This study demonstrates the ability to use Atmospheric Infrared Sounder (AIRS) hyperspectral radiance measurements and collocated Clouds and the Earth's Radiant Energy System outgoing longwave fluxes to estimate top-of-atmosphere outgoing longwave radiation (OLR) from AIRS radiance measurements. The first 35 principal component scores of AIRS radiances from its 1707 pristine channels are used as predictors, and the regression coefficients are generated in eight regimes of AIRS view angle to account for angular dependence of the AIRS radiance observations. Tests on an independence test ensemble show that the accuracy of the AIRS OLR is near zero and the precision is less than 3 Wm−2 for all scenes and 2 Wm−2 for uniform scenes. The AIRS OLR precision for uniform scenes is much higher than the High-Resolution Infrared Sounder OLR of 5 Wm−2 for similar comparisons with the Earth Radiation Budget Experiment OLR. The same technique of empirical regression OLR can be applied to other hyperspectral sounders such as the Cross-track Infrared Sounder that will be on board the National Polar-Orbiting Operational Environmental Satellite System and the Infrared Atmospheric Sounding Interferometer on the European Meteorological Polar-orbiting satellites.
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 The Atmospheric Infrared Sounder (AIRS) and two identical Clouds and the Earth's Radiant Energy System (CERES) instruments are on NASA's Earth Observing System (EOS) Aqua platform [Parkinson, 2003]. AIRS is a hyperspectral grating spectrometer that measures thermal infrared radiances with 2378 spectral channels covering the spectral range of 3.74–4.61, 6.20–8.22, and 8.8–15.4 μm [Aumann et al., 2003; Chahine et al., 2006]. Its spectral resolving power is ν/Δν = 1200 (where ν is the wave number and Δν is the width of a channel). AIRS operates in cross-track scan mode with infrared footprints approximately 13.5 km in diameter at nadir (1.1° × 0.6° field of view; FOV). It collects 90 cross-track footprints every 2.667 s in a full resolution of the sensor scan mirror. Its swath width is about 1650 km with an Earth scan angle 48.95° from nadir.
 The CERES instruments [Wielicki et al., 1996] measure Earth-atmosphere radiances in three broad channels: a shortwave channel (0.3–5 μm), a total channel (0.3–200 μm), and window channel (8–12 μm). The estimated CERES longwave radiances are converted to top-of-atmosphere (TOA) outgoing longwave fluxes by applying an empirical angular distribution mode [Loeb et al., 2005]. The CERES instruments operate in three primary scan modes: cross track, along track, and rotating azimuth plane. In cross-track scan mode, CERES collects 660 footprints every 6.6 s in two Earth scans operated with back-and-forth scanning. Its footprints are approximately 20 km in diameter at nadir (1.3° × 2.6° FOV). Its Earth scan angle is 65.8° from nadir. Figure 1 presents the spectral response functions of the three CERES broadband channels and the spectral range of the AIRS and the Cross-track Infrared Sounder (CrIS). CrIS will be on board the National Polar-orbiting Operational Environmental Satellite System satellites. Clearly, CERES has a broad spectral range, but AIRS has a much smaller spectral range and has spectral gaps in its spectral coverage.
 AIRS measurements, combined with the advanced microwave sounding unit (AMSU) and the Humidity Sounder for Brazil (HSB), have been used for the retrieval of AIRS level 2 products of atmospheric temperature, moisture, and ozone vertical profiles, surface temperature, surface emissivity and reflectivity, and cloud height and amount [Susskind et al., 2003]. The retrievals have been used to compute outgoing longwave radiation (OLR) under all-sky and clear-sky conditions by integrating the radiative transfer equation in a manner similar to that used to compute OLR from the Television Infrared Observation Satellite (TIROS) operational vertical sounder (TOVS) [Mehta and Susskind, 1999]. AIRS radiances have been demonstrated to be well calibrated and to have a high radiometric accuracy and long-term spectral stability [Pagano et al., 2003; Strow et al., 2003; Tobin et al., 2006]. AIRS radiance measurements include more information content about atmospheric state and surface and cloud properties than those of narrowband sounders such as the advanced very high resolution radiometer (AVHRR) and the High-Resolution Infrared Sounder (HIRS) instruments, which have been used previously to estimate OLR [Ohring et al., 1984: Ellingston et al., 1989]. Therefore, it is possible to derive TOA outgoing longwave fluxes directly from high-quality AIRS radiances instead of deriving them from AIRS level 2 products. A technique for PC regression [Goldberg et al., 2003; Barnet, C. D., Remote sounding notes, 2007; available at ftp://ftp.orbit.nesdis.noaa.gov/pub/smcd/spb/cbarnet/reference/rs_notes.pdf] is used in this paper to derive equations for estimating AIRS OLR by least squares regression of CERES TOA outgoing longwave fluxes with the principal component scores (PCSs) of the AIRS radiance measurements.
 A key motivation for trying to reproduce CERES TOA outgoing longwave fluxes from AIRS is to use the AIRS-derived OLR to monitor CERES performance and to apply the technique to other hyperspectral infrared sounders in other orbits, such as the European Organization for the Exploitation of Meterological Satellites (EUMETSAT) meteorological polar-orbiting satellite through the Meteorological Operational satellite program, which has crossing times of 0930 and 2130 LT. Thus, not only will high-quality OLR products be limited to the 0130 and 1330 LT orbit of Aqua and the future National Polar-orbiting Operational Environmental Satellite System, but also a failure of CERES or the Earth Radiation Budget Satellite (ERBS) can be mitigated by AIRS. Similarly, the method to generate the AIRS OLR can be extended to the CrIS, and therefore the CrIS can be used to monitor the performance of the ERBS and serve as a potential surrogate, since both will be on the future National Polar-orbiting Operational Environmental Satellite System satellites.
 In the following, section 2 describes the data sets used in generation and test of AIRS OLR regression coefficients and the spatial collocation of AIRS and CERES measurements. Section 3 gives the method of estimation of AIRS OLR, determines the number of significant eigenvectors of AIRS radiances, and investigates the impact of scene uniformity on the accuracy and precision of the AIRS regression OLR. Section 4 evaluates the AIRS OLR by comparing it with CERES and presents sensitive studies. The final section presents a summary and plans for future work.
2. Data Sets and Processing
 With the advantage of AIRS and CERES instruments being on the same Aqua satellite, CERES TOA outgoing longwave fluxes obtained from the CERES Single Scanner Footprint TOA/Surface Fluxes and Clouds (Single Scanner Footprint; SSF) collection (Geier, E. B., R. N. Green, D. P. Kratz, P. Minnis, W. F. Miller, S. K. Nolan, and C. B. Franklin (2003), Single satellite footprint TOA/surface fluxes and clouds (SSF) collection documentation; available at ttp://science.larc.nasa.gov/ceres/collect_guide/SSF_CG.pdf) are chosen as “true” OLR. The radiometric accuracy of CERES and the accuracy of the CERES OLR are given by Priestley et al.  and Loeb et al. [2001, 2007]. The observed radiances in the AIRS visible/near-infrared level 1b data set are used to build regression predictors that are the PCSs of AIRS radiance measurements.
2.1. Atmospheric Infrared Sounder (AIRS) Level 1b Data Set
 The AIRS level 1b data set (version 5) was obtained from NASA Goddard Earth Sciences Data and Information Services Center (available at: http://disc.sci.gsfc.nasa.gov/data/datapool/). There are 240 granule files per day. Every granule file contains 6 min of AIRS instantaneous radiance measurements. Each granule includes 135 cross-track scan lines, with 90 footprints per scan line. However, not all of the AIRS channels are of good quality. A channel is marked as “bad” according to the quality indicators included in the AIRS level 1b data files. A channel is also considered bad when the channel has a larger negative value, that is, less than or equal to −10 × NEΔN (where NEΔN is AIRS instrument noise). Recently, the NOAA National Environmental Satellite, Data, and Information Service, Silver Spring, Maryland, has retrained AIRS radiance eigenvectors of its 1707 pristine channels by using a large ensemble of AIRS radiance measurements. Criteria for selection of channel and generation of AIRS radiance eigenvectors were provided by Zhou et al. . In our analysis the new radiance eigenvectors of the 1707 channels are used to decompose AIRS radiances and calculate regression predictors. All the bad channels of the pristine channels are filled by using a method of principal component (PC) analysis. The PC analysis filling was well described by Barnet (Remote sounding notes, 2007; available at ftp://ftp.orbit.nesdis.noaa.gov/pub/smcd/spb/cbarnet/reference/rs_notes.pdf) and is being used in AIRS/AMSU/HSB Products Generate Software (PGS) [Aumman et al., 2003].
2.2. Clouds and the Earth's Radiant Energy System (CERES) Single Scanner Footprint Data Set
 The CERES SSF product files contain 1 h of instantaneous CERES data obtained from the Atmospheric Science Data Center at NASA Langley Research Center (available at: http://eosweb.larc.nasa.gov/PRODOCS/ceres/level2_ssf_table.html). CERES TOA outgoing longwave fluxes (also referred to as CERES OLRs) are used in our analysis and converted from CERES measured filtered radiances of the shortwave, total, and window channels. The filtered radiances for Earth-atmosphere emitted radiances are converted from CERES instrument counts using calibration coefficients that are derived in ground laboratory measurements [Priestley et al., 2000]. Then filtered radiances are converted to unfiltered radiances by using theoretically derived regression coefficients between filtered and unfiltered radiances [Loeb et al., 2001]. Finally, CERES outgoing longwave fluxes are determined by applying an empirical angular distribution mode to the unfiltered longwave radiances. The angular distribution modes are scene dependent and CERES uses coincident imager measurements from the Moderate Resolution Imaging Spectrometer to determine scene types [Loeb et al., 2005, 2007].
Aqua carried two identical CERES instruments, Flight Modes 3 and 4 (FM3 and FM4). Operationally, one of the CERES instruments is placed in cross-track scan mode for continuous Earth sampling, while the other is generally operated in rotating azimuth plane scan mode for improved angle sampling before 30 March 2005. The FM4 shortwave channel stopped functioning at 1842 UT on 30 March 2005. Since then both instruments have been operated in the cross-track scan mode and CERES FM4 has no TOA outgoing longwave fluxes during the daytime. CERES outgoing longwave fluxes from the cross-track scan mode are chosen for the purpose of generating and testing AIRS OLR regression coefficients because AIRS operates in cross-track scan mode. Measurements from the CERES FM3 instrument are selected to maintain the consistency of the training ensemble. Table 1 lists the days of the training and test ensembles. Both CERES Aqua FM3 Edition2B SSF before April 2006 and CERES Aqua FM3 Edition2C SSF after May 2006 are used in the selection of training and test ensembles. The training ensemble includes 16 days (4 days per year) and the test ensemble includes 8 days (2 days per year). For the training ensemble 1 day per season for each year is selected; the days are mostly close to the days that were used in the training of the AIRS radiance eigenvectors, and on those days, both AIRS and CERES radiance measurements are at a maximum. The days in 1 year have 1 month shift related to the days of the previous and next year. For the test ensemble 2 days per year are selected, in different months relative to the training ensemble. All of the days in the test ensemble are in eight different months, with the aim to cover all four seasons.
Table 1. Days of Training and Test Ensembles
25 Nov 2003
12 Nov 2005
6 Jun 2004
20 Jan 2004
6 Mar 2006
23 Nov 2004
13 Apr 2004
3 Jun 2006
15 Mar 2005
6 Jul 2004
6 Sept 2006
8 Sept 2005
26 Oct 2004
6 Dec 2006
20 May 2006
15 Feb 2005
26 Feb 2007
12 Jul 2006
12 May 2005
12 May 2007
1 Jan 2007
11 Aug 2005
26 Jul 2007
24 Aug 2007
2.3. Spatial Collocation of CERES and AIRS Measurements
 Since AIRS and CERES instruments are on the same EOS Aqua spacecraft, radiance measurements from AIRS are taken almost simultaneously with CERES radiance measurements. Collocation of AIRS and CERES measurements needs to be implemented in space only. To minimize the effect of the differences in the viewing and scanning properties of AIRS and CERES instruments, AIRS and CERES measurements are collocated in a 6 × 5 array of AIRS FOVs, which is called a big box. The big box is the geophysical region that is covered by the 30 AIRS FOVs that are arranged in the 6 × 5 array (6 FOVs in the scan direction and 5 FOVs along orbital the track; see Figure 2 (top) ). The diameters of the big boxes are approximately 80 km in nadir and 125 km at the maximum scan angle of AIRS. Therefore AIRS OLR in the big boxes is adequate to produce 1° longitude × 1° latitude gridded level 3 products. Figure 2 illustrates an example of collocated CERES outgoing longwave fluxes and AIRS radiance measurements in a big box as observed at about 2015:25 UTC on 6 June 2004. Averaging in big boxes can mitigate the uncertainties caused by the differences in viewing geometric properties between the two instruments, especially the differences in the size and shape of the footprints and the density of sampling Earth's scenes.
 Five consecutive AIRS scan lines are searched to find big boxes. The total number of big boxes is 15 in the AIRS cross-track direction. The CERES SSF data are searched to find all the CERES footprints whose centroids fall within an AIRS big box. CERES footprints that are at least partially within the AIRS swath are retained. As a result, only footprints with a CERES viewing zenith angle of <49° appear in our analyses. The differences in mean view angle between the two instruments in big boxes are within 2.5°. In a big box there are 30 AIRS spectra and the mean number of CERES footprints is about 21, with a standard deviation of 1.56. The number of CERES footprints within a big box shows no significant change with increasing AIRS view angle. The reason is that the size of both CERES and AIRS footprints increases proportionally with increases in the AIRS view angle.
 Collection criteria for the training and independent test ensembles are as follows: (1) there are no missing AIRS and CERES measurements in a big box, (2) the number of CERES footprints in a big box is between 15 and 30, and (3) reconstruction scores of the AIRS radiances >1.5 are excluded from the estimation of the mean AIRS radiances. The reconstruction score is a measure of the agreement between the reconstructed and the observed radiances [Goldberg et al., 2003]. The selection procedures resulted in approximately 1.5 million collocated AIRS and CERES measurements for the training ensemble and 0.76 million pairs for the test ensemble and included observations, as listed in the last row in Table 1.
 The 30 AIRS radiance measurements within a big box are averaged. Then the PCSs of the mean AIRS radiances in the big box are calculated. In addition, the mean OLR of the collocated CERES OLRs in the big box is calculated. The standard deviation of the CERES OLR within the big box is also calculated and retained for studying the effect of scene uniformity on the accuracy and precision of the AIRS regression OLR. The mean CERES OLR and the PCSs of the AIRS mean radiances are used as training pairs in the generation of OLR regression coefficients in section 3.2.
3. Technique for Estimation of AIRS Outgoing Longwave Radiation (OLR)
where As are regression coefficients determined from a regression analysis of the collocated CERES TOA outgoing longwave fluxes and the PCSs of AIRS radiances of the training ensemble. The coefficients are a function of the AIRS view angle. k is the index of AIRS radiance PCSs. K is the number of significant PCs, in order of eigenvalues (λ), from largest to smallest; it is determined in section 3.2. P is a vector of AIRS radiance PCSs. The PCSs are the AIRS radiance PCs normalized by the square root of eigenvalues:
where E is an eigenvector matrix of the covariance matrix of AIRS radiances with dimension N × K. Here N equals 1707, which is the number of AIRS channels in the subset that was used in the generation of AIRS radiance eigenvectors. The superscript T denotes the matrix transpose. The AIRS radiance eigenvalues and eigenvectors were trained from a different ensemble of AIRS radiance measurements outlined by Zhou et al. .ΔΘ in equation (2) is AIRS radiance normalized by instrumental noise.
where R is AIRS observed radiance in the subset of AIRS channels. is the mean radiance of the training ensemble that was used for generation of the AIRS radiance eigenvectors. All of ΔΘ,NEΔN, R, and have length N.
3.2. Generation of AIRS OLR Regression Coefficients
 The training ensemble described in sections 2.2 and 2.3 is used to generate AIRS OLR regression coefficients. To account for the limb effects described by Goldberg et al. , we adopted the same approach and trained the regression coefficients in the multiple regimes of AIRS viewing angle. There are 15 big boxes along the AIRS cross-track direction. With the assumption of symmetry about the nadir, the AIRS OLR regression coefficients are generated at eight regimes of AIRS viewing angle. The fringe points of AIRS view angles represent the midpoints of the big boxes and are listed in the first column in Table 2. The regression coefficients can be directly applied to the mean AIRS radiances in big boxes and applied to AIRS instantaneous radiances through linear interpolation of the regression coefficients with respect to AIRS view angle.
Table 2. Statistics of the Training and Test Ensemblesa
View Angle (deg)
Percentage of Sample
AIRS, Atmospheric Infrared Sounder; CERES, Clouds and the Earth's Radiant Energy System; OLR, outgoing longwave radiation; SD, standard deviation.
 In the implementation of regression retrievals used in the AIRS/AMSU/HSB PGS [Aumann et al., 2003], 85 PCs are used to retrieval atmospheric temperature, moisture, and ozone vertical profiles. The purpose of our analysis is to determine the number of significant PCs of the AIRS mean radiances in big boxes and study their impact on the accuracy and precision of AIRS OLR. The regression coefficients of AIRS OLR are generated in a series of PCs, which are designated by circles in Figure 3. Two sets of OLR regression coefficients are generated by using the training ensemble and a subset of the training ensemble that includes uniform scenes only. The uniform scenes have small OLR spatial variation and are measured by the CERES OLR coefficient of variation (CV). The CV is defined as the ratio of the standard deviation of CERES OLR to its mean value in a big box. If the standard deviation of CERES OLR in a big box is less than 5% of its mean flux, the box is judged to be uniform. There are about 77% uniform scenes in the training and test ensembles. Figure 4c gives an example of the global distribution of CERES OLR CVs in big boxes on 24 August 2007 for ascending. We can see the criteria (CV ≤ 5%) will generally exclude big boxes in which there are large spatial variations in cloud amount and/or cloud top height.
Figure 3 shows the fitting biases and standard deviation errors between the AIRS and the CERES OLR with respect to the number of PCs. When OLR regression coefficients are trained by using the training ensemble and applied to the test ensemble, the standard deviation (solid line in Figure 3 (bottom)) decreases rapidly as the number of PCs increases to 35 and then decreases slowly. The biases (solid line in Figure 3 (top)) decrease rapidly as the number of PCs increases to 35. When the number of PCs is larger than 75, the biases first increase and then decrease as the number of PCs increases. As the number of PCs ranged from 35 to 75, the bias errors are relatively flat and insensitive to the number of PCs. This means that the number of PCs within the range can be chosen and used to generate AIRS OLR regression coefficients. The number of PCs is set at 35 and used in the estimation of AIRS OLR in the following study. The use of the least number of PCs, namely, the number 35, is based on the fact that more significant PCs represent the variability of atmosphere, surface, and cloud parameters, and less significant PCs represent spectrally random and/or correlated noises. Moreover, our study found that the use of a smaller set of the PCs as the predicators can effectively reduce the bias at extreme OLR values (>310 Wm−2). The biases at high OLR values may be related to AIRS's scene-dependent instrumental noise at shortwave spectral range [Tobin et al., 2007].
 Biases and standard deviations between AIRS and CERES OLR are related to (1) the differences in spectral range and spectral resolution of the two instruments as shown in Figure 1; (2) the difference in viewing geometry, especially for the size, shape, and density of footprints as discussed in section 2.3; and (3) the fact that AIRS radiances and CERES OLRs are averaged in big boxes but AIRS radiance eigenvectors were generated by using instantaneous AIRS FOV radiance measurements.
 To test the effect of scene uniformity on the accuracy and precision of AIRS OLR, the regression coefficients of AIRS OLR are trained by using the uniform scenes (CV ≤ 5%) of the training ensemble and applied to the uniform scenes of the test ensemble. Biases and standard deviations between AIRS and CERES OLR are presented as dotted lines in Figure 3. The biases and standard deviation follow the same distribution pattern as does the test ensemble. But the errors have slightly larger biases (2% increases) and smaller standard deviations (20% decreases). The reason for the slightly larger biases of the subset of uniform scenes may be that AIRS radiance eigenvectors were generated by using AIRS instantaneous radiances for all-sky scenes [Zhou et al., 2008]. As for the standard deviation, it is expected that the prediction error is proportional to the variance, which is larger in all-sky scenes and smaller in uniform scenes; presumably the explained variance is of a similar magnitude for various scenes. The small standard deviation values of the uniform scenes give the “best” estimation of the precision of AIRS OLR on the spatial scale of big boxes. Use of the uniform scenes greatly reduces the radiometric differences that are associated with spatially nonuniform scenes. The AIRS OLR regression coefficients generated by using the uniform scenes of the training ensemble are used in the estimation of AIRS OLR in the following study.
Table 2 presents the agreement between AIRS and CERES OLR with respect to AIRS view angle. The second column in Table 2 gives the percentage of the training ensemble in one regime of AIRS view angle, of the total number of the training ensemble components. The range of the CERES mean OLR of the training ensemble (column 3) is from 224.5 to 225.5 Wm−2. The CERES OLR shows a 1 Wm−2 decrease from nadir to the maximum AIRS scan angle. The range of standard deviation of CERES OLR (column 4) is from 48.1 to 47.2 Wm−2. The standard deviation of the OLR differences (columns 6 and 8) has almost the same order of decrease for both the training and the test ensembles (about 0.8 Wm−2), except for the regime with the largest view angle. These statistics show that the mean differences between AIRS and CERES OLR (columns 5 and 7) are less than 0.5 Wm−2 for both the training and the test ensembles so that the difference between AIRS and CERES OLR is small.
4. Results and Discussion
4.1. Comparisons With CERES OLR
 The AIRS OLR in big boxes is evaluated by application of the AIRS OLR regression coefficients to the independent test ensemble described in sections 2.2 and 2.3. As an example, the AIRS OLR in big boxes on 24 August 2007 for ascending orbit is displayed in Figure 4a. Figure 4b presents the OLR differences between AIRS and CERES. The absolute values of the difference are generally less than 4 Wm−2. Figure 4c shows the CVs of CERES OLR. The large differences (>4 Wm−2) between AIRS and CERES OLR are collocated with large spatial variation of OLR, which is primarily related to the variation in cloud amount and/or cloud top height. The histogram of the OLR differences between AIRS and CERES has a Gaussian distribution, with a mean and standard deviation of 0.3 and 2.7 Wm−2, respectively (not shown). These values are consistent with those of the test ensemble, as shown in Figure 5b, and those in columns 7 and 8 of Table 2.
Figures 5a–5f compare AIRS OLR with CERES OLR for the test ensemble. A scatterplot of AIRS OLR versus CERES OLR is shown in Figure 5a. A histogram of OLR differences between AIRS and CERES (Figure 5b) shows a Gaussian distribution, with a mean difference of 0.26 Wm−2 and a standard deviation of the differences of 2.6 Wm−2. The AIRS OLR is an empirical relationship between the CERES outgoing longwave fluxes and the PCSs of AIRS radiances. The approach is similar to the empirical regression of AVHRR OLR but different from the physical regression of HIRS OLR. The radiances from the AVHRR window channel are converted to OLR using narrowband-to-broadband spectral corrections that are obtained from the Earth Radiation Budget narrow-FOV observations of total radiances and the infrared window radiances of the temperature-humidity infrared radiometers [Ohring et al., 1984; Gruber and Krueger, 1984]. But the theoretical radiative model calculation is used to relate the window radiances of later NOAA satellites to those of the temperature-humidity infrared radiometers. The root-mean-square flux errors of the AVHRR OLR are about 11 Wm−2. The radiances from HIRS instruments are converted to fluxes using a technique based on theoretical radiative model calculation [Ellingson et al., 1989, 1994]. The HIRS OLR is estimated by a linear combination of radiances in four HIRS channels that are sensitive to surface temperature, lower and upper tropospheric water vapor, and air temperature centered at 100 hPa. For physical regression the major problem is the error in the radiative transfer model. The physical regression usually uses balloon-borne radiosonde measurements as true atmospheric state. The soundings usually miss the information on trace constituents in atmosphere, surface skin temperature, and surface infrared emissivity. Also, as one goes from AVHRR to HIRS to AIRS, the range of the total longwave spectrum that is observed increases. This also should lead to improved correlation with OLR. We utilize CERES estimated outgoing longwave fluxes to generate AIRS OLR regression coefficients. As a result, instantaneous AIRS OLR has a small bias with respect to CERES OLR, and the standard deviation is approximately half that of the HIRS OLR, 5 Wm−2, on a comparable spatial scale of scenes.
 The differences between AIRS and CERES OLR have a slight dependence on view angle (Figure 5c). After training the AIRS OLR regression coefficients in eight view angle regimes, we can account for AIRS radiance variation with respect to AIRS view angle so that the resulting AIRS OLR has a slight angular dependence. The standard deviation of the OLR differences decreases from 3.0 to 2.2 Wm−2 when the AIRS view angle increases from zero to its maximum. The magnitude of the variation is similar to that of the training ensemble as listed in column 6 of Table 2. However, more detailed analyses of the differences in several subsets of the test ensemble revealed that there is a weak dependence on view angle in the twilight region, where the solar zenith angle is between 90° and 95°, in the South Polar region (south of 75°S), and in the tropical deep convective zones.
 The dependence of OLR differences on the solar zenith angle (Figure 5d) illustrates that there is a negative bias of about −2 Wm−2 in the solar zenith angle bin of 90°–95°. The maximum of the differences occurs in solar zenith angles from 90° to 91°. In the other solar zenith bins the biases are very small (absolute biases of <0.5 Wm−2). In the twilight region the standard deviation of the differences also has the relatively large value of 3.3 Wm−2. The standard deviation of the differences is greater than 3 Wm−2 when the sun is at a high solar zenith angle (<35°). The reason for the large discrepancies in the twilight region is unclear. Our preliminary investigation showed that the geographical distribution of the reconstruction score of the AIRS radiances shows no notable variation around the twilight region. The discrepancies in the twilight region may be related to the uncertainties in conversion of CERES unfiltered radiances to outgoing longwave fluxes [Kato and Loeb, 2003].
Figure 5e demonstrates that the biases between AIRS and CERES OLR are generally small and almost constant. There are relatively larger biases (>0.5 Wm−2) when the CERES OLR is about 350 and 80 Wm−2. The biases around 80 Wm−2 occur mainly in the South Polar region and tropical regions with deep convective clouds. The standard deviation of the difference is relatively large (>3 Wm−2) when CERES OLR is larger than 320 Wm−2. These large biases occurred mainly over the Australian and the Kalahari deserts during summer daytime. In contrast, the mean differences over the Sahara desert are smaller and fluctuate around zero.
 The OLR differences with respect to latitude (Figure 5f) have a value of less than −1 Wm−2 in the latitude bin of 85°S–80°S. In the other latitude bins the biases are near zero. The standard deviation of the difference is relatively larger (>3 Wm−2) in the tropics than at mid- and high latitudes (∼2 Wm−2).
Figure 6 compares AIRS OLR with CERES OLR for the uniform scenes of the test ensemble. The uniform scenes (Figure 6a) have less scattering than the all-sky scenes (Figure 5a). Uniform scenes show a more linear relationship between AIRS and CERES OLR. A histogram of the OLR differences between AIRS and CERES (Figure 6b) also shows a Gaussian distribution, with a mean difference near zero and a standard deviation of the differences of about 2 Wm−2. The nonuniform scenes (where CV > 5%) have a mean bias and standard deviation of 1 and 3.8 Wm−2, respectively (not shown). Apparently, nonuniform scenes have a larger variation and a slightly large bias than uniform scenes. However, the histograms of both uniform and nonuniform scenes show Gaussian distributions. The standard deviation of the uniform scenes is about 2 Wm−2, which is much smaller than that of HIRS OLR (5 Wm−2), at 104 km2 uniform scenes [Ellingson et al., 1994]. The bias and standard deviation of the uniform scenes best represent the performance of the algorithm, since the larger errors from the nonuniform scenes are due to the different spatial resolution between AIRS and CERES, and these differences cannot be corrected. The biases of the uniform scenes in Figures 5c–5f have a distribution similar to the all-sky scenes with respect to AIRS viewing angle, solar zenith angles, CERES OLR, and latitude but have smaller fluctuations than those of the all-sky scenes. Moreover, the standard deviations of the OLR differences are lowers than those of the all-sky scenes.
 We also compared AIRS OLR in sun glint scenes with collocated CERES OLR. Normalized distributions of the OLR differences between AIRS and CERES are displayed in Figure 7. The sun glint scenes are defined as big boxes in which at least one of the AIRS FOVs is contaminated by reflected solar radiation. The contaminated AIRS FOV is within 200 km of the sun glint location. The sun glint mostly occurs at an AIRS view angle in the range of −35° to −5°, a solar zenith angle of from 10° to 30°, and in the latitude belt from 40°S to 40°N. Sun glint scenes account for 3% of the test ensemble. The mean bias and standard deviation of the OLR differences in sun glint scenes have values of 0.6 and 3.2 Wm−2, respectively. The histogram distribution of the OLR differences for sun glint scenes is approximately Gaussian, with slightly larger mean differences and standard deviations than those of the test ensemble. The histogram of the OLR differences in sun glint scenes broadens, compared with that of all-sky scenes, when the absolute values of the OLR differences are greater than 3 Wm−2. In our study, the sun glint scenes are included in the generation of AIRS OLR regression coefficients and estimation of AIRS OLR for two reasons. One is that the OLR bias caused by sun glint is relatively small. The other is that sun glint scenes are included in the training of the AIRS radiance eigenvectors if their reconstruction score is less than 1.25 [Zhou et al., 2008].
 With about 0.76 million big boxes covering a wide range of atmospheric, surface, and clouds conditions in the above comparisons, AIRS OLR errors with respect to AIRS view angle, solar zenith angle, CERES OLR, and latitude are well characterized in Figures 5 and 6. In general, AIRS OLR agrees very well with CERES outgoing longwave fluxes. The standard deviation is 3 Wm−2 or less for all-sky scenes and about 2 Wm−2 for uniform scenes, except for large fitting errors in the twilight region. The differences between AIRS and CERES show a slight dependence on CERES OLR and latitude. However, detailed comparisons of AIRS OLR and CERES OLR in CERES single footprints are beyond the scope of our study.
4.2. Sensitivity Studies
 The first sensitivity study was designed to test the effect of spatial averaging in big boxes on the accuracy and precision of the AIRS regression OLR. We use two approaches to estimate AIRS OLR of the test ensemble. In the first approach regression coefficients are directly applied to the mean radiances of big boxes as described in section 3.2. In the second approach regression coefficients are applied to each AIRS spectrum in a big box, then 30 OLR values in the big box are averaged. Figure 8 displays histograms of the AIRS minus CERES OLR differences of the two approaches. The AIRS and CERES OLR have almost-identical Gaussian distributions. The standard deviation of the OLR differences is the same in the two approaches (2.6 Wm−2). But the bias is slightly larger for the second approach than for the first. The spatial average of either AIRS instantaneous radiance measurements or AIRS instantaneous OLR in big boxes does not have an appreciable impact on the accuracy and precision of AIRS OLR. Averaging in big boxes does not introduce any systematic bias. This analysis further indicates that the collocation of AIRS and CERES measurements in big boxes described in section 2.3 is an appropriate approach.
 The second sensitivity study was designed to test the temporal stability of AIRS OLR. Another set of the AIRS OLR regression coefficients is generated by using 7 days of the training ensemble from 12 May 2005 to 6 December 2006 (referred to as method 2). The regression coefficients are applied to the whole test ensemble. The residuals of AIRS regression OLR are compared with those using the whole training ensemble to train the regression coefficients as described in section 3.2 (referred to as method 1). Tables 3 and 4 display the means and standard deviations of the OLR differences in the test ensemble for the two methods. The accuracy and precision show no significant difference between the two methods or in the periods that are not covered by the training data set of method 2. The standard deviation of the bias is about 2 Wm−2 for uniform scenes, and the overall mean of the bias is nearly zero. The OLR regression coefficients of method can be confidently applied to AIRS measurements from 1 year earlier (e.g., on 6 June 2004) and from 1.5 years later (e.g., on 24 August 2007). These very small errors will allow the AIRS OLR product to monitor CERES OLR performance precisely. The AIRS OLR can be used as a surrogate for the CERES OLR in the case of CERES failure. Similarly, the method to generate the AIRS OLR can be extended to the CrIS, and therefore the CrIS could be used to monitor the performance of ERBS and serve as a potential surrogate, since both will be on the future National Polar-orbiting Operational Environmental Satellite System satellites. The same method of empirical PC regression OLR could be applied to the infrared Atmospheric Sounding Interferometer, providing additional temporal coverage.
Table 4. Standard Deviation Errors of the Test Ensemblea
6 Jun 2004
23 Nov 2004
15 Mar 2005
8 Sep 2005
20 May 2006
12 Jul 2006
1 Jan 2007
24 Aug 2007
5. Summary and Future Work
 This study demonstrates the ability to use AIRS hyperspectral radiance measurements and collocated CERES OLR to estimate TOA outgoing longwave fluxes from AIRS radiance observations. AIRS OLR is determined from an equation derived from a PC regression between the CERES outgoing longwave fluxes and the PCSs of AIRS radiances. This method is different from physical regression of the HIRS OLR, which is based on theoretical radiative model calculation. AIRS OLR is an experimental relationship based on the OLR estimates from the CERES broadband radiance observations. Therefore, by design, in this approach the instantaneous AIRS OLR has a small bias relative to CERES outgoing longwave fluxes.
 In the approach of generating AIRS OLR regression coefficients, AIRS and CERES measurements are collocated in big boxes that include a 6 × 5 array of AIRS FOVs. This reduces the uncertainties caused by the difference in geometric viewing properties between the AIRS and the CERES instruments. The spatial average in big boxes effectively removes random noise of the AIRS radiance measurements. The number of significant components of AIRS radiances is determined by using an empirical approach. At a number of PCs equal to 35, the regression fitting error has a local minimum and effectively reduces the biases at high OLR values. The 35 PCs of AIRS radiances are enough to represent the radiative information content related to TOA outgoing longwave fluxes.
 With respect to CERES OLR estimates, the precision of the AIRS OLR is less than 3 Wm−2 for all-sky scenes using the information content of AIRS radiances of its 1707 pristine channels. The precision is about 2 Wm−2 for uniform scenes and 4 Wm−2 for nonuniform scenes. The AIRS OLR precision for uniform scenes is much higher than that of the HIRS OLR, 5 Wm−2, for similar comparisons with the Earth Radiation Budget Experiment OLR [Ellingson et al., 1994]. The precision of uniform scenes best represents the performance of the algorithm, since the larger errors from nonuniform scenes are due to the different spatial resolutions between AIRS and CERES.
 The generation of AIRS OLR regression coefficients in eight regimes of AIRS view angles does account for the limb effect of AIRS cross-track scanning. The instantaneous OLR differences between AIRS and CERES do not depend on AIRS view angle over the uniform scenes. However, there is a slight dependence on AIRS view angle over the nonuniform scenes. AIRS OLR and CERES OLR have larger discrepancies (−2 Wm−2) in the twilight regions.
 The small differences between AIRS and CERES OLR indicate that AIRS (CrIS) can be used to monitor the performance of CERES (ERBS) and used as a backup in the case of CERES (ERBS) failure. Continuation of this study will include the AIRS and CERES OLR comparisons performed in CERES single footprints, which will allow characterization of our AIRS regression OLR with respect to surface type, atmospheric state, and clouds. A detailed comparison of our AIRS regression OLR and AIRS TIROS Operational Vertical Sounder-like OLR derived from AIRS level 2 products [Mehta and Susskind, 1999] is under way and will be presented in a separate paper. We will derive OLR from Infrared Atmospheric Sounding Interferometer radiance measurements.
 This work was supported by funding from the National Climatic Data Center Climate Program. The views, opinions, and findings contained in this paper are those of the authors and should not be construed as an official National Oceanic and Atmospheric Administration or U.S. Government position, policy, or decision.