Equations for ASTER radiometric calibration ver.0.20 by Satoshi TSUCHIDA, Humihiro SAKUMA National Institute of Advanced Industrial Science and Technology and Akira IWASAKI University of TOKYO under construction �c.always

Index 1. Conversion from DNL1Ato DNL1B in GDS 2. Radiance calculation from DNL1B (More precice calculation: see 5.) 3. Radiance calculation from DNL1A 4. Scaled calibration coefficient for sensor trend analysis 5. Radiance calculation from DNL1B based on the results for the trend analysis (Best for the radiance-based analysis using multi-temporal images) Appendix: Coefficients Tables Table 1 C(b, m): Unit conversion coefficients in band b and gain mode m. Table 2 R(b, v): Optical calibration coefficients for sensor degradation in band b and calibration version v. Table 3 v : Version of radiometric calibration Table 4 G(b, m): Gain switching function in band b and gain mode m.

1. Conversion from DNL1Ato DNL1B in GDS DNL1B(b,m,v)= Rad(b,v) /C(b, m)+1                                                         (1) : DNL1B(b,m,v)=1 corresponds to Rad=0. Rad(b,v)=A(b, i, v)* DNL1A(b,m)/G(b, m)+D(b, i,v)                                       (2) A(b,i, v)=A(b, i, 1.00)/R(b, v)                                                                  (3a) D(b,i, v)=D(b, i, 1.00)/R(b, v)                                                                  (3b) b: Band number i: Detector number v: Version of the radiometric calibration (1.00-) m: Mode of gain switching function Rad(b,v) : Radiance in band b and calibration version v. [W/m2/sr/micron] DNL1A(b,m)  : Digital Number of L1A data in band b, gain mode m DNL1B(b,m, v): Digital Number of L1B data in band b, gain mode m and calibration version v A(b,i, v) and D(b, i, v): The conversion coefficients for L1 data in band b, detector i and calibration version v G(b,m): Gain switching function in band b and gain mode m. R(b, v):Optical calibration coefficients for sensor degradation in band b and calibration version v. C(b,m): Unit conversion coefficients in band b and gain mode m.

2. Radiance calculation from DNL1B Rad(b,v) = C(b, m)* ( DNL1B(b,m, v)- 1 )                                                   (4) The radiances are calculated by the calibration coefficients of version v. The data are calibrated for the on-board temperature and the difference between detectors, and the degradation of the sensors after launch. Rad(b,1.00) = C(b, m)* ( DNL1B(b,m, v)- 1 ) * R(b, v)                                  (5) The radiances are calculated by the calibration coefficients before launch (version 1.00-2.00, RE02(VNIR) or PFT(SWIR)). The data are calibrated for the on-board temperature and the difference between detectors, and the degradation of the sensors after launch.

3. Radiance calculation from DNL1A Rad(b,1.00) ~ C(b, m)* ( DNL1A(b,m)- 1 )                                                   (6a) : ~ mark means "nealy eqaul". The radiances approximate the values calculated by the calibration coefficients before launch (version 1.00-2.00, RE02(VNIR) or PFT(SWIR)). The data are not calibrated for the on-board temperature and the difference between detectors, and the degradation of the sensors after launch. However, there are two problems in this equation. One is that D(b, i, v) shows sometimes large values (see below table "Example of coefficients"), which leads to large error (maybe a few to ten percent) in the eq.6. The other is that the radiance in eq.6 shows almost a few percent difference from the radiance derived from DNL1B of the eq.5 for the safety of dynamic range in radiance. More precise equations eq.6b, 6c and 6d can be obtained from eq.2 as follows. Rad(b,1.00) = ( A(b, i, 1.00) / G(b, m) ) * DNL1A(b,m)+D(b, i,1.00)                                        (6b) This is most precise equation but needs a ditector by ditector (pixel by pixel) calculation, therefore the band average A(b,*,1.0) and D(b,*,1.0) of the conversion coefficients A(b,i,1.0) and D(b,i,1.0) can be used for the calculation convenience. The values of A(b,*,1.0) and D(b,*,1.0) are shown in below table. Rad(b,1.00) ~ ( A(b, *, 1.00) / G(b, m) ) * DNL1A(b,m)+D(b, *, 1.00)                                     (6c) Moreover, if DNL1A(b,m) >> |D(b,*,1.00)*G(b,m)/A(b,*,1.00)|, the following equation is useful for the calculation from Rad(b,1.00) in eq.6a. Rad(b,1.00) ~ ( A(b, *, 1.00) / G(b, m) ) * DNL1A(b,m)+D(b, *, 1.00) = C(b, m) * ( DNL1A(b,m) + D(b, *, 1.00) * G(b, m) / A(b, *, 1.00) ) * ( A(b, *, 1.00) / G(b, m) / C(b, m) ) ~ C(b, m)* ( DNL1A(b,m)- 1 ) * ( A(b, *, 1.00) / G(b, m) / C(b, m) )                 (6d) Rad(b,1.00) in eq.6a Table Example of coefficients Band b Line i D(b, i, 2.06) A(b, i, 2.06) G(b, High) 1 2500 -1.336 1.8678 2.472 2501 -2.7967 1.8987 2.472 2 2500 -2.0651 1.5042 1.994 2501 -1.1827 1.5311 1.994 3 2500 -7.1037 0.88374 1 2501 -1.5675 0.88523 1 Table Band average A(b,*,1.0) and D(b,*,1.0) of the conversion coefficients A(b,i,1.0) and D(b,i,1.0) Band b Mode m A(b,*,1.0) * D(b,*,1.0) * A/G D*G/A * A/G/C 1 odd High 1.750 1.775 -1.914 -2.607 0.7080 0.7180 -2.704 -3.631 1.047 1.062 even 1.726 -1.221 0.6980 -1.750 1.033 2 odd High 1.459 1.466 -1.580 -1.158 0.7317 0.7354 -2.159 -1.574 1.034 1.039 even 1.452 -2.002 0.7281 -2.750 1.028 3N odd Normal 0.880 0.879 -4.348 -1.572 0.8803 0.8788 -4.939 -1.789 1.021 1.019 even 0.882 -7.123 0.8819 -8.077 1.023 4 odd Normal 0.243 0.243 -0.5 -0.4 0.243 0.243 -2 -2 1.12 1.12 even 0.243 -0.6 0.243 -3 1.12 5 odd Normal 0.0734 0.0734 -0.7 -0.8 0.0734 0.0734 -10 -11 1.05 1.05 even 0.0734 -0.7 0.0734 -9 1.05 6 odd Normal 0.0666 0.0666 -0.6 -0.6 0.0666 0.0666 -10 -9 1.07 1.07 even 0.0666 -0.7 0.0666 -10 1.07 7 odd Normal 0.0662 0.0662 -0.6 -0.7 0.0662 0.0662 -9 -10 1.11 1.11 even 0.0662 -0.6 0.0662 -9 1.11 8 odd Normal 0.0460 0.0459 -0.4 -0.4 0.0460 0.0459 -9 -8 1.10 1.10 even 0.0460 -0.4 0.0460 -9 1.10 9 odd Normal 0.0340 0.0340 -0.3 -0.3 0.0340 0.0340 -9 -10 1.07 1.07 even 0.0340 -0.3 0.0340 -8 1.07 * : A(b,i,1.0) and D(b,i,1.0) can be changed by other factors (ex. on-board temparature), however the values shown above are almost stable.

4. Scaled calibration coefficient for sensor trend analysis K(b) = Rad(b,1.00)/Radactual(b)                                                                (7) : Rad(b,1.00) should be calculated by the eq.5 in precise analysis. Radactual(b): Actual radiance in band b, which is measured by the on-board calibrator and/or the vicarious calibration. K(b): Degradation coefficient. New R(b,v) could be estimated from this K(b), so K(b) is near value of New R(b,v). L(b, m) = DNL1A(b, m)/ Radactual(b)                                                         (8) : Sometimes L(b, m) is used instead of K(b) for the comparison works of the calibration teams. The relation of L(b, m) and K(b) is shown as follows, L(b, m) = DNL1A(b, m)/ Radactual(b) ~ (Rad(b,1.00)/C(b, m)+1) / Radactual                           (by eq.6) = Rad(b,1.00) / Radactual(b)/C(b, m)+ 1/ Radactual(b) = K(b)/C(b, m) + 1/ Radactual(b)                                  (by eq.7) ~ K(b)/C(b, m)                                 (if K(b) /C(b, m) >> 1/ Radactual) : ~ mark means "nealy eqaul". K(b) ~ L(b,m) *C(b, m)                                                                                           (9a) From the eq.6b, 6c and 6d, the eq.9a can be changed to be more precise eqations eq.9b, 9c and 9d as follows, K(b) = L(b,m) * ( A(b, i, 1.00) / G(b, m) ) + D(b, i,1.00) / Radactual(b)                 (9b) ~ L(b,m) * ( A(b, *, 1.00) / G(b, m) ) + D(b, *,1.00) / Radactual(b)            (9c) ~ L(b,m) * ( A(b, *, 1.00) / G(b, m) ) = L(b,m) *C(b, m) * ( A(b, *, 1.00) / G(b, m) / *C(b, m) )                       (9d) K(b) in eq.9a The values of A(b,*,1.0) and D(b,*,1.0) are shown in the table of section 3.

5. Radiance calculation from DNL1B based on the results for the trend analysis of the on-board calibrator and/or the vicarious calibration Radreal(b) = Rad(b,1.00)/Ktrend(b, days)     = C(b, m)* ( DNL1B(b,m, v)- 1 ) * R(b, v) / Ktrend(b, days)                      (10) Radreal(b): Radiance in band b based on the results for the trend analysis of the on-board calibrator and/or the vicarious calibration. Therefore Radreal(b) is best for the radiance-based scientific analysis using multi-temporal ASTER images. days: Days since launch Ktrend(b, days): Degradation function in band b and the days since launch estimated from the sensor trend analysis (see above 4.). The following Ktrend(b, days) functions are recommended, * Band 1 to 3N (b=1,2,3N) i)   0 < days < 672 Ktrend(b, days)=X(b)days2 + Y(b)days + Z(b) Table X(b), Y(b) and Z(b) Coefficients Band b 1 2 3 X(b) 1.2945*10-7 3.221*10-8 -9.360*10-9 Y(b) -2.967*10-4 -1.5246*10-4 -5.726*10-5 Z(b) 9.802*10-1 9.879*10-1 9.817*10-1 ii)   672 ≤ days Ktrend(b, days)=Y(b) exp[-X(b)days] + Z(b) Table X(b), Y(b) and Z(b) Coefficients Band b 1 2 3 X(b) 0.002117 0.0018341 0.0015716 Y(b) 0.4007 0.3020 0.2224 Z(b) 0.7403 0.8114 0.8620 * Band 4 to 9 (b=4 to 9) Ktrend(b, days)= 1.0 These Ktrend(b, days) functions are acquired by only onboard calibrator results (see. the trend of the radiometric calibration coefficients by onboard calibration) and one of our recommended equations. In ASTER Science Team, there are other Ktrend(b, days) functions based on the results of vicarious calibration by three groups (Univ. of Arizona, Saga Univ. and AIST groups), and the best of these fuctions is still under discussion in the team.

Appendix: Coefficients Tables Table 1 C(b, m): Unit conversion coefficients in band b and gain mode m. Gain mode(m) High Normal Low1 Low2 Band (b) 1 2 3N,3B 4 5 6 7 8 9   0.676 0.708 0.423 0.1087 0.0348 0.0313 0.0299 0.0209 0.0159   1.688 1.415 0.862 0.2174 0.0696 0.0625 0.0597 0.0417 0.0318   2.25 1.89 1.15 0.290 0.0925 0.0830 0.0795 0.0556 0.0424   NA NA NA 0.290 0.409 0.390 0.332 0.245 0.265 Table 2 R(b, v): Optical calibration coefficients for sensor degradation in band b and calibration version v. Version (v) Band 1 Band 2 Band 3 1.00-2.00 1 1 1 2.01 0.972 0.982 0.978 2.02-2.03 0.948 0.972 0.982 2.04 0.931 0.966 0.985 2.05-2.06 0.921 0.959 0.982 2.07-2.08 0.892 0.950 0.983 2.09-2.11 0.802 0.872 0.917 2.12-2.15 0.779 0.852 0.902 2.16-2.17 0.760 0.833 0.886 Table 3 v : Version of radiometric calibration (Caution: Some data has older version than estimated version from this table, because ASTER Ground Data System (GDS) always started the process in newer vesion a few months after the starting date of the following time period.) Version (v) Application Time Period Day of Optical Calibration Coefficients Corresponding Telescope Ver.2.00 1996/11/09-2000/02/01     Ver.2.01 2000/02/02-2000/06/03 2000/02/02 VNIR Ver.2.02 2000/06/04-2000/09/13 2000/06/03 VNIR Ver.2.03 2000/09/14-2000/11/13 2000/09/13 TIR Ver.2.04 2000/11/04-2001/02/13 2000/11/03 VNIR Ver.2.05 2001/02/14-2001/11/30 2001/02/13 VNIR,TIR Ver.2.06 2001/12/01-2002/10/11 2001/08/16 TIR Ver.2.07 - 2001/12/25 VNIR,TIR Ver.2.08 - 2002/04/03 TIR Ver.2.09 2002/10/12-2002/12/15 2002/05/07 VNIR,SWIR*,TIR Ver.2.10 - 2002/8/13 TIR Ver.2.11 2002/12/16-2003/01/29 2002/11/20 TIR Ver.2.12 2003/01/30-2003/05/14 2002/12/23 VNIR Ver.2.13 2003/05/15-2003/08/25 2003/04/17 TIR Ver.2.14 2003/08/26-12/05 2003/08/04 TIR Ver.2.15 2003/12/06-2004/01/04 2003/11/11 TIR Ver.2.16 2004/01/05-2004/03/09 2003/11/11 VNIR Ver.2.17 2004/03/10- 2004/02/18 TIR * SWIR offset conversion coefficients D(b, i, v) were changed. Table 4 G(b, m): Gain switching function in band b and gain mode m. Band High Normal Low Gain-1 Low Gain-2 1 2.472 1 0.750 NA 2 1.994 1 0.755 NA 3N 2.041 1 0.757 NA 3B 2* 1 0.759 NA 4 2* 1 0.75* 0.75* 5 2* 1 0.75* 0.17* 6 2* 1 0.75* 0.16* 7 2* 1 0.75* 0.18* 8 2* 1 0.75* 0.17* 9 2* 1 0.75* 0.12* *: Planning value before launch. (Now checking values after launch)