S~ar ~ Vol. 22, pp. 87-90 0038-092XT'/9/0101-00871502.00/0 Pergamon Press IAd., 1979. Printed in G¢cat Britain

T E C H N I C A L N O T E

A study of Canadian diffuse and total solar radiat ion da ta - . . l l

Monthly average hourly horizontal radiat ion

M. IQBAL Department of Mechanical Engineering, The University of British Columbia, Vancouver, Canada

(Recieved 28 December 1977; revision accepted 6 July 1978)

INTRODUCTION Many solar devices such as flat-plate collectors require in- formation on the hourly solar radiation. In order to evaluate the transmissivity-absorptivity product of such collectors, knowledge of both beam and diffuse components of the hourly radiation is required.

In some countries such as Canada, radiation data are recorded at regular hourly intervals. At places where measuring stations do not exist, hourly radiation has to be estimated from the estimated daily radiation. Even for locations where hourly data are measured, tables of the hourly data are generally not avail- able to a designer. On the other hand, data of monthly average daily total radiation are widely available in the form of maps or tables [I, 2].

In this study, as attention is focussed on the monthly average radiation only, total and diffuse, the prefix "monthly average" is not always used.

Whiilier[3, 4] and Liu and Jurdan[5] have presented method of estimating hourly radiation from its daily value. Liu and Jordan outline~_ a procedure of determining_monthly average hourly total ration I from the daily total value H. They have also presented a parallel procedure to determine the hourly diffuse radiation _f~ from the daily diffuse radiation/ta. The daily diffuse radiation H~ is almost invariably estimated from the daily total value /t. A review of methods to determine daily diffuse radiation from the daily total value is given in Part I of this study[6].

The primary objective of this report is to examine whether or not the Canadian data fit Liu and Jordan's procedure. Liu and Jordan's procedure assumed symmetry of hourly radiation around solar noon; therefore, the second objective is to study if there is asymmetry in the actual data.

The Canadian network of solar radiation measuring stations includes four sites where regular hourly diffuse radiation is also measured. The diffuse data from three such stations is studied (Table 1). The fourth station, Resolute (750 4YN; 94* 59'W within the polar circle) is not treated. The hourly total radiation data of two other stations (Table 1) widely spread apart, is also examined.

The Canadian diffuse-radiation data contain'a 2 per cent correction to account for the shade-ring[7]. No correction is made, however, for completely cloudy days.

~ T S AND DISCUSSIONS Radiation data were obtained on magnetic tapes from En-

vironment Canada. From these data, monthly avenge hourly diffuse and monthly average hourly total radiation were cal- culated.

Using mean values of the pair hours around solar noon, ratios of the hourly diffuse to the daily diffuse ldH~ are plotted in Figs. !-3 for Toronto, Montreal and Goose Bay respectively. These plots are on the format of Fig. 15 of Liu and Jordan, where the solid lines represent their equation (18). In general it may be said that the hourly diffuse data of the three Canadian stations fit the theoretical curves very well. As a rule, the correspondence is

very close during the summer period. As the day-length becomes shorter and at hours substantially far away from solar noon, the experimental data do not fit the theoretical curves very well. It is known[4], however, that solar energy during late afternoon and early morning hours is very small. Therefore, divergence of data from the theoretical curves during these hours is not very serious.

In the foregoing manner, the ratios of the hourly total to the daily total radiation I/H are presented in Figs. 4-6. These figures are for Toronto, Winnipeg and Vancouver. In these figures, solid curves are recommended modifications by Liu and Jordan of their equation (18). The Canadian data fit the solid curves very well, except for a portion of the line representing 4.5 hr from solar noon. During this period, there is a consistent disagreement not only for the three stations in Figs. 4-6 but also for a number of others studied. As stated above with tespect to the diffuse hourly data, the small disagreement for the 4.5 hr from solar noon is not important, especially as it occurs during the winter period.

Liu and Jordan in their Figs. 15 and 16 have tested their theoretical analysis with experimental data from a few stations. However, the data available to them did not cover the full range of the applicability of their diagrams. In this sense, in the present Figs. 1-6, the Canadian data supplement and cover the full range of the applicability of Liu and Jordan's diagrams. After examin- ing Figs. 1--6 it can be safely said that the theoretical method of predicting hourly radiation presented by Liu and Jordan and Whillier is very good.

In Figs. 1-3, the solid curves help us to estimate the hourly diffuse radiation T~ when the daily diffuse radiation/t, is known, either as measured data or through an estimation procedure. However, another way to estimate I~ is proposed by Hay[8]. He has presented a method to obtain fa through known values of the hourly total radiation ~ This means that the daily diffuse radia- tion can he estimated as

.~ , i , = ~7, (i)

In eqn (1) the summation is to be carried over the actual day-length as indicated by radiation records. This day-length is usually slightly longer than the theoretical day-length[9]. The daily diffuse radiation /td as obtained through (i) has been' discussed at length in [6]. As Hay's correlation is obtained through diffuse radiation data of the Canadian stations consi- dered in this study, it is useful to examine briefly the hourly diffuse radiation obtained by his method.

The ratio of hourly diffuse to the daily diffuse radiation,

,2,

obtained entirely by Hay's method, was calculated for a number of locations in Canada. Figure 7 shows a plot of such a cal-

87

88 M. Ioe^L

Table 1. Canadian stations used in this study with regular hourly measurements of solar radiation on a horizontal surface

Latitude Longitude (N) (W)

Station . . . . Record Used

tToronto, Met. Res. Stn. 43 48 79 33 Aug. 1%7-Dec. 1975 tMontreal, Jean Brebeuf 45 30 73 37 Oct. 1964-Dec. 1975 fGoose Bay 53 18 60 27 May l%2-Dec. 1975 ~;Vancouver 49 15 123 15 Jan. 1959-Dec. 1975 ~Winnipeg 49 54 97 16 Jul. 1957-De¢. 1975

tStations measuring diffuse as well as total radiation. ~;Stations measuring total radiation only.

0.20

0.18

0.16

o.1 ,

a_

-- ~ 0.10

i °

'~ ° ~ f

g ~ o ~

0 8

60

I I I I I I I

'~ • TORONTO 43~48 ' N • ( 1 9 6 7 - 1 9 7 5 )

NOON

9 10 11 12 13 14 1S 16 HOURS FROM SUNRISE TO SUNSET

?'s ¢o 16s Tio SUNSET HOUR ANGLE. tu s . DEGREES

0.20

0.18

0.16

5 ~ O.lO

[- O.04

0

I I I I I I I

¢ • G O O S E BAY 53"18' N ( 1 9 6 2 - 1 9 7 5 )

HOUR FROM SOLAR NOON

• ! -- ~ 2 • •

, I

g 10 11 12 12 14 15 16 HOURS FROM SUNRISE TO SUNSET

6o lOS ~o SUNSET HOUR ANGLE. w , .DEGREES

Fig. 1. Theoretical and experimental ratio of the hourly diffuse Fig. 3. Theoretical and experimental ratio of the hourly diffuse radiation to the daily diffuse radiation, radiation to the daily diffuse radiation.

0.20 I I f I I I I

O,18 ' ~ o e M O N T R E A L 4S'30 ' N

0.14 ~ ( 1 9 6 4 - 1 9 7 5 )

,~ .~ o . NO:, , .o . . . . . . . o .

m ~ 0.12

" " •

0.06 4 ! .

0 .04 [ - • i ~ -

t S ' ] ° °

0 0 9 1 0 11 12 13 14 15 16 HOURS FROM SUNRISE TO SUNSET

~;o 7*s ~o 16s liO SUNSET HOUR ANGLE. w . . D E G R E E S

- d ' 2 ° f N , I ' ~ I I 1 i I

I x , ,

0 .16 HOUR FROM SOLAR NOON

~ 0 . 0 6

'8 4) 10 11 12 13 14 12 16 HOURS FROM SUNRISE TO SUNSET

60 is 90 1 os ! i0 SUNSET HOUR ANGLE.u~,DEGREES

Fig. 2. Theoretical and experimental ratio of the hourly diffuse Fig. 4. Theoretical and experimental ratio of the hourly total radiation to the daily diffuse radiation, radiation to the daily total radiation.

0,20

0.1a

0.16

1io.12,, i ? ot, o

O ii °' 0.06

0.04

0.02

0

__ o ~ e l = e/ INNIpIEG 4~054. N ~ I

(1957 - 1975)

• HOUR FROM SOLAR NOON

32 ,i 1 - i

•

9 10 11 12 13 14 15 16 HOURS FROM SUNRISE TO SUNSET

60 75 90 10S 120 SUNSET HOUR ANGLE. w, .DEGREES

Technical Note

0 .20 - - , , , , i ~

. ~ i VANCOUVER 49° 15' N 0.18

. ~ , , (1959- 1975)

0.16 ~ 1 0.14 • HOUR FROM SOLAR NOON

0.12 - I

0.10 O 1 3~ a~ 0"00 -

~ 4 ! < 0,06 • 2

0.04 5 1 "

0.02

• 6 ! 00 9 10 11 12 13 14 15 16

HOURS FROM SUNRISE TO SUNSET 60 120

8 9

75 90 105 SUNSET HOUR ANGLE. Lu~ ,DEGREES

Fig. 5. Theoretical and experimental ratio of the hourly total radiation to the daily total radiation.

0.20 I I I I | 1 L

~ ' ~ =•VANCOUVER 49~1S" N

o.,. L ,,,, 0"16 HOUR FROM 1SOLAR NOON

~ 0.12

oo0'o 0.08 2

• o

b'~ 0.06 4 ! 0

004 .. - -

o Hi "9 10 11 12 13 14 15 16

HOURS FROM SUNRISE TO SUNSET &O 75 90 10S 120

SUNSET HOUR ANGLE.ua, .DEGREES

Fig. 6. Theoretical and experimental ratio of the hourly total radiation to the daily total radiation.

Fig. 7. Theoretical and estimated[8] ratio of the hourly diffuse. Radiation to the daily diffuse radiation.

culation for Vancouver. Hay's procedure corresponds closely to Liu and Jordan's theoretical analysis. During the winter period, at hour pairs far away from solar noon. the disagreement of (2) with the solid lines is in accord with a similar disagreement shown by the experimental data plotted in Figs. I-3.

Figures I-6 contain mean data of hour pairs around solar noon. It is useful to examine the deviations from mean of the morning and afternoon data. Information on this deviation is necessary in such applications as fiat-plate collector orientation with respect to its due south position. Such deviation should be examined both for diffuse and total hourly radiation. Such an examination for all stations listed in Table I revealed some deviations from mean value, but no specific or established pattern appeared to exist. Therefore, without venturing into the realm of radiation climatology, the data was examined as it was.

The deviations of hourly data from solar noon are plotted as,

morning radiation-mean radiation x 100 mean radiation

vs hours from solar noon. For Montreal, Figs. 8 and 9 contain the deviation plots for diffuse and total radiation respectively. The plots are drawn for four months only, January, April, July and October. During January, in the morning, diffuse radiation is higher than the mean and the reverse is true in the afternoon. During April, diffuse radiation remains almost even around solar

Z 12.O o

' * °

4 . 0

Z 0.0

] ~ -4.0 x

~ - U.O

I I I I I I I I

M O N T R E A L 45"30" N

DIFFUSE R A D I A T I O N ~- OcToe~R

APRIL

JANUARY

- 1 2 . 0 l I I l I I I I O 1 2 3 4 5 6 7

HOURS FROM SOLAR N O O N

Fig. 8. Hourly variation of the diffuse radiation from its mean value.

SE Vol. 2 2 No. I--(3

z o_

o ,< Q¢

z

x

12.0

8.0

4.0

0.0

-4.0 t -8.0

-12.0 0

M. IQBAL

L I I I 1 1 I

MONTREAL 4 5 0 3 0 ' N

OCTOBER ~ JANUARY ~ ' - ~ "" ~'

I I I I I I I 1 2 3 4 $ 6 7

HOURS FROM SOLAR NOON

Fig. 9. Hourly variation of the total radiation from its mean value.

Z 12.0 9 ).. < <

. . o

Z 0.0

il _ . . o

x 0 - 8.0 _o

-1 2.0 0

I I 1 I I I I

_ VANCOUVER 49=15 ' N

TOTAL RADIATION OCTORER

~ ~ JULY JANUARY

~ APRIL

I I I I I I I 1 2 3 4 $ 6 7

HOURS FROM SOLAR NOON

Fig. 10. Hourly variation of the

noon while the total radiation is higher before noon. In July, diffuse radiation remains slightly higher in the afternoon while total radiation is higher in the morning. During the month of October diffuse radiation is much higher in the morning than in the afternoon, while total radiation remains about even around noon.

The deviation in total hourly radiation for Vancouver is shown in Fig. 10. It is evident from this figure that, throughout the year, total radiation is much greater in the afternoon than before noon.

in conclusion it may be added that this study provides supplementary data in support of Liu and Jordan's procedure to determine the monthly average hourly total and diffuse horizon- tal solar radiation. As the above method is valid for mean radiation at hour pairs around solar noon, this study points out some asymmetries in the actual data.

Acknowledgements--Financial support of the National Research Council of Canada is gratefully acknowledged. Numerical computations were carried out by Y. K. Lau and the diagrams were prepared by Cecilia Cameron. Thanks are also due to Dr. John E. Hay for supplying a number of tables of hourly radia- tion.

NOMENCLATURE /~ monthly average daily total radiation received on a

horizontal surface MJ m -z Day -I /-Td monthly average daily diffuse radiation received on a

horizontal surface MJ m -z Day -~ [ monthly average hourly total radiation received on a

horizontal surface over one hour kJ m -2 h -I

total radiation from its mean value.

f# monthly average hourly diffuse radiation received on a horizontal surface over one hour kJ m -2 h -~

r~ g_H~ rr II H

RgRIIIENCgt

1. R. L. Titus and E. J. Truhler, A new estimate of average global solar radiation in Canada. Environment Canada, U.D.C. 551.521.12 (71), CLI7-69, 3 July (1969).

2. G. O. G. i..6f, J. A. Duflie and C. O. Smith, World distribution of solar radiation. Rep. No. 21, published by the Engineering Experiment Station, Madison, University of Wisconsin (1966).

3. A. Whillier, Solar energy collection and its utilization for house heating. Doctor of Science thesis, Massachusetts In- stitute of Technology, (1953).

4. A Whillier, The determination of hourly values of total radia- tion from daily summations. Arch. Met. Geoph. BiokL B., 7, 197-204 (1956).

5. B. Y. H. Liu and R. C. Jordan, The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 4(2), 1-19 (1960).

6. M. lqbal, A study of diffuse and total solar radiation data of Canada. Part I. Monthly average daily horizontal radiation. Solar Energy 22(I), 81-86 (1979).

7. G. A. Mckay, Private communication. Environment Canada. Atmospheric Environment. 31 August (1977).

8. J. E. Hay, A revised method for determining the direct and diffuse components of the total short wave radiation. At. mosphere 14(4), 278-287 (1976).

9. M. lqbal, Hourly vs daily method of computing insolation on inclined surfaces. Solar Energy 22(I) 81-86 (1979).