and development of katabatic flows and, more generally, to collect a data-set on the climatic patterns in this remote area. In the first year, the measurements were performed
Ž
X
at two different sites located near the Italian base of Terra Nova Bay lat 74841 S, long
X
. 164807 E , close to the intersect point of the Priestley Glacier and the Nansen ice sheet
and, in the following year, over the Reeves Neve Glacier at 1200 m a.s.l.
`
The second set of measurement is used for the present work, which were collected Ž
. throughout December every 10 min with a Schenk mod. 8111 net pyrradiometer and a
Ž .
Schenk mod. 8104 albedometer. Both were equipped with two sensors to collect the incoming radiation from the whole sphere. A direct estimation of both the total net
radiation and the albedo was possible. The net pyrradiometer is able to estimate the total net radiation in the 0.3–30 mm.
spectral range. The black surface of the upward sensor estimates the direct and indirect solar radiation and the thermal radiation emitted by the atmosphere. The visible radiation
reflected by the surface and the long-wave radiation emitted from it are detected by the downward-looking sensor.
Ž .
The albedometer is made up of two pyranometers 0.3–3 mm
for the direct determination of the albedo. The upward sensor receives only the direct and indirect
solar radiation from the sky, while the other receives the radiation reflected by the surface.
By means of a resistance thermometer inside the pyrradiometer, it is possible to determine the total radiation coming from the sky and from the surface, according to the
following formulas S q L s V f q ´ s T
4 i
i u
u s
s
and S q L s V f q ´ s T
4 o
o 1 1
s s
respectively, where T is the internal temperature of the instrument and ´ its emissivity;
s s
signals V and V are generated in the upper and lower receiving plates, respectively,
u l
and f and f are the calibration parameters suitable for the conversion in watts per
u l
square meter. Subsequently, using the albedometer signals, the incoming and outgoing long-wave radiative components are determined.
All the analog signals are converted into digital values by a fully programmable Campbell CR-10 data-logger capable to periodically store the values in an internal
memory.
3. Results and discussion
3.1. Long-waÕe radiation Ž
. To verify the suitability of the Swinbank 1963 formulation concerning the long-wave
Ž
y2
. Ž .
radiation from the sky, the entire set of values L mW cm are plotted in Fig. 1 a , as
i
a function of the corresponding emission of a black body having the same air
Ž . Fig. 1. a Infrared atmospheric flux vs. long-wave radiation of a black-body with air temperature at screen
Ž . level. Plotted is the entire data set from Reeves Neve. b Daily mean values of the atmospheric infrared flux
`
Ž .
Ž .
Ž .
Ž .
L in comparison with the Swinbank 1963 , Idso and Jackson 1969 , and Deacon 1969 relationships.
i
temperature at screen level since the atmospheric effective emissivity is defined by the ratio of these quantities.
The analysis of L measurements shows a fairly homogeneous distribution around the
i
Ž .
trend defined by Swinbank’s 1963 relationship, which was based on a set of measures characterised by a black body radiation between 30 and 50 mW cm
y2
in a range of temperatures higher than the polar ones.
Fig. 2. Daily pattern of infrared radiation from the sky on a clear-sky day.
According to a preliminary analysis of solar radiation flux data during the whole day, it is possible to make a preliminary classification between sunny days, with a sinusoidal
trend nearly proportional to the sinus of sun elevation angle, and overcast days. Ž .
In Fig. 1 b the mean daily values of the thermal atmospheric radiation flux are plotted divided into sunny and cloudy days. As expected, L values for cloudy days are
i
higher than for sunny days, but the mean values generally seem to confirm the Swinbank Ž
. Ž
. Ž
. 1963 and Deacon 1970 relations, being distributed near the Swinbank 1963 trend
Ž .
and below the curve of Idso and Jackson 1969 . The values of the atmospheric radiation flux on one clear day are plotted them in Fig.
2 vs. the flux emitted by a black body at air temperature. Note the characteristic eight-shape pattern, a major feature of all clear days. The lowest part includes the
mid-day values. On cloudy days we notice a spread with increasing radiation and temperature values.
Ž .
According to Paltridge 1970 , the values for cloudless days were plotted as devia- Ž
. tions from Swinbank’s 1963 formula all day long. Fig. 3 displays the values of three
Ž .
nonconsecutive very clear days, which presented a similar pattern days: 332–334–344 . Ž
. They are characterised by a trend at mid-day hours where the Swinbank 1963 relation
seems to overestimate the flux of real atmospheric radiation, reaching minimal radiation values near y9 mW cm
y2
near mid-day. The absence of a day–night cycle in polar measurements removes the night plateau
characterised by a positive constant pattern. 3.2. Cloud coÕer
Ž .
Fig. 3 also shows the trend of the deviation from Swinbank’s 1963 formula during a partially cloudy day: the difference between this trend and that on clear sky days must
Ž .
Fig. 3. Deviation of the atmospheric radiation values from those predicted by the Swinbank 1963 relation: Ž
. solid lines correspond to three clear-sky days and the dashed line to a partially covered day early hours only .
Numbers refer to day from the beginning of the year 1994.
be closely connected to the cloud cover and, according to hypothesis, is independent of Ž
. the temperature and humidity ranges. Paltridge 1970 associated this difference with the
Ž .
cloud cover index between 0 and 1 : on average, one degree of cloud cover corresponds to a difference of about 0.6 mW cm
y2
. Following this argument it is possible determine the daily pattern of the cloud cover index for any given day.
The study of all the available measurement days allows us to determine local differences of up to 8–9 mW cm
y2
from the trend line, which identify the three clear-sky days that always underestimate any different point value.
Fig. 4 shows the mean hourly trend of cloud cover index for the same partially covered day as in Fig. 3; any 0.85 mW cm
y2
of difference from the mean clear sky trend corresponds to one degree of cloud cover. The relation used follows:
DS N y DS 0
Ž . Ž .
N s 8.5
Ž .
where DS N represents the difference between the real flux of infrared atmospheric
Ž .
radiation and the one expected by the Swinbank 1963 formula, which depends on the air temperature values.
Ž .
According to the Kasten and Czeplak 1980 relation, the cloud cover can also be estimated using the variation of incident solar radiation flux by comparison with a clear
day. In Fig. 4 the mean hourly values of N for the same partially covered day are plotted according to the following expression:
1rb
2
1 S N
Ž .
N s y 1
ž
b S 0
Ž .
1
Ž .
Fig. 4. Mean hourly values of the cloud cover index throughout a day obtained from infrared solid and Ž
. visible dashed radiation.
Ž . where S 0 includes the mean hourly values of a clear day with marked clearness. The
Ž .
values of b and b coefficients are those calculated by Kasten and Czeplak 1980 at
1 2
Hamburg on the basis of a 10-year data-set, assuming that in winter coefficient b has a
1
mean value of 0.7, likely due to multiscattering effects between the snow surface and the cloud base.
The analysis of the daily pattern of the cloud cover index indicates a correlation between the result obtained through the atmospheric radiation flux and that deriving
from the solar radiation flux: the partially covered day is characterised by a pronounced cloud cover in the last hours of day and a clear sky for the rest of the day. However, the
entire set of mean hourly values appears to produce a poor correlation because a spread
Ž .
Ž . range of values of DS N y DS 0 corresponds to a single value of the quantity
Ž .
Ž . S N rS 0 . Unlike the case of solar radiation, for a given cloud cover index the
incoming infrared flux strongly depends on the physical characteristics of the cloud, especially the cloud base temperature, which in turn is directly linked to the cloud
height.
Ž .
Ž . Fig. 5 plots the mean two-hourly values of DS N –DS 0 vs. the corresponding
Ž .
Ž . Ž
. Ž .
mean values of S N rS 0 y 1 with the corresponding mean values of DS N y DS 0 at the same conditions of solar radiation, the picture shows a marked spread in infrared
values which, however, seems to be limited by two linear relations. With the purpose of investigating how the cloud body height can influence the
infrared radiation fluxes, the logarithmic values for the same quantity has been reported in Fig. 6. Note that a certain variability exists in the polynomial degree that is to be
fitted to data; this could be caused by different contributions to the infrared flux by various the cloud body height.
Ž Fig. 5. Relation between the mean two-hourly values of the fraction of visible radiation with respect to a clear
. Ž
. day and the differences from the clear day trend of the deviation from Swinbank’s 1963 formula.
According to this hypothesis, the data were divided into two groups: the values set under the best fit line belong to the group characterised by clouds at middle-low altitude;
the data set below the best fit line was assigned the group characterised by clouds at
Fig. 6. Mean two-hourly values of the log of the fraction of visible radiation and of the difference between
10
Ž .
the Swinbank 1963 relation for a clear sky day.
middle-high altitude. The coefficients a and b of the following formula for the two groups were subsequently and separately determined:
S N
Ž .
b
1 y s a DS N y DS 0
Ž . Ž .
S 0
Ž .
The analysis of the middle-low cloud altitude data group resulted in good confidence coefficients a, mean value 0.02, and b, mean value 1.4. The analysis of the middle-high
altitude data produced the coefficients a of about 0.16 and b of about 0.5. The confidence in this last case is somewhat lower and this can be ascribed to the fact that
high clouds have less influence on the infrared terms than low clouds, unlike the case of visible radiation.
Ž .
The Kasten and Czeplak 1980 relationship introduced the following relation be- tween the cloud cover index and the difference between the trends of the deviation from
Ž .
the Swinbank 1963 formula and the cloudless sky trend:
d
N s c DS N y DS 0
Ž . Ž .
Ž . where DS 0 corresponds to the mean hourly values of the difference between the
infrared radiative flux and the Swinbank one on a cloudless day. Table 2 shows the values of coefficients c and d depending on the height of the cloud base.
Fig. 7 is a scatter plot relating the cloud cover index obtained using the Kasten and Ž
. Czeplak
1980 relation to that resulting from the parameterisation of long-wave
radiation. The parameterisation is subject to strong limitations at low values in the cloud cover
Ž .
index. Kasten and Czeplak’s 1980
Hamburg measurements, especially in winter, showed that the mean hourly values of the visible radiation flux for values up to about
0.3–0.4 of the cloud cover index were higher than the clear-sky day values, most likely on account of the scattering of visible radiation by clouds and surface.
3.3. Albedo The short-wave radiation terms of a snow-covered surface need to be determined
since the albedo is a crucial parameter that influences the surface energy balance. In Antarctica it presents high values limited between 0.81 and 0.85.
Because of these high values even a small variation in albedo can cause substantial variations in the absorbed visible radiation: indeed, a variation in albedo values 0.81 to
0.85 corresponds to a reduction of 21 in solar radiation absorbed by the surface. High
Table 2 Coefficients c and d in relation to the height of cloud cover base
Height of cloud base c
d High
0.65 0.15
Low 0.35
0.41
Fig. 7. Scatter diagram of the cloud cover index N obtained by visible and infrared radiation.
albedo values cause the radiation balance in Antarctica to be negative for most of the year.
Fig. 8 shows the large variation of albedo during three cloudless days. This variation Ž
. Ž
. is more marked than in the Carroll and Fitch 1981 and Iqbal 1983 relations, and does
Ž .
Ž .
Ž .
Fig. 8. Diurnal variation of albedo for three cloudless days solid curves and Iqbal’s 1983 relation dashed . Numbers refer to day from the beginning of the year 1994.
Ž .
Fig. 9. Deviation of the observed albedo from the Iqbal 1983 expression for three cloudless days.
not have a good correlation with the elevation angle. We have calculated the difference Ž
. between the measured albedo and that predicted by Iqbal 1983 :
r C s r
X
q 1 y r
X
exp y0.1C y 1 y r
X
r2
Ž .
Ž .
Ž .
Ž .
where r
X
is the albedo at the highest sun elevation angle and c the sun elevation angle. In Fig. 9 the differences of the measured albedo for three cloudless days are plotted.
Note that data refer to a set of measurements where the sun elevation was never below the horizon and an axial symmetry exists in to E–W direction with lowest albedo values
when the sun was in the east and the highest in the opposite direction. This symmetry can be explained by the geometric conditions of the snow-covered surface.
Fig. 10. Longitudinal cross-section of the modelled surface in an E–W direction. ´ is the solar elevation angle, h the height of the crest, L the distance from the next one.
Ž .
Fig. 11. Deviation in the albedo values of the modelled surface from the Iqbal 1983 formula.
A first solution to the problem of this albedo behaviour was to consider the effects of the surface slope in connection with the incident angle of the sun beam. The Reeves
glacier is in fact characterised by a constant slope in the E–W direction of about 2–38. A quick analysis shows, however, that this value is by no means sufficient to explain so
high a deviation from the expected albedo.
A strong relation has been assumed to exist between albedo and shape of the reflecting snow surface. It is well known that the surface of this Antarctic area is often
Ž .
subject to erosive and modelling phenomena sastrugi . A geometric model of such a surface that can cause these symmetry conditions has been conceived and is reported in
Ž .
Fig. 10 longitudinal cross-section . It is assumed that the longitudinal axis of this surface lies in an E–W direction and that the angle g formed by the direct radiation with
the horizontal surface can be expressed by the relation below, proposed by Wendler and Ž
. Kelley 1988 . The determination of the portion of the surface that lies in the shade at
any time during the day is then computed as follows: g s arctan tan c rcos AZ = D q p
Ž . Ž
.
C and AZ are the elevation and solar azimuth angle, respectively, and D the longitudinal direction of the surface.
For any given value of g the ratio between the surface illuminated by the sun and that corresponding to g is pr2 can be computed. Assuming the albedo is proportional
to the non-shady surface, the following relations allow for the determination of the effective albedo values from those of a perfectly horizontal surface:
pr2 y g r s 1 q
r horiz.surf.
Ž .
ž
Lrh 1
r s 1 y r horiz.surf.
Ž .
ž
Lrhtan g
Ž .
Fig. 12. Photograph of the snow-covered surface at the measurement site. Clearly visible are the sastrugi formations.
The first approximates the albedo when the solar radiation illuminates the concave side of the surface, i.e. when the sun is to the West. Conversely, when the sun is in the
East, the albedo is approximated by the second relation, with g the solar elevation angle.
Ž .
By introducing in this parameterisation Iqbal’s 1983 albedo relation instead of the albedo for the plane surface and supposing that the ratio Lrh equals 20, we plotted the
difference between the albedo values generated by this particular surface and the expected values of a plane surface throughout the day. In Fig. 11 the trend generated by
this surface model is plotted. The graph shows a reasonably good agreement with the real measured values, given also the very simple model.
To support the modelled surface pattern a photograph of the snow surface at the measurement site is reported in Fig. 12. A closer look reveals a crest about 10 cm high
and a mean shed of about 2 m.
4. Conclusions
