Introduction

Results of radiation balance measurements in the accumulation area of the Greenland ice sheet (station Carrefour, 1850 m a.s.l., lat. 69° 49’ 25” N., long. 47⁰ 25’ 57” W., EGIG II–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 of long-wave radiation balance prevails. Figure 1 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:

Fig. 1.Schematic drawing of the radiant fluxes with clear and overcast sky.

The mean values for the daily totals of the net radiation balance B obtained for a mean albedo of 84% at Station Carrefour, are the following:Footnote ^*

The radiation balance of polar snow and ice surfaces has already been studied in detail by several authors, above all by Reference HolmgrenHolmgren (1971) and Reference HoinkesHoinkes (1970). Reference HolmgrenHolmgren (1971), for example found out that the radiation balance of frozen snow surfaces (Devon Ice Cap) in mid-summer is +40 cal/cm²d with dense cloudiness, and +20 cal/cm²d with a clear sky. Reference HoinkesHoinkes (1970) mentioned that the net radiation balance is decisively influenced by long-wave radiation balance, the influence of cloudiness thus being evident (based on data from “Little America V”, Antarctica). In the Alps at 3 000 m a.s.l., Reference Sauberer and DirmhirnSauberer and Dirmhirn (1952), with an albedo of 80%, obtained a net radiation balance of –25 cal/cm² d at 0/10 cloudiness and +69 cal/cm²d at 10/10. Further studies on the radiation balance of snow and ice surfaces have been reviewed and discussed by Reference Hoinkes and OdishawHoinkes ([^c1964]).

Short-Wave Radiant Flux And Cloudiness

Figure 2 shows the ratio between the daily totals of incoming short-wave radiation G and extraterrestrial radiation I on a horizontal surface as a function of time. The ratio vanes between 0.56 and 0.85, having a mean value of 0.74. These variations are due to differences in cloudiness (Fig. 3). At 10/10, they are large because of the different opacity of clouds. The period of measurement is approximately symmetrical to 21 June (Fig, 2), showing extremely high values of extraterrestrial radiation.

Fig. 2.Daily totals of extraterrestrial radiation on a horizontal surface I and of incoming short-wave radiation G as dependent on time. The ratio G/I is plotted in the lower part of the diagram, the resulting mean value is 0.74.

Long-Wave Radiation Balance and Cloudiness

Figure 4 confirms the relation between long-wave radiation balance and cloudiness which has been found over snow and ice surfaces already by several authors: The long-wave radiation balance shows strongly negative values at a cloudiness of 0/10 and slightly negative values at 10/10, the relation being interpreted belter 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 1 247 individual observations.

Fig. 3.The ratio G/I (G = incoming short-wave radiation, I = extraterrestrial radiation) as a function of cloudiness.

Fig. 4.The long-wave radiation balance A-E as a function of cloudiness (I 247 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.

Radiation Balance and Cloudiness

Figure 5 shows the daily totals of radiant fluxes for two series of measurements over snow surfaces with high albedo (EGIG I, EGIG II) ; for the EGIG I series (Camp IV–EGIG 1959, 1 013 m a.s.l., 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 II, 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.

Fig. 5.Daily totals of the radiant fluxes as dependent on the cloudiness for two series of measurements (EGIG I and EGIG II). For groups of cloudiness see Table 1.

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 cal/ cm²d to 83 cal/cm²d and in the case of EGIG II from 18 cal/cm²d to 65 cal/cm²d. 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 understandable 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.

Table 1.Groups of Cloudiness in the EGIG I and EGIG II Series

Hourly Variations of Radiant Fluxes as Dependent on Cloudiness

Figure 6 gives the hourly variations of the radiant fluxes for a cloudiness of 0/10 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 10/10, 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 negative values of B are negligible.

Fig. 6.Mean hourly variation of the radiant fluxes G, R, A, E and B for a cloudiness of 0/10 and 10/10.

Fig. 7.Relation between the incoming long-wave radiation. A and the net radiation balance B.

Fig. 8.Relation between the incoming short-wave radiation G and the net radiation balance B.

Relations between the Radiant Fluxes (Daily Totals)

Reference HoinkesHoinkes (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 Reference HoinkesHoinkes (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 B 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 cal/cm²d (owing to increased cloudiness) is related to an increase of the long-wave radiation balance A–E by approximately 150cal/cm²d. 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 cal/cm^zd higher when the sky is overcast than when cloudless, although maximum values of the incoming short-wave radiation of more than 800 cal/cm²d 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 ice sheets fulfill the condition for this paradoxical effect. For hourly totals of net radiation balance, however, the paradox cannot in general be established.

Instrumentation, Calibration and evaluation

Instrumentation, calibration and evaluation followed a method described earlier (Reference AmbachAmbach, 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 (Reference AmbachAmbach 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 fⁱ was calculated according to the formula given by Liljequist (1956) 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.

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.

Fig. 10.Relation between the short-wave radiation balance G–R and the long-wave radiation balance A–E.

Fig. 11.The calibration factors of the solarimeter and of the Lupolene instrument (Schulze) as dependent on zenith distance.

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 f_d, which was calculated according to the formula given by Liljequist (1956):

Graphs for the evaluation of the formulae are shown in Figure 12. Days with a cloudiness of more than 0/10 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.

Fig. 12.Evaluation curves for calculating the calibration factor for diffuse isotropic radiation and for diffuse sky radiation with a clear sky.