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Raqrs06 Borel Talk 8 15 06 White Raqrs06 Borel Talk 8 15 06 White Presentation Transcript

  • Error Analysis for a Temperature and Emissivity Retrieval Algorithm for Hyperspectral Imaging Data Christoph Borel, PhD [email_address] , http://cborel.net ARTEMISS The 2nd I nternat i onal Sympos i um on Recent Advances i n Quant i tat i ve Remote Sens i ng: RAQRS ' II
  • Content
    • Introduction:
      • Multi-spectral temperature-emissivity separation
      • Hyper-spectral temperature-emissivity separation
    • In-scene atmospheric correction
    • Spectrally smooth emissivity retrieval algorithm
    • A method to find the best atmosphere
    • Error analysis of the ARTEMISS algorithm
    • Retrieving spectral smile using spectral angle mapping analysis
    • Conclusions
    • References
    ARTEMISS A utomatic R etrieval of T emperature and EMI ssivity using S pectral S moothness ( ARTEMISS )
  • Measured radiance in the thermal infrared L down L ground L path T ground , ε Problem: What is the emissivity and temperature?
  • Introduction
      • Underdetermined problem ( Realmuto, 1990 ):
        • Given are N spectral measurements – determine N+1 unknowns (N emissivities and one temperature)
      • Multi-spectral temperature-emissivity separation
        • Assumed channel 6 emittance model: Kahle et al., 1980;
        • Emissivity Spectrum Normalization (ESN): Realmuto, 1990;
        • thermal log and alpha residual: Hook et al., 1992 , and
        • Mean-Maximum Difference (MMD): Matsunaga, 1993
      • Hyper-spectral temperature-emissivity separation
        • In-Scene Atmospheric Correction (ISAC): Johnson and Young, 1998 and 2002
        • Autonomous Atmospheric Compensation by Gu et al, 1999
    + =
  • In-scene atmospheric correction (ISAC) Radiance a blackbody would have at λ : B(λ,T B ) Measured radiance: L m (λ) Intercept ~ L p (λ) Graybody pixels ( ε <1) Blackbody pixels ( ε =1) Slope ~ ((λ) Measured radiance: Scatterplot determines transmission and path radiance: T B (i,j)=B -1 (λ 0 ,Lm(λ 0 ,i,j))/ε0
  • ISAC algorithm steps in detail
    • Steps for each pixel (i,j) do:
    • Select a wavelength λ 0 such that the transmission through the atmosphere is high (  ~1 ) and the path radiance is negligible (L p ~0).
    • Compute the apparent brightness temperature: T B (i,j)=B -1 (λ 0 ,L m (λ 0 ,i,j))/ε 0 (assume ε 0 =0.95 )
    • Create scatterplot with: x=B(λ,T B (i,j)) and y=L m (λ,i,j)=B(λ,T B (i,j))  +L p
    • Fit a straight line to the upper boundary of the points (next view graph has details)
    • Slope is proportional to transmission  (λ)
    • Intercept (B(λ,0)=0 proportional to the path radiance L p . The emissivity retrieved by the ISAC method is then given by: ε(λ,i,j)=[L m (λ,i,j)-L p (λ)]/[B(λ,T B (i,j))  (λ)].
    • Notes:
    • Transmission is unity and the path radiance is zero for λ= λ 0 .
    • For wavelengths where the transmission is higher than at λ 0 , estimated transmission will rise above unity. Negative path radiances possible too.
    • Schemes ( Johnson and Young, 1998 ) exist to iteratively fix the transmission and path radiance to make them physically realistic.
  • Fitting line to upper points in scatterplot
    • Steps for each wavelength λ do:
      • Fit a linear regression to points (x,y)=( B(λ,T B (i,j)), L m (λ,i,j))
      • Discard the points below the fit: y fit (x)=a*x+b
      • Repeat steps a&b for the points above the fit only until a fraction of points are left. The coefficient a is proportional to the transmission  and the intercept b is proportional to the path radiance L p .
    Iter=1 Iter=2 Iter=3 Iter=4
  • Example of ISAC retrieved transmssion and path radiance using simulated data ISAC transmission fits well to “true” transmission ISAC path radiance has offset and scaling errors
  • Surface emissivity spectra From: Johns Hopkins spectral library
  • Atmospheric transmission and path radiance Note: The atmospheric features have sharp absorption features compared to emissivities. Modtran 4 computed τ and L p for variable water vapor amount and temperature profiles. Example of tropical atmosphere
  • Look-up-table generation
    • Select fixed:
    • Sensor height,
    • Target height,
    • View angle,
    • CO2 mixing ratio,
    • Model atmosphere (TROPICAL, MLS, MLW, SAS, SAW, USS)
    • Variables:
    • Temperature profile offset
    • RH scaling factor
    • Columnar ozone
  • Original smooth emissivity retrieval algorithm (Borel, 1997) Find a temperature T opt and so that the variance σ is minimized:
  • New version of TES based on minimizing measured and modeled sensor radiances (Borel, 2003)
    • Compute emissivity ε :
    • Where estimated ground temperature T est :
    • Compute the RMSE σ of the measured and simulated radiance or:
    • Where is the 3-point smoothed emissivity
  • Summary of useful error terms
  • Method to find the best atmosphere from ISAC
    • Perform spectral matching:
    • Spectral angle mapper (SAM):
    • Linear regression analysis – find maximum R 2
    • Select the x% best atmospheres as candidates
    Size of symbols ~ SAM or ~ R 2 Best fitting atmospheres differ by Ozone amount
  • A utomatic R etrieval of T emperature and EMI ssivity using S pectral S moothness ( ARTEMISS ) algorithm Minimize:
  • Simple sensitivity study
  • Effect of band center shifts on radiance errors The RMS radiance error for a soil at 285 º K observed from space under different columnar water vapor amounts ranging from 1.14 to 7.41 g/cm 2 as a function of spectral shifts in channel spacings.
  • Full-Width-Half-Maximum effect on radiance error The RMS radiance error for a soil at 285 º K observed from space under different columnar water vapor amounts ranging from 1.14 to 7.41 g/cm 2 as a function of FWHM scaling factor .
  • Sensitivity study for ARTEMISS
    • Variables investigated:
    • Wavelength center
    • FWHM multiplier
    • Sensor noise
    • Outputs investigated:
    • Temperature errors
    • Emissivity errors
  • Effect of spectral shifts on T and ε The RMSE and mean temperature retrieval error(left) and the RMSE and mean emissivity retrieval error as a function of spectral shift. The mean temperature error increases to over 1 º K for spectral shifts as small as 1/20th of a channel spacing. Wrong atmosphere causes temperature offset
  • Effect of Noise on Temperature T and Emissivity ε Example of the growth of the RMS temperature and emissivity error as a function of sensor noise.
    • Problem:
    • Spectral response of hyperspectral sensors can change – how can we determine spectral shifts and FWHM changes from the data itself?
    • Solution:
    • Use transmission τ ISAC estimate from ISAC and compare to LUT.
    • Break up spectral range into K intervals: τ ISAC,k
    • Compute MODTRAN transmission convolved with a sensor response function for N different spectral shifts on the waveband centers and M FWHM multipliers
    • Normalize the K x M x N base vectors S k,m,n
    • Compute spectral angle SAM k,m,n between τ ISAC,k and S k,m,n for all k, m and n
  • 3-D volume visualization of SAM k,m,n
    • The spectral angle mapper (SAM) is defined as:
    • The brightness is proportional to - log[SAM(S k,m,n , τ k )].
    • The X axis is the spectral interval (K), the Y axis is the spectral offset (N) and the Z axis is the FWHM multiplier (M).
  • Simulated retrieval of a spectral smile and FWHM variation with band number
    • Steps:
    • Obtain an estimate of the FWHM multiplier variation as a function of the spectral interval by identifying for each k and n which FWHM multiplier had the best match.
    • Fit a line or polynomial with selectable order to the smallest SAM values to find the optimum FWHM multiplier.
    • Interpolate the 3-D SAM cube using the FWHM multipliers at each spectral interval index k and spectral shift index n .
    • Fit a line or polynomial of selectable order to the smallest SAM values to find the optimum spectral smile.
  • Conclusions
    • ARTEMISS algorithm uses as the main criterion the RMSE between the measured and simulated at sensor radiance where the emissivity has been smoothed to retrieve temperature and emissivity.
    • More than 128 channels are needed to retrieve temperature, emissivities, and atmospheric parameters.
    • A good atmospheric correction is a necessary condition to retrieve accurate surface temperatures and emissivities.
    • The spectral calibration accuracy is crucial to retrieve reasonable temperatures and emissivities.
    • Developed a spectral calibration method which is able to retrieve spectral shifts and FWHM of sensors with more than 128 bands to the required accuracy.
  • Acknowledgements
    • Our thanks go to Dr. Ronald Lockwood and Dr. Michael Hoke from the Air Force Research Laboratory , Hanscom AFB, MA, which supported this research during the author’s year as a distinguished AFRL National Laboratory Fellow and later under BAA contracts F19628-03-0066 and FA8718-05-C-0065.
  • References (1)
    • A. Berk , G. P. Anderson, L. S.Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, &quot; MODTRAN4 Radiative Transfer Modeling for Atmospheric Correction, &quot; SPIE Proceeding, Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research III, Volume 3756 (1999). 
    • Borel, C.C, Iterative Retrieval of Surface Emissivity and Temperature for a Hyperspectral Sensor, First JPL Workshop on Remote Sensing of Land Surface Emissivity, May 6-8, 1997. (available only from authors website http://www.borel.net )
    • Gao, B.-C., M. J. Montes, and C. O. Davis, Refinement of wavelength calibrations of hyper spectral imaging data using a spectrum-matching technique, Remote Sens. Environ. 90, 424-433, 2004.
    • Goetz, A.F.H., Kindel, B.C., Ferri, M., Zheng Qu  , HATCH: results from simulated radiances, AVIRIS and Hyperion, IEEE TGARS, 41(6), 1215-1222, 2003.
    • Gu, D., A.R. Gillespie, A.B. Kahle, F.D. Palluconi, Autonomous atmospheric compensation (AAC) of high resolution hyperspectral thermal infrared remote-sensing imagery, IEEE TGARS, 38(6), 2557 – 2570, 2000.
    • Guanter, L., R. Richter, and J. Moreno, Spectral calibration of hyperspectral imagery using atmospheric absorption features, Applied Optics, 45(10), 2360-2370, 2006.
  • References (2)
    • Hook S.J., A.R. Gabell, A.A. Green and P.S. Kealy, A comparison of techniques for extracting emissivity information from thermal infrared data for geologic studies, Remote Sens. Environ., 42, 123-135, 1992.
    • Johnson, B.R. and S. J. Young, Inscene Atmospheric Compensation: Application to SEBASS Data at the ARM Site, Aerospace Report No. ATR-99(8407)-1 Parts I and II,(1998).
    • Kahle, A.B., D.P. Madura and J.M. Soha, Middle Infrared Multispectral Aircraft Scanner Data: Analysis for Geologic Applications, Applied Optics, 19(14):2279-2290, 1980.
    • Matsunaga, T., An Emissivity-Temperature Separation Technique Based on an Empirical Relationship Between Mean and Range of Spectral Emissivity, Proc. 14th Japanese Conf. of Remote Sensing, 47-48, 1993.
    • Realmuto, V.J., Separating the Effects of Temperature and Emissivity: Emissivity Spectrum Normalization, Proc. of the Second TIMS Workshop, JPL Publ. 90-55, 31-35, 1990.
    • Salisbury, J. W. and D. M. D’Aria, Emissivity of Terrestrial Materials in the 8-14  m Atmospheric Window, Remote Sens. Environ., 42, 83-106, 1992.
    • Young, S. J., Detection and Quantification of Gases in Industrial-Stack Plumes Using Thermal-Infrared Hyperspectral Imaging, The Aerospace Corporation Report No. ATR-2002(8407)-1.