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Effect of bit depth (8-bit vs. 13-bit) on the noise level of GOES Sounder data

This section was generated to assess the effect of 1-byte vs. 2-byte precision on the quality of data from the GOES Sounder. Data with 2-byte (13-bit) precision and the same data reduced to 1-byte (8-bit) precision were analyzed to determine the effect of bit depth on noise levels. This analysis was accomplished using spatial structure analysis to determine the noise between adjacent pixels using data/imagery from real earth scenes.

The following two figures (which are rocking back and forth very slowly to begin) give the noise levels in temperature units for GOES Sounder IR bands 1-18. Each figure gives two estimates of the noise level for each band (the two vertical shaded bars). These were determined using spatial structure analysis (see elsewhere for details on this analysis technique). The third, longer bar is the standard deviation of the measurements in the same portion of the GOES images that were analyzed using structure analysis. This third value, which indicates the variability of the measurements in the analysis area (including any gradient), is normally larger/bigger than the other two structure-estimated values which are determined using a technique which seeks to eliminate any gradient that exists among the measurements.

In one of the two figures the Sounder data originated as 2-byte (13-bit) counts, and in the other figure the same data were reduced to 1-byte (8-bit) counts. For 2-byte the raw data are expressed in GVAR counts, and for 1-byte the raw data are expressed in brightness counts. The change from 2-byte to 1-byte data is through a standard non-linear transformation that allows the data to be displayed on most image analysis systems (see elsewhere for details on this transformation process). Because of the loss of precision due to the down-conversion from 13-bits to 8-bits, there may be a resulting increase in noise. By comparing the two figures the noise appears to increase for most of the GOES Sounder bands. However the amount of increase differs for each band and may or may not be significant. Small vertically-plotted numbers above the bars give the plotted values. (The horizontally-plotted numbers are signal to noise rations, which should correspondingly decrease as the noise increases.) The reason for the differing effect on different GOES bands is due mainly to the fact that the noise level of some of the Sounder bands is larger than the limiting precision of 8-bit data. For those bands a 2-byte representation does not offer an advantage, and 1-byte (8-bit) precision is sufficient to fully represent that data without introducing additional noise. But for other bands the noise is smaller than the limiting precision of 1-byte data. For these bands a 2-byte representation offers an advantage in noise reduction. The differing effects will be explained in more detail below.

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The reason for the differing effects of bit-reduction on noise in different Sounder bands requires a look at the noise in the raw counts used for both the 2-byte and 1-byte representations of the data. In the table below GOES Sounder IR bands 1-18 are analyzed in both 2-byte (13-bit) and 1-byte (8-bit) representations of the data. Separate columns give the noise in both counts and temperature units as well.

The 2nd and 3rd columns give the noise in 2-byte and 1-byte counts respectively. In either count units, noiseless data would result in a noise level of +/-0.5 count due only to the effect of digitizing the measurements into discrete values. Each digitized value is only certain to its count value plus and minus a half count. A single measurement cannot be determined to any better precision.

GOES Sounder noise (2-byte vs. 1-byte data)
Sounder band 2-byte (13-bit) noise (GVAR counts) 1-byte (8-bit) noise (brightness counts) 2-byte (13-bit) noise (K) 1-byte (8-bit) noise (K) Ratio of temperature noise
1 142 2.63 2.61 2.63 1.01
2 109 1.95 1.95 1.95 1.00
3 86 1.40 1.38 1.40 1.01
4 59 2.01 0.99 1.01 1.02
5 51 1.73 0.85 0.87 1.02
6 43 1.34 0.64 0.67 1.05
7 44 1.42 0.70 0.71 1.01
8 43 1.40 0.70 0.70 1.00
9 28 1.05 0.50 0.52 1.04
10 19 0.59 0.26 0.29 1.12
11 27 0.67 0.32 0.33 1.03
12 58 1.08 1.06 1.08 1.02
13 58 1.55 0.78 0.77 0.99
14 48 1.81 0.90 0.91 1.01
15 82 3.07 3.09 3.07 0.99
16 36 1.57 0.78 0.79 1.01
17 46 1.73 0.87 0.87 1.00
18 29 1.14 0.55 0.57 1.04

In the 2nd column none of the noise estimates approach the digitization limit of +/-0.5 count, which means that a 2-byte representation allows full precision data. However for the 1-byte representation in the 3rd column the noise in a few Sounder bands approaches that digitization limit. In particular Sounder band-9 and 10 have the lowest estimated noise of 0.57 and 0.67 count respectively at 1-byte, very close to the limiting digitization of 0.5 count. Several other bands have low noise as well, although not down to the digitization level. The bands with low noise may be limited by the digitization into 8-bits. By looking back at the count noise for 2-byte data in the 2nd column it may be possible to determine which bands may be so affected. If the transformation between GVAR and brightness counts were linear the equivalent of 1-bit in 8-bits data is 32 bits in 13-bit data. (The difference is 5 bits or 25 = 32.) However, since the transformation is not linear it is not that easy to directly compare 1-byte and 2-byte noise. Rather, of concern are the bands with low noise in 2-byte representation. In particular GOES bands 9 thru 11 and band 18 have the lowest noise in terms of 2-byte counts.

In the 4th and 5th columns are the noise levels in temperature units for 2-byte and 1-byte data respectively. The temperature noise levels are the values plotted in the figures already presented. It is easier to compare the noise levels when they are in the same units. Finally, the last column gives the ratio of the temperature noise from the 4th and 5th columns. Here quantitatively are the increases in noise due to the decrease in precision from 2-bytes to 1-bytes. Sounder band-10 (the lowest-level water vapor band) is the worst case, with an increase in noise of 12%. Several other bands have noise that has increased by 3% or more: band 6 (longwave IR), bands 9 thru 11 (ozone and the two lower-level of the three water vapor bands), and band 18 (shortwave IR). As previously explained, for most of these bands the increase in noise is correlated with either a noise level that is low in 1-byte representation or a noise level that is near or below the linear equivalent of 1-byte noise when expressed in 2-byte form.

Summary

The effect of bit depth on the quality of GOES Sounder data has been determined for one sample of data. Because of the limited sample used in this study the noise estimates are valid only for the data that was analyzed and do not necessarily represent the best estimates of the noise levels of Sounder data. However, these noise estimates are valid for the purpose of this comparative study. The reduction from 2-byte to 1-byte precision results in an increase in existing noise by up to 12% for GOES Sounder WV band-10. The magnitude of the effect depends on the band/wavelength and on the relationship of the noise level to the digitization level. In general, several Sounder bands are measurably affected by an increase in noise of several percent when the data precision is reduced, most notably in selected IR bands and the two of the three WV bands.

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