Abstract

There is currently significant uncertainty about the extent to which cirrus clouds are composed of “small” ice crystals smaller than about 20-μm effective radius. This is due in part to concerns that in situ measurements from aircraft are plagued by ice particle shattering on instrument inlets, artificially negatively biasing effective radii. Here, space-based measurements are applied to the problem. It is found that a space-based infrared split-window technique is less sensitive but more accurate than a visible-near-infrared technique for confident assessment of whether thin cirrus clouds have small effective radii, independent of a normal range of retrieval assumptions. Because of the sensitivities of the infrared split-window technique, however, this method can only accurately determine the presence of small particles for ice clouds with optical depths between roughly 0.5 and 3.0. Applied to Moderate Resolution Imaging Spectroradiometer (MODIS) data, it is found that a very conservative minimum of 15%–20% of such thin cirrus globally are composed of small ice crystals, but that the actual value could be as high as 40%, and even higher for cold clouds or those in the tropics. Retrievals are found to be in good agreement with airborne probe measurements from the Cirrus Regional Study of Tropical Anvils and Cirrus Layers–Florida-Area Cirrus Experiment (CRYSTAL-FACE) field campaign, implying that, for the cases examined, the impact of inlet shattering on measurements must have been limited.

1. Introduction

Many field campaigns and satellite missions have been designed partly in attempt to gain a more accurate characterization of cirrus clouds. For example, the Cirrus Regional Study of Tropical Anvils and Cirrus Layers–Florida Area Cirrus Experiment (CRYSTAL-FACE), WB-57 Midlatitude Cirrus Cloud Experiment (WB57 MidCiX), and the Tropical Composition, Cloud, and Climate Coupling (TC4) experiment have pursued quantification of these ice clouds through the combination of in situ airborne measurements and coincident satellite observations. Estimates of ice cloud particle size from airborne probes employed during these field campaigns, however, have often been contradictory. For example, Heymsfield et al. (2006) argued that comparable airborne instrumentation used during the CRYSTAL-FACE field campaign gave estimates of effective radius that differed by a factor of 2–3. Although ice crystal size defines the cirrus cloud at its most basic level, appropriate characterization of size distributions remains highly disputed (Garrett et al. 2005; McFarquhar et al. 2007; Jensen et al. 2009). This debate is not simply petty bickering over a few micrometers but instead is a robust discussion over whether the ice particles are “small” or “large.”

Although some of these differences in measured ice particle size are likely due to intrinsic differences in instrument behavior, a further complication is that the in situ measurements are invasive. There is a strong possibility that ice particles may shatter during the measurement process. Korolev and Isaac (2005) showed visually that large ice particles can shatter on the edge of an instrument probe, creating a shower of small particles that subsequently enters the instrument sampling volume. Jensen et al. (2009) further argued that the ice crystals may shatter on the edge of the plane wing where the instruments are mounted. Such scenarios would result in a measurement bias toward small particles, possibly explaining some of the observed discrepancies in reported particle size between different instruments. Associated ambiguities pose difficulties for attempts to accurately model and understand cloud processes and their role in climate feedbacks (Stephens et al. 1990; Lindzen et al. 2001; Fu et al. 2002; Rapp et al. 2005).

Satellite measurements would seem an ideal means to assess the size of cirrus ice crystals. Satellite measurements, while coarse in resolution, are noninvasive and are unaffected by the inner workings of in situ aircraft instrumentation. Over the past several decades, in fact, many studies and techniques have been implemented based upon both active and passive satellite measurements to estimate global distributions of cloud effective radius and other properties [Moderate Resolution Imaging Spectroradiometer (MODIS), Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations platform (CALIPSO), and CloudSat to name just a few]. Unfortunately, remote sensing retrievals have their own potential pitfalls arising from the necessary assumptions that must be made to invert radiance measurements to estimates of ice crystal effective radius. Cooper et al. (2003, 2007), for instance, showed that the potential uncertainty that can arise from required assumptions for ice crystal shape, ice particle size distribution, and cloud temperature is of order of 30%–40% for MODIS-based retrievals of effective radius.

The purpose of this paper then is to help clarify the problem of ice crystal size in cirrus clouds. Drawing from practical insights gained from prior ice cloud studies, a robust and simple method for the confident identification of cirrus clouds whose particles are small is presented. The definition of small in this paper will be roughly less than 20 μm in effective radius, defined as

 
formula

The threshold of 20 μm in this paper is not arbitrary, but based on the radiative properties of ice crystals. Figure 1 plots the absorption efficiency for randomized aggregates as a function of effective radius for a wavelength of 11.0 μm as calculated by Yang et al. (2005). Absorption generally increases with increasing effective radius up to about 20 μm and then converges to a value near 1.0 for radii greater than 20 μm. For particles whose size is larger than the absorption depth in bulk ice of radiation, absorption is loosely governed by the area of the particle normal to the incident beam. For smaller particles, radiation penetrates the entire crystal depth, and it is the entire particle volume that absorbs. Thus, small particles have a distinct radiative signature both of practical interest to remote sensing and of climate relevance for what they imply for the efficiency of atmospheric condensate to exert a positive radiative forcing.

Fig. 1.

Absorption efficiencies at 11.0 μm for randomized ice aggregates as a function of effective radius.

Fig. 1.

Absorption efficiencies at 11.0 μm for randomized ice aggregates as a function of effective radius.

Here our goal is to exploit this radiative distinction between particle sizes to help limit any ambiguities of in situ measurements of ice crystal size. The potential for noninvasive passive remote sensing techniques to constrain the problem, using spectral measurements commonly found on satellite instrumentation, is explored. The basic idea here is to frame the retrieval in such a manner that ice crystal size is designated as being small only when the retrieved particle size is less than 20-μm effective radius, regardless of the specific inversion assumptions used. The “best” retrieved estimate might be 8 or 15 μm but what is critical is that retrieval uncertainty does not range outside some designated limit of small. So in general terms, the goal of this retrieval scheme is to produce a result that is highly accurate rather than highly precise. That is, the goal is to have a retrieval scheme that, if it indicates that the cloud particles are small, true “smallness” is unambiguous.

The outline of this paper is as follows. Section 2 of this paper introduces the general theoretical basis for selecting those radiometric signatures confidently associated with the presence of ice clouds composed of small particles. Section 3 describes the specific application of this retrieval scheme to MODIS data to explore the frequency and distribution of small ice crystals in cirrus clouds on a global scale. Section 4 applies the technique to field measurements observed during the CRYSTAL-FACE and MidCiX field campaigns.

2. Development of retrieval technique

Measuring the global distribution of cirrus cloud microphysical properties has been a primary goal of many satellite missions. Significant effort has been directed at both understanding the underlying physics of the ice cloud problem and using this knowledge to infer cirrus cloud properties from satellite-based measurements (see Miller et al. 2000, Inoue 1985; Prabhakara et al. 1988; Nakajima and King 1990; King et al. 1992). Each of these retrieval techniques was designed based upon observed spectral radiance sensitivities to cloud properties such as optical depth and effective radius. However, each also has its own potential sources of error due to the use of necessary assumptions in relating radiance and retrieval space. It is, of course, the ratio of the sensitivity to the uncertainty—or, alternately, signal to noise—that dictates the true utility of a retrieval scheme.

L’Ecuyer et al. (2006) and Cooper et al. (2006) attempted to determine an ideal cloud retrieval method and associated uncertainties through a formal information content analysis (Shannon and Weaver 1949; Rodgers 2000). These studies quantified both radiance sensitivities and inversion uncertainties due to assumptions such as ice crystal habit, cloud temperature, cloud particle size distribution, and the atmospheric temperature and humidity profile, to determine those spectral measurements that contained the most information for cloud retrievals. The split-window, infrared method (Inoue 1985; Prabhakara et al. 1988) and the combined visible, near-infrared method (Nakajima and King 1990) were found to be the most useful in minimizing retrieval uncertainties for the effective radius of thin cirrus clouds. In the following subsections, the relative merits of each of these techniques are examined in a slightly different context. Rather than finding those measurements that simply minimize uncertainty, here these two retrieval techniques are compared to identify which is best for unambiguous determination of whether observed ice cloud particles are less than roughly 20 μm in effective radius, that is, small.

a. Visible and near-infrared technique for identifying small particles

To estimate cloud properties, the Nakajima and King (1990) retrieval method exploits a combination of a purely scattering visible measurement and an absorbing near-infrared measurement. The amount of visible radiation reaching the satellite is primarily a function of cloud optical depth, whereas the amount of near-infrared radiation is also a function of ice cloud effective radius. Figure 2 shows forward model radiative transfer calculations for the combined visible, near-infrared retrieval scheme for ice clouds with effective radius from 8 to 80 μm and thin optical depths from 0 to 4. The clouds were composed of randomly oriented randomized hexagonal ice aggregates (Yang and Liou 1998) using the optical properties developed by Baran et al. (2001) and Baran and Francis (2004), arranged in a modified gamma size distribution with variance parameter equal to 2. The modified gamma distribution is of the form

 
formula

where n(D) is the number of ice crystals of size D, Nt is the number concentration, Dn is the characteristic diameter, and ν is the distribution variance. The clouds were assumed to be embedded within a standard tropical atmosphere (McClatchey et al. 1972) and over an ocean surface with an albedo of 5%.

Fig. 2.

The combined visible, near-infrared technique to estimate ice cloud properties. Optical depth is determined from the 0.66-μm measurement; effective radius from the 2.15-μm measurement. Note that small changes in an observed 2.15-μm reflectance function will result in large changes in retrieved effective radius. Curves are based on randomly oriented, randomized hexagonal ice aggregates over an ocean surface with 5% albedo.

Fig. 2.

The combined visible, near-infrared technique to estimate ice cloud properties. Optical depth is determined from the 0.66-μm measurement; effective radius from the 2.15-μm measurement. Note that small changes in an observed 2.15-μm reflectance function will result in large changes in retrieved effective radius. Curves are based on randomly oriented, randomized hexagonal ice aggregates over an ocean surface with 5% albedo.

Radiative transfer calculations were performed using the Radiant 2.0 eigenmatrix solver developed by Christi and Gabriel (2003) assuming correlated-k distributions for gaseous atmospheric absorption for MODIS bandwidths (Kratz 1995). The technique clearly has great sensitivity to a large range of cloud properties and therefore it is used in many operational retrieval schemes, including for MODIS. The radiative transfer results, or alternately the shape of the curves in Fig. 2, depend upon exact forward model assumptions. The use of different but perfectly reasonable assumptions for ice crystal habit, cloud particle size distribution, atmospheric temperature and humidity profiles, and surface albedo yields different sets of radiative transfer curves.

Figure 3 shows the forward model radiative transfer calculations for ice clouds composed of either the aggregate crystals in Fig. 2 or hexagonal columns (Yang et al. 2000) assuming three different effective radii (8, 20, and 48 μm). Notice that the 1.60-μm reflectance depends upon assumed habit, meaning that an improper assumption of ice crystal habit for a retrieval scheme could lead to errors in retrieved effective radius.

Fig. 3.

Relationship between 0.66- and 1.61-μm reflectance functions for ice clouds composed of both a modified gamma distribution of randomized aggregates and an equivalent distribution of columns. Optical depths as deduced from the x-axis 0.66-μm measurement range from 0 on the left to 50 on the right.

Fig. 3.

Relationship between 0.66- and 1.61-μm reflectance functions for ice clouds composed of both a modified gamma distribution of randomized aggregates and an equivalent distribution of columns. Optical depths as deduced from the x-axis 0.66-μm measurement range from 0 on the left to 50 on the right.

Figure 2 highlights some of the difficulties in using the visible/near-IR approach for confidently identifying whether thin ice clouds have small effective radii. The Nakajima and King (1990) technique clearly has great sensitivity to effective radius. Yet, very small changes in assumed surface reflectance can yield very large changes in retrieved cloud effective radius. To illustrate, for a cloud of optical depth 0.6, a 1% error in forward modeled 2.15-μm reflectance function (due to surface reflectance error, for example), results in the retrieved effective radius shifting from 40 to 8 μm. Even a 0.5% error in forward modeled 2.15-μm reflectance causes retrieved effective radius to shift from 40 to 20 μm. Jin et al. (2004) found that uncertainties in reflectance from a well-defined ocean surface may easily vary on the order of a few percent because of such factors as solar zenith angle, wind speed, and ocean chlorophyll concentration. Previously, Cooper et al. (2006) has shown that uncertainties in ice crystal habit can also cause such exaggerated forward model error in retrievals of thin ice clouds. Thus, small errors in assumed surface albedo or ice crystal habit used in a visible/near-IR method can inadvertently switch retrieved particle size between large and small for thin clouds.

b. Split-window infrared technique for identifying small particles

An alternative approach that may be applied is an infrared, split-window method. Absorption by ice cloud particles varies across the spectral infrared window region. Ice particles are more efficient at absorbing radiation near wavelengths of 12.0 μm than near 11.0 μm. From a satellite perspective, this means that more terrestrial radiation reaches the sensor at 11.0 μm than at 12.0 μm because clouds are colder than what lies beneath. Since the ratio of absorption at the two wavelengths is a function of particle size, the brightness difference is a strong function of cloud ice crystal effective radius. Forward model radiative transfer curves, or “arches,” for this sensitivity are shown in Fig. 4. Cloud optical depth and effective radius pairs can be identified from the 11.0-μm brightness temperature, and the brightness temperature difference (BTD) for 11.0 μm minus 12.0 μm.

Fig. 4.

Relationship between 11.0-μm brightness temperature and BTD (11.0–12.0 μm) for a number of cirrus clouds with optical depths ranging from 0 to 5 and effective radii ranging from 8 to 48 μm. Clouds with emitting temperatures of 210 (red), 230 (black), and 250 K (blue) are modeled. Vertical lines correspond to a cloud optical depth of 2 for each cloud. Each symbol along a curve represents an optical depth increment of 0.5, increasing from 0 at the right base of the arch to 10 at the left base.

Fig. 4.

Relationship between 11.0-μm brightness temperature and BTD (11.0–12.0 μm) for a number of cirrus clouds with optical depths ranging from 0 to 5 and effective radii ranging from 8 to 48 μm. Clouds with emitting temperatures of 210 (red), 230 (black), and 250 K (blue) are modeled. Vertical lines correspond to a cloud optical depth of 2 for each cloud. Each symbol along a curve represents an optical depth increment of 0.5, increasing from 0 at the right base of the arch to 10 at the left base.

The split-window method is limited to thin, graybody clouds with reasonably small effective radii. Once a cloud reaches visible optical depths near 4 or 5, the cloud emits as a Planck blackbody. Similarly, as ice particles grow greater than about 30 μm, the ratio of absorption efficiency and thus the BTD at the split-window wavelengths converges.

As is the case with the visible, near-infrared Nakajima and King (1990) technique, the exact shape of the split-window arches depends on the assumed ice crystal habit, cloud particle size distribution, atmospheric temperature and humidity profiles, and cloud temperature. To illustrate, Fig. 4 displays the forward model arches calculated using three different assumptions of cloud temperature for cirrus cloud composed of ice spheres. Depending on the assumed cloud temperature, a different effective radius and optical depth pair are found for any given combination of 11.0-μm brightness temperature and BTD.

Figure 5 illustrates forward radiative transfer calculations in the split-window arches format for a cloud temperature of 210 K, a standard tropical atmosphere, and MODIS bandwidths. Curves are shown for three different effective radii (8, 20, and 48 μm), each for six different ice crystal habit assumptions [randomized aggregates, aggregates, solid hexagonal columns, hollow hexagonal columns, droxtals (Yang et al. 2003, 2005), and spheres from anomalous diffraction theory (Flatau 1992; Stephens 1994)]. For a given effective radius, different assumptions of ice crystal habit produce curves with slightly different values of BTD (or the height of the arches) because of their differing absorption characteristics at 11.0–12.0 μm. For example, for an effective radius of 8 μm and given observed 11.0-μm brightness temperatures between 250 and 260 K, values of BTD range between 6.5 and 9.0 K depending on the specific habit assumption. For an effective radius of 48 μm and the same 11.0-μm brightness temperature range, however, brightness temperature differences range between −0.5 and 2.0 K.

Fig. 5.

Theoretical split-window arches for ice clouds composed of six different ice crystal habits (randomly oriented randomized hexagonal aggregates, aggregates, solid hexagonal columns, hollow hexagonal columns, droxtals, and spheres) with a cloud temperature of 210 K. Calculations are shown for three different effective radius (8, 20, and 48 μm) for each ice crystal type for an ice cloud embedded in a standard tropical atmosphere. Each symbol along a curve represents an optical depth increment of 0.5, increasing from 0 at the right base of the arch to 10 at the left base.

Fig. 5.

Theoretical split-window arches for ice clouds composed of six different ice crystal habits (randomly oriented randomized hexagonal aggregates, aggregates, solid hexagonal columns, hollow hexagonal columns, droxtals, and spheres) with a cloud temperature of 210 K. Calculations are shown for three different effective radius (8, 20, and 48 μm) for each ice crystal type for an ice cloud embedded in a standard tropical atmosphere. Each symbol along a curve represents an optical depth increment of 0.5, increasing from 0 at the right base of the arch to 10 at the left base.

While there is substantial spread in BTD depending upon assumed particle habit, Fig. 5 suggests that it should possible to choose a sufficiently high BTD threshold that is unambiguously associated with small values of cloud ice crystal effective radius. For example, for a very cold ice cloud of 210 K, a BTD threshold value of near 4.0 K corresponds with an ice cloud effective radius less than 20 μm, independent of ice crystal habit. Selection of such a BTD threshold would necessarily misclassify the effective radii of some clouds as not being small, simply because not all the different ice crystal habits would generate a sufficiently high BTD. It would, however, almost guarantee that such an observed radiometric signature resulted from a predominance of small ice particles. Cooler surfaces, with lower thermal emission, have smaller BTD arches, and a correspondingly lower BTD threshold is required.

Other retrieval assumptions, such as surface emissivity, ice particle size distribution and atmosphere profiles, also produce a range of brightness temperature differences that affect the BTD arch height. Although uncertainties in surface emission can lead to errors in perceived cloud temperatures, the correlation in emission between the two window channels constrains the magnitude of possible errors in BTD. As such, these effects are considered minimal for the remainder of the paper.

Cooper et al. (2003) found that the selection of ice particle size distribution has a much smaller influence on the BTD than habit. Figure 6 displays eight different size distributions, each of different form yet with the same effective radius of 15 μm. Figure 7 in turn shows the BTD calculations corresponding to these eight size distributions assuming clouds composed of both ice spheres and hexagonal columns. Variation of BTD is much greater between crystal habit (for given size distribution) than it is between size distribution (for given habit). In terms of Fig. 5, for a given effective radius and habit, the use of different size distributions would result in BTD curves within 0.5 K or so of the ones shown for the specified modified gamma form. It is the larger uncertainties in BTD associated with ice crystal habit as seen in Fig. 5 that need more thorough consideration in the selection of a BTD threshold to identify small particles. Such conclusions agree well with those of Dubuisson et al. (2008).

Fig. 6.

Eight different size distributions of modified gamma, lognormal, and bimodal forms. Each distribution has an effective radius of 15 μm. The figure is taken from Cooper et al. (2003).

Fig. 6.

Eight different size distributions of modified gamma, lognormal, and bimodal forms. Each distribution has an effective radius of 15 μm. The figure is taken from Cooper et al. (2003).

Fig. 7.

BTD relationships for a set of 220-K ice clouds. The upper set of curves corresponds to each of the distributions in Fig. 6 assuming spherical particles whereas the bottom set corresponds to hexagonal columns. The figure is taken from Cooper et al. (2003).

Fig. 7.

BTD relationships for a set of 220-K ice clouds. The upper set of curves corresponds to each of the distributions in Fig. 6 assuming spherical particles whereas the bottom set corresponds to hexagonal columns. The figure is taken from Cooper et al. (2003).

Assumed atmospheric temperature and gas profile can also impact the success of the BTD threshold scheme by changing the height of the right “base” of the arch plot. If clear-sky values of BTD are abnormally high compared to the clear-sky assumptions used in selection of the BTD threshold value, then the BTD value necessary for identification of small ice effective radii may need to be adjusted. For the MODIS example of Fig. 5, a BTD threshold of 4 K was selected for a cold cloud of 210 K and assuming a standard tropical atmosphere with clear-sky BTD of 1.5 K. Cooler and drier atmospheres as typically found in the midlatitudes and poleward have significantly lower clear-sky BTD and therefore would not require adjustment of the 4-K threshold. Because of the cautious nature in selection of the BTD threshold as dictated by crystal habit BTD variability, however, even clear-sky BTD significantly greater than 1.5 K should not cause problems for the 4-K BTD threshold assumption. Figure 8 shows theoretical arch plot calculations for a cloud of 210 K with a clear-sky BTD of 3 K. Although the right side of the arch (representing thinner cloud optical depths) is elevated compared to the clear-sky 1.5-K BTD case, it is not possible to generate BTD greater than 4 K without the influence of small ice particles even for this extreme case. The BTD is a combination of clear-sky and cloudy signals as weighted by cloud optical depth, meaning that clear-sky BTD must be greater than roughly 4 to violate our retrieval assumptions. Large clear-sky BTD conditions, of course, would be more important for warmer clouds whose arch heights are lower than those represented in Fig. 5. In practice, this sensitivity to clear-sky BTD can be constrained by examining nearby clear-sky brightness temperatures.

Fig. 8.

BTD relationship for the spheres shown in Fig. 5 for a clear-sky BTD of 3.0 (black curves) and 1.5 K (red curves). Each symbol along a curve represents an optical depth increment of 0.5, increasing from 0 at the right base of the arch to 10 at the left base.

Fig. 8.

BTD relationship for the spheres shown in Fig. 5 for a clear-sky BTD of 3.0 (black curves) and 1.5 K (red curves). Each symbol along a curve represents an optical depth increment of 0.5, increasing from 0 at the right base of the arch to 10 at the left base.

From the above example, it was found that a BTD value of 4 K is associated with the presence of small ice crystals for MODIS instrumentation and cold cirrus clouds with temperatures near 210 K embedded in a tropical atmosphere. Suitable MODIS BTD threshold values for other cloud temperatures are shown in Table 1. These values should be considered first order. The BTD threshold scheme best suited for different remote sensing instrumentation could easily be different and should ideally be calculated based on the precise instrument wavelength bands that are used. Dubuisson et al. (2008) and Heidinger and Pavolonis (2009), for instance, found similar BTD–effective radii relationships for the CALIPSO Imaging Infrared Radiometer and the National Oceanic and Atmospheric Administration (NOAA) Advanced Very High Resolution Radiometer (AVHRR) sensors, respectively.

Table 1.

Suggested BTD (11.0–12.0 μm) for application of MODIS data to identify thin cirrus with small effective radii, expressed as a function of cloud temperature. Cloud optical depths should be in the range from about 0.5 to 3; the use of clouds outside this range will simply result in the retrieval of a large particle regardless of true particle size. For valid retrieval results, clear-sky BTD should ideally be less than 2.0 K.

Suggested BTD (11.0–12.0 μm) for application of MODIS data to identify thin cirrus with small effective radii, expressed as a function of cloud temperature. Cloud optical depths should be in the range from about 0.5 to 3; the use of clouds outside this range will simply result in the retrieval of a large particle regardless of true particle size. For valid retrieval results, clear-sky BTD should ideally be less than 2.0 K.
Suggested BTD (11.0–12.0 μm) for application of MODIS data to identify thin cirrus with small effective radii, expressed as a function of cloud temperature. Cloud optical depths should be in the range from about 0.5 to 3; the use of clouds outside this range will simply result in the retrieval of a large particle regardless of true particle size. For valid retrieval results, clear-sky BTD should ideally be less than 2.0 K.

3. Application to global MODIS data

In this section, the infrared BTD scheme that was outlined above is applied to global satellite observations. Figure 9 shows the global distributions of observed values of BTD (11.0–12.0 μm) for 6 May 2004 as seen by the Aqua MODIS instrument. Observed BTD values range from slightly less than 0 K to around 10 K. Concentrations of high BTD values greater than 5 K are seen primarily in the tropics.

Fig. 9.

Global 6 May 2004, BTD (11.0–12 μm) (K) as observed from the MODIS Aqua instrument.

Fig. 9.

Global 6 May 2004, BTD (11.0–12 μm) (K) as observed from the MODIS Aqua instrument.

As discussed above, the exact BTD threshold that can be confidently associated with the presence of small particles depends upon both the characteristics of the observation system and specific environmental conditions such as cloud and surface temperature. For example, a BTD value of 4 K corresponds with ice particles less than 20 μm, assuming a very cold cloud with temperature of 210 K, a standard tropical atmosphere, and a surface temperature of 300 K using MODIS infrared bandwidths. A 4-K BTD threshold value should be more generally applicable to a much wider range of cloud types because it is by nature conservative. As clouds get warmer and the lower atmosphere colder, the BTD threshold necessary to safely identify the presence of small particles decreases. Figure 10 shows that lower BTD values near 3.5 K are sufficient to identify thin cirrus with effective radii less than 20 μm, provided cloud temperatures are near 230 K. Similarly, values of 3 K correspond to small particles for cloud temperatures near 250 K. Regardless, the large BTD values seen in Fig. 9 clearly suggest the presence of large areas of thin cirrus clouds composed of small ice crystals in the tropics. The precise fraction of clouds with small ice particles based upon different assumptions will be quantified in the following paragraphs.

Fig. 10.

Theoretical split-window arches for ice clouds composed of six different ice crystal habits (randomly oriented randomized hexagonal aggregates, aggregates, solid hexagonal columns, hollow hexagonal columns, droxtals, and spheres) with a cloud temperature of 230 K. Calculations are shown for three different effective radius (8, 20, and 48 μm) for each ice crystal type for an ice cloud embedded in a standard tropical atmosphere. Each symbol along a curve represents an optical depth increment of 0.5, increasing from 0 at the right base of the arch to 10 at the left base.

Fig. 10.

Theoretical split-window arches for ice clouds composed of six different ice crystal habits (randomly oriented randomized hexagonal aggregates, aggregates, solid hexagonal columns, hollow hexagonal columns, droxtals, and spheres) with a cloud temperature of 230 K. Calculations are shown for three different effective radius (8, 20, and 48 μm) for each ice crystal type for an ice cloud embedded in a standard tropical atmosphere. Each symbol along a curve represents an optical depth increment of 0.5, increasing from 0 at the right base of the arch to 10 at the left base.

Constant 4-K, constant 3-K, and cloud temperature–dependent BTD threshold schemes were applied to the 6 May 2004 MODIS data to determine the frequency of small ice crystals in thin cirrus clouds. Retrievals were restricted to those scenes designated as single-layer cirrus pixels by operational MODIS cloud products. To account for the radiance sensitivities of infrared cloud physics, the retrievals were restricted to clouds with thin optical depths. Retrievals for thicker clouds are impossible since, as shown in Fig. 5, the arches converge to a single value that is a function of cloud temperature alone. A restriction to more moderate optical depths is achieved in a practical sense through comparison of the observed 11.0-μm brightness temperature relative to the MODIS cloud-top and surface temperature products. Retrievals were performed when the observed brightness temperature was 15 K greater than cloud temperature and yet 15 K less than surface temperature. For the example of Fig. 5, such restrictions would correspond to a working cloud optical depth range from about 0.4 to 3. The retrievals were limited further to those pixels with surface temperatures greater than 285 K simply to ensure sufficiently large BTD arches. Initial analyses find that such restrictions limit our technique to about 15%–18% of MODIS cirrus pixels dependent upon exact optical depth assumptions.

The motivation for the aforementioned constraints is to avoid an unrealistic assessment of whether ice crystals are small. A useful point here is that any misclassification of cloud fraction, single-layer status, or cloud optical depth could not result in false identification of small crystals. Such misclassifications of cloud scene only reduce the BTD relative to the true value, and therefore lead to an underestimate of the portion of clouds with small effective radii. For example, if a MODIS pixel has a true cloud fraction less than 1.0, this would simply dilute the high cloud BTD signal with a lower surface and atmosphere BTD signal. If the atmosphere has multiple cloud layers in a scene misclassified as being single layered, this would simply reduce the effective surface emission temperature, artificially reducing the heights of the arches. Similarly, misclassification of a very thin or thick cloud as moderately thin would result in reduced BTD values via a shift to the lower BTD radiometric areas near the arch bases (Fig. 4).

As discussed in the section 2, the most likely potential source of error for this retrieval scheme is uncertainty in atmospheric profile. Even here, however, examination of clear-sky BTD for the MODIS data suggests that the impact of atmospheric profile on the retrievals should be relatively small. Over 99% of clear-sky MODIS pixels had BTD values less than 2 K, a value that could not elevate the arches high enough to cause misclassification problems for the aforementioned threshold value scenarios.

If a 4-K BTD threshold is applied to the 6 May 2004 Aqua MODIS global data, small ice crystals characterize 14.6% of the total cases (Table 2 summarizes all retrieval results of section 3). This fraction is a function of both cloud temperature and latitude. The percentage of clouds with small particles increased to 19.4% for those cold clouds with temperatures less than 220 K. Similarly, as suggested by Fig. 9, small ice crystals were more prevalent in the tropics (21%) than at midlatitudes (5%). To ensure that these latitude-dependent differences were not simply caused by different populations of cloud temperatures, the fraction of clouds with small ice particles is plotted as a function of cloud-top temperature, for both the tropics and the midlatitudes in Fig. 11. While the coldest cloud temperatures are always associated with the greatest predominance of small ice crystals, the percentage of clouds with small ice crystals is higher in the tropics than the midlatitudes (see Garrett et al. 2003; Garrett 2008).

Table 2.

Percentage of thin cirrus clouds composed of small ice particles less than 20 μm for the given retrieval scenarios. Because of the inherent sensitivities of the split-window technique, these cases were limited to those optical depths (roughly 0.5–3) where it was possible to identify small particles from our technique.

Percentage of thin cirrus clouds composed of small ice particles less than 20 μm for the given retrieval scenarios. Because of the inherent sensitivities of the split-window technique, these cases were limited to those optical depths (roughly 0.5–3) where it was possible to identify small particles from our technique.
Percentage of thin cirrus clouds composed of small ice particles less than 20 μm for the given retrieval scenarios. Because of the inherent sensitivities of the split-window technique, these cases were limited to those optical depths (roughly 0.5–3) where it was possible to identify small particles from our technique.
Fig. 11.

The fraction of thin cirrus clouds composed of small ice crystals as a function of cloud temperature (K) for both the tropics and midlatitudes. Because of the inherent sensitivities of the split-window technique, these cases were limited to those optical depths (roughly 0.5–3) where it was possible to identify small particles.

Fig. 11.

The fraction of thin cirrus clouds composed of small ice crystals as a function of cloud temperature (K) for both the tropics and midlatitudes. Because of the inherent sensitivities of the split-window technique, these cases were limited to those optical depths (roughly 0.5–3) where it was possible to identify small particles.

Selection of a lower BTD threshold such as 3 K would provide higher fractional estimates and might plausibly be more suitable. Figure 5 shows that a BTD value of 3 K is consistent with small ice crystals for several different ice crystal types. If the BTD threshold is 3 K rather than 4 K, this increases the fraction of thin cirrus clouds composed of small ice particles from 14.6% to 37.8% globally and from 19.4% to 51.9% for clouds colder than 220 K. A more precise answer will require a better understanding of the global distribution of ice cloud particle habits.

The above results are based upon fixed BTD threshold schemes. They suggest that a significant fraction of thin cirrus clouds globally are composed of small ice particles. A more sensitive scheme might account for the fact that warmer clouds require a lower theoretical BTD threshold to safely identify the presence of small ice cloud particles (see Fig. 10). On the basis of Figs. 5 and 10, BTD thresholds of 4, 3.5, and 3 K were applied for clouds with respective temperatures of less than 220 K, 220–240 K, and greater than 240 K, using the global Aqua MODIS dataset shown in Fig. 9. Under this scenario, the fraction of thin cirrus clouds composed of small particles increases from 14.6% found for the constant 4-K scheme to 23.2% for the varying scheme at the global level. Regional increases range from 21.0% to 27.6% for the tropics and 5.0% to 8.8% for the midlatitude thin cloud ice cases. Of course, it would be possible to make an even more sophisticated BTD threshold scheme. However, intrinsic uncertainties in atmospheric profile and particle size distribution would limit its utility, especially for warmer clouds with smaller BTD arches.

A final test was to apply the BTD retrieval scheme used for MODIS Aqua data to MODIS Terra data simply to ensure that the two satellites yield similar results. For the flat 4-K scheme, 16.8% of Terra thin ice clouds were composed of small ice crystals as compared with 14.6% for Aqua. For the coldest clouds less than 220 K, the fraction increased to 26.3% for Terra versus 19.3% for Aqua. If the more liberal flat 3-K scheme is applied, the fraction of these clouds with small ice crystals increases to 41.9% for Terra versus 37.8% for Aqua. Such differences between satellites are most likely due to differences in overpass time relative to areas of tropical convection where thin cirrus are most common. Although there is some variability in results between the satellites as well as for the other retrieval experiments above, it is important to remember that these values represent a first order estimate of the fraction of cirrus clouds composed of small ice crystals. A more exact answer would require an in depth analysis that is beyond the current scope of this paper.

To help examine the validity of these infrared BTD retrievals, the results were compared with the MODIS operational effective radius product. The MODIS product is based upon visible and near-infrared observations and therefore provides a spectrally independent test for our infrared retrievals. Although one would expect some differences from the retrieval techniques because of spectrally varying retrieval uncertainties as discussed in section 2, one would also expect to find general agreement when applied to a global dataset. Figure 12 shows MODIS effective radius product plotted as a function of infrared split-window BTD (0–2 K, 2–4 K, and greater than 4 K) for the 6 May 2004 test date for cloud temperatures between 220 and 245 K. As expected, a clear shift to smaller MODIS retrieved particles was found when the BTD were greater than 4 K. The majority of the particles for this high BTD case were in fact less than 20 μm, in general agreement with our selection of our 4-K BTD scheme to identify small particles. Of course, a minority of cases suggest large particles from the MODIS product yet small particles from our BTD scheme. It is again argued that such discrepancies are caused by the large uncertainties inherent to the visible, near-infrared approach and will pursue a state-dependent examination of this topic in a future paper.

Fig. 12.

MODIS effective radius product plotted as a function of infrared BTD for 6 May 2004, Aqua cirrus pixels for cloud temperatures between 220 and 245 K. The plot suggests a clear trend between smaller retrieved MODIS effective radii (based upon visible and near-infrared observations) and increased infrared BTD.

Fig. 12.

MODIS effective radius product plotted as a function of infrared BTD for 6 May 2004, Aqua cirrus pixels for cloud temperatures between 220 and 245 K. The plot suggests a clear trend between smaller retrieved MODIS effective radii (based upon visible and near-infrared observations) and increased infrared BTD.

4. Application to CRYSTAL-FACE and MidCiX data

The BTD technique developed above is now applied to infrared radiance observations from both the CRYSTAL-FACE and the MidCiX field campaigns. Because the scheme is designed to confidently identify whether thin cirrus have small effective radii, its results should provide a useful constraint on measurements from airborne probes of cloud ice particle size. Intercomparisons might yield insights as to what extent ice crystal shattering on airborne probe inlets is affecting the in situ datasets.

Figure 13 displays infrared radiance observations from MODIS aboard Terra, taken on 30 April 2002 during the MidCiX field campaign. The 11.0-μm brightness temperature and the 11.0–12.0-μm BTD are shown in the top and bottom panels, respectively, for the 1640 UTC overpass. A deep convective region is centered over southern Mississippi and Alabama as indicated by low brightness temperatures near 210 K. Thin cirrus outflow surrounds this convective region as revealed by both increasing brightness temperatures and increasing BTD away from the core. At the time of the satellite overpass, the National Aeronautics and Space Administration (NASA) WB-57 research aircraft was located in thin cirrus clouds over southern Tennessee near the common border with Alabama and Mississippi. Davis et al. (2009) provided a detailed comparison of estimates of effective radius from the MODIS operational product and two airborne instruments [the Cloud Particle Imager (CPI; Lawson et al. 2001) and the Cloud Aerosol and Precipitation Spectrometer (CAPS; Baumgardner et al. 2002)]. Depending on the in situ probe considered, results suggested ice crystal effective radii lay roughly between 10 and 25 μm. For comparison, Fig. 13 suggests that BTD values in the location of the WB-57 were typically near 3 K.

Fig. 13.

This figure displays infrared radiance measurements as observed by the MODIS Terra instrument during the MidCiX field campaign on 30 Apr 2002 for the 1640 UTC overpass. (top) The 11.0-μm brightness temperature (K) and (bottom) the 11.0–12.0-μm BTD (K). The general position of the WB-57 under the MODIS overpass is indicated by the black box near the common border of TN, MS, and AL. Specifically, the plane is in the area of elevated BTD as indicated by the orange pixels (BTD near 3 K) in the bottom panel.

Fig. 13.

This figure displays infrared radiance measurements as observed by the MODIS Terra instrument during the MidCiX field campaign on 30 Apr 2002 for the 1640 UTC overpass. (top) The 11.0-μm brightness temperature (K) and (bottom) the 11.0–12.0-μm BTD (K). The general position of the WB-57 under the MODIS overpass is indicated by the black box near the common border of TN, MS, and AL. Specifically, the plane is in the area of elevated BTD as indicated by the orange pixels (BTD near 3 K) in the bottom panel.

Although the observed values of BTD are certainly elevated compared to their surroundings, they do not unambiguously indicate that the ice crystals in these clouds were small. It is important to recognize that this does not mean that the ice particles are necessarily large. It does, however, highlight some of the practical limitations of applying this extremely simple and cautious retrieval scheme to real-world test cases. Because clouds are relatively warm at midlatitudes, large values of BTD are inherently less frequent, independent of particle size, and this makes it more difficult to unambiguously separate a size signal from the noise.

A second test case is illustrated by Fig. 14, which shows both visible and infrared MODIS Airborne Simulator (MAS) radiances obtained aboard the NASA ER-2 research aircraft during the CRYSTAL-FACE field campaign on 26 July 2002, off the northeast coast of Honduras. The visible 0.66-μm radiance in the left panel shows large regions of both convective and thin cirrus clouds covering all but the most southern parts of the observations. The infrared BTD (11.0–12.0 μm) in the right panel shows large regions of high BTD often greater than 5 K, indicating likely areas of thin cirrus clouds composed of small ice crystals. Clear-sky regions in the southern part of the observations show BTD values near 2, a value not high enough to violate the assumptions of the BTD retrieval scheme developed above.

Fig. 14.

MAS measurements found during the CRYSTAL-FACE field campaign. (left) The 0.66-μm visible reflectance (unitless) and (right) BTD (11–12 μm) (K). The black line indicates the flight path of the NASA WB-57 aircraft from 1659 to 1703 UTC.

Fig. 14.

MAS measurements found during the CRYSTAL-FACE field campaign. (left) The 0.66-μm visible reflectance (unitless) and (right) BTD (11–12 μm) (K). The black line indicates the flight path of the NASA WB-57 aircraft from 1659 to 1703 UTC.

Thus, these high-resolution MAS observations may be used to evaluate in situ observations obtained simultaneously aboard the NASA WB-57 research aircraft located beneath the ER-2. The black line on the left panel represents the flight path of the NASA WB-57 research aircraft as it flew through a layer of mostly thin cirrus from 1659 to 1703 UTC. Using a variety of airborne instrumentation [CAPS, Gerber Scientific Inc. Cloud Integrating Nephelometer (CIN; Gerber et al. 2000), and the SPP-100 cloud probe (Baumgardner et al. 2002)], both Garrett et al. (2003) and Roskovensky et al. (2004) observed effective radii smaller than 10 μm for this flight leg. Examination of MAS data corresponding to these thin cirrus cloud shows BTD values typically between 3 and 4 K but with maximum values as high as 4.5 K. If a BTD threshold of 4 K is assumed for the retrieval scheme, then small effective radii must be present at least to some extent, in accordance with the in situ estimates. While ice crystal shattering cannot be definitively ruled out, it is also not supported. Even though the entire cloud does not contain BTD greater than 4 K, Fig. 5 suggests that thin clouds with BTD values of 3.5 K are also very likely to be associated with small ice crystals.

A final test case centers on the development of a thunderstorm anvil cirrus cloud over the west coast of Florida during the CRYSTAL-FACE field campaign on 21 July 2002. Garrett et al. (2005) presented a detailed analysis of the evolution of this storm from both radiative and microphysical perspectives. Using instrumentation aboard the North Dakota Citation aircraft (CIN and a counterflow virtual impactor), Garrett et al. (2005) found these clouds to be primarily composed of small ice particles with effective radii smaller than 20 μm. Such findings, however, have been questioned. Heymsfield et al. (2006) and Jensen et al. (2009) argued that these observations simply reflect sampling artifacts produced from the shattering of ambient large crystals on instrument inlets.

Unfortunately, it was not possible to test the validity of the Garrett et al. (2005) results using the MAS as the NASA ER-2 aircraft was not flying in combination with the other planes during this flight mission. To apply the infrared BTD scheme as an independent check on the validity of these results, one must use an alternate source of infrared observations from the Geostationary Operational Environmental Satellite-8 (GOES-8) imager. Figure 15 shows GOES-8 observed BTD matched to the track of the North Dakota Citation (data are provided through the courtesy of NASA Langley CRYSTAL-FACE satellite page, available online at http://angler.larc.nasa.gov/crystal/) as well as estimated effective radii for flight leg 5 as defined by Garrett et al. (2005).

Fig. 15.

Figure shows the GOES-8 brightness temperature difference (K) matched to the North Dakota Citation flight path for 21 Jul mission. Data are provided through the courtesy of the NASA Langley satellite page. Circles show measurements of effective radii (μm) from Garrett et al. (2005).

Fig. 15.

Figure shows the GOES-8 brightness temperature difference (K) matched to the North Dakota Citation flight path for 21 Jul mission. Data are provided through the courtesy of the NASA Langley satellite page. Circles show measurements of effective radii (μm) from Garrett et al. (2005).

Assuming a BTD threshold value of 4 K for the GOES-8 retrieval scheme, the large BTD values of Fig. 15 indicate a predominance of small ice crystals in these anvil cirrus, agreeing well with the results from Garrett et al. (2005). Since the MODIS and GOES-8 infrared observations are based upon similar but different bandwidths, it is necessary to ensure that clear-sky differences for the GOES-8 imager are small compared to the values of BTD seen in the cloudy observations. Because of the lack of clear-sky conditions for this convective test case, expected clear-sky BTD for the GOES bandwidths were modeled assuming atmospheric profiles from coincident Tampa soundings. For the 2100 UTC Tampa profile corresponding to flight leg 5, the modeled GOES clear-sky BTD was 1.9 K. Such a value is in good agreement with a clear-sky BTD of 2.2 K found using a standard tropical atmosphere (McClatchey et al. 1972). Although such clear-sky BTD values are slightly elevated compared to those from either MODIS or MAS, based upon an understanding of arch plot physics as in Fig. 5, the presence of small ice particles is the only possible explanation for the elevated BTD near 5 K observed during this flight leg.

5. Summary and conclusions

This paper has described a simple technique that can be used for unambiguous identification of thin cirrus clouds with “small” effective radii, where small refers to some unknown size below about 20-μm radius. In more physical terms, small refers to ice crystals whose absorption characteristics are dominated by volume rather than particle surface area (Fig. 1). Thus, space-based measurements of the brightness temperature difference between two bands in the atmospheric infrared window are highly sensitive to the predominance of small ice crystals. If the ice crystals are not small, then the infrared characteristics of the ice crystals are more spectrally flat. A popular alternative that is based on comparisons of cloud radiance at visible and near-infrared wavelengths is more sensitive given a priori knowledge of cloud and atmospheric conditions. However, it is only the split-window infrared approach that has a sufficiently high signal-to-noise ratio to confidently assess whether ice crystals are small, independent of assumed cloud ice particle habit, size distribution, and atmospheric profile. Because of the sensitivities of the split-window technique, however, our method can only accurately determine the presence of small particles for ice clouds with optical depths roughly from 0.5 to 3.0.

The infrared BTD threshold scheme was applied to MODIS data and found that, very conservatively, 15%–20% of such thin cirrus clouds globally must have small effective radii. The precise fraction depends upon both latitude and cloud temperature. For example, for thin cirrus clouds in the tropics, with temperatures under 220 K, the fraction was 35%. If the BTD threshold value is relaxed to lower but physically reasonable values, as much as 40% of such thin cirrus globally has small effective radii, and 68% of those globally with temperatures below 220 K. In general, cold clouds were more likely to harbor small ice crystals than warm clouds, and tropical clouds more likely than midlatitude clouds. Note that such differences are qualitatively consistent with what is expected from how ice crystals homogeneously nucleate from haze particles. Smaller crystals tend to form if temperatures are colder and updraft speeds are higher (Kärcher and Lohmann 2002).

Because the split-window infrared method is accurate, if not precise, it may prove most useful for constraining coincident in situ measurements obtained from aircraft. Recent studies have called into question past measurements of ice crystal effective radius because of concerns about the shattering of ice crystals on probe inlets, which would artificially bias in situ effective radius measurements to smaller sizes. Unfortunately, the BTD method is not well-suited for determining whether ice crystals are definitively “large.” But, if ice crystals are determined to be definitively small, and in situ measurements also indicate the particles are small, then it should be possible to make a qualitative constraint of the extent to which shattering is affecting the in situ data.

This approach was applied to in situ measurements from both the CRYSTAL-FACE and MidCiX field campaigns. For MidCiX, no definitive conclusions could be made. However, on two different CRYSTAL-FACE flight cases, the BTD retrieval scheme and airborne probe measurements both indicated that small ice crystals dominated the radiative properties of observed thin clouds. While shattering on ice crystal probes cannot be ruled out, these intercomparisons imply that its influence must have been limited.

Acknowledgments

This work was funded through NASA Research Grant NNX08AH58G. We thank each of the anonymous reviewers whose efforts greatly improved this paper. MODIS data used here are distributed by the Land Processes Distributed Active Archive Center (LP DAAC), located at the U.S. Geological Survey (USGS) Earth Resources Observation and Science (EROS) Center (http://lpdaac.usgs.gov).

REFERENCES

REFERENCES
Baran
,
A.
, and
P.
Francis
,
2004
:
On the radiative properties of cirrus cloud at solar and thermal wavelengths: A test of model consistency using high-resolution airborne radiance measurements.
Quart. J. Roy. Meteor. Soc.
,
130
,
763
778
.
Baran
,
A.
,
P.
Francis
,
L.
Labonnote
, and
M.
Doutriax-Boucher
,
2001
:
A scattering phase function for ice cloud: Tests of applicability using aircraft and satellite multi-angle multi-wavelength radiance measurements.
J. Quant. Spectrosc. Radiat. Transfer
,
127
,
2395
2416
.
Baumgardner
,
D.
,
H.
Johnson
,
W.
Dawson
,
D.
O’Connor
, and
R.
Newton
,
2002
:
The Cloud, Aerosol, and Precipitation Spectrometer (CAPS): A new instrument for cloud investigations.
Atmos. Res.
,
60
,
251
264
.
Christi
,
M.
, and
P.
Gabriel
,
2003
:
Radiant 2.0: A user’s guide.
Colorado State University, 39 pp
.
Cooper
,
S.
,
T.
L’Ecuyer
, and
G.
Stephens
,
2003
:
The impact of explicit cloud boundary information on ice cloud microphysical property retrievals from infrared radiances.
J. Geophys. Res.
,
108
,
4107
.
doi:10.1029/2002JD002611
.
Cooper
,
S.
,
T.
L’Ecuyer
,
P. K.
Gabriel
,
A.
Baran
, and
G.
Stephens
,
2006
:
Objective assessment of the information content of visible and infrared radiance measurements for cloud microphysical property retrievals over the global oceans. Part II: Ice clouds.
J. Appl. Meteor.
,
45
,
42
62
.
Cooper
,
S.
,
T.
L’Ecuyer
,
P. K.
Gabriel
,
A.
Baran
, and
G.
Stephens
,
2007
:
Performance assessment of a five-channel estimation-based ice cloud retrieval scheme for use over the global oceans.
J. Geophys. Res.
,
112
,
D04207
.
doi:10.1029/2006JD007122
.
Davis
,
S.
,
L. M.
Avallone
,
B. H.
Kahn
,
K.
Meyer
, and
D.
Baumgardner
,
2009
:
Comparison of airborne in situ measurements and Moderate Resolution Imaging Spectroradiometer (MODIS) retrievals of cirrus cloud optical and microphysical properties during the Midlatitude Cirrus Experiment (MidCiX).
J. Geophys. Res.
,
114
,
D02203
.
doi:10.1029/2008JD010284
.
Dubuisson
,
P.
,
V.
Giraud
,
J.
Pelon
,
B.
Cadet
, and
P.
Yang
,
2008
:
Sensitivity of thermal infrared radiation at the top of the atmosphere and the surface to ice cloud microphysics.
J. Appl. Meteor. Climatol.
,
47
,
2545
2560
.
Flatau
,
P.
,
1992
:
Scattering by irregular particles in anomalous diffraction and discrete dipole approximations. Ph.D. thesis, Colorado State University
.
Fu
,
Q.
,
M.
Baker
, and
D.
Hartmann
,
2002
:
Tropical cirrus and water vapor: An effective Earth infrared iris feedback?
Atmos. Chem. Phys.
,
2
,
31
37
.
Garrett
,
T.
,
2008
:
Observational quantification of the optical properties of cirrus cloud.
Light Scattering Reviews 3, A. A. Kokhonavsky, Ed., Springer, 3–22
.
Garrett
,
T.
,
H.
Gerber
,
D.
Baumgardner
,
C.
Twohy
, and
E.
Weinstock
,
2003
:
Small, highly reflective ice crystals in low-latitude cirrus.
Geophys. Res. Lett.
,
30
,
2132
.
doi:10.1029/2003GL018153
.
Garrett
,
T.
, and
Coauthors
,
2005
:
Evolution of a Florida cirrus anvil.
J. Atmos. Sci.
,
62
,
2352
2372
.
Gerber
,
H.
,
Y.
Takano
,
T.
Garrett
, and
P.
Hobbs
,
2000
:
Nephelometer measurements of the asymmetry parameter, volume extinction coefficient, and backscatter ratio in Arctic clouds.
J. Atmos. Sci.
,
57
,
3021
3034
.
Heidinger
,
A.
, and
M.
Pavolonis
,
2009
:
Gazing at cirrus clouds for 25 years through a split window. Part I: Methodology.
J. Appl. Meteor. Climatol.
,
48
,
1100
1116
.
Heymsfield
,
A.
,
C.
Schmitt
,
A.
Bansemer
,
G.
van Zadelhoff
,
M.
McGill
,
C.
Twohey
, and
D.
Baumgardner
,
2006
:
Effective radius of ice cloud particle populations derived from aircraft probes.
J. Atmos. Oceanic Technol.
,
23
,
361
380
.
Inoue
,
T.
,
1985
:
On the temperature and effective emissivity determination of semi-transparent cirrus clouds by bi-spectral measurements in the 10 μm window region.
J. Meteor. Soc. Japan
,
63
,
88
89
.
Jensen
,
E. J.
, and
Coauthors
,
2009
:
On the importance of small ice crystals in tropical anvil cirrus.
Atmos. Chem. Phys.
,
9
,
5519
5537
.
Jin
,
Z.
,
T.
Charlock
,
W.
Smith
, and
K.
Rutledge
,
2004
:
A parameterization of ocean surface albedo.
Geophys. Res. Lett.
,
31
,
L22301
.
doi:10.1029/2004GL021180
.
Kärcher
,
B.
, and
U.
Lohmann
,
2002
:
A parameterization of cirrus cloud formation: Homogeneous freezing including effects of aerosol size.
J. Geophys. Res.
,
107
,
4698
.
doi:10.1029/2001JD001429
.
King
,
M.
,
Y.
Kaufman
,
W.
Menzel
, and
D.
Tanre
,
1992
:
Remote sensing of cloud, aerosol, and water vapor properties from the Moderate Resolution Imaging Spectrometer (MODIS.
IEEE Trans. Geosci. Remote Sens.
,
30
,
2
27
.
Korolev
,
A.
, and
G.
Isaac
,
2005
:
Shattering during sampling by OAPS and HVPS. Part I: Snow particles.
J. Atmos. Oceanic Technol.
,
22
,
528
542
.
Kratz
,
D.
,
1995
:
The correlated-k distribution technique as applied to the AVHRR channels.
J. Quant. Spectrosc. Radiat. Transfer
,
64
,
501
517
.
Lawson
,
R.
,
B.
Baker
,
C.
Schmitt
, and
T.
Jensen
,
2001
:
An overview of microphysical properties of Arctic clouds observed in May and July 1998 during FIRE ACE.
J. Geophys. Res.
,
106
,
14989
15014
.
doi:10.1029/2000JD900789
.
L’Ecuyer
,
T.
,
P.
Gabriel
,
K.
Leesman
,
S.
Cooper
, and
G.
Stephens
,
2006
:
Objective assessment of the information content of visible and infrared radiance measurements for cloud microphysical property retrievals over the global oceans. Part I: Liquid clouds.
J. Appl. Meteor.
,
45
,
20
41
.
Lindzen
,
R.
,
M.
Chou
, and
A.
Hou
,
2001
:
Does the Earth have an adaptive infrared iris?
Bull. Amer. Meteor. Soc.
,
82
,
417
432
.
McClatchey
,
F. A.
,
R. W.
Fenn
,
J. E.
Selby
,
F. E.
Volz
, and
J. S.
Goring
,
1972
:
Optical Properties of the Atmosphere, 3rd ed.
Air Force Cambridge Research Laboratory, L. G. Hanscom Field, MA, AFCRL-72-0497, 102 pp
.
McFarquhar
,
G. M.
,
J.
Um
,
M.
Freer
,
D.
Baumgardner
,
G. L.
Kok
, and
G.
Mace
,
2007
:
The importance of small ice crystals to cirrus properties: Observations from the Tropical Warm Pool International Cloud Experiment (TWP-ICE).
Geophys. Res. Lett.
,
34
,
L13803
.
doi:10.1029/2007GL029865
.
Miller
,
S.
,
G.
Stephens
,
C.
Drummond
,
A.
Heidinger
, and
P.
Partain
,
2000
:
A multisensor diagnostic satellite cloud property retrieval scheme.
J. Geophys. Res.
,
105
,
19955
19971
.
Nakajima
,
T.
, and
M.
King
,
1990
:
Determination of the optical thickness and effective particle radius of clouds from reflected solar radiation measurements. Part I: Theory.
J. Atmos. Sci.
,
47
,
1878
1893
.
Prabhakara
,
C.
,
R.
Fraser
,
M.
Wu
, and
R.
Curran
,
1988
:
Thin cirrus clouds: Seasonal distribution over oceans deduced from Nimbus-4 IRIS.
J. Appl. Meteor.
,
27
,
379
399
.
Rapp
,
A.
,
C.
Kummerow
,
W.
Berg
, and
B.
Griffith
,
2005
:
An evaluation of the proposed mechanism of the infrared adaptive iris hypothesis using TRMM VIRS and PR measurements.
Climate Dyn.
,
18
,
4184
4195
.
Rodgers
,
C.
,
2000
:
Inverse Methods for Atmospheric Sounding: Theory and Practice.
World Scientific Publishing, 240 pp
.
Roskovensky
,
J.
,
K.
Liou
,
T.
Garrett
, and
D.
Baumgardner
,
2004
:
Simultaneous retrieval of aerosol and thin cirrus optical depths using MODIS airborne simulator data during CRYSTAL-FACE and CLAMS.
Geophys. Res. Lett.
,
31
,
L18110
.
doi:10.1029/2004GL020457
.
Shannon
,
C.
, and
W.
Weaver
,
1949
:
The Mathematical Theory of Communication.
University of Illinois Press
.
Stephens
,
G. L.
,
1994
:
Remote Sensing of the Lower Atmosphere: An Introduction.
Oxford University Press, 544 pp
.
Stephens
,
G. L.
,
S-C.
Tsay
,
J. P. W.
Stackhouse
, and
P. J.
Flatau
,
1990
:
The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback.
J. Atmos. Sci.
,
47
,
1742
1753
.
Yang
,
P.
, and
K.
Liou
,
1998
:
Single scattering properties of complex ice crystals in terrestrial atmospheres.
Contrib. Atmos. Phys.
,
71
,
223
248
.
Yang
,
P.
,
K.
Liou
,
K.
Wyser
, and
D.
Mitchell
,
2000
:
Parameterization of the scattering and absorption properties of individual ice crystals.
J. Geophys. Res.
,
105
,
4699
4718
.
Yang
,
P.
,
B.
Baum
,
A.
Heymsfield
,
Y.
Hu
,
H.
Huang
,
S.
Tsay
, and
S.
Ackerman
,
2003
:
Single-scattering properties of droxtals.
J. Quant. Spectrosc. Radiat. Transfer
,
79
,
1159
1169
.
Yang
,
P.
,
H.
Wei
,
H.
Huang
,
B.
Baum
,
Y.
Hu
,
G.
Katawar
,
M.
Mischenko
, and
Q.
Fu
,
2005
:
Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region.
Appl. Opt.
,
44
,
2545
2560
.

Footnotes

Corresponding author address: Steven Cooper, Department of Atmospheric Science, 135 S. 1460 East Rm. 819 (WBB), University of Utah, Salt Lake City, UT 84112. Email: steve.cooper@utah.edu