4.1.1. Global Statistics
 The sample size of AIRS-O3SND 3-h matches is not sufficient to subgroup the data into different regions. Hence, statistics are computed with the global ensemble for the AIRS initial solutions (V4_FG and V5_FG), for the physical retrieval solutions (V4_PR and V5_PR), and for the ECMWF ozone profiles with O3SND matches as the truth. The data set consists of 353 matches from all over the globe. Layer ozone scatterplots (see auxiliary material) for V4_FG, V4_PR, V5_FG, V5_PR, and for the ECMWF are analyzed with reference to the ozone amounts from the O3SND measurements. Results from the analysis indicate that in general, the V4_FG underestimates larger amounts of ozone and overestimates smaller amounts of ozone. The ECMWF in general overestimates the ozone amount for most of the layers. The physical retrievals (V4_PR and V5_PR) corrects the first guess and tend to agree better with the O3SND measurements. Figures 4a and 4b show the physical retrieval solution for the V4 and V5 for layers 1–7. The V4_PR exhibits larger scatter than V5_PR, and the degree of agreement brought in by the V5_PR is better than that achieved by V4_PR. The V4_PR overestimates ozone amount in the lowest layer (1000–260 hPa, layer 1) compared to V5_PR. Another difficulty seen with the V4_PR is its inability to reach extreme values which is consistent with the smaller damping parameter 0.75 (more damping) used in V4_PR. In general, high ozone measurements that are underestimated in the V4 retrieval are increased by the V5 retrieval; and low ozone measurements that are overestimated in the V4 retrieval are decreased by the V5 retrieval. However, while improving these extreme values, the V5_PR, in general, shows a slight overestimation. This overestimation is prominent for layers 3 and 4 (Figure 4b, V5_PR_L03, violet asterisks; V5_PR_L04, red crosses). For the lower troposphere (layer 1) where the ozone amounts are considerably smaller, the V5_PR algorithm improves the retrieval, reduces the scatter and shows much better correlation with the layer ozone amounts from O3SND measurements. Thus, the differences in the V4_PR and V5_PR performance are somewhat dependent on the damping parameter that sets a threshold for the propagation of noise in the solution. Table 3 lists the Pearson correlation (R2) computed for these layers for the V4 and V5 retrievals. The V5_PR shows much higher R2 values than V4_PR for all the layers, and also reflects improvement over V5_FG for all the layers. For the lowest layer (1000–260 hPa) the improvement seen with the V5_PR compared to V5_FG is marginal (R2 values 75% versus 71%). The R2 values for the V4_FG and for the V5_FG are comparable except for the lowest layer where the V5_FG shows a larger correlation (33% versus 71%). Thus, the improvement seen in the V5_PR for the lowest layer is partially achieved through a better initial solution provided by a priori climatology. The R2 values for the ECMWF layer ozone amounts are better than V4_PR, but the V5_PR retrieval shows much better correlation for the lowest layer.
Figure 4. Scatterplots of AIRS retrieved layer ozone amounts for layers 1 to 7: 1100–260 hPa, 260–126 hPa, 126–66 hPa, 66–32 hPa, 32–16 hPa, 16–8 hPa, and 8–4 hPa. (a) V4 physical retrieval (V4_PR). (b) V5 physical retrieval (V5_PR).
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Table 3. Layer Correlations (R2 * 100) for AIRS V4 and V5 Retrievals and ECMWF Profiles With the O3SND Data
|Layer Pressure Boundaries (hPa)||Layer Number||Samples (N)||AIRS V4 Versus O3SNDs||AIRS V5 Versus O3SNDs||ECMWF Versus O3SNDs|
|First Guess V4_FG||Physical Retrieval V4_PR||First Guess V5_FG||Physical Retrieval V5_PR|
 Figures 5a and 5b show the bias and RMS difference statistics computed for V4_PR with reference to O3SNDs (solid squares). Similar statistics for V4_FG (solid circles), and for the ECMWF (solid triangles) are also shown in Figures 5a and 5b. The analysis presented here is for layers 1–6 that span from the surface to 10 hPa (typical sonde burst pressure). An examination of Figures 5a and 5b reveals the following points.
Figure 5. Ozone profile retrieval statistics for all the samples accepted by the AIRS V4 first guess (V4_FG, solid circles), physical retrieval (V4_PR, solid squares) and the ECMWF (ECMWF, solid triangles) with reference to WOUDC global O3SND ascents. (a) Percent bias. (b) Percent RMS difference.
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 1. The V4_PR shows a bias less than 5% from 10 hPa to 200 hPa, and increases to about 22% for the lowest layer (1000–260 hPa). The V4_FG shows a slightly negative bias for the stratosphere and upper troposphere, and shows a positive bias in the lower troposphere region. These results are consistent with the data shown as scatterplots for V4 and V5 retrievals (see auxiliary material) and support the contention that the AIRS first guess solution has difficulties with the extreme values of ozone.
 2. The V4_PR shows better skill from 50 to 400 hPa compared to V4_FG. The RMS difference is about 15% for layer 6 (8–16 hPa), about 20% for most of the stratosphere and upper troposphere, and degrades to about 37% near 700 hPa. The V4_PR makes no improvement for the lowest layer (1000–260 hPa). This is expected because the ozone channels have a very limited sensitivity to the lower troposphere (Figure 1), and the V4_PR uses V4_FG as a fallback option. The V4_FG also shows larger RMS difference for the lowest layer. Thus, neither the V4_FG nor the ozone channels used in the V4_PR helps the retrieval for the lowest layer.
 3. The ECMWF shows positive bias for all the layers from the surface to10 hPa, consistent with the layer ozone scatterplots (see auxiliary material). The RMS difference for the ECMWF ozone is slightly better than V4_PR. It may be noted that while the radiosonde temperature and water vapor are assimilated into the ECMWF analysis, ozone data from the O3SNDs are not assimilated. In our earlier analysis [Divakarla et al., 2006], the ECMWF temperature and water vapor shows very good agreement (both bias and RMS difference) with the radiosonde temperature and moisture, partly because of the fact that the model forecasts heavily utilize radiosonde information in the analysis. Another interesting fact is that although the V4_FG solution uses the ECMWF for training, the V4_FG and the ECMWF show significant differences. In the V4 algorithm, the initial solution offered by the fast regression first guess is much harder to characterize because the solution is a convoluted function of the radiances, statistical correlations between temperature profile T(p) and O3 and between other interacting trace gases such as CO and O3, etc. Moreover, the training ensemble used in generating regression coefficients might be better behaved because of selection processes [Goldberg et al., 2003] than the retrieval scenarios considered here. The V4_PR is thus confounded with a poor initial solution, and as a consequence, does little to improve the solution.
 Figures 6a and 6b show the bias and RMS difference statistics computed for the AIRS V5 retrieval (V5_PR, solid squares; V5_FG, solid circles). The ECMWF statistics are the same as shown in Figures 5a and 5b, and hence are not shown. A comparison of V4 and V5 statistics from Figures 5a and 5b and Figures 6a and 6b reveals the following.
Figure 6. Ozone profile retrieval statistics for all the samples accepted by the AIRS V5 first guess (V5_FG, solid circles) and the physical retrieval (V5_PR, solid squares) with reference to WOUDC global O3SND ascents. (a) Percent bias. (b) Percent RMS difference.
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 1. The V5_PR shows slightly larger positive biases for the stratospheric layers compared to V4_PR. For the lowest layer (1000–260 hPa), the V5_PR exhibits a very small positive bias (∼3%) in comparison with V4_PR (∼22%, Figure 5a). These results are consistent with the scatterplots for the layer ozone amounts (Figures 4a and 4b).
 2. The V5_PR in general shows smaller RMS differences for most of the layers. The RMS difference for the stratospheric layers is about 15%, an improvement compared to the 20% RMS difference (layer 4, 66–32hPa) seen with V4_PR. The V5_PR shows dramatic improvement for the lowest two layers (1000–260 hPa and 260–126 hPa) with an RMS difference of approximately 20%. With regards to initial solutions, the V5_FG has smaller RMS differences than V4_FG for most of the layers. The improvement seen with the V5_FG for the lowest layer (also larger R2 value of 71% in Table 3) signifies that the improvement in V5_PR is mostly due to the improved initial solution (V5_FG), and only partly due to the additional ozone channels used in the V5_PR. In contrast to the regression solution used by the V4_PR, the initial solution (V5_FG) derived from the ozone climatology offers flexibility for the V5_PR to improve upon the initial solution. The V5_PR thus addresses the shortcomings of the regression approach and provides a solution from channel observations sensitive to the ozone distribution. The profile retrieval skill offered by the V5_PR is also analyzed using a Taylor diagram [Taylor, 2001] for the coarse layers used in this paper and for the total column ozone (see auxiliary material).
4.1.2. Statistics for Tropics, NH, and SH Polar Stations
 To evaluate V4 and V5 retrievals for different regions, subsets of data samples from the tropical stations (±12 h matches from STN IDs 191, 328, 175, 205, and 443), from the SH polar station (±3 h matches from STN ID 101, Syowa, 69.0°S, 39.6°E), and from the NH polar station (±3 h matches from STN ID 089, Ny Alesund, 78.9°N 11.9°E) that have special significance to ozone events are selected. The Antarctica station 101 and the Arctic station 089 have a reasonable number of matches from ±3 h collocations and have samples from all the seasons and experience the ozone variability expected in the Antarctic and the Arctic regions, respectively.
 Figures 7a and 7b show the bias and RMS difference plots for the V4_PR for the subset of matches obtained from (1) the Arctic station 089 (large-small dashes with solid circles) and (2) the Antarctica station 101 (small dashes with solid diamonds). Also shown in Figures 7a and 7b are the statistics for the tropics (large dashes with solid triangles). Global statistics from ±3 h matches (reproduced from Figures 5a and 5b, solid line with solid squares), and global statistics computed for ±12 h matches (large-small-small dashes with open squares) are also plotted. Table 4 provides the sample size (N), O3SND layer ozone amounts and the standard deviation in Dobson Units (DU) for these data sets. The total ozone amount shown in Table 4 is a computed quantity from the O3SNDs with estimated ozone values above the balloon burst pressure. The NH station 089 has the highest mean ozone amount (356.6 DU) and has a standard deviation of 56.9 DU. The SH station 101 experiences polar vortex during the southern winter and exhibits large variations during the southern spring due to the ozone hole events. The station also launches a relatively large number of O3SNDs to intensely observe ozone hole events, and as a consequence, shows a smaller mean ozone amount and a large variability. The station data also shows large standard deviation for the layers most affected by ozone hole events. Data for the tropical stations show minimum total ozone and least variability. The tropical data set also shows larger ozone amounts at higher altitudes (source region). The tropospheric layers contribute approximately 13% to the total ozone amount for the tropical data set.
Figure 7. Ozone profile retrieval statistics for the AIRS V4 physical retrieval algorithm for the subset of samples from the station 089 (STN ID 089, Ny Alesund, 78.9°N, 11.9°E, V4_PR_STN089, solid circles), station 101 (STN ID 101, Syowa, 69.0°S, 39.6°E, V4_PR_STN101, solid diamonds), from a set of tropical stations (STN IDs 191, 328, 175, 205, and 443, V4_PR_TRP, solid triangles), for all the global samples with 3 h matches (V4_PR, solid squares), and for all the global samples with 12 h matches (V4_PR_12H, open squares). (a) Percent bias. (b) Percent RMS difference.
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Table 4. Mean Ozone Amount and SD From O3SNDs for Individual Station Locations (STN IDs 089 and 101), Over the Tropics, and for 3 h and 12 h Global Collocationsa
|Layer Pressure Boundaries (hPa)||Layer Number||NH Station 089 Ny Alesund 78.9°N, 11.9°E||SH Station 101 Syowa 69.0°S, 39.6°E||Tropical Stations 191, 328, 175, 205, and 443||Global ±3 h Matches||Global ±12 h Matches|
|N||Mean (DU)||SD (DU)||N||Mean (DU)||SD (DU)||N||Mean (DU)||SD (DU)||N||Mean (DU)||SD (DU)||N||Mean (DU)||SD (DU)|
|Total O3|| ||53||356.6||56.9||50||276.4||60.0||54||223.9||24.6||350||324.5||65.9||834||315.4||75.8|
 An examination of the bias and RMS differences (Figures 7a and 7b) for the station 101, station 089 and the tropical stations reveals the effect due to the upward movement of the ozone kernel functions and the associated sensitivity changes (Figure 1) from higher latitudes to the tropics. In general, retrievals over the tropics exhibit smaller RMS differences for the upper stratosphere layers and retrievals over high latitudes exhibit smaller RMS differences for the lower tropospheric layers. In addition, deficiencies in the first guess solution given to the physical retrieval also affect the bias and RMS differences. For the tropics, the ECMWF, and the V4_FG initial solution have large bias and RMS differences (not shown here). Since the ozone channels also have very limited sensitivity to the lower troposphere, and especially so over the tropics (Figure 1), the V4_PR shows large bias and RMS differences for the lowest layers. With regards to station 101 (Syowa, 69.0°S, 39.6°E), many of the retrieved profiles from the ECMWF, V4_FG, and V4_PR fail to reproduce ozone hole characteristics (not shown here) and show large bias and RMS differences. The inability of V4_FG to reproduce ozone hole events could be partly due to the deficiencies in the ECMWF training data used in the generation of ozone regression coefficients [Goldberg et al., 2003]. The training data may not have enough cases to represent ozone hole events from the SH springtime, and the V4_PR is confounded to an incorrect but accepted retrieval because of a flawed first guess solution (V4_FG). With regards to station 089 (Ny Alesund, 78.9°N, 11.9°E), the improvement seen in the RMS difference for the lowest layers is probably due to the increased sensitivity of the ozone channels for the lower troposphere at polar latitudes.
 Figures 8a and 8b show similar plots for the AIRS V5 retrievals. The V5_PR shows relatively smaller RMS difference for the tropics (large dashes with solid triangles), and for the Antarctica station 101 (small dashes with solid diamonds). The use of a priori climatology as the initial solution in the V5_PR helps both the tropical cases as well as the SH station, and provides more versatility to the V5_PR to improve upon the initial solution. The RMS difference for the tropics is close to 10% for the uppermost layers, and grows to about 30% for layer 3 (66–126 hPa), 50% for layer 2 (126–260 hPa), and reduces to about 40% for the lowest layer (260–1100 hPa). Both the V4_PR and V5_PR show negative bias for the uppermost layers, and a positive bias for the layers covering the troposphere. Since most of the ozone resides in the midstratosphere source region in the tropics, the small percentage of negative bias for a large amount of ozone nullifies the large positive bias seen for the tropospheric layers 1–2 that contribute only about 13% to the total ozone (Table 4). This, leads to an underestimation of the total ozone in the tropical region. The negative bias for the upper stratospheric layers coupled with reduced positive bias for the tropospheric layers from V5_PR makes the total ozone estimates a little lower compared to the estimates from the V4_PR. The statistics presented for the tropics are found to be consistent with the statistics presented by other investigators using ±3 h AIRS retrieval matches with Southern Hemisphere Additional Ozonesondes [Thompson et al., 2004] and other validation experiments (F. Irion, NASA, JPL, unpublished data, 2006). With regards to station 101, the initial solution from V5_FG helps V5_PR in retrieving the ozone hole characteristics reasonably. With regards to station 089, the V5_PR tends to overestimate ozone for the stratospheric layers, and underestimate ozone for the tropospheric layers. Statistics are also computed grouping station matches covering the Arctic Circle (stations IDs 18, 315, 439, 460) and the Antarctic Circle (station IDs 323, 450). It is found that the statistics computed for the stations 089 and 101 very closely represent the Arctic Circle and the Antarctic Circle respectively. Evaluation of V4_PR statistics for the ±3 h and ±12 h matches reveals that the 3-h matches show approximately 5% improvement in the RMS difference (Figure 7b, solid squares for ±3 h matches, open squares for ±12 h matches), and a minor improvement of few percentage points in bias for the lowest layers 1, 2 and 3 (1000–260 hPa, 260–126 hPa, and 126–66 hPa). The V5_PR shows an improvement of about 2–3% in RMS difference for the lowest layers for the 3-h matches (Figure 8b, solid squares for ±3 h matches, open squares for ±12 h matches). No appreciable change in the bias is observed. The initial solution (V4_FG) used by the V4_PR for a 3 h match and for a 12 h match AIRS observation might be changing on the basis of the fast regression first guess solution. The V5_FG solution from a priori climatology is static for the same day and for the same location for the 3 and 12 h matches of AIRS observations. Consequently, the percent change in RMS difference for the V5_PR is smaller than that of V4_PR. Fioletov et al.  have evaluated the ozone variability and instrument uncertainties using same day matches of ozonesonde data, SBUV/2 and other instrument retrievals. They found that as horizontal matchup distance exceeds 200 km, the standard deviation of differences between SBUV/2 lowest layer (1000–63.9 hPa) retrieval and the ozone measurement has increased markedly. However, differences in the time coincidences within a day had little effect on the standard deviation of ozone differences for that layer. Since the AIRS ozone information comes from a smaller FOV (∼50 km) compared to the SBUV/2 retrieval (∼200 km), and appears to be sensitive to changes in the ozone in upper troposphere and lower stratosphere, we thought that the RMS difference for the two lowest layers with the 12 h collocations would be much larger than 3%. The small change in RMS difference with a larger time collocation window warrants a more detailed study of the spatial and temporal variability in ozone using the measured O3SND profiles.