Introduction

The climate of the Antarctic Plateau, like everywhere else on the earth, is strongly affected by clouds, and the clouds are, in turn, affected by other meteorological variables. The radiative effects of clouds are determined by the clouds' vertical location, optical thickness, and particle sizes. Radiation measurements correspondingly can be used to infer these properties.

We use longwave emission spectra measured at the surface (Walden et al. 1998) to infer cloud-base heights, optical thicknesses, and particle sizes. Measurements made twice daily through one full year are used to obtain frequency distributions and seasonal cycles of these cloud properties. The measurements were made at only one location (South Pole Station), but because of the horizontal uniformity of the ice-sheet surface they are probably representative of a large area. We therefore offer them as an annual cycle of cloud properties for the East Antarctic Plateau, which should be useful for climate models of the Antarctic and surrounding regions (Simmonds 1990; Lubin et al. 1998). The determination of optical thicknesses and particle sizes is discussed in this paper (Part II); the method requires knowledge of the cloud-base height, obtained from Part I (Mahesh et al. 2001, this issue).

This study is related to others that develop remote sensing techniques using infrared spectral radiance measurements to determine cloud properties. A ground-based study of cirrus clouds was carried out in Wisconsin by Collard et al. (1995) during the First International Satellite Cloud Climatology Project Regional Experiment, Phase II. As in this study, the authors used window radiances together with model calculations to obtain cloud particle effective radii. These techniques have also been applied to data from a coastal Antarctic station (Lubin 1994). A year-long dataset of cloud particle sizes and optical depths over the Antarctic Plateau has not previously been compiled, but short-duration studies have been conducted. Stone (1993) compared emissivities obtained from radiometersonde data with theoretically computed values for model clouds with various particle sizes and ice water contents (IWCs), but his study was based on only eight observations of winter clouds. His calculations were made with cloud particles represented as spheres with surface areas equal to those of the ice crystals, yielding radii of 4–16 μm and IWCs of 0.3–6 mg m⁻³. Particle sizes have also been obtained previously from ice crystals collected over the plateau (Kikuchi and Hogan 1979), but these were limited to summer.

The determination of particle sizes and optical depths utilizes three pieces of spectral information: the transmittance of the cloud determined from spectral radiances in the 9.6-μm ozone band, and cloud emissivities obtained at two microwindows near 10 and 11 μm in the atmospheric window. The first two sections of this paper describe the procedures to determine these quantities. These are followed by the algorithm to determine particle sizes and optical depths using both the emissivities and transmittances. The annual cycle of these properties is then presented, followed by a discussion of the findings. The particle sizes obtained from the spectral measurements are compared with values obtained from near-simultaneous photographs of falling ice crystals.

Retrieval of ozone-band transmittance

Description of the retrieval technique

Ozone emission from above a cloud is often seen in our spectral measurements at the surface, because the cloud's optical thickness is usually not large enough to obscure this signal. Figure 1 shows a typical measurement sequence made under a cloud, in which emission from ozone above the cloud in the 9.6-μm band is detectable at the surface at all three viewing angles at which observations were made. However, at 75° the ozone signal is much less prominent than at 45°, because the path length through the cloud is much longer at 75°; the radiance itself is greater at the larger viewing angle because of cloud emission. Grund et al. (1990) showed that such incomplete attenuation of the ozone signal can be used to estimate cloud optical depths if the ozone signal is compared with the signal that would be recorded by the instrument in the absence of a cloud but under otherwise identical atmospheric conditions. This is accomplished by interpolating across the ozone band between frequencies that are dominated by emission from the cloud only. This background signal is subtracted from the observed spectrum within the ozone band. Then the resulting difference is used to determine the transmittance of the cloud.

The radiance I_obs received by the interferometer can be expressed as a sum of six terms. Four of these represent contributions to the measured radiance from ozone, and the other two are independent of the ozone profile. This can be written mathematically as

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where t(p_x, p_y) is the transmittance from pressure level x to pressure level y, p_B is the pressure at cloud base, p_T is the pressure at cloud top, p_s is the surface pressure, B(T) is the Planck radiance at temperature T, ε_c is the cloud emissivity, r_c is the cloud base reflectance, t_c is the cloud transmittance, t_o(p) is the cloud transmittance for downward emission by in-cloud ozone, and ε_s is the emissivity of snow. The infrared emissivity of snow is greater than 0.98 in the 11-μm window (Dozier and Warren 1982; Grenfell 1998). As a result, very little cloud radiance is reflected between the surface and cloud base, and the contribution of multiple reflections to the observed downward radiance can be ignored.

The first term on the right side of Eq. (1) is the downward emission by ozone in the atmosphere below the cloud. Part of the upward emission from this ozone is reflected downward by the cloud; this radiance is term 2. The third term is the fraction of the emission from ozone above the cloud that is transmitted through the cloud to the surface. The fourth term is the downward emission from ozone within the cloud itself, the fifth term is the nonozone contribution to radiance from the cloud (i.e., emission by ice crystals), and the sixth term is the portion of the upward radiance from the ground that is reflected back to the instrument by the cloud.

Term 1 can be calculated using a radiative transfer model if the cloud-base height (from Part I) and the ozone concentration as a function of altitude are known. (The vertical profile of ozone over the South Pole is measured at least once per week by ozonesondes throughout the year. During the spring when the ozone concentration changes more rapidly, ozonesondes are launched every three days.) Term 2 is usually much smaller than term 1, because the reflectance of the cloud at 9.6 μm is at most 2%–3%. Ozone in the lower troposphere is less than 10% of the total column ozone and is usually much less because the clouds are low. So term 1 is small, and term 2 is only about 2% of term 1; therefore term 2 is ignored.

Calculation of the cloud transmittance

The integrals in terms 3 and 4 are computed using a radiative transfer model. Using the assumed value for t_o, the remaining unknown in Eq. (1) is the transmittance t_c of the cloud. After combination of the background terms, Eq. (1) can be written as

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where Σ₃ and Σ₄ are the integrals in terms 3 and 4 [after removing t_o(p) from the integrand of term 4]. Equation (2) is then solved for t_c at each wavenumber (Fig. 2c).

Window emissivities

Figure 4 shows absorption, scattering, and extinction efficiencies (Q_abs, Q_scat, and Q_ext) at six different microwindows in the 11-μm window region, over a range of particle sizes, computed using Mie theory (Wiscombe 1979, 1980) for ice spheres. The complex refractive index of ice was taken from Warren (1984). The microwindows were chosen at locations where absorption by atmospheric gases is negligible. The absorption efficiency varies with cloud particle size at all wavenumbers, but is more sensitive at some wavenumbers than at others. Variation in Q_abs with particle size is necessary to determine the cloud particle effective radius. Although there is sufficient variation at all wavenumbers to distinguish particle radii less than 10 μm, it is only at 988 cm⁻¹ that variation in Q_abs continues monotonically to radii of 20–30 μm. The ability to obtain unique solutions, as well as the two extremes of sensitivity to a broad range of particles (1–25 μm) can be achieved by using just the two microwindows at 903 and 988 cm⁻¹. Further, most of the variation in emissivity between 810 and 1000 cm⁻¹ occurs between 903 and 988 cm⁻¹ (Fig. 5), making these wavenumbers adequately representative of the variation in absorption by ice across the window.

Figures 6a,b show calculations of cloud emissivity at ν = 903 and 988 cm⁻¹. Extinction efficiencies, single-scattering albedos, and phase-function moments were calculated for ice spheres using Mie theory. Morley et al. (1989) had previously reported that clouds over the Antarctic Plateau were mostly made of ice particles. For this work, the spectra were all analyzed as if the clouds consisted of ice crystals, although some of the summer clouds probably contained supercooled liquid water droplets. Cloud emissivities were computed using the Discrete Ordinates Radiative Transfer code (DISORT; Stamnes et al. 1988). Thermal emission radiances I_calc from clouds were computed using 40 streams in DISORT; the cloud emissivities were then computed using cloud base temperatures T_c obtained with information from Part I as

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However, I_calc includes not only emission from the cloud but also emission from the surface, which is reflected back to the instrument by the cloud. Therefore, the emissivity obtained from Eq. (3) is an “effective” emissivity, which includes reflection, which in the infrared is typically about 2%. Obtaining the effective emissivity using Eq. (3) and implicitly including this additional radiance makes the calculations comparable to our measurements of downward radiance, which also include reflection. For the DISORT computation, the snow surface temperature was set equal to the cloud-base temperature, but because of the small reflectance of the cloud this assumption does not significantly alter the results.

Mie and DISORT calculations were made for clouds with several different particle radii (r_eff between 0.5 and 100 μm) and many values of optical depth in the geometric-optics limit (τ_g between 0.01 and 100). The “effective radius” r_eff is the area-weighted mean radius, introduced by Hansen and Travis (1974). The optical depth in the geometric-optics limit is used to describe the clouds because it is a quantity that is independent of wavenumber. For particle sizes greater than 5 μm, the emissivity at 903 cm⁻¹ (ε₁) is insensitive to particle size, whereas at 988 cm⁻¹ the sensitivity to particle size extends up to particles of r_eff = 25 μm. Figure 6c shows that transmittance in the ozone band (t_c) is as sensitive to particle size as the emissivity at 988 cm⁻¹ (ε₂). This variation in sensitivity with wavenumber means that the two desired quantities (r_eff and τ_g) can be inferred from the three measured quantities (ε₁, ε₂, and t_c).

The computed emissivities and their difference (ε₁ − ε₂) are shown as contour plots in Fig. 7 over a range of cloud thicknesses (expressed both as optical depths and as ice water paths). For r_eff greater than 25 μm, ε₁ − ε₂ is negative; for r_eff less than 25 μm it is positive. Over a range of particle sizes and geometric optical depths, the two emissivities together indicate specific particle radii and optical depths. Model computations of those quantities can then be compared with observations made under the cloud to obtain r_eff and τ_g.

The effective emissivities are determined from the spectral radiance measurements and the cloud-base temperature. To reduce the effect of random measurement errors, the emissivities ε₁ and ε₂ for each observation are obtained as averages over 3-cm⁻¹ intervals centered at 903 and 988 cm⁻¹, respectively, rather than at single wavenumbers. The temperature at cloud base is obtained from radiosonde data together with the cloud-base height determined in Part I.

Minimization routine

From each measured radiance spectrum, we obtain three different quantities, the two effective emissivities and the transmittance in the ozone band. These quantities can now be compared with corresponding values computed over a wide range of particle sizes and optical depths. This approach—comparing observed emissivities and transmittances to model calculations—is similar to that used by others (Smith et al. 1993; DeSlover et al. 1999), but it uses fewer microwindows in the atmospheric windows than they did.

In the minimization algorithm, the emissivities and transmittance are weighted according to the reciprocal of the relative magnitude of their uncertainties. Uncertainty in cloud-base height determined by radiance ratioing propagates to uncertainty in cloud-base temperature and thereby to uncertainty in emissivities determined at the two wavenumbers. Uncertainties in ozone-band transmittance also result from errors in spectral radiance measurements within the band, and from uncertainties in determining the emission from stratospheric ozone. Day-to-day variability in stratospheric ozone emission is nearly constant at about 1 mW m⁻² sr⁻¹ (cm⁻¹)⁻¹ (1 radiance unit; RU) throughout the year (Fig. 8). However, the monthly average emission undergoes a large seasonal cycle, ranging from 16–18 RU in summer to 5 RU in winter and spring. As a result, the uncertainties in ozone transmittance values due to uncertainty in the ozone profile are larger in winter and spring (∼20%) than in summer and autumn (<10%).

Uncertainties in the emissivities were estimated to be typically 5%–8% of the emissivity values themselves; these result mostly from uncertainties in cloud-base temperature and uncertainties due to measurement error. Uncertainties in the measured radiances were determined by Walden (1995). Errors in cloud-base temperature correspond primarily to errors in cloud-base heights, which are estimated in Table 1 of Part I. Both sources of uncertainty are, however, correlated across the window region; that is, errors in ε₁ are correlated with errors in ε₂. As a result, the difference Δε ≡ (ε₁ − ε₂) can be estimated more accurately than either ε₁ or ε₂. The algorithm to minimize the differences between observations and calculations takes advantage of this.

In the minimization process, the individual quantities in the vectors are then weighted according to their relative accuracies; Δε is weighted 5 times as much as ε₁. The relative accuracy of ε₁ and t_c is determined as follows. The emissivity at 903 cm⁻¹ depends on the assumed cloud-base temperature; uncertainties in this quantity result from uncertainties in the temperature. The cloud-base temperature is perturbed by its estimated uncertainty of 3 K, and the corresponding change in ε₁ is determined. The transmittance in the ozone band is most sensitive to day-to-day variation in stratospheric ozone emission. For each observation made under cloudy skies, the uncertainty in transmittance due the variability in stratospheric ozone emission is determined. Uncertainties in ε₁ and t_c are then compared and assigned relative weights. The combination of particle radius and geometric optical depth is chosen such that the weighted combined difference in the measured and calculated values of ε₁, Δε, and t_c is minimized. The values of particle radius and geometric optical depth are determined at all viewing angles. When the same cloud is seen at more than one viewing angle, the angle at which the transmittance is closest to 0.5 is used. This is because τ is most accurately determined where the derivative d[log(τ secθ)]/dt is least, which occurs at t = 0.5.

Results

Figure 9 shows the optical depths and ice water paths (IWP) obtained for each cloud during the year; Fig. 10 shows histograms of the same quantities. These are related by

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where ρ_ice is the density of pure ice, 917 kg m⁻³. Optical depths are shown for all observations in which clouds were detected, but IWP are shown only for those observations in which both particle size and optical depth could be determined. This was possible in three-fourths of the observations; in other cases, only a lower limit to either the optical depth or particle size could be obtained. Fewer than 10% of the clouds have τ_g > 5, and about two-thirds have τ_g < 1. The histograms show frequencies of observations separately for the winter and nonwinter months. Optical depths greater than 5 are twice as common in nonwinter months as in winter months.

Stone (1993) obtained similar values from radiometersonde measurements of upward and downward fluxes at the South Pole. He determined cloud-top and -base heights of eight wintertime clouds from vertical profiles of flux and temperature. He then estimated the emissivity and optical depths of the clouds by comparing the observations to model comparisons made at 10.8-μm wavelength; he found the average emissivity to be 0.6 and the average optical depth to be 1.0. These values are consistent with our results. Stone's model calculations, which used ice spheres, implied particle radii from 4 to 16 μm (also consistent with our results shown below), and IWCs of 0.3 to 6 mg m⁻³.

We considered the possibility that the smallest optical depths we obtain may in fact be of Pinatubo aerosol rather than clouds, but rejected it. The infrared optical depths of stratospheric aerosol are between one-quarter and one-half of the visible optical depths (Lacis et al. 1992), which through most of 1992 were about 0.1 or less (E. Dutton 1994, personal communication); measurements of aerosol under cloud-free conditions lie within our threshold for cloud detection (optical depth of 0.06 or less; see Part I).

Figure 10 shows a predominance of thin clouds (τ_g < 2). This finding contrasts with results from the coast of Antarctica, where Ricchiazzi et al. (1995), using solar irradiance data from a ground-based multichannel radiometer, found τ_g ∼ 20 for clouds at Palmer Station (65°S, 64°W). Such clouds are effectively semi-infinite in the infrared; our methods would therefore not be appropriate for determining their optical thicknesses.

The effective particle radii r_eff obtained from the spectral measurements are shown in Fig. 11; histograms of these values are shown, for winter and nonwinter months separately, in Fig. 12. The median value of r_eff, computed including particles larger than 25 μm, is 15.2 μm. As suggested by Fig. 7, when r_eff is greater than 25 μm an accurate determination of r_eff is not possible, so only a lower limit is indicated in these cases. Approximately 20% of the clouds have retrieved r_eff > 25 μm. Clouds with r_eff > 25 μm are rarely seen in winter, and clouds with r_eff < 10 μm are rarely seen during the rest of the year. Lubin and Harper (1996) estimated effective radii using the Advanced Very High Resolution Radiometer channels at 11 and 12 μm and also found summer crystals to be larger than those in the winter. However, the values they obtained (mean r_eff of 12.3 μm in summer and 5.6 μm in winter) are smaller than the values of r_eff we obtain. This may be because crystals at cloud top are smaller than at cloud bottom. Precipitating ice crystals in summer were measured at South Pole Station by Kikuchi and Hogan (1979). For the 1200 crystals they sampled, the average c-axis length was 90 μm, and the ratio c/a typically varied between 2.5 and 5.5; we relate these dimensions to an effective radius in section 6a.

Uncertainties in the emissivities at 903 and 988 cm⁻¹ and transmittance in the ozone band produce uncertainties in the derived particle radius and optical depth. The uncertainties in the emissivities and transmittance were estimated, and the particle radius r^′_eff and optical depth τ^′_g were computed after the values of ε₁, ε₂, and t_c were perturbed by these uncertainties and were compared with r_eff and τ_g, respectively. The “resolution” of r_eff and τ_g was then determined as |ln(r_eff/r^′_eff)| and |ln(τ_g/τ^′_g)|, respectively, and are shown in Fig. 13. For small values of resolution, the resolution is the same as the fractional uncertainty; for example, the 0.2 contour means 22% uncertainty, and the 0.5 contour means 65% uncertainty. Smaller particle sizes are generally more reliably determined than larger particle sizes; this is expected from Fig. 6, which shows that particle radii larger than 25 μm cannot be distinguished. Emissivity errors produced by representing nonspherical crystals as equal volume-to-area-ratio spheres (discussed below) are small (Grenfell and Warren 1999; Fu et al. 1998). Optical depths are not very sensitive to errors in emissivity and t_c; so τ_g can be reliably determined over a broad range of cloud optical thicknesses.

Figure 14 shows a comparison of particle sizes and optical depths obtained for the same clouds at two different viewing angles. As expected, the agreement is poor for particle sizes greater than 20–25 μm, whereas smaller particle sizes determined at different viewing angles are very similar. The values can also be different if two different clouds at different heights are being viewed at the two angles.

Comparison with independent observations

Conclusions

A method has been developed for ground-based remote sensing of optical depth τ and effective ice particle radius r_eff for clouds over the Antarctic Plateau. To infer these two quantities the method uses three measurements: cloud emissivity at two wavelengths in the infrared atmospheric windows and cloud transmittance of emission by stratospheric ozone. The inference of τ becomes inaccurate for τ greater than 5 (Fig. 13b), so its utility is limited to thin clouds, which, however, do predominate over the Antarctic Plateau. The inference of r_eff becomes inaccurate for r_eff greater than 25 μm (Fig. 14a). We do not have independent measurements of τ that could be used to assess the accuracy of the optical depth retrieval. However, we do have direct measurements of crystal dimensions from photographs, and they are comparable to the remotely sensed effective radii if the equal-V/A prescription is used.

Cloud optical thickness over the Antarctic Plateau is considerably less than on the coast. Whereas clouds on the coast typically have τ greater than 20, nearly two-thirds of the clouds detected at the South Pole have τ less than 1. There is a seasonal cycle in optical depth on the plateau, with thick clouds being less common in winter.

Effective cloud particle radius could be estimated in 80% of the observations; in the remaining 20%, only a lower limit of 25 μm could be established. The median r_eff is 15.2 μm; it is smaller in winter than in summer. This tendency is also seen in photomicrographs of falling snow crystals: the winter crystals we photographed are smaller than the summer crystals photographed by Kikuchi and Hogan (1979) and by Tape (1994).

The three tendencies we find (larger crystals in summer than in winter, larger optical depths in summer than in winter, and larger optical depths at the coast than in the interior) conform to expectation, because the atmosphere contains more water vapor at the coast than in the interior and more water vapor in summer than in winter.

Note added in proof: Direct sampling of cloud particles from a tethered balloon at South Pole Station in a recent field experiment (summer 2000/01) has shown several examples of clouds consisting mostly or entirely of supercooled liquid water droplets at temperatures −25° to −35°C. Such water clouds are likely to have occurred in 1992 as well during the summer season (December–January). Our inference of τ_g and r_eff in summer may be sensitive to the assumption of ice phase; this question will be examined in future work.