AAPP calculates the lunar angles for each scan and all four DSVs and writes part of this information in the level 1b file. Therefore, it is possible to identify the smallest lunar angle for each DSV. Unfortunately the calculation with AAPP is subject of several uncertainties.

The error in the moon calculation is at worst 0.3∘ . This value has been confirmed by the analysis of Moon intrusions in . It is caused by incomplete knowledge of the alignment of the satellite; the position of the Moon is known with very high accuracy.

The value for a from the second Gauss fit now gives the number of counts the Moon would have provided, if it had been in the centre of the DSV, and it was used, after division by the gain, to calculate the ratios of the brightness temperatures in channels 18, 19, and 20 (last column in Table ). The values from channels 18 and 19 were averaged in order to reduce the noise in the reference, to which channel 20, the one with the highest bias (see Sect. 1), is compared. In cases where the Moon could only be detected in two DSVs, we used the brightness temperatures as measured in the DSV that came closest to the Moon. This method was only applied, when we could conclude from the relative strengths of the signals in the two DSVs, where the Moon appeared, that the lunar angle must have been very small (< 0.2∘) in one of them. This way the impact of pointing uncertainties on the signal from the Moon is kept as small as possible. However, our values do not represent the actual temperature of the Moon, because we did not correct for the fact that it does not fill the beam.

This calculation ignores the cold space correction factors, i.e. the correction for Earth and platform radiation entering through the side lobes, but they should be the same for each sounding channel, because they use the same quasi-optic feed, and thus cancel out in the ratios of the signals that we consider here. The same is true for the warm load correction factors, which according to AAPP differ among the sounding channels only for AMSU-B on NOAA-17. The effect of the band correction that allows for the fact that the sounding channels receive slightly different fluxes because of their side bands being at different distances from 183.311 GHz was ignored, because it amounts to less than 2 ‰ and does not change with time.

An important characteristic of the beam, namely its full width at half maximum, follows immediately from the peak width of the Gauss fit, which is related to the full width half maximum via σ=FWHM/8×ln⁡2. In the across-track direction the Moon can only be detected in three DSVs with sufficient signal-to-noise ratio, and the smear effect alters the measured beam shape. Therefore, it is less accurate than the one measured in the along-track direction, where the FWHM of the beam can be determined from light curves with dozens of points representing an almost perfect Gaussian. Random samples showed no deviations ≥ 0.15∘ from the nominal value of 1.1∘ for the FWHM of the beam.

The average ratio between the signals obtained in channels 18, 19, and 20 is 1.001 ± 0.006 for all observations in Table  combined. It is 0.993 ± 0.008 for the twelve values from the years 2001 and 2004 and 1.007 ± 0.008 for the later Moon intrusions. Within the calculated uncertainties these figures are in agreement with the values derived by and from simultaneous nadir overpasses. The uncertainties were determined from the distribution of the measured values, i.e. they include contributions from the noise in each sounding channel.

For a comparison of the pointing directions of DSVs two and three in the across-track direction, as calculated with AAPP (min moon angle) and with the aid of a Gauss fit (see Sect. ), we now consider only the years 2001 and 2004, because the noise was lowest in the beginning of the mission. We find a difference of -0.113∘ ± 0.019∘, i.e. the DSV direction determined with the Gauss fit leads the one calculated with AAPP by about 0.1∘ in the scan direction. The systematic error in the absolute pointing direction of the sounding channels of AMSU-B on NOAA-16 lies well below the upper limit of the overall, i.e. across- and along-track, pointing error of 0.2∘ for channel 16 that was given by .

The above mentioned smear effect can cause a pointing error, because the Moon moves a short distance through the field of view during the finite duration of the measurement. However, the same effect is present with observations of Earth scenes, hence the pointing positions derived from the intrusions of the Moon in the DSV are more relevant than those calculated with AAPP.

The non-linearity correction coefficient is zero for all sounding channels of all AMSU-B flight models at all reference temperatures in the file of AMSU-B calibration parameters (amsub_clparams.dat, version 25) used by AAPP. In order to investigate whether a non-linearity developed during the mission, we consider how the corresponding bias would change as a function of scene temperature, bearing in mind that Q∝(Cs-C‾w)⋅(Cs-C‾c). find for Channel 20 (they call it Channel 5) of AMSU-B on NOAA-16 a bias of about 3 K in the year 2008 relative to AMSU-B on NOAA-15, which is mainly due to an anomalous decreasing trend of unknown origin for N16. This bias is independent of the natural target chosen for the Earth scene, Antarctica or tropical oceans. Similar phenomena with AMSU-A were corrected by postulating a modified, time dependent u . However, the values in Table  demonstrate that the bias should be between 6 and 11 times larger in observations of polar regions and between 5 and 8 times larger in observations of the Moon than when derived from data collected over warm bodies of water, if it was due to non-linearity with AMSU-B as well. The reason is that the effect of the non-linearity on the calculated radiance becomes very small for scene temperatures close to those of the black body or the cosmic microwave background. The brightness temperature of the atmosphere in Channel 20 is of course subject to variations, and the difference between the counts from black body and deep space is rather small because of the instrument gain degradation. However, when we allow an uncertainty of a factor of 2 in its difference to the temperature of the black body, the spread of values of Q for the different scenes in Table  is incompatible with the observation that the biases depend very little on radiance. Non-linearity can thus be ruled out as an explanation for the inter-channel trends.

The cold space temperature bias correction δTc,ch is for a given DSV, the same for all sounding channels of AMSU-B on NOAA-16 in the file of calibration parameters (version 25) used by AAPP. It varies between 1.09 and 1.26 K among the four possible DSV directions. In order to investigate whether the cold space temperature bias changed during the mission, we consider how its impact varies with scene temperature, bearing in mind that in first approximation, i.e. neglecting the non-linearity term, δTc,ch∝Cs-C‾wC‾w-C‾c. We make use of the same reasoning as in Sect.  by constructing a contradiction between expected and observed variation of the bias with scene brightness.

The values in Table  demonstrate that the bias should be up to 60 times larger in observations of the Moon than when derived from data collected over warm bodies of water. The reason is that the effect of the cold space temperature bias on the calculated radiance is largest for scene temperatures close to those of the cosmic microwave background. Even when the bias in Channel 20 were only 1 K, a lower limit in view of the variations reported by , it would amount to an error of 40–60 K in the combined signal from Moon and CMB in the DSV. The actual error is about an order of magnitude smaller , hence cold space temperature bias can be ruled out as an explanation for the inter-channel trends as well.

The warm target bias correction δTbb,ch is zero for all sounding channels of all AMSU-B flight models at all reference temperatures in the file of AMSU-B calibration parameters (version 25) used by AAPP, except for channel 20 on FM3, where it is -0.16 K. Here the situation is the opposite of the previous case insofar as the warm target bias affects the measurements less for lower scene temperatures. This is intuitively clear and follows from the fact that the second term of the sum on the right side of the measurement equation is negative for Cs≤C‾w. The Moon intrusions do therefore not help to characterize effects originating in the black body. A warm target bias correction for channel 20 about 10 times as large as the biggest value used by AAPP for any flight model would be needed. On top of that the correction for the other sounding channels, where the bias is different or not existent, would have to have opposite sign or be zero. While this possibility cannot be ruled out completely, it seems highly unlikely, especially given the fact that the platinum resistance thermometers (PRTs) on the black body of the instrument in question gave no hint at dramatic alterations to the temperature pattern of the black body; see Fig.  and for a discussion of temperature drifts .

Another effect that cannot be characterized with Moon intrusions is the emission of the main reflector and the variation of its contribution to the antenna temperatures as it rotates during a scan. According to Eq. (3) a correction to the measured radiance is required that is proportional to trigonometric functions of the distance of the rotating reflector from nadir position and α. Its value for Earth scenes is quite different than the one for observations of the Moon, because of the different position of the reflector in either case. However, in the first approximation, it must be the same for all sounding channels, because they all operate at the same centre frequency of 183 GHz and should therefore have very similar values for α. The values found in the relevant calibration file from AAPP for MHS are ∣α∣=0.0022 at 183 GHz and ∣α∣=0.0021 at 190 GHz. The sign must be the same for all channels of AMSU-B, because they have the same polarization. Hence the maximum difference the non-unity antenna reflectivity can make among the sounding channels is 10-4⋅(Rw-Rs), a negligible amount.

Having discussed the main sources of error in the flux calibration we turn our attention to drifts of channel frequencies as a possible explanation of the bias that channel 20 exhibits when observing Earth scenes. (A change of centre frequency would make no difference to the Moon observations, see Sect. 2.3). An accurate value of B(ν+δν), i.e. the impact of a change in frequency on the measured flux, is difficult to calculate for channels 18 and 19, because the exact shape of the water vapour absorption line depends on the state of the atmosphere. However, it is possible to give at least an estimate of the shift in frequency required to change the measured radiance by 0.4 %, i.e. causing an error of about 1 K, for channel 20 because this one probes the well-characterized wings of the line profile . It amounts to 3.5 GHz. This value is 50 times larger than the specification for frequency stability . As all sounding channels use the same local oscillator, the same frequency shift would apply to channel 18 with 10 times the effect on radiance. However, such an enormous bias is not observed.

As we found no fault with the calibration of AMSU-B on NOAA-16, we searched for instrumental effects that could alter the counts used as input of the calibration process. Malfunction of the processing electronics can be ruled out, because the data from all channels are clocked into the same AMSU instrument processor. However, there is another phenomenon with the potential to strongly affect the counts, namely radio-frequency interference (RFI). The bias it causes can be positive or negative and depends on channel, scan angle, and the transmitter in use. It was demonstrated in ground tests that AMSU-B on NOAA-16 was susceptible in all channels to radiation of the spacecraft transmitters. The strongest effects were observed with channel 19 at the SARR (Search And Rescue Repeater) frequency, with channel 16 at the SARR frequency, and with channel 17 at the STX-1 (S-Band Transmitter #1, 1698 MHz) frequency . Modifications of the instrument, e.g. wrapping cables with electrically conductive aluminum tape, were carried out as a consequence of the problems encountered with AMSU-B on NOAA-15 and reduced this susceptibility by 1–2 orders of magnitude. From the NOAA-16 post launch orbital verification tests it was estimated that the remaining Earth view biases, though difficult to quantify, were within ±0.5 K when the transmitter is active . However, Channel 17 produced even after launch a bias of 1.2 K for the space view due to interference with the STX-2 omni-directional antenna. Additionally, during the lifetime of the satellite the gain of the sounding channels decreased tremendously (see Table  and ). A reduced gain produces a reduced signal, which means that interference becomes relatively more important, as described by . The overall reduction of signal during the mission lifetime due to gain degradation, a factor of 6 for channel 19 between 2001 and 2010, could boost a bias of 0.5 K pre-launch up to 3 K and more during flight. Therefore, we conjecture that individual interference events caused a bigger and bigger bias over the years, but at the same time the noise equivalent difference in temperature (NEΔT) increased, making them still difficult to detect. We know from the experience with NOAA-15 that interference effects can be quite different for Earth and space views, hence RFI could be absent in the observations of the Moon while still affecting Cs.