Raqrs06 Borel Talk 8 15 06 White

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Raqrs06 Borel Talk 8 15 06 White

  1. 1. 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
  2. 2. Content <ul><li>Introduction: </li></ul><ul><ul><li>Multi-spectral temperature-emissivity separation </li></ul></ul><ul><ul><li>Hyper-spectral temperature-emissivity separation </li></ul></ul><ul><li>In-scene atmospheric correction </li></ul><ul><li>Spectrally smooth emissivity retrieval algorithm </li></ul><ul><li>A method to find the best atmosphere </li></ul><ul><li>Error analysis of the ARTEMISS algorithm </li></ul><ul><li>Retrieving spectral smile using spectral angle mapping analysis </li></ul><ul><li>Conclusions </li></ul><ul><li>References </li></ul>ARTEMISS A utomatic R etrieval of T emperature and EMI ssivity using S pectral S moothness ( ARTEMISS )
  3. 3. Measured radiance in the thermal infrared L down L ground L path T ground , ε Problem: What is the emissivity and temperature?
  4. 4. Introduction <ul><ul><li>Underdetermined problem ( Realmuto, 1990 ): </li></ul></ul><ul><ul><ul><li>Given are N spectral measurements – determine N+1 unknowns (N emissivities and one temperature) </li></ul></ul></ul><ul><ul><li>Multi-spectral temperature-emissivity separation </li></ul></ul><ul><ul><ul><li>Assumed channel 6 emittance model: Kahle et al., 1980; </li></ul></ul></ul><ul><ul><ul><li>Emissivity Spectrum Normalization (ESN): Realmuto, 1990; </li></ul></ul></ul><ul><ul><ul><li>thermal log and alpha residual: Hook et al., 1992 , and </li></ul></ul></ul><ul><ul><ul><li>Mean-Maximum Difference (MMD): Matsunaga, 1993 </li></ul></ul></ul><ul><ul><li>Hyper-spectral temperature-emissivity separation </li></ul></ul><ul><ul><ul><li>In-Scene Atmospheric Correction (ISAC): Johnson and Young, 1998 and 2002 </li></ul></ul></ul><ul><ul><ul><li>Autonomous Atmospheric Compensation by Gu et al, 1999 </li></ul></ul></ul>+ =
  5. 5. 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
  6. 6. ISAC algorithm steps in detail <ul><li>Steps for each pixel (i,j) do: </li></ul><ul><li>Select a wavelength λ 0 such that the transmission through the atmosphere is high (  ~1 ) and the path radiance is negligible (L p ~0). </li></ul><ul><li>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 ) </li></ul><ul><li>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 </li></ul><ul><li>Fit a straight line to the upper boundary of the points (next view graph has details) </li></ul><ul><li>Slope is proportional to transmission  (λ) </li></ul><ul><li>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)]. </li></ul><ul><li>Notes: </li></ul><ul><li>Transmission is unity and the path radiance is zero for λ= λ 0 . </li></ul><ul><li>For wavelengths where the transmission is higher than at λ 0 , estimated transmission will rise above unity. Negative path radiances possible too. </li></ul><ul><li>Schemes ( Johnson and Young, 1998 ) exist to iteratively fix the transmission and path radiance to make them physically realistic. </li></ul>
  7. 7. Fitting line to upper points in scatterplot <ul><li>Steps for each wavelength λ do: </li></ul><ul><ul><li>Fit a linear regression to points (x,y)=( B(λ,T B (i,j)), L m (λ,i,j)) </li></ul></ul><ul><ul><li>Discard the points below the fit: y fit (x)=a*x+b </li></ul></ul><ul><ul><li>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 . </li></ul></ul>Iter=1 Iter=2 Iter=3 Iter=4
  8. 8. 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
  9. 9. Surface emissivity spectra From: Johns Hopkins spectral library
  10. 10. 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
  11. 11. Look-up-table generation <ul><li>Select fixed: </li></ul><ul><li>Sensor height, </li></ul><ul><li>Target height, </li></ul><ul><li>View angle, </li></ul><ul><li>CO2 mixing ratio, </li></ul><ul><li>Model atmosphere (TROPICAL, MLS, MLW, SAS, SAW, USS) </li></ul><ul><li>Variables: </li></ul><ul><li>Temperature profile offset </li></ul><ul><li>RH scaling factor </li></ul><ul><li>Columnar ozone </li></ul>
  12. 12. Original smooth emissivity retrieval algorithm (Borel, 1997) Find a temperature T opt and so that the variance σ is minimized:
  13. 13. New version of TES based on minimizing measured and modeled sensor radiances (Borel, 2003) <ul><li>Compute emissivity ε : </li></ul><ul><li>Where estimated ground temperature T est : </li></ul><ul><li>Compute the RMSE σ of the measured and simulated radiance or: </li></ul><ul><li>Where is the 3-point smoothed emissivity </li></ul>
  14. 14. Summary of useful error terms
  15. 15. Method to find the best atmosphere from ISAC <ul><li>Perform spectral matching: </li></ul><ul><li>Spectral angle mapper (SAM): </li></ul><ul><li>Linear regression analysis – find maximum R 2 </li></ul><ul><li>Select the x% best atmospheres as candidates </li></ul>Size of symbols ~ SAM or ~ R 2 Best fitting atmospheres differ by Ozone amount
  16. 16. A utomatic R etrieval of T emperature and EMI ssivity using S pectral S moothness ( ARTEMISS ) algorithm Minimize:
  17. 17. Simple sensitivity study
  18. 18. 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.
  19. 19. 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 .
  20. 20. Sensitivity study for ARTEMISS <ul><li>Variables investigated: </li></ul><ul><li>Wavelength center </li></ul><ul><li>FWHM multiplier </li></ul><ul><li>Sensor noise </li></ul><ul><li>Outputs investigated: </li></ul><ul><li>Temperature errors </li></ul><ul><li>Emissivity errors </li></ul>
  21. 21. 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
  22. 22. 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.
  23. 23. RETRIEVING SPECTRAL SMILE USING SPECTRAL ANGLE MAPPING ANALYSIS <ul><li>Problem: </li></ul><ul><li>Spectral response of hyperspectral sensors can change – how can we determine spectral shifts and FWHM changes from the data itself? </li></ul><ul><li>Solution: </li></ul><ul><li>Use transmission τ ISAC estimate from ISAC and compare to LUT. </li></ul><ul><li>Break up spectral range into K intervals: τ ISAC,k </li></ul><ul><li>Compute MODTRAN transmission convolved with a sensor response function for N different spectral shifts on the waveband centers and M FWHM multipliers </li></ul><ul><li>Normalize the K x M x N base vectors S k,m,n </li></ul><ul><li>Compute spectral angle SAM k,m,n between τ ISAC,k and S k,m,n for all k, m and n </li></ul>
  24. 24. 3-D volume visualization of SAM k,m,n <ul><li>The spectral angle mapper (SAM) is defined as: </li></ul><ul><li>The brightness is proportional to - log[SAM(S k,m,n , τ k )]. </li></ul><ul><li>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). </li></ul>
  25. 25. Simulated retrieval of a spectral smile and FWHM variation with band number <ul><li>Steps: </li></ul><ul><li>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. </li></ul><ul><li>Fit a line or polynomial with selectable order to the smallest SAM values to find the optimum FWHM multiplier. </li></ul><ul><li>Interpolate the 3-D SAM cube using the FWHM multipliers at each spectral interval index k and spectral shift index n . </li></ul><ul><li>Fit a line or polynomial of selectable order to the smallest SAM values to find the optimum spectral smile. </li></ul>
  26. 26. Conclusions <ul><li>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. </li></ul><ul><li>More than 128 channels are needed to retrieve temperature, emissivities, and atmospheric parameters. </li></ul><ul><li>A good atmospheric correction is a necessary condition to retrieve accurate surface temperatures and emissivities. </li></ul><ul><li>The spectral calibration accuracy is crucial to retrieve reasonable temperatures and emissivities. </li></ul><ul><li>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. </li></ul>
  27. 27. Acknowledgements <ul><li>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. </li></ul>
  28. 28. References (1) <ul><li>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).  </li></ul><ul><li>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 ) </li></ul><ul><li>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. </li></ul><ul><li>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. </li></ul><ul><li>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. </li></ul><ul><li>Guanter, L., R. Richter, and J. Moreno, Spectral calibration of hyperspectral imagery using atmospheric absorption features, Applied Optics, 45(10), 2360-2370, 2006. </li></ul>
  29. 29. References (2) <ul><li>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. </li></ul><ul><li>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). </li></ul><ul><li>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. </li></ul><ul><li>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. </li></ul><ul><li>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. </li></ul><ul><li>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. </li></ul><ul><li>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. </li></ul>

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