An algorithm for detection and correction of the lunar contamination in the Advanced Microwave Sounding Unit–A (AMSU-A) data is applied to study the observed lunar contamination in the NOAA 18 AMSU-A data. The algorithm is based on a physical model of the lunar surface brightness temperature and the AMSU-A antenna pattern powers to detect the lunar contamination in cold space calibration counts over a large number of scans. The algorithm performs a scan-by-scan detection and correction of the effect of lunar contamination on the AMSU-A data. It is found that the lunar contamination is significant only when the separation angle between the lunar disk and the antenna space viewing is less than 4°, beyond which no significant lunar contamination is detected, as the AMSU-A antenna power drops below 40 dB from its peak. The parameters of the AMSU-A antenna pattern powers are determined from least squares fit to the observed lunar contamination counts extracted from the cold space counts. Using the best fit parameters, we investigated the effect of the lunar contamination on the AMSU-A scene temperatures. It is found that the differences ΔTS between the near-nadir (field of view, FOV 16) scene antenna temperatures calculated with and without correction of lunar contamination vary with channels. It is about 1.5 K over ocean at channels 1 and 2 but only 0.38 K at channel 4. This trend in the ΔTS variation as a function of channels is easily understood by examining the two-point calibration equation. The results presented in this study show that the lunar contamination in the AMSU-A space calibration counts can be accurately detected and that its effect on the measured scene antenna temperatures can be corrected. The algorithm provides a practical approach for scan-by-scan correction of the lunar contamination in AMSU-A data and improves the accuracy of operational calibration of NOAA Level 1B data. An assessment of the postlaunch instrument performance is also presented.
 The Advanced Microwave Sounding Unit-A (AMSU-A) is a new generation of total-power microwave radiometers built for the NOAA-K, L, M, N, and N' series of Polar-orbiting Operational Environmental Satellites (POES). Traditionally, a NOAA Satellite is named by an alphabetical letter before launch, after which a numerical series number replaces its letter nomenclature. The AMSU-A radiometers onboard NOAA 15, 16, 17, and 18, which were launched in May 1998, September 2000, June 2002, and May 2005, respectively, are the first four of the series. Each AMSU-A instrument is composed of two separate units: AMSU-A2 with channels 1 and 2 at 23.8 and 31.4 GHz, and AMSU-A1 with twelve channels in the range of 50.3 to 57.3 GHz which are used for temperature sounding from the surface to about 50 km, (i.e., from ∼1000 to ∼1 mb) plus channel 15 at 89.0 GHz. In total, AMSU-A furnishes 15 channels. A more complete description of the AMSU-A instrument and its radiometric performance were reported elsewhere [Mo, 1996, 1999]. The main channel characteristics of the NOAA 18 AMSU-A instruments were described by Mo . Channels 1–3 and 15 are referred to as the window channels, as they sense atmospheric temperatures near the surface. These window channels aid the retrieval of atmospheric temperatures by providing information to correct the effects due to surface emissivity, atmospheric liquid water, and total precipitable water vapor. The two low-frequency channels also provide information on precipitation, sea ice, and snow cover.
 AMSU-A is a cross-track, step-scan instrument and executes one complete revolution every 8-s period. The AMSU-A antenna systems have a nominal field of view (FOV) of 3°20′ at the half-power points (covering a 50-km diameter footprint at nadir) and execute a cross-track scan with 30 Earth FOVs within ±48°20′ from the nadir location, one cold calibration FOV, and one warm blackbody FOV per 8-s scan period. FOVs 1 and 30 are the outermost scan positions of the Earth views, while FOVs 15 and 16 (at ±1.67° from nadir) straddle the nadir.
 AMSU-A is a self-calibrating total power radiometer. The on-board calibration is achieved by viewing the cold space and an internal blackbody target. This provides a two-point calibration reference. AMSU-A has four possible space view (SV) positions, which are referred to as SV1, SV2, SV3, and SV4, located at 83.3°, 81.67°, 80.0°, and 76.67°, respectively, from the Nadir. SV1 is closest to the satellite platform and therefore possibly susceptible to contamination from the spacecraft. SV4 is closest to the Nadir therefore possibly susceptible to contamination from the atmosphere and Earth's limb. One of the space views must be chosen in the normal on-orbit operation. An optimally chosen space view position will produce space radiometric counts with minimum contamination from all sources (including the spacecraft, atmosphere, and the Earth). In current NOAA 18 operation, SV1 is used by AMSU-A1 and SV2 by AMSU-A2.
 Lunar contamination of the space radiometric counts occurs whenever the Moon moves across the space FOV. It has been observed that this happens several times a year, typically affecting several successive orbits. On the basis of the area ratio of the lunar disk to the effective area of the antenna main beam cone, the increment in the cold space brightness temperature when viewing the Moon is approximately 1.5% of the lunar surface brightness temperature. Since the lunar surface brightness temperature can vary from 120 to 380 K which is much higher than the deep space cosmic background temperature of 2.73 K, the lunar contamination can seriously impact the calibration accuracy if it is not corrected.
 In a previous investigation, Kigawa and Mo  studied the lunar contamination in the NOAA 15 and 16 AMSU-A data (available at ftp://ftp.orbit.nesdis.noaa.gov/pub/smcd/spb/tmo/NOAA TR NESDIS 111.pdf). They observed that the lunar contamination can contribute a maximum of 40 extra counts to the nominal AMSU-A space counts. In the worst case, such extra space counts can produce an error of ∼1.5 K in the measured ocean brightness temperature of 150 K at channels 1 and 2. The AMSU-A data (G. Goodrum et al. (Eds.), 2000, NOAA KLM User's Guide, available at http://www.ncdc.noaa.gov/oa/pod-guide/ncdc/docs/klm/html/c7/sec7-3.htm) have been used extensively in many applications [Ferraro et al., 2000; Goldberg et al., 2001; Rosenkranz, 2001; Baker and Campbell, 2004; Karbou, 2005; Karbou et al., 2005; Prigent et al., 2005] at NOAA and worldwide agencies to generate products for weather forecasting, atmospheric temperature retrieval, and hydrological studies. An error of ∼1.5 K may have significant adverse effect on these products. An algorithm [Kigawa and Mo, 2002], which was developed for detection and correction of the lunar contaminations in the NOAA 15 and 16 AMSU-A data, has attracted considerable interest among the microwave data user community. In this study, the algorithm is further developed and applied to study the lunar contamination in the NOOA 18 AMSU-A data. It shows that the algorithm is reliable and accurate to detect the lunar contamination in the space counts, and that the effect of lunar contamination on the AMSU-A measurements can be eliminated. The adverse effect of lunar contamination on the scene antenna temperatures is demonstrated if the lunar contamination is not corrected.
 The theoretical model of lunar contamination is described in section 2, and the detection of lunar contamination is presented in section 3. Section 4 shows how to obtain the antenna pattern parameters from least squares fit to the lunar contamination counts. The effect of the lunar contamination on a scene antenna temperature is demonstrated in section 5. A brief assessment of the postlaunch performance of the NOAA 18 AMSU-A is presented in section 6. A summary and discussion are given in section 7.
2. Theoretical Model
2.1. Effective Moon Temperature
 To correct the lunar contamination in AMSU-A data, it is required to know the effective lunar surface brightness temperature. In this section the lunar surface temperatures are examined to derive a simple expression for the effective lunar surface brightness temperature. Figure 1 shows a sketch of the lunar surface geometry that can be used to derive the effective Moon temperature (EMT) as a function Sun-Moon separation angle θ. The origin is at the center of the Moon, the x axis is directed toward AMSU-A, and the Sun is on the x-y plane. Longitudinal and latitudinal angles are denoted by λ and Φ, respectively.
 Assuming that the average emissivity of lunar surface soil and rock is 0.95, then the effective emissivity of lunar disk, ɛ, can be calculated by
Assume that the cavity effect is proportional to the cos(satellite zenith angle) which is described by cosϕcosλ in Figure 1; the EMT as a function of θ is given by
where the lunar surface temperature, T(χ), which ranges from 120 K in night to 380 K in day time, can be expressed as a function of the solar zenith angle, χ, by
Numerical calculation of the EMT values from equation (2) as function of θ from 0° to 180° was performed in an early report [Kigawa and Mo, 2002], and the calculated results were represented by a parametrical expression, Tmoon, in the form,
The effective Moon brightness temperature in equation (4) is suitable for use to correct the lunar contamination in AMSU-A data.
2.2. Correction of Lunar Contamination
 When the lunar disk appears in the AMSU-A space view, the space counts are contaminated as the lunar surface temperature is much higher than the deep space cosmic background radiation temperature of 2.73 K. The magnitude of lunar contamination in space counts, ΔCc, can be expressed in terms of the channel gain and the increased cold space temperature ΔTc due to lunar surface temperature by the formula,
Where the increased cold space temperature ΔTc is related to the antenna pattern power function G(α, δ) and the effective lunar surface brightness temperature Tmoon by
deep space cosmic background temperature;
observed space counts, including lunar contamination;
lunar azimuth angle;
FOV center of lunar azimuth angle;
azimuth size factor;
lunar elevation angle;
FOV center of lunar elevation angle;
elevation size factor;
area ratio of lunar disk to FOV convolved with the antenna pattern powers. In equation (8), the 0.259 is the half cone angle that the lunar disk subtends at the satellite at its normal distance;
distance ratio = (60.3 × 6378/d)2, where d is the distance (in km) between the satellite and Moon. The range of r is from 0.94 to 1.06.
Figure 2 shows a sketch of the lunar azimuth and elevation angles. In equation (5), the quantities within the bracket define the channel gain in terms of the increased effective cold space temperature (Tc + ΔTc) and the contaminated space count Cc. as observed in the data stream.
Figure 3 shows a set of samples of the observed lunar contaminations in the space counts from NOAA 18 AMSU-A data. The lunar contamination in space counts, ΔCc, can also be estimated numerically and removed from the data. Description of such approach was given in a NOAA technical report [Kigawa and Mo, 2002]. The results of such approach are shown in Figure 3, where the portions in red denote the corrected space counts after the lunar contamination is removed from the contaminated data. One can see that corrections are quite good at all channels.
3. Detection of Lunar Contamination
 The lunar contamination is detectable (Figure 4) only when the separation angle μ between the Moon and the antenna space viewing direction is less than 4°, beyond which the lunar contamination is negligible as the AMSU-A antenna power drops 40 dB below its peak. In the NOAA operational software, each scan of data is checked for lunar contamination in space count by calculating the μ angle. If any lunar contamination is detected (i.e., μ < 4°) it is corrected in the calibration process. The antenna function (equation (7)) attenuates the lunar contamination rapidly if the lunar disk moves away from the AMSU-A antenna boresight. The correlation between the μ angle and the lunar contamination is demonstrated in Figure 4, which shows the cold space radiometric counts (bottom part) and the corresponding calculated μ angles (top part). The horizontal line (top part) represents the μ angle of 4°. One can easily see the lunar contamination (bottom part) occurs only when μ is less than 4° and it reaches maximum when μ approaches 0°.
4. Least Squares Fit to Lunar Contamination
Figure 5 shows the extracted lunar contamination ΔCC from the AMSU-A data as shown in Figure 3. These data are obtained by taking the difference between the lunar contamination spikes and the smoothed curves underneath. These ΔCC values are least squares fitted with equation (5). The best fit results are also shown in Figure 5 with the best fit parameters listed in Table 1. The α and δ values are calculated using the spacecraft navigation information in the 1B data sets for individual scans. Similarly, the Sun-Moon angle θ and the distance d between the satellite and Moon are also calculated for derivation of the lunar surface brightness temperature. In the fitting process, the parameters (i.e., α0, αS, δ0, and δS) are obtained by least squares fitting to the ΔCC values as shown in Figure 5. There may be misalignment of the instrument with respect to the spacecraft. Therefore the quantities α0, αS, δ0, and δS, which are affected by these errors, are treated as parameters and varied to fit the observed ΔCC values. Conversely, the values of these parameters (particularly, the α0 and δ0) may reflect magnitudes of the misalignment of the instrument with respect to the spacecraft. Figure 5 shows that the best–fit results agree well with the observed ΔCC values at all channels.
Table 1. Best Fit Parameters From Seven Orbits of Data
5. Effect of Lunar Contamination on the Scene Antenna Temperatures
 The above discussion concerns the magnitude of lunar contamination ΔCC in space counts. In reality, it is more interesting to know the effect of the lunar contamination on the AMSU-A scene antenna temperatures. With the best fit parameters in Table 1, one can calculate the AMSU-A scene antenna temperatures with the effect of lunar contamination corrected and then compare the results to similar calculations without such correction. This is shown in Figure 6 which demonstrates the differences ΔTS between the near nadir (FOV 16) scene antenna temperatures calculated with and without correction of lunar contamination. The magnitude of ΔTS varies with channel. It is about 1.5 K at both channels 1 and 2, but only 0.38 K at channel 4. There is a clear trend in the ΔTS values as a function of channels. The magnitude of ΔTS increases gradually from channel 4 to 8 and then decrease from channel 9 to 14. This trend of the ΔTS variation follows the atmospheric temperature profile as the antenna temperatures from the sounding channels gradually decrease from channels 3 to 9, but then increase from channels 9 to 14. Channel 9 has a weighting function with peak near the tropopause, and channel 14 has a weighting function with peak near the stratopause. Channels 1–8 and 15 sense temperatures at levels below the tropopause, while channels 10–14 sense temperatures at levels above the tropopause. The four window channels 1–3 and 15 sense the temperatures near the surface. Over the ocean, which has very low emissivity, the antenna temperatures sensed by the window channels are very low (e.g., ∼150 K at channels 1 and 2). To further understand the trend of the ΔTS variation as a function of the scene temperature TS, we examine the standard two-point calibration equation for a scene antenna temperature TS and its dTS/dCC as follows:
Equation (9) defines the uncorrected scene antenna temperature TS if the lunar contaminated space count, CC, is used whereas equation (10) provides the error in TS per count of lunar contamination in the space count. One can see that dTS/dCC is proportional to (TW − TS). As the scene antenna temperature TS increases, the magnitude of error decreases, and vice versa. The results in Figure 6 agree well with equation (10). For example, over ocean, the scene brightness temperature at channel 1 is TS ≅ 150 K which gives the largest difference in (TW − TS) ≅ (291 − 150) = 141 K. At the maximum lunar contamination ΔCC = 35 counts and (CW − CC) = 3520 counts. Substituting these values into equation (10), one obtains the result, ΔTS = −1.4 K (at channel 1). This shows that the scene antenna temperature TS calculated without correction of lunar contamination is 1.4 K lower than its true value. This agrees well with the result as shown in Figure 6.
6. Postlaunch Performance of the NOAA 18 AMSU-A
 After launch, a systematic postlaunch calibration and validation of the instrument performance was conducted with on-orbit data. Some of the assessments of the instrument performance are presented here. Scan-by-scan examination of the radiometric calibration counts is employed to confirm normal functioning of the instrument and to detect any anomalous evens, such as lunar contamination in the space radiometric counts, which are accurately detected, flagged, and corrected using a physical model of lunar surface temperature and antenna patterns derived from on-orbit data. The long-term trends of the space and warm calibration counts, channel gains, and housekeeping temperature sensors are monitored. Temperature sensitivity (or NEΔT) values for individual channels are also monitored since launch.
Figure 7 shows the AMSU-A specification of the NEΔT values and the calculated ones from prelaunch and on-orbit data. The NEΔT is defined as the minimum change in a scene radiometric temperature that can be detected. In practice, it is calculated as the standard deviation of radiometric outputs of an antenna system that looks at a scene target at a constant temperature (normally 300 K). The prelaunch values were calculated from data taken at a scene target temperature of 305 K. The on-orbit NEΔT values were calculated from the blackbody radiometric temperatures over one orbit (∼800 scans) during which the blackbody temperature variation was of order of 0.1 K with the blackbody targets at 288, 285, and 281 K, respectively, for the AMSU-A2, AMSU-A1-1, and AMSU-A1-2 channels. Owing to lower temperatures of the blackbody targets, the on-orbit NEΔT values for most channels are smaller than the prelaunch ones.
 The long-term trends of NEΔT in 2006 are shown in Figure 8. Most of these NEΔT values meet the AMSU-A specifications as shown in Figure 7. In addition, the results in Figure 8 demonstrate that the NEΔT values are very stable except at channels 1 and 4 in which some higher noises are observed. Similarly, the long-term trends of daily mean channel gains versus Julian day in 2006 are shown in Figure 9. These values are within the range of the ones determined from the prelaunch calibration data at three fixed instrument temperatures. Long-term trends of daily mean offsets versus Julian day are presented in Figure 10. These offset values are calculated from the formula (CC − GTC) with the cold space counts CC, the channel gain G, and the deep cold space temperature TC.
 The nonlinearity contribution, Q, to the AMSU-A measurements is expressed in terms of the channel gain G and the radiometric counts [Mo, 1996]:
radiometric counts of Earth scene target;
radiometric counts of warm blackbody target, averaged over seven scans;
radiometric counts of cold space, averaged over seven scans;
nonlinearity parameter determined from prelaunch calibration data.
 The nonlinearity parameter u is determined from prelaunch calibration data at three fixed instrument temperatures (low, nominal, and high). After launch, the u values at the actual on-orbit instrument temperatures are linearly interpolated from the three values.
 Samples of calculated nonlinearities as function of scene antenna temperatures from one orbit of AMSU-A data are shown in Figure 11. The values in Figure 11 are in good agreement with the simulated results calculated from the prelaunch calibration test data [Mo, 2002].
7. Summary and Discussion
 An algorithm for detection and correction of the lunar contamination in the AMSU-A space counts is applied to correct lunar contamination in the NOAA 18 AMSU-A data. The algorithm is based on a physical model of the lunar surface brightness temperature and the AMSU-A antenna pattern powers to detect the distribution of the lunar contamination in the radiometric space calibration counts over a large number of scans. A brief assessment of the postlaunch instrument performance is also presented.
 To detect the lunar contamination, the separation angle μ between the lunar disk and the antenna space viewing direction is calculated for individual scans. It is found that the lunar contamination is significant only when the separation angle μ is less than 4°, beyond which no significant lunar contamination is detected as the AMSU-A antenna power drops 40 dB below its peak value.
 In the NOAA operational software, each scan of data is checked for lunar contamination in space count by examining the μ angle. If any lunar contamination is detected (i.e., μ < 4°) it is corrected in the calibration process using the best fit parameters of AMSU-A antenna pattern powers. The lunar positions, as defined by α and δ, are calculated using the spacecraft navigation information, which may have small errors. Values of the parameters (particularly, the α0 and δ0) may be affected by the AMSU-A beam misalignment relative to the satellite platform.
 The effect of the lunar contamination on the AMSU-A scene antenna temperatures is investigated. It is found that the differences ΔTS between the near nadir (FOV 16) scene antenna temperatures calculated with and without correction of lunar contamination vary with channel. It is about 1.5 K (over ocean) at both channels 1 and 2, but only 0.38 K at channel 4. The trend in the ΔTS variation as a function of channels is easily understood by examining the two-point calibration equation. For AMSU-B and Microwave Humidity Sounder (MHS), there is no need to use this technique as presented in this study since there is at least one view (out of four) without lunar contamination.
 The results presented in this study show that the lunar contamination in the AMSU-A space calibration counts can be accurately detected and that its effect on the measured scene antenna temperatures can be corrected. The algorithm provides a practical approach for scan-by-scan correction of the lunar contamination in AMSU-A data and improves the accuracy of operational calibration of NOAA Level 1B data which are distributed to data users.
 Postlaunch assessment of the instrument performance shows that the NEΔT values calculated from the on-orbit data meet the specification and are very stable over 1-a period. There are some variations in both channel gains and offsets of the radiometric calibration counts. The contributions from nonlinearity are more than 1 K at some channels.
 The contents of this manuscript are solely the opinions of the authors and do not constitute a statement of policy, decision, or position on behalf of NOAA or the U.S. Government. Comments and suggestions from three anonymous reviewers resulted in improvement of the final manuscript.