Results of RMS differences are discussed in section 5.1 with individual subsections dedicated to global “all,” “land,” “sea,” and “cloud-cleared” versus “clear-only” categories (sections 5.1.1, 5.1.2, 5.1.3, and 5.1.4). This is followed by the RMS differences for the tropics, midlatitude and high-latitude zones (section 5.1.5). The bias characteristics and possible sources for the biases seen in the AIRS retrievals are discussed in section 5.2. Section 5.3 provides a brief discussion on the statistics when all the AIRS retrievals are processed with a tighter time and distance collocation criteria (±1 hour and 50 km radius). Section 5.3 also discusses the retrieval statistics for day and night cases using subsets of samples extracted from all the accepted retrievals.
5.2. Bias Characteristics
 Figures 11a and 11b show the bias characteristics for the temperature and water vapor profiles for “all” accepted global samples. Here, the RAOB observation is taken as a reference and the difference, denoted bias, is calculated between the RAOB and the following collocated data sets: the AIRS physical retrieval (AIRS_PHYRET, solid squares), ATOVS (open diamonds); NCEP_GFS (solid circles); ECMWF (solid triangles); AIRS fast regression (AIRS_FGRET, open circles). The corresponding RMS differences for these biases are shown in Figures 4a and 4b. The water vapor bias is presented as percentage to the reference (RAOB) water vapor in the 2 km layer (100 x (AIRS-RAOB)/RAOB). The AIRS_PHYRET, AIRS_FGRET, and the ECMWF show a negative water vapor bias for the upper troposphere region. This could be due to the RAOB measurements having a wet bias above 400 hPa, a tendency observed for soundings in cold polar and midlatitude air masses (T. Reale, 2005, http://foehninter.nesdis.noaa.gov/PSB/SOUNDINGS/ORA/index.html). Overall, the water vapor biases are within expected error bounds and are consistent with the results discussed by other investigators (McMillan et al., submitted manuscript, 2005). It may be noted that unlike the temperature biases, the water vapor biases (axis shown on expanded scale ±30) are a small fraction of the percent RMS indicative of the high spatial variability of water vapor.
Figure 11. (a) Global temperature biases for all the accepted samples for the “all” category: RAOB versus AIRS_PHYRET, solid squares; RAOB versus NCEP_GFS, solid circles; RAOB versus ATOVS, open diamonds; RAOB versus AIRS_FGRET, open circles; and RAOB versus ECMWF, solid triangles. (b) Global water vapor biases for all the accepted samples for the “all” category: RAOB versus AIRS_PHYRET, solid squares; RAOB versus NCEP_GFS, solid circles; RAOB versus ATOVS, open diamonds; RAOB versus AIRS_FGRET, open circles; and RAOB versus ECMWF, solid triangles.
Download figure to PowerPoint
 With respect to the temperature bias, the AIRS_PHYRET (Figure 11a) shows a larger temperature bias as compared to NCEP_GFS, ECMWF, and ATOVS. The ATOVS retrievals show a relatively smaller bias. This may be due to the tuning of ATOVS radiances using RAOB information, and the use of prior RAOB collocations to define first guess used in the ATOVS final retrieval algorithm [Reale, 2003]. Both the ECMWF and NCEP_GFS forecast models show smaller biases with RAOBs. This is expected since model forecasts utilize RAOB information in the analysis. The AIRS_FGRET bias follows the same trend as the ECMWF, probably because of use of ECMWF forecast/analysis as the training data set in the generation of regression coefficients [Goldberg et al., 2003]. The AIRS_FGRET bias, although a little larger than that of ECMWF, is still smaller than the AIRS_PHYRET suggesting that the AIRS final physical retrieval step is increasing the bias from the fast regression first guess. Thus, out of all the collocated retrievals and forecasts, the AIRS retrieval is the only one that has no prior information or use of the RAOB profiles in its retrieval steps.
 Figure 12 shows the AIRS_PHYRET temperature bias for the “land” (LAND_AIRS_PHYRET, solid circles) and “sea” (SEA_AIRS_PHYRET, open diamonds) subsets along with the bias from the “all” category (shown earlier in Figure 11a, AIRS_PHYRET, solid squares). It is evident from Figure 12 that the land samples contribute predominantly to the overall bias. The sea samples also exhibit the oscillating trend in bias but the amplitude (about 0.3°K at 680 hPa) is quite small. When statistics are computed separating the global samples into many subsets (tropical-land, tropical-sea, midlatitude-land, midlatitude-sea, high-latitude-land, and high-latitude-sea), the samples from land and coastal categories for midlatitude and high-latitude regions seem to contribute mainly to the bias in AIRS_PHYRET because of the larger variability in those regions. The variability in the tropical samples (Table 6) is relatively less, and consequently the bias and the RMS differences are less for the tropical samples.
Figure 12. Global temperature bias over “all” (RAOB versus AIRS_PHYRET, solid squares), “land” (LAND_AIRS_PHYRET, solid circles), and “sea” (SEA_AIRS_PHYRET, open diamonds) categories.
Download figure to PowerPoint
 Many factors might contribute to the amplification of the bias in the AIRS physical retrieval. One major factor could be the amplification of noise in the cloud-cleared radiance [Susskind et al., 2003]. This is evident from Figure 13 where the AIRS_PHYRET bias is plotted for both the “clear-only” cases (AIRS_PHYRET_CLR, solid circles) and for all accepted (cloud-cleared) cases (AIRS_PHYRET, solid squares) from “all” category. The RMS differences corresponding to these biases are shown in Figure 7a. The “clear-only” retrieval also show similar trend in bias, but the magnitude of the bias is significantly lower than the cloud-cleared retrievals, suggesting that some proportion of the bias amplification is caused by the algorithm deficiencies (may retain some residual cloud amount) in cloud-clearing methodology. Samples from land and coastal categories contribute significantly to the bias; therefore the higher degree of difficulty of cloud clearing associated with the spatially heterogeneous (land and coastal) surfaces might be the contributing factor for the amplification of bias. Another plausible source could be errors in the upper atmospheric state sensed by the tails of the highest-peaking kernel functions. These errors appear to be inducing the oscillation into the upper stratosphere and lower troposphere. The biases in the lower troposphere appear to be dominated by an interaction with the microwave channels. In addition, there are other phenomena contributing to the bias.
Figure 13. Global temperature bias for all the accepted “cloud-cleared” (RAOB versus AIRS_PHYRET, solid squares) and “clear-only” (RAOB versus AIRS_PHYRET_CLR, solid circles) samples for the “all” category.
Download figure to PowerPoint
 Engelen et al.  have shown that the zonal, seasonal, and annual variations in CO2 could cause errors in retrieved temperatures from theoretical instruments with similar spectral resolution to that of the AIRS. In addition, using the offline retrieval system for AIRS we have found that CO2 variations of similar magnitude to expected seasonal and zonal variability will induce a bias in AIRS temperature retrievals relative to RAOB data over the entire troposphere. Because RAOB temperatures do not depend on an assumption of atmospheric CO2 concentration, we therefore expect that differences between RAOB temperatures and AIRS retrieved temperatures in the troposphere will correlate with physical CO2 variations.
 Figure 14 shows monthly global average differences between RAOB temperatures and AIRS retrieved temperatures (solid circles). Because IR sounders rely on thermal gradients to retrieve temperature and gas concentrations, the cold and nearly isothermal nature of the tropopause in midlatitude/polar regions represents a difficult portion of the atmosphere to resolve. Indeed most of the correlative RAOBs in our ensemble are located in the midlatitude to high-latitude regions (Table 1). Therefore, in order to mitigate uncertainties in the determination of the variable tropopause with season, we used a coarse layer between 450 hPa and the surface to calculate the trend in the difference between RAOB and AIRS retrievals over the 2-year period (September 2002 to September 2004). Also shown in Figure 14 is a smoothed representation of the raw differences using a 2-month sliding boxcar average (dotted line). The solid curve is the zonally weighted linear-least squares fit of the NOAA's Climate Monitoring Diagnostics Laboratory's (CMDL) Marine Boundary Layer (MBL) CO2 product [GLOBALVIEW-CO2, 2004]. A least squares fit is used in lieu of the raw CMDL MBL product because this data set ends in December 2003; therefore trends beyond this month are extrapolated using the fitting coefficients. To produce the fitting coefficients, we calculated a global average of the raw CMDL MBL product weighted by the distribution of RAOB observation between January 2002 and December 2003 and then fit these averaged raw data to a second-order polynomial and third-harmonic terms. Differences between the averaged raw data and least squares fit are less than 0.5 parts-per-million by volume (ppmv).
Figure 14. Seasonal trends between AIRS retrieval bias 450 hPa to surface and CMDL MBL CO2, 90°N–90°S. Average differences between RAOB and AIRS temperatures are indicated by solid circles, smoothed differences using a 2-month sliding boxcar average are indicated by the dashed line, and zonally weighted linear least squares fit for the CMDL MBL product are indicated by the solid line.
Download figure to PowerPoint
 In Figure 14, the temperature differences and CO2 variations show consistent annual and seasonal trends. We note that CO2 variations should correlate with temperature variations in the lower troposphere and surface due to the temperature dependence of photosynthesis; however, we do not expect the precision of temperature retrievals to vary because of these small seasonal changes. In light of these findings, we have advised the AIRS science team that the addition of a CO2 error term in the temperature retrieval and the incorporation of a realistic CO2 first guess into the retrieval system are necessary.
 Although the bias trends and CO2 seasonal trends agree very well, the vertical oscillation apparent in all bias plots cannot be removed by incorporating a simple CO2 first guess into the retrieval system. We are currently investigating possible causes for the vertical oscillation in the bias statistic. Some of the investigations being carried out are (1) incorporation of CO2 and other trace gas error terms and climatologies in the AIRS initial guess profiles, (2) assessment of the contribution of upper atmospheric state errors and minimization, and (3) deficiencies in the cloud-clearing algorithm, microwave versus IR inconsistencies, etc.
5.3. RMS Difference and Bias for Tighter Collocations and Day/Night Cases
 When the collocated sample is chosen on the basis of a tighter control of time and distance collocation (±1 hour and 50 km radius) the number of input samples to the retrieval system shrinks to 33,000. As expected, the percentage of accepted samples by version 4.0 QA flags does not change appreciably. The temperature and water vapor statistics for AIRS_PHYRET show similar trends as seen for the ±3 hours and 100 km radius collocations. A minor improvement of about two tenths of a degree is observed in the temperature RMS. The water vapor RMS shows an improvement of 5–8% in the lower troposphere 2 km layers. There is no appreciable difference in the bias characteristics compared to the biases shown for the ±3 hours and 100 km radius collocations, and hence figures are not shown.
 When the collocated samples are separated into day and night cases, the statistics generated for AIRS_PHYRET for different categories did not show appreciable change from the RMS difference and biases for the corresponding categories using all samples. In general, the daytime temperature RMS difference shows an improvement of one tenth of a degree. An improvement of 3–5% in the surface water vapor RMS is observed for nighttime cases. With respect to biases, nighttime cases show larger negative bias in the temperature (about 0.4°K) at the surface. This may be due to difficulties connected with nighttime cloud clearing. This trend tapers down with height, and between 700 hPa and 400 hPa, the daytime cases show a larger positive bias of the order of 0.2°K. The water vapor shows a 5% change in bias in the upper troposphere with the daytime cases showing less negative bias than the nighttime cases indicating that daytime RAOBs are drier than nighttime RAOBs [Whiteman et al., 2006; McMillan et al., submitted manuscript, 2005]. Since the differences are not that prominent, figures are not shown.