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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 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],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 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],+ =
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 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Fitting line to upper points in scatterplot ,[object Object],[object Object],[object Object],[object Object],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 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
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) ,[object Object],[object Object],[object Object],[object Object]
Summary of useful error terms
Method to find the best atmosphere from ISAC ,[object Object],[object Object],[object Object],[object Object],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 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
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.
RETRIEVING  SPECTRAL SMILE USING SPECTRAL ANGLE MAPPING ANALYSIS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
3-D volume visualization of  SAM k,m,n ,[object Object],[object Object],[object Object]
Simulated retrieval of a spectral smile and FWHM variation with band number ,[object Object],[object Object],[object Object],[object Object],[object Object]
Conclusions ,[object Object],[object Object],[object Object],[object Object],[object Object]
Acknowledgements ,[object Object]
References (1) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
References (2) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Raqrs06 Borel Talk 8 15 06 White

  • 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
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  • 3. Measured radiance in the thermal infrared L down L ground L path T ground , ε Problem: What is the emissivity and temperature?
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  • 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
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  • 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. Surface emissivity spectra From: Johns Hopkins spectral library
  • 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
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  • 12. Original smooth emissivity retrieval algorithm (Borel, 1997) Find a temperature T opt and so that the variance σ is minimized:
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  • 14. Summary of useful error terms
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  • 16. A utomatic R etrieval of T emperature and EMI ssivity using S pectral S moothness ( ARTEMISS ) algorithm Minimize:
  • 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. 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 .
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  • 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. 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.
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