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GOES image noise characteristics in different unit scales

All measurements contain noise. In the case of GOES imagery, the satellite measurements are collected as radiances (digitized into 10-bit GVAR counts) and are then converted into temperatures or further converted into brightness (8-bit display) counts for users of the data. The process of converting GOES measurements into different unit systems is covered at: http://rammb.cira.colostate.edu/research/calibration/goes_image_display/calibration.asp.

In each step, the noise in the original measurements is transformed into noise in the new units. The following information is provided to explain how that measurement noise in manifest in temperatures and in 8-bit display counts.

The noise specifications for the GOES Imager bands are given in the following table. The noise is constant in radiance units. When converted into temperature units the noise changes depending on the scene temperature due to the non-linear (Planck) relationship between radiance and temperature. The noise is specified at two scene temperatures (230 K and 300 K) for all of the GOES infrared bands except band-3.

GOES Band Central Wavelength Instrument Noise Specifications Radiance Noise Derived from Specifications
1 0.7 m 0.67% albedo @ 100% albedo 3.4 W/(m2·sr·m)
2 3.9 m 1.4 @ 300 K, 19.1 @ 230 K 0.053 mW/(m2·sr·cm-1)
3 6.7 m 1.0 @ 230 K 0.14 mW/(m2·sr·cm-1)
4 10.7 m 0.35 @ 300 K, 0.82 @ 230 K 0.59 mW/(m2·sr·cm-1)
5 12.0 m 0.35 @ 300 K, 0.71 @ 230 K 0.61 mW/(m2·sr·cm-1)

GOES-8, GOES-9, and GOES-10 noise levels

The noise levels for GOES-8, GOES-9, and GOES-10 (launched in 1994, 1995, and 1998 respectively) are given in columns 3, 4, and 5 in the following table. These noise levels are compared to the instrument specifications from the table above, reproduced in column 2 below. The GOES noise levels are also compared to the radiance associated with 10-bit GVAR digitization in the last column. The radiance noise levels for GOES-8, 9, and 10 will be translated below into noise levels in temperature units, which are easier for the user to understand.

GOES Band Radiance Noise Derived from Specifications GOES-8 Radiance Noise GOES-9 Radiance Noise GOES-10 Radiance Noise 10-bit GVAR Digitization Radiance Units
1 3.4 1.5 1.7 1.5 0.275 W/(m2·sr·m)
2 0.053 0.006 0.003 0.005 0.0022 mW/(m2·sr·cm-1)
3 0.14 0.040 0.022 0.019 0.0129 mW/(m2·sr·cm-1)
4 0.59 0.20 0.11 0.17 0.096 mW/(m2·sr·cm-1)
5 0.61 0.35 0.24 0.20 0.100 mW/(m2·sr·cm-1)

From the table above, GOES-8, 9, and 10 perform much better than specifications. Also the available precision of 10-bit GVAR counts for Imager is lower (better) than the noise levels for all bands on all three GOES. As a result, the precision of 10-bit scaling of the data is able to capture all of the signal available in GOES measurements without imposing any additional restriction on the noise in those measurements.

Relationship of radiance noise to temperature noise

(NEDR* to NEDT**)

The following three plots show the relationship between radiance noise (a constant value) and temperature noise (a function of the scene temperature) for GOES band-4, band-2, and band-3, respectively. On each plot the radiance noise is represented by three closely-spaced dashed vertical lines at each of three different locations (at radiances corresponding to scene temperatures of 230 K, 265 K, and 300 K). The three dashed vertical lines represent a radiance value and that same value plus and minus the constant increment of radiance noise. In each plot the increment of noise is the GOES-8 measured noise for that band in radiance units.

The resulting temperature range associated with the radiance noise, at each of the three scene temperatures, is represented by thee dashed horizontal lines connected to the dashed vertical lines where they intersect at the radiance-to-temperature plot. Those three horizontal lines are the temperature and the temperature plus and minus noise. This is graphically the process of converting radiance noise into temperature noise as a function of temperature. The noise in temperature units is not constant like the noise in radiance units, but increases for colder scene temperatures, since the slope of temperature-to-radiance is not constant.

For GOES band-4 (10.7 m) the temperature vs. radiance line is almost linear. (The same is true for GOES band-5, not shown.) Therefore the slope of the line is nearly constant. This translates into an only slightly varying temperature noise over the range of earth-scene temperatures normally encountered in this band. The temperature noise increases slightly for colder scenes, by a little over a factor of 2 from +/-0.12 (at 300 K) to +/-0.28 (at 230 K).

band-4 noise equivalent delta temperature derivation

Unlike GOES band-4, for GOES band-2 (3.9 m) the temperature vs. radiance plot is highly non-linear. The slope of the line is far from constant and is quite steep for cold scene temperatures. For the coldest scenes, where the slope is the steepest, the resulting temperature noise is very large, plus and minus 4 K for 230 K scene temperatures. Users of GOES band-2 (shortwave) imagery need to be aware of the potential for very noisy measurements from cold scenes in this band. (The noisy values occur only at night for earth scenes. During the day there is an additional reflected solar component to measurements in this band, increasing the scene temperature above the surface radiance alone.)

band-2 noise equivalent delta temperature derivation

For GOES band-3 (6.7 m) the temperature vs. radiance plot is not quite as linear as that for GOES band-4, nor is it as steep as that for GOES band-2. For colder temperatures, where the slope is steeper, the temperature noise is much larger than it is for warmer temperatures, +/-0.28 K at 230 K versus +/-0.05 K at 300 K (although the noise is not specified at that temperature).

band-3 noise equivalent delta temperature derivation

Noise as a function of temperature

The following three plots show a continuous representation of temperature noise (NEDT = Noise Equivalent Delta Temperature) vs. temperature for GOES band-4, band-2, and band-3, respectively. (The results for GOES band-5 are very similar to those for GOES band-4.) Four lines are plotted in each graph. Three of the four lines, the three curved lines, represent the temperature noise for GOES data as converted from different values of radiance noise. Three of the four lines, the three curved lines, represent the temperature noise for GOES data as converted from different values of radiance noise. The three curved lines represent the temperature noise associated with the actual measurements from GOES-8, 9, and 10. The upper line represents the GOES-8 values, the middle line represents the GOES-10 values, and the lower line represents the GOES-9 values. The lines appear in this order on these graphs because the noise levels for GOES-10 band-4 and band-2 are lower than the noise levels for the same GOES-8 bands, and the noise levels for GOES-9 infrared bands are lower than those for the same GOES-10 bands.

Finally, the change from 10-bit GVAR counts into 8-bit display counts may result in a loss of precision as well. That conversion is a bi-linear conversion of temperatures into 8-bit counts. The process of converting GOES measurements into different unit systems is covered at: http://rammb.cira.colostate.edu/research/calibration/goes_image_display/calibration.asp.

Each 8-bit count is precise to +/-0.5 count (for example, a count of 100 can represent any value between 99.5 and 100.5). This count precision can be converted into an equivalent temperature precision as a function of temperature. The following table summarizes the conversion from count precision into temperature precision using the slope of the 8-bit bi-linear temperature LUT.

Scene temperature range T < -31C [242 K] T > -31C [242 K]
Count precision +/-0.5 count +/-0.5 count
Slope of temperature to counts 1 K / count 0.5 K / count
Temperature precision +/-0.5 K +/-0.25 K

This results in the two-part straight line in each graph below. That line represents the temperature precision associated with the conversion to display counts used by image display systems, or the maximum precision allowed by the digitization of the measurements into 8-bit display counts. If these values are anywhere larger than the instrument noise, then there is an additional constraint on the precision of measurements from that GOES band.

For GOES band-4 (10.7 m) the precision associated with the conversion to an 8-bit bi-linear scale is larger than the measured instrument noise for all but the coldest scenes for both GOES-8 and GOES-10. This means that there is a loss of precision by digitization to the 8-bit level for nearly all earth-scene temperatures (and for all temperatures for GOES-9). For this band, 10-bit precision is needed to realize the full signal in GOES Imager data.

band-4 noise equivalent delta temperature vs. temperature

For GOES band-2 (3.9 m) the precision associated with the conversion to an 8-bit bi-linear scale is lower than the noise level for all three GOES except for the warmest scenes. Thus there is no additional restriction for colder scenes, where the measurements are already quite noisy due to the steep slope of temperatures to radiances at this wavelength. For both GOES-8 and GOES-10 the digitization to 8-bits limits the precision of measurements only for scenes above about 285 K, and for GOES-9 (with lower noise) the digitization to 8-bits limits the precision of measurements only for scenes above about 270 K. Full 10-bit data in this band would improve the precision of measurements from these warmer scenes only, unlike for GOES band-4 where there is improvement for nearly all earth scenes.

band-2 noise equivalent delta temperature vs. temperature

For GOES band-3 (6.7 m) the relative precision associated with the 8-bit scale has a similar relationship to the noise levels for GOES-8, 9, and 10 as it does for GOES band-4, although the absolute values of the noise are much greater in temperature units. The precision associated with the conversion to 8-bits is larger than the measured instrument noise for all but the coldest temperatures for all three GOES. This means that there is a loss of precision by digitization to the 8-bit level for nearly all earth-scene temperatures. For this band, as was true for GOES band-4, 10-bit precision is needed to realize the full signal in GOES Imager data.

band-3 noise equivalent delta temperature vs. temperature

Summary

The relationship between radiance noise, a constant, and temperature noise, which is an increasing function for colder scenes, was explained above. The noise levels for GOES-8, 9, and 10 were also compared to the precision available from measurements digitized to the 8-bit brightness count levels. The full signal from all three GOES can be realized only by using 10-bit measurements, whereas there is loss of precision when the data are converted into 8-bit brightness counts, especially for the GOES infrared bands with lower noise, such as GOES band-4.

Back to RAMM Branch GOES image display page.