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Crop Agriculture

Revised Landsat 8 Custom Relative Scatter Lookup Table

 Related Pages: Updated Landsat 8 SR Tutorial w/ Imagery    L8 SR Results

Landsat 8 imagery can be converted to surface reflectance independently (though it can be downloaded for free from the USGS based on their algorithm, which is not purely a dark object subtraction [DOS, Chavez, 1988] method). The effect of scatter (haze) needs to be removed to convert from Top of Atmosphere visible band and near infrared (to a lesser extent) reflectance to surface reflectance. Different methods can be applied to remove scatter. The methods recommended here are to establish the Lowest Valid Value and use the Updated Custom Landsat 8 Continuous Relative Scatter Table (below) or the Relative Scatter Calculator & Lookup Table. The Custom Lookup Table (below) has been designed to acquire values more similar to USGS Landsat 8 Algorithm surface reflectance, while the Relative Scatter Calculator & Lookup Table has a proper power line correlation between band center wavelength and scatter of R² = 1.00 (Chavez, 1988). Scatter should be deducted as outline in the Tutorial. A continuous relative scatter lookup table was suggested by Chavez (1988).

Continuous Relative Scatter Background

In clearer atmospheres, the the ratios of scatter between blue and larger wavelength bands (e.g. green, red, and NIR) are greater. Conversely as haze increases and scatter overall increases, the ratio of scatter between blue and larger wavelength bands decreases and proportion of scatter between bands becomes more similar. Continuous relative scatter deduction was suggested by Chavez (1988). Values in the tables below were derived in part from principles in Chavez (1988) and from Landsat 8 research here. 

To use the table below, establish haze reflectance from the RED BAND then use the corresponding relative scatter for the other bands. Scatter reflectance can be deducted from the red band and relative scatter can be deducted from the other bands as shown in the Tutorial. It is important that scatter has a high power line correlation with band center wavelength (Chavez, 1988); selecting values from the table below enables high (but not perfect) correlations for visible band reflectance values (R² values range from 0.90 and 0.99;  Landsat 8 band center wavelengths are: blue, .480; green; .560; red, .655); however, correlations drop significantly when NIR (.865) is included due to the customization of the table. Landsat 8 bandwidth information can be accessed here or here. The table below has been custom-developed for Landsat 8, based, in part, on comparing derived values to USGS Landsat 8 Algorithm surface reflectance. We have also developed a  Landsat 8 Perfect Power Line Correlation Calculator & Table (based on principles in Chavez [1988]), if you prefer to apply the perfect theoretical power line principles (as previously mentioned, USGS Landsat 8 Algorithm surface reflection is not purely DOS).

Values in the table below were derived from principles and relationships in Chavez (1988) and from Landsat 8 research here; the table was calibrated with actual Landsat 8 Lowest Valid Values. The Original Table was validated with Lowest Valid Values from 21 images (not included in the calibration) and resulted in blue, green, and red band average error of .00285, .00228, and .00003, respectively; as well as blue, green, and red band median error of .00252, .00185, and .00003, respectively. Additional research and experience produced the Revised Table. The changes are described next.

 

Table 1

REVISED (12/2016) Landsat 8 Custom Relative Scatter Lookup Table (a link to Original Table is included below)

The Lookup Table is revised as follows based on research and experience working with imagery here. Blue (band 2) scatter has been decreased by 0.002 to improve the match between blue and red band Lowest Valid Value amounts. Green is centered between Green and Green 2 (is nearly the average). Relative scatter is based on the red band (which is listed every 0.00010 units); the Table now starts at Red 0.00800. NIR is virtually half of the NIR listed on the original table. Power relationship between visible band center wavelength (where, blue = 0.480, green = 0.560, red = 0.655) and scatter remains quite high (but are clearly not perfect), varying from R² = 0.90 to R² = 0.99; correlations decrease when including NIR (0.865) due to customization. Power line exponents become larger (as they should) as scatter increases (changing from -5.7 for Red = 0.01000 to -2.1 for Red = 0.05000). Realistic very clear values can be somewhat lower than -4.0 based on our research here. At Red 0.015, a very clear (but realistic) atmosphere, R² = 1.0 with a power exponent of -4.2. 

* An important aspect to be aware of, in regards to Landsat 8 DOS surface reflectance (SR) versus USGS Landsat 8 Algorithm SR, is that the USGS Landsat 8 SR algorithm is associated with scatter variability (as opposed to DOS), where (USGS Algorithm SR - TOA) will produce varying values. Also worth considering is that values in the Relative Scatter Table are based numerous images representing mainly vegetated (but also soil) surface in agricultural and mountainous areas in the United States. *

Important: USE RED BAND Lowest Valid Value as the starting value UNLESS red values are excessively disconnected (for example, if there are numerous breaks from 50 to 99), IN THAT CASE, use the blue band Lowest Valid Value as the starting value - DO NOT USE THE GREEN OR NIR BAND AS THE STARTING VALUE.

For Landsat 8, Blue, Green, Red, and NIR are Bands 2, 3, 4, and 5, respectively; NIR Scatter at 5 significant digits starts at Red 0.01000.

     Blue
   Green     Red     NIR*
  0.05132   0.02510   0.00800        x
  0.05143   0.02518   0.00810        x
  0.05154   0.02526   0.00820        x
  0.05166   0.02534   0.00830        x
  0.05177   0.02543   0.00840        x
  0.05188   0.02551   0.00850        x
  0.05200   0.02559   0.00860        x
  0.05211   0.02567   0.00870        x
  0.05222   0.02575   0.00880        x
  0.05234   0.02583   0.00890        x
  0.05245   0.02592   0.00900        x
  0.05256   0.02600   0.00910        x
  0.05268   0.02608   0.00920        x
  0.05279   0.02616   0.00930        x
  0.05290   0.02624   0.00940        x
  0.05302   0.02632   0.00950        x
  0.05313   0.02640   0.00960        x
  0.05325   0.02649   0.00970        x
  0.05336   0.02657   0.00980        x
  0.05347   0.02665   0.00990        x
  0.05359   0.02673   0.01000   0.00001
  0.05370   0.02681   0.01010   0.00004
  0.05381   0.02689   0.01020   0.00008
  0.05393   0.02697   0.01030   0.00011
  0.05404   0.02706   0.01040   0.00014
  0.05415   0.02714   0.01050   0.00018
  0.05427   0.02722   0.01060   0.00021
  0.05438   0.02730   0.01070   0.00024
  0.05449   0.02738   0.01080   0.00028
  0.05461   0.02746   0.01090   0.00031
  0.05472   0.02754   0.01100   0.00034
  0.05483   0.02763   0.01110   0.00038
  0.05495   0.02771   0.01120   0.00041
  0.05506   0.02779   0.01130   0.00044
  0.05517   0.02787   0.01140   0.00048
  0.05529   0.02795   0.01150   0.00051
  0.05540   0.02803   0.01160   0.00054
  0.05552   0.02812   0.01170   0.00058
  0.05563   0.02820   0.01180   0.00061
  0.05574   0.02828   0.01190   0.00064
  0.05586   0.02836   0.01200   0.00067
  0.05597   0.02844   0.01210   0.00071
  0.05608   0.02852   0.01220   0.00074
  0.05620   0.02860   0.01230   0.00077
  0.05631   0.02869   0.01240   0.00081
  0.05642   0.02877   0.01250   0.00084
  0.05654   0.02885   0.01260   0.00087
  0.05665   0.02893   0.01270   0.00091
  0.05676   0.02901   0.01280   0.00094
  0.05688   0.02909   0.01290   0.00097
  0.05699   0.02917   0.01300   0.00101
  0.05710   0.02926   0.01310   0.00104
  0.05722   0.02934   0.01320   0.00107
  0.05733   0.02942   0.01330   0.00111
  0.05744   0.02950   0.01340   0.00114
  0.05756   0.02958   0.01350   0.00117
  0.05767   0.02966   0.01360   0.00121
  0.05779   0.02974   0.01370   0.00124
  0.05790   0.02983   0.01380   0.00127
  0.05801   0.02991   0.01390   0.00131
  0.05813   0.02999   0.01400   0.00134
  0.05824   0.03007   0.01410   0.00137
  0.05835   0.03015   0.01420   0.00140
  0.05847   0.03023   0.01430   0.00144
  0.05858   0.03032   0.01440   0.00147
  0.05869   0.03040   0.01450   0.00150
  0.05881   0.03048   0.01460   0.00154
  0.05892   0.03056   0.01470   0.00157
  0.05903   0.03064   0.01480   0.00160
  0.05915   0.03072   0.01490   0.00164
  0.05926   0.03080   0.01500   0.00167
  0.05937   0.03089   0.01510   0.00170
  0.05949   0.03097   0.01520   0.00174
  0.05960   0.03105   0.01530   0.00177
  0.05972   0.03113   0.01540   0.00180
  0.05983   0.03121   0.01550   0.00184
  0.05994   0.03129   0.01560   0.00187
  0.06006   0.03137   0.01570   0.00190
  0.06017   0.03146   0.01580   0.00194
  0.06028   0.03154   0.01590   0.00197
  0.06040   0.03162   0.01600   0.00200
  0.06051   0.03170   0.01610   0.00204
  0.06062   0.03178   0.01620   0.00207
  0.06074   0.03186   0.01630   0.00210
  0.06085   0.03194   0.01640   0.00213
  0.06096   0.03203   0.01650   0.00217
  0.06108   0.03211   0.01660   0.00220
  0.06119   0.03219   0.01670   0.00223
  0.06130   0.03227   0.01680   0.00227
  0.06142   0.03235   0.01690   0.00230
  0.06153   0.03243   0.01700   0.00233
  0.06164   0.03252   0.01710   0.00237
  0.06176   0.03260   0.01720   0.00240
  0.06187   0.03268   0.01730   0.00243
  0.06199   0.03276   0.01740   0.00247
  0.06210   0.03284   0.01750   0.00250
  0.06221   0.03292   0.01760   0.00253
  0.06233   0.03300   0.01770   0.00257
  0.06244   0.03309   0.01780   0.00260
  0.06255   0.03317   0.01790   0.00263
  0.06267   0.03325   0.01800   0.00267
  0.06278   0.03333   0.01810   0.00270
  0.06289   0.03341   0.01820   0.00273
  0.06301   0.03349   0.01830   0.00276
  0.06312   0.03357   0.01840   0.00280
  0.06323   0.03366   0.01850   0.00283
  0.06335   0.03374   0.01860   0.00286
  0.06346   0.03382   0.01870   0.00290
  0.06357   0.03390   0.01880   0.00293
  0.06369   0.03398   0.01890   0.00296
  0.06380   0.03406   0.01900   0.00300
  0.06391   0.03414   0.01910   0.00303
  0.06403   0.03423   0.01920   0.00306
  0.06414   0.03431   0.01930   0.00310
  0.06426   0.03439   0.01940   0.00313
  0.06437   0.03447   0.01950   0.00316
  0.06448   0.03455   0.01960   0.00320
  0.06460   0.03463   0.01970   0.00323
  0.06471   0.03471   0.01980   0.00326
  0.06482   0.03480   0.01990   0.00330
  0.06494   0.03488   0.02000   0.00333
  0.06505   0.03496   0.02010   0.00336
  0.06516   0.03504   0.02020   0.00340
  0.06528   0.03512   0.02030   0.00343
  0.06539   0.03520   0.02040   0.00346
  0.06550   0.03529   0.02050   0.00349
  0.06562   0.03537   0.02060   0.00353
  0.06573   0.03545   0.02070   0.00356
  0.06584   0.03553   0.02080   0.00359
  0.06596   0.03561   0.02090   0.00363
  0.06607   0.03569   0.02100   0.00366
  0.06618   0.03577   0.02110   0.00369
  0.06630   0.03586   0.02120   0.00373
  0.06641   0.03594   0.02130   0.00376
  0.06653   0.03602   0.02140   0.00379
  0.06664   0.03610   0.02150   0.00383
  0.06675   0.03618   0.02160   0.00386
  0.06687   0.03626   0.02170   0.00389
  0.06698   0.03634   0.02180   0.00393
  0.06709   0.03643   0.02190   0.00396
  0.06721   0.03651   0.02200   0.00399
  0.06732   0.03659   0.02210   0.00403
  0.06743   0.03667   0.02220   0.00406
  0.06755   0.03675   0.02230   0.00409
  0.06766   0.03683   0.02240   0.00413
  0.06777   0.03691   0.02250   0.00416
  0.06789   0.03700   0.02260   0.00419
  0.06800   0.03708   0.02270   0.00422
  0.06811   0.03716   0.02280   0.00426
  0.06823   0.03724   0.02290   0.00429
  0.06834   0.03732   0.02300   0.00432
  0.06845   0.03740   0.02310   0.00436
  0.06857   0.03749   0.02320   0.00439
  0.06868   0.03757   0.02330   0.00442
  0.06880   0.03765   0.02340   0.00446
  0.06891   0.03773   0.02350   0.00449
  0.06902   0.03781   0.02360   0.00452
  0.06914   0.03789   0.02370   0.00456
  0.06925   0.03797   0.02380   0.00459
  0.06936   0.03806   0.02390   0.00462
  0.06948   0.03814   0.02400   0.00466
  0.06959   0.03822   0.02410   0.00469
  0.06970   0.03830   0.02420   0.00472
  0.06982   0.03838   0.02430   0.00476
  0.06993   0.03846   0.02440   0.00479
  0.07004   0.03854   0.02450   0.00482
  0.07016   0.03863   0.02460   0.00486
  0.07027   0.03871   0.02470   0.00489
  0.07038   0.03879   0.02480   0.00492
  0.07050   0.03887   0.02490   0.00495
  0.07061   0.03895   0.02500   0.00499
  0.07073   0.03903   0.02510   0.00502
  0.07084   0.03911   0.02520   0.00505
  0.07095   0.03920   0.02530   0.00509
  0.07107   0.03928   0.02540   0.00512
  0.07118   0.03936   0.02550   0.00515
  0.07129   0.03944   0.02560   0.00519
  0.07141   0.03952   0.02570   0.00522
  0.07152   0.03960   0.02580   0.00525
  0.07163   0.03969   0.02590   0.00529
  0.07175   0.03977   0.02600   0.00532
  0.07186   0.03985   0.02610   0.00535
  0.07197   0.03993   0.02620   0.00539
  0.07209   0.04001   0.02630   0.00542
  0.07220   0.04009   0.02640   0.00545
  0.07231   0.04017   0.02650   0.00549
  0.07243   0.04026   0.02660   0.00552
  0.07254   0.04034   0.02670   0.00555
  0.07265   0.04042   0.02680   0.00558
  0.07277   0.04050   0.02690   0.00562
  0.07288   0.04058   0.02700   0.00565
  0.07300   0.04066   0.02710   0.00568
  0.07311   0.04074   0.02720   0.00572
  0.07322   0.04083   0.02730   0.00575
  0.07334   0.04091   0.02740   0.00578
  0.07345   0.04099   0.02750   0.00582
  0.07356   0.04107   0.02760   0.00585
  0.07368   0.04115   0.02770   0.00588
  0.07379   0.04123   0.02780   0.00592
  0.07390   0.04131   0.02790   0.00595
  0.07402   0.04140   0.02800   0.00598
  0.07413   0.04148   0.02810   0.00602
  0.07424   0.04156   0.02820   0.00605
  0.07436   0.04164   0.02830   0.00608
  0.07447   0.04172   0.02840   0.00612
  0.07458   0.04180   0.02850   0.00615
  0.07470   0.04189   0.02860   0.00618
  0.07481   0.04197   0.02870   0.00622
  0.07492   0.04205   0.02880   0.00625
  0.07504   0.04213   0.02890   0.00628
  0.07515   0.04221   0.02900   0.00631
  0.07527   0.04229   0.02910   0.00635
  0.07538   0.04237   0.02920   0.00638
  0.07549   0.04246   0.02930   0.00641
  0.07561   0.04254   0.02940   0.00645
  0.07572   0.04262   0.02950   0.00648
  0.07583   0.04270   0.02960   0.00651
  0.07595   0.04278   0.02970   0.00655
  0.07606   0.04286   0.02980   0.00658
  0.07617   0.04294   0.02990   0.00661
  0.07629   0.04303   0.03000   0.00665
  0.07640   0.04311   0.03010   0.00668
  0.07651   0.04319   0.03020   0.00671
  0.07663   0.04327   0.03030   0.00675
  0.07674   0.04335   0.03040   0.00678
  0.07685   0.04343   0.03050   0.00681
  0.07697   0.04351   0.03060   0.00685
  0.07708   0.04360   0.03070   0.00688
  0.07719   0.04368   0.03080   0.00691
  0.07731   0.04376   0.03090   0.00695
  0.07742   0.04384   0.03100   0.00698
  0.07754   0.04392   0.03110   0.00701
  0.07765   0.04400   0.03120   0.00704
  0.07776   0.04409   0.03130   0.00708
  0.07788   0.04417   0.03140   0.00711
  0.07799   0.04425   0.03150   0.00714
  0.07810   0.04433   0.03160   0.00718
  0.07822   0.04441   0.03170   0.00721
  0.07833   0.04449   0.03180   0.00724
  0.07844   0.04457   0.03190   0.00728
  0.07856   0.04466   0.03200   0.00731
  0.07867   0.04474   0.03210   0.00734
  0.07878   0.04482   0.03220   0.00738
  0.07890   0.04490   0.03230   0.00741
  0.07901   0.04498   0.03240   0.00744
  0.07912   0.04506   0.03250   0.00748
  0.07924   0.04514   0.03260   0.00751
  0.07935   0.04523   0.03270   0.00754
  0.07946   0.04531   0.03280   0.00758
  0.07958   0.04539   0.03290   0.00761
  0.07969   0.04547   0.03300   0.00764
  0.07981   0.04555   0.03310   0.00768
  0.07992   0.04563   0.03320   0.00771
  0.08003   0.04571   0.03330   0.00774
  0.08015   0.04580   0.03340   0.00777
  0.08026   0.04588   0.03350   0.00781
  0.08037   0.04596   0.03360   0.00784
  0.08049   0.04604   0.03370   0.00787
  0.08060   0.04612   0.03380   0.00791
  0.08071   0.04620   0.03390   0.00794
  0.08083   0.04628   0.03400   0.00797
  0.08094   0.04637   0.03410   0.00801
  0.08105   0.04645   0.03420   0.00804
  0.08117   0.04653   0.03430   0.00807
  0.08128   0.04661   0.03440   0.00811
  0.08139   0.04669   0.03450   0.00814
  0.08151   0.04677   0.03460   0.00817
  0.08162   0.04686   0.03470   0.00821
  0.08174   0.04694   0.03480   0.00824
  0.08185   0.04702   0.03490   0.00827
  0.08196   0.04710   0.03500   0.00831
  0.08208   0.04718   0.03510   0.00834
  0.08219   0.04726   0.03520   0.00837
  0.08230   0.04734   0.03530   0.00840
  0.08242   0.04743   0.03540   0.00844
  0.08253   0.04751   0.03550   0.00847
  0.08264   0.04759   0.03560   0.00850
  0.08276   0.04767   0.03570   0.00854
  0.08287   0.04775   0.03580   0.00857
  0.08298   0.04783   0.03590   0.00860
  0.08310   0.04791   0.03600   0.00864
  0.08321   0.04800   0.03610   0.00867
  0.08332   0.04808   0.03620   0.00870
  0.08344   0.04816   0.03630   0.00874
  0.08355   0.04824   0.03640   0.00877
  0.08366   0.04832   0.03650   0.00880
  0.08378   0.04840   0.03660   0.00884
  0.08389   0.04848   0.03670   0.00887
  0.08401   0.04857   0.03680   0.00890
  0.08412   0.04865   0.03690   0.00894
  0.08423   0.04873   0.03700   0.00897
  0.08435   0.04881   0.03710   0.00900
  0.08446   0.04889   0.03720   0.00904
  0.08457   0.04897   0.03730   0.00907
  0.08469   0.04906   0.03740   0.00910
  0.08480   0.04914   0.03750   0.00913
  0.08491   0.04922   0.03760   0.00917
  0.08503   0.04930   0.03770   0.00920
  0.08514   0.04938   0.03780   0.00923
  0.08525   0.04946   0.03790   0.00927
  0.08537   0.04954   0.03800   0.00930
  0.08548   0.04963   0.03810   0.00933
  0.08559   0.04971   0.03820   0.00937
  0.08571   0.04979   0.03830   0.00940
  0.08582   0.04987   0.03840   0.00943
  0.08593   0.04995   0.03850   0.00947
  0.08605   0.05003   0.03860   0.00950
  0.08616   0.05011   0.03870   0.00953
  0.08628   0.05020   0.03880   0.00957
  0.08639   0.05028   0.03890   0.00960
  0.08650   0.05036   0.03900   0.00963
  0.08662   0.05044   0.03910   0.00967
  0.08673   0.05052   0.03920   0.00970
  0.08684   0.05060   0.03930   0.00973
  0.08696   0.05068   0.03940   0.00977
  0.08707   0.05077   0.03950   0.00980
  0.08718   0.05085   0.03960   0.00983
  0.08730   0.05093   0.03970   0.00986
  0.08741   0.05101   0.03980   0.00990
  0.08752   0.05109   0.03990   0.00993
  0.08764   0.05117   0.04000   0.00996
  0.08775   0.05126   0.04010   0.01000
  0.08786   0.05134   0.04020   0.01003
  0.08798   0.05142   0.04030   0.01006
  0.08809   0.05150   0.04040   0.01010
  0.08820   0.05158   0.04050   0.01013
  0.08832   0.05166   0.04060   0.01016
  0.08843   0.05174   0.04070   0.01020
  0.08855   0.05183   0.04080   0.01023
  0.08866   0.05191   0.04090   0.01026
  0.08877   0.05199   0.04100   0.01030
  0.08889   0.05207   0.04110   0.01033
  0.08900   0.05215   0.04120   0.01036
  0.08911   0.05223   0.04130   0.01040
  0.08923   0.05231   0.04140   0.01043
  0.08934   0.05240   0.04150   0.01046
  0.08945   0.05248   0.04160   0.01050
  0.08957   0.05256   0.04170   0.01053
  0.08968   0.05264   0.04180   0.01056
  0.08979   0.05272   0.04190   0.01059
  0.08991   0.05280   0.04200   0.01063
  0.09002   0.05288   0.04210   0.01066
  0.09013   0.05297   0.04220   0.01069
  0.09025   0.05305   0.04230   0.01073
  0.09036   0.05313   0.04240   0.01076
  0.09048   0.05321   0.04250   0.01079
  0.09059   0.05329   0.04260   0.01083
  0.09070   0.05337   0.04270   0.01086
  0.09082   0.05346   0.04280   0.01089
  0.09093   0.05354   0.04290   0.01093
  0.09104   0.05362   0.04300   0.01096
  0.09116   0.05370   0.04310   0.01099
  0.09127   0.05378   0.04320   0.01103
  0.09138   0.05386   0.04330   0.01106
  0.09150   0.05394   0.04340   0.01109
  0.09161   0.05403   0.04350   0.01113
  0.09172   0.05411   0.04360   0.01116
  0.09184   0.05419   0.04370   0.01119
  0.09195   0.05427   0.04380   0.01122
  0.09206   0.05435   0.04390   0.01126
  0.09218   0.05443   0.04400   0.01129
  0.09229   0.05451   0.04410   0.01132
  0.09240   0.05460   0.04420   0.01136
  0.09252   0.05468   0.04430   0.01139
  0.09263   0.05476   0.04440   0.01142
  0.09275   0.05484   0.04450   0.01146
  0.09286   0.05492   0.04460   0.01149
  0.09297   0.05500   0.04470   0.01152
  0.09309   0.05508   0.04480   0.01156
  0.09320   0.05517   0.04490   0.01159
  0.09331   0.05525   0.04500   0.01162
  0.09343   0.05533   0.04510   0.01166
  0.09354   0.05541   0.04520   0.01169
  0.09365   0.05549   0.04530   0.01172
  0.09377   0.05557   0.04540   0.01176
  0.09388   0.05566   0.04550   0.01179
  0.09399   0.05574   0.04560   0.01182
  0.09411   0.05582   0.04570   0.01186
  0.09422   0.05590   0.04580   0.01189
  0.09433   0.05598   0.04590   0.01192
  0.09445   0.05606   0.04600   0.01195
  0.09456   0.05614   0.04610   0.01199
  0.09467   0.05623   0.04620   0.01202
  0.09479   0.05631   0.04630   0.01205
  0.09490   0.05639   0.04640   0.01209
  0.09502   0.05647   0.04650   0.01212
  0.09513   0.05655   0.04660   0.01215
  0.09524   0.05663   0.04670   0.01219
  0.09536   0.05671   0.04680   0.01222
  0.09547   0.05680   0.04690   0.01225
  0.09558   0.05688   0.04700   0.01229
  0.09570   0.05696   0.04710   0.01232
  0.09581   0.05704   0.04720   0.01235
  0.09592   0.05712   0.04730   0.01239
  0.09604   0.05720   0.04740   0.01242
  0.09615   0.05728   0.04750   0.01245
  0.09626   0.05737   0.04760   0.01249
  0.09638   0.05745   0.04770   0.01252
  0.09649   0.05753   0.04780   0.01255
  0.09660   0.05761   0.04790   0.01259
  0.09672   0.05769   0.04800   0.01262
  0.09683   0.05777   0.04810   0.01265
  0.09694   0.05785   0.04820   0.01268
  0.09706   0.05794   0.04830   0.01272
  0.09717   0.05802   0.04840   0.01275
  0.09729   0.05810   0.04850   0.01278
  0.09740   0.05818   0.04860   0.01282
  0.09751   0.05826   0.04870   0.01285
  0.09763   0.05834   0.04880   0.01288
  0.09774   0.05843   0.04890   0.01292
  0.09785   0.05851   0.04900   0.01295
  0.09797   0.05859   0.04910   0.01298
  0.09808   0.05867   0.04920   0.01302
  0.09819   0.05875   0.04930   0.01305
  0.09831   0.05883   0.04940   0.01308
  0.09842   0.05891   0.04950   0.01312
  0.09853   0.05900   0.04960   0.01315
  0.09865   0.05908   0.04970   0.01318
  0.09876   0.05916   0.04980   0.01322
  0.09887   0.05924   0.04990   0.01325
  0.09899   0.05932   0.05000   0.01328

 

* ORIGINAL LANDSAT 8 RELATIVE SCATTER LOOKUP TABLE - REVISED TABLE ABOVE IS RECOMMENDED *

 

References

Chavez, P.S., Jr. 1996. Image-based atmospheric corrections–revisited and improved. Photogrammetric Engineering and Remote Sensing 62(9): pp.1025-1036.

Chavez, P.S., Jr. 1988. An improved dark-object subtraction technique for atmospheric scattering correction of multispectral data. Remote Sensing of Environment 24: pp.459-479.

USGS. 2013. Using the USGS Landsat 8 Product.  Cited at: http://landsat7.usgs.gov/Landsat8_Using_Product.php  

 

Background Information

Table was developed by calibrating values to actual Landsat 8 Lowest Valid Value scatter values and complies with principles described in Chavez (1988). Main principles are: 1) There should be high power correlations between band center wavelengths (x-axis) radiance (y-axis). Reflectance converted from radiance should still have a high, though not precisely the same, power line correlation with band center wavelength; reflectance converted from radiance typically has a larger power value (for example, if a radiance power value is -4, reflectance may be approximately -3 or -3.5). Power values associated with the correlation between Landsat 8 center bandwidth (x-axis) and Lowest Valid Values (y-axis) reflectance here are typically about 1.0 lower than from Chavez (1988) when radiance from Chavez is converted to reflectance and correlated to band center wavelength (and adjustments are made for Landsat 8 center bandwidth differences); for example, a power value of -4.5 here as opposed to -3.5 for a clear to very clear atmosphere in Chavez). 2) As the atmosphere becomes less clear, scatter from different bands becomes overall proportionally more similar as the ratio between blue and the larger wavelength bands becomes smaller. 

It is important to understand, that a Landsat 8 NIR scene commonly has many DN values that correspond to negative reflectance. Of the twenty-three images assessed here, four have had any value at all above zero reflectance; none of those four have been greater than .01 reflectance which is a realistic minimum reflectance.