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

3. Measured radiance in the thermal infrared L down L ground L path T ground , ε Problem: What is the emissivity and temperature?

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

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

12. Original smooth emissivity retrieval algorithm (Borel, 1997) Find a temperature T opt and so that the variance σ is minimized:

14. Summary of useful error terms

16. A utomatic R etrieval of T emperature and EMI ssivity using S pectral S moothness ( ARTEMISS ) algorithm Minimize:

17. Simple sensitivity study

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 .

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.