Principles of Remote Sensing: 2

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Principles of Remote Sensing 2

• Dr. Mathias (Mat) Disney
• UCL Geography
• Office 301, 3rd Floor, Chandler House
• Tel [phone] (x24290)
• Email mdisney_at_ucl.geog.ac.uk
• www.geog.ucl.ac.uk/mdisney

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EMR arriving at Earth

• We now know how EMR spectrum is distributed
• Radiant energy arriving at Earths 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 1.5x108m so total solar
  energy emitted 4?d2x1373 3.88x1026W
• Incidentally we can now calculate Tsun
  (radius6.69x108m) from SB Law
• ?T4sun 3.88x1026/4? r2 so T 5800K

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Departure from blackbody assumption

• Interaction with gases in the atmosphere
• attenuation of solar radiation

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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

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Radiation passing through media

• Various interactions, with different results

From http//rst.gsfc.nasa.gov/Intro/Part2_3html.ht
ml
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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 (or radiant exitance) (Wm-2) is
  radiant flux density emitted by a surface

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Radiation Geometry spatial relations

• Flux dF 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 dF/d? (Wsr-1)

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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.

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Radiation Geometry solid angle
From http//www.intl-light.com/handbook/ch07.html
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Radiation Geometry radiance
?
dF
?
Plane source dS
dS cos ?
Intensity dI dF/d? Radiance (dF/?) / dS cos ?
dI/dS cos ?

• Flux dF 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 dF/d? (Wsr-1)

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Radiation Geometry terms and units
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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 ?

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Radiation Geometry cosine law
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 ?

Adapted from Monteith and Unsworth, Principles of
Environmental Physics
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Radiation Geometry Lamberts 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 may need to specify
  directions of both incident AND reflected
  radiation, then reflectivity is described as
  bi-directional

Adapted from Monteith and Unsworth, Principles of
Environmental Physics
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Recap radiance

• Radiance, L
• power emitted (dF) 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 d2F / (dF 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.fr8100/cdrom-97/ceos1/s
cience/baphygb/chap2/chap2.htm
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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
• M ?L

Ad. From http//ceos.cnes.fr8100/cdrom-97/ceos1/s
cience/baphygb/chap2/chap2.htm
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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

Ad. From http//ceos.cnes.fr8100/cdrom-97/ceos1/s
cience/baphygb/chap2/chap2.htm
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Interactions with the atmosphere
From http//rst.gsfc.nasa.gov/Intro/Part2_4.html
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Interactions with the atmosphere

• 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/f
inal_version/final_pdf/chapter2a.pdf
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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 gt 1 i.e. cn lt c
• Examples
• nair 1.0002926
• nwater 1.33

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Refraction Snells Law

• Refraction described by Snells 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 Snells Law
  can be removed

After Jensen, J. (2000) Remote sensing of the
environment an Earth Resources Perspective.
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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/tuto
rials/fundam/chapter1/chapter1_4_e.html
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Atmospheric scattering 1 Rayleigh

• Particle size ltlt ? 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/sunse
  t/
• http//www.nws.noaa.gov/om/educ/activit/bluesky.ht
  m

After http//www.ccrs.nrcan.gc.ca/ccrs/learn/tuto
rials/fundam/chapter1/chapter1_4_e.html
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Atmospheric scattering 1 Rayleigh

• So, scattering ? ?-4 so scattering of blue light
  (400nm) gt scattering of red light (700nm) by
  (700/400)4 or 9.4

From http//hyperphysics.phy-astr.gsu.edu/hbase/at
mos/blusky.html
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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/tuto
rials/fundam/chapter1/chapter1_4_e.html
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Atmospheric scattering 3 Non-selective

• Particle size gtgt ? 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/tuto
rials/fundam/chapter1/chapter1_4_e.html
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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

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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....

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Atmospheric CO2 trends
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Atmospheric windows

• As a result of strong ? dependence of absorption
• Some ? totally unsuitable for remote sensing as
  most radiation absorbed

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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....

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Atmospheric windows

• Vivisble NIR part of the spectrum
• windows, roughly 400-750, 800-1000, 1150-1300,
  1500-1600, 2100-2250nm

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Summary

• Measured signal is a function of target
  reflectance
• plus atmospheric component (scattering,
  absorption)
• Need to choose appropriate regions (atmospheric
  windows)
• ?wave region largely transparent i.e. can see
  through clouds in this region
• one of THE major advantages of ?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

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Summary

• Generally, solar radiation reaching the surface
  composed of
• lt 75 direct and gt25 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

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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)

From http//www.ccrs.nrcan.gc.ca/ccrs/learn/tutori
als/fundam/chapter1/chapter1_5_e.html
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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
• Most surfaces have some level of anisotropy

From http//www.geog.ucl.ac.uk/mdisney/phd.bak/f
inal_version/final_pdf/chapter2a.pdf
38
Directional reflectance BRDF

• Reflectance of most real surfaces is a function
  of not only ?, 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.
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

From http//www.geog.ucl.ac.uk/mdisney/phd.bak/f
inal_version/final_pdf/chapter2a.pdf
40
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)

From http//www.geog.ucl.ac.uk/mdisney/phd.bak/f
inal_version/final_pdf/chapter2a.pdf
41
Directional Information
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Directional Information
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Features of BRDF

• Bowl shape
• increased scattering due to increased path length
  through canopy

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Features of BRDF

• Bowl shape
• increased scattering due to increased path length
  through canopy

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Features of BRDF

• Hot Spot
• mainly shadowing minimum
• so reflectance higher

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Directional reflectance BRDF

• Good explanation of BRDF
• http//geography.bu.edu/brdf/brdfexpl.html

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• Hotspot effect from MODIS image over Brazil

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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

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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

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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)

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Typical albedo values
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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)

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Surface spectral information vegetation
vegetation
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Surface spectral information vegetation
vegetation
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Surface spectral information soil
soil
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Surface spectral information canopy
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Summary

• Last week
• Introduction to EM radiation, the EM spectrum,
  properties of wave / particle model of EMR
• Blackbody radiation, Stefan-Boltmann Law, Wiens
  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