GEOGG141/ GEOG3051
Principles & Practice of Remote Sensing
EM Radiation (ii)
Dr. Mathias (Mat) Disney
UCL Geography
Office: 113, Pearson Building
Tel: 7679 0592
Email: mdisney@ucl.geog.ac.uk
http://www2.geog.ucl.ac.uk/~mdisney/teaching/GEOGG141/GEOGG141.html
http://www2.geog.ucl.ac.uk/~mdisney/teaching/3051/GEOG3051.html
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
2
Departure from blackbody assumption
• Interaction with gases in the atmosphere
– attenuation of solar radiation
3
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
Radiation passing through media
•Various interactions, with different results
From http://rst.gsfc.nasa.gov/Intro/Part2_3html.html
5
Radiation Geometry: spatial relations
•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 http://www2.geog.ucl.ac.uk/~mdisney/teaching/PPRS/papers/schaepman_et_al.pdf
6
Radiation Geometry: point source
Point source
dϕ
d
dA
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)
7
Radiation Geometry: plane source


Plane source dS
dϕ
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)
8
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 4 steradians at its centre.
9
Radiation Geometry: solid angle
•Cone of solid angle  = 1sr
from sphere
•Radiant intensity
• = area of surface A / radius2
From http://www.intl-light.com/handbook/ch07.html
10
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 = 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 
11
Radiation Geometry: cosine law
X
Radiometer
dA
Y X
Radiometer

Y
•Case 1: radiometer ‘sees’ dA, flux proportional to dA
dA/cos 
•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
12
Radiation Geometry: Lambert’s cosine law
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.
Observed intensity (W/cm2·sr)) for a normal and offnormal 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.
•Radiant intensity observed from a ideal diffusely reflecting surface
(Lambertian surface) surface directly proportional to cosine of angle between
view angle and surface normal
http://en.wikipedia.org/wiki/Lambert's_cosine_law
13
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-directional
Adapted from Monteith and Unsworth, Principles of Environmental Physics
14
Recap: radiance
•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)
d

Projected surface dS cos 
• 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 http://ceos.cnes.fr:8100/cdrom-97/ceos1/science/baphygb/chap2/chap2.htm
15
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  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
ò
p 2
0
Lcosydw = 2pL ò
p 2
0
cosy sinydy = pL
16
Ad. From http://ceos.cnes.fr:8100/cdrom-97/ceos1/science/baphygb/chap2/chap2.htm
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)
Direct
•Emittance, M, hemispheric
•Why??
•Solar radiation scattered by
atmosphere
Diffuse
•So we have direct AND diffuse
components
Ad. From http://ceos.cnes.fr:8100/cdrom-97/ceos1/science/baphygb/chap2/chap2.htm
17
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
18
Interactions with the atmosphere
From http://rst.gsfc.nasa.gov/Intro/Part2_4.html
19
Interactions with the atmosphere
R4
R1
R2
target
target
R3
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
From: http://www.geog.ucl.ac.uk/~mdisney/phd.bak/final_version/final_pdf/chapter2a.pdf
20
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 = 1.0002926
•nwater = 1.33
21
Refraction: Snell’s Law
•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
Incident
radiation
Optically
less dense
n2
1
n1
Optically
more
2
dense
Optically
less dense
n3
3
Path
unaffected
by
atmosphere
Path affected by
atmosphere
22
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: http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/fundam/chapter1/chapter1_4_e.html
23
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
•http://www.spc.noaa.gov/publications/corfidi/sunset/
•http://www.nws.noaa.gov/om/educ/activit/bluesky.htm
24
After: http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/fundam/chapter1/chapter1_4_e.html
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
25
From http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html
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: http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/fundam/chapter1/chapter1_4_e.html
26
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: http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/fundam/chapter1/chapter1_4_e.html
27
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
28
Atmospheric absorption
•CO2 as a “greenhouse” gas
•strong absorber in longer (thermal) part of EM
spectrum
•i.e. 10-12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....
29
Atmospheric CO2 trends
•Antarctic ice core
records
•Keeling et al.
•Annual variation + trend
•Smoking gun for anthropogenic
change, or natural variation??
30
Atmospheric “windows”
Atmospheric
windows
•As a result of strong  dependence of absorption
•Some  totally unsuitable for remote sensing as most
radiation absorbed
31
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....
32
Atmospheric “windows”
• Vivisble + NIR part of the spectrum
– windows, roughly: 400-750, 800-1000, 1150-1300, 1500-1600, 2100-2250nm
33
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
34
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
35
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
36
From http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/fundam/chapter1/chapter1_5_e.html
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.
37
Reflectance: angular distribution
•Real surfaces usually
display some degree of
reflectance ANISOTROPY
•Lambertian surface is
isotropic by definition
(a)
(b)
(c)
(d)
•Most surfaces have some
level of anisotropy
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).
38
From: http://www.geog.ucl.ac.uk/~mdisney/phd.bak/final_version/final_pdf/chapter2a.pdf
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.
BRDF (Ω, Ω' ) 

dLe (Ω, Ω' )
sr 1
dEi (Ω' )

• 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.
39
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
viewer
exitant solid
angle 
incident solid
angle 
incident
diffuse
radiation
direct irradiance
(Ei) vector 
v
i
2-v
surface tangent
vector
i
surface area A
Configuration of viewing and illumination vectors in the viewing
hemisphere, with respect to an element of surface area, A.
40
From: http://www.geog.ucl.ac.uk/~mdisney/phd.bak/final_version/final_pdf/chapter2a.pdf
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).
41
From: http://www.geog.ucl.ac.uk/~mdisney/phd.bak/final_version/final_pdf/chapter2a.pdf
Directional Information
42
Directional Information
43
Features of BRDF
• Bowl shape
– increased scattering due
to increased path length
through canopy
44
Features of BRDF
• Bowl shape
– increased scattering due
to increased path length
through canopy
45
46
Features of BRDF
• Hot Spot
– mainly shadowing
minimum
– so reflectance higher
47
The “hotspot”
See http://www.ncaveo.ac.uk/test_sites/harwood_forest/
48
49
Directional reflectance: BRDF
•Good explanation of BRDF:
•http://geography.bu.edu/brdf/brdfexpl.html
50
•Hotspot effect
from MODIS
image over Brazil
51
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
52
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 =  Ω; 2  
1

2
2
BRDF Ω, ΩdΩ
BHR =  2 ;2     ΩdΩ 
1

2
2
  BRDF Ω, ΩdΩdΩ
53
Albedo
•Actual albedo lies somewhere between DHR and BHR
•Broadband albedo, , can be approximated as

 p   d
SW
• 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)
54
Typical albedo values
55
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)
56
Surface spectral information: vegetation
57
vegetation
Surface spectral information: vegetation
58
vegetation
Surface spectral information: soil
59
soil
Surface spectral information: canopy
60
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
61