Topics: Visible & Infrared Measurement Principal Radiation and the Planck Function Infrared Radiative Transfer Equation

Transcription

1 Review of Remote Sensing Fundamentals Allen Huang Cooperative Institute for Meteorological Satellite Studies Space Science & Engineering Center University of Wisconsin-Madison, USA Topics: Visible & Infrared Measurement Principal Radiation and the Planck Function Infrared Radiative Transfer Equation Selected Material Provided by Bill Smith, Paul Menzel, Paolo Antonelli, Steve Miller & Gerald van der Grijn 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 1

2 Earth System Energy Balance 2

3 Radiative Energy Balance 3

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

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 5

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. 6

7 The Electromagnetic (EM) Spectrum 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 7

8 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. 9

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

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

11 MODIS Reflected Solar Bands 12

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

13 Terminology of radiant energy Energy 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 The Planck function can be inverted to Brightness temperature 14

14 Terminology of radiant energy Energy (Joules) from the Earth Atmosphere over time is Flux (Joules/sec or W) 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 The Planck function can be inverted to Brightness temperature (K) 15

15 Definitions of Radiation QUANTITY SYMBOL UNITS Energy dq Joules Flux dq/dt Joules/sec = Watts Irradiance dq/dt/da Watts/meter 2 Monochromatic dq/dt/da/dλ W/m 2 /micron Irradiance or dq/dt/da/dν W/m 2 /cm -1 Radiance dq/dt/da/dλ/dω W/m 2 /micron/ster or dq/dt/da/dν/dω W/m 2 /cm -1 /ster 17

16 Radiation is governed by Planck s Law In wavelength: In wavenumber: B(λ,T) = c 1 /{ λ 5 [e c2 /λt -1] } (mw/m 2 /ster/cm) where λ = 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) B(ν,T) = c 1 ν 3 / [e c2ν/t -1] (mw/m 2 /ster/cm -1 ) where ν = # 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. 21

17 Using wavelengths Planck s Law where c 2 /λt B(λ,T) = c 1 / λ 5 / [e -1] (mw/m 2 /ster/cm) λ = 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(λ max,t) / dλ = 0 where λ(max) =.2897/T indicates peak of Planck function curve shifts to shorter wavelengths (greater wavenumbers) with temperature increase. Note B(λ max,t) ~ T 5. Stefan-Boltzmann Law E = π B(λ,T) dλ = σt 4, where σ = 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 / [λ ln( + 1)] is determined by inverting Planck function λ 5 B λ 22

18 Spectral Distribution of Energy Radiated from Blackbodies at Various Temperatures 23

19 24

20 Using wavenumbers Wien's Law db(ν max,t) / dt = 0 where ν(max) = 1.95T indicates peak of Planck function curve shifts to shorter wavelengths (greater wavenumbers) with temperature increase. Note B(ν max,t) ~ T**3. Stefan-Boltzmann Law E = π B(ν,T) dν = σt 4, where σ = 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 ν 3 T = c 2 ν/[ln( + 1)] is determined by inverting Planck function B ν Brightness temperature is uniquely related to radiance for a given wavelength by the Planck function. 25

21 26

22 B(λmax,T)~T 5 B(νmax,T)~T 3 Planck Radiances λ max (1/ ν max ) B(λ,T) B(λ,T) versus B(ν,T) mw/m2/ster/cm (cm-1) B(ν,T) wavenumber (in hundreds) wavelength [µm]

23 Using wavenumbers Using wavelengths c 2 ν/t c 2 /λt B(ν,T) = c 1 ν 3 / [e -1] B(λ,T) = c 1 /{ λ 5 [e -1] } (mw/m 2 /ster/cm -1 ) (mw/m 2 /ster/μm) ν(max in cm-1) = 1.95T B(ν max,t) ~ T**3. λ(max in cm) = /T B(λ max,t) ~ T**5. E = π B(ν,T) dν = σt 4, E = π B(λ,T) d λ = σt 4, o o c 1 ν 3 c 1 T = c 2 ν/[ln( + 1)] T = c 2 /[λ ln( + 1)] B ν λ 5 B λ Wavelength (µm) vs. Wavenumber (cm -1 ) 28

24 Energy conservation: τ + a + r = 1 =ε λ B λ (T s ) Reflected τ + a + r = 1 T Absorbed Transmitted R λ =(a λ +r λ +τ λ ) R λ τ + a + r = 1 29

25 Temperature sensitivity db/b = α dt/t The Temperature Sensitivity α is the percentage change in radiance corresponding to a percentage change in temperature Substituting the Planck Expression, the equation can be solved in α: α=c 2 ν/t 30

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

27 B=B ref (T/T ref ) α B=(B ref / T refα )T α B T α The temperature sensitivity indicates the power to which the Planck radiance depends on temperature, since B proportional to T α satisfies the equation. For infrared wavelengths, α = c 2 ν/t = c 2 /λt. Wavenumber Typical Scene Temperature Temperature Sensitivity

28 Temperature Sensitivity of B(λ,T) for typical earth scene temperatures B (λ, T) / B (λ, 273K) 4μm 2 6.7μm 10μm 15μm 1 microwave Temperature (K) 36

29 B(10 um,t) / B(10 um,273) T 4 B(10 um,273)= 6.1 B(10 um,200)= B(10 um,220)= B(10 um,240)= B(10 um,260)= B(10 um,280)= B(10 um,300)=

30 B(4 um,t) / B(4 um,273) T 12 B(4 um,273)= 2.2 x 10-1 B(4 um,200)= 1.8 x B(4 um,220)= 9.2 x B(4 um,240)= 3.6 x B(4 um,260)= 1.1 x B(4 um,280)= 3.0 x B(4 um,300)= 7.2 x

31 B(0.3 cm, T) / B(0.3 cm,273) T B(0.3 cm,273)= 2.55 x 10-4 B(0.3 cm,200)= B(0.3 cm,220)= B(0.3 cm,240)= B(0.3 cm,260)= B(0.3 cm,280)= B(0.3 cm,300)=

32 Reflection and Transmission of Plane-Parallel Layers F 0 τ = 0 transmission T(τ t ; µ, φ; µ 0, φ 0 ) reflection R(τ t ; µ, φ; µ 0, φ 0 ) τ = τ t R(τ a, ω 0 ; µ, µ 0, φ) = where πi(0, µ, φ) µ 0 F 0 µ = absolute value of the cosine of the zenith angle cosθ µ 0 = cosine of the solar zenith angle cosθ 0 φ = relative azimuth angle between the direction of propagation of the emerging radiation and the incident solar direction 41

33 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 43

34 Sensor Geometry Sensor Electronics Optics 44

35 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 45

36 Soil Vegetation Snow Ocean 46

37 Radiance observed In the Blue Band At 0.41 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 Before Atmospheric Correction Values Range [50 100] W/ster/cm 2 / µm After Atmospheric Correction Values Range between [0 25] W/ster/cm 2 / µm 49

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

39 Band micron Strong H

40 Only High Clouds Are Visible 53

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

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

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

44 MODIS Thermal Emissive Bands Primary Atmospheric Band Bandwidth 1 T typical Radiance 2 NEΔT (K) Application (K) at T typical Specification NEΔT (K) Predicted Surface Temperature Temperature profile Moisture profile Ozone Surface Temperature Temperature profile

45 MODIS Infrared Spectral Bands Short Wave IR Long Wave IR 58

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

47 AIRS (Atmospheric Infrared Sounder) & MODIS 60

48 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 61

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

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

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

52 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 65

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

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

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

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

57 Weighting Functions 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 72

58 73 Radiance measured by IR Sensor RTE (no scattering) in LTE sun s sun s sun p s s p S s s r p R p d p T B r p d p T B T B R s s ν ν ν ν ν ν ν ν ν ν ν ν ν τ θ τ τ τ ε τ + + = ) ( ) cos( ) ( )) ( ( ) ( )) ( ( ) ( 0 0 Upwelling IR radiation from surface Upwelling IR radiation from atm. layers Reflected downwelling IR radiation Reflected solar radiation R radiance, υ wavenumber, s surface, p pressure, sun solar, T temperature, B Planck function, ε emissivity, τ level to space transmittance, θ...local solar zenith angle r reflectivity, with r = (1- ε)/π, τ* level to surface (downwelling) transmittance [τ*= τ υ2 (p s )/ τ υ (p)]

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

60 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.. 75

61 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 76 color, land and ocean surface temperature