Snow albedo and grain size on a traverse from the East Antarctic Plateau down to the coast
Richard E. Brandt and Stephen G. Warren
Department of Atmospheric Sciences, University of Washington,
Seattle, Washington, 98196-1640, USA
For submission to Journal of Glaciology
4 December 2008
v.04
2
Abstract.
On two traverses with the French Antarctic Expeditions from Dome C to Dumont
d’Urville, spectral albedo was measured to determine the variability of snow grain size
(and therefore albedo) across the slope region. Ratios of near-infrared albedo to visible
albedo were used to infer optically-effective grain radius. The average inferred radius
was 38 μm, smaller than at Dome C (80 μm) and smaller than at the coast of Antarctica
(~150 μm), probably because of drifting and sorting of snow grains by the strong winds
of the slope, leaving smaller grains at the top surface. The average inferred grain radius
was larger in February (45 μm) than in January (28 μm), probably because the snow in
February had experienced summer temperatures facilitating metamorphism for a longer
time. Simultaneous measurements of reflected sunlight by the MODIS satellite
instrument implied grain sizes larger than those obtained from the surface measurements,
by a factor 1.7, probably because of the satellite’s use of a shorter (less absorptive)
infrared wavelength than those used in the surface measurements, together with the
increase of grain size with depth. Broadband albedos are computed for the East Antarctic
Plateau for various cloud thicknesses and compared to Kuhn’s simultaneous
measurements of albedo and cloud transmittance at Plateau Station in 1967.
3
Introduction
The spectral albedo of snow has been measured at established research stations on
the East Antarctic Plateau: South Pole Station and Vostok Station by Grenfell and others
(1994) and Dome C Station by Hudson and others (2006, Figure 6). The albedo is
consistently high at visible wavelengths but variable in the near-infrared (near-IR), where
it is sensitive to grain size. At these stations, day-to-day variations of grain size due to
precipitation, drifting, and metamorphism caused temporal variations of near-IR albedo,
but no systematic geographical variation of albedo was found among these three
locations. These results suggest that measurements at the stations can be used to
represent the radiative properties of snow all across the East Antarctic Plateau.
However, those measurements may not be appropriate to represent snow on the
Antarctic Slope and in coastal regions, where the snow is exposed to stronger winds and
higher temperatures. We addressed this question by making measurements along the
traverse route from Dome C (elevation 3250 m) down to the coast at Dumont d'Urville
(DDU).
Measurements
A tractor train is used to resupply the Dome C station. In the summer of 2003-4,
three round-trips were accomplished from DDU to Dome C. We travelled with the
second northbound traverse in early January (Brandt) and the third northbound traverse in
early February (Warren). The route is shown in Figure 1, which also identifies the
locations where measurements were made. The route began in a region of weak winds on
the dome and proceeded into the “slope” region of persistent strong easterly winds, which
4
caused drifting of snow and development of surface roughness in the form of sastrugi.
The height of sastrugi was estimated as 4 cm at Dome C (at latitude 75°), 30-50 cm at
latitudes 71°-73°, and 100 cm at latitudes 67°-69°.
Spectral albedo (Figure 2) was measured at Dome C using a spectral radiometer
manufactured by Analytical Spectral Devices (ASD). That radiometer was needed for
other work at Dome C, so on the traverses we used a different instrument, the PM1
(Grenfell and others, 1994), which takes readings at several discrete wavelengths using
11 filters mounted on a rotating wheel. The filters used on the traverses spanned the
wavelengths 360-1060 nm. Shadowing corrections are needed for both radiometers (see
Appendix).
Figure 2 shows that the spectral albedo dips to a local minimum at 1030 nm,
where ice exhibits a small absorption peak (Grenfell and Perovich, 1981). The depth of
this minimum is sensitive to grain size, as shown in the model calculations in Figure 3,
whereas the albedo for 360-500 nm is insensitive to grain size.
The traverse crew stopped for one hour each day at about 13:30 local time, and
stopped for the night at about 20:30. Albedo measurements were made during the
midday stop to take advantage of the high sun; measurement errors due to tilt of the
instrument are smaller when the sun is high. On the January traverse, evening
measurements were also made, but the sky condition was sufficiently stable for albedo
analysis only on two evenings.
Strong winds, changing cloud conditions, and local surface slopes (sastrugi)
meant that accurate measurements of absolute albedo were in general not possible in the
limited time available. However, to first order the tilt will cause albedos at all
5
wavelengths to be in error by the same scale factor. We therefore use the ratio of
measured albedos at wavelengths λ>500 nm to the albedo at λ=500 nm to infer the
optically-effective grain size. Even so, midday albedo measurements were too noisy to
use on two of the days.
We also photographed snow grains at midday stops and evening stops. However,
our concern here is with radiative properties of snow, not grain size per se. The
optically-effective grain size for a nonspherical snow grain is proportional to the ratio of
volume to surface area (Grenfell and Warren, 1999). Estimates of optically-effective
grain size from the photographs appear to be consistent with the values we infer from the
albedo measurements. Here we have not analyzed the photographs in detail; instead we
use the radiation measurements to infer the optically-effective grain sizes.
Analysis
The raw measurements of spectral albedo were corrected for tilt and shadowing
by multiplying each scan by a scale factor that brought the albedo to 0.99 at λ=500 nm.
The measurement at this wavelength was more reliable (less variable) than at the shorter
wavelengths (360, 420, 470 nm), because the product of instrument sensitivity and solar
spectrum peaks near 500 nm. Four or more scans were obtained at each location; the
scans were averaged. Figure 4 shows these scaled averaged albedos measured on the two
traverses. At each of the four longest wavelengths the albedo from Figure 4 was
compared to the model albedo in Figure 3 (also scaled to bring the albedo to 0.99 at
λ=500 nm), to infer an effective grain radius reff. These values are plotted in Figure 5; the
error-bars represent the standard deviation of the four inferred values of reff. They are
6
plotted as a function of latitude along the traverse; the corresponding elevations are
shown in the upper panel of the figure.
One might expect grain size to increase toward the coast because snow
metamorphism is more rapid at higher temperature (LaChapelle, 1969). On the other
hand, wind-drifting causes sorting of the grains, leaving the smallest grains at the top
surface where they have the most influence on the near-IR albedo (Liljequist, 1956;
Stephenson, 1967; Grenfell and others, 1994). The fact that we see no significant
variability with latitude could mean either that these processes have only small effects, or
else that their effects compensate each other.
Figure 5b shows that the average grain size of the February traverse (reff ≈ 45 μm)
was larger than on the January traverse (reff ≈ 28 μm). In an attempt to explain this
difference we examined records of wind and temperature at four automatic weather
stations (AWSs) near the traverse route: Italian stations Giulia and Irene, and University
of Wisconsin stations Dome CII and D-47. Based on the AWS data, the February
traverse was colder by 9 K, and windier by 6 m s-1, both of which would be expected to
result in smaller grain sizes. However, snow metamorphism is the result of the
temperature history, not the instantaneous temperature. So the likely cause of larger
grains in February is that the surface snow had experienced summer temperatures for a
longer time.
The few stops made by the traverses in the steep region below 1500 m were made
at times of little or no sunlight, so we lack grain-size estimates for this region. However,
we can make grain-size estimates for snow at sea level near the coast of Antarctica, using
the same method, from our measurements on snow-covered sea ice under clear sky at
7
solar zenith angle 60° near Mawson Station (66°S; Allison and others, 1993, Figure 11),
and from measurements by others at McMurdo Station (78°S, overcast sky; Kuhn and
Siogas, 1978) and on the Fimbul Ice Shelf (72°S, partly cloudy sky; Winther, 1994,
Figure 2). These albedo spectra indicate effective radii of 210, 170, and 150 μm,
respectively.
The same procedure can be applied to Figure 2 to infer the grain size at Dome C,
but here we can also use longer wavelengths. We obtain reff = 80 μm for visible and near-
IR wavelengths with α>0.4, and reff =50 μm for near-IR wavelengths with α <0.4. [This
difference is expected because of the increase of grain size with depth (Grenfell and
others, 1994).] We plot the point reff =80 μm in Figure 5b to conform with the
wavelength range measured on the traverses.
Why would the grain size on the traverses be smaller than at Dome C? The most
likely explanation is that strong winds cause drifting and sorting, leaving the smallest
grains at the top; this process is less important at Dome C because of the weak winds on
the dome. Another possible explanation is the fact that the measurement of Figure 2 was
made on a day with surface frost, but it is not clear that reff would be larger for frost
crystals than for aged snow. Frost crystals are large, but for optical properties it is the
short dimension rather than the long dimension that is most relevant (Grenfell and
Warren, 1999).
Direct measurements of snow grain size were made by Gay and others (2002) on
the traverse route from Dome C to DDU, as well as on a traverse from Terra Nova Bay to
Dome C, and in the interior of Dronning Maud Land. Their conclusion was that surface
snow grains are "uniformly small," with mean convex radius (mcr) 100-200 μm. These
8
radii are larger than the reff we infer from albedo measurements, by a factor of 3-4,
probably because of the different definitions used. [The optically effective grain size is
biased toward the size of the topmost grains, for example in the topmost 0.3 mm of the
snowpack (Figures 4 and 6 of Grenfell and others, 1994).] However, the finding of Gay
and others that the mcr is "surprisingly spatially homogeneous" is consistent with the lack
of a latitudinal gradient of reff in our Figure 5b.
Methods have been developed for remote sensing of effective grain size from
satellite measurements of reflected sunlight. Scambos and others (2007) use the
normalized difference between MODIS Band 1 (620-670 nm) and Band 2 (841-876 nm),
after screening for clouds, to infer snow grain size, quoting an uncertainty of 50-100 μm.
The results for the times and locations of our traverse measurements have been kindly
provided by Ted Scambos and Jennifer Bohlander (personal communication, 2008). A
plot of satellite-inferred grain size versus surface-inferred grain size, for the 11 points on
the traverses, shows that they are uncorrelated. The surface estimates range from 22 to
52 μm (Figure 5b), with an average of 38 μm. The MODIS estimates range from 47 to
90 μm, with an average of 64 μm. The MODIS-inferred grain size is thus larger by an
average factor of 1.7. This difference is most likely caused by the increase of grain size
with depth, due to both wind-drifting of the topmost layer and snow metamorphism in the
lower layers. We are using wavelengths out to 1060 nm, but MODIS uses 860 nm, where
ice is less absorptive so that the penetration depth of radiation is deeper and larger grains
are sensed. The variation of albedo-inferred grain size with wavelength is shown perhaps
most clearly in Figure 1 of Warren and others (1986).
9
Kuipers Munneke and others (2008, Figure 12) found MODIS-inferred grain sizes
to be larger than surface-inferred grain sizes, by an even larger factor, ~2.8. However,
the surface measurements they used were broadband (from AWSs), so it would be harder
to pin down the reasons for the discrepancy.
Broadband solar albedos on the East Antarctic Plateau
The broadband albedoα can be obtained by integrating the spectral albedo α(λ)
over wavelength, weighted by the incident solar spectrum S(λ):
( ) ( )
( )
S d
S d
α λ λ λα
λ λ= ∫
∫.
We compute α(λ) using a delta-Eddington radiative transfer model for various grain
sizes. This model’s α(λ) was shown to agree with that measured at the South Pole
(Grenfell and others, 1994).
For S(λ) we use solar spectra from 300 nm to 10 μm wavelength computed using
the ATRAD model (Wiscombe and others, 1984), for January conditions at Plateau
Station (Wiscombe and Warren, 1980b): Computations were done for clear sky and for
several cloud optical depths. The measurements of atmospheric transmittance at Plateau
Station by Kuhn and others (1977) indicate cloud optical depths 0.1-1.0. These are
consistent with optical depths determined from spectral longwave measurements at the
South Pole by Mahesh and others (2001), who found that ~70% of the clouds had optical
depth τ<1. Clouds are much thicker in coastal regions and over the Antarctic Ocean,
with average optical depths 11-24 (Fitzpatrick and Warren, 2005).
10
Figure 6 shows computations of broadband (spectrally averaged) albedo at the
snow surface (αs) and at the top of the atmosphere ("planetary" albedo, αp), as functions
of atmospheric transmittance, for four different snow grain sizes. [The atmospheric
transmittance decreases as cloud optical depth increases. The rightmost ends of the plots
represent clear sky.] Also shown are daily values of broadband surface albedo measured
at Plateau Station, plotted versus the corresponding daily values of measured atmospheric
transmittance (from Figures 6 and 7 of Kuhn and others, 1977). The data indicate
average grain radii near 100 μm; i.e., as for Dome C, reff is larger than we obtained on the
traverses. The broadband albedos at Plateau Station, averaging 0.81 for clear sky, are
similar to those at other locations. Pirazzini (2004) reported an average clear-sky albedo
of 0.80 at Dome C, 0.81 at Reeves Névé (at 1200 m near the Ross Sea coastline), and
0.82 at Neumayer Station (at 20 m on an Atlantic ice shelf).
The top-of-atmosphere albedo, αp, increases with τ because the cloud ice particles
are smaller than the surface snow grains (Figure 1b of Masonis and Warren, 2001). The
surface albedo αs also increases with τ, but for a different reason: the cloud acts as a
filter, absorbing the same near-IR wavelengths that the snow can absorb, thus biasing
S(λ) toward the visible wavelengths, for which snow has high albedo (Section K of
Warren, 1982). Because most clouds over the Antarctic Plateau are optically thin (τ<1),
αs is not much higher under cloud than under a clear sky. A value of τ=0.6 was used for
model computations in Table 7 of Grenfell and others (1994), in which αs for clear sky
differed from αs for cloudy sky only in the third significant figure; they both were
rounded to αs=0.83.
11
Figure 7 shows computed values of αs and αp as functions of solar zenith angle θo
for clear sky. The surface albedo increases with θo because at low sun the photons
undergo their first scattering event closer to the surface and are thus more likely to escape
(Section J of Warren, 1982). [The plots flatten at very large zenith angle because the
incident radiation field becomes dominated by diffuse (Rayleigh-scattered) radiation
rather than a direct beam.] The planetary albedo also increases with θo for θod72°. For
θo t72°, αp decreases with θo because of absorption of visible radiation by ozone (in the
Chappuis band, centered at 600 nm); the slant path through the ozone layer is
proportional to sec θo (Figure 12b of Warren, 1982).
A model calculation by Kuipers Munneke and others (2008, their Figure 4),
shows broadband albedo 0.80 for reff =100 μm and θo=60°, a bit lower than our value of
0.818, even though their model atmosphere had more water vapor than ours (which
would tend to raise the surface albedo). They modeled snow as hexagonal plates with
aspect ratio 0.2, such as are sometimes found in falling snow (Figure 4 of Walden and
others, 2003), whereas our model used spheres to represent the rounded grains typical of
windpacked surface snow (Figure 1 of Grenfell and others, 1994). However, Neshyba
and others (2003, Figures 4 and 7) showed that asymmetry factors and single-scattering
coalbedos for plates with aspect ratio 0.2 are accurately mimicked by spheres, so this
difference between the models cannot explain their albedo differences. The falloff of
ultraviolet albedo in Figure 3a of Kuipers Munneke and others suggests that their
calculation used the old values of ice absorption coefficient (Warren, 1984) rather than
those of Warren and others (2006); this might explain the small difference in computed
12
albedo relative to our value. Other subtle differences in the radiative transfer modeling
may also contribute.
Conclusions
We found no systematic variation of grain size along the traverse, but the inferred
grain sizes were all smaller than the Dome C value, and smaller than values at coastal
locations, probably because of drifting and sorting of snow grains by strong wind. In the
katabatic zone the albedo at 10 meters height would probably be higher than we
measured at 1 meter height, because of ubiquitous blowing snow; the particles of blowing
snow are on average smaller than surface snow grains. Therefore, if we had measured
albedo from higher above the surface (to better represent what the satellite sees) we
would have inferred even smaller grains and would have obtained an even larger
discrepancy with MODIS. We offered a possible explanation for the discrepancy, in that
the 860-nm channel used in the satellite retrieval penetrates deeper into the snow where
the grains are larger. This suggests that better agreement would be obtained if MODIS
channels at longer wavelength were used (e.g. Band 5 at 1240 nm, Band 6 at 1640 nm,
and Band 7 at 2130 nm); a multi-band approach could even try to infer the vertical
gradient of grain radius.
Broadband albedos at the surface increase with cloud optical thickness, because
the cloud filters out light at wavelengths where snow has low albedo. Top-of-atmosphere
(TOA) albedo over snow also increases with cloud thickness because cloud particles are
smaller than surface snow grains. For clear sky over the East Antarctic Plateau, the TOA
albedo is computed to be about 0.1 lower than the surface albedo; for example, for reff =
13
100 μm the albedos would be 0.73 and 0.83. Under clear sky, broadband surface albedo
increases with solar zenith angle θo, but the planetary albedo shows only a weak
dependence on θo from 50° to 77°, but beyond 77° declines sharply because the visible
absorption by ozone is proportional to sec θo.
Acknowledgements
We thank Michel Fily (LGGE, Grenoble, France) for sponsoring our project.
Patrice Godon, the traverse leader and chief of logistics for the French Antarctic
Expeditions, welcomed us on the traverses and facilitated our measurements underway.
We thank Delphine Six (LGGE) for measuring surface roughness at Dome C, Warren
Wiscombe for the use of his atmospheric radiation model, and Tom Grenfell for
computation of the shadowing correction and for discussions. Ted Scambos and Jennifer
Bohlander (NSIDC, University of Colorado) provided information about snow grain-size
retrievals from MODIS. AWS data were obtained from Charles Stearns's Automatic
Weather Stations Project, and the Italian Antarctic Research Programme's on-line Meteo-
climatological Observatory. The research was supported by National Science
Foundation grant OPP-00-03826 and OPP-06-36993.
Appendix: Shadowing correction.
A shadowing correction had to be applied to the raw albedo data to obtain Figure
2, as well as for similar figures in Warren and others (2006) and Hudson and others
(2006). The shadowing correction for these figures is for the ASD radiometer, under
diffuse illumination: a factor f is derived, by which raw albedos must be multiplied to
14
obtain the true albedo. This factor was derived geometrically by Grenfell (personal
communication); he obtained a 4% correction (f = 1.04) for the experimental setup at
Dome C. [We have since improved the support system for the radiometer, thereby
reducing the correction to ~1.5%.] We also obtain the same result by trying various
values of f and choosing the value that gives the best consistency of reff inferred at
different wavelengths. This procedure gave f = 1.042, with reff = 80 μm for visible and
near-IR wavelengths with α>0.4 and reff = 50 μm for near-IR wavelengths with α<0.4, as
mentioned above. The shadowing correction for the PM1 instrument used on the
traverses is ~1%.
In Figures 4 and 5 of Grenfell and others (1994) there is a discontinuity in albedo
at λ = 400 nm, apparently due to the use of different instruments for λ<400 nm and for
λ>400 nm, suggesting that one or both of the shadowing corrections used were
inappropriate. The revised values of the absorption coefficient of ice (Warren and others,
2006; Warren and Brandt, 2008) indicate that the albedo should not be lower at 300-400
nm (ultraviolet; UV) than it is in the visible at 400-500 nm, so the UV values of 0.975
reported in Figure 5 of Grenfell et al. (1994) should probably instead be 0.99. The albedo
plot shown here in Figure 2, made with a single instrument, does show the UV albedo as
high as the visible albedo, as expected.
15
References
Allison, I., R.E. Brandt, and S.G. Warren. 1993. East Antarctic sea ice: Albedo,
thickness distribution, and snow cover. J. Geophys. Res., 98, 12,417-12,429.
Fitzpatrick, M.F. and S.G. Warren. 2005. Transmission of solar radiation by clouds over
snow and ice surfaces, Part 2: Cloud optical depth and shortwave radiative forcing
from pyranometer measurements in the Southern Ocean. J. Climate, 18, 4637-4648.
Gay, M., M. Fily, C. Genthon, M. Frezzotti, H. Oerter, and J.-G. Winther. 2002. Snow
grain-size measurements in Antarctica. J. Glaciol., 48, 527-535.
Grenfell, T.C., and D.K. Perovich. 1981. Radiation absorption coefficients of
polycrystalline ice from 400 to 1400 nm, J. Geophys. Res., 86, 7447-7450.
Grenfell, T.C., and S.G. Warren. 1999. Representation of a nonspherical ice particle by a
collection of independent spheres for scattering and absorption of radiation. J.
Geophys. Res., 104, 31697-31709.
Grenfell, T.C., S.G. Warren, and P.C. Mullen. 1994. Reflection of solar radiation by the
Antarctic snow surface at ultraviolet, visible, and near-infrared wavelengths. J.
Geophys. Res., 99, 18669-18684.
Heymsfield, A. 1975. Cirrus Uncinus generating cells and the evolution of cirriform
clouds, Part I: Aircraft observations of the growth of the ice phase. J. Atmos. Sci.,
32, 799-808.
Hudson, S.R., S.G. Warren, R.E. Brandt, T.C. Grenfell, and D. Six. 2006. Spectral
bidirectional reflectance of Antarctic snow: Measurements and parameterization.
2006. J. Geophys. Res., 111, D18106, doi:10.1029/2006JD007290.
16
Kuipers Munneke, P., C.H. Reijmer, M.R. van den Broeke, G. König-Langlo, P.
Stammes, and W.H. Knap. 2008. Analysis of clear-sky Antarctic snow albedo using
observations and radiative transfer modeling. J. Geophys. Res., 113, D17118,
doi:10.1029/2007JD009653.
Kuhn, M., and L. Siogas. 1978. Spectroscopic studies at McMurdo, South Pole and Siple
Stations during the austral summer 1977-78. Antarctic J. U. S., 13, 178-179.
Kuhn, M.H., L.S. Kundla, and L.A. Stroschein. 1977. The radiation budget at Plateau
Station, Antarctica, 1966-1967. Antarctic Research Series, 25, American
Geophysical Union, 41-73.
LaChapelle, E.R. 1969. Field Guide to Snow Crystals. University of Washington Press,
Seattle.
Liljequist, G.H. 1956. Energy exchange of an Antarctic snow-field: short-wave
radiation (Maudheim 71°01'S, 10°65'W). Norwegian-British-Swedish Antarctic
Expedition, 1949-1952. Sci. Results, 2(1A).
Mahesh, A., V.P. Walden, and S.G. Warren. 2001. Ground-based infrared remote
sensing of cloud properties over the Antarctic Plateau, Part II: Cloud optical depths
and particle sizes. J. Appl. Meteor., 40, 1279-1294.
Masonis, S.J, and S.G. Warren. 2001. Gain of the AVHRR visible channel as tracked
using bidirectional reflectance of Antarctic and Greenland snow. International
Journal of Remote Sensing, 22, 1495-1520.
Neshyba, S.P., T.C. Grenfell, and S.G. Warren. 2003. Representation of a nonspherical
ice particle by a collection of independent spheres for scattering and absorption of
17
radiation: II. Hexagonal columns and plates. J. Geophys. Res, 108, D15, 4448,
doi:10.1029/2002JD003302.
Pirazzini, R. 2004. Surface albedo measurements over Antarctic sites in summer. J.
Geophys. Res., 109, D20118, doi:10.1029/2004JD004617.
Scambos, T.A., T.M. Haran, M.A. Fahnestock, T.H. Painter, and J. Bohlander. 2007.
MOSIS-based Mosaic of Antarctica (MOA) data sets: Continent-wide surface
morphology and snow grain size. Rem. Sens. Environ., 111, 242-257.
Stephenson, P.J. 1967. Some considerations of snow metamorphism in the Antarctic ice
sheet in the light of ice crystal studies. In Physics of Snow and Ice (Ed. H. Oura),
Bunyeido, Sapporo, Japan, 725-740.
Walden, V.P., S.G. Warren, and E. Tuttle. 2003. Atmospheric ice crystals over the
Antarctic Plateau in winter. J. Appl. Meteor., 42, 1391-1405.
Warren, S.G. 1982. Optical properties of snow. Rev. Geophys. Space Phys., 20, 67-89.
Warren, S.G. 1984. Optical constants of ice from the ultraviolet to the microwave.
Applied Optics, 23, 1206-1225.
Warren, S.G., and R.E. Brandt. 2008. Optical constants of ice from the ultraviolet to the
microwave: A revised compilation. J. Geophys. Res., 113, D14220,
doi:10.1029/2007JD009744.
Warren, S.G., T.C. Grenfell and P.C. Mullen. 1986. Optical properties of Antarctic
snow. Antarctic Journal of the U.S., 21, 247-248.
Warren, S.G., R.E. Brandt, and T.C. Grenfell. 2006. Visible and near-ultraviolet
absorption spectrum of ice from transmission of solar radiation into snow. Applied
Optics, 45, 5320-5334.
18
Winther, J.-G. 1994. Spectral bi-directional reflectance of snow and glacier ice
measured in Dronning Maud Land, Antarctica. Annals of Glaciology, 20, 1-5.
Wiscombe, W.J., and S.G. Warren. 1980a. A model for the spectral albedo of snow, I:
Pure snow. J. Atmos. Sci., 37, 2712-2733.
Wiscombe, W.J., and S.G. Warren. 1980b. Solar and infrared radiation calculations for
the Antarctic Plateau using a spectrally-detailed snow reflectance model.
Proceedings of the International Radiation Symposium, Colorado State University,
380-382.
Wiscombe, W.J., R.M. Welch, and W.D. Hall. 1984. The effects of very large drops on
cloud absorption, I: Parcel models. J. Atmos. Sci., 41, 1336-1355.
19
Figure Captions
Figure 1. Map of route from Dome C to Dumont d'Urville, showing contours of surface
elevation and locations of albedo measurements.
Figure 2. Spectral albedo of snow at Dome C, measured under overcast sky on 30
December 2004 (from Figure 6 of Hudson and others (2006), with modifications). Part
of this same plot is shown in Figure 2a of Warren and others (2006).
Figure 3. Albedo computed for the discrete wavelengths used on the traverses, using the
delta-Eddington radiative transfer model (Wiscombe and Warren, 1980a) for diffuse
incident radiation, for grain radii reff from 20 to 400 μm. The computation differs from
that of Wiscombe and Warren (1980a) and Grenfell and others (1994), because it uses the
revised values of absorption coefficient of ice given by Warren and others (2006) and
Warren and Brandt (2008).
Figure 4. Albedo measurements on the traverses from Dome C to Dumont d'Urville in
January and February 2004. The raw albedo plots α(λ) were scaled to give a constant
value at λ=500 nm, as explained in the text, to remove errors due to non-horizontality of
the radiometer and of the snow surface.
Figure 5. (a) Altitude as a function of latitude along the traverse route, with snow
sampling locations marked. (b) Optically effective snow grain radius reff, inferred from
spectral albedos at λ= 930, 980, 1030, and 1060 nm, relative to albedo at λ=500 nm,
20
using the computations shown in Figure 3. The point for Dome C (reff = 80μm) was
obtained from Figure 2, using spectral albedos for all near-IR wavelengths with α >0.4,
relative to the albedo at λ=500 nm.
Figure 6. Broadband solar albedo computed for the surface and top of atmosphere using
the atmospheric radiation model ATRAD (Wiscombe and others, 1984), for January
conditions at Plateau Station (Wiscombe and Warren, 1980b): surface pressure 619
millibars, solar zenith angle 66°, troposphere saturated with respect to ice, precipitable
water 0.6 mm, total ozone 300 Dobson units. Computations were done for four snow
grain sizes, for clear sky and for cloud optical depths τ = 0.17, 0.56, 1.7, 5.6, and 17. The
size distribution of ice crystals in the cloud was taken from aircraft measurements in a
cirrostratus cloud by Heymsfield (1975, Figure 3), giving an effective radius of 13.2 μm.
Clouds are represented on the horizontal axis by the resulting atmospheric transmittance
(the ratio of downward solar flux at the surface to downward solar flux at the top of the
atmosphere), for comparison to the measurements in December 1966 and January 1967
by Kuhn and others (1977; their Figures 6 and 7) (points marked with plus-sign in open
circle).
Figure 7. Broadband solar albedo computed for the Antarctic Plateau at the surface and
top of atmosphere as in Figure 6, for four different snow grain radii, under clear sky.
"
"
!?
!?
!?
!?
!?
!
!
!
!
!
!
3000
2800
3200
2600
24003000
3000
3000
3000
3200
3200
2200
2400
2000
2600
1800
1600
2800
1400
12008001000
3000
2600
2600
2400
2000
2000
2200
2400
2600
2800
3000
1800
1600
1800
1600
800
600
400
200
1000
12001400
1600
1800
2000
200
800600
800
600
400
200
1400
1200
1000
1600
1800
1600
1000Dome C
Dumont D'Urville0 100 200 Kilometers
" Station
!? 4 - 7 January 2004
! 1 - 7 February 2004
Figure 1
120°E
130°E
140°E
72°S
67°S
400 600 800 1000 1200 1400 1600 1800 2000 22000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Alb
edo
Wavelength (nm)
Figure 2
400 500 600 700 800 900 1000 11000.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Alb
edo
Wavelength (nm)
20
50
100
150
200
30
300
70
400
grainradius(μm)
Figure 3
500 600 700 800 900 1000 11000.7
0.8
0.9
1.0500 600 700 800 900 1000 1100
0.7
0.8
0.9
1.0
(b)
1 - 7 Feb 2004
Alb
edo
Wavelength (nm)
Figure 4 A
lbed
o
4 - 7 Jan 2004
(a)
76 74 72 70 68 660
10
20
30
40
50
60
70
80
90
100
0
500
1000
1500
2000
2500
3000
3500
(b)4 - 7 January 20041 - 7 February 2004
Dom
e-C
Dum
ont D
'Urv
ille
Alti
tude
(m)
Effe
ctiv
e gr
ain
radi
us (μ
m)
Latitude (°S)
4 - 7 January 20041 - 7 February 2004
Dum
ont D
'Urv
ille
Dom
e-C
Figure 5
(a)
50 55 60 65 70 75 80 85 90 95 1000.65
0.70
0.75
0.80
0.85
0.90
0.95
planetaryalbedo αp
200 μm
200 μm
100 μm
50 μm
A
lbed
o
Atmospheric transmittance (%)
30 μm
100 μm
50 μm
30 μm
Figure 6
surfacealbedo αs
effective snow grain radius r
45 50 55 60 65 70 75 80 85 900.65
0.70
0.75
0.80
0.85
0.90
surface albedo αs
Figure 7
200μm
200μm
100μm
100μm
50μm
50μm
r = 30μm
A
lbed
o
Solar zenith angle θo (degrees)
r = 30μm
planetary albedo αp
