measurement and analysis of solar radiation data

Energy and Buildings, 3 (1981) 1 - 29 1 © Elsevier Sequoia B.A., Lausanne -- Printed in The Netherlands

Measurement and Analysis of Solar Radiation Data

F. KASTEN

Deutscher Wetterdienst, Meteorologisches Observatorium Hamburg (Fed. Rep. Germany)

EXTRATERRESTRIAL SOLAR RADIATION

The radiation of the sun is the primary natural energy source of the planet Earth. Other natural energy sources are the cosmic radiation, the natural terrestrial radioactivity and the geothermal heat flux from the interior to the surface of the earth bu t these sources are energetically negligible as compared to solar radiation.

From the sun, the planet Earth receives electromagnetic as well as particle radiation. The latter, the so-called solar wind, induces important physical effects in the high atmosphere but is of minor importance for the lower atmosphere and negligible for its energy budget.

When we speak of solar radiation, we mean the electromagnetic radiation of the sun. The energy distribution of electromagnetic radiation over different wavelengths )~ is called spectrum. The electromagnetic spectrum is divided into several spectral ranges as shown in Fig. 1.

The solar radiation incident on the upper border of the terrestrial atmosphere is called extraterrestrial solar radiation. The spectrum of the irradiance (= power per unit area) of extraterrestrial solar radiation is tabulated in Table 1. The accuracy of these spectral data is of the order of +2%. Below ), = 2900 A = 0.29 #m and above ), = 40 000 A = 4 #m, less than 1% of the total solar power are present in each case. At )~ = 7300 A = 0.73/~m which wavelength, incidentally, is the upper limit of the visible spectral range, the solar spectrum is divided into two halves of equal energy; thus, one half of the extraterrestrial solar power falls into the infrared spectral range.

An approximate sketch of the spectral distribution of extraterrestrial solar radiation is shown in Fig. 2. The maximum of the dis- tr ibution curve lies around )'max = 0.48 #m. If we consider the sun as a radiating black body following Planck's spectral distribution law, the so-called color temperature T of the sun may be calculated from )~max with the help of Wien's displacement law,

,Vm

10 "@

y-togs

X - rags

extreme ultra~o/el

(EUV) ulhwviolet (UF)

10-B near l~fr~red (near IR ]

far/nfrared (far .we ) 10 -'~

7

rad/bwa~es 10 3

I0 G

~ O pm

Into

lOOnm ~ 400nm

3y.m ~-//ght ?5Ohm

7 m/n

lOcm

lO0 Km

Fig. 1. Spectral ranges of electromagnetic radiation; )~ = wavelength.

• O A /WlII-~ II m -I

L~"~ ' l ' I ' I ~ I ' l ' I , I T I ' I ' I ' I ' I ' I ' I

2.0 ~ ~ x

1.5 X\

"° \ \ 0.1;

x

I I I I I I I , I , I , I , t I i - - j " - ~ ' ' ~ ' ~ - - i - - ~ - ~ - - i . l - ~ - ~ 0 o o.z o.* o.~ o.e 1.e ~.2 ~..~ ~.~ ~.8 e.o a..~ 2., 2.~ z.a ..¢.o .~.z

~ / ~ m

Fig. 2. Spectral distribution of extraterrestrial solar radiation (solid line) compared with that of a black body of 5900 K (dashed line), (After Gut et aL [13] .)

TABLE 1

Spectral irradiance of extraterrestrial solar radiation, Iok. (After Smith and Gott l ieb [ 21 ].)

Column 1: Spectral interval, in ~ = 0.1 nm. Column 2: Mean spectral irradiance within that spectral interval, in W m - 2 ~ - 1 . Column 3: Total irradiance up to and including that spectral interval, in W m -2 . Column 4: Total irradiance up to and including that spectral interval, in percent of total irradianee of the whole solar spectrum. Values in parenthesis give power of 10.

Wavelength Solar irradiance (W m - 2 ) Wavelength Solar irradianee (W m - 2 ) range (~k) range (A)

Per A Total % Per A Total %

1.500-1600 1.05 ( - -5 ) 1.27 ( - -2 ) O0,O01 6600-6700 15.55 ( - 2 ) 5.87 ( + 2 ) 43.220 1600-1700 1.78 ( - -$ ) 1.45 ( - -2 ) O0.O01 6700-6800 IS.16 ( - -2 ) 6.02 ( + 2 ) 44.337 1700-1800 7.96 ( - 5 ) 2.24 ( - 2 ) 0 0 . 0 0 2 6800-6900 14.89 ( - 2 ) 6.17 ( + 2 ) 45.43.1 1~00--1900 1.63 ( - 4 ) 3.86 ( - 2 ) 00 .003 6900-7000 14,50 ( - -2 ) 6.31 ( + 2 ) 46. J01 1900-2000 4.00 ( - 4) 7.86 ( - 2) 0 0 . 0 0 6 7000-7100 14.16 ( - -2 ) 6,46 ( + 2) 47..S44 2000--2100 1.10 ( - 3 ) 1.89 ( - - I) 0 0 . 0 1 4 7100-7200 13.85 ( - -2) 6.59 ( + 2 ) 48.564 2100-2200 4.69 ( - 3 ) 6.58 (- - I) 00.04,8 7200-7300 13.56 ( - 2 ) 6.73 ( + 2 ) 49.562 2200--2300 6.41 ( - 3 ) 1.30 00.096 7300-7400 13.16 ( - 2 ) 6.86 ( + 2 ) 50.$32 2300-2400 5.72 ( - -3 ) I.$7 00.138 7400-7.500 12.84 ( - 2 ) 6.99 ( + 2 ) 51.478 2400-2~ 6.42 ( - -3 ) 2.31 00.185 7~0-7600 12.65 ( - 2 ) 7.12 ( + 2 ) 52.409 2.~X3-2600 9.0.5 ( - 3 ) 3.42 00.252 7600-7700 12.36 ( - 2 ) 7.24 ( + 2 ) $3.320 26iX3-2700 2.10 ( - 2 ) 5.52 00.406 7700-7800 12.07 ( - 2 ) 7.36 ( + 2 ) 54.209 2700-2800 2.04 ( - 2) 7.56 00.557 7800-7900 I 1.83 ( - 2) 7.48 ( + 2) $$.0~) 7800-2900 2.90 (- - 2) 1.05 ( + I) 00.770 7900,-.8000 I 1.61 ( - 2) 7.59 ( + 2) $$.935 2900-3000 5.24 ( - 2 ) I.$7 ( + I) 01.156 8000-8100 11.36 ( - 2 ) 7.71 ( + 2 ) S0.771 3000-3100 5.18 ( - 2 ) 2.09 ( + I) 0 1 . $ 3 8 8100-8200 11.04 ( - -2) 7.82 ( + 2 ) $7.585 3100-3200 6.35 ( - 2 ~ 2.72 ( + I) 02.00.5 8200.-8300 10.75 ( - 2 ) 7.93 ( + 2 ) $8.376 3200-3300 7.81 ( - 2) 3.S0 (-t- I) 02..580 8300-84100 IO..SI ( - -2 ) 8.03 (4-2) $9.150 3300-3400 9.00 ( - 2 ) 4.40 (+'1) 03 .243 8400-85(10 10.06 ( - -2 ) 8.13 ( + 2 ) 59.891 3400-3500 8.94 ( - 2 ) .5.30 ( + I) 03.902 8~0-.-8600 9.86 ( - -2) 8.23 ( + 2 ) 60.617 3~G--3600 9.49 ( - 2 ) 6.2.5 ( + 1 ) 04 .601 8600.-8700 9.68 ( - 2 ) 8..13 ( + 2 ) 61,330 3600-3700 10..51 ( - 2) 7.30 ( + I ) 0.5.37.5 8700-8800 9.47 ( - 2) B.42 ( + 2) 62.028 3700-3800 10.40 ( - -2 ) 8.34 ( + I) 06 .141 8800-8900 9,24 ( - -2 ) 8.51 ( + 2 ) 62.708 3800-3900 9.45 ( - 2 ) 9.28 ( - t - I ) 06.836 8900-9000 9,20 ( - -2 ) 8.61 ( + 2 ) 63.386 3900.--4000 I 1.34 ( - 2) 1.04 ( + 2) 07.672 9000-9100 8,98 ( -- 23 8.70 ( + 23 64.047 4000-4100 16.31 ( - 2 ) 1.20 ( + 2 ) 08 .873 9100-9200 8.74 ( - -2 ) 8.78 ( + 2 ) 64.691 4100-4200 17.00 ( - -2 ) 1.37 ( + 2 ) 10 .125 9200-9300 8.57 ( - -2 ) 8.$7 ( + 2 ) 6.5.322 4200--4300 16.59 ( - 2 ) 1.54 (+ '2) 11 .347 9300-9400 8.41 ( - 2 ) 8.95 ( + 2 ) 6.5.941 4300-4400 16.72 ( - -2 ) 1.71 ( + 2 ) 12 .$78 9400.-9~0 8.23 ( - -2 ) 9.04 ( + 2 ) 66.547 4400-4/~X) 19.28 ( - 2 ) 1.90 ( + 2 ) 13 .998 9S00--9600 8.06 ( - -2 ) 9.12 ( + 2 ) 67.141 4S00-4600 20.06 ( -- 2) 2.10 ( + 2) 1.5.475 9600-9700 7.89 ( -- 2) 9.20 ( + 2 ) 67.722 4600-4,'~0 19.86 ( - -2 ) 2.30 ( + 2 ) 16 .938 9700-9800 7.73 ( - 2 ) 9.27 ( + 2 ) 68.291 4700-4800 19.89 ( - -2 ) 2.50 ( + 2 ) 18 .403 9800-9900 7.$6 ( - -2 ) 935 ( + 2 ) 68.848 4800-4900 18.88 ( - -2 ) 2.69 ( + 2 ) 19 .793 9900-10000 7.39 ( - -2 ) 9.42 ( + 2 ) 69.392 4900-5000 19.56 ( - 2 ) 2.88 ( + 2 ) 21 .234 IOO00-11000 6.82 ( - 2 ) 1.01 ( + 3 ) 74.417 .5000-.5100 19.02 ( - 2 ) 3.07 ( + 2 ) 22.63.5 11000-12000 .5..58 ( - -2 ) 1.07 ( + 3 ) 78.-530 5100--.5X)0 18.31 ( - 2 ) 3.26 ( + 2 ) 23 .983 12000-13000 4.64 ( - -2 ) I . I I ( + 3 ) 81.943 5200--5300 18.59 ( - 2 ) 3.44 ( + 2 ) 2.5.352 13000-14000 3.85 ( - 2 ) I.I.5 ( + 3 ) $4.7/7 5300-5400 19.17 ( - 2 ) 3.63 ( + 2 ) 26 .764 14¢J00--I~00 3.23 ( - 2 ) 1.18 ( + 3 ) 87.154 5400-$.~00 18.56 ( - 2 ) 3.82 ( + 2 ) 28.131 15000-16000 2.67 ( - 2 ) 1.21 ( + 3 ) 89.118 .5.500-5600 18.41 ( - 2 ) 4.00 ( + 2 ) 29.487 16000-17000 2.14 ( - -2 ) 1.23 ( + 3 ) 90.697 .56,(X)--5700 18.2~1 ( - 2 ) 4.19 ( + 2 ) 30.833 17000-18000 1.75 ( - 2 ) 1.25 ( + 3 ) 91.983 5700-5800 18.34 ( - 2 ) 4.37 ( + 2 ) 32 .184 18000-19000 1.44 IL --2) 1.26 ( + 3 ) 93.042 .5800-5900 18.08 ( - 2 ) 4.5.5(+2) 33.51.5 19000-20000 1,20 ( - -2 ) 1.21 ( + 3 ) 93.923 5900--6000 17.63 ( - -2 ) 4.73 ( + 2 ) 34.814 20000-30000 5,53 ( -3 ) 1.33 ( + 3 ) 97.9911 6000-6100 17.41 ( - 2 ) 4.90 ( + 2 ) 36 .096 30000-40000 1,53 ( - 3 ) 1.35 ( + 3 ) 99.125 6100-6200 17.05 ( - 2 ) 5.07 ( + 2 ) 37.3.51 40000-50000 $.71 ( - -4 ) 1.35 ( + 3 ) 99.~16 6200-6300 16.58 ( - 2) 5.24 ( + ~') 38..573 ~000-60000 2.54 ( - 4) 1.33 ( + 3) 99.733 6300-6400 16.33 ( - 2) 5.40 ( + 2) 39.778 60000--70000 1.32 ( - -4 ) 1.36 ( + 3) 99.8.t0 64U0--6500 15.99 ( - 2 ) 5.36 ( + 2 ) 40 .956 70000-80000 7.36 ( - -3 ) 1.36 ( + 3 ) 99.886 6500-6600 1.5.20 ( - 2 ) 5.71 ( + 2 ) 42.075 800GO-CAIrO0 4.64 ( - 5 ) 1.36 (-I. 3) 99,920

kmaxT = 2897.8 a m K (1)

giving T ~ 6000 K. In Fig. 2, the spectra! distribution curve of a 5900 K black body is plot ted for comparison. As can be seen, the curve is only a rough approximation to the extraterrestrial solar spectrum. It may be worthwhile to mention that in the spectral range between 100 and 200 nm (UV-C) , the sun behaves like a black body of T = 4500 K whereas between 4 and 10 nm (E-UV), the solar spectrum corresponds to that of a 5 0 0 000 K black body.

The temperature of the earth's surface and of the lower atmosphere is of the order of 3 0 0 K. According to Wien's displacement law (eqn. 1) this terrestrial temperature corresponds to a black body with a spectral distri- but ion peaking at kmax = 9.6 am. In Fig. 3, the spectral distributions of a 6000 K radiatior (= sun) and a 300 K radiatior (= earth) are plotted. Since there is only a minor overlap, solar radiation on the one hand and terrestrial radiation on the other hand can most of ten be treated separately in measurements and computat ions. Solar radiation is sometimes called shortwave, and terrestrial radiation is called longwave radiation in meteorology.

If the spectral irradiance Iok according to Table 1, in W m -2 A -1, is integrated over all wavelengths k, in A, the total irradiance of extraterrestrial solar radiation, in W m - 2 , is obtained:

dk = I0. (2) 0

The subscript 0 means "extraterrestrial", and the bar indicates "a t mean earth-sun distance". The quanti ty I0 is called the solar constant. Its value was recently [1, 2] determined with a much higher accuracy (bet ter than 0.7%) than the spectral data Iox, a n d a m o u n t s to

F0 = 1.37 kW m -2. (3)

If there should exist short t ime fluctuations of the solar constant as occasionally supposed or asserted, they are to be expected within that uncertainty of 0.7%. Secular or even longer t ime variations of the solar constant, on the other hand, cannot firmly be excluded on the basis of the present state of knowledge.

=

O.5

0

0 5 70 /5 20

Visible and ultra- violet radiation

Fig. 3. Relative spectral distribution B(k)/B(kmax) of a black b o d y of T = 6000 K (kma x = 0.48 am) and of T = 300 K (kraax = 9.6 ]am).

Survey:

Thermal radiation

Infrared radiation (thermal radiation in

the narrow sense)

I T ~ 6 0 0 0 K T ~ 3 0 0 K Solar radiation Terrestrial radiation (shortwave radiation) (longwave radiation)

Since the earth orbits the sun in an ellipse during one year, the extraterrestrial solar irradiance varies with the time of year. Its actual value I0 on a given day_may be computed from the solar constant I0 by the rela- tionship

Io = Fo(V/r) 2 (4)

where r -- actual earth-sun distance V-- mean earth-sun distance

= 1 astronomical unit = 149.598 • 106 kin. The "distance correct ion" (V/r) 2 is tabulated in Table 2.

RADIATION FLUXES AT THE GROUND

The energy balance of a horizontal surface of the ground, or of a solid body near t h e

ground, is given by

Q + K + H + L + (W) + (P) = 0. (5)

Each term in this equation stands for an energy flux density or power density, in W m-2. The fluxes in eqn. 5 are counted positive when they are directed towards the surface from above or from below. Since the surface, as an infinitely thin layer, cannot store or deliver energy, the sum of all energy fluxes to

4

TABLE 2

Distance correction (F~) 2 for computing actual extraterrestrial solar irradiance I 0 from solar constnat/o , for each day of the year. I 0 ffi lo(F/r) z.

Jan Feb Mar Apr May

I . 1.03428 !.02981 1.0~935 1.0012~ .98580 2. 1.03~29 1.02951 1.0~784 1.00063 .98530 3. 1.03430 1.02920 1.01733 1.00006 .98382 h. 1.03529 1.02888 1.01682 .999h~ .98333 5. 1.03527 1.o2~55 1.o163o 6. 1.0352h 1.02821 1.0!578 7. 1.03520 1.02736 I.o1525 8. 1.03415 1.02751 I.CI~72 9. 1.03409 1.32715 1.01519 10. 1.03502 1.32677 1.01365 11. 1.03393 1.02639 1.01311 12. 1.03384 1.02600 1.01256 13. 1.03373 1.02561 1.01201 14. 1.03362 1.02520 1.01156 15. 1.03349 1.02579 1.01090 16. 1.03336 1.0253B 1.01035 17. 1.03321 1.02395 1.oo979 18. 1,03306 1.02352 1.00923 19. 1,03289 1,02308 1.00866 20. 1,03271 1.02263 1.00809 21. 1.03252 1.0221~ 1.00753 22. 1.03233 1.02172 1.00696 23. 1.03212 1.02126 ~.00639 2~. 1.03190 1.02079 1.00581 25. 1.03167 1.02031 1.00524 26. 1.03154 1.01983 1.00h67 27. 1.03119 1.01935 1.90409 28. 1.03093 1.01885 1.00351 29. 1.03067 1.00295 ~0. 1.03039 1.00236 31. 1.03011 1.00179

.99891 .98256 • 99~3~ .98238 .99777 .9S192 .99720 .93156 .99663 .98100 .996o6 .93055 • 995b9 .98o~I • 99493 .97967 .99h37 .9792U .993Sl .97882 • 99325 .9784O .99270 .97798 .992~5 .97758 .99160 .97718 .99105 .~-r/679 .99o51 .9764o .98997 .97603 • 9891'5 .97565 .9389t .97529 .9883~ .97893 .987~5 .97459 • 98733 .9742h .9852 .97391 .98630 .97358 .98580 .97326 • 98529 .97295

.97265

Jun Jul Aug Sep Oct Nov Dec

.97235 .96753 .97o8~ .98202 .99789 1.01537 I.o2~62

.97207 .967~1 .97105 .982~9 .99847 1.01590 1.C2895

.97179 .96739 . 97131 .98296 .99905 1.01652 1.02927

.97152 .96738 .97158 .98355 .~9961 1.01694 1.0295e

.97125 .96738 .97185 .93393 1.00019 1.01755 1.9296~

.97100 .96739 .97213 .98551 1.00076 1.01796 1.03017 • 97075 .96751 .97252 .98591 1.00135 1.01856 1.03055 .97051 .967h4 .97272 .98551 1.00192 1.01S96 1.03073 .97028 .967h8 .97302 .98591 1.00249 1.01955 1.03099 .97006 .96752 .97333 .98642 1.00307 1.0199~ 1.03125 .96985 .96758 .97366 .98693 1.0036h 1.02052 1.03159 .96964 .9676h .9739~ .98745 1,00522 1.02089 1.03173 .96945 .96772 .97432 .98797 1.00h79 1.02136 1.03195 • 96926 .96780 .97h66 .98849 1.00537 1.02183 1.03217 .96908 .96789 .97501 .98902 1.00595 1.02228 1.03237 .96891 .96799 .97537 .98956 1.00651 1.02273 1.03257 • 96~75 .96810 .97575 .99009 1.00708 1.02318 1.o3275 .96860 .96322 .97611 .99063 1.00765 1.02362 1.03293 .96S55 .96835 .976b9 .99117 1.00822 1.02505 1.03309 .96832 .968h9 ..~'689 .99172 1.00879 1.02&h7 1.03325 .96819 .96863 ,97727 .99227 1.00935 1.02589 1.03339 .96808 .96879 .97767 .992~2 1.00991 1.02530 1.03352 • 96797 .96895 .979o8 .99338 1.010&7 1.02570 1.03365 .96787 .96912 .97859 .99393 1.01103 1.02609 1.03376 .96778 .96930 .97891 .99549 1.01158 1.026~8 1.03386 .96770 .969h9 .97934 .99506 1.01213 1.03685 1.03395 • 96763 .96969 .97977 .99562 1.01268 1.02722 1.03503 .96757 .96989 .98021 .99619 1.01323 1.02759 1.03510 .96751 .97011 .98065 .99675 1.01377 1.0279~ 1.03516 .96757 .97033 .98110 .99732 1.01431 1.02828 1.03421

.97056 .98156 1.01h8h 1.03525

and from the surface is zero. The symbols have the following meaning:

Q = net total radiation = sum of all positive and negative radiation fluxes to the surface;

K = heat flux from the interior of the body (ground) to its surface;

H = sensible heat flux from the atmosphere to the surface due to molecular and convective heat conduct ion (diffusion and turbulence);

L = latent heat flux due to condensation or evaporation at the surface;

W= heat flux due to advection, i.e., heat transported by horizontal air currents. W is set zero if: (a) the measuring surface is located at a horizontal and h o m o g e n e o u s plane of sufficient extension so that the s o , a i l e d katabatic f low is negligible; and (b) the measuring time is small compared to the time of an air mass exchange (approach of a cold front, for instance);

P = heat f lux brought to the surface by falling precipitation. P is most often not

taken into consideration because the measurements are confined to times without precipitation.

As an example, Fig. 4 shows the daily courses of the energy fluxes Q, K, H and L. The net total radiation Q is, at daytime, to be compensated by the heat f luxes K, H and L.

mW cm "2 QUICKBORN neer HAMBURG

g Summer 19£4,

4

$

2

7

0

-g

-5

-4

• l I ] [ I I ~ I lJ~ / '~ ' f f le /h 6 " B , l i , ,

Fig. 4. Mean daily courses of the different terms of the energy balance of the earth surface on clear days with low wind,,. (After Geiger [14 ] , based on measured data of Frankenberger [ 15 ] . )

The net total radiation Q in eqn. 5 is by itself composed of

Q = (G - - R ) + (A - -E ) . (6)

Q is also called the total radiation balance. The other radiation flux densities in eqn. 6 are defined as follows: G = global radiation = sum of direct and

diffuse solar radiation on the horizontal plane;

R = reflected global radiation = that fraction of G which is reflected by the body (ground);

A = atmospheric radiation = downward thermal radiation of the atmosphere (from atmospheric gases, mainly water vapor, and from clouds);

E = terrestrial surface radiation = upward thermal radiation of the body (ground).

G and R are solar or shortwave radiation fluxes therefore

Q, = G - - R (7)

is called net solar or net global radiation, or shortwave radiation balance. A and E are terrestrial or longwave radiation fluxes so that

Q] = A - - E (8)

is called the longwave radiation balance, and

--Q~ = E - - A (9)

the (upward) net terrestrial surface radiation. An example of the daily courses of Q, G,

R, A and E is given in Fig. 5. Whereas the shortwave radiation fluxes exhibit a pronounced variation during daylight hours, the longwave radiation fluxes vary but slightly

mW cm "2 9

kIAMBUR6;- FU ,9 ~ S June 1954

7

6

S

$

2

7

0

-7 i ~ i i i 19 J~ 21 2 J 25

ff..R. ,,¢,S. TL T/h

Fig. 5. Daily courses of the different terms of the radmtion b ~ n e e o f t he e~-fla surface o n a clear day. S.R. = su~r~, S.S. = ~ t . (After Fle~;eher and Gr~e [161.)

because the temperatures of the atmosphere and the ground vary by bu t a few K during the day.

The ratio

p , = R / G (10)

is called the (shortwave) albedo of the body (ground). Ps mainly depends on the optical properties of the body, that is, on its spectral reflectance Ps()~). But there is also a slight dependence on the spectral distribution of the incoming global radiation, Gx, as is demon- strated by

; Ps(X)Gxdx R k=0

p , - - (11)

G ; Gxd~, kffi0

Some representative albedo values are tabulated in Table 3.

Strictly speaking, the terrestrial surface radiation E is composed of two terms:

(1) the thermal radiation of the body (ground)

E 1 = ~loT 4 (12)

where al = effective longwave absorptance of the

surface, slightly depending on its temperature T;

a = Stefan-Boltzmann-constant = 5 . 6 6 9 7 × 10 - s W m -2 K-4;

and (2) the reflected atmospheric radiation

E 2 = PIA (13) i

where Pl = 1 -- al = effective longwave reflectance of the surface. Thus, E is strictly given by

E = E 1 + E 2 = a l o T 4 + ( I -- al )A. (14)

A table of a I for different surfaces is presented in Table 4. Experience shows that in most cases, eqn. 14 can be approximated by

E = aT ~ (15)

with an error of the order of 2%.

DIRECT AND DIFFUSE SOLAR RADIATION

In the radiation balance Q, it is the global radiation G which is to be used as a natural

6

T A B L E 3

Shor twave a lbedo Ps o f several surfaces

Artif icial surfaces Natural surfaces

velvet, black 0.04 water surfaces 0.06 - 0.12 paper, black 0.05 - 0.06 earth, black, mois t 0.08 road, black top 0.08 earth, grey, mois t 0.10 - 0.12 tiles, l imes tone 0.25 forest , coniferous 0.10 - 0.14 road, concre te 0.25 - 0.35 forest , deciduous 0.12 - 0.20 cardboard, ye l low 0.30 earth, black, dry 0.14 wood , pine 0.40 grass land 0.15 - 0.35 paper, white 0.60 - 0.80 sand, grey 0.18 - 0.23 enamel 0.72 - 0.79 earth, grey, dry 0.25 - 0.30 a luminum 0.77 - 0.81 sand, whi te 0.34 - 0.40 magnesium oxide 0.98 snow, fresh 0.74 - 0.93

T A B L E 4

Effec t ive longwave absorptance al o f several surfaces ( for T = 300 K)

Artif icial surfaces Natural surfaces

metal , pol ished 0.04 - 0.06 bright sand 0.89 brass, dead 0.22 bright l imes tone 0.92 paper 0.8 - 0.9 coarse gravel 0.92 roof ing fe l t 0.93 plant leaves 0.96 glass 0.94 soil with lawn 0.98 brick wall 0.94 water 0.98 " R u b e n s ' b lack" 0.96 snow 0.996

energy source for engineering applications. G is composed of two terms:

G = B + D (16)

where B = direct solar radiation on the horizontal

plane; D = diffuse solar or sky radiation on the

horizontal plane. B is connected with I, the direct solar radiation on a receiving plane being normal to the direction of incidence, by the cosine- projection

B = I c o s ~ = I s i n 7 (17)

where = zenith angle of the sun,

7 = 90 ° -- ~ = elevation angle of the sun; a formula for sin 7 will be given in eqn. (20).

I is that part of the extraterrestrial solar radiation Io which reaches the earth surface after extinction by scattering by the molecules of the air, by scattering and absorption by the aerosol particles suspended in the air ("tur-

bidi ty") and by absorption by the molecules of ozone and water vapor. Figure 6 gives an example of how the extraterrestrial solar spectrum is modified by stepwise introducing the four extinction processes just mentioned. The direct solar radiation reaching the ground, /, is represented by the area under curve 4.

250-

0,2 0.5 10 S p 2 0

Fig. 6. Solar spectrum: 1) extraterrestrial; 1') below the ozone layer; 2) af ter addi t ional scat ter ing by the molecules o f the air; 3) af ter addi t ional ex t inc t ion by aerosol particles; 4) af ter addi t ional absorpt ion by water vapor. (After M~ller [17] . )

If the sun is covered by clouds, the direct solar radiation is zero so that G = D. The diffuse solar radiation or sky radiation is pro- duced by scattering of direct solar radiation by the air molecules, aerosol particles and cloud droplets and crystals. The diffuse solar radiation received by a horizontal plane at the ground, D, depends on the position of the sun at the sky, on the turbidity of the atmosphere, and on the amount and thickness of clouds and their spatial distribution over the sky hemisphere. Figure 7 serves to introduce the spherical coordinates 0 = zenith angle and'

= azimuth angle of the unit hemisphere as well as the solid angle element

dfZ = sin 0 dO da gZ o (18)

where g2 0 = uni t solid angle = 1 steradian (st). If L(0,a) is the radiance received at the

ground from the solid angle element with the spherical coordinates 0 and ~ of the sky, the diffuse solar radiation D at the ground is given by

D = fL(o, ) cos 0 dg2

/~r / /2 = L(0,a) cos 0 sin 0 dO d~ ~2o. (19)

affi0 O=0

As may be seen from eqn. 19, D heavily depends on the spatial distribution of sky radiance, L(0,a). Examples of sky radiance distributions for cloudless and for partly clouded sky are given in Fig. 8.

Fig. 7. Definition of zenith angle 0 and azimuth angle ~ and of the solid angle element d ~ = sin 0 d0 ci~ • ~o- (After Kasten and Raschke [18] .)

N

W E

S N

w ~ i' ~ ~ . . ~ / ~ ~ : . ,-I '

\

\ .

s

Fig. 8. Spectral sky radiance distributions Lk(O,a), in /2W em - 2 nm -1 sr -1 , of cloudless sky (above) and of partly clouded sky (below) for wavelength k = 561 nm, presented as isophots on a polar diagram. Zenith is in the center. (After Dehne [19].)

SOLAR COORDINATES AND TIME

From astronomical considerations which cannot be discussed extensively here, the coordinates of the sun in the horizontal system are given by

sin 7 = sin ~ sin ~ + cos ~ cos 8 cos co ; (20)

sin ~ sin 7 -- sin cos a = (21)

cos ~ cos 7

where

7 = solar elevation angle;

8

TABLE 5

Solar declination 8, in deg, for each day of the year

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

I. -23.01 -17.12 -7.62 b.50 15.0~ 22.04 23.12 15.05 8.32 -3.1b -14.39 -21.79 2. -22.9~ -16.84 -7.2L 4.89 15,3b 22.17 23.05 17.79 7.96 -3.53 -I~.71 -21.92 3. -22.83 -16.5~ -6.86 5.27 15.64 22.30 22.97 17.57 7.59 -3.92 -15.05 -22.0~ 4. -22.73 -16,25 -6.~ 7 5.65 15.93 22.42 22.89 17.27 7.22 -4.30 -15.3b -22.22 5. -22.62 -15.95 -6.0~ 6.07 16.22 22.53 22.80 17.00 6.85 -~.69 -15.6~ -22,36 6. -22.51 -15.6~ -5.70 6.41 16.50 22.6~ 22.70 16.73 6.~B -5.07 -15.95 -22.48 7. -22.3~ -15.33 -5.31 6.79 16.78 22.74 22.60 16.45 6.11 -5.46 -16.24 -22.60 ~. -22.25 -15.02 -~.92 7.16 17.06 22.84 22.49 16.17 5.73 -5.8~ -16.54 -22.71 9. -22.12 -14.70 -4.53 7.54 17.33 22.92 22.37 15.89 5.36 -6.22 -16.83 -22.~I 10. -21.97 -I~.38 -~.14 7.91 17.59 23.00 22.25 15.60 ~.98 -6.60 -17.11 -22.90 11. -21.82 -14.05 -3.75 8.28 17.85 23.08 22.12 15.30 4.60 -6.98 -17.39 -22.99 12. -21.66 -13.72 -3.36 8.64 18.11 23.15 21.99 15.01 4.22 -7.35 -17.66 -23.07 13. -21.h 9 -13.38 -2.96 9.01 18.35 23.21 21.85 14.70 3.84 -7.73 -17.93 -23.I~ Ih. -21.32 -13.05 -2.57 9.37 18.60 23.26 21.70 lh.hO 3.45 -8.10 -18.20 -23.21 15. -21.14 -12.70 -2.17 9.73 18.84 23.~1 21.55 Ih.09 3.07 -8.47 -18.b5 -23.26 16. -20.95 -12.36 -1.78 10.08 19.07 23.35 21.39 13.TT~ 2.69 -8.84 -18.71 -23.31 17. -20.76 -12.01 -I,38 I0.~ 19.30 23.38 21.22 13.46 2.30 -9.21 -18.96 -23.35 18. -20.56 -11.66 -.99 10.79 19.52 23.~I 21.05 13.1b 1.91 -9.57 -19.20 -23.39 19. -20.35 -11.31 -.59 11.14 19.74 23.42 20.~7 12.81 1.53 -9.9 h -19.h3 -23.41 20. -20.14 -I0.95 -.20 11.48 19.95 23.h~ 20.6P 12.k8 1.14 -I0.30 -19.66 -23.43 21. -19.92 -I0.59 .20 11,82 20.16 23.~4 20.50 12.15 .75 -I0.65 -19.89 -23.44 22. -19.70 -I0.23 .59 12.16 20.36 23.~4 20.30 11.82 .36 -11.01 -20.11 -23.44 23. -19.46 -9.86 .99 12.49 20.56 23.43 20.10 11.~8 -.03 -11.36 -20.32 -23.~4 24. -19.23 -9.49 1.38 12.83 20.75 23.~2 1 9 . 8 9 11.14 -.42 -11.71 -20.53 -23.42 25. -18.98 -9.12 1.77 13.15 20.93 23.~0 19.68 10.80 -.81 -12.06 -20.73 -23.40 26. -18,73 -8.75 2.17 13.48 21.11 23.37 19.46 1 0 . 4 5 -1.20 -12.h0 -20.92 -23.37 27. -18.~8 -8.37 2.56 13.80 21.28 23.33 19.2~ 10.10 -1.59 -12.7~ -21.11 -23.33 28. -18.22 -8.00 2.95 I~.12 21.k~ 23.29 19.01 9.75 -1.98 -13.08 -21.29 -23.29 29. -17.95 3.34 lh.~3 21.60 23.24 18.78 9.~0 -2.37 -13.~1 -21.46 -23.24 30. -17.68 3.73 I~.7~ 21.75 23.18 18.5~ 9.0~ -2.75 -13.74 -21.63 -23.18 31. -17.40 ~.12 21.90 18.30 8.68 -I~.07 -23.11

= solar azimuth angle, counted from South positive to West, negative to East;

-- geographical latitude of the point of observation;

5 = solar declination -- elevation of the sun above the equator at the time of observation;

co = solar h o u r angle = angle be tween the h o u r circle (geographical d i rec t ion o f the sun) and the mer id ian (geographical S ou th d i rec t ion) , at the t ime o f observa- t ion.

The var ia t ion o f 6 dur ing 1 day is small so t ha t fo r pract ical purposes , 6 is cons ide red to be i n d e p e n d e n t o f co. A table o f 6 f o r each day o f the yea r is p r e sen t ed in Table 5. The re is a small var ia t ion o f 6 dur ing the leap-year cycle bu t fo r mos t appl ica t ions it is suf f ic ien t to use the 6-values o f the th i rd year o f the leap year cycle as representa t ive means. 6 varies f r o m - - 2 3 . 4 4 ° at win te r solst ice t h rough 0 ° a t the equ inoxes to +23.44 ° a t the summ er solstice.

Whereas the solar dec l ina t ion ~ describes the d e p e n d e n c e o f solar e levat ion angle 7 on the t ime o f year (date) , the h o u r angle co

def ines the d e p e n d e n c e o f 7 on the t ime o f day (c lock t ime) , co is c o u n t e d f ro m the mer id ian ( south d i rec t ion) as posi t ive in the a f t e r n o o n (wester ly d i rec t ions o f the sun), as negative on f o r e n o o n (easter ly sun):

co (deg) - - 1 8 0 - - 9 0 0 +90 + 1 8 0

TLT (h) 0 6 12 18 24

position N E S W N o f the sun

The term TLT = true local time will be explained later on.

Special cases o f eqn. 20 are: ( a ) sunrise or sunset: 7 = 7 o ffi 0.

0 = sin 70 = sin ~ sin 6 + cos ~ cos 6 cos co 0.

sin ~ sin 6 cos coo = = - - t a n ~0 tan 8. (22)

cos ~ cos 6 Example : equ inoxes , 6 = 0. Th en cos co o = 0;

c o o = -+90° ; T L T = 18 h (sunset)

6 h (sunrise).

T A B L E 6

E q u a t i o n o f t i m e Z, in ra in , for each day o f t h e year . Va lues r o u n d e d t o ful l m i n u t e s .

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1. -~. -14. -12. -~. 3. 2. -4. -6. - . 10. 16. 11. 2. -h. -14. -12. -~. 3. 2. -~. -6. 11. 16. 11. 3. -~. -IL -12. -3. 3. 2. -~. -6. I~ 11. 16. 1o. 4. -5. -1~. -12. -3. 3. 2. -~. -6. 1. 11. 16. 10. 5. -5. -I~. -12. -3. 3. 2. -~. -6. i. ~I. 16. 9. 6, -6. -I~. -11. -3. 3. I. -5. -6. 2. 12. 16. 9. 7. -6. -1~. -11. -2. 3. 1. -5. -6. 2. 12. 16. 9. 8. -7. -14. -11. -2. 3. 'i. -5. -6. 2. 12. 16. 8. 9. -7. -I~. -11. -2. ~. I. -5. -5. 3. 13. 16. 8. 10. -7. -i~. -10. -i. ~. i. -5. -5. 3. 13. 16. 7. 11. -8. -14. -10. -1. ~. -5. -5. 3. 13. 16. 7. 12. -8. -I~. -10. -I. h. -5. -5. ~. 13. 16. 6. 13. -9. -I~. -IC. -I. L. -6. -5, ~. t4. ~6. 6. I~. -9. -I~. -9. -. L. -. -6. -5. ~. i~. 15. 5. 15. -9. -lb. -9. -. h. -. -6. -4. 5, lb. 15. 5. 16. -ic. -I~. -9. h. -I. -6. -~. 5. 14. 15. ~. 17. -IO. -I~, -8. h. -I. -6. -h. 5. 15. 15. h. 18. -Io. -lb. -8, I[ h. -I. -6. -~, 6. 15. 15. 3. 19. -11. -14. -%. I. h. -I. -6. -h. 6. 15. 15. 3. 20. -11. -lb. -8. I. 3. -I0 -6. -3. 7. 15. lb. 2. 21. -11. -14. -7. 1. 3. -2. -6. -3. 7. 15. 1~. 2. 22. -12. - l b . -7. 1. 3. -2. -6. -3. 7. 15. 14. 1. 23. -12. -13. -7. 2. 3. -2. -6. -3. 8. 16. lb. 1. 2h. -12, -13. -6. ~. 3. -~. -6. -2. 8. 16. 13. 25. -12. -13. -6. 2. 3. -3. -6. -2. 8. 16. 13. -, ~6. -13. -13. -6. 2. 3. -3. -6. -~. 9. 16. 13. - 27. -13. -13. -5. 2. 3. -3. -6. -2. 9. 16. 12. -I[ 28. -13. -13. -5. ~. 3. -3. -6. -I. 9. 16. 12. -I. 29. -13. -5. 3. 3. -3. -6. -I. 10. ~6. 12. -2. 30. -13. -5. 3. 3. -4. -6, -I. 10. 16. 11. -2. 31. -13. -h. 2. -6. -. 16. -3.

(b) culmination at noon (TLT = 12 h): Then co N = 0 ;cos CON = 1.

sin 7N = sin~ sin 8 + c o s ~ c o s 5 = c o s ( ~ - - 8 ).

7N = 9 0 ° - - (~ - - ~ ). ( 2 3 )

The conversion of the hour angle co of the sun to time defines the so .a i l ed true solar or true local time. During 1 day (1 d = 1440 min), the hour angle co runs from --180 ° at TLT ffi 0 h through 0 ° at TLT = 12 h (noon) to +180 ° at TLT = 24 h. Therefore the following proport ion holds:

TLT -- 12 h 1 d rain

co 360 deg d e g '

TLT = co • 4 min/deg + 12 h . ( 2 4 )

At TLT = 12 h = true local noon, the sun culminates at south. In order to make solar radiation measurements at different locations of ~he earth comparable, a convention of the World Meteorological Organization (WMO) recommends to perform all meteorological radiation measurements according to TLT.

Then all radiation records have the natural symmetry with respect to true noon.

True local time TLT is a time running unevenly because the hour angle co runs unevenly with time, for two reasons:

(a) the apparent orbit of the sun, the so-called ecliptic, is no t a circle but an ellipse;

(b) the time is not measured on the ecliptic but because of the definition of time by the rotat ion of the earth around its axis, it is. measured on the equator.

For practical purposes, a mean hour angle is derived by astronomical considerations,

and a corresponding mean local time MLT is defined. The difference of both time scales is called the equation of time, Z:

Z = TLT -- MLT. (25)

The variation of Z during the year results from the overlap of a sine curve due to the effect (a) mentioned above, and a double sine curve from the effect (b). As in the case of the declination of the sun, the small variations of Z during one day and from one year to the other during the leap year cycle can be neglected for most applications. Table 6 pre-

i0

sents a table of Z for each day of the year. Extreme values are Z = - -14 min in February and Z = +16 rain in October /November .

As mentioned, the hour angle co is measured from the meridian of the point of observation. Consequently, true local t ime TLT and also mean local t ime MLT are only valid for the po in t of observation.

Civil life requires the use of a uniform time scale within a certain region, the so-called standard time ST. It is defined by the MLT of a certain selected standard meridian of geographical longitude ks. The MLT of the 0- meridian which passes through Greenwich in England is called Greenwich Mean Time GMT:

G M T = MLW(ks = 0). (26)

The standard time of another meridian ks east of Greenwich is related to GMT by

ST(k,) = GMT + ks • 4 min/deg. (27)

Example: Central European Time CET is the MLT of the standard meridian ks = 15 °E. Thus,

CET = GMT + 1 h. (28)

Analogously, the mean local time of any point located on a meridian k is connected to GMT by

MLT(k) = GMT + k • 4 min/deg. (29)

By combining eqns. 27 and 29, we obtain

MLT(k) = ST(ks) + (k -- ks) • 4 min/deg (30)

as the relation between MLT and ST. Finally, we combine eqns. 30 and 25 and obtain an equation which allows us to compute true local t ime from standard time:

TLT = ST(ks) + (k -- ks) • 4 min/deg + Z. (31)

Note: If locations west of the Greenwich meridian are considered, the longitudes k, ks in the above equations are to be taken as negative.

GLOBAL RADIATION ON A TILTED PLANE

A plane surface tilted by an angle/~ against the horizontal and with its normal directed to the azimuth a receives radiation G(~, a) which is basically composed of three radiation fluxes:

G(~, a) = I(~, a) + D(~, a) + R(~, a). (32)

I(~,a) is the direct solar radiation on the tilted plane and is given by

I(/~, a) = I cos ,7 (33)

where I is the direct solar radiation at normal incidence, and ,7 is the angle between the direction of the sun and the normal of the tilted plane. By spherical geometry, ~ is given by

cos ~ = sin 7 cos ~ + cos 7 sin j3 cos(~ -- t~)

(34)

where 7 = solar elevation angle,

= solar azimuth angle, = tilt angle of the plane against the

horizontal, = azimuth angle of the normal of the plane.

D(~, a) is that part f of diffuse solar radiation D which can be seen by the plane, and R(~, a) is the part 1 -- f of reflected global radiation R falling on the plane:

D(/~,a) = fD; (35)

R(fl,a) = (1 -- f )R = (1 -- f ) p s G (36)

with Ps = mean shortwave albedo of the ground facing the plane. Thus,

G ( ~ , a ) = I c o s ~ + f D + ( 1 - - f ) p s G . (37)

Assuming isotropic sky radiation and isotropic reflection from the ground, spherical geometry yields

f = COS2(~/2) (38)

so that in this simplified case, eqn. 37 pro- ceeds to

G(~, ~) = I cos ,7 + D cosS(M2) +

+ psG[1 -- cos2(~/2)]. (39)

Equation 39 can be used to compute G(~, a) from measured data of G and D; I is given by

I = B/s in 7 = (G - - D ) l s i n 7, (40)

using the definitions in eqns. 17 and 16. For further details and refinements of

calculating G(/~, a) from meteorological radiation data, the reader is referred to the special literature. Good surveys can be found in the books of Robinson [3] and Kondratyev [41.

RADIATION INSTRUMENTS

The instruments used for meteorological radiation measurements may be classified into two main groups: those for measuring solar (shortwave) radiation and those for measuring total, that is solar plus terrestrial (shortwave plus longwave), radiation. If terrestrial (longwave) radiation fluxes are to be determined, a combination of both types of instruments is to be used. The sensor of all instruments described in the following sections is a black surface connected with a thermopile, the thermovoltage of which is the electrical signal to be recorded or processed.

Global radiation G is measured by pyranometers. In Fig. 9, a Moll-Gorczynski pyranometer, also called a solarimeter (Kipp & Zonen, Delft, The Netherlands) is shown. The ring-shaped shield is to prevent the thermopile in the socket of the instrument from being heated up by direct solar radiation. The two concentric glass domes are for weather protec- tion and, since the transmission of glass is limited to the spectral range 300 nm < ~ < 2500 nm, to confine the spectral response of the instrument to shortwave radiation. For the same reason, the inner dome shields the sensor from the longwave thermal radiation of the weather-exposed outer dome. To reduce deposition of dust, dew and rime, it is recommended to ventilate the outer dome through special nozzles by a blower. For measuring reflected global radiation R, a pyranometer facing downward is applied.

Fig. 9. Mol l -Gorczynsky pyranometer = solarimeter (Kipp & Zonen, Delft , The Netherlands).

Respdnsivi ty: 0 .11 m V / m W • cm - 2 ; temperature dependence: - -0 .15%/K; internal resistance: 10 o h m ; t ime constant: 4 s; cosine error: wi th in ± 5% for angles o f

incidence up to 80 ° .

11

Fig. 10. Solarimeter wi th sun-shading ring.

Diffuse solar radiation D is also measured by a pyranometer but additionally equipped with a sun-shading ring on an equatorial mount, see Fig. 10. The specifications for the shading ring are given by CSAGI [5] and WMO [6]. The shading ring shields the horizontal surface of the sensor from direct solar radiation so that the system measures

O -- B = D. (41)

The ring has to be reset once every few days according to the declination 5 of the sun. Since the ring shields not only from direct solar radiation but also from part of the diffuse solar radiation, accurate determination of D by this measuring system requires some correction for the loss of diffuse radiation caused by the ring. On the basis of field exper- iments at the Meteorological Observatory, Hamburg, correction factors for the daily sums of D were determined and tabulated as function of solar elevation at noon, 7N, and of relative dally sunshine duration S/So which is a rough measure for the cloud coverage of the sky; see Table 7. The correction factors range from 1.005 (21 Dec., cloudy) to 1.15 (21 June, cloudless} in Hamburg.

The overall accuracy of pyranometers mainly depends on solar elevation angle 7.

12

TABLE 7

Correction factors for diffuse solar radiation D measured by a solarimeter with shading ring of 5 cm width and 60 cm diameter, as used by the Meteorological Observatory, Hamburg. 7N = solar elevation angle at noon; S I S 0 = relative daily sunshine duration

~/Jv S /So: o .o o. 1 o .2 o .3 o .~ o .~ o.~ 0 .7 0.8 0 .9 ~.o

O 2

6 8

10

12 14 16 18 2O

22 2it 26 28 30

32 3~ 36 38 40 42 ~4 46 48 50 52 5~ 56 58 60

1,000 1=0OO 1=000 lpOOO 1,0OO 1=0OO 1,O00 ,OOO 1lOO0 11OOO 11000 t~OO1 I=O01 lt001 1~O01 ltO01 le001 1~001 ,001 1=OO2 l t002 1~OO2 loOO1 loOO1 10OO2 1=O02 1~OO2 ltO03 1,003 pO03 1~OO3 lsOO& 19OO4 1#O02 loOO2 1,O03 1=O03 1,004 1,004 1~O04 sO05 1=005 l t006 1,OO6 1,O03 loOO4 1=00~ l t005 10005 1=OO6 le007 ,007 1~008 1pOO8 1=009 1,O0~ 1tO05 11006 ltOO6 Ip007 I t008 1~O09 ,O10 1,010 1 ,Ol l 1,O12

l t005 1~006 1=OO7 1,OO9 1=010 1=011 1=O12 ltO13 1=O14 10015 ltO16 l t007 1=OO8 1=009 1,011 1=O12 1,013 1,014 l t015 11017 11018 1=019 l t008 1,O10 1=Oll 11013 1001~ 1,O16 1,017.1=019 lo020 1~O22 1,023 10010 10012 1=O14 11015 10017 l t019 1,021 1=O23 l t024 1,O26 1=O28 1,011 ljO13 1=O15 11018 1,020 10022 1,O24 1pO26 1=O28 I,O30 1=O32

ltO13 1~015 1=018 ltO20 1=023 ltO25 1,O27 1,O30 1,O32 1,C)35 1,O37 10014 1=O17 1=O20 1=023 1~O26 1,029 1,O31 1,034 1=037 1=040 1,O43 ltO16 1,019 1=022 1,Oa6 1=O29 1~032 1=O35 1,0~8 1,O~2 1~O45 1,048 10018 1=O22 ltO25 ltO29 1,O~2 1,036 1,040 1,O43 1~067 1,O~0 1,094 10019 1,O23 1~O27 1=O31 1~O35 1,O~O 1,064 1,048 1,052 1,0~6 1,060

I t021 I=02~ 1~030 1,034 1=039 1=043 1,0~8 1,0~2 1,0~7 1~061 1,066 1=023 1~028 1,033 1,038 1,04~ 1,048 1,0~2 1~0~7 1,062 1,067 1,072 1~O25 1=O30 1~O36 100~1 1,O~6 1,O52 1,O57 1,062 1,067 1,O73 1,O78 1~O27 1=O33 1=O38 1 , O ~ 1=050 1,O56 1,O61 1,O67 I,O73 1,O78 1,08~ 1,O29 1,O35 1,O41 100~7 1,O53 1~O60 1,O66 1=O72 1,078 1=084 1~O90

1,031 1=O38 1,04~ 1,051 1,057 1,06h 1~071 1,O77 1008~ 1,090 1~097 1,O33 1,040 1,Oh7 1=0~ 1~O61 1,O68 1,O75 I,O82 1,O89 1,096 1~103 1oO3~ 1=O42 1,O49 1,O57 1,O65 1,072 1=O79 1=O87 1=094 1,102 1,109 1=O37 I~Oh5 1=O52 I,O60 1,O68 1=076 1,083 1,O91 1,099 l t106 1,114 1,O39 1~Oh7 1~055 1,O63 1,O71 1,079 1=O87 1,095 1=104 1=112 1,120

1@O~1 1~0~9 1~O58 1,O66 1,O75 1=O83 1,091 1,100 1,108 I=1t7 1,12~ 1=042 1~051 1=O60 1,O68 1~O77 1~086 1,O95 1,10~ 1=113 1,122 1=131 1~O~ 1~O53 1=062 1,O72 1,081 1,090 1,099 1,108 1,118 1,127 1,136 1=O~6 1,O56 1=O6~ 1,O75 1~08h 1,09~ 1,103 1,113 1,122 1,132 1,1~1 1=0~8 1=O58 1,068 1,077 1~087 1,O97 1,107 1,117 1~126 1,136 1,1L~6

For 7 ~ 10°, it is considered to be better than 5% for G and R, and between 5 and 10% for .... D.

An instrument for measuring direct solar radiation on a receiving plane being normal to the direction of incidence, I, is called a pyrheliometer. As an example, Fig. 11 shows the Eppley Normal Incidence Pyrheliometer (Eplab Inc., Newport, R.I., USA). A long tube and several diaphragms allow radiation from only a narrow solid angle to reach the sensor at the end of the tube. A filter wheel permits selection of certain spectral ranges of the incident radiation.

Pyrheliometers are mainly used either as primary reference standards or as secondary calibration standard instruments. With the help of the first type, the secondary standard pyrheliometers are calibrated which in turn serve as standards for calibrating pyranometers. Secondary standard pyrheliometers are to have an accuracy of ± 1% or better.

Fig. 11. Eppley Normal Incidence Pyrheliometer (Eplab Inc., Newport, R.I., USA).

Responsivity: 0.08 mV/mW • cm -2 ; temperature dependence: compensated for +1% of

responsivity in the temperature range - -30 °C to +40 °C;

internal resistance: 200 ohm; time constant: 1 s; angle of view: 5.7 ° .

For continuously recording direct normal incidence solar radiat ion/ , the pyrheliometer has to be installed on a motor-driven equatorial mount which allows the pyrheliometer axis to follow the sun. Since this device requires some care and service, it is only used at selected observatories. For routine radiation stations, it is recommended to determine I from B, the direct radiation on a horizontal receiving plane. B may be computed from measurements of G and D with the help of

B = G - -D; (42)

and from that, direct solar radiation on the normal plane by

I = B/s in T. (40)

It can be shown that eqn. 40 also holds for hourly sums of I and B with sufficient accuracy if instead of ~( the solar elevation angle ~m of the middle of the respective hour is taken. ~m is given by an equation being analogous to eqn. 20:

sin ~'m = sin ~ sin 8 + cos ~ cos 8 cos oJ m (43)

with G~ m - - - - hour angle of the middle of the respective hour.

Next to global radiation G, the total radiation balance or net total radiation Q is the most important radiation quantity in meteorology. Q is measured by net pyrradiometers also called radiation balance meters. Figure 12 shows the Schulze-D~/ke radiation balance meter (B. Lange, Berlin (West)). The instrument is basically similar to a pair of pyranometers; but instead of glass domes it possesses hemispherical covers of polyethylene which is transparent to wavelengths up to more than 50/am so that solar (shortwave) plus terrestrial (longwave) radiation is received by the sensors. By connecting the thermopiles of the upward and downward facing sensors against each other, the electrical output of the instrument is directly proportional to the net total radiation provided both sensors have the same calibration constants in both the shortwave and longwave spectral range.

In the general case, the different magnitude of the calibration factors of the upward facing sensor for shortwave and longwave radiation, fus and ful, and of the corresponding calibration factors of the downward facing sensor, fd, and fdl, have to be accounted for. The instrument temperature Tl has also to be

13

Fig. 12. Schulze-D~ke radiat ion balance m e t e r = net pyrradiometer (B. Lange, Berlin (West)).

Respons i t ivy : 0.9 mV/mW • cm - 2 ; temperature dependence: ± 6% in the temperature

range from --10 °C to +30 °C;

internal resistance: 2.5 ohm; time constant: 150 s for 99% value; cos ine error: w i th in ± 2.5% for angles of

inc idence up to 80 ° .

known for which reason a resistance thermo- meter is provided in the instrument. The upward facing sensor records the difference between incoming total radiation G + A and the thermal radiation oTl 4 emitted by the instrument: G + A -- oTl4; the downward facing sensor measures the difference between incoming R + E and emitted oTl4: R + E -- aTi 4. The radiation fluxes G and R have to be known from independent measurements by pyranometers.

In this way, atmospheric radiation A and terrestrial surface radiation E are determined. The net total radiation is then easily computed from its components G, R, A, E:

Q = (G - -R) + (A --E) . (6)

14

The overall accuracy of the quantities A, E and Q determined by the net pyrradiometer is around 10%.

For further details on radiation instruments, their calibration, installation and maintenance, the reader is referred to the surveys given by Robinson [3], WMO [6], Latimer [7], Coulson [8] and Dehne [9].

DAILY COURSE OF HOURLY RADIATION

In order to get a feeling for the variation of solar radiation, a few examples of original

5 0

TL T/h

Fig. 13. Global radiation G and diffuse sky radiation D on two cloudless days in June and December, resp. G6, De: 29 June 1976; G12 , D 1 2 : 3 1 Dec 1969. Note: Time runs from right to left on this diagram. (After Dehne [10].)

records will be presented. Figure 13 is a reproduction of the records of global radiation G and diffuse solar radiation D on two selected days with no clouds and low turbidity, one day close to winter solstice, the other day close to summer solstice. Global radiation on these two extreme days differs by a factor 4.1 in maximum, and by 8.4 in the daily sums which are given by the areas below the respective curves. To the contrary, diffuse solar radiation D in winter reaches the same maximum as in summer, and the ratio of the daily sums is 2.6.

Figure 14 illustrates the large variation of global radiation due to changing cloudiness during one day. Bright towering cumulus of a thunderstorm approaching the site of observation make, by reflection, G momentaneously to increase up to 1000 W m - 2 ; after the front has reached the site, the sky is com- pletely covered by thick dark cloudiness and G is reduced to about 10 W m -2. Later on, the cloud deck is varying in thickness so that G undergoes relatively smooth variations.

This example of a clouded day exhibiting large radiation fluctuations within short time intervals demonstrates that the evaluation of radiation records on a routine basis requires some kind of smoothing or averaging. In meteorology, hourly sums of the radiation fluxes are considered to give representative

1 0 0 0

900

800

700

600

500

4,00

500

200

7 0 0

0

i I i

Wm-2

l l l l l I f I I r I I , I I 1 i i I

G l o b a l Red/~t/on

llemburg - S a s e I 16 J U N E 77

• . . . . - . .

?": : ~!:= if ?. C ?

21 20 L9 18 17 18 15 l~ ;'5 12 1 ! lO 9 8 7 6 5 4 3

TL T/h Fig. 14. Gloh~l radiation G on a day with varying cloudiness. Note: Time is running from right to left on this diagram. (After Dehne [10] .)

radiation values even in cases of large varia- 200 tions in cloudiness and consequently of widely scattered points on the chart records. On the other hand, the time resolution of one hour ,50 seems to be short enough to permit correla- tion with other meteorological quantities such as actual cloud observations, for instance.

The hourly sum is a time integral of the irradiance or energy flux density or power density of radiation, and is called (hourly) irradiation. Whereas the basic unit of irradiance is W m -2, the basic unit of irradiation is Ws m- 2 = j m- 2. Alternate units of irradiance are mW cm-2 or kW m-2, of irradiation J cm-2 , MJ m - 2 , and Wh c m - 2 o r kwh m - 2 .

For demonstrating typical mean daily courses of the different radiation quantities, the results of a 10 year period of measurements at the Meteorological Observatory, Hamburg are presented. In Fig. 15, mean hourly sums of global radiation G, in J c m - 2 , are plot ted versus true local t ime for each of the twelve months indicated by the figures • at the curves. G reaches its maximum at true solar noon but a slight depression is noticed in the spring months March and April just before noon due to convective cloudiness which disappears in the afternoon.

Diffuse sola~ radiation D (Fig. 16) exhibits values being about half of G in summer but of almost equal magnitude in winter. Direct solar radiation on the horizontal plane, B (Fig. 17) has a distinct minimum before noon in March

, , , , t , , , , , , , , , , i J i i J i i i i 200

O / J c.m "z #AMaU,~O - FU 1~4 - 1973

750

100 S

0

50

0 , , , , , , , , , , , , , , , , , , , , , , , ,T 6 9 72 IS I 8 21 TLT21~

Fig. 15. Global radiat ion G: 10 year means of the hourly sums, in J cm - 2 , for each of the twelve months. Time of day is given as true local time. Figures at the curves indicate number of the months. (After Kasten [20] . )

15

i i J i i i i J L , , i , , i ~ i , , , , , , ,

0 / 3 c m "2 /~.~MSURO - FU 1961 / - / 9 ; 5

6 7

5 O

6

3 6 9 12 75 18 21 7~T2~ '

Fig. 16. Diffuse solar radiat ion D. See legend to Fig. 15.

2 0 0 ' ' , , , , , , , , , L , , , J a , i , , , , i

B / J cm -2 #AMSURO- /~u 1964 ° 197$

150

I 00

0 , , r f r i , , , , , , , , , , , , , , , i , ,

3 6 9 12 15 18 ~ ! TLT20

Fig. 17. Direct solar radiation B. See legend to Fig. 15.

and April which is caused by convective cloudiness as just mentioned.

Atmospheric radiation A (Fig. 18) has a daily course which is quite different f rom those of the preceding solar radiation sums. Due to delayed warming of the atmosphere, there is a typical asymmetry with a maximum around 1400 TLT. For the same reason, the night values in the spring months March and April are relatively low in contrast to the corresponding months in fall, September and October. Peculiar are the minima in March, April and May around the t ime of sunrise, and the broad minima around noon from October through February. Rise of radiating inversion layers to higher, colder levels of the atmosphere and finally their dissolution are believed to be responsible for these reduced values of downward thermal radiation.

Finally, the curves of the net total radiation or total radiation balance Q (Fig. 19)

16

HAt4BUR~ - FU

- "--~1 a cJn " ~ ~ 9~,~ - m r ~

200 -

79O -

180 -

~70 -

160 -

150 -

120 ~ ~ .

I 00~ , , , , . . . . . , , , . . . . . . . ' ' '

Fig. 18. Atmospheric radiation A. See legend to Fig. 15.

0/3cm "e ~,~au~ - fu 796~ - I 973

150

100

50

Fig. 19. Net total radiation (total radiation balance) Q ffi (G - - R ) - - (E --A). See legend to Fig. 15.

show a course similar to global radiation G for which reason several parameterizations of Q by G have been proposed in the literature. Of course, the negative values of Q at night cannot be expressed in terms of G. The nighttime values of Q are more negative in the summer months than during winter corresponding to the opposite behaviour of the net terrestrial surface radiation because Q = --(E -- A) at nighttime.

FREQUENCY DISTRIBUTION OF HOURLY RADIATION

Many applications of solar energy require a certain minimum of incoming solar radiation in order to operate efficiently. Therefore, the probabilities for the occurence of irradiance above given threshold levels are of interest.

Continuous measuring series of all solar and terrestrial radiation fluxes have been per-

formed since 1954 at the Meteorological Observatory, Hamburg of the Deutscher Wetterdienst (DWD). This institute also operates the radiation network of DWD, see Fig. 20. At the end of 1979, 22 global radiation stations were in operation, 15 of which additionally record diffuse solar radiation. The numbers at the stations give the starting year of operation. From 8 global radiation stations, continuous records of more than 10 years of hourly radiation sums are available.

These data were analyzed month by month with regard to the number of hours when the hourly irradiations were >0, 9, 18, 2 7 . . . J cm -2 corresponding to mean hourly irradiances of >0, 25, 50, 75 . . . . . . W m -2. The results are plotted as mean monthly means of cumulative frequency, in hours per day (h/d), of mean hourly irradiance, in W m -2, for each month (see Fig. 21) for the station Hamburg. In the upper row, the frequency curves of

J

a ~ , ~ r mAo u ~ l * ~ a

®

~Rc imv~ c# c ~s

~ H z

Fig. 20. Radiation network of Deutscher Wetterdienst (as of 31 Dec. 1979), ~ global and diffuse radiation (15 stations), • global radiation (7 stations), o global (radiation planned (6 stations). The numbers at the stations give the year of the beginning of the measuring series of global (or diffuse, respectively) radiation.

~000 . . . . I . . . . I . . . . I [ , fOl

W I,~m 600 g~

2 2~

o s w ~ l~/d 600 ~ O 0 ~ J A N - 3 U N E ( I ' ~ ]

u s 1o Is h/d

o s 1o ,s h/d 600

o

Fig. 21. Cumulative frequenc.,y (hours per day) of mean hourly irradiance ( W m - ' ) of global radiation G and diffuse radiation D in each month at Hamburg (1966- 1975).

....... No~m~e v

. . . . B~uf~chwe,d ~ 0 0 0 . . . . , . . . . , . . . . , . . . .

W m" JUNE eoe . xoo. "~ '~

~,foo .

2oo.

o S ,o ~S h/d

. . . . . . Tr/er . . . . . . HolPer~ei/~enben]

. . . . . . Wd rZ~ . . . . . . . . B~Un /~

. . . . . . . . . . . W e / h e n s ~ o . * ~

t o ~ o . . . . , . . . . , . . . . , . . . .

DE CEMS£R aoo 7oo . soo . $oo.

• ~ IX ~oo. ~

too.

o o" "; . . . . ,; . . . . , ; ' h / ~ " ~

Fig. 22. Cumulative frequency (hours per day) of mean hourly irradiance (W m -2) of global radiation G at 8 stations in Germany in the months June and December (1966 - 1975).

global radiation G for January to June (I - VI) and July to December (VII - XII) are plotted, in the lower row the corresponding curves of diffuse solar radiation D. Global radiation fre- quencies for all 8 German stations were summarized on one diagram for each month (see Fig. 22) for June and December as examples.

The frequency of global radiation at Ham- burg was also analyzed with respect to the D/G-ratio in the following manner: for each month, the hourly sums or mean hourly irradiances, respectively, of G were assorted into the classes defined above. For each individual G-value within a class, the corresponding simultaneously measured D-value was taken irrespectively of any D-threshold. The ratios D/G of individual G,D-palrs within each class were averaged and then plotted versus G. As examples, the resulting diagrams for March, June, September and December are presented in Fig. 23.

17

4000

6/tMm'a I ""

° i 1 . . . . . . . o e.s ^ ,_ ,t.o o ' ' 'o~'~/~ ','o

¢0000t 4000 ~ , ~/~"~t .:EPTEMB£R 6#"~"z I D

I

0 i O.E ~/G; 4.0 0 i. I I I o.g ~)/6' ~ .*.0

Fig. 23. Ratio of diffuse to global radiation, D / G , for given G above specified threshold in four months at Hamburg. Mean monthly means of hourly irradiances (1966- 1975).

YEARLY COURSE OF DAILY RADIATION

To illustrate the yearly course of the different radiation quantities, daffy radiation sums seem to be most suitable. Figure 24 presents the 20 year average, 1954 - 1973, of the five radiation quantities directly measured at the Meteorological Observatory, Hamburg. Dif- fuse solar radiation D seems to follow the astronomical seasons with only minor distur- bances. But global radiation G exhibits several peculiar deviations from the astronomically conditioned course. A depression is noticed from end of June through end of August which is caused by enhanced cloudiness during the so-called "European Monsoon". Another depression appears in May which is known as May coolness to farmers. Several other features which are called singularities in meteorological literature, can be traced in the yearly course of G.

Direct solar radiation B = G - - D (not shown here) follows the course of G very closely because the curve of D is smooth. Reflected global radiation R is relatively high in the winter months especially in February due to snow cover on the ground. The longwave radiation sums E and A are influenced by the delayed warming of the ground and the atmosphere so that their maxima appear at the end of July. The yearly courses of E and A are almost parallel but because of the inertness of the ground, the terrestrial surface radiation E comes out smoother than the atmospheric radiation A. Both quantities

18

2 0 0 0

10oo

I

Fig. 24. 20 year means of daily sums, in J cm - 2 , of global radiation G, diffuse solar radiation D, reflected global radiation R, terrestrial surface radiation E and atmospheric radiation A. (After K ~ n [20] .)

show a marked minimum during the May coolness. Several other singularities are observed in the curve of A, especially the winterly cold breaks.

In order to get a general view of the sea- sonal variations of the radiation sums,

3 5 0 0

O cm-Z

3000

1500

1000

5OO

0

1500

0 cm -z

1000

5O0

0

HAMBURG "FU 1955 - 7973

O F M A M ~ 7 O A S O N D

I I I I I I IAISIOINI D J F M A M ,.7 ,J

3 / / 9 .

2810 -

9 5 8 .

569 =

* 9 9 - R

7 5 0 - G - R

ae9 .

Fig. 25. 19 year means of monthly means of daily sums of radiation fluxes, in J cm - s . Circles and numbers on right hand vertical scale give 19 year means of yearly means of daily sums. (After Kasten [20] .)

monthly means of the daily sums were computed and averaged over 19 full years of records, see Fig. 25. Since each discrete point is obtained by averaging about 570 single values, the connecting polygons are very smooth. Clearly the time lag of the longwave fluxes E and A with respect to the shortwave solar fluxes is seen. The curve of direct solar radiation B exhibits the marked "monsoon" depression in July ment ioned earlier. The deficit of incoming solar radiation induces a cooling of the ground which shows up as a minimum of the net terrestrial surface radiation E -- A. On the right edge of the diagram, the mean yearly means of the daily radiation sums are indicated.

Individual yearly means of the daily radiation sums for the period 1955 to 1975 are presented as percentage deviations from their 21 year means in Fig. 26. The longwave radiation sums show little variation, being less than 7%. Largest amplitudes are displayed by direct solar radiation B which reached +35% in 1975. Cloudiness is the factor most influencing B but since much of the direct radiation scattered by clouds reaches the ground as diffuse solar radiation D, the year to year variation of the yearly mean of global radiation G is much smaller. In the diagram of the net radiation sums, large amplitudes are exhibited by the net terrestrial surface radiation E - A which are caused by the yearly warming or cooling of the ground relative to the atmosphere. Since the net global radiation G -- R has relatively small variations, the net total radiation Q runs opposite to E -- A in most years.

19

- 701 ~L~ i ~4 L I I I L I I I I I I I I I I #41 I I 55 60 65 70 75

ol 30 t

zo~-_s_ .~ ~ / ' /AMSURO-FU 8 / -1 ,o~- G ', ,~'~, ,̂ ,,,'.~

55 @O 65 70 75

%.'% -.~ ~. ~ ' . . . . . . . . . . . . . . . . . 2 0 ~ ~ ~ - / \ E - A '

- ~ ' 0 I ~1 I I I I I I I I I I I I I I I I I I I | 55 &O 6 5 70 75

Fig. 26. Deviations of yearly means, 1955 to 1975, of daily sums of radiation fluxes from their 21 year means, in percent. (After Kasten [20] .)

the geographical distribution of mean daily global radiation in June and December, respectively, are displayed. Figure 30 shows the mean minimum of daily global radiation in June, and Fig. 31 the mean maximum in December.

In the geographical distribution of global radiation, the different climates in the various regions of the EC are reflected because solar radiation is the primary factor governing all other climatic parameters. Further, the inter- act ion of various air masses of either maritime or continental origin, having different optical properties such as transparency of the air and cloudiness, and of pronounced orography such as the Alps and the highlands, cause essential differences in the global radiation pattern from country to country.

Principle features of the monthly G-maps are:

(a) The daffy sums of G generally decrease with increasing geographical latitude as partic-

GEOGRAPHICAL DISTRIBUTION OF DAILY GLOBAL RADIATION

In cooperation with the responsible national institutions, an inventory of existing radio- metric and heliographic stations in the Euro- pean Communities (EC) and of their available data records has been screened with respect to quality of maintenance and to length of continuous recording. On the basis of the available data of the selected stations, the years from 1966 till 1975 have been defined as common reference period. Figure 27 gives the geographical distribution of the 56 selected stations.

Daffy sums of global radiation and of sunshine duration were collected and subjected to quality control procedures. The screened data were arranged in 1344 tables, one for each station and each month, of the individual daily sums from which the 10 year means of the monthly means, maxima and minima were compiled in another set of 56 tables, one for each station. On the basis of these summary tables, preliminary maps of global radiation for each month and the year were designed. The summary tables and the maps have been published by the Commission of the European Communities [11].

Examples of the preliminary maps are given in the following Figures. In Figs. 28 and 29,

Fig. 27. Stations in the region of the European Com- munities selected for the global radiation atlas. ® only sunshine duration available.

20

Fig. 28. Global radiation distribution in June. 10 year means (1966 - 1975) of monthly means of daily sums. (Preliminary).

Fig. 29. Global radiation distribution in December. 10 year means (1966 - 1975) of monthly means of daily sums. (Preliminary).

ularly evidenced by comparing the areas South and North of 45 °N. For astronomical reasons, the gradient of the isolines is weaker in the summer half-year when the greater length of day counteracts the meteorological influences on the daily radiation sums.

(b) Besides the latitudinal effect just mentioned, the pattern of the isollnes show a meridional componen t especially at the West coasts of Ireland, the British Isles and the continental countries Belgium, Netherlands, Ger- many (F.R.) and Denmark. However, this meridionality of the isolines is much less pronounced in autumn and winter.

The conformity of the G-isolines with the coastlines can of ten be observed on cloud pictures taken by meteorological satellites. It is caused by the differences in roughness and temperature of the sea and the solid earth surface which produce an uplift of the air masses moving generally from West to East; the raised air is cooled and its water vapor content is partly condensed to clouds. This

effect is called coastal convergence in meteorology.

(c) Superimposed on the general distribution as described in (a) and (b) are regional differences which are caused by the orography influencing the formation and extent of clouds, and by the variable transmittance of the atmosphere particularly at higher alti- tudes above sea level.

Decreased values of global radiation are observed around large cities such as London, Milano and Napoli and/or in industrial areas such as the Rhein-Ruhr-Basin or the Belgian industry center; high turbidity of the atmosphere due to air pollution is believed to be responsible for these reduced G-values.

In the neighbourhood of highlands, steeper gradients of the isolines are noticed, particularly in Southern France and in Italy, but also in Germany at the Harz mountains near Braunschweig, for instance. Extremely strong G-gradients are observed with increasing altitude and are most pronounced in the Alps.

21

Fig. 30. Minimum global radiation in June. 10 year means (1966 - 1975) of monthly minimum of daily sums. (Preliminary).

The global radiation pattern in the Alps and other highlands should be interpreted with caution because remarkable differences in irradiation from one place to the next are found due to either the mountain chain shielding the direct solar radiation or to upslope and lee effects on the formation of cloudiness. On the other hand, an annual mean of daily global radiation exceeding 4700 Wh m -2 is measured at some mountain tops of the Central Alps which are above the clouds most of the time.

The isolines on the geographical maps shall only give a general impression of the large scale features of the distribution of global radiation. Local details or peculiarities cannot be read from these maps.

DEPENDENCE OF RADIATION FLUXES ON CLOUD AMOUNT

10 years systematic hourly cloud observations have been evaluated with regard to

Fig. 31. Maximum global radiation in December. 10 year means (1966 - 1975) of monthly maximum of daily sums. (Preliminary).

simultaneous hourly sums of radiation fluxes [12]. Figure 32 presents the mean hourly irradiance of global radiation G as funct ion of total cloud amount N, in okta = 1/8, for different solar elevation angles 7. In the upper diagram, the absolute values in W m -2 are plotted; in the lower diagram, the ratio of G at cloud amount N divided by G at cloudless sky, G(N)/G(O), is shown as function of N. This ratio slightly increases above the cloudless case at N = 1 okta, then slowly decreases up to N = 6 okta from where the curves sharply drop to about 0.25 at N = 8 okta. Since the ratio G(N)/G(O) turns out to be independent of solar elevation 7, a common parameterization formula for all 7 can be established:

G(N)/G(O) = 1 -- 0.75(N/8) s'4. (44)

In order to determine global radiation G(N) from total cloud amount N on the basis of eqn. 44, the global radiation under cloudless sky, G(0), is to be known. G(0) naturally depends on solar elevation 7. From Fig. 33,

22

HAMBURG' - FU s

796~ - 1973 8 0 0 I I # [ I I I

/ l / m - Z " "" ~ " ~ N - . G ( ) 700 ~ _.., S o ° ' \

BOO /.~L7 o "'~. ",.~

F" ~" ~ " "~ "\ \"~

4oo }- ....... .~ .\.

20 ° ".,. ',~,~ 5 ° ° F . . . . . . . ',,. '~k~

2 0 0 ~ ",1

lO0

0 0 2 4 6 N 8

Y E A R 1.5

G(o) 1.0

0.5

0 O 2 4 G N 8

Fig. 32. Global radiation G as function of total cloud amount N for different solar elevations % Upper row: irradiance of G(N) in W m-~; lower row: ratio G(N)/ G(0) where G(0) = global radiation under cloudless sky. (After Kasten and Czepl~ [12].)

800 Wm-e

700

600

500

400

.,zOO

200

tO0

0 Co o) 0

O (a) 7"°

G(o ) ~ e

0.6

o.2

HAMBURG - FU~

l p r r J r

t

e ? ? / i t t i i i

(2o o) (~,o o) (60 o) as s in i"

- - H , A , M .... ,.v,, j , A ......... S , O . N . . . . . D,.7,F

1 9 6 4 , - 1 . 9 7 3

BOO

700 b

Go0 k

5OO k

~00 b

500 f

20O

I 0 0 I-

0 , (0 o)

D /.0

~8

~6

~2

0(0o )

0

I i I I i J (2oo/ (~oo/ r6o o)

o.s s / n i"

Y E A R

O i i I i I i I I I i - - CO e) C2O °) (~°) (60 °) C20 °) (40 °) (GOo)

o ~s s/n~, 7 ~s s/n iv x

Fig. 33. Global radiation as function of the sine of solar elevation T 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). (After Kasten and Czeplak [12].)

upper right hand, the following linear parameterization can be concluded:

G(0; 7) = (910 sin 7 -- 30) W m -2. (45)

Of course, this equation represents an average over all occuring atmospheric turbid- ities. The diagram in the lower right hand of Fig. 33 depicts the ratio of overcast to clear sky global radiation, G(8)/G(O), as a function of sin 7; on average, 20 - 25% of the incoming global radiation is transmitted through an overcast sky.

In contrast to G, diffuse solar radiation D (Fig. 34) increases with increasing cloud amount to a maximum at N = 6 okra from where the curves sharply drop to levels below the cloudless sky. Obviously, reflection from the side-walls of the clouds is responsible for those high values of D. The increase of D 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) coin- cide.

Additionally, a diagram of the ratio of diffuse to global radiation, D(N)/G(N), is presented at the bottom of Fig. 34. These curves also turn out to be almost identical for solar elevations 7 > 20° showing a steady but not linear increase with N. A rather good approximation is

D(N)/G(N) = 0.3 + 0.7(N/8) 2. (46)

For completeness, the dependence of D(0) and D(8) on sin 7 is shown in Fig. 35. Both quantities 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 radiation being incident on top of the cloud deck is obviously reflected back and thereby lost to the diffuse radiation D penetrating the cloud to the ground, whereas for 7 /> 50°, about 80% of the cloudless case are attained on the average.

Figure 36 presents longwave atmospheric radiation A in dependence on total cloud amount N and solar elevation 7. For meteorological reasons, the data material was grouped

23

HAMBURG - FU, 7,,°64 - 1975

400 , I l , , . . . .

Win'2 L D(/V) ~..~o ° . . . . . ., soop --" .." ~;'(, I

.... ,.--,.-- . oo ,,:,J f-- --:::::: ........... 2;; :':1

,ooF- o F , T T , , ,-, ,

0 2 4, 6 N 8

0 2 ~ G N 8

1.0

6,IV) aS _ _ T ~ w w

0 2 4 6 N B

YEAR

Fig. 34. Diffuse solar radiation D as function of N for different 7. 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. (After Kasten and Czeplak [12] .)

into the four seasons M, A, M = March, April, May; J, J, A = June, July, August; S, O, N = September, October, November; and D, J, F = December, January, February. With the

See

Wm-e ~,00

3 o 0

2 0 o

1 o o

o ( o '

Dfa/"° Ore)

0 8

~6

0,2

0(0o ) 0

0(O)7 "°

G(o) OB

O6

04

G2

O (0 o) 0

HAMBURO-FU, 1.96#- 197J

D(o~

i i

(20 °) (~o*) (60 °) as s/h ¥

........

, , / . - . / . . .

- - M,A,H . . . . 3,3, A . . . . . . . . . S,O,N . . . . . o, 3 , F

i ~ I i i i (20 °) (#0 °) (60 °)

0.5 s in ~,

5 0 0 i , r , i i

4 0 a

5 0 0

2 0 0

I00

I l I i I r O(O ) (20 °) (#0 °) (GO °)

o a5 sln y 1.0

O.6

o.* YEAR

o.2

J 4 I l i i 0 (09 (2o ~) (40D ( 6 0 °)

o a s s ln 1.0

o.8

o.6

0 , 2

I I ) I I I 0 { I I I r J (20 °) (40 o) (60 °) (0 °) (20 °) (~0 °) (60 °)

a s sJn y z o ~ s s/n ~ l

Fig. 35. Diffuse solar radiation as function of sin 7 under cloudless sky, D(0), and under overcast sky, D(8). Top row: irradiance in W m-2; center row: ratio D(8)/D(O); bottom row: ratio D(O)/G(O). (After Kasten and Czeplak [12] . )

H A M B U R O - E L / , 1 ,964 - 1 9 7 , 5

3oo ~ ~ 22:-T2"'~ ~'~" ~ "

-~o 2 0 6 N 8

M,A,M

0 . 5 1 i - I I ' I ' ' J I O 2 4 6 N B

SO0 , I I f I I I I

450 t

4 0 0 ~ ' , .~

550 - ' - ' ~ I .... P f 6 0 o

~ 0 0 . . . . - - 5 0 0

. .... ~0 o

. . . . . . . . 3 0 °

2"50 1 . . . . 20°10 o

200 i I I I I I I I 0 2 4 6 N 8

J,3,A 1 . 5

o 2 4 G N 8

SO0

450

400

350

300

250

200

I I I I I I I S O 0 , I ] I I I I ]

r j -

25O F ~ ~ ~ -

l I I I I I I 2001 I I I I I I I 0 2 Z~ 6 N 8 O 2 4 6 N 8

S,O,N D,3,F

i S I i ~ I - - i - - ' ; ' ~ " , 1 , 5 1 , ] i i , l ] 0 2 4 6 N B 0 2 ,$ 6 N B

Fig. 36. Atmospheric radiation A as function of N for different 7 in the four seasons. For further explanations, see legend to Fig. 32. (After Kasten and Czeplak [12] .)

24

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 tempera- tares at different times of the day and of the year, respectively. Averaging over the seasons or over 7 is no t possible in the case of atmospheric radiation.

To the contrary, the net radiation of the earth surface, E - - A , exhibits a behaviour similar to global radiation G. Since a variation with season could not be recognized, yearly averages are permitted, see Fig. 37. There is a slight dependence of E -- A on solar elevation 7, but the curves of the ratios "c louded to cloudless" are almost identical to the corresponding G-rat ios so that the parameterization formula eqn. 44 may also be applied to E - - A .

Finally, the net total radiation or total radiation balance Q = ( G - - R ) - ( E - - ~ ) was evaluated, see Fig. 38. Since the shortwave balance G -- R and the longwave bala~ce -- (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 confirm-

/ - I A M B U R ~ - F~ 1964 - 197,5

150 Win-2 ~

1oo .

50

0 o 2 4 6 N 8

YEAR

ce-.vro) L... ?

0 2 z~ 6 N 8

Fig. 37. Net terreatrial surface radiation E - - A as function of N for different 7. For further explanations, see legend to Fig. 32. (After Kasten and Czeplak [ 12 ]. )

600 Wm-Z

500

HAMBURG- FU, 7.964 - 1.9 7.5

r r ~ i i i i

.. ..~'~ s°° Q (.Iv )

4,00 - 4 0 ° -..~.\,.

300 "~~'" \" "~ e " \ "\x.

2 0 0 . . . . . . . . . . " , \'x\~--

2 0 ° "" . . . . ,

7 0 0

70° ~ I I I I i

o 2 4 6 N 8

YEA R (w/thoa,," g 4 F) "I. 5

~(o~ ~ 0

~ 5

0 o 2 ~ 6 N 8

Fig. 38. Net total radiation ffi total radiation balance Q as function of N for different 7. For further explanations, see legend to Fig. 32. (After Kasten and Czeplak [12] . )

ing the parameterization of Q by G which is of ten described in the meteorological literature. Naturally, this does not hold for 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, the values of the winter season were no t taken into account. The ratio Q ( N ) / Q ( O ) may again be parameterized by eqn. 44 observing the precautions just mentioned.

INFLUENCE OF CLOUD TYPE

The same data of 10 years hourly observations from 1964 to 1973 was analyzed with regard to cloud types which were condensed into 5 groups: Ci, Cc, Cs = Cirrus; Ac, As = A]tus; Sc, Cu = Cumulus; St = Stratus; and Ns = Nimbostratus. In order to obtain unequi- vocal information of the single cloud groups, only observations of N = 8 okta overcast by one cloud group were taken into account.

In Fig. 39, upper row, global radiation under overcast sky, G(8), is p lot ted versus the sine of solar elevation 7 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

25

HA M 8 URO - FU, 1964- 797,5

600

o (3) 500

Wm-Z 40O

30O

200

100

0 (O'9 0

o(o) F

o (o o) 0

/ i

/ :

i " i

/ / . l ° .

¢ s'~, ,'° i .<:"<~

(ZO*) ' (~0°)(#0 *) 0.S sin~ I

M,A,M

600

500

~00

.TOO

• t

0.Ssin~' I 0 O.5s/n~' I

I '

I

! I /

/ l ' ° eoo / ,k

i ." . .# 100 / z:'~. ~ ' .

~<~-"

0 ~ ' ' (0") (2o*) 'C4O°)(~0 *) 0 0.5s/n@" I

O, 3,A

7"0 1 . :'" O. S t / "~N ' . ' I \

600 , I I , , 600

500 t-

l~O0 I- Cl ; Cc , C~

/ soar /

I /

200 F / / A c, As : _~.:;Sc, cv

IOOF I , .~ ; / st

(o ~) (~o o) ' (~o~)(~o.) o 0.5 ~in#" 1

S,O,N 1.0 1 "--"':" 0.5 / C/,C4C~

Ac, A~

~...x.~. =. St , ,-T~.~,~,, °(o~) C20 o) (~")(~0)

o 0.5sin~" /

500 -

4,00-

300 -

200 - /

lO0 - i" /

CO o) (zo o) Os/n~' o.~

,.oO,,-7,,F

0 COT (~o °) O.C/n~ 0.5

GO0

GO0

bOO

300

200

I , , ,

i i i }

I

/ A 4 A s t I .~." Sc, Cu

.I /.." . %,

,oo / s ,

o ~ :,va (o ~) (zo*) 'C#O*)(~*) o O.5sin@, f

YEAR

I° I : . =.. : ' ~I M~,~: ...... .....-- ~C/~cc, c~ o . ~

0.5 ~ Ac m~ 0.Z7 . . . . . . . :.-.. -t..¢c,'t'~ " 0.25"

-iNs o. /~ 0 (o ~) (zo*)'(#o*)(~o o) 0 O.5S/n~ I

Fig. 39. Global radiat ion G as function of sin ~l' under overcast sky (N = 8 okra) separated in%o cloud groups in the four seasons and for the whole year. (After Kasten and Czeplak [12] .)

5OO

Dfa) 4O0

Wm -~ 500

200

lO0

%° 0

2.O D(m~ O(o~ 1,5

LO

0`S

I I [ r , i

1

/ /

j "

/ / . 1 .

/ . , .~

~2o9' (~o°)(~0 ~) o.5 B/n~" z

M,A,M

i / . , / I '

' i -L. . i . . ,o*

5.'>"

~00

;,00

~ro0

200

100

0

0

2.0

1.5

1.0

0.5

HAMSURO-FU, 1964- 7.97,5

, L , , , 5"00 , , , , 5001

l

i" / I

/ . "l~

I I ] I I I

o.5 sin~, z

/

I

i /

i ,,:.~

4 0 0 -

500 -

200 I !. /

zOO //j~

0 , i CO*) (zo*) OsiriS" 0 . 5

D,~F • ~ O i .

400 t C/, Cc, Cs

800 f / " i"

200 i

i ~ : :.".,e¢,c. I ioo L f . s, i

o o.5 s/n~" l

S,O,N 2.0

,/"c'; ; cc, cs ['

i t

1.o . . , . A c ~ A ~

~>.,. $c, Cu / : . " / ' W

o,s ~;'" . ~ - - - N s

, , [ , , i

(o0) "zoo)' C~O") (~o °) 0 ~ lSS in~ l 7

[ . .5 - . °

. /

1.0

/./ ° 0.5

l i I , t i l , I l t ' I I

0(0' Fz~')' i~o*)(8o °) 0C0") (zoo) 'C~o")C6~') 0(o") (2o") 0 O.5s/n#" I 0 0.ssln@" 7 o~'n I, 0.5

500 , , i , ,,

~00 / ! /

~00 / .o

/

' ; t I : /2" : /°.* / /.."

zoo i .z..."

(o o) &~o") ' CJJo") fso °1 O O.ssin~ l

Y E A R .2.0

!

1.5- !." i

7.o / . ~ . . . . ~ T s

j /o. . o.°~

0.5 :~"*

, , t i , ,

(o*) (20")'(4~')(Go*} o 0.55in~ I

Fig. 40. Diffuse solar radiat ion D as function of sin T under overcast sky separated into cloud groul~ in the four season~and for the whole year. (After Kasten and Czeplak [12] .)

26

also for the whole year. Since a systematic variation with season is not visible, all cases can be summarized and presented on one diagram on the far fight marked by "year" .

In view of the great variety of cloud forma- tions within each cloud group and of the low number of cases of Cirrus and Nimbostratus overcasts, the curves can roughly be considered as straight lines like the curve G(8) in Fig. 33 which described the average over all possible cloud types. This mean curve of Fig. 33 is represented almost identically by the curves for Ac, As and Sc, Cu in Fig. 39 whereas the Cirrus curve lies much higher and the Stratus and Nimbostratus slightly lower.

The bo t tom row of diagrams in Fig. 39 shows the ratios of global radiation under a sky overcast by a 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, Cumu- lus, Stratus, Nimbostratus. The increase of the ratios with solar elevation ~f is rather small so that on the average, the transmittances of Cirrus, Altus, Cumulus, Stratus and Nimbo- stratus may be taken as 0.61, 0.27, 0.25, 0.18 and 0.16, respectively.

The corresponding diagrams for diffuse solar radiation D are given in Fig. 40. 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 the solar radiation incident on top of the cloud deck is reflected back to space and thereby lost to the diffuse radiation D emerg- ing from the cloud base and received at the earth surface. The dependence of D(8)/D(O) on sin ~ is strongest in the case of Cirrus;

A ( 8 )

40O

W m - Z

5So

500

l u j u i J

\ . / "

I I I I I I 25O(0°] (209 CV,~)(6O ' o 0.5 s in ~'

l .B A ( 8 )

1.4'

T2

A,M

% 1.0

0.6'

HAMBURG - FLY, 196~ - l..°Z~

~50 ' ' l ' ' ' 450 , l l ~ ' ' l ~ 5 0 '

400 400 --"~"\ /

• : 550 3S0 "" I

. . . . . . o; cc, cs " ' /

. . . . . Ac, As 500 ......... 5c, Cu 500

. . . . 5 f

- - N s

5 0 I I J I I I 2 5 0 I I I I I I I 2 ( 0 o ) (20 o) (~oo)c~o o) (0 ~) (2o o) C~os)(6o o)

0 0.5 sin ~" I 0 0.5 s/n~, l

,.7,0,A S, O,N l.G l.B

1.4,

1.2

1.0 ~ \

o.6

1.2

7.0

O.8

O'G(OO ) 0

I I I I I I 0,6 i i I i l i I l I I I I I

O'B(o°) (20 °) N~O°){GO °) CO °) (20°) ~ C~O") (60 °) (2o °) C~o°)(6o °) 0 0.Ssin~, 7 0 o.ssin~' I 0.Ss/n~" I

4OO

35O

500 ~!

2 S 0 I (o o) (2o o) osir is, 0.5

, . 8 0 , ~ :

N 1.4,-

L2 -

1.0

0 . 8 -

O.B I I

(o o) C20 o) 0 s/'n a, 0.5

Fig. 41. Atmospheric radiation A as function of sin 7 under overcast sky separated into cloud groups in the four seasons and for the whole year. (After Kasten and Czeplak [12].)

Cirrus overcasts may amplify diffuse solar 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. 41. 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 radiators. Atmospheric radiation is therefore determined by the air temperature at or closely above the cloud base. Consequently, there is a variation of A(8) 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 overcast sky 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 rela-

27

tively cool; an overcast sky with relatively 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 42 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 solar radiation (Figs. 39 and 40). From the lower row of Fig. 42 one learns that a Cirrus overcast sky reduces the net radiative emission of the earth surface to about 50 - 60% of the values measured under cloudless sky. There is a moderate

I00

C E - A ) ( 8 )

BO

Wm - z 6O

r i i , , ,

o;c~, . 1 " " C$

. l " f "

~O ,,." . AMsl ." ,. / .~,tu I

.,'.",,,v~ I

(0,) (2~')' (~0°)(~ °) 0 0.5~in~ /

M,

......... ..-..c"~ 1 ,4c,,A~

• , /'..~,Cu . . . . / " " . o ' ~ N 8

0 . 2 ~ ' ~ ¢

(o °) (20°/(x,0,)(~0,) 0 O . 5 s / n ~ 7

(E-A) re) ~ o

{E-A) [o ) o, 8

O.B

7 0 0 [ l ' , l

8O

/,, .!

~0 ..... "..." e

2 0 . . f . . ~

(o °) (20°)' (~°)(c,0,) o O.5s in~" 1

J ,4A 1.o

0.8 A i',

o.8 ,. i "',, j

0.~

..... .,-.-.:..,",': 0.2 .".'.

(0 °) (20") ' (~0,)(60,) 0 0 . 5 s , " n c z

HAMBURO - FU,

I 0 0 l l ' , [

80

6O /-..,..

• ~0 i" \

2o ..")~'~" oio.. , oo

(0 °) (20*) ' (40,)(6~ 0 0.ssin~"

S,O,N 1.0

0 . 8 F

0.61-

% 0,/~ F '

o+" f 0.2 F /...'1

i , i L , i

0C0°) (20')' (~0") (6~'1 o o.Ssin~ I

19G~ - 1 9 7 3

1oo

8 0 -

G O -

4 0 -

i 20 l ' , .

o Co o) (20 o) O s / n ~ 0.5

,.oO, J, F

0.6 ' -

0 . 6 -

O.z~

I " 0.2 l "

o Z (O o) (20 o) O sin$, 0.5

7 0 0 I I I , I

BO

GO /~

. . . . . . " ~ o;G4cs

~0 . / Ac, As

.~-~:"" sc, cu 20 !" ..'~, Sf

0 i , I , , ,

Co o) C20,) ' C~O) (6o o) 0 0 . 5 s / n ~ 7

YEAR I.o

o.6

A 0.6 j ~ O;C4Cs

O.q ~.~. Ac, As ~'." • Sc, Cu

N s

0 , , i , , , C~) (2o °) ' C~o") (6o °)

0 P , 5 s / n ~ !

Fig. 42. Net terrestrial surface radiation E - - A as function of sin 7 under overcast sky separated into cloud groups in the four seasons and for the whole year. (After Kasten and Czeplak [12] .)

28

increase of (E - - A)(8)I(E - - A)(O) with solar elevation 3" 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.

Finally, the net total radiation or total radiation balance Q = (G -- R) -- (E -- A) is analyzed with respect to cloud type in Fig. 43. As mentioned earlier, Q behaves similarly to global radiation G as far as the solar elevation is not too low in which case Q approaches zero or even becomes negative. For the same reason, averaging over the seasons has to exclude the winter months. 8 okta Cirrus reduces Q to about 60% of its value under cloudless sky. The other cloud groups have Q(8)/Q(O)-ratios between 0.3 (Altus) and 0.1 (Nimbostratus).

The foregoing analysis of solar and terrestrial radiation fluxes at the earth surface in dependence on cloud amount and cloud type is intended to give typical values of the dependence of different radiation quantities on different cloud conditions and should be appli-

cable 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 a parameter, the relations shown are in principle not dependent on geographical latitude of the site and are considered to be valid for any other place with a climate similar to that of Hamburg. On the other hand, the figures given here depend largely on the density and frequency of occurrence of the different cloud types. There- fore, places with other climates would require a separate investigation.

REFERENCES

1 C. FrShlich, Contemporary measures of the solar constant. In: The Solar Output and its Variations, ed. by O. R . White, Colorado Associated Univer- sity Press, Boulder, Colo. (1977), pp. 9 3 - 1 0 9 .

2 C. FrShlich, The solar constant: a criticaireview, in: Proceedings o f the symposium on radiation in

H A M B U R G - FLl~ 1964 - 1975

8 0 0 I l ] I '

0 (8) EO0

W m - Z

400

500

200 / / /

I00 / .,: , , t I '°

(L (20 ° ) ' (40 °) (Bo °) 0.5 sin ~ I

A,M

oro, F ",

°" I /i 0(0~) (20 o) (00*)('g,P o)

O O.Ss/n~' 7

6 0 0 , ~ i , , ,

5OO

4OO

300

200

i' /

7 o o / /../

o (0 ~) (20') ' (4~0 °) (6O~) 0 O.Es/n~' /

O,J,A 1.0 I I'. /'%,

/ \ - . . / • o.5

L , I i J ,

(0 ) (2oo)' (~o) fgo o) 0 ° O.5"sin~ I

EO0

500

~'00

300

200 / /

/ 100 / A c , A~

.. ~ ~;c,

o ~ , [ s (~) (20 °) ' (4,o~) (6o o) o o,5#/n@, /

S,O,N I.O

0 (0 o) (2o °) ' (~oo) (Eo o) o o.ss/'n~, /

600

5"00 -

400-

300 - L

200 -

I 0 0 - +/

(0 °) (2o' OS/n~' 0.5

600 I , , ,

-° I 4°0 1 / c/; c~ cs

500 t [ /

/ 200 ~- /

. . / .~." A c , A s / (.. Sc, Cu

| N$ ;o) MO o) '(400)(6O o) O 0 .s& /n~ 7

YEAR (without D, J, F)

0.5 "~" .... ~_ Ac, As

"~ J St J , I = , , I N S

0 ( 0 0 . ) ( 2 0 " ) I ( ~ o ) ( ~ ° )

0 O.5S/n@" l

Fig. 43. Net total radiation = total radiation balance Q as function of sin T under overcast sky separated into cloud groups in the four seasons and for the whole year. (After Kasten and Czeplak [12] .)

the atmosphere, ed. by H. J. Bolle, 589 - 593, Science Press, Princeton/New Jersey (1977).

3 N. Robinson, Solar radiation, Elsevier Publishing Company, Amsterdam (1966).

4 K. Y. Kondratyev, Radiation in the atmosphere, Academic Press, New York (1969).

5 Annals of the International Geophysical Year, ed. by Special Committee for the International Geo- physical Year (CSAGI), vol. V, part VI: Radiation instruments and measurements. Pergamon Press, London (1958).

6 WMO, Guide to meteorological instrument and observing practices, 4th edition, WMO-No. 8 TP.3, Secretariat of the World Meteorological Organiza- tion (WMO), Gen~ve, (1971).

7 J. R. Latimer, Radiation measurements. Interna- tional Field Year for the Great Lakes, Technical Manual Series No. 2, Secretariat of the Canadian National Committee for the International Hydro- logical Decade, Ottawa/Canada (1972).

8 K. L. Coulson, Solar and terrestrial radiation, methods and measurements, Academic Press, New York (1975).

9 K. Dehne, Messinstrumente zur Beobachtung der Strahlungsintensit~t, lnformationswerk Sonnen- energie, Vol. 3, Udo Pfriemer Verlag, Miinchen, (1977) pp. 199 - 217.

10 K. Dehne, Solare Strahlungsmessungen im Rahmen der Weltorganisation fiir Meteorologie (WMO), 1st German Solar Energy Forum, Pro- ceedings, Vol. II, Deutsche Gesellschaft fiir Sonnenenergie e.V. (DGS), Miinchen, (1977)pp. 15 - 23.

11 W. Palz, (ed.), European solar radiation atlas, vol. I: Global radiation on horizontal surfaces, Gr~ss- chen, Dortmund (1979).

29

12 F. Kasten and G. Czeplak, Solar and terrestrial radiation dependent on the amount and type of cloud, Sol. Energy, 24 (1980) 177 - 189.

13 P. R. Gast et al., Solar electromagnetic radiation, in: Handbook of Geophysls and Space Environ- ments, ed. by S. L. Valley, 16-1 - 16-38, Air Force Cambridge Research Laboratories, Bed- ford/Massachussetts (1965).

14 R. Geiger, Das Klima der bodennahen Luftschicht, 4th edition, p. 246. Vieweg, Braunsehweig (1961).

15 E. Frankenberger, Uber vertikale Temperatur-, Feuchte- und Windgradienten in den untersten 7 Dekametern der Atmosphere, den Vertikal- austausch und den W~rmehaushalt an Wiesen- boden bei Quickborn/Holstein 1953/54, Berichte des Deutschen Wetterdienstes, 3, No. 20 (1955).

16 R. Fleischer and K. Gr~fe, Die Ultrarot-Strah]ungs- str~me aus Registrierungen des Strahlungsbilanz- messers nach Schulze, Annalen der Meteorologie 7 (1955/56) 87- 95.

17 F. M~ller, Einfiihrung in die Meteorologie, Vol. 2, Bibliographisches Institut, Mannheim, (1973) p. 20.

18 F. Kasten and E. Raschke, Reflection and transmission terminology by analogy with scattering, Appl. Opt., 13 (1974) 460 - 464.

19 K. Dehne, Entwicklung eines Sky-Scanners zur schnellen Vermessung der r~iumlichen Verteilung spektraler Himmelsstrahldichten, Berichte des Deutschen Wetterdienstes, 17, No. 134 (1974).

20 F. Kasten, Daily and yearly time variation of solar and terrestrial radiation fluxes as deduced from many years records at Hamburg, Sol. Energy, 19 (1977) 589 - 593.

21 E. V. P. Smith and D. M. Gottlieb, Solar flux and itsvariations, Space Sci. Rev., 16 (1974) 771 - 802.

measurement and analysis of solar radiation data

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