4.1. Comparisons With CERES OLR
[23] 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.
[24] 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 narrowbandtobroadband spectral corrections that are obtained from the Earth Radiation Budget narrowFOV observations of total radiances and the infrared window radiances of the temperaturehumidity 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 temperaturehumidity infrared radiometers. The rootmeansquare 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 balloonborne 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.
[25] 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.
[26] 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].
[27] 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.
[28] 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}).
[29] 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 allsky 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 10^{4} km^{2} 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 allsky scenes with respect to AIRS viewing angle, solar zenith angles, CERES OLR, and latitude but have smaller fluctuations than those of the allsky scenes. Moreover, the standard deviations of the OLR differences are lowers than those of the allsky scenes.
[30] 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 allsky 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].
[31] 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 allsky 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
[32] 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 almostidentical 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.
[33] 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 Polarorbiting 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 3. Biases of the Test Ensemble^{a}Day  Uniform Scenes  Nonuniform Scenes  AllSky Scenes 

Method 1  Method 2  Method 1  Method 2  Method 1  Method 2 


6 Jun 2004  0.16  0.13  1.31  1.37  0.42  0.41 
23 Nov 2004  −0.28  −0.33  0.88  0.93  −0.02  −0.05 
15 Mar 2005  0.18  0.14  1.11  1.16  0.39  0.37 
8 Sep 2005  0.31  0.27  1.13  1.17  0.50  0.48 
20 May 2006  −0.03  −0.06  1.12  1.17  0.24  0.23 
12 Jul 2006  0.09  0.04  1.00  1.04  0.31  0.28 
1 Jan 2007  −0.27  −0.31  0.86  0.90  −0.03  −0.05 
24 Aug 2007  −0.01  −0.07  1.03  1.06  0.23  0.19 
Table 4. Standard Deviation Errors of the Test Ensemble^{a}Day  Uniform Scenes  Nonuniform Scenes  AllSky Scenes 

Method 1  Method 2  Method 1  Method 2  Method 1  Method 2 


6 Jun 2004  2.02  2.02  3.82  3.81  2.59  2.60 
23 Nov 2004  2.08  2.09  3.90  3.89  2.65  2.67 
15 Mar 2005  2.07  2.07  3.96  3.94  2.65  2.65 
8 Sep 2005  2.08  2.07  3.83  3.81  2.62  2.61 
20 May 2006  2.04  2.04  3.82  3.82  2.62  2.63 
12 Jul 2006  2.03  2.02  3.78  3.76  2.60  2.60 
1 Jan 2007  2.12  2.13  3.72  3.70  2.59  2.60 
24 Aug 2007  1.96  1.95  3.87  3.86  2.56  2.55 