Journal o/GlacioloD, Vol. 13.- No. 67,1974
THE INFLUENCE OF CLOUDINESS ON THE NET
RADIATION BALANCE OF A SNOW SURFACE WITH
HIGH ALBEDO
By W. AMBACH
(Physikalisches Institut der Universitat Innsbruck, Schopfstrasse 4 I , 6020 Innsbruck, Austria)
ABSTRACT. The short-wave and long-wave radiant fluxes measured in the accumulation area of the
Greenland ice sheet during a mid-summer period are discussed with respect to their dependence on cloudiness. At a cloudiness of 10/10, a mean val ue of 270 J /cm 2 d is obtained for the daily totals of net radiation
balance, whereas a mean value of only 75 J /cm2 d is observed at 0/ 10. The energy excess of the net radiation
balance with overcast sky is due to the significant influence of the incoming long-wave radiation and the high
albedo of the surface (average of84% ). High values of net radiation balance a re therefore correlated with
high values of long-wave radiation balance and low values of short-wave radiation balance.
RESUME . L'injluence de la nebulositi SlIr le bilan radialif net d'une slIrface de neige a jort albedo . Le flux de
rayonnement en ondes courtes et longues, mesure dans la zone d'accumulation de la calotte glaciaire du
Groenland pendant un e demi-periode estivale est discute dans sa dependance par rapport a la nebulosit<'.
Par une couverture nuageuse de 10/10 on obtient une valeur moyenne de 270 J /cm 2 d pour le totaljournalier
du bilan radiatifnet, alors qu'on observe une valeur moyenne de seulement 75 J /cm 2 d a 0/10 de nebulosite.
L'excedent energetique du bilan radia tif net sous ciel couvert est dil a I'influence significative du rayonnement
incident de grande longueur d'onde et au fort albedo de la surface (en moyenne 84% ). Les valeurs elevees du
bila n radiatif net sont done liees a ux fortes valeurs du bilan radiatif de gran de longueur d 'onde et aux faibles
valeurs du bilan de rayonnement de courtes longueurs d'onde.
ZUSAMMENFASSUNG.
Der Einjluss von Bewolkung allj die Gesamtstrahl,mgsbilanz einer Schneejliiche mit hoher Albedo.
Die kurzwelligen und langwelligen Strahlungsstri:ime werden fur eine Station im Akkumulationsgebiet des
Gri:inlandischen Inlandeises fur eine hochsommerliche Periode in ihrer gegenseitigen Abhangigkeit und
ihrer Abhangigkeit von der Bewi:ilkung diskutiert. Bei 10/ 10 Bewi:ilkung erhalt man als Mittelwert fur die
Tagessummen der Gesamtstrahlungsbilanz 270 J /cm2 d wahren:l bei 0/ 10 Bewi:ilkung nur 7~ .J /cm2 d
resultieren. Der gri:issere Energiegewinn durch Strahlung bei bedecktem Himmel ist in dem signifikanten
Einfluss d er langwelligen Einstrahlung und der hohen Albedo (Mittel 84% ) begrundet. Grosse vVerte der
Gesamtstrahlungsbilanz sind daher mit hohen Werten del' langwelligen Strahlungsbilanz und geringen
'Vert ~ n del' kurzwelligen Strahlungsbilanz korreliert.
INTRODUCTION
Results of radiation balance measurements in the accumulation area of the Greenland ice
sheet (station Carrefour, 1850 m a.s.!., lat. 69 ° 49' 25" N., long. 47 ° 25' 57" W., EGIG U 1967), made between 13 May and 28 July 1967, are discussed from the viewpoint of a paradox
which may be formulated as follows: The daily totals of the net radiation balance of a snow
surface with high albedo increase with increasing cloudiness. This is also valid for midsummer periods, when the extraterrestrial incoming short-wave radiation is extremely
high. The core of the paradox lies in the accentuation of the validity of this statement during
mid-summer periods. If it were restricted to periods with low solar elevation it would be a
triviality.
An analysis of the short-wave and long-wave radiation balance as dependent on the
cloudiness makes the paradox understandable. Cloudiness decreases the short-wave radiation
balance and increases long-wave radiation balance, which means that it has opposite effect in
the two spectral ranges. From the results of measurements it follows that the influence oflongwave radiation balance prevails. Figure I gives a schematic drawing of radiant fluxes, the
indices 0/10 and 10/ 10 being the degree of cloudiness. It shows that the incoming short-wave
radiation G, the reflected short-wave radiation R, the incoming long-wave radiation A, and
the outgoing long-wave radiation E, vary with cloudiness in the following manner:
G(IO/IO)
R( IO/ 10)
." :
<
<
G(0/ 10),
R(O/ IO),
A(IO/10)
E (10/10)
73
> A(0/10),
~
E (0/10).
JOURN AL
74
OF
GLACIO LOGY
incomi ng extrate rrestri al
shortw ave radiation
I
I
~
atmosp here
clear sky
overca st sky
0/10
10/10
R
G
shortw ave
range
A
G
E
shortw ave
range
longwave
range
net radiation flux
Fig.
I.
R
A
E
longwave
range
B=G-R +A - £
Schematic drawing of the radiant jlllxes with clear and overcast sky.
The mean values for the daily totals of the net radiatio n
albedo of 84 % at Station Carrefo ur, are the following: *
daily totals at 0 /10 cloudin ess: 18
daily totals at 10/ 10 cloudin ess: 65
differen ce: 47
balance B obtaine d for a mean
cal/cm 2 d
cal /cm 2 d
cal/cm 2 d
been studied in detail by
The radiatio n balance of polar snow and ice surface s has already
Holmg ren (1971), for
(1970).
s
several authors , above all by Holmg ren (1971) and Hoinke
(Devon Ice Cap) in
s
surface
snow
frozen
of
balance
n
radiatio
exampl e found out that the
2 d with a clear sky.
cal/cm
2
mid-su mmer is +40 cal/cm d with dense cloudiness, and +20
ly influen ced by long-w ave
Hoinke s (1970) mentio ned that the net radiatio n balance is decisive
on data from "Little
(based
evident
being
thus
radiatio n balance , the influen ce of cloudin ess
rn (1952), with
Dirmhi
and
er
Sauber
a.s.l.,
m
000
3
at
Americ a V", Antarc tica). In the Alps
2 d at 0/10 cloudin ess
cal/cm
25
of
balance
n
radiatio
net
a
d
an albedo of 80%, obtaine
of snow and ice surface s
and +69 cal/cm 2 d at 10/10. Furthe r studies on the radiatio n balance
J).
([CI964
s
have been reviewe d and discussed by Hoinke
SHORT- WAVE RADIAN T FLUX AND CLOUDIN ESS
ave radiatio n G and
Figure 2 shows the ratio betwee n the daily totals of incomi ng short-w
The ratio varies
time.
of
n
functio
a
as
surface
tal
horizon
a
extrate rrestria l radiatio n I on
'" SI-units: 1 cal/cm> d
=
0.484 W/m2 ; 1 cal/cm 2 h
=
11.63 W/m2.
INFLUENCE
OF
CLOUDINESS
ON
NET
R ADIATION
75
BALANC E
.....
EGIG J[.
HOOO
-
CARREFOUR
:1=69°1,9 ' 25" N
)., =1,7°25 ' 57 " W
-900
-800
800
~ 700
700 -
~600
600 -
~500
500 -
I
MAY
JUNE
JULY
I
0,8
mean value
=0,74
MAY
Fig.
-
JUNE
21
;:
JULY
D aily totals of extraterrestrial radiation on a horizontal surface I and of incoming short-wave radiation G as dependent on
time. T he ratio CI I is plotted in the lower part of the diagram, the resulting mean value is 0.74 .
2.
between 0.56 and 0.85, having a mean value of o. 74. These variations are due to differences
in cloudiness (Fig. 3). At 10/ 10, they are large because of the different opacity of clouds. T he
period of m easu rement is approximately symmetrical to 2 I June (Fig. 2), showing extremely
high values of extraterrestrial radiation.
LONG-WAVE RADIAT ION BALANCE AND CLOUDINESS
Figure 4 confirms the relation between long-wave radiation balance and cloudiness which
has been found over snow a nd ice surfaces already by several authors : T h e long-wave radiation balance shows strongly negative values at a cloudiness of 0/ 10 and slightly negative
JOURNAL
6
_
0,8
~
6
OF
6
66
_ 6_
6
6
6
666
66 _ _ 6
6
GLACIOLOGY
66
6
6
6
6
66 6
6
6
-
6
6
6
66
66
6
666
1f6
6
6
.......
6
11)
0,6
6-
E
;:,
11)
EG/GII
~
III
"t>
'-
~
0,4
(!)
0, 2
cloudiness
0110
4110
2110
6110
.
10110
8110
Fig. 3. The ratio C/I (C = incoming short-wave radiation, I = extraterrestrial radiation) as afunction of cloudiness.
-12
~
~
E
~
Iij
~
-10
lu
,
-8
!~
1,09
11272
1,1
I
'«
I
1,0 3330
I
~
50
o
I
I
0110 2110
o
-8
'«
-6
'03
"-+---+---+---t
cloudiness
frequency
100
-1
lu
,
25 31
cloud. 0110
150
~
Iij
59
o ----+---- +----0 r--+
---+ 0
..
-12
~
""E
~
I
-5
....,
~!
EGIGII
0
h
r
.
6110
8110
10/10 0
-2
I
j
-
0
-.2
cloud. 10lTO
I
-
50
100
frequency
I
'110
-4
+I,
~
150
Fig. 4. The long-wave radiation balance A-E as a function of cloudiness (1247 individual values) . The arrows give the
standard deviation, figures indicate numbers of samples for each group of cloudiness, the frequency distribution at 0/10 and
10/10 cloudiness are given in the left part and right part of the diagram.
INFLUENCE
OF
CLO UDINESS
ON
NET
RADIATION
77
BALANCE
values at 10/10, the relation being interpreted better in terms of a quadratic law than a linear
one. Hourly estimates of cloudiness and hourly totals of long-wave radiation balance were
used for the evaluation, comprising I 247 individual observations.
RADIATION BALANCE AND CLOUDINESS
Figure 5 shows the daily totals of radiant ftuxes for two series of measurements over snow
surfaces with high albedo (EGIG I, EGIG 11 ); for the EGIG I series (Camp IV-EGIG 1959,
I 013 m a .s.!., lat. 69° 40' 05· N., long. 49° 37' 58· W .) only those daily totals which satisfy
the condition of albedo larger than 70 % have been used. For EGIG 11, the condition of
albedo larger than 70 % was satisfied throughout the whole series. The mean value of the
albedo was 84%, a value which has been stated for dry snow surfaces of polar regions also by
other authors .
800
(JOO
~
_6
600
~--~
:>.:===:::::::::!"':!_ E
"A
-R
"-
3
~I.l _ _------~--:
-R
EGIG 11
mun
200
:
:
m~an ~/b~do~70%
~/G-R ~~G-R
:-+--:t---+---+---
~
0110
400
EGIGI
~/b~do=84%
-8
2110 4110
6110 8/10
~
.-
200
-0-8
-------- t---t---t---t---t---t------.
.
.
~--A-E
"A-E
cloudiness
-200
600
-6
400
o
_E
-A
10110
_______
0110
cloudiness
•
o
-200
2110 4110 6110 8110 10110
Fig . 5 . Daily totals of the ra:iiantjiuxes as dependent on the cloudiness for two series of meaSllrements (EGIG I and EGIG 11).
For groups of cloudiness see Table I.
The paradox is evident in Figure 5: The increase in the net radiation balance from minimum cloudiness toward maximum cloudiness, amounts in the case of EGIG I from 27 call
cm2 d to 83 cal/cm 2d and in the case of EGIG 11 from 18 cal/cm 2d to 65 cal/cm 2d. In order
to get a sufficient number of cases for the various groups of cloudiness, the classification of
Table I was used. The increase in net radiation balance with cloudiness becomes better
understa!ldable when comparing the respective dependence of short-wave and long-wave
radiation balances on cloudiness. The increase in the long-wave balance A-E with increasing
cloudiness is greater than the corresponding decrease of short-wave balance G-R.
JOURNAL
OF
GLACIOLOGY
TABLE I. GROUPS OF CLOUDINESS IN THE EGIG I AND EGIG II SERIES
Groups of cloudiness c in the series of EGIG I : Estimation of cloudiness in tenths, three times a day
o ~ c ~ 5.1; 1.5 < c ~ 4.5 ; 4·5 < c ~ 8.5; 8·5 < c ~ 10
Number of samples
3
3
3
8
Groups of cloudiness c in the series of EGIG II: Hourly estimations of cloudiness in tenths
0;
0 < c ~ 2;
2 < C ~ 4;
4 < c ~ 6; 6 < c ~ 8 ; 8 < c < 10;
Number of samples 13
12
7
II
4
9
10
9
HOURLY VARIATIONS OF RADIANT FLUXES AS DEPENDENT ON CLOU DINESS
Figure 6 gives the hourly variations of the radiant fluxes for a cloudiness OfO/ 1O and 10/10
and an albedo larger than 70%. Although the amplitude of the hourly variation of net
radiation at 0 / 10 is larger than at 10/ I 0, at a cloudiness of 0 / 10 the daily total , represented as
the area below the curve of B is composed of almost equal negative and positive parts. At a
cloudiness of 10/10, however, only the positive part of net radiation balance will be important,
as n egative values of B are negligible.
90
1
Albedo > 70%.cIo u d. 0/70
60
~
1~
30
0
TST
-20
Oh
•
12h
24h
EGIG J[
90
Albedo> 70%,cloud. 10/70
60
~
E
~
~
u
30
o
-20
•
Fig. 6. Mean hourly variations of the radiant jiuxes G, R, A, E and B for a cloudiness of 0/ IO and la/la.
INFLUENCE
OF
CLOUDINESS
ON
NET RADIATION
79
BALANCE
....
~
E
..
~
100 r-
~ -.----+---------~--------_4----------+_--------~--------_4----------+
III
I
EGIG J[
A6. A6.
50 +--------+------+-----+-------+----- ~
6.
ll~
I>
'"
---------t.._
o ---+---t---+--- ---+--100
200
A
A
'"
'"
A
A'"
i
A
I>
'"
--~+-a~~~+~~A~---+---
300
I>
J.A
A
-50
A A
:
-
MJ.
I
I
1>'"
I>
I>
AA
'" II> I>
I>"'~
I>
A [cal/cm 2dJ
~ -f-----
500
---+---
500
I
I
i
!
700
Fig. 7. Relation between the incoming long-wave radiation A and the net radiation balance B.
EGIG J[
+
r,.
~slimal~d
50+-------+-------4-------~
+
lA
-50~~--4---~_4--~--+_~--~--~--~~--~i--~~
Fig. 8. Relation between the incoming short-wave radiation G and the net radiation balance B.
80
JOURNAL
OF
GLACIOLOGY
RELATIONS BETWEEN THE RADIANT FLUXES (DAILY TOTALS)
Hoinkes (1970) has already pointed out that the radiation balance at high albedo values
is governed mainly by long-wave radiant fluxes. Figure 7 proves that the incoming long-wave
radiant flux A is in positive correlation with the net radiation balance B. The range of values
coincides also quantitatively with the range given by Hoinkes (1970) whose data, measured
during the early Antarctic summer (September 1957 to January 1958), also show very well
the range of negative values of net radiation balance. The incoming short-wave radiation G,
however, is in a weak negative correlation to the net radiation balance B (Fig. 8). The fact
that the present series of measurements is nearly symmetrical with respect to the solstice
( 13 May to 28 July) means that the change in extraterrestrial radiant flux is small.
The relations between the net radiation balance B and the short-wave and long-wave
balances are shown for individual months in Figure 9. Owing to the separate treatment of
the individual months, changes of extraterrestrial radiant flux are of minor importance.
Again, long-wave radiation balance A-E is in good positive correlation to the net radiation
balance B; the short-wave radiation balance G-R, however, shows only weak negative correlation to the net radiation balance B. The relation between the short-wave radiation balance
G- R and the long-wave radiation balance A- E in Figure 10 is still clearer. The paradox
mentioned above is expressed numerically as follows: A decrease of the short-wave radiation
balance G-R by 100 caljcmld (owing to increased cloudiness) is related to an increase of the
long-wave radiation balance A-E by approximately 150 cal/cm 2 d . This relation is applicable
to each individual month .
Hence the quantitive explanation of the paradox follows: at a high albedo, a decrease
(owing to greater cloudiness) in the short-wave radiation balance G-R even in mid-summer
is more than compensated for by an increase in the long-wave radiation balance A- E. The
energy gain owing to radiation is about 50 caljcm 2 d higher when the sky is overcast than when
cloudless, although maximum values of the incoming short-wave radiation of more than
800 cal/cm 2 d occur in this period. On the basis of the measured radiant fluxes, it can be
estimated that the effect under discussion occurs at an albedo larger than 75 %. This means
that large areas of the polar i<;e sheets fulfill the c9ndition for this paradoxical effect. For hourly
totals of net radiation balance, however, the paradox cannot in general be established.
INSTRUMENTATION, CALIDRATlON AND EVALUATION
Instrumentation, calibration and evaluation followed a method described earlier (Ambach,
1963). Two solarimeters (Moll-Gorczynski) and a Lupolene instrument by R. Schulze were
used as radiation detectors . Calibration in the short-wave range was made in the field using
direct solar radiation at levelled detector surfaces by means of a Linke-Feussner actinometer.
The temperature coefficient of the instruments was applied. Calibration in the long-wave
range was made in the laboratory following a previously described method (Ambach and
others, 1963). For the evaluation, the difference in the sensitivities of the thermopiles of the
Lupolene instrument to short-wave radiation and long-wave radiation was taken into account.
The results of calibration in the short-wave range confirm the dependence of the calibration factor on solar elevation as observed in earlier studies. Because of an azimuth effect,
there are slight differences in the calibration factor for series measured before noon and after
noon (Fig. 11). The calibration factor for isotropic radiation 11 was calculated according to
the formula given by Liljequist (1956)
I
~
=
f",.
sin 2h
f (h) dh,
o
INFLUENCE
OF CLOUDINESS
ON
NET RADIATION
EGIGI
100
100
I
53
E
i
Ii
MAY_
III
I
I
r
C\j
~
50
~
I
i
,
I
'0
0
0
o 01
0
0%
0
0
1
I
I
-
o
-50
-100
JULY
~
c
o °o l lXl o
III
o
----
~
6
b.
50
~
III
6
o
----
-6- -6-A
11
b.
/1
~
I
i
50
100
I
E
~
Cij .
0-
•
-
Ii
-so
150
o
C'\j
50
-
6
i
6
-
~
100
i
!tJ
6 ·
-r -
I
I
100
-
I
I
-150
-t-
I
G-R fca/km 2dJb.
0
~
-so
-
E
i
6 !
I
-
!ti
C'\j
!
I
I
I
A -£ [cal/cm 2dJ
I
I
I
i---- M~Y_
- - -I-
1
---- + --~~t- ~-- ~---
o
orP
0
!
o
,
0
0
I
I
o
6
I
I
- 50
6
:
6 6
t~
_ _ _ _ ~ --b.-~-Q~~+----
.
A-E [cal!cm 2dJ
00
JULY
o
4:,-lr- ..... -~-- -+- ---0
G-R [ca/!cm 2dJ
•
I
6 /1/1
I
I
-50
81
BALANCE
o
4
i
L----+----+----+----...I-.----+----_ _ _~_ _____!1_50
-150
-100
-50
o
50
100
150
Fig. 9. Relation between the net radiation balance B and the long-wave radiation balance A-E, as well as short-wave radiation
balance G-R.
JO U RNAL
..,
'"E
....,
....,
~
E
u
-"
"
~
l<J,
~
A
A
~
~A
A
A
AA
A
'<{
A
GLAC IOL OGY
I
;::
'"E
EGIG 1l
~
~
-150
OF
~
- -r-
A
"
-
l<J,
AA
'<{
A
~
L!:l
..:
A
-150
A
'<{
A A"l
6,AAA
A
AA
A
A
A
A
AAA
-100
-100
A
A
~
A
A
AA
A
A
A
;AA ~
- 50
A
A
-50
A
A
I
A
.
o - -'- - + - -1- 0
100
2000
I
... 50
Fig.
10 .
,
A
A
G -R [callcm 2 dJ
A
A
G-R [callcm 2 dJ
AA
A
..
--'1--+--1- -
..
100
I
I
-
100
200
G- R [ca/lcm 2dJ
200 0
A
I
I
MAY
JUNE
I
I
JULY
I
... 50
Relalioll betwee/! the short-wave radiatioll balance G-R and the long-wave radiation balance A - E .
t
£GIGll
....,
'"
.-::
c:
;:,
I
..;
Jxl0-J
o
--:a:I.J,.-----I--
'"
·5
~r:
.......-:
Lupo/~n~ radiom~l~r
.6
-t
-----
i
I
I
~
I
,
f.(z=OJ=2.7t.xl0-J-
fSo/arim~l~r
pt:
f.(z=0J=1.5t.7xlO-J __
1
I
•
morning
0
afl~rnoon
I
1
600
Fig.
11.
1-- z~n;lh
d;sl.. nc~
z
1
soo
The calibration fa ctors of the solarimeter and of the L/lpolene instrument (Schulze ) as dependent on zenith distance.
INFLUENCE
OF
CLOUDINESS
ON
NET RADIATION
BALANCE
where f (h) represents the dependence of the calibration factor on the solar elevation h,
averaged over values measured in the morning and in the afternoon.
For cloudless days, the evaluation was made by using the calibration factor as dependent on
solar elevation. The share of sky radiation on cloudless days known from calibration measurements was evaluated with an adequate calibration factor h, which was calculated according
to the formula given by Liljequist (1956) :
Jcos h
= f (h) dh.
"/2
I
h
o
Graphs for the evaluation of the formulae are shown in Figure 12. Days with a cloudiness
of more than 0/ IO were treated with a calibration factor for isotropic radiation, as there exist
no continuous records of diffuse sky radiation. The influence of the instrument holder on the
albedo was accounted for by relative measurements with a portable solarimeter.
EGIGI
4
,
,I
Lupo/Me rlldiometer
I
.......
I
/
f
.......
.......
300 "..c:
:::::;.
~
.!:;
Cl)
I
,
E
~
,
/
800
I
I
I
Solarimeter
,
E
o.!
1
~
'~
~
~
~
0
0
V)
u
V)
u
t
.......
E
o.!
"-
~
.!:;
600
Cl)
1.00
Fig .
Evaluation curves/or calculating the calibration/actor/or diffuse isotropic radiation and/or diffuse sky radiatioll with a
clear sky.
12.
ACKNOWLEDGEMENTS
The Fonds zur Forderung der wissenschaftlichen Forschung is thanked for supporting
the evaluations. I also want to thank Mr G. Markl for assisting in the field work and Mr P.
Quehenberger and Mrs J. Conen for helping with the evaluation.
MS. received 16 July 1973
JOURNAL
OF
GLACIOLOGY
REFERENCES
Ambach, W. 1953. Untersuchungen zum Energieumsatz in der Ablationszone des griinlandischen Inlandeises
(Camp IV- EGIG, 59° 40' oS" N, 49° 37' SS" W). Meddelelser om Grenland, Bd. 174, Nr. 4·
Ambach, W., and others. 1953. Ober die Eichung des Strahlungsbilanzmessers nach R. Schulze (Lupolengerat),
von W. Ambach, E. Beschorner und H. [C.] Hoinkes. Archiv fur Meteorologie, Geophysik und Bioklimatologie,
Ser. B, Bd. 13, Ht. I, p. 75-95.
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