Although the advanced microwave sounding unit (AMSU) on board the NOAA 15 and NOAA 16 satellites is primarily designed for profiling atmospheric temperature and moisture, the products associated with clouds and precipitation are also derived using its window channel measurements with a quality similar to those derived from microwave imagers such as the Special Sensor Microwave Imager. However, the AMSU asymmetry in radiance along the scan was found to be obvious at its window channels and could severely degrade the quality of cloud and precipitation products if not properly corrected. Thus a postlaunch calibration scheme is developed for these channels, and the causes of the asymmetry are analyzed from the AMSU instrument model. A preliminary study shows that the asymmetry may be caused by either the AMSU polarization misalignment or the antenna pointing angle error. A generic radiative transfer model is developed for a single-layered cloud using a two-stream approximation and can be utilized for the retrievals of cloud liquid water (L) and total precipitable water (V), cloud ice water path (IWP), and particle effective diameter (De). At the AMSU lower frequencies the scattering from cloud liquid is neglected, and therefore the retrieval of L and V is linearly derived using 23.8 and 31.4 GHz. However, for ice clouds the radiative transfer model is simplified by neglecting the thermal emission, and therefore the retrieval of IWP and De is analytically derived using the AMSU millimeter wavelength channels at 89 and 150 GHz. These cloud algorithms are tested for the AMSU on board the NOAA 15 and NOAA 16 satellites, and the results are rather promising. It is also found that the AMSU-derived cloud ice water path is highly correlated with the surface rain rates and is now directly used to monitor surface precipitation throughout the world.
 During the past decade there has been a dramatic increase in the use of microwave-derived products by the worldwide community of meteorological and oceanographic organizations. This greater emphasis is primarily attributed to the launch of the Special Sensor Microwave Imager (SSM/I) in 1987 on board the first of a series of Defense Meteorological Satellite Program (DMSP) satellites. The SSM/I contains six channels in window regions (19, 37, and 85 GHz) with dual polarization and a seventh channel centered on the 22.23-GHz water vapor line with vertical polarization. Products such as rainfall, snow cover, cloud liquid water, water vapor, sea surface winds, and sea ice concentrations are produced each day on a global basis using all of the SSM/I channel measurements. The SSM/I was developed by the U.S. Navy and was first launched on the DMSP F8 satellite. As a result of a shared processing agreement, all of the SSM/I products are generated by the U.S. Navy and are distributed to both the U.S. Air Force and NOAA. These three agencies utilize the products in various ways to improve the analysis and forecast capabilities of weather systems.
 The knowledge learned from the SSM/I accelerated the development of more products from other microwave sensors. Since the first launch of the advanced microwave sounding unit (AMSU) on board NOAA 15 in July 1998, products including cloud liquid, water vapor, rain rate, snow cover, and sea ice concentration have been operationally generated by NOAA with a quality similar to those derived from SSM/I, although the AMSU only has four window channels. New products such as cloud ice water and ice particle size are also derived, owing to the unique AMSU millimeter wavelength channels.
 The ability of AMSU to derive cloud and precipitation products is remarkable for a variety of applications. These products, combined with those derived from the DMSP SSM/I, offer more global observations in time and space and reduce the uncertainty for weather and climate analyses. For satellite data assimilation studies the cloud and precipitation products can be utilized to identify the microwave sounding channels contaminated by clouds and to control the quality of good radiances being assimilated into the numerical prediction models. The algorithms developed for the AMSU can also be used for risk reduction studies and will play a vital role in developing the calibration and validation activities for future microwave sensors. In this millennium, several microwave sensors on board U.S. satellites will inherit channels similar to the AMSU. For example, the National Polar-Orbiting Environmental Satellite System (NPOESS) will first have the Advanced Technology Microwave Sounder (ATMS) flown on board the NPOESS Preparatory Project satellite. The ATMS has the same frequencies as the AMSU, with a broader scan swath to provide complete coverage of the global environment twice a day.
 This study will present the various important issues in deriving cloud and precipitation products from a cross-track scanning microwave instrument like the AMSU. In section 2, the AMSU postlaunch performance is first discussed. The physical base of the algorithms is presented in section 3, and emission and scattering models are developed for retrievals of cloud liquid and ice water paths. In section 4, the precipitation algorithm based on the cloud ice water path is described.
2. AMSU Postlaunch Performance
 The advanced microwave sounding unit is flown on board the NOAA 15, NOAA 16, and NOAA 17 satellites. The instrument has been operational since 1998. The AMSU contains two modules: A and B. The Advanced Microwave Sounding Unit-A module (AMSU-A) has 15 channels (see Table 1) and is mainly designed to provide information on atmospheric temperature profiles; the Advanced Microwave Sounding Unit-B module (AMSU-B) allows for profiling the vertical moisture structure. The AMSU-A has an instantaneous field of view of 3.3° at the half-power points, providing a nominal spatial resolution at nadir of 48 km. The antenna provides a cross-track scan, and can scan ±48.3° with a total of 30 Earth-viewing angles per scan line.
Table 1. Advanced Microwave Sounding Unit (AMSU) Instrument Characteristics
 The AMSU-A is a cross-track scanning total power radiometer. It is divided into two physically separate modules, each of which operates and interfaces with the spacecraft independently. Module A1 contains 13 channels and module A2 contains two channels. Atmospheric temperature profiles are primarily based on the measurements obtained at channels 3–14 near 60 GHz, which is an oxygen absorption band, whereas the information on cloud liquid water and surface properties is obtained by using the measurements at channels 1–2 in addition to some AMSU-B window channels. Since the satellite provides a nominal spatial resolution of 48 km at its nadir, the temperature perturbations from synoptic to mesoscale can be reasonably depicted. In addition, several AMSU imaging channels at frequencies of 31.4, 89, and 150 GHz are utilized to determine cloud liquid and ice water contents because they directly respond to the emission from liquid droplets and the scattering from ice particles [Weng and Grody, 2000].
2.1. AMSU-A Cross-Track Asymmetry
 The onboard calibration for the AMSU is performed every 8 s by viewing an internal blackbody target at 180° from nadir and the cold space in one of four possible viewing positions, located between −76° and −84° from nadir. However, the antenna temperature is different from the brightness temperature (seen by the main lobe of the antenna) due to the antenna sidelobes, which can view cold space and the satellite platform.
 A significant problem was encountered on AMSU-A after its launch into orbit. The measurements from the AMSU-A2 module and the AMSU-A1 channels 3 and 15 display an asymmetry of radiance along the scan line that significantly degrades the quality of cloud and precipitable water products [Weng et al., 2000]. The asymmetry is the most prominent at 31.4 GHz and over oceans where the emissivity is lower. The presence of clouds and precipitation in the atmosphere tends to smear out the asymmetry.
 To identify the asymmetry along the scan, we simulate the brightness temperatures at 23.8, 31.4, 50.3, and 89 GHz over oceans corresponding to each AMSU-A beam position and compare the simulations with the measurements. Radiative transfer modeling is performed under clear atmospheric conditions using sea surface temperature (SST), wind vector, and temperature/moisture profiles obtained from the National Centers for Environmental Prediction Global Data Assimilation System (GDAS) as inputs. The SST is generated using a blended technique of satellite and conventional observations. Surface wind data are analyzed through assimilating available microwave satellite estimates from the SSM/I with buoy measurements. The GDAS global analyses have a resolution of 1° in latitude and longitude and are produced 4 times a day. The difference between simulated and observed brightness temperatures is illustrated in Figure 1. It appears that the bias is asymmetric relative to the nadir. For example, at 31.4 GHz (Figure 1b) a bias is positive for the beam position from 1 to 14 and negative for the beam position from 15 to 30. While the measurements at 23.8 and 31.4 GHz are obtained from the same AMSU-A2 module, the bias seems to be smaller at 23.8 GHz (Figure 1a) than the bias at 31.4 GHz (Figure 1b). Also, the bias at 50.3 GHz (Figure 1c) is smaller than the bias at 89 GHz (Figure 1d), although both channels are situated on the AMSU-A1 module. The asymmetry appears to be the worst at 31.4 GHz, where the atmosphere is most transparent. For the observations obtained over the oceans, empirical correction schemes were developed to adjust the asymmetry at each AMSU window channel [Weng et al., 2000]. Also, schemes were made separately for each NOAA 15 and NOAA 16 AMSU:
where Tb is the brightness temperature and θs is the local zenith angle; the coefficients A0–5 are given in Tables 2a–2d.
Table 2a. Coefficients Used to Correct NOAA 15 AMSU-A Cross-Track Asymmetry (Ascending)
Table 2b. Coefficients Used to Correct NOAA 15 AMSU-A Cross-Track Asymmetry (Descending)
Table 2c. Coefficients Used to Correct NOAA 16 AMSU-A Cross-Track Asymmetry (Ascending)
Table 2d. Coefficients Used to Correct NOAA 16 AMSU-A Cross-Track Asymmetry (Descending)
 The asymmetry may be due either to the error in encoding the AMSU antenna pointing angle or to the polarization misalignment in the AMSU radiometer receiver. As a cross-track scanning radiometer, the AMSU radiometer front end is composed of a scan motor, an encoder, an antenna reflector, and a feed horn and is shown in Figure 2. The rotation of the scan motor is encoded into the pointing direction of the reflector. The actual pointing direction may be different from the direction determined by the encoder. The asymmetry could occur as a result of the pointing angle bias.
 The AMSU radiometer at the window channels is designed to receive the radiance of the vertical polarization at the satellite nadir. As the reflector scans across the track, the electric components at both horizontal and vertical polarization states from the Earth's surface are measured by the receiver. The radiance received from any scan angle is a weighted average derived by
where A and B are related to the antenna reflector normal angle (θ), the polarization alignment angle (ψ), and the scan angle (φ); the variables Ih and Iv are the radiances received by the satellite at a horizontal and a vertical polarization state, respectively. Using the AMSU instrument parameters as shown in Figure 2, we derive
A nominal performance is set by θ = 45° and ψ = 90°. Thus A = sin φ and B = cos φ.
2.2. AMSU-B Radio Frequency Interference
 The AMSU-B instrument contains five channels from 16–20 (see Table 1) and provides the atmospheric profile of moisture. However, the radiances from the first AMSU-B on board NOAA 15 are severely contaminated by the S band data transmitters and the Search and Rescue Repeater. It appears that AMSU channels 17 and 19 are mostly affected by radio frequency interference (RFI) [Atkinson, 2000]. The levels of RFI affecting the AMSU-B are routinely monitored by NOAA and the Met Office, with the Met Office proving updated correction tables every 2 months along with recommendations to NOAA on whether the current correction table needs to be updated. The RFI correction is only needed for the AMSU-B on board NOAA 15.
3. Cloud Algorithms
 Microwave radiometers from space offer limited information regarding cloud vertical structure because the incident wavelength is larger or comparable to the particle size and the scattering and absorption is often in Rayleigh's regime. For nonraining clouds the brightness temperatures are almost linearly related to the vertically integrated cloud liquid water. Thus the retrieval of cloud parameters such as liquid and ice water paths can be based on an approximated radiative transfer scheme. For a single-layered cloud as shown in Figure 4 the solution of the radiative transfer equation including the scattering can be approximated by [Weng et al., 2001]
where μ is the cosine of local zenith (polar) angle, B is the thermal radiance emitted by the cloud with the temperature of T, I0 and I1 are the downwelling and upwelling radiances from the medium above and below the cloud layer, respectively, τ is the optical thickness, and κ and β are related to cloud optical parameters using
where ω, α, and g are cloud single-scattering albedo, similarity parameter, and asymmetric factor, respectively. The coefficients of γ1, γ2, γ3, and γ4 are related to the reflectivity at the boundaries and are discussed in detail by Weng et al. .
3.1. Cloud Liquid Water Algorithm
 Microwave measurements at lower-frequency window channels have been exploited to derive the cloud liquid water of nonraining clouds [Greenwald et al., 1993; Weng and Grody, 1994a; Weng et al., 1997, 2000; Wentz, 1997]. The retrievals of cloud liquid water normally require multiple microwave window channels so that the effects of the absorption of atmospheric gaseous constituents and the emission of the surface can be removed. At low frequencies the atmospheric scattering can be further neglected in equation (2). Thus:
where ε and Ts are the sea surface emissivity and temperature, respectively.
 Since in microwave frequencies the radiance is linearly proportional to temperature, the brightness temperatures are preferred in the algorithm. Using equation (4), the cloud liquid water and total precipitable water can be derived using two AMSU window channels at 23.8 and 31.4 GHz [Weng et al., 2000] by further assuming an isothermal atmosphere. Essentially, cloud liquid water (L) and total precipitable water (V) are derived using
respectively, and where
where κv and κl are the water vapor and cloud liquid water mass absorption coefficients, respectively. Using Rayleigh's approximation, one can express κl in terms of cloud layer temperature (Tl(c)) as
Oxygen optical thickness is parameterized as a function of sea surface temperature through
Table 3 illustrates some coefficients that can be used for various AMSU channels. In this study, only 23.8 and 31.4 GHz are used for L and V retrievals. The retrievals used in Table 3 were validated against the liquid water obtained from the ground-based radiometer measurements. The RMS error for nonprecipitating cloud liquid is ∼0.05 mm [Grody et al., 2001]. Figure 5 shows a global distribution of cloud liquid water over oceans derived using the AMSU on board NOAA 16. As discussed in section 2.1, the AMSU antenna temperatures are first corrected for the asymmetric bias. The correction scheme is also made separately for each individual satellite. Notice that the AMSU descending measurements during a 24-hour period do not completely cover the globe because of the orbital gaps. It is shown that the algorithm depicts cloud liquid water associated with various systems. The low clouds over oceans off the west coast of South America are detected, although the amount of cloud liquid is small.
Table 3. Parameters Calculated at Four AMSU-A Channels and Used in Total Precipitable Water and Cloud Liquid Water Algorithms
AMSU-A Channel, GHz
3.2. Cloud Ice Water Path/Particle Size Algorithm
 Microwave remote sensing offers the advantage of being able to measure the ice water path of clouds compared to existing visible and infrared techniques. Visible methods require a number of gross assumptions about ice particle shape, size distribution, and cloud spatial homogeneity to convert from radiance to optical depths to IWP. In addition, thermal infrared techniques require accurate knowledge of cloud temperature. Compared to existing visible and infrared techniques, microwave radiation interacts with ice particles primarily through scattering. The emission and cloud temperature are relatively unimportant. Since ice clouds are above the absorbing part of the atmosphere, they simply modulate the upwelling microwave radiation from below. While the effects of particle shape and size distribution are also important for microwave remote sensing of clouds since they determine the relation between optical depth and IWP, they are more amenable to calculation because the particle sizes are comparable with or smaller than the size of the wavelength. Microwave methods are also complementary to visible and IR methods because the microwave radiation is sensitive to larger ice crystals and to thicker cirrus layers whereas visible/IR radiation is more sensitive to smaller particles and cirrus clouds having lower IWP.
 The retrieval was also recently tested using aircraft millimeter wavelength measurements [Liu and Curry, 1999; Weng and Grody, 2000]. Liu and Curry  presented a method to retrieve IWP using airborne Millimeter-Wave Imaging Radiometer data at 89, 150, and 220 GHz channels. Although the IWP algorithm works well for cirrus clouds in the tropics, an uncertainty arises due to the unknown particle size [Liu and Curry, 1999]. Weng and Grody  proposed an algorithm to derive both IWP and De using dual millimeter wavelength measurements. They found that for a given particle bulk volume density, the brightness temperature at millimeter-wave frequencies can be uniquely related to IWP and De through a two-stream radiative transfer solution. However, the retrievals of cloud ice water path suffer a great amount of uncertainty due to an unknown bulk volume density of ice particles [Weng and Grody, 2000]. Thus it would be a major impact on the ice cloud remote sensing to utilize other sensors, such as visible and infrared radiometers, to identify a possible range of the bulk volume density.
 For a single-layered ice cloud, the radiance at the cloud top can be expressed in a simple form, assuming that cloud optical thickness is very small. The upwelling radiance emanating from an ice cloud is approximated from equation (4) as follows:
where Ω is the scattering parameter and I (τ1, μ) is the upwelling radiance at the cloud base.
 It is clearly seen that microwave radiance is independent of the cloud layer temperature and is directly related to the incident radiation at the cloud base. From a space platform (satellite or aircraft) the upwelling radiance decreases as the scattering parameter increases. A previous study shows that the brightness temperatures calculated using equation (6) have biases of less than a few degrees [Weng and Grody, 2000]. The best accuracy is achieved at the local zenith angles near 54°.
 The variable Ω is important in relation to cloud single-scattering albedo (ω), asymmetry factor (g), and optical thickness (τ) as follows:
For ice particles distributed according to a gamma function, Ω is calculated with Mie theory and is expressed as a function of cloud ice water path (IWP), particle effective diameter (De), and particle bulk volume density (ρi) as follows:
where ΩN is the normalized scattering parameter and is dependent only on the particle effective size parameter being defined as xe = 2π De /λ and m is the complex refractive index. For a smaller De, ΩN at 150 GHz is significantly higher than it is at 89 GHz. However, for a larger De (>1.5 mm), ΩN at both frequencies approaches the same value, indicating that the particle scattering may enter a regime of geometrical optics and become independent of wavelength [Weng and Grody, 2000].
 Using the AMSU-B measurements at 89 and 150 GHz, the scattering parameter ratio is directly related to the particle effective diameter [Zhao and Weng, 2002]:
Note that equation (9) defines a scattering parameter ratio varying between 0 and 1 and allows for a direct determination of De. The ice water path can be derived using
It is evident that IWP and De can be uniquely determined from equations (6–10) for a given constant bulk volume density.
 Notice that the major difficulty in deriving the cloud ice parameters is due to an unknown particle volume density. As shown in equation (10), IWP is directly proportional to the scattering parameter. However, the relationship between ΩN and De is nonlinear and may depend on the particular particle size distribution and bulk volume density. Therefore measurements at two distinct frequencies are normally required to unambiguously determine both IWP and De for a given particle bulk volume density [Evans and Stephens, 1995; Weng and Grody, 2000]. Provided that the bulk volume density of ice particles can be determined independently from other sources, IWP essentially only depends on Ω and De. An error of 30% in the density could result in an error of 25% in IWP [Zhao and Weng, 2002].
 The scattering signature resulting from sea ice and snow particles at higher microwave frequencies is similar to that of the ice particles because the dielectric constants among these scatterers are almost the same. Therefore, for a global application of the IWP and De retrieval algorithm, a procedure is developed to discriminate between the scattering signatures of atmospheres and various surface materials. However, the AMSU alone provides very limited information on surface types due to its lack of polarization measurements. Other data sets such as Advanced Very High Resolution Radiometer infrared data and GDAS surface temperature and surface type data are used in the screening procedure, as well [Zhao and Weng, 2002].
 Surface scattering from snow and sea ice can be largely removed using the measurements at lower AMSU-A frequencies. AMSU-A-derived products of snow cover and sea ice concentration are first used to indicate their presence. The GDAS surface temperature <269 K is used as an additional threshold to identify the scattering signatures of frozen surfaces. The retrieval of atmospheric ice is not performed under these surface conditions. Furthermore, there is no retrieval over high terrains such as the Tibetan Plateau, where the surface temperatures usually are <273 K.
 Deserts also scatter at AMSU 89 and 150 GHz [Weng et al., 2001]. However, scattering from the clouds can be easily separated from scattering from the surface using the satellite infrared measurements and GDAS surface temperatures. If the atmosphere is free from ice clouds, the IR temperature is close to the surface temperature, and therefore the scattering at 89 and 150 GHz must result from the surface. More specifically, for desert scatterers the temperature difference is <10 K and Ω is positive. If the satellite infrared data are not available, AMSU measurements at 183 ± 7 GHz can be used as a substitute because the channel peaks in the lower troposphere and is less affected by the surface. The screening procedure is discussed in detail by Zhao and Weng .
Figures 6a and 6b display an example of cloud ice water path and effective diameter derived from AMSU for a squall line system over the continental United States. Note that higher amounts of cloud ice water path are associated with larger sizes, which are obvious in northern Mississippi to Alabama where a surface tornado was reported. However, the sizes near 0.5 mm are very common in the system.
4. Precipitation Algorithm
 Precipitation is one of the most difficult of all atmospheric variables to measure. No single standard of accuracy exists with which to assess new measurement methods. Rain gauge networks over populated continents provide, at best, poor sampling. Over vast deserts and jungle areas, measurements are sparse while over the oceans they are virtually nonexistent. Pioneering efforts have been made to estimate rain from infrared and visible data of both polar-orbiting and geosynchronous satellites. Using IR data, Arkin  found a relationship between high cold clouds and rainfall. Quantitatively, his results could explain 50–70% of rainfall variance in low latitudes. High clouds were defined by the area on the satellite infrared image with a temperature threshold of <235 K. The major cause of measurement error was the presence of high cold clouds, such as thick cirrus, which were not precipitating.
 Satellite microwave data were also used to infer global oceanic rainfall [Ferraro et al., 1996]. Over oceans the measurements from lower microwave frequencies are directly related to the rainfall rate [Wilheit et al., 1977] because the cloud and rain droplets produce the emission and significantly increase the brightness temperature relative to the background. Over land the scattering signals from precipitation-sized ice particles are used to detect the raining clouds [Grody, 1991].
 The AMSU measurements at its window channels contain precipitation information, although the channels are primarily designed for improving atmospheric temperature and water vapor sounding. The AMSU window channel at 31 GHz is sensitive to emissions from clouds and precipitation in the liquid phase. However, the scattering associated with precipitation-sized raindrops tends to saturate this channel when the liquid water path is >1.0 kg m−2 [Weng and Grody, 1994b], which corresponds to the rain rate of 5–10 mm h−1.
 The AMSU high-frequency window channels are also useful in delineating precipitation due to the correlation between ice scattering and the surface rain rate. AMSU sensitivity to light rain events is significantly improved compared with the previous microwave sensors such as SSM/I because of the availability of 150 GHz. Meanwhile, a rain rate of 10 mm h−1 or larger can also be successfully retrieved due to the use of information at AMSU 89 GHz.
 The relationship between the surface rain rate and ice water path is derived using the Goddard precipitation profiling algorithm data sets that contain the profiles of various hydrometeors generated from the cloud models [Kummerow et al., 1996]. Figure 7 shows the scatter diagrams of rain rate versus cloud ice water path. A fitted relationship is derived to represent the mean:
where RR is surface rain rate in mm h−1 and IWP is in kg m−2.
Figure 8 displays the surface precipitation fields derived from AMSU in the eastern United States. In comparison with the surface composite derived from radar and rain gauges, AMSU depicts most rain areas. However, over complex terrain such as West Virginia the AMSU rain areas are broader than surface reports. It should be mentioned that the surface radar may also have difficulty detecting rain events due to the radar being blocked by the mountain; the rain gauges are also sparse.
5. Summary and Conclusions
 The advanced microwave sounding unit has provided new tools for monitoring Earth's atmosphere due to its unique capability of penetrating through thin cirrus clouds and improving spatial and temporal resolutions as compared with the previous NOAA microwave instruments. Since the launch of the first NOAA 15 in 1998, various utilities have been developed within NOAA and have been made available internationally for deriving atmospheric sounding and nonsounding products. A routine method is developed for examining the instrument performance after its lunch. As shown in this study, AMSU users may also develop their own asymmetry correction scheme using the same procedures as we discussed.
 In summary:
AMSU asymmetry is analyzed using a newly developed instrument model, and the simulated biases at four window channels exhibit similar characteristics to those obtained from the measurements.
The cloud liquid water and total precipitable water can be derived using AMSU channels at 23.8 and 31.4 GHz. The algorithm performance is significantly improved by the use of global analyses of sea surface temperature and surface wind from the numerical weather prediction model.
The ice water path associated with thick and precipitation ice clouds can be estimated primarily using AMSU millimeter measurements at 89 GHz and 150 GHz. The retrieval can be performed over land and oceans.
The uncertainty in the retrieval of cloud ice water path and particle size remains high due to an unknown particle bulk volume density.
The surface rain rate can be derived using AMSU cloud ice water path in addition to some auxiliary data sets.
 This work was supported by NOAA/NESDIS/Office of System Development and NOAA Integrated Program Office.