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
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
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
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
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 .
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
Spectral response of hyperspectral sensors can change – how can we determine spectral shifts and FWHM changes from the data itself?
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
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.
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