Hi-gain and low-gain bands (13 and 14) of MODIS Aqua
Question:
How beneficial is the improved radiometric quality of the Hi-gain bands (13 and 14) at low radiances for ocean color products ?
Short answer:
At typical radiances, the SNR as calculated by a formula provided by MCST (based on on-orbit measurements
of the solar diffuser at varying illumination levels) are:
SNR for band 13L at 14.7052 [MODIS units] : 1961.66
SNR for band 13H at 14.7052 [MODIS units] : 2139.02
SNR for band 14L at 13.7836 [MODIS units] : 2174.53
SNR for band 14H at 13.7836 [MODIS units] : 2523.31
The improvement in SNR is only about 10% for band 13H, and 20% for band 14L. Even at lower radiance levels
(1/2 of Ltyp in the following calculations)
SNR for band 13L at 7.35260 [MODIS units] : 1157.91
SNR for band 13H at 7.35260 [MODIS units] : 1344.59
SNR for band 14L at 6.89180 [MODIS units] : 1278.55
SNR for band 14H at 6.89180 [MODIS units] : 1633.05
the improvement is only 15% and 30%, respectively. The FLH algorithm depends (implicitly) on the TOA radiance
difference between bands 13 and 14. At 1/2 Ltyp, the expected error of this difference due to the noise in the two bands
is 1.8% for the low-gain bands, and 1.5% for the high-gain bands.
It is likely that the improved SNR is mostly due to an improved readout (quantization), but the main noise source is something
else (e.g. detector intrinsic noise). The gain ratios of 13H/13L and 14H/14L are
2.0 and 2.7, resp. These differences are much larger than the change in SNR, which implies that the Hi-gain bands at TOA radiance
levels are not limited by quantization noise, whereas the Low-gain bands are affected by quantization noise, although it is probably not
the dominating error source.
A closer look:
Based on a recommendation by Sean Bailey, I used the MODIS Aqua granule A20072732135 to investigate the benefits of substituting bands 13H
and 14H for bands 13L and 14L.
From this granule, I selected only pixels where the flags ATMFAIL,LAND,STRAYLIGHT,CLDICE,CHLFAIL,MODGLINT were not set, and also where band
14H did not saturate (I chose a threshold of 12.5 MODIS radiance units,
13H always saturated when 14H saturated). The ratio of the Low-gain to the High-gain L1B radiances for the selected pixels
are shown in the following plots as a function of Low-gain radiance, for each band 13 and 14:
It can be seen that there is some variation in the ratio of about +/- 0.2%, and a bias of about 0.2% as well (Low-gain bands are higher than
the High-gain bands). With some additional analysis, it might be possible to reduce this bias to 0.1% (or at least to ensure that it is
consistent between bands 13 and 14), but this has not been shown yet.
Presumably, if the High-gain bands were to be used instead of the Low-gain bands, they would be used in both bands 13 and 14. The FLH algorithm
depends on the difference of the radiance between the two bands. The plot below shows the ratio of 14L/13L over 14H/13H as a function of 14L/13L:
It can be seen that there is no bias (the mean ratio of 14L/13L over 14H/13H is 1.00013), but there is a significant variation. In order to test whether
this variation can be explained by the SNR obtained with the MCST formula, I simulated this ratio, assuming the SNR at Ltyp for all radiance levels
(this assumption underestimates the noise, because most radiances where 14H does not saturate are below Ltyp). The results are shown in the plot below
(click here for IDL code used to create this plot):
The simulated ratios are very similar to the measured ratios (the cluster is a little tighter, which is expected because I used the SNR at Ltyp). This
is an indication that indeed most of the measured variation can be explained by the SNR of the individial bands. Therefore, it is reasonable to evaluate
the benefits to the FLH algorithm of using the high-gain bands based on the SNRs alone, as was done in the short answer at the top of this page.
The images below show the FLH values from a subscene of the granule (from the center, US westcoast is part of the subscene)
processed (using SeaDAS 5.1.3) with the Hi-gain bands (top, for more details on how the High-gain FLH was calculated
see explanation for Hi-gain nLw below) and Low-gain bands (bottom). The images look very
similar, possibly the Low-gain image shows more noise. The Hi-gain image has more stripes. For the Low-gain bands, Ewa Kwiatkowska
calculated a correction based on TOA residuals. This correction has not been calculated for the Hi-gain bands. I expect that the striping would be similar
in both images if corrections specific for the High-gain bands were applied.
It could be argued that other algorithms might benefit from the increase in SNR for the high-gain bands. Below are scatter plots of the nLw for bands 13 and
14, High-gain versus Low-gain, the red dashed line is the 1-to-1 line:
SeaDAS usually calculates the nLw of bands 13 and 14 using the Low-gain band. To create the nLw using the High-gain bands for the above plots,
the Low-gain bands in the L1B file were overwritten
with the High-gain bands, after adjusting the mean L1B radiance of the High-gain bands to the mean L1B radiance of the Low-gain bands. These plots show that
apart from calibration differences (which were removed by the above adjustment), there does not seem to be any fundamental difference between the High-gain and
the Low-gain bands. Although this result was expected, it is a nice confirmation.
For further information, please contact:
Gerhard Meister, Futuretech Corp.
Ocean Biology Processing Group, NASA/GSFC Code 614.2
Building 28, Room W119, Greenbelt, MD 20771 USA
Tel #: (301) 286 - 0758, FAX #: (301) 286 - 0268
email: meister@simbios.gsfc.nasa.gov
