In this section we use the collocations within AIRS golf balls explained in 3.1, and we concentrate on high clouds in the layer 150–200 hPa in the tropics and 300–400 hPa in the midlatitudes as they are close to and below the tropopause and provide the highest number of events among the selected scenes (see again Figure 1).
4.1. Correlation Between RHice and Cloud Thickness
 Kahn et al. , computing RHice as in the work by Gettelman et al.  and not distinguishing different pressure layers, suggest that most probable values of RHice distributions around 60–80% may be caused by a geometrical thickness of cirrus clouds being smaller than the vertical resolution of temperature and specific humidity profiles (given 2–3 km). However, we have observed that the thickness of the AIRS standard pressure layers in our analysis is quite similar to the vertical extent of cirrus found by CALIPSO (around 2 km). The geometrical thickness of our selected layers corresponds to 1.8 km for the tropical layer 150–200 hPa and to 1.9 km for the midlatitude layer 300–400 hPa. Cloud average thickness is found to be = 1.9 km with standard deviation σΔz = 1.1 km for tropical cirrus in the layer 150–200 hPa and = 2.1 km with standard deviation σΔz = 1.1 km for midlatitudinal cirrus in the layer 300–400 hPa. A distribution of cloud thickness (CT) is shown in Figure 5, very large CT may seem unphysical but other authors have also observed some cirrus with large vertical extent both in the tropics and in the midlatitudes [e.g., Wang et al., 1997; Sassen and Comstock, 2001].
Figure 5. Normalized distributions of cloud geometrical thickness (km), tropics (20°N–20°S) at 150–200 hPa, midlatitudes (40–60°N and S combined) at 300–400 hPa.
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 We are now interested in how RHice is correlated with CT. To highlight the difference between the vertical extent of the cloud and the vertical extent of the pressure layer we also use relative cloud thickness (cloud thickness normalized by the thickness of the pressure layer). Figure 6 presents mean RHice for intervals of CT (Figure 6, left) and of relative cloud thickness (Figure 6, right) with standard deviations, indicating the width of each distribution. We assume the distribution in each interval to be nearly Gaussian. Each interval includes between 300 and 3000 points. We observe that mean RHice increases with cloud thickness in both latitudinal bands. The increase is much stronger in the midlatitudes than in the tropics (50–90% versus 60–75%), probably linked to different formation mechanisms and consistent with Kahn et al. [2008, Figure 11]. CT in the work by Kahn et al.  is limited to 4 km. This is probably due to statistical reasons, which is supported by the distributions in Figure 5 showing a small amount of very large CT. We have tested the stability of the inferred relationship by considering separately land and ocean scenes and by considering only the CALIPSO pixel in the middle of the AIRS golf ball. Results are similar, showing the robustness of this relationship. A mean RHice close to 100% is only approached in the midlatitudes for clouds much more vertically extended than the standard pressure layer. However, when the cirrus vertical extent is the same as the vertical extent of the pressure layer (relative cloud thickness around 1) mean RHice is only about 65%.
Figure 6. Relative humidity with respect to ice as a function of (left) cloud geometrical thickness (km) or (right) relative cloud thickness. Tropics (20°N–20°S) at 150–200 hPa and midlatitudes (40–60°N and S combined) at 300–400 hPa, error bars indicate standard deviation around mean value.
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 One reason for the low values of mean RHice is the variation of the humidity within the pressure layers and how drier or moister parts of the profile are taken into account by the retrieval over a larger vertical extent. Small-scale fluctuations but also vertical gradients of humidity [e.g., Sakai et al., 2003] may lead to an underestimation of RHice. One has to consider the variability of RHice between the cloud and its environment as well as the variability of RHice inside the cloud [e.g., Comstock et al., 2004]. Especially since the saturation pressure depends strongly on the temperature, the ratio of integrated values of humidity and saturation humidity will differ from the maximum of the ratios (maximum RHice) within the layer. The latter, helpful to determine the presence of ice supersaturation, is unfortunately not available and direct comparisons with collocated in situ measurements would be helpful for further investigations.
 Another reason arises from the distinction between the AIRS L2 vertical gridding and the actual vertical resolution. Even though many authors [Gettelman et al., 2004; Susskind et al., 2006; Tobin et al., 2006] argue a vertical resolution of temperature and moisture products of 2–3 km (more or less the size of the standard gridding) a recent study [Maddy and Barnet, 2008] shows that the vertical resolution of temperature and humidity profiles from AIRS could be much coarser, especially in situations with small vertical temperature gradients in the upper troposphere. The temperature (resp. specific humidity) resolutions are found to be 6–7 km (resp. ≈4 km) over a corresponding 100–300 hPa pressure layer and ≈4 km (resp. ≈3 km) over a corresponding 300–600 hPa pressure layer. Mean RHice close to 100% is only approached in the midlatitudes for clouds extending vertically to 5–6 km, which is then more in line with the figures given by Maddy and Barnet  at 300–600 hPa.
 These points raise concerns on the ability of AIRS to detect ice supersaturation as dry biases may also occur over clear sky profiles with thin portions of supersaturated air inside, all the more as supersaturation is suspected to occur on even thinner portions of the profile than clouds (for a case in the midlatitudes see Spichtinger et al. ).
 Figure 7 shows RHice distributions obtained for the midlatitudes in the layer 300–400 hPa: we distinguish between geometrically thin (CT < 2 km) and geometrically thick (CT > 4 km) clouds, both compared to the overall distribution. The peaks of the distributions are located at 40–50% for CT < 2 km and located at 90–100% for CT > 4 km while the peak of the overall distribution is situated at 70–80%. The overall RHice distributions can be seen as the sum of the distributions of each interval of CT weighted by the probability of the given CT. As indicated by the standard deviations there exists a variability of RHice in each interval of CT representing various atmospheric conditions. For example, very thin cirrus clouds may be embedded in a large supersaturated region and then show a large RHice for a low CT, like persistent contrails with a large spatial cover [e.g., Duda et al., 2003].
Figure 7. Normalized distributions of relative humidity with respect to ice. Midlatitudes (40–60°N and S combined) at 300–400 hPa: cloud geometrical thickness <2 km, cloud geometrical thickness >4 km, and all cases.
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 In the following section we examine a possible influence of the cloud optical depth on these relationships.
4.2. Influence of Cloud Optical Depth
 We use the corrected optical depths described in section 3. Considering the large uncertainties in our optical depth retrieval, two distinct classes of optical depths are defined: optically thin cirrus and optically thicker cirrus, with a gap to avoid overlapping between the categories. The optical depth distributions in Figure 4 (showing optically thicker cirrus in the midlatitudes) lead to use the following thresholds: τ < 0.3 (0.5) for thin cirrus and τ > 0.6 (1.0) for thicker cirrus in the tropics (midlatitudes). Error bars on τ result from uncertainties over η(τ) discussed in section 3, we show results using η(τ). Results are similar using η(τ) ± δη with δη = 0.05 or δη = 0.1 (not shown).
 For both cirrus classes we present distributions of RHice (Figures 8a, 8b, 9a, and 9b), distributions of cloud geometrical thickness (Figures 8c, 8d, 9c, and 9d) and mean RHice as function of cloud thickness (Figures 8e, 8f, 9e, and 9f). These are shown in Figure 8 for the midlatitudes in 250–300 hPa (Figures 8a, 8c, and 8e) and 300–400 hPa layers (Figures 8b, 8d, and 8f), and in Figure 9 for the tropics in 150–200 hPa (Figures 9a, 9c, and 9e) and 200–250 hPa layers (Figures 9b, 9d, and 9f).
Figure 8. (a and b) Relative humidity with respect to ice distributions, (c and d) cloud geometrical thickness (km) distributions, and (e and f) relative humidity with respect to ice as a function of cloud geometrical thickness for two distinct classes of optical depth (τ < 0.5 and τ > 1.0). Figures 8a, 8c, and 8e are for midlatitudes (40–60°N and S combined) 250–300 hPa, and Figures 8b, 8d, and 8f are for midlatitudes 300–400 hPa. Error bars indicate standard deviation around mean values.
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Figure 9. (a and b) Relative humidity with respect to ice distributions, (c and d) cloud geometrical thickness (km) distributions, and (e and f) relative humidity with respect to ice as a function of cloud geometrical thickness for two distinct classes of optical depth (τ < 0.3 and τ > 0.6). Figures 9a, 9c, and 9e are for the tropics (20°N–20°S) 150–200 hPa, and Figures 9b, 9d, and 9f are for the tropics 200–250 hPa. Error bars indicate standard deviation around mean values.
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 Regarding the distributions of relative humidity, on average a larger cloud optical depth infers a slightly larger mean RHice and a much larger cloud geometrical thickness for both latitudinal bands and for both layers. A large variability of geometrical thickness exists in each category of optical depths. In the tropics, this is consistent with studies of Wang et al.  with the Stratospheric Aerosol and Gas Experiment (SAGE II): they find a wide range of geometrical thicknesses among subvisible cirrus (τ < 0.02) including both very thin and very thick clouds (up to 6 km). In the midlatitudes it is consistent with Sassen and Comstock  who find a large standard deviation when correlating cirrus optical depth and cloud geometrical thickness.
 In the work by Kahn et al.  RHice distributions are obtained for five classes of thin cirrus between τ = 0 and τ = 1 using 29 days of retrieved AIRS cloud properties. The distributions also peak around lowest values for optically thinnest clouds. These distributions were obtained regardless of the vertical extent of the clouds, and a direct effect of this is the large width of the distributions. We use the classification of τ described above to investigate how the relationship between RHice and the vertical extent of the clouds found in Figure 6 is affected.
 Figures 8 and 9 also present RHice as a function of cloud thickness for the two classes of optical depth. The same intervals as in Figure 6 are used, and the error bars indicate again the standard deviation of the distributions in each interval. Intervals containing less than 100 points are not taken into account. We observe that, for a comparable geometrical thickness, RHice is in general slightly larger for the smallest optical depths than for the largest optical depths with a difference up to 5% in both latitudinal bands and for all layers. This makes sense as it might be more probable that the former class contains more cirrus in formation whereas the latter contains more clouds well after formation, which may have depleted a larger part of water vapor, leading to a decrease of the observed mean relative humidity. These results also show that the geometrical thickness of clouds has a greater influence on the mean RHice than the optical depth, which corroborates [Kahn et al., 2008] on this matter.
 A last point of concern remains the global differences of mean RHice between the two pressure layers in each region. On one hand the midlatitudes 250–300 hPa curves show an average of 15% more relative humidity compared to the 300–400 hPa curves, which may be a consequence of an averaging of humidity over higher hence colder portions of the atmosphere [e.g., Korolev and Isaac, 2006] or an artefact due to a smaller pressure layer. Also, because of the selection with regard to the tropopause, the layer 250–300 hPa considers a larger proportion of summer scenes.
 On another hand the tropics show a reverse tendency with 5% to 15% more RHice for large cloud thicknesses in the 200–250 hPa layer which contradicts the previous observation. Although RHice values are good enough in the 150–200 hPa to show the influence of cloud geometrical thickness and optical depth on the mean RHice they may not fit the same quality as the 200–250 hPa layer (differences in RHice distributions for the two classes of optical depth are less well resolved for the layer 150–200 hPa). This is consistent with [Gettelman et al., 2004] who show with airborne validations of AIRS that RHice quality is questionable at pressures lower than 200 hPa. Moreover, the RHice values found in the layer 200–250 hPa are more in line with those given by Kahn et al. .
 More statistics and complementary information on particle size distribution, ice water content or dynamical situations can help clarify further the relationships found in Figures 8 and 9 and are the subjects of ongoing research.