Solar and terrestrial radiation dependent on the amount and type of cloud

Solar Energy Vol 24, pp. 177 189 Pergamon Press Ltd., 1980. Printed in Oreat Britain

SOLAR A N D TERRESTRIAL RADIATION D E P E N D E N T O N THE A M O U N T A N D

TYPE OF C L O U D

FRITZ KASTEN and GERHARD CZEPLAK Deutscher Wetterdienst, Meteorologisches Observatorium Hamburg, 2000 Hamburg, F.R.G.

(Received 4 June 1979: revision accepted 13 September 1979)

Abstract- Ten-year (1964--73) continuous records at Hamburg of hourly sums of solar and terrestrial. downward and upward radiation flux densities have been evaluated with regard to simultaneous hourly cloud observations. The irradiance at given solar elevation is plotted vs total cloud amount for each season and for the whole year; in the same way, the ratio of the irradiance under clouded to that under cloudless sky is presented. Additional diagrams show the irradiance under cloudless and under overcast sky as function of solar elevation. The ratio of global radiation at total cloud amount N okta, G(N), to global radiation at cloudless sky. GI0), at the same solar elevation ~,, turned out to be independent of ), and can be parameterized by G(N)/G(O) = 1 -0.75(N/8) 3"4. The influence of cloud type is demonstrated by diagrams showing the irradiance under skies overcast by a specific cloud type as function of solar elevation for each season and for the year; also, the corresponding ratios "overcast" to "cloudless" are presented. In the case of global radiation, the ratios G(8)/G(0) which may be interpreted as the transmittances of the specific cloud types for global radiation, turned out to be independent of solar elevation and have the following mean values: Ci, Cc, Cs 0.61; Ac, As 0.27; Sc, Cu 0.25; St 0.18; Ns 0.16.

I. INTRODUCTION

For quantitative estimates of the energy budget of the earth surface and their application to solar energy use, knowledge of the influence of clouds on the radiation regime at the ground is useful. Due to the great variety and variability of cloudiness on the one hand and the lack of methods to measure cloudiness quan- titatively on the other hand, the dependence of radiation fluxes on cloud amount and type has been tried to be parameterized by many authors in the past. Most investigations were based either on daily or even monthly means of both radiation and cloudiness [1- 11], or on case studies of a set of single observa-

tions [ 12 13], Lurnb[14] evaluated hourly observations during

the period 1958-61 of global radiation and cloudiness aboard two weather ships on the North Atlantic Ocean and derived regression lines of the ratio of global radiation to extraterrestrial radiation versus solar elevation for 9 categories of cloudiness defined by different combinations of total cloud amount and the amounts of low, middle and high clouds. Norris[15] applied the linear regression method of Lumb to global radiation measurements and total cloud reports from three hourly synoptic observations during the year 1964 at Melbourne, Australia, but found little correlation. The work of Lumb was extended by Parker[16] to observations taken in 1967-69 at the island Gan in the equatorial Indian Ocean: another set of 12 cloudiness categories appro- priate to tropical conditions was introduced and also daily satellite nephanalyses extracted and categorized. Parker extended Lumb's linear regression formula for

cloudless sky by three factors which are linear in the amount of low, middle and high clouds, respectively, as proposed by Gadd and Keers [17].

A careful analysis of hourly global radiation recorded over a 1 yr period 1944-45 at Os near Ber- gen, Norway is given in the monograph by Schieldrup Paulsen [18] who proposed a second order regression for the dependence on total cloud amount of global radiation relative to the cloudless case; linear regres- sions were proposed for relating the global radiation ratio separately to the amount of low, middle and high cloud, respectively. The influence of cloudiness on diffuse sky radiation was thoroughly investigated by Bener [19] on the basis of 3577 momentaneous irradiances recorded during the full 2-yr period 1944-45 at Davos, Switzerland. Diffuse sky irradia- tion was plotted vs solar elevation in 10 ° intervals fbr different cloud types and separated into summer and winter season; furthermore, the diffuse sky radiation "'clouded/cloudless" is given in dependence on the amount of low, middle and high clouds, showing a maximum at 7 9 tenths cloudiness.

The probably most comprehensive investigation so far on global radiation related to cloud amount and type was undertaken by Haurwitz [20-22] who evaluated 11 yr records of hourly sums of global radiation and corresponding cloud observations at Blue Hill near Boston, Massachusetts; global radiation was presented versus relative optical air mass m = l/sin 7' where ), = solar elevation, for different cloud amounts and cloud densities or cloud types, respectively, and an exponential dependence on m was proposed.

An analysis of both solar and terrestrial radiation fluxes in dependence on cloud amount was performed

177

178 FRtTZ KASTEN and GERHARD CZEPLAK

by W6rner [23] by evaluating hourly radiation sums recorded during 1957-59 at Potsdam near Berlin. Diagrams show the ratios "clouded to cloudless" of global radiation, of the quotient (direct beam)/(global radiation}, of net terrestrial surface radiation and of atmospheric radiation vs the amount of low, middle and high clouds; square root equations were proposed by W6rner [24] for relating the global radiation ratio to the different cloud amounts.

The present investigation is intended to give additional, new information on the correlation of radiation with cloudiness for the following reasons: (1) Neither daily totals nor monthly means nor case studies of single observations, but actual hourly values were correlated. (2) The data material is not from an incidental period of one or a few years, but is a complete, homogeneous set of 10yr continuous hour by hour records at a research site. (3) Not only global radiation, but all solar and terrestrial radiation fluxes on the' horizontal plane have simultaneously been recorded and are included in the analysis. Among the results derived below, the new parameterization formula (I) correlating global radiation to total cloud amount, and the mean transmittances of the different groups of cloud types for global radiation, as given at the end of the abstract, are considered to be most valuable.

2. DATA SOURCE AND PROCESSING

At Meteorological Observatory Hamburg of the German Weather Service, both solar and terrestrial radiation flux densities have been recorded continu- ously since 1954 by means of Moll-Gorczynski pyran- ometers (man. by Kipp and Zonen, Delft, Nether- lands) and Schulze net pyrradiometers (man. by B. Lange, Berlin). The measurements are based on the International Pyrheliometric Scale of 1956 (IPS 1956) i.e. the solar constant is taken io = 1.94cal cm 2rain ~ = 1 3 5 k W m - 2 . Introduction of i 0 = 1.37 kW m -2 according to the World Radiometric Reference (WRR) proposed for 1981 [25] will not influence the results given below because a change of irradiance by 2.2 per cent is far within the statistical fluctuations caused by varying cloudiness.

From 1964 on, use of automatic integrators allowed to generate hourly sums of all measured radiation fluxes on a routine basis. Hourly sums are a mean to obtain quantitative values even in cases of large vari- ations in cloudiness and consequently of widely scattered points on the radiation records; on the other hand, the time resolution of l hr seems to be short enough to permit correlation with actual cloud observations. Cloud observations are performed every hour by the Air Weather Station at Hamburg Fuhlsbiittel Airport in the immediate vicinity of the Observatory. The 10-yr period from 1964 to 1973 was selected and only daytime data were used for this study.

The data were first grouped into 4 seasons: March, April, May = spring: June, July, August = summer;

September, October, November = autumn; Decem- ber, January, February = winter. Within each season, the hourly values were assorted into classes of equal mean hourly solar elevation 7 by intervals of A)' = 10 °. The radiation data within each of these classes were then assorted according to total cloud amount N. Since the radiation data are hourly sums whereas the cloud data are momentaneous observations at the end of the respective hour, only such cases were admitted when the reported cloud amount at the foregoing hour was identical to the hour under consideration. This condition was fulfilled by 25,521 observation hours within the period 1964-73; the distribution on seasons, classes of solar elevation 7 and total cloud amount N is given in Table 1. Classes containing sparse numbers of cases were omitted.

Table 1. Number of pairs of consecutive hourly observations of a certain total cloud amount N at a certain mean hourly solar elevation 7 + 5° within each season and for the whole year during the 10-yr period 1964C73 at

Hamburg-Fuhlsbiittel

Season

months)

M,A,M

J,J,A

S,O,N

D,J,F

Year

All cases

N

(o~ta)

0

1-2

3-4

5-6

7

8

O

1-2

3-4

.5-6

7 8

o

1-2

3-4

5-6

7 8

o

1-2

3-4

5-6

7 8

0

1-2

3-4

5-6

7

8

S o l a r e l e v a t i o n ~ (degree)

1o ao ~o 40 ~o 60

90 84 133 68 24

186 208 220 166 185

64 74 98 90 88

149 165 202 265 228

300 360 456 389 311

525 547 735 548 313

101 76 69 77 82 52

403 257 210 249 293 156

149 128 126 173 229 112

195 142 185 24O 369 20O

434 360 363 439 584 308

398 245 266 282 372 221

51 89 77 35

215 220 154 85

83 90 103 36

184 220 179 106

468 543 355 199

672 694 317 12o

132 68

21o 76 -

76 20

142 70

681 276

1648 634

374 317 281 180 106 52

1014 761 595 500 478 191

372 312 332 299 317 133

670 597 579 611 597 243

1883 1539 1208 1027 895 380

3243 2120 1415 950 685 265

7556 5646 441o 3567 3078 1264

Solar and terrestrial radiation

800 [ l I T I i ] W m "r 6 (iv)

700 ~ - . ~ . . ~ , 5 0 o

"..~, 600 . - . , . ~ -,,

"~... 400'\

500 "~', "\ "'-. ou \.,

4 , 0 0 -...., ,\ \ "',%, '\i~.

JO0 200 ' ' ~l

",.. 2 0 0 \ ' ,

l O 0 o ~

i i i i i I

0 2 4~ G N 8

M,A,M

HAMBURO-FU~ 7964-1973 8 0 l l l l ' l l ~OO l l ~ l l r ,

~ - - " " ~ " ' 7 " 6 0 ° I 7G Z---~"--.. ~\ 700 - ~ , , ffBe. \

6~ - "'~, \ GOG

~.- . - .~ boo",..\. .~--.~ 2-40 ° &t - ~"-. '\..\'. 506

~'~ \ ' 50 \ \ \ 4~ S ............. .....,.50° 'x.., .'\\', 400

"%..\ 3~ 21 -- -- 2 0 0 11''1 "Xl ~OCl . . . . . . z o ° . . . ~

26 - \ ". 2001 ~ ',\ o ,,' ~ !

O i i ~ [ ~ J i o i i i i i i 1 0 2 X, 6" N 2 4, 6 N 6'

J,Y,,A .9,0,N

800

700

GO~

5OO

4O0

200 x x

700t ~

O i t i i [ i i . 2 ~ 6 N 8

O,J,f ; ' . 5

G(,'¢)

7 . 0 ~ 1 kO 1.0 --

0.5 0.5

4 O0 2 4 6 N 8

Fig. 1. Global radiation G as function of total cloud amount N for different solar elevations 7 in the four seasons M,A,M = March, April, May; J,J,A = June, July, August; S,O,N = September, October, November; D.J.F = December, January, February. Upper row: irradiance of G(N) in W m-2; lower

row: ratio G(N)/G(O) where G(0) = global radiation under cloudless sky.

179

The hourly radiation sums were converted to mean hourly irradiances. By this way, the irradiances of the fol lowing directly measured radiation quantities were obtained as function of total cloud amount N, in okta, for solar elevations 7 = 10; 20; 30; 40; 50; 60 ° and the four seasons M, A, M; J, J, A; S, O, N; D, J, F: global radiation G, diffuse sky radiation D, reflected global radiation R, upward terrestrial radiation of the ,earth surface E, and downward atmospheric radiation A. By mere computat ion from these basic data, the means of absorbed global radiation G-R, net upward radiation of the earth surface E-A, and total radiation balance Q = (G-R) - (E-A) were obtained. The results are presented in diagrams where the irradiances are plotted vs total cloud amount N for different solar elevations 7, separated according to season. In addition, the ratios of irradiance at cloud amount N divided by the irradiance at cloudless sky, N = 0, are shown as function of N.

3. RADIATION AS FUNCTION OF TOTAL CLOUD AMOUNT

Figure 1 shows global radiation G as function of total cloud amount N for different solar elevations 7 in the four seasons. The ratio G(N)/G(O) slightly increases above the cloudless case at N = 1 okta, then slowly decreases up to N = 6 okra from where on the curves drop to about 0.25 at N = 8 okta. This behaviour is independent of the season so that averaging over the whole year is permitted, see Fig. 2. Since the ratio G(N)/G(O) also turns out to be independent of sola~r elevation 7, a common parameterization for-

mula can be established:

G(N)/G(O) = 1 - 0 .75 ( N / 8 ) 34. (10)

On the other hand, the absolute values of G(N) seem to be slightly higher in the winter and spring months than in the rest of the year as also demonstrated by

G HAMBURO - Ft.,',

7964 - 7,975 800 I I I I I r I

Wm-2 "-" ~" Z'6°° G (N)

. \ 600 ~ . . . . ~ 4 O o -,..,\.

300 "~, ' \ . \

4 0 0 ...,. .\ \~

3 0 0 2 0 ° "", x'l~l:

200 "~ \ "

700

o i i i i i i ~ 2 ~ 6 N

YEAR

o 2 ~ G N 8

Fig. 2. As Fig. 1 but for the whole year.

180 FRITZ KASTEN and GERHARD CZt-PLAK

G HAMBU, q6 - F[-/, 1 9 6 4 - 1,97~5

BOO p ~ , , , ~ <300 , ~ ~ l r Wm-z

700 / ¢ 0 ( 0 1 "/ 700

600 / / 600 ~- / t 1-

500 r e ( ~?' 500

400 / f ~00

500 300

200 200 ~ G(8)

I00 700

i l I l k ~ 0 l t I l l p 9(0°) (2o o) (oo °) (6o o) (o o) (20 °) (~7 o) (60 °)

0 0.5 S/~ ~' 7 0.5 s in ~e LO LO

O(8..__2) - - b4~A,M

0(0)0. 8 . . . . a,a,A o.s Y E A R ......... S,O,N . . . . . O, 3, F

0.6 O.G

0.4 0.4

0.2 ~ ' - 0.2

I i I L I 0 I I [ I L I o coo ) ceoo) (~ao) Cao o) coo) ceoo) c~o o) ,,~o)

o 0.s sin ~e r o o.s s i n ? z

Fig. 3. Global radiation as function of the sine of solar elevation 7 under cloudless sky, G(0), and under overcast sky, G(8). On the left: in the four seasons; on the right: for the whole year. Upper row:

irradiance in W m-2; lower row: ratio G(8)/(G(O).

Fig. 3, left hand, where global radiation under cloudless and overcast sky, G(0t and G(8), respectively, is plotted vs sin 7. Multiple reflection between atmosphere and snow covered ground and less turbidity is supposed to be responsible for the slightly higher winter and spring values. On the yearly average, 20-25 per cent of the incoming global radiation is transmitted through an overcast, see Fig. 3, lower right corner.

In order tO determine global radiation G(N) from total cloud amount N on the basis of (1), the global radiation under cloudless sky, G(0), is to be known.

G(0) naturally depends on solar elevation angle 7. From Fig. 3, right hand, t h e following linear parameterization can be concluded

G(0; 7) = (910 sin 7 - 301W m -2 (2)

Of course, this equation represents an average over all occurring atmospheric turbidities. It corresponds, in our nomenclature, to Haurwitz' [20] equation G(0) = 1098 sin 7"exp(-0.057/sin 7) which by expan- sion of the exponential function leads to G(0) = 1 0 9 8 s i n 7 - 63. Dividing (2) by the extraterrestrial solar radiation on horizontal plane, Go = io sin 7 with Io = 1350 W m - 2. yields

G(0; )')/Go = 0.67 - 0.02/sin 7 (3)

which comes close to Lumb's[14] corresponding equation G(O;7) /Go=0.61 +0 .20s inT: both func- tions increase with solar elevation 7, the ratio of corresponding values varying around 1.1-1.2.

The findings for G were substantiated by the evalu- ation of net global radiation G-R as function of N and 7 which is not shown here. Since G-R = G (1 - p) with p = R/G = albedo of the earth surface, the curves of G-R run proportional to the corresponding G-curves as long as the albedo p does not change as in wintertime. In particular, eqn. (1) also holds for (G-R) (N)/(G-R) (0) if p is constant.

In contrast to G, diffuse sky radiation D, Fig. 4, increases with increasing cloud amount to a maximum at N = 6 okta from where on the curves sharply drop to levels below the cloudless case, as also observed by Bener[19]. Obviously, reflection from the side-walls of the clouds is responsible for those high values of D. The dependence of D on N is not very different in the four seasons so that again the yearly averages may be taken, see Fig. 5. The increase of D with N is less pronounced at low solar elevations 7 because in these cases, a large part of the incoming solar radiation is diffuse anyway. But for 7 > 20 ~', the ratios D(N)/D(O) coincide and have a peak at N = 6 okta, then the curves sharply decrease to a value of about 0.8 at N = 8 okta (overcast).

4 0 0 f , , , , r

~°°L J ' - ~ ' % t [. J " ".. - """ "~b'; '\,"\ I

200 F-"'. . . . . . . .............. ..~, ;7.7 .......... go ° ',.ix

tOO - - , - - ' - - ' . . t O ° " \ "

o o 2 ~ 6 N 8

M,A,M !

t, S ~ .~:~'--LT 4 D(N) [ ~V;"" ~. ' ~

a S f l L I ~ I \ 0 2 ~ 6 N

Solar and terrestrial radiation

D HAMBUR6 -FU, 7..o64 - 7,,073 4 0 0 ,

ZOO / "~ ." ~ ~;}'a:; 3"00 .11 --~ .~. . . . . X.' X

2oo :'--:--.':'-"" 7.~-'L"~<,"~,~ 2oo . . . . ...." "" "" ~ 20 ° ',. X

0 i i i O | i 0 2 4 6 N 8 o

E,,gA

. . . . .:..e ...... 2oo"..~ _ - z--'. e ° °

lO0 - - - I0 ~ ~x

i i i i J 0 [ - i i r , ' ~

TO ~'~

l i i i i l l 2 ~ 6 N

0

0 0 2 4 G N

2 4 G N 8 0 2 4 E N , q

S,O,N O,3,F

0 5 I i

O 2 .4 G N 8

7.5 x:.-.. - '~

• ~ 1 i i i i i i

O 2 4, 8 N

/6

a s

o 0 2 4 G N

LO L 6 ~ .

0 I i O 0 2 4 6 1 V 8 0 2 ~+ 6 N 8

Fig. 4. Diffuse sky radiation D as function of N for different 7 in the four seasons. Top row: irradiance of D(N) in W m 2; center row: ratio D(N)/D(O); bottom row: ratio D(N)/G(N) where G(N)= global

radiation at the same total cloud amount.

181

Additionally, a diagram of the ratio of diffuse to global radiation, D(N)/G(N), is presented at the bottom of Fig. 5. These curves also turn out to be almost identical for solar elevations y > 20 ° showing a steady but not linear increase with N. A rather good approx- imation is

D(N)/G(N) = 0.3 + 0.7 (N/8) 2. (4)

This expression may be used to estimate total cloud amount N from simultaneous records of D and G; a similar proposal was made by W6rner [23].

For completeness, the dependence of D(0) and D(8) on the sine of solar elevation ), is shown in Fig. 6. Both quantit ies run almost parallel to each other so that their ratio D(8)/D(O) exhibits a pronounced dependence on sin 7- At low solar elevations, an appreciable part of the solar radiat ion being incident on top of the cloud deck is obviously reflected and thereby lost to the diffuse radiat ion D emerging from the bo t tom of the cloud to the ground, whereas for 7 > 50° about 80 per cent of the cloudless case are at ta ined on the yearly average. A more detailed analysis has to take account of the cloud type and will be given below.

Figure 7 presents iongwave atmospheric radiation A in dependence on total cloud amount N and solar elevation ?. With the exception of the summer season, A steadily increases with increasing N because the clouds are warmer than the clear sky. The increase with N is more pronounced at low solar elevations 7. Evidently, the screening of the sky by relative warm clouds is more effective on A in the cold times of the day (sunrise and sunset) and of the year (winter). The absolute values of A are smaller at lower 7 and largely

depend on the season• Again, this behaviour clearly is a consequence of the different air temperatures at different times of the day and of the year, respectively• Averaging over the seasons or over 7 is not possible in the case of a tmospheric radiation.

To the contrary, the net radiation of the earth sur- .lace, E-A, exhibits a behaviour similar to global radiation G, see Fig. 8. Since a variation with season can not be recognized., yearly averages may be permitted

D H A M B U R O - FU, 7964- 1.973

4 0 0 , , , , , ,

~,_ -~ L at ,+) r - ~ o = . . . . . V# III . 7 " .r io ° 504 f . - - za4,1

• . . . . z ~-~ 3"0 ° \t 3 eoo ..... "_,.--{ ........... ~o:"

s o o F - - " la* '~

0 2 4 6 N 8

o 2 4 8 N 8

o,,Tf L_.....--'~. ...-'.Y I

oET-, . . . . . . o 2 z, 6N8

YEAR

Fig. 5, As Fig. 4 but for the whole year.

182 FRITZ KASTEN a n d GERHARD CZEPLAK

D HAMBURO-FU, 7966- 797,5

SO0

Wm-e 400

500

200

100

0. (0 o) 0

O(8/° Dfa)

0.8

0.6

0.~

0.2

0(007 0

D(o) 7.0

G(o) 0.8

O.6

GZt

0.2

0 (0 °) 0

D(o) D(oL

i t t i } i i i (20 o) fz~Oo) (60 o) (20 °) (/¢~7 °) (60")

0.s sin ir 0.s sin 7"

...;- /.:

. . . . J,.7,,A

......... S,O, IV

. . . . . p, ~ F

S

YEAR

J ' I ~ , t t I t ' J J (2o o) (4,0 o) (80 °) (20 o) (4,0 o) (60 o)

0.s sin 7" o.s sin ~e

500

400

500

200

7o0

0 (0 o) 0

LO

0.8

0.6

0.2

0 (0 o) 0.

LO

z28

0.6

0.2

0 (0 o) 0

i l I t L i J t l t l J (20 °) (4,0o) (60 °) (20 °) (40 °) (60 °)

~s sin ~" 7 O.S sin ~" 7

Fig. 6. Diffuse sky radiation as function of sin 7 under cloudless sky, D(0), and under overcast sky, D(8). On the left: in the four seasons; on the right: for the whole year. Top row: irradiance in W m- 2; center

row: ratio D(8)/D(O); bottom row: ratio D(O)/G(O).

(Fig. 9). There is a slight dependence of E-A on solar elevation ~, see Fig. 10; but the curves of the ratios "clouded to cloudless" (lower part of Fig. 9) are almost identical to the corresponding G-ratios so that the parameterization formula [1) may also be applied to E-A.

Finally, the radiation balance of the earth surface, Q = (G-R) - (E-A), was evaluated (Fig. 11). Since the shortwave balance G-R and the negative longwave balance E-A showed close affinity to global radiation G, it is not surprising that the curves of Q also exhibit a course similar to G thereby confirming the parameterization of Q by G which is often described in the meteorological literature. Naturally, this does not hold for the cold times of day and year, i.e. at low solar elevations when Q approaches zero or even becomes negative. Therefore, when averaging over the year (Fig. 12), the values of the winter season were not taken into account. The ratio Q(N)/Q(O) may again be parameterized by eqn. (1) observing the precautions just mentioned.

An interesting remark was made by Malberg [26]: In his objective method for maximum temperature forecast, the warming of the atmospheric layer near the ground on clouded or overcast days amounted to about 35 per cent of that on cloudless days. This value corresponds to our ratio Q(N)/Q(O) at N = 7-8 okta.

Figure 13 presents Q(0) and Q(8) as function of solar elevation 7. These curves resemble the corresponding G-curves as far as ? is not below 20 °.

4. INFLUENCE O F CLOUD TYPE

The same data material of 10yr hourly observations from 1964-73 was analyzed with respect to cloud types which were condensed into 5 groups: Cir- rus = Ci, Cc, Cs; Altus = Ac, As; Cumulus = Sc, Cu; Stratus = St and Nimbostratus = Ns. In order to obtain unequivocal information on the single cloud groups, only observations of N = 8 okta overcast by one cloud group were taken into account.

Solar and terrestrial radiation 183

A HA IIdBURO - FU~ 7.,q6Z,, - 7973"

500 , , i i i [ I

Win-2 A ( N ) 4,50

4,00

J50

300

25O

2 0 0 I I J I I J I

2 4, 6 N ,9

/VI, A,M 7.8

A(x ' , ~ .

7.0 . . . . . . . " . . . .

O 2 4, 8 N B

5 0 0 1 l I l I l l {

4,50 I

.4`00 ~12 ~. 35o : - 2 ~

JOOF . . . . 7" ~0 o o

~0 ° 30 ~

250 20 ° 10 o

280 1 I i I I I ~ i 8 2 z+ 6 N 8

SO0 I I I r I ~ I

45O

~00

350

3OO

250

200 J i i i i i i 2 z., 8 N 8

S,O,N

8 2 4 B I V 8 0 2 4, 6 N B

50O,,,,]f~]

4501 t

4001

s s o l

2so l

2 ~ t l J I t r ~ l J 2 4 6 N 8

1.K

L O ~ ~

~5 t l ~ , , 1 I i 0 2 4, B N 6 '

Fig. 7. Atmospheric radiation A as function of N for different 7 in the four seasons. For further explanations, see legend to Fig. 1.

E -A HAMBURG - FU, 796/, - 1.973

750 . . . . . . . 750 1 ' ' ' ' = ' ' I ] , , i r , , , [

W m - e L (E-A)flV) [ 700 ~'~.~ ~ . 100 . . . . . ~ . _~ ~--:. 700 ~c,*~.~

f

0 2 Z+ 6 N 8 0 2 i=, 6 N 8 0 2 z+ 6 , / V 8

M,A,H 3,J,A $,O,N

750 , , r ~ , , ,

OL i i i i i i i i 0 2 o 6 , 4 / 8

D,J,F

1.o - - - - - ~ z~ 1.o 1.o / " "

0 . 5 0 . ~ • t25 0.5

0 [ I I I I I ~ I I (7 0 I I I I I L I I ~ 0 ~

0 2 {~ 6 N 8 0 2 /~ 6 N 8 0 2 z~ 6 N 8 0 2 ~, 6N8

Fig. 8. Net terrestrial surface radiation E-A as function of N for different ;, in the four seasons• For further explanations, see legend to Fig. 1.

E - A HAM8UR6- F~ 7964 - 1975

750

Win'2 7O0

50

O0 2 ~ G N8

YEAR 1.5

(E-A)(O~ 7.0

o.5

0 0 2 .<' 6 N 8

Fig. 9, As Fig. 8 but for the whole year.

As in the foregoing analysis, the data were first grouped into the four seasons, then within each season assorted into classes of equal mean hourly solar elevation ). by intervals of A7 = 10 °. The radiation data within each of these classes were assorted according to the cloud groups mentioned above. Again, only such cases were admitted when the reported overcast by 8 okta of a certain Cloud group at the beginning was identical to that at the end of the hour under consideration• This stringent condition was fulfilled by a total number of 4696 cases which are distributed to seasons, classes of solar elevation 3' and cloud groups as shown in Table 2. Naturall>, the numbers of cases within each class are much lower than in Table 1. Especially the numbers of Cirrus and Nimbus overcasts are sparse so that the results derived thereof have necessarily a greater scatter and uncertainty.

184 F R I T Z K A S T I i N and G E R H A R D C Z E P L A K

E*'A HAMBURO - FU) 1,964 - ~ 7 3

75o l

win-% I 0 (0 °)

7.0 (E-A)(a~

(E-A)(o) ~

0.6

~4,

0.2

0 ( 0 o )

0

t I I 1 I I l S O l ) I I I )

( E - A ) (o ) I ( E - A } (o)

~---J(E-A)(~) 50 1 ~ - " ~ ' ( E - A ) g a )

0 ~ I I I I I ( 2 0 o) (4,0 o) ( 6 0 o) ( 0 o) (2O o) (K,O o) (gO o)

O.s s i n ~, 0 as s i n ~' L(

- - M,A,M . . . . J ,J ,A ......... s ,o ,N . . . . . D,J ,F

0.6

0.6

0.4,

0.2

YEA R

( 2 0 o) (4,o o) ( 6 0 o) ( o o) ( 2 o o) ( o 0 o) (Go o) aS sin ~ 7 0 O.S Sin

F i g . 10. Net terrestrial surface radiation E - A as function of sin 7 under cloudless and under overcast sky. For further explanations, see legend t o F i g . 3.

In Fig. 14, upper row, global radiation under over- case sky, G(8), is plotted vs the sine of solar elevation ), for each of the five cloud groups, separated according to the seasons M, A, M; J, J, A; S, O, N; D, J, F and also for the whole year. Since a systematic variation with season is not visible, all cases can be sum- marized and presented on one diagram on the far right marked by "'year".

In view of the great variety of cloud formations within each cloud group and of the low number of

600

W m - Z 500

4oo

Joo

200

too

o

2.O a(N)

, , , , , , ., 600

Gt(N)

i . . . . . ~ "60°- 5OO

_,_. 002" ' ' ~ ooc

o "\ . "~. 300 $0

~o ° ,:.;, 2o0

0 2 ~ G N 8

M, A, M

0 e <, 6 N e

ZO

LS

cases of Cirrus and Nimbostratus overcasts, the curves can roughly be considered as straight lines like the curve G(8) in Fig. 3 which describes the average over all possible cloud types. This mean curve of Fig. 3 is represented almost identically by the curves for Ac, As and Sc,Cu in Fig. 14 whereas the Cirrus curve lies much higher and the Stratus and Nimbo- stratus slightly lower.

The bottom row of diagrams in Fig. 14 shows the ratios of global radiation under a sky overcast by a

HAMBURO - FU,

] l l , [ l r 6 0 ~

. . . . . " ' " ~" * 60° 50(

. . . . . . - 4`00 ~\~'x

30 ° ~ \ . " ~ . . . . . . , A

2 0 ° ".. ',',1

,.oo "'-.~ t i i i i

2 # 6 N 8

J,~A

~s

I I ; I I I I O 0 2 /4 6 N 8

1964 - 1973

t i , p , i E

~ . . . . / ' - 4 0 °

JOl - "~. ............ 3 0 ° \ . \

20~ .......... • "\ 20 ° "'.,.. ,,.

10 °

6 I i I I I I i "

2 4, g N 8

S,O,N 2.0

1.5

i I t L I i l Do 2 ~ G N 8

6 0 0 I I p I f [ I

5001-

4'001-

• ,zOO k

200 F i t , .20 °

tOO I- ~ ~ . . . . . . . . . .

70 ° ~ . . D ' i i i

o 2 4. 6 N 8

D,~F

F i g . 1 1.

seasons. Net total radiation = total radiation balance Q as function o f N for different ? in the four The ratios Q ( N ) / Q ( O ) for o , J , F (winter) are not s h o w n because of large scatter. For further

explanations, see legend t o F i g . 1.


O HAMBURO- FU, 7,964 - 197,75

600 , ~ , , , , ,

W rn-e ~: l-.~ ~0° 0(N)

500 f ~" ~;~'""

,oo

L 300 o "\ "\ ~. 50 ., ",~

2 0 0 1 ~ "',. "~ 20o ' " . ,

1OO 700 " ,

0 ~ I I I L I 0 2 ~. 6 N B

YEA R (without D, 4 F)

0 o 2 o 6 N 8

Fig. 12. As Fig. I I but for the whole year except D, J, F (winter).

certain cloud type to that of cloudless sky, G(8)/G(O).

These ratios can be comprehended as the transmittances of the different cloud types for global radiation. The curves are arranged in the same order as the curves of the absolute values depicted in the upper row of diagrams: Cirrus, Altus, Cumulus, Stratus, Nimbostratus. The increase of the ratios with solar

elevation 7 is rather small so that on the average, the transmittances of Cirrus, Altus. Cumulus, Stratus and Nimbostratus may be taken as 0.61, 0.27, 0.25, 0.18 and 0.16, respectively.

The corresponding diagrams for d!ffi~se sky radi-

ation D are given on Fig. 15. Whereas the curves of the absolute values of D(8) show a course similar to G(8). the ratios D(8)/D(O) exhibit a marked increase with solar elevation 7. At low sun, obviously an appreciable part of solar radiation being incident on top of the cloud deck is reflected back tO space and thereby lost to the diffuse radiation D emerging from the cloud base and received at the earth surface. The dependence of D(8)/D(O) on sin 7 is strongest in the case of Cirrus; Cirrus overcasts may amplify diffuse sky radiation by factors typically ranging from 1 to almost 2. The curves for the five cloud groups are arranged in the same order as the corresponding G-curves.

A quite different picture is presented by atmospheric radiation A in Fig. 16. Under overcast sky, A is almost exclusively determined by the thermal radiation of the clouds. With the exception of Cirrus, most cloud layers are so dense that they act as black body radia- tors. Atmospheric radiation is therefore determined by the air temperature at or closely above the cloud base. Consequently, there is a variation of A(~) with season whereas the variation with cloud type. except Cirrus, and also with solar elevation is small.

The diagrams of the ratio A(8)/A(O) show that an

H A M B U R G - FU, 7 9 6 4 - 797,5

6OO Wm-e

N00

ooo

5oo

200

700

(o o) 0

Q(o) /

/ i J

/ /

) .

t"1 I

(200) C~P °) (60 °) o.s s/n iv

6 0 0

soo

4O0

500

20O

100"

0 w o) 1 0

i I i i 1

(20 o) (4o o) (Go o) 0.5 sin ~ I

Q(8~ 7"0

Kilo)as

0.6

o,.9

o.2

0 ( 0 , 0

, / ~ , A , M . . . . J,..7, A ........ S,,O,N . . . . . O, 3,F

I I I I I I

(20 ° ) (40 ° ) (6o ° ) o.s s i n ~" z

I,o

o.8

0.8

o.2

o ,0.o) o

I I I I "1 I (2o o) (~o o) (6D o)

0.5 sin ~v

Fig. 13. Net total radiation = total radiation balance Q as function of sin 7 under cloudless and under overcast sky. Winter values (D, J, F) left out. For further explanations, see legend to Fig. 3.

186 FRITZ K A S T E N and GERHARD CZEPLAK

Table 2. As Table 1 but numbers referring to observations of overcast by a certain cloud type

Season Cloud

(months) type

M,A,M Ci,Cc,Cs

Ac,As

Sc,Cu

S~

Ns

J,J,A Ci,Cc,Cs

Ac,As

Sc,Cu

St

Ns

S,O,N Ci,Ce,Cs

Ac,As

Sc,Cu

St

Ns

D)S,F Ci,Cc,Cs

Ac,As

Sc,Cu

St

Ns

Year Ci,Cc)Cs

Ac,As

Sc,Cu

St

Ns

A l l c a s e s

Solar elevation ~ (degree)

1o 2o }o 4o )o 60

14 7 28 I ~ 13

7o 86 89 63 45 -

8 4 9 2 1 2 5 1 0 0 6 0 -

lo9 108 136 105 28 -

5 7 h 9 7 -

5 5 7 3 7 8

1 1 5 56 56 69 89 44

58 41 46 60 86 45

39 23 2 6 2 9 25 14

6 5 8 3 5 5

11 19 7 1 -

53 66 52 29 -

lO5 96 55 2 0 -

169 180 63 12 -

9 7 3 3 -

11 18

69 23

268 105

5 7 5 193

6 8

41 49 45 18 20 8

307 231 2 0 0 161 15~ 52

515 334 232 180 146 56

892 5O4 254 146 53 17

26 27 15 15 12 6

1781 1145 746 52o 365 139

overcast raises atmospheric radiation above the values for cloudless sky the more, the lower the solar elevation is. As mentioned earlier, this behaviour is an effect of temperature: low solar elevation means the time of sunrise or sunset when the air is relatively cool; an overcast by relativity warm clouds will therefore increase the effective black body temperature of the sky. For the same reason, the ratios A(8)/A(O) are higher in the cold seasons winter and spring than in the warm seasons summer and autumn. Differences between different cloud types are barely visible but slightly larger A(8)/A(O)-values of the lower, warmer clouds Ns and St are indicated.

Figure 17 shows the influence of cloud type on net terrestrial surface radiation E-A. Despite the relatively large scatter of the curves, it may be seen that E-A behaves quite similarly in the four seasons so that averaging over the year seems to be allowed. The curves for the five cloud groups are arranged in the same order as already known from global radiation and diffuse sky radiation, Figs. 14 and 15. From the lower row of Fig. 17 one learns that a Cirrus overcast reduces the net radiative emission of the earth surface to about 50-60 per cent of the values measured under cloudless sky. There is a moderate increase of (E-A)(8)/(E-A)(O) with solar elevation 7 for all cloud types, just opposite to the corresponding A(8)/A(O)- curves, as expected: the upwelling (E-A)-radiation is influenced by cloudiness in a way opposite to the downwelling A-radiation as may also be seen by com- paring Figs. 8 and 7.

Finally, the radiation balance or net total radiation Q = (G-R) - (E-A) is analyzed with respect to cloud type in Fig. 18. As mentioned earlier, Q behaves simi-

600 , , q , , , 6OG

0(3) 500 50£ -

Wm-Z 400 400 -

/

/ 500 300 / I

200 i' / 20~ / / / "

i / . - " too 'Z,/4;:- 1oo

% (m'/(~9(~ o) °m.) 0 ~5~in~ I 0

M,A,M 1.0 XD

o(o) [

o 0 (o o) (zo') '(~oo)(~o °) (o o) 0 O.5$ing I 0

G HAMBURO-FU, 195~- 1~7~

, , ) , , ,

f . I

f /

/

/ / ,~"

S /

, , t , , ,

(zo °) ' l ~ ) ( ~ o) o.5Mng t

,.7, J,A

~,. /, x

, , = , , ,

(,'o') ' (4o') f fo o) O,5 Mn ~ 7

6o0 , , i , , ,

300 ,.I .I

/ 2oo /

- : Ac, A~ / t,'" 5GCu

m s - / ,.fYst : / -

(o e) (2o~/(4o°)(~) 0 0.sm'ng I

S,O,N

1"6 I 4 - - " - . 0_~ / Ci, gc,,~

Ac,,*~. _ ~ _ . r - , , l t ; ~ g L ,

0(o~) (ZO ~) ' {~ ) (~ ) o o .5#n F /

600, , 6 0 0 , , ~ , , ,

5001- 500~ / " Ci, CC, Cs

I 400F 4,00)- t ! i

300 ~- 300 k , / / i

200 F 200 k / ..~." At, As i : i ; SC, Co • / i: /

" i i . / / lOP F / ' / . ;00 F .. /"~" " St

(o o) (co o) (o ~) (2oo)'(~o~)(6o o) o~n i" ~5 0 D52Jn~ I

LO L£ MEAN:

~5 05 / . . . . . . . . / . - C/~Cc,,Cs 0.6I

A'C,A,~ O, Z7 $C~ ~ZG ~" o.~a

~NS O. IG 0 O

(o o) (2~') (o ~) (~.~')'(.~o')(g,~) Ore'rig ~ 5 0 0.5mhjw t

Fig. 14. Global radiation G as function of the sine of solar elevation 7 under overcast sky (N = 8 okta) separated into cloud groups as indicated at the curves, in the four seasbns and for the whole year. Upper row: irradiance G(8) in W m-2 ; lower row: ratio G(8)/G(O) where G(0) = global radiation under cloud-

less sky.


5OO

O(~) ~,00

W m - a 500

100

2.0

P(o~ LS

LO

~ 5

O

/

i i /

/ .' , 1

) (2o °) (~°)(6~ o.5 5in ~

M , A , M

I ' - ' - I"

/ ../ / l / - [ . . .

i ' /""

D 5 0 0 , , , ~ , , ,

.1

f / 500 /

/

2001- .l" .i~ / ,,.

tO0 b : .. ".

O(O o) (20°)'[¢0")i6t

/

! i

i LO

, .'.;;. _ . , D S -

D , ' I i i , {o') (~o °) (4~?(6~') 0 05sln~ 7

HAMBURO-FU, 1 9 6 4 , - 797=3

g,00-

5 0 0 -

200 -

./ yOo 7

0 , i (o o) (2o o) O~" 0,5

D,,7,,F ~0

zS - . - /

z o ~

- , ' b

'if" 0

(o °) (co*)

400 F Ci, C¢Cs 5001- /."

/ 200 k !

i " : AC~

/ .<; sc, c.

,oat / "¢" "

(09 (eO*)=(~*)(60 ' 0 a 5 sin~"

s,o,N 2.0 I - - / " 7,; cc, cs

./" ~s l i

i'

z o l /

/:.."/'st os l ,,>2/

~ Ns

(o °) (~1 (~o~)(so °) O L~5~itr~ l

~0 0 ' , l 1 , ,

• oo / I

500 / / / /

200 / " / /;/ : I/" l X."

lO0 ~i I.~ -~

0 O.S~n F I YEAR

"°f l I.S [- /." -~

(0 °) (co') (4o*)C60 ~) 0 0"ssin F I

Fig. 15. Diffuse sky radiation D as function of sin 7 under overcast sky separated into cloud groups. For further explanations see legend to Fig. 14.

~;50

A ( a )

,~00

Wm -a

350

A , , j , , , z c S O

~00

HAMBURG - F U , 1 9 6 4 - 1 9 7 . . z

, I ~ ' I { ~ 5 0 [ I ' ~ 1 [ ,

55O

. . . . . . c,; cc, cs

..... AC, A5 ZOO ZOO ......... $C, CU

.... St ~hls

2S0(0o] (200), (#0~)(6 O" 250 ( 0 0.5 g/n~'

M,A,M 1.6, A(8) z'6 A(o) l. Z~ I..#. l-

i ! ~ . , ~ 1.2 ~'/ ~"~ aSI- l.O I 1.2 F_ " ~ " I

0 O.Ss/n~' I 0 O.Ssin@' I

z~O0 I

550 ~ • ~./"

Joo

' ' ' ' ' ' ' 250 ' ' ~, ' ' ' ,) (20o)'(~)(60 o) (0 o) (2o o) (40°)fro "

O.5 ..¢/n ~" I 0 D 5 G/n ~" !

,.7,,7,A S, O, N zs

z/4

1.0

O.8

O.G ~ , t J , t I (o o) (20") ' (¢o*)(~ °) 0 O.Ss/n~' Z

450 , ,

400 -

5so-

500

250 ~ (0 o) (2O °)

O S/nj" O.S

L 2

LO

" t 0.6 l (09 (2~] 0 s/n@" 0.5

Fig. 16. Atmospheric radiation A as function of sin 7 under overcast sky separated into cloud groups. For further explanations, see legend to Fig. 14.

188 FRITZ KASTEN a n d GERHARD CZEPLAK

IDO ! , , ~ , T ,

(E-A)(8~ -

80-

I / I c~

~0 -- . / IAC~

- / . , ' z¢~

20 - j g t

0 L . . . . . .

0 O.S61n~ l

M,A,M ( E - A ) f S ) t ° ]

( E - A ) ( O ) a 8 ]

...... ..l"- cs

0 .2 ~ st

0(0°) (20o)'v~Bo)[eoo? 0 OlSS/n~" I

E-A I 0 0 , r r ' ' '

8 O F

ea k I"~ ! ,

.i 40 k ..... - . /

0 o.ssing" l

~, ,.Z, A 1.0

HAMBURO-F~ 19G4-1975 tO0 , , ~ , , r

80

60

40 / ' l [

20 ,,.'~....'2

0(0° ) ¢20~) ' tZ¢0°)(60 ~) O O . ~ / n ~ l

S,O,N 1.0

100 T T I00 , ~ ' l T

80 k 80 k

GO k 60 k

~s A

DB \ /: \ . /

L~h

...... ":i;;' 0.2

O(oo) {20~)' ( z~o) f6V ,) o a ~ s / n g z

128

O# "

~ . . ; /

0 ~ S S t ~ r I

A,

"~ 7t)C4Cs

de, As ~c, Cu

20 ,,'. 20

0 (0 ° ) ' (20--°) 0 ~ ' I ' I ] I (0 o) (2O o) ( ~ ° ) ( 8 0 * ) O s l ' n ~ 5 0 12S~;l~q~ I

I.O D ~ F 1.o Y E A R

D 8 Z28 I-

0.6 ¸

Z2~ I / .

( 0 °) ( 20 °)

^ / \

t~ q AC, AS 5~ Cu

0 ~ZS$/>7#" I 2

Fig. 17. Net terrestrial surface radiation E-A as function of sin 7 under overcast sky separated into cloud groups. For further explanations, see legend to Fig. 14.

larly to global radiation G as far as the solar elevation is not too low in which case Q approaches zero or becomes even negative. For the same reason, averaging over the seasons has to exclude the winter months. 8 okta Cirrus reduces Q to about 60 per cent of its value under cloudless sky, The other cloud groups have Q(8)/Q(O)-ratios between 0.3 (Altus) and 0.1 (Nimbostratus).

5. CONCLUSIONS

The foregoing analysis of solar and terrestrial radiation fluxes at the earth surface in dependence on

cloud amount and cloud type is based on 10-yr continuous and homogeneous hourly records at Ham- burg Meteorological Observatory. The diagrams derived from this data material are intended to give typica! values of the different radiation quantities on different cloud conditions and should be applicable to estimates of the radiation climate such as required for solar energy planning. Of course, actual radiation values for a given specific weather condition cannot be derived from the diagrams presented here.

Since solar elevation and not hour of the day was used as parameter, the relations shown are in prin-

Q HAMBURO-FU~ 196~-1~73

BOO l ' I

(H8) 5OO

Win-2 400

5OO

/ 200 /" /"

I' /

°o~ ) ¢zo~)<(~o0)(6o0) o CSsin I , !

M, A,M

0.51 " ~.._

0 ' " J . . . . (0 °) (20 °) ' V~t?o)¢~o) o OlSSthj" f

GO0 , r '

500

I

300 k i i

I

200 ~ ..i:

lO0 k i "./ . i # .. ¢ / -.

9 ¢0 °) 120 ~) (X~°)(60 ~) 0 O.Sslhg" 7

J,O,A 1.0 ! I'. /"x

LZ5 ~ " " J

0 ° 0.55/?;'~" !

500

4OO

JO0

/&;CcIs 1

200 Ill [ I

1. 700 i' AC, A~

0 O.SFIn~ 7

S,O,N ~a[ [ ' ' ' ' l ? i aC ,

--~.~,c~

o ~ss /n 2, t

GO0 ~ , ,

5O0

~00 I ,,~00

2O0

I00

0(oo) (20 o)

o6in C 0...¢

600 , , ~ . ,

500 k

400 F

/ C~/c, Es 500 F i -

/ /

200 h i " AC AS I , ,

100 / ,~/ I" ~" " 5#

(0 ) (20°I (40 °) fGe"] 0 O.5st'n t" t

YEAR (without D,4F)

St O I I I I , , l / N S

CO ~) (20 °) (40°](GO °)

Fig. 18. Net total radiation = total radiation balance Q as function of sin 7 under overcast sky separated into cloud groups. For further explanations, see legend to Fig. 14.


ciple not dependent on geographical latitude of the site but tire considered to be valid for any other place with a climate similar to that of Hamburg. On the other hand, the figures given here largely depend on the density and frequency of occurrence of the different cloud types. Therefore, places with other climates would require a separate investigation.

Turbidity of the a tmosphere was not accounted for in this study because cloudiness has the dominant influence on the radiat ion regime at the ground. Of cou~rse, turbidity is an impor tant parameter under cloudless sky so that our figures given for this case should be taken as an average. A further study is planned to incorporate turbidity as a kind of second order effect into the relations between radiation and

cloudiness. Since solar elevation was taken as parameter in this

investigation, night time data of the !ongwave radiation fluxes A and E or E-A, respectively, and of cloudiness have not been considered so far. The dependence of these radiat ion fluxes and of total radiation balance Q on cloudiness, with temperature as parameter, shall be analyzed in a further study includ- ing night time data.

REFERENCES

I. H. H. Kimball, Measurements of solar radiation. Momhly Weather Rer. 55. 155 169 (1927).

2. I. Dirmhirn, Untersuchungen der Himmelsstrahlung in den Ostalpen mit besonderer Beriicksichtigung ihrer H6henabh~ingigkeit. Arch. Met. Geoph. Bioklim., Ser. B 2, 301-346 !.1951).

3. K. Griife, Uber M6glichkeiten der Bestimmung, Be- rechnung und kurzfristigen Vorhersage der Global- strahlung am Erdboden. Arch. Met. Geoph. Bioklim., Ser. B 5. 344-376 (1954).

4. F. Albrecht, Methods of computing global radiation. GeoL Pura Appl. 32, 131 138 (1955),

5. ,I. N. Black, The distribution of solar radiation over the earth's surface. Arch. Met. Geoph. Bioklim.. Ser. B 7. 165 189 {1956).

6. 5;. Fritz, Solar radiation on clear and cloudy days. Sei. Moplthly 84. 55 65 (1957).

7. C. L. Mateer, On the relationship between global radiation and cloudiness at Ocean Station P. Arch. Met. C, eoph. Bioklim., Set. B 12, 482-490 (1963).

8. E. V. Ashburn, The radiative heat budget at the ocean- atmosphere interface. Deep-Sea Res. 10, 597 606 (1963).

9. S. Tabata, Insolation in relation to cloud amount and sun's altitude. Stud. Oceanogr. 202-210 (1964).

10. W. Schiiepp, Direct and scattered radiation reaching the earth, as influenced by atmospheric, geographical and astronomical factors. In Solar RadiatioJl (Edited by N. Robinson) pp. 111 160. Elsevier, Amsterdam (1966).

I1. R. Schulze, Strahlenklima der Erde, pp. 80 86. Stein- kopff Verlag, Darmstadt (1970).

12. G. A. Franceschini, The influence of clouds on solar radiation at sea. Deurseh. Hydrogr. Z. 21, 162 165 (19681.

13. J. A. C. Kaiser and R. H. Hill, The influence of small cloud covers on the global irradiance at sea. d. Geoph. Res. 81,395 398 (1976).

14. F. E. Lumb, The influence of cloud on hourly amounts of total solar radiation at the sea surface. Qtly J. R. Met. Soc. 90. 43 56 (1964).

15. D. J. Norris, Correlation of solar radiation with clouds. Solar Energy 12, 107 112 {1968).

16. D. E. Parker, The effect of cloud on solar radiation receipt at the tropical ocean surface, Met. Mag. 100, 232 240 (1971).

17. A. J. Gadd and J. F. Keers, Surface exchanges of sen- sible and latent heat in a 10-level model atmosphere. Qtly J. R. Met. Soc. 96, 297 308 (1970).

18. H. Schieldrup Paulsen, On radiation, sunshine and cloudiness. Universitetet i Beryen, Arbok 1948, Natur- vitenskapeliy rekke. No. 7, Bergen, Norway (1949).

19. P. Bener, Der Einflul3 der BewOlkung aufdie HimmeJs- strahlung. Arch. Met. Geoph. Bioklim., Set. B 12, 442 457 (1963).

20. B. Haurwitz, Insolation in relation to cloudiness and cloud density. J. Met. 2, 154 166 (1945).

21. B. Haurwitz, Insolation in relation to cloud type. J. Met. 3, 123 124 (1946).

22, B. Haurwitz, Insolation in relation to cloud type. J. Met. 5. I1(~ 113 (1948).

23. H. W6rner, Zur Frage der Automatisicrbarkeit der Bewtilkungsangaben durch Verwendung von Strah- lungsgriJgen. Abh. Met. Dienst DDR 11, No. 82 (1967).

24. H. W6rner, Die Berechnung der Globalstrahlung aus Triibungswert und Bew61kung. Pugeoph 93, 177 186 (1972).

25. World Meteorological Organization, Commission [or Instruments a~ld Methods ol Obsercation, Abridged Final Rep. ol" the 7th Sessiotl, Hamburg. 1 12 August 1977, 75~76 and 97 100. WMO-No. 490. Geneva (1977).

26. H. Malberg et al., OI2jektivierte H6chsttemperatur- vorhersage an wolkigen bis bedeckten Tagen, Met. Rnndschau 29, 190-191 (1976).

Documents

Solar and terrestrial radiation dependent on the amount and type of cloud