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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
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
+ =
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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
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.
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
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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
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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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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.
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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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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
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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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RETRIEVING SPECTRAL SMILE USING SPECTRAL ANGLE MAPPING ANALYSIS
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
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).
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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.
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.
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.
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, " MODTRAN4 Radiative Transfer Modeling for Atmospheric Correction, " 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 )
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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.
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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).
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.
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