NOAA-18 Advanced Microwave Sounding Unit-A (AMSUA), Microwave Humidity Sounder (MHS), and Advanced Very High Resolution Radiometer/3 (AVHRR/3), along with collocated CloudSat data under nonprecipitation conditions, are used to validate the accuracy of the Community Radiative Transfer Model (CRTM). The observed brightness temperatures (BTs) from NOAA-18 instruments are compared to those simulated by the CRTM using the inputs of CloudSat retrieved hydrometeor profiles. The forward model biases are computed for various cloudy conditions, which are required for the assimilation of satellite cloudy radiances in operational forecast systems. Simulated BTs under nonprecipitation, cloudy conditions are averaged in space to account for the cloud inhomogeneity within the sensors' fields of view. The simulated and observed BT fields, BT distributions, and BT difference distributions show good agreement for all microwave channels. Simulations under clear skies in general have low biases and standard deviation errors, and these errors are only marginally increased under cloudy conditions for microwave channels. For AVHRR channels 4 and 5, the biases and standard deviation errors are low and very accurate for clear and water cloud conditions. However, there are larger standard deviation errors under cirrus and mixed-phase cloud conditions for those channels. The spatial averaging method significantly reduced the standard deviation errors under cloudy conditions. In this study, we have validated the CRTM modules (gaseous absorption model, cloud absorption and scattering model, and surface emissivity models over ocean) that generate optical properties of the atmosphere and surface in the microwave and thermal infrared spectral region.
 Numerical weather prediction (NWP) relies increasingly on the assimilation of radiance data provided directly from satellite observations, rather than from derived products [Andersson et al., 1994; English et al., 2000]. Currently, infrared (IR) and microwave (MW) radiances are successfully assimilated under cloud- and precipitation-free conditions [LeMarshall et al., 2007]. One of key components that have led to this success is the development of the Community Radiative Transfer Model (CRTM) [Han et al., 2006] at the Joint Center for Satellite Data Assimilation (JCSDA). CRTM includes both fast forward and Jacobian radiative transfer (RT) models for all weather conditions. It has been successfully used in the NCEP GFS data assimilation system (GDAS), as well as for satellite-based retrieval and sensor calibration algorithms.
 Because satellite cloudy and precipitating radiance measurements contain important information related to the atmospheric hydrological cycle, NWP centers must consider the implementation of assimilated IR and MW radiances under all weather conditions [Greenwald et al., 2002, 2005; Andersson et al., 2005; Weng, 2007; Weng et al., 2007]. European Center for Medium range Weather Forecasting (ECMWF) have operationally assimilated microwave radiances under cloudy and precipitating conditions since June of 2005 [Bauer et al., 2006a, 2006b]. Given the significant impact of the radiances on model forecasts, it is critical to develop fast RT models with well-understood error characteristics in not only clear-sky conditions, but cloudy and precipitating conditions as well. Thus, quality cloud and precipitation data sets are necessary to accurately represent atmospheric absorption, scattering, and polarization in the RT model to further reduce and quantify error when presented with nonclear conditions.
 CloudSat provides an opportunity for CRTM validation and error characterization. The primary CloudSat instrument is a 94 GHz, nadir-pointing, Cloud Profiling Radar (CPR) which measures the power backscattered by clouds as a function of distance from the radar. Its purpose is to measure the vertical structure of clouds from space, while simultaneously observing clouds and precipitation. The CloudSat level-2 data are used as the hydrometeor profile input for CRTM, and simulated cloudy radiances are then compared with satellite observations. These comparisons allow for quantified forward model biases under various cloudy conditions, a very important and necessary step toward the application of cloudy radiances in data assimilation systems. Improvements to the CRTM performance will also be made on the basis of these comparisons.
 The use of cloudy radiances in data assimilation systems will ultimately enhance the benefits that have been previously demonstrated through clear-sky radiance assimilation and also add to our knowledge of clouds, the surface and the hydrological cycle. In this study, we establish high-quality data sets for the comparison between the hydrometeor retrievals from NOAA-18 microwave sensors and the CloudSat retrieval, and the validation of the cloud absorption/scattering component in CRTM.
 The paper is structured as follows: section 2 briefly describes the CRTM model; section 3 introduces the validation data sets used for this work; section 4 utilizes these data sets to validate the CRTM and presents the main results of this work; and section 5 summarizes the conclusions of this study.
2. Community Radiative Transfer Model
 The JCSDA Community Radiative Transfer model (CRTM) is used to simulate radiance and radiance gradients (or Jacobians) at the top-of-atmosphere for satellites and other space-borne radiometers. CRTM is a vital software application used in satellite radiance data assimilation for NWP, Observing System Simulation Experiments (OSSEs), physical retrievals of atmospheric and surface state variables, air quality monitoring and forecasts, as well as radiometric instrument design, instrument calibration and monitoring.
 The radiative transfer problem in CRTM is split into various components (e.g., gaseous absorption, surface emissivity/reflectivity, aerosol absorption/scattering, cloud absorption/scattering), and each component defines its own structure definition and application module to facilitate independent development. The input to the model includes atmospheric state vectors (pressure, temperature, water vapor, and ozone profiles at user defined layers, and optionally, water content and mean particle size profiles with up to six cloud types), and surface state vectors which are used to calculate the surface emissivity (or supplied by the user). The CRTM currently covers the microwave and infrared spectral regions. The six cloud types include water, ice, rain, snow, graupel and hail. The microphysical properties (extinction coefficient, single-scattering albedo, asymmetry factor, and Legendre phase function coefficients) of cloud particles are stored in lookup tables for thermal infrared and microwave wavelengths on the basis of widely known publications [Simmer, 1994; Yang and Liou, 1995; Macke et al., 1996; Mishchenko et al., 2000; Baum et al., 2005; Yang et al., 2005]. The Mie theory is assumed in all calculations for spherical liquid and ice water cloud particles, and modified gamma size distributions are assumed in the microwave spectral region. The same assumptions (Mie scattering, a modified gamma size distribution) are made for the water clouds in the thermal infrared spectral region. However, the ice cloud particles are assumed as nonspherical hexagonal columns and with gamma size distribution in the infrared thermal spectral region, and the single-scattering properties of ice particles are computed from a composite method on the basis of the finite difference time domain technique, an improved geometric optics method, and the Lorenz-Mie solutions for equivalent spheres [Fu et al., 1998; Yang et al., 2005]. The surface emissivity/reflectivity modules in CRTM include IR and MW modules over different surface types (land, ocean, snow and ice). In this study, we use FASTEM-1 microwave ocean emissivity model [English and Hewison, 1998] for higher microwave frequencies (greater than 80 GHz), while use NESDIS ocean emissivity model [Yan and Weng, 2007] for lower microwave frequencies. For IR, the IR Sea Surface Emission Model (IRSSE) model [van Delst and Wu, 2000] is used, which is a parameterized Wu-Smith model [Wu and Smith, 1997] for rough sea surface emissivity. The radiative transfer scheme which is currently used in operation is the Advanced Adding and Doubling (ADA) method [Liu and Weng, 2006]. This method is 1.7 times faster than Vector Discrete Ordinate method (VDISORT) [Weng, 1992], 61 times faster than the classical adding and doubling method (DA) [Evans and Stephens, 1991], and the maximum brightness temperature differences for typical clear sky among ADA, VDISORT, and DA are less than 0.01 K. The main components for the highly modularized CRTM are showed in Figure 1. In this study, the modules (gaseous absorption model, cloud absorption and scattering model, and surface emissivity models over ocean) that generate optical properties of the atmosphere and surface, in the microwave and thermal infrared spectral region, are being tested.
3. Validation Data Sets
 CloudSat, launched on 28 April 2006, flies in a Sun-synchronous orbit at an 89° inclination angle, and a nominal altitude of 705 km, crosses the equator at around 1330 local time. The CloudSat data footprint is approximately 2.5 km along track by 1.4 km across track. There are approximately 36,383 profiles per granule which is one orbit of data beginning at the first profile on or after the equator on the descending node. Each profile has 125 vertical bins, each approximately 240m thick (CloudSat Standard Data Product Handbook, available at http://www.cloudsat.cira.colostate.edu/cloudsat_documentation/CloudSat_Data_Users_Handbook.pdf). CloudSat level-2 data provide cloud vertical profile, cloud classification, cloud optical depth, liquid (ice) water content, as well as ECMWF fields and Moderate-resolution Imaging Spectroradiometer (MODIS) products mapped to CloudSat profiles. The Sun-synchronous polar satellite NOAA-18 was launched in May 2005, orbiting the Earth 14 times per day while crossing the equator at around 1346 local time. In this paper, we use the simultaneous nadir overpass (SNO) method to find the collocated satellite data set between CloudSat and NOAA-18. The SNO method, which uses satellite orbit perturbation models with appropriate two-line elements, has been widely used for the calibration and validation of sensors across many satellites [Cao et al., 2004]. We apply this method to CloudSat and NOAA-18 on the period of 7 July to 16 August 2006 (nadir-viewing position), 1 October to 11 November 2006, and 1 January to 2 February 2007 (off-nadir-viewing position) to represent different times (seasons) of year. There are a total 31 SNOs during these periods. After acquiring the orbit data (which include the SNOs) from CloudSat and NOAA-18 Advanced Microwave Sounding Unit-A (AMSUA, resolution ∼50 km at nadir), Microwave Humidity Sounder (MHS, resolution ∼17 km at nadir), and Advanced Very High Resolution Radiometer/3 (AVHRR/3, resolution ∼4 km for Global Area Coverage), we perform a pixel-by-pixel match of the data from the satellite pairs, with minimized navigation errors. The strict requirements for coincidence largely limit the data quantities with just a few points in several days. However, when we loosen the coincidence requirements by increasing the time difference to within ∼3 min and the distance difference to within ∼50 km for AMSUA (∼17 km for MHS, ∼4 km for AVHRR/3), the collocated data points increase tremendously. The match-up data set, which contains both clear- and cloudy-sky conditions, has been constructed using loose time/distance coincidence requirements. For validation of the cloud absorption/scattering model, we only choose the match-up points over ocean within latitude ranges of −50S to 50N to reduce the surface emissivity effects on the simulated radiances/brightness temperatures. We may point out that most of the matched pixels for AMSUA (MHS) are near nadir.
 The CloudSat LWC/IWC retrieval algorithms are described by Austin and Stephens  and Benedetti et al. , where 2B-CWC is retrieved along with a spectral width that characterizes the particle size distribution for liquid (assuming a lognormal size distribution of spherical cloud droplets)/ice (assuming a modified gamma size distribution of spherical ice crystals). The 2B-CWC retrieval uses radar reflectivity and visible optical depth from MODIS if both these data are available, but is limited to daytime orbits. A radar-only retrieval (2B-CWC-RO) has also been used by the CloudSat team for LWC/IWC, and provides data for both day and night. In this study, we use the first released LWC/IWC from the 2B-CWC-RO algorithm. The algorithm has separate retrievals for liquid and ice clouds, and does not attempt to retrieve both solid and liquid microphysical properties simultaneously in the same cloud column. Instead, separate retrievals are performed assuming that the entire cloud column is liquid-only and ice-only, and the two sets of results are combined into a composite profile according to a simple temperature relation due to no independent source of phase information. Ice-phase results are used for cold temperatures, liquid-phase results for warm temperatures, and a linear combination of the two are used in an intermediate temperature range, yielding an approximate mixed-phase solution.
 On the basis of the established coincident/collocated satellite data set between CloudSat and NOAA-18 AMSUA/MHS, we compared liquid water path (LWP)/ice water path (IWP) retrieved from CloudSat and AMSUA/MHS on NOAA-18. The AMSUA LWP and the MHS IWP are derived by the Microwave Surface and Precipitation Products System (MSPPS). The LWP algorithm was developed by Weng et al. , and the IWP algorithm described by Zhao and Weng .
 One of the useful statistical tools to compare the same cloud ensemble is the normalized probability density function (PDF). A number of studies have used the PDF method to analyze the cloud liquid/ice properties for different cloud measurements [e.g., Mace et al., 2001; Hogan and Illingworth, 2003; van Zadelhoff et al., 2004]. A PDF can preserve measurement noise and sensitivity information. Most importantly, each cloud ensemble has only one PDF, and therefore all the measurements on the same cloud ensemble must agree with each other in terms of their observed cloud PDFs. Figure 2 shows LWP/IWP PDF comparisons between CloudSat and NOAA-18 AMSUA/MHS for the collocated data set. Good agreement is found between AMSUA LWP and CloudSat LWP in the overlapped sensitivity range, showing PDF differences less than 50%. The MHS IWP has a high bias (a factor of 5) in the overlapped sensitivity range with CloudSat. The MHS PDF drops with a steeper slope at IWP > 400 g/m2, likely due to saturation in its sensitivity.
4. Validation Results
 Comparing the model simulated radiances with the observations under cloudy sky becomes challenging because of large inhomogeneity and intermittency associated with the cloud phenomena. CloudSat measurement noise, sensitivity limitation and sampling issues can further make comparisons difficult to interpret. The sensor sensitivity and cloud inhomogeneity problems are often mixed together, producing inconclusive results if these effects are not quantified. For example, dissimilar cloud occurrence frequencies have been derived from IR and microwave observations [Weisz et al., 2007], and different sensitivities exist for the AMSUA/MHS microwave sensors compared to active CloudSat CPR.
 Cloud inhomogeneity within a field-of-view (FOV) may cause problems when comparing measurements by instruments with improperly matched or different footprints, or differences in spatial averaging. This issue is exhibited in the case where AMSUA views clouds in a footprint of 50 km at nadir, while CloudSat views a part of the scene in a footprint of 2.5 km by 1.4 km. All other parameters being equal, the differences in cloud amount within the two footprints may yield much different measurements by each sensor. Another effect from cloud inhomogeneity, the so-called beam-filling effect, could reduce the measured radiance values if, for instances, the AMSUA FOV is not completely filled with clouds. Since clouds are small-scale phenomena, many satellite sensors including AMSUA and MHS have a FOV larger than the typical cloud sizes. Therefore, the CRTM simulations using cloud vertical profiles retrieved from a much smaller footprint (e.g., CloudSat) must first apply spatial averaging within the larger footprint size in order to compare with the satellite observed radiances.
 For an ideal match-up case, each AMSUA (MHS) FOV contains approximately 48 (16) CloudSat FOVs along its center transect. If it is assumed that the cloud distribution inside the AMSUA (MHS) FOV is random, the cloud information along track could be representative of the entire FOV. Furthermore, we use the independent pixel approximation concept to obtain the average radiances (brightness temperatures) along track as
where m is the total number of pixels along the center transect; Ri is the CRTM simulated radiance with input from the ECMWF analysis atmospheric profile (pressure, temperature, water vapor, ozone), surface pressure, surface temperature, and CloudSat retrieved cloud information; is the average radiances for the center transect. The brightness temperature difference between the observation and the CRTM simulation is defined by
where Bt(RO) is the satellite measurement brightness temperature over the AMSUA/MHS FOV after applying the antenna correction [Mo, 1999; Hewison and Saunders, 1996]; and Bt() is the average brightness temperature computed along track.
 The liquid and ice cloud retrieval algorithms used in CloudSat assume distributions of cloud particles without a substantial number of larger precipitation particles, causing retrieval failure in regions of high radar reflectivities (precipitation). Fortunately, the 2B-CWC-RO products have bits to indicate the failure of the LWC and IWC retrievals, and possible precipitation. In our validation results, we have removed the AMSUA (MHS) FOV if these have possible precipitation inside the FOV based on the 2B-CWC-RO bits. Therefore, our validation results are only valid for nonprecipitating weather. We have carried out the microwave simulations at the CloudSat spatial resolution by using CloudSat retrieval cloud information as well as ECMWF analysis atmospheric profiles, performed spatial averaging on these radiances and directly compared to the collocated NOAA-18 AMSUA/MHS satellite observations. In addition, simulations corresponding to the NOAA-18 AVHRR/3 thermal IR window channel 4 (10.3–11.3 μm) and channel 5 (11.5–12.5 μm) have also been calculated from the same input and are compared to AVHRR observations directly at the AVHRR resolution of ∼4 km. The IR channels at 11 and 12 μm are essentially sensitive to the cloud top properties, providing a complementary source of cloud information.
4.1. Observed and Simulated Fields
 Observations from NOAA-18 AMSUA and MHS are compared to the simulated brightness temperature (BT) fields, along with the AVHRR/3 observed and simulated BT for the same time. Figures 3, 4, and 5display the time series of NOAA-18 AMSUA, MHS and AVHRR BT differences between observations and averaged CRTM simulated BTs over the transect within the instrument FOVs using CloudSat data on 27 July 2006 over ocean for selected channels. The BT standard deviation of the 3 × 3 MHS 89.0 GHz channel FOVs, which are within the AMSUA FOV, is also shown (triangles) in 89.0 GHz channel (Figure 3), which indicate the variation of the atmosphere and surface conditions. AMSUA channels 1–3 and 15 are particularly sensitive to surface features and lower-troposphere atmospheric constituents, while channels 4–14 are sensitive to the atmospheric constituents at increasingly higher altitudes. Over the ocean, because of the low surface emissivity (about 0.5), BTs at channels 1–3 and 15, which are sensitive to the combination of surface temperature and surface emissivity, appear to be cold for clear-sky conditions. Any adding of clouds, rain, and water vapor, which have higher emissivities, will result in a “warm” scene in BT space, in contrast to the “cold” water background. The overall agreement between simulated and measured BTs in the microwave is reasonable for clear and cloudy sky. Comparing the 89.0 GHz channel in Figures 3 and 4, we found that the MHS channel BT differences (observation minus simulation) are more scattered than AMSUA. The discrepancy may be due to two factors: (1) spatial resolution difference and (2) the chance of displacement of clouds. Although AMSUA channel 15 and MHS channel 1 have same frequency, their spatial resolutions are different. Each AMSUA FOV includes nine MHS FOVs. Larger spatial averaging will lead to more smooth results. At the same time, the chance of displacement of clouds for two collocated data set will increase for smaller FOVs with same time difference compared to larger FOVs. On the basis of Figure 5, the following qualitative statements can be made about BT agreement in the IR with AVHRR: (1) when cirrus clouds are present, the AVHRR 3 × 3 FOVs BT standard deviation (STD) is very high, which implies high inhomogeneity for IR channels (not shown); (2) the higher STD accompanies a higher ΔBT between observations and simulations for IR channels; when we use STD less than 2.5 K as a screen to the homogeneous clouds, the ΔBT are less than 20 K; (3) IR radiances have high sensitivity for ice clouds while the CloudSat 94 GHz radar does not; and (4) the simulated IR radiances are far larger than the observations when deep convective clouds are present, and where CloudSat has high radar reflectivities and is saturated. The high ΔBTs for IR channels imply that CloudSat may miss thin cirrus cloud because of reduced radar sensitivity. We may need additional cirrus cloud information from other instruments, such as the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite, in stead of CloudSat alone, to improve the IR radiance simulations under cloudy condition.
4.2. Observed and Simulated BT Distributions
 For a more quantitative comparison between the simulated and observed BTs, their statistical distributions are shown in Figure 6 for selected AMSUA and MHS channels. At all frequencies, the distributions of the BTs are very broad over ocean because of the lower emissivity of the ocean surface. The presence of clouds in the scene causes a significant warming and therefore a widening of the BT distribution. Reasonable agreements of observed and simulated BT distributions at all frequencies are found in Figure 6. The largest bias (channel 23.8 GHz) between measured and simulated BTs is less than 2.4 K, whereas the largest root-mean-square (RMS) error is less than 3.9 K at channel 89.0 GHz.
 We further compare the microwave ΔBTs between observation and simulation, which are separated into cloudy (based on CloudSat retrieval and AMSUA/MHS retrieval) and clear pixels. Their normalized histograms are displayed in Figure 7. The distributions are in Gaussian function shapes with maximum observation at or near zero, which confirm that the agreement between observed and simulated BTs are very good under clear and cloudy conditions. However, there are clear-sky biases in certain surface-sensitive microwave channels of the order of 1–2 K which is due to the sea-surface emission model used in CRTM [Kazumori et al., 2008].
Figure 8 shows the normalized histogram ΔBTs of NOAA-18 AVHRR/3 channels 4 and 5 under different atmospheric conditions (clear, ice cloud, water cloud, and mixed-phase cloud) over ocean based on CloudSat retrieval and AVHRR/3 cloud flag and using AVHRR 3 × 3 FOVs less than 2.5 K as a screen to the homogeneous clouds and surfaces. The clear sky biases and STDs are very small with only −0.179 K (−0.204 K), and 0.553 K (0.564 K) for channel 4 (channel 5). It implies that the surface emissivity model and gaseous absorption model are reasonable accurate for broadband thermal infrared radiation. For water cloud, the biases (−2.427 K for channel 4, and −1.886 K for channel 5) and STDs (3.755 K for channel 4, and 3.372 K for channel 5) are also acceptable although the ranges of LWP are wide (from 10−2 to 103 g/m2). However, when ice clouds are present (cirrus cloud and mixed-phase cloud), the STDs increase dramatically to about 7 K. Besides the one possible reason mentioned in section 4.1 (missing thin cirrus), another two possible reasons could be (1) The ice particles being assumed as nonspherical hexagonal columns in CRTM are inconsistent with those assumed by CloudSat 2B-CWC-RO algorithm (spherical particles); Huang et al.  showed that the brightness temperatures for spherical ice particles are 0.5–2.6 K lower than that for nonspherical particles given fixed visible optical thickness 1 in the 800–1000 cm−1 spectral region. (2). The assumption of mixed-phase cloud may not be valid by simply using a linear combination of the ice and liquid cloud based on temperature relation.
4.3. Relationship Between Biases and LWP/IWP and Between Biases and Cloud Fraction
 The cloud thickness is directly linked to LWP/IWP. The larger LWP/IWP are, the thicker the cloud would be. If the ΔBTs between observation and simulation are worst in thicker clouds, it would imply that there are potential problems in the microwave cloud optical depth properties module of CRTM. Figures 9 and 10 show the scatterplots of NOAA-18 AMSUA channels 1 and 15, and MHS channels 1 and 2 observation minus CRTM simulation biases over ocean versus LWP/IWP retrieved by CloudSat. The biases do not increase with increasing LWP/IWP. Given the wide ranges of LWP (from 10−2 to 103 g/m2)/IWP (from 10−3 to 103 g/m2) and the biases not largely different, it implies that microwave optical properties of the clouds are correctly modeled in CRTM.
 We define the cloud fraction for each AMUSA (MHS) FOV as the percentage of cloud pixels detected by CloudSat over total CloudSat pixels within the AMSUA (MHS) FOV. The scatterplots of observation minus simulation biases versus the cloud fraction/LWP within AMSUA/MHS FOV over ocean are shown in Figure 11. The biases do not reduce in overcast situations versus partially cloudy situations. It suggests that spatial averaging method work very well under inhomogeneous cloudy conditions within the FOV.
4.4. Cloud Inhomogeneity Effects
 Comparisons between microwave observations and simulations show a satisfactory agreement by using appropriate spatial averaging method (equations (1) and (2)), which considers the cloud inhomogeneity within the FOV. To show the cloud inhomogeneity effects within the FOV, we also calculated the “matched” results for minimum distance between CloudSat pixels and the center of the corresponding AMSUA (MHS) FOV. Tables 1 and 2 show biases and standard deviations for clear and cloudy sky conditions with/without averaged simulated BTs over the transect line within the observed FOV for AMSUA and MHS, respectively. Under clear conditions, the biases and standard deviations between observed and simulated TBs are almost identical for matched and averaged methods, which are understandable because of the uniform sea emissivity and atmospheric conditions within the FOVs. The larger biases for AMSUA channels 1, 3, and 15, and MHS channel 1, which are strongly sensitive to surface features, are due to the sea-surface emission model used in CRTM. To reduce the biases, it is necessary to improve the surface emissivity modeling, which is beyond the scope of this paper and requires further study [Liu and Weng, 2003; Kazumori et al., 2008]. Under cloudy conditions, the matched and averaged biases show small changes, however, the averaged standard deviations are reduce significantly compared to the matched, especially for those channel weighting functions peaking at lower altitudes in which clouds are mostly likely located (e.g., AMSUA channels 1–3, 15, and MHS channel 1). For example, the matched standard deviation for AMSUA channel 89.0 GHz is 7.95 K, where the averaged standard deviation is reduced to 4.01 K. Those differences between matched and averaged methods show that we should be more careful comparing the observed and simulated radiances (or BTs) when clouds are present. The biases under nonprecipitation cloudy conditions have almost the same accuracy as under the clear conditions for AMSUA and MHS with the averaging method, where standard deviations are larger under cloudy conditions than under the clear conditions.
Table 1. AMSUA Biases and Standard Derivations for Clear Sky and Cloudy Sky With/Without Averaged Simulated BTs Over the Transect Line Within the Observed FOVa
Table 2. MHS Biases and Standard Derivations for Clear Sky and Cloudy Sky With/Without Averaged Simulated BTs Over the Transect Line Within the Observed FOVa
Clear Sky (6924)
Cloudy Sky (6179)
MHS: Microwave Humidity Sounder.
183.311 ± 1.0
183.311 ± 3.0
 The AMSUA channels 5 to 9, which are sensitive to the atmospheric constituents at higher altitudes, show similar biases and standard deviations under clear and cloudy conditions due to less sensitive to the surface emissivity and clouds. These channels show relatively larger biases (1–2 K) with smaller standard deviations (0.3–0.5 K). There are three possible explanations for the larger biases at these channels:
 1. The input atmospheric profiles. In this study, we used the CloudSat ECMWF-AUX profile data, which are mapped to the CloudSat profiles and only provide atmosphere profiles up to about 25 km (we extended the ECMWF profiles by using six model atmosphere profiles based on latitude), as our model input. The extended profiles may not accurately present the “true” atmosphere states. We also performed the same calculation by using NCEP analysis data mapped to the CloudSat with the results being almost the same as using the ECMWF data.
 2. The RT model. CRTM uses the Optical Path Transmittance (OPTRAN) model, which is a regression-based fast radiative transmittance model [McMillin et al., 1995], to compute gaseous optical depth on the basis of Liebe MPM-89/92 model [Liebe, 1989; Liebe et al., 1993] for the microwave channels. We further use another well known fast radiative transfer model RTTOV (Radiative Transfer for TOVS) [Saunders et al., 1999] to calculate the microwave radiances by using the same ECMWF data. The biases and standard deviations for AMSUA channels 5 to 9 from CRTM and RTTOV have the same accuracy, with same sign and similar magnitudes.
 3. The quality of NOAA 18 microwave radiances. We may check the radiance quality by intersatellite calibration using the simultaneous nadir overpass methods for the microwave instruments on NOAA-18/NOAA-16, and NOAA-18/Metop-A, which is our next research focus.
 We established the coincidental/collocated satellite data set between CloudSat and NOAA-18 AMSUA, MHS, and AVHRR on the period of 7 July to 16 August 2006, 1 October to 11 November 2006, and 1 January to 2 February 2007. The hydrometeor retrievals from active microwave radar on CloudSat have been compared with the retrievals from NOAA-18 passive microwave sensors. Good agreement is found between the CloudSat LWP/IWP and AMSUA (MHS) LWP/IWP in the overlapped sensitivity range.
 The ability of the CRTM model to accurately compute the observed microwave radiances has been tested with the retrieved cloud data from active Cloud Profiling Radar on CloudSat under nonprecipitation cloudy conditions (a limitation of the current CloudSat retrievals; in the future we may have precipitation products from CloudSat). Using a combination of the ECMWF analysis data and the CloudSat retrieved cloud information for the atmospheric state vectors as input to the CRTM, radiances are simulated at the CloudSat footprint resolution. To directly compare with the observed microwave radiances of the NOAA-18 AMSUA and MHS sensors which have much larger FOVs, we used a simple spatial averaging method to average the simulated radiances along the center transect of the CloudSat pass within the AMSUA/MHS FOV. This is preceded by the assumption that the cloud distribution along the CloudSat track equals the cloud distribution of the entire AMSUA/MHS FOV. The simulated and observed BT fields, BT distributions, and BT difference distributions are in good agreement for all the microwave channels. For AVHRR channels 4 and 5, the biases and standard deviation errors are low and acceptable accurate for clear and water cloud conditions. However, there are larger standard deviation errors under cirrus and mixed-phase cloud conditions for those IR channels which may be due to CloudSat missing thin cirrus, spherical particle approximation, and mixed-phase assumption. Simulations under clear skies in general have low bias and standard deviation errors, and these errors are only marginally increased under cloudy conditions for AMSUA and MHS channels. The spatial averaging method, which attempts to constrain the effects of cloud inhomogeneity over the sensors' FOV, significantly reduced the standard deviation errors under cloudy conditions.
 On the basis of the comparison results between simulation and observation brightness temperatures for AMSUA/MHS/AVHRR, we have validated the ocean surface MW emissivity model based on the surface-sensitive AMSUA channels (on the order of 1–2 K bias) and the ocean IR emissivity model based on AVHRR channels 4 and 5 (on the order of 0.2 K). We also validated the gaseous absorption model under clear sky. There seems to be a bias in some of the middle-atmosphere sensing channels of AMSUA (channel 6–8), which may mostly be due to the input extend atmospheric profiles by using model atmospheres. The cloud (water and ice) absorption and scattering models for MW are roughly correct given the wide range of brightness temperatures at these MW frequencies caused by the presence of clouds. The IR water cloud absorption and scattering model is also acceptable accurate given the large range of LWP.
 Continuation of the CRTM validations under cloudy environments, especially for precipitation weather conditions by using CloudSat and radar data, and validation for infrared sounders when cirrus clouds and aerosols are present in the atmosphere using a combination of CloudSat/CALIPSO data, are our next logical steps to improve the CRTM performance. These future studies will help to accelerate the use of satellite data under all weather conditions by data assimilation systems, resulting in improved weather and climate prediction.
 The authors thank Graeme Stephens and the CloudSat team for providing the CloudSat data. The authors would also like to thank Kevin Garrett for his detailed corrections and comments. Thanks to three anonymous reviewers for their very useful suggestions to improve our paper. This research was supported by funding from the Joint Center for Satellite Data Assimilation program. The contents of this paper are solely the opinions of the author(s) and do not constitute a statement of policy, decision, or position on behalf of NOAA or the U.S. Government.