1 Review of Remote Sensing Fundamentals Allen Huang Cooperative Institute for Meteorological Satellite Studies Space Science & Engineering Center University of Wisconsin-Madison, USA MODIS direct broadcast data for enhanced forecasting and real-time environmental decision making IGARSS 2009 MODIS DB Short Course 7-10 July 2009, Cape Town, South Africa Selected Material Provided by Bill Smith, Paul Menzel, Paolo Antonelli, Steve Miller & Gerald van der Grijn Topics:  Visible & Infrared Measurement Principal  Radiation and the Planck Function  Infrared Radiative Transfer Equation

2 Earth System Energy Balance

3 Radiative Energy Balance

4 Visible & Near IR Infrared (IR) Remote Sensing of Natural Radiation (Reflective Bands)(Emissive Bands)

5 What do satellites actually measure ? They measure TEMPERATURE, HUMIDITY, WIND, TRACE GASES, CLOUDS, AEROSOLS, OTHERS…, indirectly! Instead, satellite observations are obtained using remote sensing techniques based on measurements of electromagnetic radiation

6 Electromagnetic Radiation Every object with a temperature larger than 0 K emits electromagnetic radiation. Electromagnetic radiation therefore extends over a wide range of energies and wavelengths. The distribution of all radiant energies can be plotted in a chart known as the electromagnetic spectrum.

7 Remote sensing uses radiant energy that is reflected and emitted from Earth at various “wavelengths” of the electromagnetic spectrum Our eyes are sensitive to the visible portion of the EM spectrum The Electromagnetic (EM) Spectrum

8 Electromagnetic Spectrum IR

9 Electromagnetic Radiation In the earth’s atmosphere, the radiation is partly to completely transmitted at some wavelengths; at others those photons are variably absorbed by interaction with air molecules. Blue zones mark minimal passage of incoming and/or outgoing radiation, whereas, white areas denote atmospheric windows in which the radiation doesn’t interact much with air molecules. Most remote sensing instruments operate in one of these windows by making their measurements tuned to specific frequencies that pass through the atmosphere. Some sensors, especially those on meteorological satellites, directly measure absorption phenomena.

10 UV, Visible and Near-IR Far-Infrared (IR) UV, Visible and Near-IR and IR and Far-IR Infrared (IR)

11 H2O O2 CO2 H2O O2 O3 H2O O2 MODIS Visible and Near-infrared Bands VisibleNear IR

12 MODIS Reflected Solar Bands

13 Units: Wavelength ( µm ) vs. Wavenumber ) ( cm -1 ) wavelength (µm) : distance between peaks wavenumber ( cm -1 ) : number of waves per unit distance =1/ d =-1/ 2 d Radiation is characterized by wavelength and amplitude a (µm) = 10,000 / (cm -1 )

14 Terminology of radiant energy Energy from the Earth Atmosphere Flux over time is which strikes the detector area Irradiance at a given wavelength interval Monochromatic Irradiance over a solid angle on the Earth Radiance observed by satellite radiometer is described by can be inverted to The Planck function Brightness temperature

15 Terminology of radiant energy Energy (Joules) from the Earth Atmosphere Flux (Joules/sec or W) over time is which strikes the detector area Irradiance (W/m 2 ) at a given wavelength interval Monochromatic Irradiance (W/m2/micrometer) over a solid angle on the Earth Radiance (W/m2/micromenter/ster) observed by satellite radiometer is described by can be inverted to The Planck function Brightness temperature (K)

16 Terminology of radiant energy Energy (Joules) from the Earth Atmosphere over time is Flux which strikes the detector area Irradiance at a given wavelength interval Monochromatic Irradiance over a solid angle on the Earth Radiance observed by satellite radiometer is described by can be inverted to The Planck function Brightness temperature

17 Definitions of Radiation __________________________________________________________________ QUANTITYSYMBOLUNITS __________________________________________________________________ EnergydQJoules FluxdQ/dtJoules/sec = Watts IrradiancedQ/dt/dAWatts/meter 2 MonochromaticdQ/dt/dA/d W/m 2 /micron Irradiance or dQ/dt/dA/d W/m 2 /cm -1 RadiancedQ/dt/dA/d /d  W/m 2 /micron/ster or dQ/dt/dA/d /d  W/m 2 /cm -1 /ster __________________________________________________________________

18 Radiation from the Sun The rate of energy transfer by electromagnetic radiation is called the radiant flux, which has units of energy per unit time. It is denoted by F = dQ / dt and is measured in joules per second or watts. For example, the radiant flux from the sun is about 3.90 x 10**26 W. The radiant flux per unit area is called the irradiance (or radiant flux density in some texts). It is denoted by E = dQ / dt / dA and is measured in watts per square metre. The irradiance of electromagnetic radiation passing through the outermost limits of the visible disk of the sun (which has an approximate radius of 7 x 10**8 m) is given by 3.90 x E (sun sfc) = = 6.34 x 10 7 W m  (7 x 10 8 ) 2

19 The solar irradiance arriving at the earth can be calculated by realizing that the flux is a constant, therefore E (earth sfc) x 4πR es 2 = E (sun sfc) x 4πR s 2, where R es is the mean earth to sun distance (roughly 1.5 x m) and R s is the solar radius. This yields E (earth sfc) = 6.34 x 10 7 (7 x 10 8 / 1.5 x ) 2 = 1380 W m -2. The irradiance per unit wavelength interval at wavelength λ is called the monochromatic irradiance, E λ = dQ / dt / dA / dλ, and has the units of watts per square metre per micrometer. With this definition, the irradiance is readily seen to be  E =  E λ dλ. o

20 In general, the irradiance upon an element of surface area may consist of contributions which come from an infinity of different directions. It is sometimes necessary to identify the part of the irradiance that is coming from directions within some specified infinitesimal arc of solid angle dΩ. The irradiance per unit solid angle is called the radiance, I = dQ / dt / dA / dλ / dΩ, and is expressed in watts per square metre per micrometer per steradian. This quantity is often also referred to as intensity and denoted by the letter B (when referring to the Planck function). If the zenith angle, θ, is the angle between the direction of the radiation and the normal to the surface, then the component of the radiance normal to the surface is then given by I cos θ. The irradiance represents the combined effects of the normal component of the radiation coming from the whole hemisphere; that is, E =  I cos θ dΩ where in spherical coordinates dΩ = sin θ dθ dφ. Ω Radiation whose radiance is independent of direction is called isotropic radiation. In this case, the integration over dΩ can be readily shown to be equal to  so that E =  I.

21 Radiation is governed by Planck’s Law In wavelength: B(,T) = c 1 /{ 5 [e c2 / T -1] } (mW/m 2 /ster/cm) where = wavelength (cm) T = temperature of emitting surface (deg K) c 1 = x 10-8 (W/m 2 /ster/cm -4 ) c 2 = (cm deg K) In wavenumber: B(,T) = c 1 3 / [e c2 /T -1] (mW/m 2 /ster/cm -1 ) where = # wavelengths in one centimeter (cm-1) T = temperature of emitting surface (deg K) c 1 = x 10-5 (mW/m 2 /ster/cm -4 ) c 2 = (cm deg K) Brightness temperature is uniquely related to radiance for a given wavelength by the Planck function.

22 Using wavelengths c 2 / T Planck’s Law B(,T) = c 1 / 5 / [e -1] (mW/m 2 /ster/cm) where = wavelengths in cm T = temperature of emitting surface (deg K) c 1 = x 10-5 (mW/m 2 /ster/cm -4 ) c 2 = (cm deg K) Wien's Law dB( max,T) / d = 0 where (max) =.2897/T indicates peak of Planck function curve shifts to shorter wavelengths (greater wavenumbers) with temperature increase. Note B( max,T) ~ T 5.  Stefan-Boltzmann Law E =   B(,T) d =  T 4, where  = 5.67 x 10-8 W/m2/deg4. o states that irradiance of a black body (area under Planck curve) is proportional to T 4. Brightness Temperature c 1 T = c 2 / [ ln( _____ + 1)] is determined by inverting Planck function 5 B

23 Spectral Distribution of Energy Radiated from Blackbodies at Various Temperatures

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25 Using wavenumbers Wien's Law dB( max,T) / dT = 0 where (max) = 1.95T indicates peak of Planck function curve shifts to shorter wavelengths (greater wavenumbers) with temperature increase. Note B( max,T) ~ T**3.  Stefan-Boltzmann Law E =   B(,T) d =  T 4, where  = 5.67 x 10-8 W/m 2 /deg 4. o states that irradiance of a black body (area under Planck curve) is proportional to T 4. Brightness Temperature c 1 3 T = c 2 /[ln( ______ + 1)] is determined by inverting Planck function B Brightness temperature is uniquely related to radiance for a given wavelength by the Planck function.

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27 B( max,T)~T 5 B( max,T)~T 3 B(,T) B(,T) versus B(,T) wavelength [µm] max ≠(1/ max )

28 Using wavenumbersUsing wavelengths c 2 /T c 2 / T B(,T) = c 1 3 / [e -1]B(,T) = c 1 /{ 5 [e -1] } (mW/m 2 /ster/cm -1 )(mW/m 2 /ster/  m) (max in cm-1) = 1.95T (max in cm) = /T B( max,T) ~ T**3. B( max,T) ~ T**5.  E =   B(,T) d =  T 4, o c 1 3 c 1 T = c 2 /[ln( ______ + 1)] T = c 2 /[ ln( ______ + 1)] B 5 B Wavelength ( µm ) vs. Wavenumber ( cm -1 )

29  + a + r = 1 Energy conservation: =  B (T s ) T R =(a +r +  ) R Reflected Absorbed Transmitted  + a + r = 1

30 Temperature sensitivity dB/B =  dT/T The Temperature Sensitivity  is the percentage change in radiance corresponding to a percentage change in temperature Substituting the Planck Expression, the equation can be solved in  :  =c 2 /T

31 ∆B 11 ∆B 4 ∆B 11 > ∆B 4 T=300 K T ref =220 K

32 ∆B 11 /B 11 =  11 ∆T/T ∆B 4 /B 4 =  4 ∆T/T ∆B 4 /B 4 >∆B 11 /B 11   4 >  11 (values in plot are referred to wavelength)

33 ∆B/B=  ∆T/T Integrating the Temperature Sensitivity Equation Between T ref and T (B ref and B): B=B ref (T/T ref )  Where  =c 2 /T ref (in wavenumber space) (Approximation of) B as function of  and T

34 B=B ref (T/T ref )   B=(B ref / T ref  ) T   B  T  The temperature sensitivity indicates the power to which the Planck radiance depends on temperature, since B proportional to T  satisfies the equation. For infrared wavelengths,  = c 2 /T = c 2 / T. __________________________________________________________________ Wavenumber Typical Scene Temperature Temperature Sensitivity

35 Temperature sensitivity, or the percentage change in radiance corresponding to a percentage change in temperature, , is defined as dB/B =  dT/T. The temperature sensivity indicates the power to which the Planck radiance depends on temperature, since B proportional to T  satisfies the equation. For infrared wavelengths,  = c 2 /T = c 2 / T. __________________________________________________________________ Wavenumber Typical Scene Temperature Temperature Sensitivity

B (λ, T) / B (λ, 273K) Temperature (K) 4μm4μm 6.7μm 10μm 15μm microwave Temperature Sensitivity of B(λ,T) for typical earth scene temperatures

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38 B(10 um,T) / B(10 um,273)  T 4 B(10 um,273)= 6.1 B(10 um,200)= 0.9  0.15 B(10 um,220)= 1.7  0.28 B(10 um,240)= 3.0  0.49 B(10 um,260)= 4.7  0.77 B(10 um,280)= 7.0  1.15 B(10 um,300)= 9.9 

39 B(4 um,T) / B(4 um,273)  T 12 B(4 um,273)= 2.2 x B(4 um,200)= 1.8 x  0.0 B(4 um,220)= 9.2 x  0.0 B(4 um,240)= 3.6 x  0.2 B(4 um,260)= 1.1 x  0.5 B(4 um,280)= 3.0 x  1.4 B(4 um,300)= 7.2 x 

40 B(0.3 cm, T) / B(0.3 cm,273)  T B(0.3 cm,273)= 2.55 x B(0.3 cm,200)= 1.8  0.7 B(0.3 cm,220)= 2.0  0.78 B(0.3 cm,240)= 2.2  0.86 B(0.3 cm,260)= 2.4  0.94 B(0.3 cm,280)= 2.6  1.02 B(0.3 cm,300)= 2.8 

41 Reflection and Transmission of Plane-Parallel Layers  = 0  =  t R  t ; µ,  ; µ 0  0  F0F0 T  t ; µ,  ; µ 0  0  reflection transmission R(  a,  0 ; µ, µ 0,  ) = where µ=absolute value of the cosine of the zenith angle |cos  | µ 0 =cosine of the solar zenith angle cos  0  =relative azimuth angle between the direction of propagation of the emerging radiation and the incident solar direction  I(0, –µ,  ) µ0F0µ0F0

42 Reflectance Ratio Test Basis Based on our knowledge of reflectance spectra, we can predict: cloud R2/R1 = 1.0 for cloud (if you can’t see the surface underneath) R2/R1 > 1.0 for vegetation ( look at pinewoods spectra) R2/R1 << 1.0 for water R2/R1 about 1 for desert R1R2 Glint is a big limiting factor To this test over oceans. Also, smoke or dust can look Like cloud in R2/R1.

43 Visible: Reflective Bands Used to observe solar energy reflected by the Earth system in the: Visible between 0.4 and 0.7 µm NIR between 0.7 and 3 µm About 99% of the energy observed between 0 and 4 µm is solar reflected energy Only 1% is observed above 4 µm

44 Sensor Geometry Sensor Optics Electronics

45 Reflectance To properly compare different reflective channels we need to convert observed radiance into a target physical property In the visible and near infrared this is done through the ratio of the observed radiance divided by the incoming energy at the top of the atmosphere The physical quantity is the Reflectance i.e. the fraction of solar energy reflected by the observed target

46 Soil Vegetation Snow Ocean

47 Reflectances On Same Color Scale

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49 Before Atmospheric Correction Values Range [50 100] W/ster/cm 2 / µm Radiance observed In the Blue Band At 0.41 µm After Atmospheric Correction Values Range between [0 25] W/ster/cm 2 / µm More than 75% of the Observed energy Over Ocean In the blue bands Is due to atmospheric Scattering. Less than 25% is due to Water Leaving Energy

50 Band 4 (0.56 Micron) Band 1 Band 4 Band 3 snow clouds sea desert Transects of Reflectance

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52 Band micron Strong H 2 0

53 Only High Clouds Are Visible

54 Ocean: Dark Vegetated Surface: Dark Clouds: Bright NonVegetated Surface: Brighter Snow: Bright Sunglint

55 Ocean: Dark Vegetated Surface: Dark Clouds: Bright NonVegetated Surface: Brighter Snow: Bright Sunglint

56 Ocean: Dark Vegetated Surface: Dark Clouds: Bright NonVegetated Surface: Brighter Snow: Bright Sunglint

57 MODIS Thermal Emissive Bands

58 MODIS Infrared Spectral Bands Short Wave IRLong Wave IR

59 AIRS (Atmospheric Infrared Sounder) & MODIS – IR only

60 AIRS (Atmospheric Infrared Sounder) & MODIS

61 Emissive Bands Used to observe terrestrial energy emitted by the Earth system in the IR between 4 and 15 µm About 99% of the energy observed in this range is emitted by the Earth Only 1% is observed below 4 µm At 4 µm the solar reflected energy can significantly affect the observations of the Earth emitted energy

62 Spectral Characteristics of Energy Sources and Sensing Systems IR 4 µm 11 µm

63 Observed Radiance at 4 micron Range [ ] Values over land Larger than over water Reflected Solar everywhere Stronger over Sunglint Window Channel: little atmospheric absorption surface features clearly visible

64 Observed Radiance at 11 micron Range [2 13] Values over land Larger than over water Undetectable Reflected Solar Even over Sunglint Window Channel: little atmospheric absorption surface features clearly visible

65 Brightness Temperature To properly compare different emissive channels we need to convert observed radiance into a target physical property In the Infrared this is done through the Planck function The physical quantity is the Brightness Temperature i.e. the Temperature of a black body emitting the observed radiance

66 Observed BT at 4 micron Range [ ] Values over land Larger than over water Reflected Solar everywhere Stronger over Sunglint Window Channel: little atmospheric absorption surface features clearly visible Clouds are cold

67 Observed BT at 11 micron Range [ ] Values over land Larger than over water Undetectable Reflected Solar Even over Sunglint Window Channel: little atmospheric absorption surface features clearly visible Clouds are cold

68 AIRS (Atmospheric Infrared Sounder) & MODIS – IR only

69 A lot of radiation is emitted from the dense lower atmosphere, but very little survives to the top of the atmosphere due to absorption. At some level there is an optimal balance between the amount of radiation emitted and the amount reaching the top of the atmosphere. High in the atmosphere very little radiation is emitted, but most will reach the top of the atmosphere. K(z) z Real atmospheric weighting functions

70 MODIS IR Bands Profile Sensitivity - Temperature

71 MODIS IR Bands Profile Sensitivity – Water Vapor

72 Longwave CO CO2, strat temp CO2, strat temp CO2, upper trop temp CO2, mid trop temp CO2, lower trop temp H2O, lower trop moisture H2O, dirty window Midwave H2O & O window O3, strat ozone H2O, lower mid trop moisture H2O, mid trop moisture H2O, upper trop moisture Weighting Functions

73 Radiance measured by IR Sensor RTE (no scattering) in LTE  Upwelling IR radiation from surface  Upwelling IR radiation from atm. layers  Reflected downwelling IR radiation  Reflected solar radiation R…radiance,  …wavenumber, s…surface, p…pressure, sun…solar, T…temperature, B…Planck function,  …emissivity,  …level to space transmittance, ...local solar zenith angle r…reflectivity, with r = (1-  )/ ,  *…level to surface (downwelling) transmittance [  *=   2 (p s )/   (p)]

74 Solar Effects (Day Vs. Night) on Infrared Measurements

75 Radiative Transfer Equation Summary Radiative Transfer Equation in Infrared: models the propagation of terrestrial emitted energy through the atmosphere by absorption, scattering, emission and reflection of gases, clouds, suspended particles, and surface. The modeled radiances can be converted to brightness temperature and inverted to obtain atmospheric variables such as profile of temperature and water vapor profiles and clouds (height, fraction, optical thickness, size), aerosol/dust, surface temperature, and surface types etc…..

76 Summary Radiance is the Energy Flux (emitted and/or reflected by the Earth) which strikes the Detector Area at a given Spectral Wavelength (wavenumber) over a Solid Angle on the Earth; Reflectance is the fraction of solar energy reflected to space by the target; Given an observed radiance, the Brightness Temperature is the temperature, in Kelvin, of a blackbody that emits the observed radiance; Knowing the spectral reflective (Vis) and emissive (IR) properties (spectral signatures) of different targets it is possible to detect: clouds, cloud properties, vegetation, fires, ice and snow, ocean color, land and ocean surface temperature ……