So/ar Energy Vol. 22, pp. 81-86 003g-.092X/79/0101--0¢gl/$02.0010 © Pergamon Press Ltd,, 1979. Printed in Great Britain

TECHNICAL NOTE

A s tudy of C a n a d i a n diffuse and total so la r r ad i a t i on d a t a - - I

M o n t h l y a v e r a g e dai ly ho r i zon ta l r a d i a t i o n

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

(Received 18 December 1977; revision accepted 6 July 1978)

INTRODUCTION

In order to design a solar system, it is necessary to determine the amount of energy actually available at the various orientations of a collector. A tilted flat-plate collector receives beam radiation and diffuse radiation from the portion of the sky-dome it actually sees, plus radiation reflected from the ground. Most solar radia- tion recording stations measure only the total horizontal flux. Therefore, it is necessary to determine the beam and diffuse components of the total radiation for horizontal surfaces. Once these two components are determined, they then can be trans- posed over an inclined plane.

It is very common to design solar systems based on long-term monthly averages of radiation and other climatic data. Monthly average daily total radiation on horizontal surfaces is known for a large part of the world. Such information is generally available in the form of maps or tables. Whenever such information is not available, it can be easily obtained through its correlations with hours of bright sunshine. Data on diffuse horizontal radiation, however, is very rare. It is therefore necessary to develop correlations between the widely available total and the rarely available diffuse radiation data.

In this report, attention is concentrated on the monthly average daily radiation (unless specifically mentioned t o t he contrary). Monthly average hourly radiation is studied in Part II of this report[l]. The monthly average daily radiation quite often is written as average daily or simply daily radiation. A review of the correlations between diffuse and total horizontal radiation follows.

Page [2] developed correlations between daily total and its diffuse component for ten widely spread sites located between 40*N and 40"S. His correlations were of the linear form

HdlH = c +d/~r (I)

where /~¢ =/~//~o is the cloudiness index. Page evaluated the coefficients c and d for each site and then recommended the following average values of these coefficients,

/-/,,//~ = !.00- 1.13Kr. (2)

Page used a solar constant of 2.0 langley per min in developing (2).

Liu and Jordan[3] developed a statistically based theoretical correlation between H,,4H and the cloudiness index, /~r. They' then tested their theoretical correlation against diffuse radiation data from four widely spread stations. The /~o in Liu and Jordan's correlation was calculated for the Ifah of each month except for February when the IJth of the month was used. Also they employed a solar constant of 2.0 langley per min. Klein[4] developed the following mathematical expression for Liu and Jordan's correlation [Fig. 14 in Ref. 2].

?Before this article went to press, Klein[g] has communicated that there is an error in his Table 5.

/'I~//'1 = 1.39- 4.027/~r + 5 .531 /~ - 3.108/~ (3)

where/'Io in/~r was based on the actual average extraterrestrial radiation during a month and a revised solar constant of 1.94 langley per min was used.

It should he noted that neither eqn (2) nor (3) are valid for extreme values of/~r- According to Klein, Page's correlation fits better some additional data reported from India by Choudhury[5], from Israel by Stanhill[6] and from Australia by Norris[7]. Klein has shown that, on the other hand, when in- solation on a vertical wall is computed, Liu and Jordan's cor- relation fits the available data from Blue Hill, Massachusetts, better.?

A summary of the Canadian studies follows. There are 52 Canadian stations which report global (total)

horizontal solar radiation. Data is recorded on an hourly basis. Diffuse solar radiation is measured at 4 locations fI'able I).

Canadian diffuse radiation data has been examined previously by Ruth and Chant[9], Orgill and Hoilands[10], Hay[IlL and Tulier[12]. Ruth and Chant developed a correlation between diffuse and total radiation applicable to particular days and showed that it gives generally a higher value of diffuse radiation compared to a corresponding correlation developed by Liu and Jordan[Fig. 7 in Ref. 3]. Orgill and Hullands' correlation is ap- plicable to particular hours. In this report, since attention is concentrated on the monthly average daily diffuse radiation, the studies in Refs. [9] and [10] are not discussed for the time being.

Hay developed a correlation between monthly average hourly diffuse radiation, id, and the monthly average hourly total radia- tion L His correlation is derived through an analysis of multiple reflections between ground and cloud cover and atmospheric back-scatterance. From his method, the daily diffuse radiation/~d can also be estimated by summing up over a day the estimated hourly values f~. Such estimated daily diffuse radiation may be written as

f , = ~ , . (4)

The accuracy of Hay's method can be examined by comparing (4) with the experimental data.

Tuller analyzed the monthly average daily diffuse radiation. By combining the data of all four stations (one of them, Resolute, is within the polar circle), he developed the linear correlation

Hd//'l = 0.84- 0.62/~r. (5)

In the above equation, a solar constant value of !.95 langley per min was used.

Ruth and Chant, Hay and Tuller have indicated that Resolute data give anomalous results. As such, the inclusion of Resolute data by Tufter in developing the above correlation is unfortunate.

The general purpose of the present report is to compare the radiation models mentioned above and to improve upon (5) by ignoring Resolute data. The specific objectives were: (i) to

81

82 Technical Note

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

Lat. Long. (N) (W)

Station 0 ' 0 ' Record Used

~roronto, Met. Res. Stn. 43 48 79 33 Aug. 1967-Dec. 1975 tMontreal, Jean Breheuf 45 30 73 37 Oct. 1964-Dec. 1975 tGoose Bay 53 18 60 27 May 1962-Dec. 1975 tResolute 74 43 94 59 July 1957-Dec. 1975 ~Winnipeg 49 54 97 16 July 1957-Dec. 1975 ~:Edmonton 53 34 113 31 July 1957-Dec. 1975 ~Vancouver 49 15 123 15 Jan. 1959-Dec. 1975

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

Table 2. Monthly average daily total and diffuse solar radiation on a horizontal surface, MJm-2day -j

Daily total radiation/~ Daily diffuse radiation/'ld Month Toronto Montreal Goose Bay Toronto Montreal Goose Bay

January 6.046 5.255 3.554 3.53 2.89 2.04 February 8.209 8.728 6.927 5.05 4.38 3.72 March 12.944 12.471 11.439 6.20 5.85 6.25 April 17.649 15.790 16.027 7.60 6.61 9.32 May 19.304 18.484 18.163 8.78 8.18 9.99 June 20.947 20.936 18.748 9.98 9.18 9.60 July 22.240 21.171 17.929 9.16 9.24 9.10 August 19.022 17.180 14.653 8.19 8.01 7.74 September 14.022 13.167 10.491 6.31 5.88 5.67 October 9.016 8.264 6.097 4.48 3.96 3.57 November 4.612 4.55 3.165 2.96 2.55 2.10 December 4.260 3.785 2.587 2.68 2.27 1.54

develop a regional correlation based on Toronto-Montreal data and Toronto-Montreal-Goose Bay data; (ii) to compare the mon- thly variation of experimental diffuse data with that obtained from the regional correlation; (iii) to compare the slope radiation computed by using the regional correlation with that using the experimental horizontal diffuse radiation; (iv) to carry out a solar building heating simulation study using the regional correlations and compare results with those obtained by using the experi- mental diffuse radiation data; finally, (v) to recommend one specific correlation valid for a wide region.

Before proceeding further to discuss results, it is useful to point out that the Canadian diffuse data contain a 2 per cent correction factor to account for the shade ring[13]. No correction is made, however, for completely cloudy days.

iIE~JLTS AND DISEUS810~S The hourly radiation data of Toronto, Montreal and Goose Bay

were converted in terms of long-term average daily total and diffuse radiat ion,/ t and_/td respectively (Table 2)._The fraction of diffuse radiation tta/H and the cloudiness index Kr are shown plotted in Fig. I. The cloudiness index of the three stations lies between 0.3 and 0.6.

A curve fitting program[14] that employs the Gaussian- Newton least-squares_technique_was used to develop regional correlations between Hs/H and Kr. The following linear best, fits were obtained:

Hd//t = 0.958 - 0.982/~r, (6)

for combined Toronto--Montreal data resulting in a standard error of estimate of 0.04.

/~¢/H = 0.914- 0.847/~r, (7)

for combined Toronto--Montreal--Goose Bay data resulting in a standard error of estimate of 0.05.

Equations (2), (3), (5)--(7) are also plotted in Fig. 1. When the cloudiness index is low, of the order of 0.2, all correlations give almost identical results. At higher values of the cloudiness index, Liu and Jordan's correlation gives minimum amounts of diffuse radiation, while Tuller's correlation gives maximum amounts. At this juncture it is difficult to say whether at higher cloudiness index the divergence of various correlations are due only to latitude effect or to climate or both.

The daily diffuse radia t ion/~ was also estimated through eqn (4). The hourly diffuse radiation ld in this equation had a unique correlation with the hourly total radiation I[11]. Therefore, it is necessary to examine whether or not the daily diffuse estimation

fa also produces a unique correlation with the daily total day radiation/~. Figure 2 shows such estimated values of the fraction of daily diffuse radiation vs the actual fraction. When viewed in this manner, Hay's method does not produce a well-defined correlation.

In the opinion of this writer, the correlations of/~a//~ with/~r and plots of corresponding data are sometimes deceptive. This form of correlation approach is used since it presents the governing parameters in a non-dimensional and universal manner. However, the main objective is to obtain an accurate estimate of the daily diffuse radiation. Therefore, another direct approach to verify accuracy of the estimated diffuse radiation is to compare its value with the measured data.

The measured values of the daily diffuse radiation were compared with those estimated through eqns (2)-(7). The mon- thly variations of the daily diffuse radiation are plotted in Figs. 3--6. Figures 3 and 4 are for Toronto and Fig. 5 and 6 for Montreal.

Figure 3 for Toronto contains plots of the monthly variation of daily diffuse radiation obtained from (i) measured data; (ii) Page's correlation, eqn (2); (iii) Liu and Jordan's correlation, eqn (3); and (iv) the present correlation based on Toronto-Montreal data, eqn (6). It is apparent from this diagram that none of the

Technical Note 83

a~

kb

i

<

O.8

az

0 . 6

~ o.4

0 . 2

<

0 . 0

o :£

I 1 I I I I I 4 TerenOe 4~'48'N (1967-~P75)

• Montrqml 4S"30'N (19G4-1975)

"'.._~t------~l~ • Oeoeo BOy 53"| lrN (1962-1975)

• • • / ~ Teller Eq.(5)

. . " . ° . , .

l a g . Eo,(2) - / ~ ' ~ . ""

~o,,oao Co,r, lo*l~ wooh ~ ~ ' ~ Torento-Mqmtrool Data lq.(6) _ / "

Tcwonto - Mont tea I oGoose

I ] I [ I I I 0 . 0 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8

R M O N T H L Y AVERAGE DAILY TOTAL R A D I A T I O N RATIO KT--Ro-~ EXTRATERRESTRIAL DAILY I N S O L A T I O N

I I

I ~ r 'r"

Fig. 1. The ratio of the monthly average daily diffuse radiation to the monthly average daily total radiation as a function of the cloudiness index KT.

i ' I -

0 . 6 5

0 . 6 0

0 . 5 5

0 . 5 0 - -

0 . 4 5 - -

0 . 4 0 0 . 3 !

I I I u I I

• O

4 • • • TORONTO

• • ~ • MONTREAL

• J I ° J [ I I 0 . 4 0 0 . 4 5 0 . 5 0 0 . 5 5 0 . 6 0 0 . 6 5 0 . 7

day

Fig. 2. Comparison of the measured monthly average daily diffuse radiation with the estimated monthly average' daily diffuse radiation obtained from Hay[Ill.

correlations coincide exactly with the experimental data throughout the year. However, the present correlation comes very close to it. From August to December, eqns (2) and (6) correspond very closely with the experimental_ data. Liu and Jordan's correlation gives the lowest values of H~ throughout the year.

Figure 4, again for Toronto, shows the monthly variation of/~d obtained from measured data and the remaining correlations; (i) Hay's equation (4); (ii) TuHer's correlation, eqn (5); and (ill) present correlation based on Toronto-Montreal-Goose Bay data, eqn (7). From September to December, all three correlations correspond closely with the measured data. During the remaining. part of the year, each correlation varies in a different manner and correspondences, wherever they are, are over shorter periods. Tuller's correlation gives the highest estimate of diffuse radiation from March to October.

From Figs. 3 and 4 it may be concluded that as far as Toronto is concerned, the present correlation (6) corresponds most closely with the measured data.

Figure 5 for Montreal shows plots of the monthly variation of daily diffuse radiation obtained from actual data and eqns (2), (3) and (5). Liu and Jordan's correlation gives the lowest value of the diffuse radiation. From August to March, there is close cor- respondence between the other two correlations and the actual

data. During the rest of the year, Page's correlation as well as the present correlation (6) agree about evenly with measured data.

F'tgure 6, again for Montreal, shows the comparison of the remaining three correlations with the actual data. From January to April, both (5) and (7) correspond closely to the measured data. For the remaining period, eqn (4) gives better results. As expected, Tuller's correlation (5) gives the highest estimate of diffuse radiation almost throughout the year.

From Figs. 5 and 6 it may he concluded that on an overall basis, Page's correlation, Hay's estimation method and the present correlation (6) correspond fairly closely with the measured data. Equation (6) gives better results during the winter period and Hay's method gives better results during the summer period.

An examination of the daily diffuse radiation of Goose Bay similar to that done for Toronto and Montreal was also carried out. Without presenting diagrams it may he said that the present correlation (6) gave the best results. In fact, the correspondence was perfect from June to December. It has been dimcult to determine why, for Goose Bay, the correlation based on combined Toronto-Montreal data gave better results than the one based on combined Toronto-Montreal-Goose Bay data.

Finally, it may be concluded that for the three stations examined, on the whole, eqn (6) gives the best results. It is known that such correlations as studied in this report at best can

84 Technical Note

1 3 ' > , O

P" 6 u .

2 <[

>: 3: ~. 0 Z O :E

I I I I I i I I I I J

_ T O R O N T O 4 3 ° 4 8 ' N

Measured Data ~

Page Eq. (2) - - -

Presen! C o r r e l a t i o n Eq.(6) ~ *

1 I I I I I I I I I J A N FEB MAR APR MAY JUN JUL AUG SEP OCT N O V DEC

M O N T H

1 3 T>.

O " 0

12 --

. z l O

a < 8

~ 6

< D 4

~ 2

-1,-

O

I I I I I I I I I I

M O N T R E A L 45°30 'N

M e a s u r e d D a t a

Page Eq. {2) - - - - - -

Present C o r r e l a t i o n Eq. (6) - - " - -

o I I I I I I I I I I J A N FEB MAR APR MAY J U N JUL A U G SEP OCT N O V DEC

M O N T H

Fig. 3. Comparison of the monthly variation of measured average daily dilfuse radiation for Toronto with that obtained from

eqns (2), (3), (6).

Fig. 5. Comparison of the monthly variation of measured average daily diffuse radiation for Montreal with that obtained

from eqns (2), (3), (6).

1 3 T>+.

~E

3[ I0 0 l -

a <i[ 8 oc

i,i. . . 6 ,,.,,

< I~ 4

,<

+~ 2 < >.

I I I I I I I I I I

T O R O N T O 43°48 'N

../;+/',,,<- / , . , / I " ' ~ . , , ,~_

- i ,// _ ....~, ".~',~:

T-,e, Eq.(s) . . . . . . . . . . . M e a s u r e d Dale

H a y Eq. {4) . . . .

Present C o r r e l o t l o n Eq.(7~ . . . .

I i i J i f i l I I J A N FEg MAR APR MAY JUN JUt AUG SIP OCT N O V DEC

M O N T H

D ,,g

?E

IX z" 2 < m a < ¢d

a

< o

¢[

<

"i-

O ~E

1 3

1 2 - -

1 0 - -

I I I I I I I I I I

M O N T R E A L 4 5'~10' N

. . , . . . . . . . .

Ah"",Y. . ' / / w % ~ . .

i - : , : / / -

. . . ' / . ' / ~ ":

/ " " ~ X

4 r . ~' "

Tu l l e r Eq. (5) " ' "

M e a s u r e d D a t a 2 Hay Eq {4) . . . .

Present C o r r e l a t i o n Eq. (7) . . . .

o I I I I 1 I I I I I JAN FEB MAR APR MAY JUN JUL AUG IEP OCT NOV DEC

M O N T H

Fig. 4. Comparison of the monthly variation of measured average daily diffuse radiation for Toronto with that obtained from

eqns (4), (5), (7).

Fig. 6. Comparison of the monthly variation of measured average daily diffuse radiation for Montreal with that obtained

from eqns (4), (5), (7).

have regional validity only. Therefore, for the rest of Canada, it is difficult to state which one of the correlations would be best.

In Figs. 3-6. the monthly variation of the daily diffuse radiation on a horizontal surface obtained from various procedures was discussed. However. in practice, the amount of total insolation on a sloped surface is more important than the individual values of beam and diffuse radiation on a horizontal surface. Therefore, slope radiation for all six stations (Table I) was studied. Only south-facing surfaces were considered. The main objective was to investigate the difference in total slope radiation obtained through various correlations. To avoid confusion resulting from too many lines on a diagram, results are presented only for eqn (2)--(4) and (7) and actual horizontal diffuse data where applic- able.

Slope radiation was calculated through the well-established method of Liu and Jordan[15]. Following Klein[4], instead of calculating the slope radiation itself, only the parameter ,q defined as the ratio of total radiation on a tilted surface to that on a horizontal surface are presented.

Plots of R for Montreal are given in Fig. 7 and 8. These plots are for surfaces facing due south and tilted at 50 ° and 90 ° respectively. These figures contain ,q calculated with estimated daily diffuse radiation obtained from eqns (2), (3), (4) and (7), and the actual measured horizontal diffuse data. The present cor- relations based on Toronto-Montreal data (6) and Toronto- Montreal-Goose Bay data (7) produced almost identical results and therefore only one of them is shown. Considering these two diagrams, on the whole, correlations (6) and (7) were closest to

i - r

, £ I I

Technical Note

MONTREAL 4sOao ' N

S L O P E 5 0 °

2 . 0

1 . 5

1 . 0

O .S Liu and Jordan Eq. 13)

Hay Eq.(4) . . . .

Page Eq. (2 ) ~ --

Present Correlat ion Eq.(7) . . . .

o . o 1 I 1 I I I I I I I JAN FEB MAR APR MAY JUN JUL AUG S|P OCT NOV DEC

M O N T H

Fig. 7. Comparison of the ratio ~ obtained from the measured horizontal diffuse data with that obtained from eqns (2), (3), (4) and (7)..q is the ratio of insolation on an inclined plane to that on

a horizontal plane.

1 . 5 i ' r

,£ II

t ~ 1 . 0

l 1 MONTREAL 4 s ° 3 o ' N

S L O P E 9 0 °

2 . 0 Measured Data - - I

Liu and Jordan IEq, ~3) ~ / /

& POO. E q . ( 2 ) - - -- - - / A ~

, . . . . . , C o , , . , o . a . Eq. t,~ . . . . --//Z' i / :

0 . 5 - -

I I I 1 I I 1 I I I 0.~JAN/'I FEB MAR APR MAY JUN JUL AUG SEP OCT NOV OIEC

M O N T H

Fig. 9. Comparison of the ratio R obtained from the measured horizontal diffuse data with that obtained from eqns (2), (3), (4) and (7). R is the ratio of insolation on an inclined plane to that on

a horizontal plane.

tSIope radiation using a bright sunshine correlation has been compared[16] with tables prepared by Hay[IT]. It is pertinent to point out here that values in these tables do not agree with those calculated by this writer using eqn (4).

85

those obtained by using measured horizontal diffuse data. Results obtained through (2) and (4yf were also very good. Between (2) ands,(4) correspondence was sometimes better during certain mohths than others.

Liu and Jordan's correlation (3) consistently resulted in higher values of R, except during summer periods. However, it is apparent from these two figures that all sources produced iden- tical results during _the summer months.

Calculations of R for Toronto and Goose Bay also revealed that both (6) and (7) give results very close to those obtained by using meas_ured horizontal diffuse data.

Factor R was also computed for the remaining three stations listed in Table I. The correlations (6) and (7) produced almost identical r',sults: the former, however, had relatively slight conservative values. Correlation (5) always resulted in minimum values of i~, while Liu and Jordan's correlation produced maxi- mum values of this parameter. During summer periods, all cor- relations produced almost identical results.

Impetus for much of the recent work in solar radiation studies in Canada comes from its potential applications for solar heating of buildings. It would therefore be very useful to see the differences in results produced by using various correlations in a solar heating system.

The slope radiation calculations mentioned above were employed as input data to carry out a specific example in solar building heating simulation. A residential building of 150 m 2 floor area with insulation conforming approximately to ASHRAE standards 90-75118] was used. A constant hot water load of 43 MJ per day was assumed. Double glazed collectors facing due south and tilted at 50 ° from the ground were used. The collector and collector-heat exchanger characteristics were,

Fs(¢-) = 0.674

FI~UL = 11.28 kJh -t *C -z m -2

and

F ~/ FR = 0.979.

For such a house in Montreal, the yearly fraction of the load supplied by the solar system was computed following the/-chart method laid down by Klein et all19]. The results of these calculations are given in Table 3. An examination of this table shows that the correlation based on combined Toronto-Montreal data, eqn (6), gives results closest to those obtained by using measured horizontal diffuse radiation data. Equation (7), based on combined Toronto-Montreal-Goose Bay data, comes next in accuracy. Hay's correlation (4) and Page's correlation (2) come third. Liu and Jordan's correlation (3) gives the highest fraction and Tuller's correlation (5) gives the lowest fraction. An identical calculation carried out for Toronto also showed that (6) cor- responded closely to values from measured/~.

From the foregoing it can he concluded that: (i) the present correlation (6) gives very good results for the estimation of horizontal daily diffuse radiation; (ii) both correlations (6) and (7) produce almost identical results to compute slope radiation; (iii) the slope radiation obtained by employing (6) and (7) corresponds closely to that obtained by employing measured horizontal diffuse data; and (iv) the slope radiation obtaiincd through (6) when used as an input for solar heating of houses gives results aLmost identical to those obtained through the actual diffuse data. It is recommended that eqn (6) he used to estimate diffuse radiation.

Addeadum. At the beginning of this report it was stated that, unless otherwise mentioned, at present only monthly average daily values are discussed. The following is the one exception.

As mentioned earlier, Ruth and Chant[9], using Canadian data, developed a correlation between daily diffuse radiation for particular days and corresponding daily total radiation. Whereas that correlation was presented in graphical form, it is also useful to present it in mathematical form, as given below:

H, tH = 0.910- 1.154Kr - 4.936K~ + 2.848K~,

0.1 ~ K r ~ 0 .7 (8)

86 Technical Note

Table 3. Yearly fraction of load supplied by the solar system for a 150m z floor area house in Moutxeal and using various correlations between the horizontal diffuse radiation/~d and

the cloudiness index/~r

Area Fraction of load supplied by solar system m 2 Actual Hd - eqn (6) eqn (7) eqn (2) eqn (3) eqn (4) eqn (5)

5 0.094 0.094 0.094 0.095 0.099 0.093 0.092 10 0.169 0.168 0.168 0.170 0.178 0.167 0.164 15 0.227 0.226 0.224 0.230 0.240 0.224 0.220 20 0.278 0.277 0.275 0.281 0.294 0.274 0.270 25 0.324 0.324 0.320 0.328 0.343 0.320 0.315 30 0.365 0.364 0.361 0.370 0.387 0.360 0.355 35 0.402 0.402 0.398 0.408 0.427 0.397 0.391 40 0.435 0.435 0.431 0.442 0.463 0.429 0.423 45 0.466 0.466 0.462 0.473 0.496 0.460 0.453 50 0.495 0.496 0.491 0.503 0.528 0.489 0.482 55 0.523 0.524 0.518 0.532 0.557 0.516 0.509 60 0.549 0.550 0.544 0.558 0.585 0.542 0.534

Acknowledsemems--Fmuncial support of the National Research Cotmcil of Can a0a is 8rafefuIIy acknowledged. The numerical computations and drafting work was done by Y. K. Lan and Cecilia Cameron. Tbank~ are due also to Dr. John E. Hay for supplying a number of tables of hourly radiation.

N O ~ T U R I g c,d constants in eqn (1) Fa collector heat removal factor Fk collector-heat exchanger eiciency factor H daily total radiation received on a horizontal surface,

Mlm-ZDay -, Ha daily diffuse radiation received on a horizontal surface,

Mjm-2Day -I Ho extraterrestrial daily insolation received on a horizontal

surface, MJm-ZDay -~ /4 monthly average daily total radiation received on a

horizontal surface, MJm-2Day -t /~ monthly average daffy diffuse radiation received on a

horizontal surface, MJm-q~y-' /~o extraterrestrial monthly avm'a~ daily insolation received

on a horizontal surface, MJm-~Day - ' /~ monthly average daily total radiation received on an in-

dined plane, MJm-2l~y -t [ monthly average hourly total radiation received on a

horizontal surface over I hr, Idm-2h -~ l,c solar constant, 1.94 langley per min, 4871 kJm-Zh -I g Hdtt

~ ~1~o K c H IH~

R H~H UL collector overall energy loss coeicient, kJh-tm-2C -I (~) weightedmonthly average of the transmittance-absorp-

tance product.

1. M. lqbal, A study of diffuse and total solar radiation data of Canada---II. Monthly averase hourly horizontal radiation. , Solar Energy 22(i), 87-90 (1979).

2. J. K. Page, The estimation of monthly mean values of daffy total short-wave radiation on vertical and inclined surfaces

from sunshine records for latitudes 40°N-40°S. Proc. UN Conf. on New Sources of Energy, Paper No. S/98 (1961).

3. B. Y. H. Liu and R. C. Jordan, The interrelationship and characteristic distribution of direct, diffuse, and total solar radiation. Solar Energy 4(3), 1-19 (1960).

4. S. A. Klein, Calculation of monthly average insolation on tilted surfaces. Solar Energy 1~(4), 325-329 (1977).

5. N. K. O. Choudhury, Solar radiation at New Delhi. Solar Energy 7(2), 44-52 (1963).

6. G. Stanhill, Diffuse sky and cloud radiation in Israel. Solar Energy 10(2), 96-101 (1966).

7. D. J. Norris, Solar radiation on inclined surfaces. So/ar Energy 10, 72-77 (1966).

8. S. A. Klein, Erratum, Solar Energy 26(5), 441 (1978). 9. D. W. Ruth and R. E. Chant, The relationship of diffuse

radiation to total radiation in Canada. Solar Energy 18(2), 153-154 (1976).

10. J. F. Orgill and K. G. T. Hollands, Correlation equation for hourly diffuse radiation on a horizontal surface. Solar Energy 19(4), 35%359 (1977).

il. 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).

12. S. E. TuBer, The relationship between diffuse, total and extraterrestrial solar radiation. So/ar Energy 18(3), 250.-263 (1976).

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

14. J. Streat and C. M. Lee, U.B.C. Curve, curve fitting tech- niques. Computing Centre, University of British Columbia, Vancouver, B.C. (1976).

15. B. Y. H. Liu and R. C. Jordan, Daily insolation on surfaces tilted toward the equator. Trans. ASHRAE 526-541 (1962).

16. M. lqbal, Estimation of the monthly average of the diffuse component of total insolation on a horizontal surface. Solar Energy ~(I), 101-105 (1978).

17. Canada's Renewable Energy Resources--An assessment of potential. Middleton Associates, Toronto, pp. 514 (1976).

18. American Society of Heating, Refrigeration, and Air Condi- tioning Engineers, Standards 90-75, Esergy Conseroation in New Building Des/gn, New York (1975).

19. S. A. Klein, W. A. Beckman and J. A. Duroc, A design prodedure for solar heating system analysis. SO/at Energy IS(2), 113-127 (1976).