 = 3.88x1026W Incidentally we can now calculate Tsun (radius=6.69x108m) from SB Law T4sun = 3.88x1026/4 r2 so T = ~5800K

Departure from blackbody assumption
Interaction with gases in the atmosphere attenuation of solar radiation

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

Various interactions, with different results From

Definitions of radiometric quantities For parallel beam, flux density defined in terms of plane perpendicular to beam. What about from a point? Schaepman-Strub et al. (2006) see

dA Point source r Consider flux dϕ emitted from point source into solid angle d, where dF and d very small Intensity I defined as flux per unit solid angle i.e. I = dϕ/d (Wsr-1) Solid angle d = dA/r2 (steradians, sr)

Plane source dS dS 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 normal Radiant 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)

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 4 steradians at its centre.

Cone of solid angle  = 1sr from sphere  = area of surface A / radius2 Radiant intensity From

Emission and absorption Radiance 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 viewed So intensity of radiation from point on surface, and areal element of surface MUST be independent of , angle to surface normal OTOH flux per unit solid angle divided by true area of surface must be proportional to cos 

X Radiometer dA Y X Radiometer Y dA/cos  Case 1: radiometer ‘sees’ dA, flux proportional to dA Case 2: radiometer ‘sees’ dA/cos  (larger) BUT T same, so emittance of surface same and hence radiometer measures same So 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 Law Adapted from Monteith and Unsworth, Principles of Environmental Physics

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

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-directional Adapted from Monteith and Unsworth, Principles of Environmental Physics

Recap: radiance Radiance, L L = d2ϕ / (d dS cos ) (in Wm-2sr-1)
Projected surface dS cos  Radiance, L power 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

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 surface Remember L = d2ϕ / (d dS cos ) = constant, so M = dϕ/dS = M = L Ad. From

Recap: irradiance Radiance, 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, hemispheric Why?? Solar radiation scattered by atmosphere So we have direct AND diffuse components Direct Diffuse Ad. From

Reflectance Spectral 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

Interactions with the atmosphere
From

Interactions with the atmosphere
1 target R 4 target R 2 target R 3 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 From:

Interactions with the atmosphere: refraction
Caused by atmosphere at different T having different density, hence refraction path of radiation alters (different velocity) Towards normal moving from lower to higher density Away from normal moving from higher to lower density 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 = nwater = 1.33

Refraction: Snell’s Law
Optically less dense Optically more dense Incident radiation  2  3  1 Path affected by atmosphere Path unaffected by atmosphere Refraction described by Snell’s Law For given freq. f, n1 sin 1 = n2 sin 2 where 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 removed After: Jensen, J. (2000) Remote sensing of the environment: an Earth Resources Perspective.

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:  of radiation abundance of particles or gases distance the radiation travels through the atmosphere (path length) After:

Atmospheric scattering 1: Rayleigh
Particle size <<  of radiation e.g. very fine soot and dust or N2, O2 molecules Rayleigh 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 red Even more so if dust in upper atmosphere After:

Atmospheric scattering 1: Rayleigh
So, scattering  -4 so scattering of blue light (400nm) > scattering of red light (700nm) by (700/400)4 or ~ 9.4 From

Atmospheric scattering 2: Mie
Particle size   of radiation e.g. dust, pollen, smoke and water vapour Affects longer  than Rayleigh, BUT weak dependence on  Mostly in the lower portions of the atmosphere larger particles are more abundant dominates when cloud conditions are overcast i.e. large amount of water vapour (mist, cloud, fog) results in almost totally diffuse illumination After:

Atmospheric scattering 3: Non-selective
Particle size >>  of radiation e.g. Water droplets and larger dust particles, All  affected about equally (hence name!) Hence results in fog, mist, clouds etc. appearing white white = equal scattering of red, green and blue  s After:

Atmospheric absorption
Other major interaction with signal Gaseous molecules in atmosphere can absorb photons at various  depends on vibrational modes of molecules Very dependent on  Main components are: CO2, water vapour and ozone (O3) Also CH4 .... O3 absorbs shorter  i.e. protects us from UV radiation

Atmospheric absorption
CO2 as a “greenhouse” gas strong absorber in longer (thermal) part of EM spectrum i.e m where Earth radiates Remember peak of Planck function for T = 300K So shortwave solar energy (UV, vis, SW and NIR) is absorbed at surface and re-radiates in thermal CO2 absorbs re-radiated energy and keeps warm \$64M question! Does increasing CO2  increasing T?? Anthropogenic global warming?? Aside....

Atmospheric CO2 trends Antarctic ice core records Keeling et al.
Annual variation + trend Smoking gun for anthropogenic change, or natural variation?? Antarctic ice core records

Atmospheric “windows”
As a result of strong  dependence of absorption Some  totally unsuitable for remote sensing as most radiation absorbed

Atmospheric “windows”
If you want to look at surface Look in atmospheric windows where transmissions high If you want to look at atmosphere however....pick gaps Very important when selecting instrument channels Note atmosphere nearly transparent in wave i.e. can see through clouds! V. Important consideration....

Atmospheric “windows”
Vivisble + NIR part of the spectrum windows, roughly: , , , , nm

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 region one of THE major advantages of μ-wave remote sensing Top-of-atmosphere (TOA) signal is NOT target signal To isolate target signal need to... Remove/correct for effects of atmosphere A major part component of RS pre-processing chain Atmospheric models, ground observations, multiple views of surface through different path lengths and/or combinations of above

Summary Generally, solar radiation reaching the surface composed of
<= 75% direct and >=25 % diffuse attentuation even in clearest possible conditions minimum loss of 25% due to molecular scattering and absorption about equally Normally, aerosols responsible for significant increase in attenuation over 25% HENCE ratio of diffuse to total also changes AND spectral composition changes

Natural surfaces somewhere in between
Reflectance When EMR hits target (surface) Range of surface reflectance behaviour perfect specular (mirror-like) - incidence angle = exitance angle perfectly diffuse (Lambertian) - same reflectance in all directions independent of illumination angle) Natural surfaces somewhere in between From

Surface energy budget Total amount of radiant flux per wavelength incident on surface, () Wm-1 is summation of: reflected r, transmitted t, and absorbed, a i.e. () = r + t + a So need to know about surface reflectance, transmittance and absorptance Measured RS signal is combination of all 3 components After: Jensen, J. (2000) Remote sensing of the environment: an Earth Resources Perspective.

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 ANISOTROPY Lambertian surface is isotropic by definition Most surfaces have some level of anisotropy From:

Directional reflectance: BRDF
Reflectance of most real surfaces is a function of not only λ, but viewing and illumination angles Described 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 angles So in sun-sensor example,  is position of sensor and ’ is position of sun After: Jensen, J. (2000) Remote sensing of the environment: an Earth Resources Perspective.

Directional reflectance: BRDF
Note that BRDF defined over infinitesimally small solid angles , ’ and  interval, so cannot measure directly In practice measure over some finite angle and  and assume valid surface area A surface tangent vector i 2-v v i incident solid angle  incident diffuse radiation direct irradiance (Ei) vector  exitant solid angle  viewer Configuration of viewing and illumination vectors in the viewing hemisphere, with respect to an element of surface area, A. From:

Directional reflectance: BRDF
Spectral behaviour depends on illuminated/viewed amounts of material Change view/illum. angles, change these proportions so change reflectance Information 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:

Directional Information

Directional Information

Features of BRDF Bowl shape
increased scattering due to increased path length through canopy

Features of BRDF Bowl shape
increased scattering due to increased path length through canopy

Features of BRDF Hot Spot mainly shadowing minimum
so reflectance higher

The “hotspot” See

Directional reflectance: BRDF
Good explanation of BRDF:

Hotspot effect from MODIS image over Brazil

Measuring BRDF via RS Need 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

Albedo Total irradiant energy (both direct and diffuse) reflected in all directions from the surface i.e. ratio of total outgoing to total incoming Defines lower boundary condition of surface energy budget hence v. imp. for climate studies - determines how much incident solar radiation is absorbed Albedo is BRDF integrated over whole viewing/illumination hemisphere Define directional hemispherical refl (DHR) - reflectance integrated over whole viewing hemisphere resulting from directional illumination and bi-hemispherical reflectance (BHR) - integral of DHR with respect to hemispherical (diffuse) illumination DHR = BHR =

Albedo Actual albedo lies somewhere between DHR and BHR
Broadband albedo, , can be approximated as where p() is proportion of solar irradiance at ; and () is spectral albedo so p() is function of direct and diffuse components of solar radiation and so is dependent on atmospheric state Hence albedo NOT intrinsic surface property (although BRDF is)

Typical albedo values

Surface spectral information
Causes of spectral variation in reflectance? (bio)chemical & structural properties e.g. In vegetation, phytoplankton: chlorophyll concentration soil - minerals/ water/ organic matter Can consider spectral properties as continuous e.g. mapping leaf area index or canopy cover or discrete variable e.g. spectrum representative of cover type (classification)

Surface spectral information: vegetation

Surface spectral information: vegetation

Surface spectral information: soil

Surface spectral information: canopy

Summary Last week Introduction to EM radiation, the EM spectrum, properties of wave / particle model of EMR Blackbody radiation, Stefan-Boltmann Law, Wien’s Law and Planck function This week radiation geometry interaction of EMR with atmosphere atmospheric windows interaction of EMR with surface (BRDF, albedo) angular and spectral reflectance properties

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