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Quick Review of Remote Sensing Basic Theory Paolo Antonelli CIMSS University of Wisconsin-Madison South Africa, April 2006

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Outline Visible and Near Infrared: Vegetation Planck Function Infrared: Thermal Sensitivity

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Visible (Reflective Bands) Infrared (Emissive Bands)

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MODIS BAND 1 (RED) Low reflectance in Vegetated areas Higher reflectance in Non-vegetated land areas

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MODIS BAND 2 (NIR) Higher reflectance in Vegetated areas Lower reflectance in Non-vegetated land areas

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RED NIR Dense Vegetation Barren Soil

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NIR (.86 micron) Green (.55 micron) Red (0.67 micron) RGB NIR Ocean NIR and VIS over Vegetation and Ocean Vegetation

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Visible (Reflective Bands) Infrared (Emissive Bands)

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Spectral Characteristics of Energy Sources and Sensing Systems IR NIR

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Spectral Distribution of Energy Radiated from Blackbodies at Various Temperatures

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Radiation is governed by Planck’s Law In wavelenght: 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 = 1.191044 x 10-8 (W/m 2 /ster/cm -4 ) c 2 = 1.438769 (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 = 1.191044 x 10-5 (mW/m 2 /ster/cm -4 ) c 2 = 1.438769 (cm deg K)

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B( max,T)~T 5 B( max,T)~T 3 B(,T) B(,T) versus B(,T) 2010543.36.6100 wavelength [µm] max ≠(1/ max )

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wavelength : distance between peaks (µm) Slide 4 wavenumber : number of waves per unit distance (cm) =1/ d =-1/ 2 d

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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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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/cm) (max in cm-1) = 1.95T (max in cm)T = 0.2897 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

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Planck Function and MODIS Bands MODIS

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MODIS BAND 20 Window Channel: little atmospheric absorption surface features clearly visible Clouds are cold

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MODIS BAND 31 Window Channel: little atmospheric absorption surface features clearly visible Clouds are cold

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Clouds at 11 µm look bigger than at 4 µm

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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

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

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∆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)

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∆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 (in wavenumber space) (Approximation of) B as function of and T

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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 900300 4.32 250030011.99

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Non-Homogeneous FOV N 1-N T cold =220 K T hot =300 K B=NB(T hot )+(1-N)B(T cold ) BT =N BT hot +(1-N)BT cold

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For NON-UNIFORM FOVs: B obs =NB cold +(1-N)B hot B obs =N B ref (T cold /T ref ) + (1-N) B ref (T hot /T ref ) B obs = B ref (1/T ref ) (N T cold + (1-N)T hot ) For N=.5 B obs =.5B ref (1/T ref ) ( T cold + T hot ) B obs =.5B ref (1/T ref T cold ) (1+ (T hot / T cold ) ) The greater the more predominant the hot term At 4 µm ( =12) the hot term more dominating than at 11 µm ( =4) N 1-N T cold T hot

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Consequences At 4 µm ( =12) clouds look smaller than at 11 µm ( =4) In presence of fires the difference BT 4 -BT 11 is larger than the solar contribution The different response in these 2 windows allow for cloud detection and for fire detection

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Conclusions Vegetation: highly reflective in the Near Infrared and highly absorptive in the visible red. The contrast between these channels is a useful indicator of the status of the vegetation; Planck Function: at any wavenumber/wavelength relates the temperature of the observed target to its radiance (for Blackbodies) Thermal Sensitivity: different emissive channels respond differently to target temperature variations. Thermal Sensitivity helps in explaining why, and allows for cloud and fire detection.

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