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

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

Visible (Reflective Bands) Infrared (Emissive Bands)

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

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

RED NIR Dense Vegetation Barren Soil

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

Visible (Reflective Bands) Infrared (Emissive Bands)

Spectral Characteristics of Energy Sources and Sensing Systems IR NIR

Spectral Distribution of Energy Radiated from Blackbodies at Various Temperatures

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 = 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)

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

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

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.

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 = 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

Planck Function and MODIS Bands MODIS

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

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

Clouds at 11 µm look bigger than at 4 µm

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

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

∆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)

∆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

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

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

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

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

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.