A combination of spatially collocated Atmospheric Infrared Sounder (AIRS) radiances and Moderate Resolution Imaging Spectroradiometer (MODIS) cloud products are used to quantify the impact of cloud heterogeneity on AIRS-based assessments of cloud thermodynamic phase. While radiative transfer simulations have demonstrated that selected AIRS channels have greater sensitivity to cloud thermodynamic phase in comparison to the relevant MODIS bands, the relative trade-offs of spectral and spatial resolution differences that are inherent between AIRS and MODIS have not been quantified. Global distributions of AIRS field-of-view scale frequencies of clear sky (13–14%), heterogeneous cloud (26–28%), and homogeneous cloud (59–60%) are quantified for a four week time period using cloud fraction, and further categorization of cloud uniformity is assessed with the variance of cloud top temperature. Homogeneous clouds with window brightness temperatures (Tb) between 250 and 265 K are shown to have larger cloud thermodynamic phase signatures than heterogeneous clouds. Clouds in this limited Tb range occur 30–50% of the time in the mid- and high latitude storm track regions, are generally difficult to identify as being water or ice phase, and show strong responses in forced CO2 climate change modeling experiments. Two-dimensional histograms of Tb differences sensitive to cloud phase (1231–960 cm−1) and column water vapor (1231–1227 cm−1) show distinct differences between many homogeneous and heterogeneous cloud scenes. The results suggest the potential for a quantitative approach using a combination of hyperspectral sounders with high-spatial-resolution imagers, and their derived geophysical products, to assess cloud thermodynamic phase estimates within increasingly complex subpixel-scale cloud variability.
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 Variability in climate sensitivity among climate model projections is primarily due to uncertainty about cloud feedbacks as a result of anthropogenic climate change. The cloud feedback response includes spatial and temporal changes in the frequency, vertical distribution, and microphysical and optical properties of the clouds as well as changes in the thermodynamic and dynamic structure of the atmosphere [Schneider et al., 2010]. Modeling experiments with CO2-induced warming [e.g., Wetherald and Manabe, 1988; Mitchell and Ingram, 1992; Trenberth and Fasullo, 2010; Zelinka and Hartmann, 2010] have shown that upper tropospheric clouds tend toward higher altitudes in the subtropics and tropics (positive cloud feedback), while low and middle tropospheric cloud frequency and water content increases in the high latitudes, causing greater shortwave reflectance (negative cloud feedback). Recent studies have shown that there exists a wide range of inter-model variability of subtropical and tropical boundary layer cloud amount in 21st century climate projections when compared to current observations [Stephens, 2005; Williams and Tselioudis, 2007; Medeiros et al., 2008]. Improvements in the representation of low-latitude boundary layer clouds could significantly reduce cloud-climate feedback uncertainties [Bony and Dufresne, 2005].
 Despite the importance of low-latitude boundary layer clouds, the radiative implications of uncertainty in cloud phase (liquid, mixed-phase, and ice) are substantial [Sun and Shine, 1995; Yang et al., 2003]. For example, Mitchell et al.  and others have shown that a large variation of climate sensitivity is obtained in response to the treatment of cloud phase in CO2 doubling experiments. Senior and Mitchell  showed that a substantial increase in cloud water amount is observed in the “mixed phase” temperature range (0°C to −15°C) for a similar CO2 doubling experiment. Since the ratio of liquid to ice cloud was shown to increase and Senior and Mitchell  noted a greater temporal “persistence” of liquid compared to ice cloud, an increase in cloudiness in the mid- and high latitudes resulted in higher shortwave reflectance (negative cloud feedback). In another CO2 doubling experiment, Li and Le Treut  showed that a simple model parameter adjustment of the transition of liquid to ice cloud from 0°C to −15°C causes a vertical ascent of cloud in the low latitudes and a poleward migration of cloudiness in the mid- and high latitudes. Both effects are associated with positive feedback, the first because of increased IR trapping and the second because of reduced shortwave reflectance at lower sun angles, which compete with the negative feedback associated with increased water content. In a comparison of several climate models with doubled CO2, Tsushima et al.  showed that models with higher climate sensitivity produce smaller increases in cloud water amount than models with lower climate sensitivity. To diagnose the physical mechanisms of the cloud-climate response, Ogura et al.  partitioned the terms of the nonconvective cloud condensate tendency equation in the MIROC 3.2 and HadGEM1 models. The zonal patterns of the cloud response closely resembled the response of the condensation-evaporation and deposition-sublimation terms, arguing for an explicit representation of competing microphysical processes in climate models, for instance, with bin microphysical parameterizations [e.g., Morrison and Gettelman, 2008].
Doutriaux-Boucher and Quaas  used POLarization and Directionality of the Earth's Reflectances (POLDER) retrievals of cloud phase to develop a statistical cloud phase technique that is incorporated into the Laboratoire de Météorologie Dynamique (LMD) GCM. Simulations using this statistical approach showed improvements in the shortwave forcing produced by the LMD GCM. Toward this end, a multiyear, global “best estimate” record of cloud phase, with sufficient spatial and temporal resolution to resolve small-scale process [e.g., Naud et al., 2006], would offer a highly useful observational constraint for climate model evaluation. However, at present, large differences in the sensitivity, sampling, precision, and accuracy exist between various active and passive cloud phase detection approaches [Goloub et al., 2000; Chylek et al., 2006; Nasiri and Kahn, 2008; Cho et al., 2008, 2009; Hu et al., 2010; Naud et al., 2010; Riedi et al., 2010]. The largest discrepancies are in high latitudes where clouds are prevalent with temperatures between −40 and 0°C. For example, approximately 20–25% of all clouds globally are classified as “mixed” or “unknown” for the month of January 2005, according to the Moderate Resolution Imaging Spectroradiometer (MODIS [Barnes et al., 1998]), but these percentages are much higher poleward of 40° [Nasiri and Kahn, 2008, hereinafter NK08; Morrison et al., 2011].
 In the case of cloud phase determined from active profiling by the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP [Winker et al., 2010]), the greatest frequency of clouds in this temperature range is highest from 40–70° in both hemispheres, but approximately 95% of these clouds are identified as liquid [Hu et al., 2010], much higher than passive estimates of cloud phase [Jin et al., 2010]. Preliminary efforts to infer cloud phase with the Atmospheric Infrared Sounder (AIRS [Aumann et al., 2003]) indicate that, between −30 and 0°C, AIRS generally classifies a lower percentage of clouds as liquid compared to CALIOP [Jin et al., 2010]. While CALIOP has greater phase sensitivity than any existing passive satellite instrument, it also has some limitations. CALIOP is not a scanning instrument and therefore observations are only made along a narrow track. Additionally, the CALIOP data set is of limited duration, beginning in 2006 and without immediate plans for a follow-on mission at the end of the current instrument's lifespan. While the phase sensitivity of infrared instruments is lower, the AIRS data set is global and extends back to 2002. In addition, AIRS retrieves atmospheric temperature and humidity profiles along with cloud top temperature and effective cloud fraction, which makes is possible to relate clouds to the existing thermodynamic regime. Because it appears likely that high-spectral-resolution infrared sounders will be launched in the foreseeable future (e.g., CrIS and IASI), a long-term global IR cloud phase data set is possible.
NK08 determined MODIS and AIRS sensitivities to cloud phase using 8–11 μm [Strabala et al., 1994; Baum et al., 2000] and 1231–960 cm−1 brightness temperature differences (ΔTb), respectively, for a range of cloud top temperatures, optical thicknesses, and effective diameters. Although the hyperspectral simulations of AIRS ΔTb showed a robust separation of liquid and ice for most single-layer cloud configurations that were not obtainable in the MODIS narrowband simulations, the trade-offs between spatial and spectral resolution were not investigated. The nominal spatial resolution of the AIRS footprint is 13.5 km at nadir, but cloud structure can vary at much smaller spatial scales; Chylek and Borel  saw cloud phase variations at scales of 10s of meters. Small-scale cloud heterogeneity is also important for assessing deviations from plane-parallel cloud structure [e.g., Cahalan et al., 1994; Oreopoulos and Cahalan, 2005; Di Girolamo et al., 2010] and subsequent passive visible/near-infrared retrievals of cloud optical thickness and effective particle size [Wolters et al., 2010]. Biases of several Kelvins in Tb and cloud top temperature, along with ∼20% errors in cloud top emissivity, result from plane-parallel assumptions about heterogeneous clouds that resemble cubes or have aspect ratios on the order of 1.0 [Liou and Ou, 1979; Harshvardhan and Weinman, 1982; Coakley et al., 2005]. Furthermore, in the mid-infrared spectral region, water vapor in the lower atmosphere impacts ΔTb in the 8–12 μm window within clear, partially overcast, and transparent overcast conditions. This may cause spectral variations in ΔTb for heterogeneous cloud cover that otherwise would not be present in homogeneous and opaque cloud cover located above most of the water vapor column.
 This study quantifies the impacts of cloud heterogeneity on cloud thermodynamic phase assessment at spatial scales smaller than the AIRS footprint using collocated MODIS cloud products. The coincident observations are spatially collocated using the method of Schreier et al. . Section 2 describes the data and methodology used in this study. Several AIRS channel combinations are exploited to highlight sensitivity to cloud thermodynamic phase, column water vapor, and cloud particle size. These are used in conjunction with cloud products from MODIS, whose variability within the AIRS field of view (FOV) is retained to quantify cloud thermodynamic phase sensitivity as a function of this variability. Section 3 presents statistical results of global distributions of cloud heterogeneity and homogeneity as viewed at the AIRS FOV. Section 4 outlines a set of simulations describing typical ΔTb in clear skies for particular window channel differences of interest that are sensitive to cloud phase, particle size, and water vapor. The simulations help quantify ranges of ΔTb that likely either contain cloud or potentially clear sky. Then, section 5 describes two-dimensional histograms of ΔTb conditioned by cloud heterogeneity in the context of simulations presented in section 4. Histograms of ΔTb are presented for a wide variety of “cloud types” that are characterized by scan angle and cloud heterogeneity using MODIS cloud fraction, cloud top temperature [Menzel et al., 2008], and infrared cloud thermodynamic phase. In section 6, the findings in this study are summarized and the implications for using hyper-spectral infrared radiances for cloud thermodynamic phase assessment are discussed.
2. Data and Methodology
 The Aqua MODIS and AIRS pixel-scale observations are spatially combined following the methodology of Schreier et al.  for four separate time periods: 1–6 January, April, July, and October 2005. Approximately 10–12 million oceanic AIRS IR FOVs are quantified for each time period in sections 4 and 5. The scan angle-dependent truncated, rotated, and smeared spatial response functions determined from AIRS prelaunch calibration are used to collocate the Collection 5 (C5) MODIS Level 1b and Level 2 derived products within each AIRS FOV. The collocation files preserve the AIRS FOV-scale variability and also help simplify the spatial averaging of MODIS properties to the AIRS FOV. The spatial averaging uses a weighting coefficient determined for each individual MODIS pixel that is a function of the magnitude of the AIRS spatial response. The 1 km C5 MODIS cloud mask (MYD35) [Ackerman et al., 2008; Frey et al., 2008] quantifies the AIRS FOV-scale cloud heterogeneity, while the 5 km C5 IR cloud phase mask (“Cloud_Phase_Infrared” in MYD06_L2) [Platnick et al., 2003] determines the cloud phase of the MODIS pixels. Although it is anticipated that Collection 6 (C6) will have improvements in the IR phase from the use of cloud emissivity ratios [Pavolonis, 2010] and a higher spatial resolution of 1 km rather than 5 km, C6 operational products are not yet available. The MODIS cloud mask uses 19 of 36 MODIS bands and a variety of spectral tests to assess the likelihood that a given pixel contains clouds or clear sky. The likelihood is described in terms of clear sky confidence: confident clear, probably clear, probably not clear, and confident not clear. The MODIS cloud mask is robust for most cloud types, although thin cirrus with optical depths <0.4 are an exception and are frequently missed [Ackerman et al., 2008; Cho et al., 2008]. The infrared cloud phase [Platnick et al., 2003] is reported at 5 × 5 km resolution and requires the MODIS cloud mask and two MODIS channels, one at 8.5 μm (band 29) and the other at 11 μm (band 31). Clouds are reported as ice, liquid water, unknown, and mixed phase. As described by NK08, the unknown and mixed-phase categories can be considered together as one larger “unknown” category that contains ice, liquid, or a mixture of phases. Several studies have described in detail the strengths and limitations of the MODIS infrared cloud phase mask [NK08; Cho et al., 2008, 2009]. To summarize the results of Cho et al. , the C5 MODIS infrared phase algorithm compares well with CALIPSO for opaque high and low clouds, but tends to classify thin cirrus clouds as either water or unknown phase, and classifies the majority of opaque mid-temperature (roughly 250–265 K) clouds as unknown phase. This is because there is not enough spectral phase information in the relatively broad MODIS 8.5 and 11 μm channels to distinguish phase for mid-layer clouds and the thermodynamic phase–cloud temperature relationships assumed by the MODIS algorithm break down for the transparent-cloud cases.
 The AIRS instrument is designed to observe atmospheric temperature, water vapor, minor gas species (e.g., H2O, O3, N2O, CH4, CO, SO2, and CO2), clouds, and surface properties [Chahine et al., 2006]. AIRS is an IR grating spectrometer observing the terrestrial thermal IR spectrum from 3.7–15.4 μm while scanning ±48.95° off-nadir at a spectral resolution of λ/Δλ ∼ 1200 for near daily global coverage. The observational gap from 8.22–8.81 μm makes direct radiance comparisons to MODIS Channel 29 centered at 8.55 μm unfeasible (NK08). The footprint diameter is approximately 13.5 km at nadir expanding to 30 km or greater at high scan angles. The channel noise (NEdT) is well characterized and is on the order of 0.1–0.3 K at 250 K for the channels of interest in this study. Cross-comparisons of AIRS and MODIS Tb in clear sky [Tobin et al., 2006], and in heterogeneous and homogeneous cloud cover [Schreier et al., 2010], show agreement within 0.1–1.0 K for the mid IR channels in the 8–12 μm region.
 The AIRS spectrum is rich with an assortment of channels located on gaseous absorption lines, as well as “window channels” in between absorption lines. Window channels are preferable for cloudy remote sensing because absorption line effects that complicate the interpretation of cloudy IR spectra are either minimized or eliminated. To maximize the sensitivity of AIRS to phase discrimination, the approach presented in Kahn et al.  and NK08 is used, namely, to maximize the spectral differences in the liquid water and ice indices of refraction while selecting the cleanest window channels possible that have high clear sky transmissivity and low noise over the length of the AIRS mission. Four channels were selected: three minimize the effects of absorption lines and NEdT (857.358, 960.664, and 1231.330 cm−1, abbreviated as 857, 960, and 1231 respectively), and the fourth is centered on a weak water vapor absorption line (1227.709 cm−1, abbreviated as 1227).
 The four AIRS channels were combined to form three different ΔTb that are primarily sensitive to ice cloud particle size (ΔT960−857, abbreviated as ΔTsi) [e.g., Kahn et al., 2003], column water vapor (ΔT1231−1227, abbreviated as ΔTwv) [Aumann et al., 2006], and cloud thermodynamic phase (ΔT1231−960, abbreviated as ΔTph) (NK08). Although the emphasis of this paper quantifies phase sensitivity ΔTph as a function of cloud state, it is not decoupled from other forms of geophysical variability. For instance, in high altitude transparent and broken clouds or low altitude clouds of any character, variations in the column water vapor (CWV) burden (ΔTwv is useful as a proxy) lead to variations in the magnitude of the emission from the water vapor continuum, which in turn impacts ΔTph. Similarly, variations in ice cloud particle size (ΔTsi is useful as a proxy) can lead to variations in ΔTph with all else equal. Global maps of the mean values of ΔTsi, ΔTwv, and ΔTph for January and July 2005 are shown in Figure 1. Focusing on ΔTsi, observe that the largest values are associated with regions of convection where small particle and semi-transparent ice clouds are most frequent [Prabhakara et al., 1988; Kahn et al., 2008]. The values are reduced at higher latitudes and in regions with stratocumulus clouds, and negative values are found over Antarctica and eastern Siberia during winter (high frequency of thermal inversions) and desert surfaces such as the Sahara and Tibet (strong surface emissivity features). For ΔTwv, the highest values are in the tropics with lower values associated with regions of subsidence in the subtropics and higher latitudes, tracking the well-characterized climatology of CWV [Randel et al., 1996].
 Next, ΔTph shows a more variable pattern than ΔTsi and ΔTwv, although the positive differences tend to track thin cirrus in the tropics with an overall lower magnitude than ΔTsi. For ΔTph < −0.5 K, the highest frequencies are found in the stratocumulus and trade cumulus regions in the subtropics and in the mid- and high latitude storm tracks. However, the greatest frequencies of ΔTph < −0.5 K are concentrated in the summer hemispheres, consistent with climatologically larger frequencies of liquid water clouds, while values of 0.0 K > ΔTph > −0.5 K are more frequent in the winter hemispheres. The values of −0.5 and 0.0 K approximately correspond to bounds for ice (ΔTph > 0.0 K) and liquid (ΔTph < −0.5 K) cloud sensitivity according to idealized near nadir simulations of homogeneous and opaque cloud layers (NK08). Very low values of ΔTph associated with low surface emissivity at 1231 cm−1 are seen over the Saharan, Australian, and Kalahari deserts.
3. Cloud Variability Within the AIRS FOV
 Determining the spatial and temporal distribution of cloud heterogeneity within the AIRS FOV is essential for identifying candidate geophysical conditions for improving cloud phase estimates from the passive IR, either by a simple approach using ΔTph as used in this study, or a more complex algorithm [Jin et al., 2010]. A more refined approach that quantifies cloud uniformity using the variability of MODIS cloud top temperature TCLD will be described in section 5. This is an important distinction because an AIRS FOV completely covered with cloud may contain a wide variety of single and multilayered cloud configurations that could ultimately impact the determination of cloud thermodynamic phase.
 Using the collocation methodology of Schreier et al. , individual AIRS FOVs are classified as “homogeneous” cloud cover (HOM) when all MODIS pixels within the AIRS FOV are classified as probably cloud or confident cloud by the MODIS cloud mask. Scenes fall into our “clear” category (CLR) when the co-located MODIS scenes all are classified as either probably or confident clear by the cloud mask. The “heterogeneous” cloud cover category (HET) is applied when the co-located MODIS scenes have a mix of clear and cloudy categories. For the time periods in 2005, zonal averages are shown in Figure 2. HOM and CLR have similar distributions as established cloud and clear sky climatologies [e.g., Rossow and Schiffer, 1999], while CLR is consistent with expectations of a sensor with AIRS-like spatial resolution [Krijger et al., 2007]. In the case of HET, it is correlated in latitude to CLR with peaks in the subtropics (30–40%) on either side of the ITCZ. Low frequencies of HET (10–25%) are found in the midlatitude storm tracks, especially in the SH. HOM dominates the tropics (50–70%) and the midlatitude storm tracks (60–90%). There is a distinct seasonal migration of CLR and HOM with latitude in the subtropics and high latitudes, and a smaller shift observed with HET. Figure 3 illustrates the horizontal distributions of HOM frequencies shown in Figure 2. As in Figure 1, the highest frequencies of HOM are found in the tropics and storm tracks; however, there are significant differences between the oceans and continents in the tropics and NH, while the distributions are more or less zonally symmetric in the SH.
 To address the spatial heterogeneity of clouds in the Tb range of potentially mixed-phase (PMP) clouds where contemporary passive techniques cannot differentiate between liquid and ice (e.g., NK08), the samples in Figure 3 are limited to 250 < Tb,1231 < 265 K in Figure 4. In the SH storm track region, 30–50% of clouds are simultaneously HOM and within 250 < Tb,1231 < 265 K, with a ∼10% increase or decrease depending on season. The seasonal differences may be a partial result of the limited sample size (∼6 days) for each time period, but may also be caused by seasonal changes in temperature and baroclinic wave activity. However, they are consistent with reduced cloud inhomogeneity observed in the summer with MODIS Level 3 data [Oreopoulos and Cahalan, 2005]. A significant drop-off occurs over the Antarctic continent, where fewer clouds are observed. In the NH storm track and Arctic region, the values are highly variable especially between land and ocean, although this behavior may be a partial consequence of the sample size. Note that a wide area of 10–30% frequency is found between 40 and 70°N for all time periods.
 Although HOM clouds are better candidates for cloud thermodynamic phase assessment than HET clouds (Figure 5), some HET may exert a large enough spectral signature in ΔTph to discriminate liquid from ice cloud. However, HET cases within 250 < Tb,1231 < 265 K are essentially nonexistent at low and middle latitudes, but the frequencies are as high as 10–20% south of 60°S, and in the Arctic, N. American, and Asian landmasses at lower latitudes during winter (not shown). Later in this study, a nonnegligible proportion of HET will be shown to contain ΔTph differences large enough to determine the presence of liquid or ice cloud. The land/ocean differences and zonal symmetry seen in HOM are similar for HET, except that there is a strong inverse relationship in frequencies of occurrence. For both time periods, CLR frequencies greater than 30% are only observed over or near major landmasses (Figure 6).
4. Simulations of Clear Sky ΔTb
 The high frequency of HOM at the AIRS FOV-scale in the mid- and high latitudes suggests that AIRS, and other hyperspectral infrared sounders including the Infrared Atmospheric Sounding Interferometer (IASI) and Cross-track Infrared Sounder (CrIS), will be relevant for improved estimates of cloud phase. Idealized radiative transfer simulations (e.g., NK08) demonstrate that AIRS has skill to identify the radiative signature of cloud phase more often than MODIS, even when liquid and ice clouds occur at the same altitude. However, the simulations in NK08 were limited to standard midlatitude winter and summer atmospheres that do not capture the full range of variability of atmospheric CWV. The impacts on ΔTph will be, to first order, a function of the magnitude of CWV [Kahn et al., 2005] for CLR and HET. In this section, results from a series of radiative transfer calculations of ΔTsi, ΔTwv, and ΔTph for clear sky are presented. These calculations are used to interpret observed differences of ΔTsi, ΔTwv, and ΔTph. The primary objective for simulating ΔTb is that it is necessary for determining if the signal for cloudy (HET or HOM) ΔTb is significantly different from that of clear sky conditions.
 The radiative transfer simulations are based on a version of the AIRS Stand-Alone Radiative Transfer Algorithm (SARTA) [Strow et al., 2006]. Nadir (7° scan angle) and off-nadir (23° and 40° scan angles) simulations were performed for a standard midlatitude summer atmosphere temperature profile in clear skies, while a profile of water vapor was adjusted between 10 and 120% (in increments of 10%) of a base column value (51.4 mm). The surface emissivity (ɛ) is a composite wave number dependent value obtained from numerous clear-sky AIRS profiles from the subtropical eastern Pacific Ocean. A second set of simulations is shown to demonstrate its sensitivity assuming ɛ = 0.98 at all wave numbers. The impact of this test depends on the particular ΔTb considered. The magnitude of ΔTph increases by 0.3 K in the fixed ɛ case at low CWV, while ΔTsi and ΔTwv are less affected because ɛ in both simulated cases are nearly identical at each channel. When considering potential impacts from different temperature and water vapor profiles, Kahn et al.  showed that the dominant source of ΔTb is primarily driven by the magnitude of CWV rather than variability in the vertical structure of temperature and water vapor. The results of these simulations for ΔTsi, ΔTwv, and ΔTph are shown in Figure 7. Even though all three ΔTbs increase as CWV is increased, the relationships between ΔTb and CWV is not necessarily linear nor identical between the different sets of ΔTbs.
 Clear sky “bounds” between pairs of ΔTb (i.e., ΔTsi versus ΔTwv, ΔTph versus ΔTsi, and ΔTph versus ΔTwv) are simulated at near nadir view using observed values of NEdT for the four channels discussed in section 2 (Figure 8) using the spectrally varying ɛ. The clear sky bounds depend slightly on scan angle (not shown). A total of 10,000 randomized simulations are performed assuming the channel noise is Gaussian. The 1-σ bounds of the noisy simulations are also shown in Figure 8; these simulations are used in the remainder of this work to highlight the range of ΔTb that could be explained by clear sky. The noisy clear sky simulations are most compact for the ΔTph versus ΔTwv histogram compared to the other two-dimensional histograms.
5. Observations of ΔTb
 In this section, we present AIRS observations of the same ΔTb relationships shown in Figures 7 and 8. As described earlier, we selected three channels that minimize the effects of absorption lines and NEdT (857, 960, and 1231 cm−1), and one centered on a weak water vapor absorption line (1227 cm−1). These channels were combined to form three different ΔTb that are primarily sensitive to ice cloud particle size (ΔTsi, 960–857 cm−1), column water vapor (ΔTwv, 1231–1227 cm−1), and cloud thermodynamic phase (ΔTph, 1231–960 cm−1). Each two-dimensional histogram and its relevance are described in detail below.
5.1. ΔTsi Versus ΔTwv and ΔTph Versus ΔTsi
 Three different two-dimensional histograms of AIRS, ΔTsi versus ΔTwv, ΔTph versus ΔTsi, and ΔTph versus ΔTwv for all sky conditions (1–6 January 2005) are shown in Figure 9 for three sets of AIRS scan angles (±15° within nadir, ±15–30°, and > ± 30°). The ΔTph versus ΔTsi histogram (middle row) shows that a large majority of observed values have ΔTph < 0 K and ΔTsi > 0 K (Figure 9). There is a notable area of scatter that is skewed toward positive values of ΔTph and even larger positive values of ΔTsi that are associated with cirrus clouds. The scatter associated with these cirrus clouds are truncated in these diagrams. The peak frequency of occurrence resides within the simulated bounds of clear sky. However, a significant portion of the observations is located outside of the clear sky bounds. HET clouds dominate the points within the clear sky bounds (not shown), while a majority of HOM clouds reside outside of the clear sky bounds (not shown). Similarly, for ΔTsi versus ΔTwv (top row), most values of ΔTsi and ΔTwv are positive, but two distinct modes of scatter are observed. The first is associated with ΔTwv < 0.5 K while the second is associated with positive increases in both ΔTsi and ΔTwv. The first mode is dominated by HOM cloud (not shown) while the second is dominated by HET cloud (not shown). This is entirely consistent with an increasing magnitude of ΔTwv in the presence of broken cloud cover, where higher values of CWV increase ΔTwv, especially in the tropics [Aumann et al., 2006]. In opaque cloud cover or in regions with low CWV, the magnitude of ΔTwv remains minimal.
5.2. ΔTph Versus ΔTwv
 The previous two-dimensional histograms (top and middle rows of Figure 9) reveal that the most frequent observational occurrences of ΔTb are found within the simulated bounds of clear sky. This is not the case with ΔTph versus ΔTwv as a large majority of points are located outside of the clear sky bounds (bottom row Figure 9). Since the instrument noise for 857 cm−1 is 3–4 times larger than that of the other channels, ΔTsi offers a less useful constraint on phase detection compared to ΔTwv. Figure 8 shows a broader area of scatter associated with clear sky ΔTsi because of higher noise at 857 cm−1. This implies that isolating geophysical variability (e.g., cloud thermodynamic phase) is more challenging when using ΔTsi. For a particular AIRS FOV, it is possible that ΔTsi may be able to discriminate between liquid and ice phases when other ΔTbs cannot. For practical purposes, multiple tests could be implemented in a retrieval of cloud thermodynamic phase [e.g., Jin et al., 2010]. However, these results suggest this channel difference is less relevant compared to ΔTph and ΔTwv. Additionally, channel noise is an important consideration for phase assessment, and composites of several channels with nearly identical weighting functions should be formed to obtain further reductions in channel noise. Furthermore, ΔTsi is not strongly correlated with cloud heterogeneity, unlike ΔTwv, which is correlated to cloud fraction within a given AIRS FOV. Clouds located in altitude above maximum values of water vapor near the surface can obscure larger values of ΔTwv that arise when CWV is elevated and the sky is otherwise clear.
 In the remainder of this paper, the focus is on the ΔTph versus ΔTwv histogram (Figure 9, bottom row). For ΔTph versus ΔTwv, a complex picture of ΔTb scatter is revealed. At near nadir view, there is one distinct frequency maximum centered near a value of ΔTph = −0.8 to −1.0 K, and a less distinct mode near +0.2 K. The mode at ΔTph = −0.8 to −1.0 K extends toward higher ΔTwv and curves toward ΔTph = 0 K when ΔTwv is about +2.0 K. For the off-nadir angles, the negative ΔTph mode shifts toward increasingly negative values, whereas this does not occur for the mode near 0 K.
 These distinct modes are revealed in more detail in Figure 10 for near nadir observations. The two-dimensional histogram in Figure 9 (bottom row, left) is partitioned into CLR, HET, and HOM portions for all values of Tb,1231 (top row), cases with significant cloud layer uniformity with the standard deviation of TCLD (σT) < 2 K, and reduced cloud uniformity with σT ≥ 2 K. Subsets for Tb,1231 between 250 and 265 K are also shown (left column). As before, the 1-σ simulated bounds of clear sky are superimposed on top of the observed ΔTb for CLR and HET, while the phase delineation in NK08 is shown as vertical lines for HOM (Figure 8). A majority of cases (59.5%) are identified as HOM (Table 1). The two modes identified above for small values of ΔTwv separate more clearly in the HOM case than for all sky conditions in Figure 9. The portion of the first mode with higher values of ΔTwv is mostly associated with HET, although a similar pattern is observed in CLR as well. For HET and CLR, the mode that appears near 0 K for both ΔTwv and ΔTph is associated with cold surfaces at high latitudes. The mode in the HET and CLR cases with ΔTwv > 0 K and ΔTph < 0 K is primarily located over lower latitude oceanic regions within the trade wind cumulus regime. Furthermore, the scatter toward positive values of ΔTwv is less pronounced in CLR compared to HET, consistent with drier air in clear regions that dominate the subtropics. Finally, significant differences are found between more uniform (σT < 2 K) and less uniform (σT ≥ 2 K) clouds. The phase separation is much more pronounced for clouds with σT < 2 K compared to those with σT ≥ 2 K.
Table 1. Shown is the Global Relative Frequency of All Scene Types for 1–6 January and 1–6 July 2005a
Type of Sky
1–6 January 2005
1–6 July 2005
The italicized first, second, and fourth rows (CLR, HET, and HOM) sum to 100% following Figure 2. Several other categories are shown that restrict observations from 250 to 265 K and the scene type is based on the MODIS infrared cloud phase mask (ice, liquid, and unknown + mixed phase).
Hom Ice Cld
Het Liquid Cld
Hom Liquid Cld
Hom Unknown + Mixed Phase Cld
 Note that in both the CLR and HET cases, the peak frequency tends to occur toward more negative values of ΔTph rather than centered between the two clear sky bounds. This suggests that (1) the clear sky simulations may not represent the full range of clear sky ΔTb observed in nature, (2) we are seeing the effects of undetected cloud in the MODIS probably clear and confident clear categories, and (3) the classification of cloud phase in HET footprints with AIRS radiances could be challenging because of close similarities to CLR. However, the scatter in HET is significantly broader than CLR, suggesting that some proportion of HET is classifiable as either ice or liquid phase. Given that a higher proportion of scatter is to the negative side of ΔTph and is spatially correlated to trade cumulus over the oceans (not shown), most cases of HET are probably liquid phase. For challenging cases of HOM when Tb,1231 is between 250 and 265 K, very good separation is found between likely cases of liquid and ice clouds, with the vast majority as liquid phase. For CLR and HET, the frequencies are far fewer than HOM (Table 1).
5.3. ΔTph versus ΔTwv Conditioned by Cloud Phase, Effective Cloud Fraction, and Column Water Vapor
 To assess the potential overlap in phase identification between AIRS and MODIS, the infrared cloud phase from MODIS is mapped to the ΔTph versus ΔTwv histogram for the near nadir view (Figure 11) with both high (σT < 2 K) and low (σT ≥ 2 K) cloud uniformity. The nine panels in Figure 11 are partitioned by single-phase classifications of ice, liquid, and unknown + mixed phase within the AIRS FOV and one category containing a mixture of LIQ and ICE. The most frequent type is LIQ HOM cloud with σT < 2 K, consistent with the MODIS phase climatology (NK08). A vast majority of these cases have ΔTph < −0.5 K, demonstrating that AIRS phase estimates are likely to be consistent with MODIS-detected LIQ HOM clouds. The tail of scatter extending toward larger values of ΔTwv and ΔTph is consistent with transparent HOM (or low altitude HOM with a large portion of CWV above cloud top) that allows the radiative signature of water vapor to be observed. For LIQ HOM clouds with σT ≥ 2 K, these cases are less frequent and contain a smaller ΔTph difference. For LIQ HET clouds, they behave in a similar manner as all types of HET clouds (Figure 10) and little difference between the two categories of cloud uniformity is observed. However, a significant population of the scatter is to the left of the clear sky 1-σ bounds. In the presence of broken liquid clouds such as trade cumulus, which frequently have cloud fractions <20–30% [e.g., Medeiros et al., 2008], the ΔTb resembles a spectral signature somewhere in between that of uniform liquid water cloud and clear sky, perhaps closer to the latter than the former given their expected range of cloud fraction. Furthermore, a small proportion of MODIS-identified liquid clouds may be misclassified [Cho et al., 2009]. Clearly, HET clouds are a substantial challenge for phase identification, but most occur in the subtropics and tropics and are easily classified as liquid by other means, such as TCLD.
 With regard to HOM unknown + mixed phase (UNK) clouds, the peak frequency of ΔTph is centered within the bounds of phase uncertainty described in NK08 for σT ≥ 2 K, but is outside of the bounds for σT < 2 K. This suggests that in more uniform “uncertain” clouds, AIRS may be able to more easily infer that these clouds are liquid phase. Next, HOM ice clouds (according to MODIS) are shown in Figure 11. The vast majority have ΔTph > 0 K, although a small number have values of ΔTph < 0 K. These kinds of misclassifications are consistent with multilayer clouds containing overlapping ice above liquid layers. There is little difference between HOM ice clouds with σT ≥ 2 K and σT < 2 K, indicating that cloud uniformity does not greatly impact ice phase discrimination. Also note that a mixture of ICE and LIQ for either HET or HOM clouds is shown for σT ≥ 2 K and, surprisingly, occurs fairly infrequently. There are virtually no counts for cases with σT < 2 K (not shown). This mixed category does show that many outliers may be dominated by ICE or LIQ spectral signatures, but the largest number of cases reside approximately within the clear sky bounds of NK08. Since these mixtures are dominated by low values of cloud uniformity (σT ≥ 2 K), this suggests at the AIRS FOV scale that LIQ and ICE are frequently located within different vertical layers and very rarely is LIQ and ICE observed in the same layer.
 The scan angle dependence of LIQ HOM clouds and unknown + mixed phase HOM uniform clouds (σT < 2 K) are shown in Figure 12. Unlike the UNK clouds that contain liquid-like ΔTph signatures more often at nadir compared to off-nadir, LIQ have increasingly negative values of ΔTph with scan angle. This result suggests that cloud thermodynamic phase determination may depend on scan angle in a different manner for each type of cloud. An operational phase algorithm should take scan angle into account.
 Zonal averages of the cloud categories presented in the previous figures are shown in Figure 13 separately for the four time periods in 2005. The HOM UNK category in Figure 13 is as high as 5–15% of the overall frequency of total cloud amount in the high latitudes. About half of these cases are probably LIQ or ICE according to AIRS (Figure 11), demonstrating that AIRS will contribute to improvements in cloud phase assessment in the poorly characterized high latitudes. This may also be true of HET clouds with mixtures of UNK, LIQ, and ICE (not shown). A more detailed examination of the effects of phase mixtures on ΔTph warrants further investigation. Both the HOM and HET liquid categories similarly track the HOM and HET for all cloud types (Figure 2). However, the sharp peak observed in the high latitude SH for HOM in Figure 2 is contained in HOM PMP, not in HOM LIQ, in Figure 13.
 Cloud coverage and cloud opacity simultaneously impact the ΔTph versus ΔTwv histogram. To quantify this simultaneous effect, the ΔTph versus ΔTwv relationships are sorted into four bins of AIRS effective cloud fraction (ECF [see Kahn et al., 2007]) in Figure 14 for all scan angles: ECF < 0.1, 0.1 ≤ ECF < 0.5, 0.5 ≤ ECF < 0.9, and ECF > 0.9. The AIRS ECF is a convolution of both cloud coverage and emissivity, unlike the MODIS cloud mask, which represents coverage only. For thin and/or broken cloud cover (ECF < 0.1), most values are near ΔTph = −0.8 K, with an elongated mode extending toward more positive values of ΔTph and ΔTwv similar to CLR in Figure 10. However, there is more scatter extending in all directions that is consistent with thin and broken clouds with radiance signatures consistent to liquid or ice phase. Similarly, for higher values of ECF, this scatter increases and the mode consistent with CLR in Figure 10 is further reduced in magnitude. For ECF > 0.5 in Figure 14, the scatter organizes into two distinct modes centered near ΔTph = −0.8 K and +0.2 K that closely resemble HOM in Figure 10. Lower values of ΔTwv are found for ECF > 0.9 in Figure 14 compared to HOM in Figure 10. This shows that some clouds, although uniformly overcast, may be semi-transparent for HOM in Figure 10, causing an increase of ΔTwv; similar values are found in Figure 14 when 0.5 ≤ ECF < 0.9. These results are also consistent with an increased sensitivity to cloud thermodynamic phase in the presence of homogeneous and opaque clouds (high ECF) when compared to heterogeneous clouds (low ECF).
 To quantify the relationships of CWV to the ΔTph versus ΔTwv histogram, Figure 14 (ECF < 0.1), repeated in Figure 15, is partitioned into four bins of CWV (CWV < 10 mm, 10 mm < CWV < 30 mm, 30 mm < CWV < 50 mm, and CWV > 50 mm) and one bin for failed retrievals of AIRS/AMSU CWV that are common in precipitating clouds [Kahn et al., 2007]. Low values of ECF that are simply retrieval artifacts are also observed within failed temperature and water vapor retrievals [Kahn et al., 2007]. As expected, the mode centered near ΔTph = −0.8 K occurs for values of CWV <30 mm. Similarly, the mode with increasing values of ΔTph and ΔTwv is associated with higher values of CWV. If the bins of CWV are restricted to narrower ranges, the scatter within each bin in the direction of ΔTwv is significantly reduced (not shown). This is consistent with a strong observed correlation between CWV and ΔTwv in AIRS observations [Aumann et al., 2006]. Other bins of ECF (not shown) also reveal a similar behavior, although the higher values of ΔTwv are reduced with increasing values of ECF.
6. Discussion and Conclusions
 A combination of spatially collocated Atmospheric Infrared Sounder (AIRS [Aumann et al., 2003]) radiances and Moderate Resolution Imaging Spectroradiometer (MODIS [Platnick et al., 2003]) cloud products are used to quantify the impact of cloud heterogeneity on AIRS-based assessments of cloud thermodynamic phase. The smeared, rotated, and truncated AIRS spatial response functions obtained from prelaunch calibration are used to spatially co-locate radiances and geophysical parameters from AIRS and MODIS [Schreier et al., 2010]. Radiative transfer simulations have demonstrated that AIRS channels (in principle) have greater sensitivity to cloud thermodynamic phase when compared to MODIS channels in similar spectral bands [Nasiri and Kahn, 2008]. However, the relative trade-offs of spectral and spatial resolution differences that are inherent between AIRS and MODIS have not been quantified to date. In this investigation, the relative heterogeneity of cloud cover within different cloud and regime types for four time periods (1–6 January, 1–6 April, 1–6 July, and 1–6 October 2005) is globally quantified and related to the potential of AIRS to improve infrared-based estimates of cloud thermodynamic phase.
 The rigorous pixel-scale collocation methodology facilitates a quantitative and rigorous estimate of scene type within a given AIRS field of view (FOV). The MODIS cloud mask [Frey et al., 2008], infrared-based cloud thermodynamic phase [Platnick et al., 2003], and cloud top temperature (TCLD) [Menzel et al., 2008] are used to characterize cloud structure within the AIRS FOV. Global distributions of AIRS FOV-scale frequencies of clear sky (cloud mask probably or confident clear), homogeneous cloud cover (probably or confident cloud), and heterogeneous cloud cover (cloud and clear) for a four week time period are found to be 13–14%, 59–60%, and 26–28%, respectively, depending on the time period of study. Homogeneous cloud cover occurs 70–90% of the time in the mid- and high latitude storm track regions, and 30–50% of the time when brightness temperatures (Tb) are between 250 and 265 K. Estimates of the spatial uniformity of TCLD within the AIRS FOV are used as a further quantification of cloud uniformity. The high latitudes have a poor characterization of cloud thermodynamic phase and also show strong responses in forced CO2 climate change modeling experiments such as changes in cloud altitude, cloud water content, and the poleward migration of clouds [e.g., Li and Le Treut, 1992; Senior and Mitchell, 1993]. Recent results obtained from the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP [Hu et al., 2010]) indicate many of these clouds are liquid phase, while MODIS identifies a majority of these clouds as either “unknown” or “mixed-phase.” Since cloud cover is overwhelmingly homogeneous and clouds are more uniform at the AIRS FOV scale in these critical geophysical regimes, AIRS and other hyper-spectral sounders including IASI and CrIS will play a key role toward establishing a global “best estimate” of cloud thermodynamic phase.
 Four AIRS channels with low NEdT in between absorption lines with sensitivity to thermodynamic phase and small-scale cloud heterogeneity were identified with approximate wave numbers of 857, 960, 1227, and 1231 cm−1. They are combined to form three different ΔTb that are primarily sensitive to ice cloud particle size (960–857 cm−1, ΔTsi), column water vapor (1231–1227 cm−1, ΔTwv), and cloud thermodynamic phase (1231–960 cm−1, ΔTph). Both ΔTph and ΔTwv are shown to be better correlated to cloud heterogeneity and cloud thermodynamic phase than ΔTsi. Thus, the focus of this work is on two-dimensional histograms of ΔTph versus ΔTwv. Homogeneous cloud cover scenes with Tb between 250 and 265 K have substantially larger phase radiance signatures than heterogeneous cloud cover. Furthermore, clouds that are uniform (lower TCLD variability) show even better cloud thermodynamic phase separation than those with higher TCLD variability. A major portion of heterogeneous cloud cover falls within simulated bounds of clear sky of ΔTph, although a minority of the clouds exert a radiative signature probably large enough to be identified as liquid or ice. Two-dimensional histograms of ΔTph versus ΔTwv sorted by MODIS cloud thermodynamic phase suggest that approximately 50% of homogenous “unknown + mixed phase” clouds could be identified as liquid or ice with AIRS. At near nadir view angles with low TCLD variability, a majority of clouds appears to be liquid phase. At off-nadir view angles with high TCLD variability the frequencies of liquid and ice phase clouds are more or less similar. A disproportionate number of these clouds are located in the mid- and high latitude storm tracks.
 The results of this investigation suggest a new quantitative approach that leverages a combination of existing hyperspectral sounders (e.g., AIRS) with high-spatial-resolution imagers (e.g., MODIS) and their derived geophysical products, to improve infrared-based assessments of cloud thermodynamic phase for a small but important subset of clouds that plays a key role in cloud-climate feedback. This investigation also lays the groundwork for similar observations to be obtained from VIIRS and CrIS on the Joint Polar Satellite Platforms (JPSS) [Lee et al., 2010]. Similarly, this approach is potentially applicable to the characterization of other types of cloud and aerosol parameters, along with temperature and water vapor profiles, and minor gases that are present within complicated scene heterogeneity.