The effective scene temperature, or “brightness temperature,” measured in channel 3 (3.5–3.9 μm) of the Advanced Very High Resolution Radiometer (AVHRR) is shown to be sensitive, in principle, to the effective particle size of snow grains on the Antarctic plateau, over the range of snow grain sizes reported in field studies. In conjunction with a discrete ordinate method radiative transfer model that couples the polar atmosphere with a scattering and absorbing snowpack, the thermal infrared channels of the AVHRR instrument can, therefore, be used to estimate effective grain size at the snow surface over Antarctica. This is subject to uncertainties related to the modeled top-of-atmosphere bidirectional reflectance distribution function resulting from the possible presence of sastrugi and to lack of complete knowledge of snow crystal shapes and habits as they influence the scattering phase function. However, when applied to NOAA-11 and NOAA-12 AVHRR data from 1992, the snow grain effective radii of order 50 μm are retrieved, consistent with field observations, with no apparent discontinuity between two spacecraft having different viewing geometries. Retrieved snow grain effective radii are 10–20-μm larger when the snow grains are modeled as hexagonal solid columns rather than as spheres with a Henyey–Greenstein phase function. Despite the above-mentioned uncertainties, the retrievals are consistent enough that one should be able to monitor climatically significant changes in surface snow grain size due to major precipitation events. It is also shown that a realistic representation of the surface snow grain size is critical when retrieving the optical depth and effective particle radius of clouds for the optically thin clouds most frequently encountered over the Antarctic plateau.
The time series of multispectral imagery from meteorological satellites, such as the National Oceanic and Atmospheric Administration (NOAA) polar orbiters, now spans more than two decades, and, thus, offers an opportunity to study polar atmospheric processes in the context of climate change. The International Satellite Cloud Climatology Project (ISCCP) is taking advantage of this long time series on a global basis (Rossow and Lacis 1990), and ISCCP data products have already been applied to the Arctic (Schweiger and Key 1994). Advanced Very High Resolution Radiometer (AVHRR) data from the NOAA polar orbiters have been applied with success to the retrieval of Arctic cloud optical properties and the radiation budget. The AVHRR's multispectral capability enables useful retrievals of cloud amount (Ebert 1987), cloud thermodynamic phase (Key and Intrieri 2000), and cloud optical depth and effective particle size (Han et al. 1999; Dong et al. 2001; Xiong et al. 2002).
To date, there have been fewer investigations of the Antarctic atmosphere's radiative properties using AVHRR, but there are some compelling scientific issues that lend themselves to study with this type of sensor; an important one concerns the influence of continental Antarctic cloud cover on Southern Hemisphere climate. Using climate model simulations, Lubin et al. (1998) have shown how Antarctic surface temperatures, and surface pressure fields over the Southern Ocean, are sensitive to cloud microphysical properties over the Antarctic plateau. The microphysical and radiative properties of clouds over the high Antarctic plateau are coming under rigorous study from current field programs based at the South Pole (Mahesh et al. 2001a,b), and multispectral satellite imagery has the potential to generalize these findings to larger geographical areas and longer time scales.
This investigation of Antarctic snow properties is primarily motivated by the need to properly represent the Antarctic snow surface in cloud retrieval algorithms. However, there are other good reasons to develop methods to monitor snow properties over the Antarctic continent from space. Because Antarctic interior temperatures are always well below freezing and the visible albedo remains high and is much less variable than in the Arctic, much less attention has been paid to the potential role of changes in snow cover and properties on climate in this region than in northern polar regions. However, the Antarctic surface energy budget is dominated by radiation, and most of the shortwave absorption by the snow takes place in the near-infrared (NIR) (Carlson and Arakelian 1993), where reflectances are strongly influenced by snow surface properties, such as grain size. Thus, even if the snow does not melt, changes in its microphysical and optical properties could have a large impact on the climate. A recent study of the Greenland Ice Sheet (Nolin and Stroeve 1997) demonstrated the need for climate models to more accurately represent snow properties and snowpack energy balance, especially for studying the ice-albedo feedback. Current questions about the Antarctic ice-mass balance might also be addressed by satellite sensors that provide information about changes in surface properties in recent decades.
The potential utility of AVHRR over the Antarctic continent can best be introduced by comparison with existing work for the Arctic. The fundamental problem with high-latitude satellite cloud remote sensing using shortwave or middle-infrared imagery involves the lack of radiometric contrast between high-latitude surfaces and clouds. This is due to high surface albedos, which are easily confused with cloud cover in visible wavelength imagery, and temperature inversions or isothermal atmospheres, which can forestall identification of cloud cover in middle-infrared imagery. However, the Arctic Ocean surface offers some mitigating characteristics. During much of the sunlit part of the year, Arctic sea ice cover is a complicated surface, exhibiting leads, melt ponds, variable snow cover, and other textural features, which together have the overall effect of lowering the shortwave albedo below that of pure snow (e.g., Grenfell and Perovich 1984). The Arctic sea surface albedo is sufficiently moderate at near-infrared wavelengths that AVHRR channel-2 data (0.72–1.00 μm) can be used to infer cloud optical depth (Han et al. 1999). AVHRR channel-3 data (3.5–3.9 μm), which is used successfully to retrieve Arctic cloud amount (Ebert 1987) and thermodynamic phase (Key and Intrieri 2000), can then be used in conjunction with channel-4 data (11 μm) to retrieve effective droplet radius and cloud-top temperature (Han et al. 1999; Xiong et al. 2002). Over high ice sheets, such as those of Greenland and continental Antarctica, the noticeably higher albedo and greater spatial uniformity of the pristine snow cover render AVHRR channel 2 much less sensitive to the optical depth of overlying clouds. Indeed, the Greenland and Antarctic Ice Sheets have previously been studied as potential radiometric calibration sources for the AVHRR shortwave channels (Masonis and Warren 2001). To learn anything about cloud properties over such surfaces, we must utilize wavelengths longer than 1.0 μm where liquid water droplets, ice cloud particles, and snow grains absorb, as well as scatter, radiation.
In this study, we compare satellite-measured radiances with detailed radiative transfer calculations and show that AVHRR infrared measurements are sensitive to the details of the Antarctic snow cover. The results suggest the potential for monitoring changes in snow grain size over time with AVHRR, and also inform us how the lower boundary condition of an Antarctic cloud retrieval algorithm must be treated.
In this investigation, we consider AVHRR imagery over the South Pole sector of the Antarctic plateau, between November through December and January through March, of 1992. This particular year is chosen because a useful set of Fourier Transform Infrared (FTIR) surface-based remote sensing measurements exists for comparison with the cloud retrieval algorithms we are developing (Mahesh et al. 2001a,b). Over the South Pole, the orbital inclination of the NOAA spacecraft yields a nadir viewing angle that is nearly constant at 55°. This is a larger viewing angle than optimal, given the bidirectional reflectance distribution function (BRDF) considerations discussed below, but it is not too large to prevent useful retrievals. As discussed below, our in situ validation data for 1992 are very limited, but the South Pole remains a logical choice for algorithm development because it is the site of the major research station on the Antarctic plateau. Future climatological research projects at the South Pole offer the promise of useful validation data.
The AVHRR is a five-channel line-scanning radiometer, having a nadir ground instantaneous field of view (GIFOV) of 1.1 km. The wavelength range of channel 1 (0.58–0.68 μm) is difficult to utilize for high-latitude cloud remote sensing because the underlying surface albedos are generally large enough to obscure the effects of overlying cloud opacity (Grenfell and Perovich 1984) when interpreting the top-of-atmosphere (TOA) radiance. Han et al. (1999) were able to use channel 2 (0.72–1.00 μm) for cloud optical depth retrieval over Arctic sea ice surfaces. These surfaces, usually involving a mixture of snow of different ages, bare sea ice, and melt ponds, have moderately large albedos that begin to drop noticeably for wavelengths longer than ∼0.8 μm (Grenfell and Perovich 1984), and, hence, there remains enough useful sensitivity in TOA radiance to cloud opacity. However, snow cover over the high Antarctic plateau is much more spatially uniform and pristine than over Arctic sea ice, and its albedo remains greater than 0.8 for wavelengths as long as 1.0 μm (Warren 1982). Thus, we cannot expect much utility in channel 2 for cloud property retrieval over the Antarctic continent.
In this study we use channels 3 and 4, which have nominal spectral bandwidths 3.5–3.9 μm and 10–11 μm, respectively. For cloud studies, it will also be necessary to use channel 5 (11–12 μm). In channel 3, the surface albedo of snow is not only small, but is also sensitive to the effective snow grain size as discussed below. The TOA radiance measured in channel 3 contains both solar backscattered radiation and thermally emitted radiation from the scene. Snow surfaces in the channel-4 and -5 spectral intervals have high but nonunit emissivities (Dozier and Warren 1982; Salisbury et al. 1994), and the TOA radiances in channel 4 are used in our snow retrieval algorithm. Channels 3, 4, and 5 are all calibrated with reference to an onboard blackbody source, and the absolute radiometric calibration accuracy is generally recognized as ±1 K.
The AVHRR data used in this study were collected using the U.S. National Science Foundation Office of Polar Programs (OPP) satellite-tracking equipment at McMurdo and Palmer Stations. These data are archived at the Scripps Institution of Oceanography's Arctic and Antarctic Research Center (AARC). From the raw satellite telemetry, an image containing a ∼104 km2 area centered about the South Pole was extracted, geolocated, and reduced from detector counts to radiance (W m−2 sr−1) and effective scene temperature, or “brightness temperature” (K), using the SeaSpace, Inc., TeraScan satellite data analysis package. Radiometric calibration procedures in this package include the latest updates on sensor performance by NOAA, and also correct for the known nonlinearities in detector response (Weinreb et al. 1990). A total of 98 images were analyzed from the NOAA-11 and NOAA-12 spacecraft, and all had some cloud-free regions near the South Pole as determined by the multispectral cloud detection technique of Yamanouchi and Kawaguchi (1992).
Modeling the Antarctic snow–atmosphere system
Following Wiscombe and Warren (1980), we represent the snow as layers of ice particles that scatter radiation independently. Multiple scattering in the snowpack is evaluated with the discrete ordinate method (Stamnes et al. 1988). This model is, thus, similar to previously applied snow models, such as those of Nolin (1998) and Han et al. (1999). A model atmosphere, including gaseous absorption and Rayleigh scattering, is included above the snow-scattering layers, as discussed in Lubin et al. (1996). Representative values of snow density were taken from fieldwork reported by Grenfell et al. (1994). The complex refractive index of ice is specified from tabulations provided by Prof. S. G. Warren and Dr. W. J. Wiscombe (available online under anonymous file transfer protocol to ftp://climate.gsfc.nasa.gov/pub/wiscombe/Refrac_Index/ICE/), and based on Warren (1984), Kou et al. (1994), and Perovich and Govoni (1991).
The size distribution of the snow grains is modeled according to a gamma distribution (Stone et al. 1990):
where n(r) is the number of particles in the size range from radius r to r + dr. The parameter a is analogous to the effective radius of the distribution, and parameter b, related to the dispersion, is set to 0.1. This distribution is not based on observations, and its main purpose is to average out peaks in the phase function that would result from an individual particle. The particular shape of the size distribution is unimportant, because the single scattering properties of the distribution depend mostly on the effective radius, as was shown for water clouds by Hansen and Pollack (1970). More recently, by analyzing field observations of cirrus clouds, Macke et al. (1998) found that the details of the size distribution were usually less important than the crystal size or habit. This suggests that this particular choice of size distribution will not significantly limit the applicability of our results. Using usual properties of the gamma functions, one can show that Eq. (1) implies
in which case the parameter a constitutes a common definition of the effective radius re of a size distribution (e.g., Parol et al. 1991). It is worth noting that various definitions of the effective radius have been used, which can complicate the comparison of different studies (McFarquhar and Heymsfield 1998).
Vertical structure of the snowpack
An important issue involves the detail required in the vertical structure of the model snowpack to accurately calculate radiances in the three AVHRR instrument channels. Several in situ studies have reported an increase in snow grain size with depth in natural snow (e.g., Wiscombe and Warren 1980; Grenfell et al. 1994). Wiscombe and Warren (1980) show that due to large changes in the absorption coefficient of ice with wavelength, the penetration depth of photons in the snowpack is much smaller at near-infrared (0.8–2.2 μm) rather than visible wavelengths. As a consequence, visible wavelength photons will penetrate deeper into a snowpack, and, thus, will tend to be scattered by larger grains. To match albedo measurements at both visible and near-infrared wavelengths, two layers were needed in their snow model: a thin upper layer, whose effective radius is adjusted to match near-infrared measurements, and an underlying layer of larger grains, not reached by near-infrared photons, to match the visible wavelength data.
It is worth investigating if the differences in volume extinction and single scattering albedo between channels 3 and 4 result in large penetration depth differences that would imply the need for several layers in the snow model. Figure 1 shows brightness temperatures calculated in the AVHRR instrument channels for typical viewing conditions, using a layer of snow of increasing depth overlying a semi-infinite layer of unit emissivity. For these calculations we used Mie theory to specify the single scattering albedo, asymmetry factor, and volume extinction, but for the phase function (see the discussion in the following section) a Henyey–Greenstein (HG) function is used (Henyey and Greenstein 1941). The basic conclusions of Fig. 1 hold for more complicated crystal shapes. It can be seen that the channel-3 radiance is very sensitive to snow grain size up to re ∼ 50 μm, whereas emissivity changes in channel 4 are small and result in smaller brightness temperature differences. For all realistic values of grain size, radiances in channels 3 and 4 have converged to their asymptotic value when the snow layer is thicker than about a millimeter. Any structure deeper in the snowpack is invisible in these measurements. For both channel-3 and -4 radiances, which are sensitive to approximately the same depth of snow, measurements of radiance at these two wavelengths depend essentially on the same grain size. We, therefore, do not need an additional degree of freedom in the model, in the form of a second layer's adjustable effective radius, to match measurements among the AVHRR thermal infrared channels.
Single scattering by snow grains
Because we are interpreting radiances from a narrow-field-of-view instrument, it is critical that the model realistically simulate the BRDF of the snow. Although this type of model has been shown to suitably reproduce the broadband albedo (e.g., Han et al. 1999) and the spectral hemispherical albedo of snow (e.g., Wiscombe and Warren 1980; Grenfell et al. 1994; Fily et al. 1998), several authors have reported deficiencies in modeling the BRDF.
One problem involves the correct representation of the single scattering properties of snow grains. The relative abundance of various crystal shapes in Antarctic snow is unknown. Because the single scattering properties strongly depend on crystal shape, there is considerable uncertainty as to the real single scattering parameters of snow crystals. Several studies have shown, however, that this type of plane-parallel, discrete ordinate model correctly reproduces the broadband albedo (Han et al. 1999) and spectral albedo of natural snow (Wiscombe and Warren 1980; Grenfell et al. 1994; Fily et al. 1998). This agreement suggests that the single scattering albedo, asymmetry parameter, and extinction coefficient from Mie theory are not unreasonable. However, the broadband and spectral albedo are not overly sensitive to the phase function of individual snow grains (Aoki et al. 2000), and, thus, the phase function representation in albedo calculations could contain large errors. The BRDF, on the other hand, can be very sensitive to the phase function of individual snow grains, especially in the near-infrared where, due to strong absorption by ice, most photons emerging from the snowpack have undergone only low-order scattering (or else they would have been absorbed).
The calculation of scattering phase functions for various ice crystal shapes has seen much progress in the past decade, mostly motivated by the remote sensing of ice clouds (e.g., Mischencko et al. 1999). Although several methods have been developed to calculate the phase function for increasingly complex shapes of ice crystals (e.g., Takano and Liou 1989; Draine and Flatau 1994; Macke et al. 1998), the lack of data on the relative occurrence of various habits still impedes the modeling of natural scattering layers.
Key et al. (2002) integrated theoretical individual scattering properties from Yang et al. (2000) over size distributions observed in cirrus clouds, and obtained a parameterization of the single scattering albedo, asymmetry parameter, and volume-weighted extinction coefficient as a function of particle shape and effective radius. We use these parameters obtained by Key et al. (2002) with an HG phase function.
From comparison with mountain snow observations, Leroux et al. (1998) found significant improvement in the BRDF when using hexagonal crystals in the model rather than spheres with a Mie scattering phase function. Stroeve and Nolin (2002) also report errors in the BRDF when a Mie phase function is used with spheres in this type of model. The Mie scattering phase function is clearly not suitable for this problem. However, when used with an HG phase function, single scattering parameters from Mie theory yield more realistic BRDFs (Aoki et al. 2000). In ice cloud remote sensing, it is common to use Mie scattering parameters with the HG rather than the Mie scattering phase function.
As with modeling of cirrus clouds, there is no compelling reason to choose one particular shape for snow grains in the model. In a study of crystals falling to the ground at the South Pole station (clear-sky precipitation, or diamond dust, a common occurrence in Antarctica), Kikuchi and Hogan (1979) found a prevalence of columnar crystals, although on occasion various forms of plates were dominant. No one particular habit, thus, seems to dominate in the precipitating crystals observed in Antarctica. Various processes cause crystals to change their initial shape after deposition. Furthermore, as was pointed out by Aoki et al. (2000), optical phenomena such as halos are only occasionally observed over natural snow, and this does not support the idea that one habit should be dominant, although it does not rule it out (e.g., Mischenko and Macke 1999).
Because the combination of Mie scattering parameters and an HG phase function gives good results for the BRDF (Aoki et al. 2000), this should be an adequate choice for modeling the single scattering by snow grains in this study. However, to examine the sensitivity of our results on the assumed particle shape, we also consider the Key et al. (2002) parameterization of optical properties for columnar and plates and various types of crystals.
Figure 2 shows the brightness temperatures in channel 3 calculated for various models of snow grains and typical South Pole viewing conditions (solar zenith angle θo = 75°, viewing polar angle θ = 65°, relative azimuth ϕ = 160°). For the same snow grain effective radius, the Mie phase function yields much lower radiances than those from the crystal parameterizations. Spheres with an HG phase function also yield smaller radiances than the three other crystals, for which the brightness temperatures are close. For this typical scene, interpreting the channel-3 radiances in terms of snow grain size returns snow grain effective radii, which are 10–20-μm smaller when using spheres with HG phase function instead of the Key et al. (2002) parameterization. Using the Mie phase function would return snow grain effective radii to at least a factor of 2 or even smaller. For the computations represented in Fig. 2, the effective radius is defined as in Key et al. (2002):
where Ptot is the total projected area of the distribution. The orientationally averaged cross section of a convex particle is one-quarter of its surface area (C. Bohren, cited in Wiscombe and Warren 1980). Thus, in the case of solid columns and plates Ptot = 1/4 Stot, so that this definition is equivalent to (2). Because the total volume Vtot of ice is the same for all distributions in the model, we also have equality of total area when the effective radii are equal. This is probably the best way to simulate nonspherical particles with spheres, as argued by Grenfell and Warren (1999). These authors caution, however, that this prescription works well for calculating fluxes but radiances may be problematic. In the NIR, the shape of the phase function is particularly important and, indeed, the calculated radiances can be quite different even when satisfying equality of total surface and volume, as seen in Fig. 2.
Surface roughness and pollutants
An important simplification is the representation of the snow surface as perfectly flat and horizontal in the (plane parallel) radiative transfer model. The surface roughness of the snow can influence both the BRDF and albedo. Over Antarctica, the wind often erodes elongated, usually meter-scale features (sastrugi), which are known to modify the angular reflectance pattern of snow (Kuhn 1974; Frezzotti et al. 2002). From measurements of the snow BRDF at South Pole Station, Warren et al. (1998) recommend that small viewing zenith angles be used for satellite remote sensing over snow with developed sastrugi. Warren et al. (1998) and O'Rawe (1991) also show that sastrugi reduce the albedo from the flat-surface equivalent, and this reduction is greater (up to 14%) for larger height-to-width ratios (approaching unity) and for lower flat surface equivalent albedos (0.4–0.8, as opposed to near unity; thus, this source of uncertainty matters in the NIR). Mondet et al. (1998) analyzed angular reflectance patterns over Antarctica with the spaceborne Polarization and Directionality of Earth Reflectances (POLDER) instrument and also recommend small viewing zenith angles. Models of snow reflectance, including sastrugi effects, have been developed (Leroux and Fily 1998), which successfully reproduce some of the reflectance features due to sastrugi, but so far do not fully simulate the BRDF (Warren et al. 1998). In the absence of information on the direction and depth of sastrugi, it is, therefore, unclear whether the representation of surface roughness can be improved in our model. We must regard sastrugi as a persistent source of uncertainty that is difficult to quantify at present.
Last, the presence of even small quantities of pollutants in the snow, most notably soot, has been shown to have a significant effect on the visible reflectance of snow (Wiscombe and Warren 1980; Warren and Wiscombe 1980). Over the high Antarctic plateau we expect such effects to be minimal because the atmosphere is generally very clean (Warren and Clarke 1990). Furthermore, the effect of these particles on NIR reflectance are negligible because of the strong absorption of ice itself. Thus, we can safely assume that the effect of soot and other pollutants need not be represented in our model for this study.
Snow grain size retrieval
Our objective is to interpret clear pixels radiances in terms of snow grain size. This hinges upon a good discrimination between cloudy and cloud-free pixels, which can be difficult in Antarctic satellite imagery. The multispectral cloud-masking technique of Yamanouchi and Kawaguchi (1992) has proven effective for us. In sunlit scenes over Antarctica, the reflectance of clouds in AVHRR channel 3 (3.7 μm), which is larger than that of the snow, can be used to identify cloudy pixels. This is because the clouds contain smaller particles than the underlying snow, and NIR reflectances decrease notably with increasing particle size (Warren et al. 1998).
We now illustrate the snow effective radius retrieval for one case. Figure 3 shows a 100 × 100 pixel AVHRR image in channels 3 and 4, centered about the South Pole, from a NOAA-12 overpass on 23 January 1992. The channel-3 image shows a large cloud deck (brighter pixels) and a smaller, clearer area (darker pixels). Comparison with the channel-4 image shows that, as is often the case over the plateau, the cloud is warmer than the surface. Figure 4 shows a scatterplot of each pixel's brightness temperature difference between channels 3 and 4 (ΔT34) against its brightness temperature in channel 4 (T4). Because brightness temperatures in these two channels would be approximately the same if ice particles were as dark in channel 3 as in channel 4, ΔT34 is a good index of the NIR reflectance. The upper cluster on this plot, for ΔT34 > 60 K, is the group of cloudy pixels (large value of ΔT34, due to a contribution of the solar backscatter to the total channel-3 radiance). The lower cluster, for ΔT34 < 50 K and T4 < −35 K, is from the clearer area. The pixel with the lowest (nonoutlying) value of ΔT34 is taken to be the clearest pixel. This is a reasonable assumption for this scan: radiative transfer calculations show that only a cloud with unrealistically large particles could be this dark in channel 3. This method would not work if the image was completely cloud covered, but in the several hundred scans considered in this study, all 100 × 100 pixel images contained at least a small, clear area. We then compare the measured channel-3 radiance in this pixel with model values, and by iteration find the snow effective radius that gives the model snowpack the same reflectance as the measurement.
Although this method should in principle give useful information on surface properties from satellite observations, two important limitations are noted. The first involves the uncertainty in the simulated BRDF as discussed above. The resulting errors in retrieved re are difficult to quantify at present. However, because the viewing geometry of the satellite overpasses varies slowly at the South Pole, so should the error related to the BRDF. Thus, although the absolute values of retrieved radii might be in error, a time series of these retrievals can probably provide at least a relative indicator of the surface snow grain size variations over time. For other locations on the Antarctic plateau, where both viewing angles might vary considerably, some of the sources of error in the re retrieval may need to be quantified further.
The second limitation arises from the possibility that some of the pixels identified as clear might actually contain thin cloud. There is a possibility that the NIR reflectances are affected by the presence of polar stratospheric clouds (PSCs). PSCs are, however, much less prevalent during late spring and summer and, because of much lower stratospheric temperatures, should leave a clear signature in ΔT45, which we do not observe. Two other common Antarctic meteorological phenomena, clear-sky precipitation (CSP) and blowing snow, might be more difficult to discriminate from the snow surface. As mentioned above, in an atmosphere with a small lapse rate, the only radiometric contrast between the snow surface and a low cloud is provided by the difference in effective radii (and possibly shape). But for fine surface grains, such as those expected during snow deposition by CSP, channel 3 is only sensitive to the uppermost millimeter or less of the snowpack (Fig. 1). The crystals in this thin layer might be very similar to the precipitating ones overlying them. CSP might be indistinguishable from the underlying snow in our data. If a cloudy pixel is assumed to be clear, the model will tend to overestimate the snow reflectance to match the increased radiance at the top of the atmosphere. The result is, thus, an underestimate of the snow grain size.
Last, some AVHRR channel-3 data from the earlier spacecraft exhibit a radiometric problem that results in artificial “striping” in images over lower temperatures, even with solar backscatter present. Images with this obvious problem were omitted from the analysis.
Figure 5 shows the retrieved snow effective radius from NOAA-11 and -12 images available for 1992. For these retrievals, the model snow grains are assumed to be spheres with an HG phase function. For some data, the clear pixel radiances were out of the model output range, either too low or too high. For these, a grain size cannot be retrieved with this model. Because the clearest pixel is the one where the near-infrared radiances are the lowest, it will also tend to be the noisiest and could, thus, have an uncertainty too large for our model's retrieval. The nonretrievable cases could also result from limitations with the plane-parallel radiative transfer model.
Despite the few unretrievable cases (not depicted in Fig. 5), the time series of retrieved re shows relatively little scatter and for most of the year the retrieved re varies smoothly between scans. This is encouraging, because this would probably not be the case if a large number of these retrievals were biased by undetected cloud.
Because the clearest pixel is often in a different location from one image to the next, and is the one for which the effective radius is retrieved, the small scatter in this time series also suggests that the correlation scale in surface snow grain size is at least as large as the image size (∼100 km). Although some subpixel-scale spatial variability in snow accumulation has been observed (Braaten 2000), it appears that, at least averaged over the scale of a pixel or more, there is a good uniformity in snow deposition over distances of order 100 km. This uniformity may result in part from wind drift helping to homogenize the spatial distribution of snow grains. Carlson et al. (1992), using ratios of reflectance at two near-infrared wavelengths, mapped snow grain size over the Antarctic continent with the NIR mapping spectrometer onboard the Galileo spacecraft. Their map also supports the idea that large regions of the plateau have approximately the same grain sizes at a given time.
If the retrievals are done, assuming the grains are hexagonal solid columns, as parameterized by Key et al. (2002), the estimated snow grain re are usually higher by 10–20 μm (not shown). This could be expected from Fig. 2. This bias is fairly constant with time, reassuring us that despite possible errors in the BRDF, as discussed above, this method should at least provide a good index of snow grain size variations.
The mean value of the retrieved re is about 50 μm (70 μm when using solid columns), with occasional dips to 15–20 μm, and rarely exceeding 100 μm. However, as can be seen in Fig. 1, the channel-3 radiance becomes much less sensitive to effective radius for large grains, so some of the large retrieved values could be underestimates.
In situ measurements of snow grain size at the South Pole and Vostok Stations have been presented in Grenfell et al. (1994), who found the grain size to be usually in the 50–70-μm range in the first few millimeters of snow at the South Pole. Carlson and Arakelian (1993) found similar values in another field experiment. However, Grenfell et al. (1994) observed that the grain size could drop to as low as 25 μm after new snow deposition. Using a snowpack model similar to ours, they found that the addition of a very thin (0.25 mm) surface layer of fine grains (15 μm) could match NIR spectral albedo measurements after new snow deposition. Because at channel-3 wavelengths such a layer of fine grains is effectively semi-infinite when its thickness reaches 0.1 mm (Fig. 1), our retrieval is a measure of the effective radius in this thin uppermost layer. Both our mean re and our minima are, thus, consistent with Grenfell et al. (1994), and also with Gay et al. (2002).
These values of snow grain re are smaller than what has been measured in the Arctic, or on the Greenland Ice Sheet (e.g., Han et al. 1999; Stroeve and Nolin 1992). One reason could be that over the plateau the very low temperatures inhibit snow metamorphism (La Chapelle 1969), so the grain size increases more slowly.
Despite scatter in the retrieved re values, two events of decreasing re are suggested in Fig. 5 (e.g., around day 25 and day 285). These events span several independent retrievals from different satellite overpasses, and are, thus, unlikely to be entirely due to errors in the retrievals. Instead, they may be related to new snow deposition. As mentioned above, the small re retrieved during these local minima are consistent with the range used by Grenfell et al. (1994) to model fresh snow at the South Pole. The frequency of these events is also not inconsistent with the observations of Braaten (2000) that a few deposition events contribute for most of the yearly accumulation.
We investigated if the retrieved re are correlated with any of the surface observations at South Pole Station. The Antarctic snow albedo is known to increase after snowstorms (e.g., Liljequist 1956), and snow accumulation is influenced by the meteorology (Pettre 1986). We examined the South Pole Weather Office logs, which contain observations of sky coverage, visibility, wind speed and direction, near-surface air temperature, surface air pressure, and some qualitative indications of near-surface conditions affecting visibility at synoptic intervals. These logs unfortunately lack specific measurements of snow accumulation rates, and most of the meteorological variables did not correlate with our snow grain size retrievals. However, the time series of station visibility, and related notations, may be a proxy for precipitation and surface accumulation. In these weather logs, the maximum reported visibility is 7 km. This maximum is usually reported for clear-sky conditions, and may be interpreted to mean “visibility unrestricted.” Decreases in visibility from 7 km are often accompanied by notations such as “ice fog,” “ice crystals,” or “blowing snow.” There is also a separate remark in the weather logs about the presence of precipitation.
Figure 6 shows the time series of station visibility, both the instantaneous synoptic observations and as a 5-day moving average, for the same time period as in Fig. 5. Throughout the first half of January, clear skies and unrestricted visibilities prevailed. During mid- to late January, the visibility was consistently reduced. Ice crystals and ice fog are the most consistent reasons for visibility reduction throughout the season. In addition, several episodes of precipitation are indicated during the period of reduced visibility during mid- to late January. In our AVHRR snow grain size retrievals, we see re steady at 40–50 μm in early January, followed by a local minimum around day 25. Between days 35–45, our retrieved snow re are at or above 50 μm, following several days of clear skies and mostly unrestricted visibility after day 30, as shown in Fig. 6a.
Similarly, our re retrievals yield three small values (<25 μm) between days 279 and 285, followed by a steady increase to a range of 50–100 μm over the next 60 days, and finally values smaller than 30 μm after day 350. Figure 6b shows an extended period of reduced station visibility and several episodes of precipitation between days 275 and 285, and also an episode of reduced station visibility just after day 350. Comparing Figs. 5 and 6, it is clear that not every drop in station visibility or episode of precipitation is associated with a local minimum in our retrieved snow grain re, but the reverse is true. In addition to Fig. 6, we attempted to find a direct correlation between our re retrievals and visibility reported at South Pole Station. A reasonable correlation was suggested for the NOAA-11 retrievals, having a linear regression coefficient of 0.5 (figure omitted), but a convincing correlation for the NOAA-12 retrievals was not apparent. As opposed to visibility and episodes of precipitation, the presence of ice crystals/ice fog, and blowing snow, both appear largely uncorrelated with changes in snow grain size from AVHRR. This comparison is, therefore, not conclusive, but is suggestive that AVHRR can observe changes in snow grain size associated with major changes in precipitation events over the Antarctic plateau.
Cloud remote sensing implications
We now examine how the variability in Antarctic snow grain size might affect the retrievals of overlying cloud properties. We added a cloud layer to our model of the snow–atmosphere system to investigate how TOA radiances, as would be measured for satellite cloud remote sensing, are influenced by the snow properties. Apart from finite ice water paths (IWPs), and usually smaller particles, this cloud layer is represented in the model in the same fashion as the snow layer. We used the same model particle in the ice cloud as in the snow, with single scattering parameters for spheres combined with a HG phase function. Because the sensitivity of TOA radiances to snow properties is strongly modulated by cloud properties, it is necessary to consider the problem in the space formed by the three independent cloud variables (cloud particle effective radius, optical depth, and cloud temperature), which we hereinafter refer to as cloud variable space.
Figure 7 shows the contour levels of the effective scene temperatures calculated for AVHRR channels 3 and 4 (T3 and T4) as a function of cloud particle effective radius rec and optical depth τc. The snow is assumed to be bright (snow grain effective radius re = 35 μm). Based on summertime radiosonde data, we fix the surface temperature at 242.2 K and assume a physical cloud temperature of 246 K. Here, we refer to the shortwave (conservative scattering) cloud optical depth:
where IWP is the ice water path. Although both T3 and T4 are scalar functions of three variables, we fixed the cloud temperature for the following reasons. The mid-IR thermal emission shows little sensitivity to grain size (Fig. 1), and the change in NIR brightness temperature due to a different snowpack is mostly due to the change in the reflected solar radiation. Therefore, the effect of snow grain size on cloud retrievals is similar for other cloud temperatures (confirmed numerically, figure omitted). Last, visualization of the most essential radiative transfer results is facilitated by reducing the problem to two dimensions.
As an example in interpreting Fig. 7, the isotherm for T3 = 293 K (thick line in Fig. 7) is the ensemble of (rec, τc) that satisfy T3 (rec, τc) = 293 K. The points that satisfy both T3 = 293 K and T4 = 245.1 K are then the intersection of these two isotherms, that is, the point of coordinates (rec = 15 μm and τc = 2.3). This point would be the model solution for cloud property retrieval if a satellite measured these values of radiances over this scene.
If cloud temperature Tc is also allowed to vary, we need a third measured radiance to find the three unknowns (rec, τc, and Tc). In this case, we use also the intersection of two other isotherms, for example, T4 and T5, or T4 and ΔT45. The solution then is the intersection of the three isothermal surfaces. The shape of these isotherms show that for τc larger than 2, T3 is insensitive to optical depth and is a function of cloud particle effective radius rec only (the T3 isotherms are vertical). For large rec (and cloud temperature fixed), T4 is mostly a function of τc (the T4 isotherms are horizontal, but only for small τc and up to Tc).
One advantage of plotting a lookup table in the cloud variable space, as in Fig. 7, is that this helps visualize how retrievals depend on measurement errors. Errors in the retrieved cloud properties are more sensitive to instrument and model limitations when 1) a channel's isotherms are far apart, implying decreased sensitivity of this channel's measurements to cloud variables; or 2) the two channels isotherms become parallel, implying that the two measurements are not independent. The latter is obviously not the case for T3 and T4, except for unrealistically small rec or optically very thin clouds. It is often a problem, though, for channel-4 and -5 measurements over a thick cloud. From the shape of these isotherms, it appears that optical depth retrievals are less reliable for thick clouds (T4 isotherms far apart), whereas the effective radius retrievals are less reliable for large radii (T3 isotherms far apart). This result for the asymptotic cases is expected, but this type of plot allows a good visualization of the range in cloud variables for which the retrievals are reliable.
To investigate what happens in a cloud retrieval algorithm without accounting for variability in snow grain size, we can make a second calculation with everything held the same, except for a darker underlying snow or a darker underlying snow layer. In this example, we let the brighter, “correct” snowpack have effective grain size re = 35 μm, as estimated from the AVHRR data of Figs. 3 and 4. In the absence of such retrieval information, one might assume an effective snow grain size of re = 100 μm, and we use this value in the calculation of radiance backscattered from the darker, “incorrect” snowpack. For each point (rec, τc) in the Tc = 246 K plane, we can subtract the value of T3 calculated over the dark snow from the one calculated over the bright snow. The procedure is repeated for T4. Figure 8 shows the contour levels of these calculated differences in the cloud variable space. It can be seen that the errors in T4, arising from using the wrong snow, are undetectable by current (AVHRR) radiometers. Because the mid-IR thermal emission problem seems decoupled from the role of the snow grain size in the NIR, this is also an indication that the role of snow is similar for different cloud temperatures. The errors in T3, however, can be significant for small cloud optical depths. For instance, at rec = 15 μm and τc = 0.5, using the wrong (too dark) snow results in an underestimation of about 2 K in the AVHRR channel-3 radiance.
We now calculate what errors in the retrieved cloud properties result from the errors in T3 (Fig. 9). The modeled effective TOA scene temperatures that would result from a cloud having effective particle radius rec (1) and optical depth τc (1), overlying the bright snow, are the ones plotted in Fig. 7. For each [rec (1), τc (1)] point in that plane, using the procedure outlined above, we retrieve the cloud particle effective radius and optical depth rec (2) and τc (2), that, when using the wrong (dark) snow model, would give the radiances obtained with the bright snow overlain by a cloud [rec (1), τc (1)]. The values rec (2) and τc (2) are, thus, the cloud particle effective radius and optical depth that would be retrieved if we were to interpret the satellite-measured radiances with the wrong snow.
Figure 9 shows the contour levels of the cloud particle effective radius retrieved using the wrong snow re, as a function of the real cloud particle effective radius and optical depth [rec (1), τc (1)]. The error is negligible when the (real) cloud optical depth is larger than unity, although the error does increase with the (real) cloud particle effective radius. The error is significant, however, for smaller optical depths, which are probably the most frequent situation over the Antarctic plateau. For instance, when the real cloud optical depth is 0.25 and the real cloud particle effective radius is 20 μm, the retrieved effective radius is 15 μm. For thinner clouds, the error can become quite large. This reflects the fact that for thin clouds, through which the snow surface is visible from the TOΛ in the NIR, the deficit in NIR radiance from assuming too dark a snow has to be compensated for by increasing the reflectivity of the cloud, thus, decreasing the retrieved effective radius. The large errors near rec = 1 μm result from a Mie scattering resonance effect near rec ∼ 2.5 μm.
The error in retrieved optical depth, related to snow grain size, is negligible for rec > 5 μm and τc > 1. For very thin clouds, however, the error increases. To compensate the deficit of channel-3 radiance, we not only need a cloud of smaller effective radius, but also of sufficient optical thickness to increase the reflected solar component. This result should be regarded with caution, however, because unlike the effective radius retrieval, the optical depth retrieval depends strongly on the thermal infrared radiances and on the surface-to-cloud temperature difference.
We now propose a method to minimize these errors. As argued above, the modest scatter in the time series of retrieved effective radii suggests that the variations in surface snow grain size are well correlated over the scale of our images (∼100 km). Because many images over the Antarctic plateau show at least some breaks in the cloud cover, one can then retrieve the snow grain size for clear pixels and use this estimate in a cloud retrieval algorithm for cloudy pixels. Note that because the snow grain size is retrieved from very nearly the same viewing angle as the cloud retrievals, the impact of errors in the snow BRDF should be reduced because the clear-sky snow-reflected radiance is matched for this viewing angle.
Despite current limitations in our ability to model the snowpack optical properties, the time series of effective radii suggests that the method yields at least a useful index of snow grain size variation in the top few millimeters of the snow surface. The mean retrieved effective radius is about 50 μm for that period when we model the snow grains with the single scattering properties of spheres and a HG scattering phase function. This value is consistently 10–20-μm larger when using solid hexagonal columns instead. The time series exhibits some variability on a time scale of a few weeks, where the retrieved values range as low as 15 μm and higher than 100 μm. The former may be related to new snow deposition events.
Variability in grain size can have a large effect on the clear-sky surface energy budget, as was pointed out by Carlson and Arakelian (1993). Our calculations suggest that even in the presence of the optically thin cloud typical of the Antarctic plateau, the change in NIR reflectance due to grain size may also have an effect on top-of-atmosphere outgoing radiation.
Examining the problem of cloud property retrieval in the space formed by the cloud variables allows a clear visualization of ranges of values where satellite-retrieved cloud variables are most sensitive to errors in the representation of the snow. If the grain size temporal variability is not taken into account, the error on the retrieved cloud particle effective radius can be significant for the optically thin clouds that are commonly observed on the Antarctic plateau. The results presented here have the potential to notably improve the representation of snow in a cloud retrieval algorithm by providing a useful contemporaneous estimate of snow grain size. A rigorous method for retrieving cloud optical properties over the Antarctic plateau is the subject of a paper to follow.
This research was supported in part by the National Science Foundation under ATM98-14151, and by the U.S. Department of Energy under DOE DE-FG03-97-ER62338. The Arctic and Antarctic Research Center is supported by the National Science Foundation under NSF-OPP98-06941.
Corresponding author address: Dr. Dan Lubin, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093-0221. firstname.lastname@example.org