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Solar radiation on cloudy days
Kimura, K.; Stephenson, D. G.
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https://nrc-publications.canada.ca/eng/view/object/?id=44793409-cc30-4993-8fcf-dcadd7ae3eea https://publications-cnrc.canada.ca/fra/voir/objet/?id=44793409-cc30-4993-8fcf-dcadd7ae3eeaNo.
2106
D. G. STEPHENSON
Member ASHRAE
Solar Radiation on Cloudy Days
S o l a r r a d i a t i o n i s o n e of t h e m o s t important com- p o n e n t s of the h e a t b a l a n c e a t t h e o u t s i d e s u r f a c e s of b u i l d i n g s , a n d t h e s o l a r h e a t that e n t e r s a build- i n g through t h e w i n d o w s i s a major e l e m e n t in t h e t o t a l h e a t g a i n by t h e building. T h e r e f o r e , a c c u r a t e d a t a o n s o l a r i n t e n s i t i e s a r e important in s e v e r a l p h a s e s of b u i l d i n g d e s i g n , p a r t i c u l a r l y i n t h e de- s i g n of t h e a i r - c o n d i t i o n i n g s y s t e m . A s s o l a r radia- tion r e c o r d s a r e a v a i l a b l e f o r o n l y a v e r y l i m i t e d number of w e a t h e r s t a t i o n s , i t i s n e c e s s a r y to f i n d a way of e s t i m a t i n g the hourly v a l u e s of s o l a r in- t e n s i t y f o r l o c a t i o n s w h e r e r e c o r d s a r e not a v a i l a b l e . T h e A S H R A E T a s k Group o n E n e r g y Require- m e n t s for H e a t i n g a n d C o o l i n g B u i l d i n g s is devel- o p i n g a p r o c e d u r e for c a l c u l a t i n g e n e r g y require- m e n t s t h a t u s e s t h e hourly v a l u e s of s u r f a c e o b s e r - v a t i o n s m a d e a.t a l l f i r s t c l a s s w e a t h e r s t a t i o n s . T h e s e o b s e r v a t i o n s i n c l u d e c l o u d t y p e a n d a m o u n t , but n o t s o l a r i n t e n s i t y . I t i s n e c e s s a r y , t h e r e f o r e , to try to i n f e r t h e hourly v a l u e s of s o l a r i n t e n s i t y from t h e c l o u d o b s e r v a t i o n s . T h i s p a p e r p r e s e n t s t h e r e s u l t s of a p i l o t s t u d y t h a t w a s m a d e to d e t e r -
K. Kimura is a P o s t Doctoral F e l l o w , D i v i s i o n of Building
Research, N a t i o n a l Research C o u n c i l of Canada, Ottawa, on l e a v e from the Department of Architecture, Woseda University,
Tokyo, Japan. D . G. Stephenson i s a Research Officer, Build-
ing Services Section, D i v i s i o n of B u i l d i n g Research, N a t i o n a l Research C o u n c i l of Canada, Ottawa. T h i s paper i s a contri- bution fram the D i v i s i o n of B u i l d i n g Research, N a t i o n a l
Research C o u n c i l of Canada, and is published w i t h t h e ap- proval of t h e Director of the D i v i s i o n . T h i s paper was pre- pared for presentation at t h e A S H R A E Semiannual Meeting,
Chicago, I l l i n o i s , January 27 - 30, 1969.
mine t h e r e l a t i o n s h i p b e t w e e n s o l a r i n t e n s i t y o n a h o r i z o n t a l s u r f a c e a n d hourly o b s e r v a t i o n s of cloud c o v e r for ~ t t a w a ' , Ontario.
CLOUD COVER FACTOR (CCF)
T h e s i m p l e s t w a y of e s t i m a t i n g t h e s o l a r i n t e n s i t y on a h o r i z o n t a l s u r f a c e on c l o u d y d a y s i s to c a l c u - l a t e t h e i n t e n s i t y t h a t w o u l d b e o b t a i n e d if t h e s k y w e r e c l o u d l e s s a n d then multiply t h i s c l e a r s k y in- t e n s i t y by a f a c t o r t h a t d e p e n d s o n t h e c l o u d cover. T h i s f a c t o r i s c a l l e d the c l o u d c o v e r f a c t o r ( C C F ) . T h u s t h e s o l a r r a d i a t i o n o n a h o r i z o n t a l s u r f a c e for c l o u d y d a y s , I T H C , is given by t h e e x p r e s s i o n ITHC =
IT^
.
C C F (1) w h e r e I T H is t h e t o t a l s o l a r i n t e n s i t y on a horizon- t a l s u r f a c e g i v e n by t h e f o r m u l a s a n d d a t a i n t h e ASHRAE H A N D B O O K O F FUNDAMENTALS' ( C h a p t e r 28). T h e r e a l problem, t h e r e f o r e , is to d e t e r m i n e C C F a s a f u n c t i o n of c l o u d c o v e r . T h i s c a n be d o n e by u s i n g t h e r e c o r d e d v a l u e s of t h e t o t a l s o l a r inten- s i t y on a h o r i z o n t a l s u r f a c e , I,,,,
a n d c o r r e l a t i n g t h e r a t i o I r e c / I T H w i t h t h e c l o u d c o v e r r e c o r d s on a n hourly b a s i s .DATA
USED
An a n a l y s i s of t h i s .type w a s m a d e u s i n g t h e s o l a r r a d i a t i o n a n d c l o u d c o v e r o b s e r v a t i o n s for O t t a w a , O n t a r i o(45'
2 7 ' N , 75' 37'W) t h a t a r e p u b l i s h e d by t h e M e t e o r o l o g i c a l B r a n c h of t h e C a n a d i a n Depart-Fzg. I Ratro of radzatzon znczdent or1 h o r z z o n ~ a l surface to amount calculated for c l o u d l e s s day for Srn
P:
( a ) O . I - 0 . 3 , ( b ) 0 . 3 - 0 . 5 , ( c ) O . 5 - 0 . 7 , ( d ) 0 . 7 - 0 . 9 ,L E G E N D O F S Y M B O L S I N F I G U R E S 1 - 2 S y m b o l
S~np
*
0. 9 - 1 . 0+
0. 7 - 0. 9 0 . 5 - 0. 7 o 0. 3 - 0 . 5 0 0. 1-
0. 3 Flg. 2 Correlatzon b e t w e e n c a l c u l n t e d rrldlatlon b a s e d on C C F and recorded radzatzon on horzzontal sur/ace /or a l l d n y l ~ g k t hours zn ( a ) cblarck 1967, ( b ) l u n e 1967, ( c ) September 1967, and ( d ) Decernber 19670 20 40 6 0 80 100 I rec ( L a n g l e y l h r ) 0 20 40 60 8 0 100 I r e c ( L a n g l e y l h r ) 0 20 40 6 0 8 0 100 ' r e c ( L a n g l e y l h r )
m e n t of T r a n s p o r t 2 . 3 . T h e r a d i a t i o n v a l u e s a r e
I
a l t i t u d e but t h e s c a t t e r of t h e p o i n t s a r e s u b s t a n - m e a s u r e d by a t h e r m o p i l e t y p e of p y r a n o m e t e r c o u -I
t i a l l y l o w e r f o r t h e h i g h e r s o l a r a l t i t u d e s . T h i s is p l e d w i t h a n i n t e g r a t i n g t y p e of r e c o r d e r t h a t g i v e s t h e t o t a l s o l a r r a d i a t i o n i n c i d e n t o n a h o r i z o n t a l s u r f a c e d u r i n g a p e r i o d of o n e hour e n d i n g o n t h e h o u r i n A p p a r e n t S o l a r T i m e . T h e c l o u d c o v e r ob- s e r v a t i o n s a r e m a d e e v e r y h o u r ( S t a n d a r d T i m e ) by e x p e r i e n c e d o b s e r v e r s w h o e s t i m a t e t h e a m o u n t of c l o u d o n a s c a l e of 0 t o 1 0 a n d i n d i c a t e t h e t y p e of c l o u d i n f o u r d i f f e r e n t l a y e r s . T h e s e d a t a w e r e a v a i l a b l e o n p u n c h e d c a r d s s o t h e a n a l y s i s c o u l d b e m a d e by c o m p u t e r w i t h o u t a n y d a t a t r a n s c r i p t i o n . T h e a n a l y s i s w a s m a d e for t h e m o n t h s of March, J u n e , S e p t e m b e r a n d D e c e m b e r i n 1 9 6 7 , to s e e if t h e r e w a s a s e a s o n a l v a r i a t i o n i n t h e r e l a t i o n s h i p b e t w e e n I r e c / I T H a n d t h e c l o u d c o v e r ( C C ) . T h e v a l u e of I T H w a s c a l c u l a t e d for e v e r y h o u r i n a p p a r e n t s o l a r time ( i e : for h o u r a n g l e s t h a t a r e e v e n l y d i v i s i b l e b y 1 5 d e g s ) , b u t t h e v a l u e u s e d a s t h e d e n o m i n a t o r i n e a c h r a t i o w a s t h e a v e r a g e of t h e v a l u e s c o m p u t e d for t h e b e g i n n i n g a n d e n d o f t h e h o u r d u r i n g w h i c h I,,, w a s m e a s u r e d . S i m i l a r l y , t h e v a l u e of C C a s s o c i a t e d w i t h e a c h v a l u e of I r e c / ~ T H W a s t h e a v e r a g e of t h e v a l u e s a t t h e be- g i n n i n g a n d e n d of t h e hour. No a l l o w a n c e w a s m a d e for t h e f a c t t h a t t h e c l o u d o b s e r v a t i o n s w e r e m a d e i n S t a n d a r d T i m e r a t h e r t h a n i n A p p a r e n t S o l a r T i m e . T h e v a l u e o f C C u s e d for t h i s a n a l y s i s is d e - f i n e d a s t h e r e c o r d e d t o t a l a m o u n t of c l o u d m i n u s half of t h e a m o u n t s of c i r r u s , c i r r o s t r a t u s a n d c i r - r o c u m u l u s . T h i s d i s c o u n t i n g of t h e a m o u n t s for t h e s e t h r e e t y p e s of c l o u d m a k e s t h e v a l u e of C C a g r e e v e r y c l o s e l y w i t h t h e o p a c i t y v a l u e for t h e c l o u d c o v e r . T h e v a l u e o f C C d e f i n e d i n t h i s w a y w a s u s e d i n s t e a d o f o p a c i t y , b e c a u s e o p a c i t y is n o t g i v e n i n t h e r e c o r d s f o r s t a t i o n s i n t h e U n i t e d S t a t e s .RESULTS
I T h e v a l u e s o f Ir,,/ITH w e r e s e p a r a t e d i n t o d i f f e r - e n t g r o u p s o n t h e b a s i s of t h e s o l a r a l t i t u d e a n g l e ,P.
F i g . 1 ( a - e ) s h o w s t h e r e s u l t s f o r J u n e 1 9 6 7 for O . l < S i n @ < 0 . 3 , 0 . 3 < S i n P t 0 . 5 , 0 . 5 < S i n P < 0 . 7 , 0.7<
S i nP
<
0 . 9 a n d 0.9<
S i nP,
r e s p e c t i v e l y . T h e g e n e r a l form of t h e r e l a t i o n s h i p b e t w e e n I,,,/I TH a n d C C is s i m i l a r for t h e d i f f e r e n t v a l u e s of s o l a r t o b e e x p e c t e d a s t h e t o t a l s o l a r r a d i a t i o n i n c i d e n t o n a h o r i z o n t a l s u r f a c e is much l e s s a t t h e - l o w a l - t i t u d e a n g l e s a n d c o n s e q u e n t l y t h e c l o u d r e f l e c t e d c o m p o n e n t , w h i c h is q u i t e v a r i a b l e d e p e n d i n g o n t h e p o s i t i o n a n d t y p e of t h e c l o u d , a n d is a h i g h e r p r o p o r t i o n of t h e t o t a l f o r t h e l o w a l t i t u d e a n g l e s . A l l o f t h e p o i n t s i n F i g s . 1 ( c - e ) ( i e : s i nP
> 0 . 5 ) w e r e u s e d to d e t e r m i n e t h e c o e f f i c i e n t s P, Q a n d R i n t h e e x p r e s s i o n C C F = P+
Q.
C C+
R ( C C ) 2. ( 2 ) V a l u e s of P , Q a n d R for t h e o t h e r m o n t h s w e r e o b t a i n e d i n t h e s a m e m a y , a n d t h e v a l u e s for a l l four m o n t h s a r e g i v e n i n T a b l e I. T h e v a l u e of C C F g i v e n by E q 2 a n d t h e d a t a i n T a b l e I w e r e u s e d t o c a l c u l a t e I T H C , t h e s o l a r i n t e n s i t y t h a t c o u l d b e e x p e c t e d w i t h t h e o b s e r v e d c l o u d c o n d i - t i o n s for a l l t h e d a y l i g h t h o u r s d u r i n g e a c h month. T h e s e c o m p u t e d v a l u e s of I T H C vs t h e a c t u a l m e a s u r e d v a l u e s of I,,, a r e p l o t t e d i n F i g . 2 ( a - d ) . T h e s e g r a p h s s h o w t h a t a l l t h e p o i n t s f a l l i n a b a n d c e n t e r e d o n t h e 4 5 d e g l i n e . T h i s i n d i c a t e s t h a t t h e a b s o l u t e e r r o r i n t h e s o l a r i n t e n s i t y e s t i - m a t e d u s i n g t h e C C F b a s e d o n t h e h i g h s o l a r a l t i - t u d e m e a s u r e m e n t s is fairly c o n s t a n t r e g a r d l e s s of t h e a c t u a l s o l a r a l t i t u d e . F i g u r e 1 ( a - e ) a l s o s h o w s t h a t i t is not un- c o m m o n for t h e v a l u e of I,,, to e x c e e d t h e c a l c u - l a t e d I T H . . T h i s i n d i c a t e s t h a t t h e v a l u e s of I T H g i v e n by t h e f o r m u l a s i n t h e A S H R A E H A N D B O O K O F F U N D A M E N T A L S a r e n o t o v e r l y c o n s e r v a t i v e for d e s i g n p u r p o s e s . T h e f r e q u e n c y w i t h w h i c h t h e s e v a l u e s a r e e x c e e d e d s u g g e s t s t h a t t h e y s h o u l d p r o v i d e a r e a s o n a b l e b a s i s for c o m p u t i n g t h e l o a d s t h a t t h e a i r - c o n d i t i o n i n g s y s t e m n e e d s to b e a b l e t o h a n d l e . T A B L E I C O N S T A N T S IN E Q 2 F O R OTTAWA Month sin $3 PQ
R March 0.5 -0.9 1.06 0.012 -0.0084 June 0.5 - 1.0 0.96 0.033 -0.0106 September 0.5 - 0.9 0.95 0.030 -0.0108 December 0.3 - 0.5 1.14 0.003 -0.0082CLOUDLESS-SKY FACTOR
The formulas for calculating s o l a r intensity that are given in the ASHRAE HANDBOOK O F FUNDA- MENTALS a r e for average cloudless s k y condi- tions. Some localities have a very clean atmos- phere and consequently have higher than average solar i n t e n s i t i e s when the sky i s cloudless; and other places with an "industrial" atmosphere have l e s s than average solar intensities. T h e s e local peculiarities a r e taken into account by the Cloud Cover Factor. The value of C C F for a cloud cover of zero (ie: cloudless s k y ) can be considered the Cloudless-Sky Factor for the locality. T h e data analysis yields values of C C F for cloudy condi- tions a l s o e s t a b l i s h e s the value of this factor for cloudless conditions. This Cloudless-Sky Factor is just the constant term, P , in the polynomial re- lating C C F to cloud cover, a s used in Eq 2.
DIRECT AND DIFFUSE INTENSITIES
This study h a s only been concerned with the total solar radiation incident on a horizontal surface: there were no data on the direct or diffuse com- ponents separately. I t i s often necessary, how- ever, to be a b l e to estimate the direct and diffuse components separately. T h i s can be done for the cloudless sky by using the d a t a of Parmelee.4 The proportions of direct and sky-diffuse s o l a r radia-
tion given by the formulas in the ASHRAE HAND- BOOK O F FUNDAMENTALS are consistent with the information presented in Parlnelee's paper. Thus, if P turns out to be 1, the proportion of direct and diffuse should be appropriate. When P i s greater than 1, ie: the total solar radiation incident on a horizontal surface under a cloudless sky i s greater than the values indicated by the formulas in the ASHRAE HANDBOOK O F FUNDAMENTALS, the intensity of the diffuse solar radiation from the sky i s l e s s than that indicated by the formulas; and conversely when P i s l e s s than 1, the diffuse component i s larger than under the standard condi- tions. Parmelee showed that the diffuse and direct components for cloudless conditions are related by an expression of the form:
where X and Y are functions of the s o l a r altitude;
I d H and I D H are diffuse and direct s o l a r radiation on horizontal surfaces for cloudless s k y condi- tions, respectively.
Thus,
I T H = X
+
( 1 - Y ) I D H (4)If an
*
i s added to indicate that P i s other than unity, and no asterisk indicates P = 1, it followsthat
I*TH =
X
+
( 1 - Y)I*DH= P ~ X + ( ~ - Y ) I D H I (5)
The increase of direct component due to P larger than unitv i s Therefore and a s I D H - - - s i n ,8 I T H C t s i n P (9)
where C i s given in Table 8, p. 476 of Ref 1.
The function Y i s expressible by a second order polynomial in s i n ,8 viz:
Y = 0.309 - 0.137 s i n ,8
+
0.394 s i n 2 P , (11) thus K can be evaluated for any value o f s i nP.
It seems reasonable to assume that the direct component with a partly cloudy sky should be pro- portional to the fraction of the s k y that i s clear, a s explained in Ref 5. Thus for a partly cloudy sky
- C L O U D C O V E R ( C C ) Fig. 3 Dlrect a n d d i l l u s e c o m p o n e n t s o / C l o u d C o v e r F a c t o r ( C C F ) F i g .
3
s h o w s t h e m a g n i t u d e of t h e s e c o m p o n e n t s for a l o c a t i o n w i t h a c l o u d l e s s - s k y f a c t o r t h a t i s g r e a t e r t h a n 1. O n c e t h e d i r e c t a n d d i f f u s e c o m p o n e n t s of s o l a r r a d i a t i o n o n a h o r i z o n t a l s u r f a c e a r e k n o w n f o r c l o u d y d a y s , i t is p o s s i b l e t o e s t i m a t e both t h e c o m p o n e n t s o n a n y i n c l i n e d s u r f a c e u s i n g t h e s t a n d a r d f o r m u l a s as i n R e f 1.V A R I A T I O N O F C C F
T h e r e s u l t s g i v e n i n T a b l e I s h o w t h a t t h e r e is a s m a l l i n c r e a s e i n P d u r i n g D e c e m b e r a n d March c o m p a r e d w i t h t h e o t h e r m o n t h s . T h i s i n c r e a s e m a y be a s s o c i a t e d w i t h t h e f a c t t h a t t h e g r o u n d is c o v e r e d b y s n o w d u r i n g m o s t of D e c e m b e r a n d March. T h e h i g h a l b e d o for a s n o w - c o v e r e d s u r f a c e m e a n s t h a t a s u b s t a n t i a l p a r t of t h e s o l a r r a d i a t i o n-
--
-
- - - --
O t t a w a W i n n i p e g 1 1 9 6 7 1 1 1 9 6 6 1 M a r c h -.-.- - J u n e- -
S e p t e m b e r---
- - - - - - D e c e m b e r-
-
-
- - - - LFig. 4 C l o u d C o v e r F a c t o r /or /our m o n t h s at O t t a w a a n d Cl'innip eg f a l l i n g o n t h e s n o w s u r f a c e i s r e f l e c t e d b a c k to- w a r d t h e s k y w h e r e i t is a g a i n s c a t t e r e d a n d re- f l e c t e d , a n d s o c o n t r i b u t e s t o a g r e a t e r d i f f u s e s o l a r i n t e n s i t y t h a n w o u l d o c c u r o t h e r w i s e . I t is a l s o r e a s o n a b l e t o a s s u m e t h a t t h e r e a r e f e w e r d u s t a n d s m o k e p a r t i c l e s i n t h e a t m o s p h e r e d u r i n g t h e w i n t e r t h a n t h e s u m m e r . A l l o w a n c e is m a d e f o r t h i s s e a s o n a l v a r i a t i o n b y t h e v a l u e s of t h e A, B a n d C c o n s t a n t s i n t h e A S H R A E f o r m u l a s , b u t i t is p o s s i b l e t h a t t h i s s e a s o n a l e f f e c t is more pro- n o u n c e d a t O t t a w a . If t h e i n c r e a s e i n P i s d u e t o ground r e f l e c t i o n , t h e i n c r e a s e w o u l d b e i n t h e d i f - f u s e c o m p o n e n t , w h e r e a s if i t i s d u e t o l o w e r tur- b i d i t y of t h e a t m o s p h e r e , t h e d i r e c t c o m p o n e n t s h o u l d b e t h e o n e t h a t is i n c r e a s e d . S e p a r a t e m e a s u r e m e n t s of t h e d i f f u s e a n d d i r e c t c o m p o n e n t s I a r e n e e d e d t o i n d i c a t e w h i c h o n e c a u s e s t h e h i g h e r P d u r i n g t h e w i n t e r . B e c a u s e of t h i s u n c e r t a i n t y t h e O t t a w a r e s u l t s s h o u l d o n l y b e a p p l i e d t o a r e a s t h a t h a v e a s i m i l a r c l i m a t e . T h e g e o g r a p h i c a l v a r i a t i o n of t h e CCF v s CC r e l a t i o n s h i p w a s c h e c k e d by m a k i n g a v e r y l i m i t e d
s t u d y of s o m e d a t a for W i n n i p e g , M a n i t o b a (49'
5 4 '
N, 97' 1 4 'W).
I n t h i s c a s e , f o u r 1.0-day p e r i o d s w e r e u s e d r a t h e r t h a n c ~ m p l e t e m o n t h s . T h e re- s u l t s a r e s u m m z r i z e d i n F i g . 4 w h i c h s h o w s t h a t C C F is h i g h e r t h a n a t O t t z w a b u t t h e r e l a t i v e s e a s o n a l v a r i a t i o n is much t h e s a m e a s a t O t t a w a .CONCLUSION
T h e r e s u l t s of a n a n a l y s i s of f o u r m o n t h s of s o l a r r a d i a t i o n a n d c l o u d c o v e r r e c o r d s for o n e l o c a t i o n i n d i c a t e t h a t r a d i a t i o n i n t e n s i t i e s c a n b e e s t i m a t e d w h e n c l o u d c o v e r r e c o r d s a r e a v a i l a b l e . I t is a l s o p o s s i b l e t o e s t i m a t e t h e p r o p o r t i o n of t h e t o t a l s o l a r r a d i a t i o n f a l l i n g o n a h o r i z o n t a l s u r f a c e t h a t i s d u e t o t h e d i r e c t s o l a r b e a m a n d t h e p r o p o r t i o n d u e t o s k y s c a t t e r i n g a n d r e f l e c t i o n from t h e c l o u d s . T h e r e s u l t s a l s o s h o w t h a t t h e s o l a r in- t e n s i t y o n a p a r t l y c l o u d y d a y c a n b e h i g h e r t h a n o n a c o m p l e t e l y c l o u d l e s s d a y ; a n d t h a t t h i s maxi- C . W. P E N N I N G T O N ( D e p ' t . of Mech. E n g r . , U n i v . of F l o r i d a ) : I t s e e m s o b v i o u s t h a t t o c a l c u l a t e t h e h e a t - i n g a n d c o o l i n g l o a d s o n a b u i l d i n g i n o r d e r t o es- t i m a t e t h e e n e r g y r e q u i r e m e n t s , t h e s o l a r f l u x o n t h e s u r f a c e s of t h e b u i l d i n g m u s t b e known. T h e a u t h o r s h a v e s u g g e s t e d a m e t h o d by w h i c h t h i s s o l a r f l u x c a n b e m e a s u r e d o n a n h o u r by h o u r b a s i s . While t h e i r m e t h o d i n v o l v e s p e r s o n a l o b s e r v a t i o n a n d j u d g e m e n t f a c t o r s , t h e r e s u l t s a g r e e w e l l w i t h m e a s u r e d v a l u e s . R a t h e r t h a n d e p e n d u p o n v i s u a l o b s e r v a t i o n a n d j u d g e m e n t , i t a p p e a r s to me t h a t t h e a c t u a l s o l a r f l u x c o u l d a n d s h o u l d b e m e a s u r e d a n d r e c o r d e d . We h a v e b e e n r e c o r d i n g s o l a r i n t e n s i t i e s o n a h o r i z o n t a l s u r - f a c e f o r y e a r s a n d r e p o r t i n g d a i l y a n d m o n t h l y t o t a l s of s o l a r i n c i d e n c e t o t h e w e a t h e r b u r e a u . S i n c e t h e r e c o r d i n g is c o n t i n u o u s , hourly t o t a l s c o u l d b e re- p o r t e d a s w e l l . T h e c o s t of e q u i p m e n t is n o t e x c e s - s i v e . O u r e q u i p m e n t a t t h e U n i v e r s i t y of F l o r i d a c o s t less t h a n $ 2 , 0 0 0 , a n d c o m p a r a b l e e q u i p m e n t , a l t h o u g h p e r h a p s n o t a s a c c u r a t e , c a n b e p u r c h a s e d for less t h a n o n e - h a l f t h a t a m o u n t . mum c a n b e g r e a t e r t h a n t h e v a l u e i n d i c a t e d b y t h e A S H R A E f o r m u l a s . It w o u l d b e v e r y d e s i r a b l e t o h a v e a s i m i i a r s o r t of a n a l y s i s d o n e f o r s e v e r a l p l a c e s i n d i f f e r e n t p a r t s of North A m e r i c a .REFERENCES
1. ASHRAE HANDBOOK O F FUNDAMENTALS, 1967.
2. Monthly r a d i a t i o n summary, March, J u n e , September, December, 1967, Meteorological Branch, Departmenr of T r a n s p o r t , 315 Bloor St. W. Toronto 5, Ontario, C a n a d a .
3. Canada-Hourly Surface Observation R e c o r d s , March, J u n e , September, December, 1967, hleteorological Branch, Department of T r a n s p o r t , Toronto, Ontario, C a n a d a .
4. G. V. P a r m e l e e , Irradiation of V e r t i c a l and Hori- z o n t a l S u r f a c e s by D i f f u s e S o l a r Radiation from C l o u d l e s s S k i e s , ASHVE TRANSACTIONS, Vol. 60,
1954.
5. N. Robinson, (ed.) Solar Radiation, E l s e v i e r Pub- l i s h i n g Co., Amsterdam, 1966, p. 125. We w o u l d be p l e a s e d t o m a k e a s t u d y s i m i l a r t o t h a t m a d e f o r O t t a w a f o r o u r a r e a , n o r t h e r n F l o r i d a . If c l o u d c o v e r o b s e r v a t i o n s o n a n h o u r l y b a s i s a r e a v a i l a b l e from t h e W e a t h e r B u r e a u , t h e s e c o u l d b e u s e d for c o m p a r i s o n s of s o l a r i n t e n s i t i e s a l r e a d y re- c o r d e d . If s u c h o b s e r v a t i o n s a r e n o t a v a i l a b l e , i t w o u l d b e n e c e s s a r y to o b s e r v e a n d r e c o r d s o l a r i n - t e n s i t i e s o v e r t h e n e x t y e a r o r two. T h e s e o b s e r v a - t i o n s c o u l d b e e x t e n d e d t o i n c l u d e v e r t i c a l s u r f a c e s a n d s e p a r a t i o n i n t o d i f f u s e a n d d i r e c t . In e i t h e r c a s e , s o m e f i n a n c i a l s p o n s o r s h i p w o u l d b e n e c e s s a r y t o c o v e r s a l a r y c o s t s i n v o l v e d . T H E A U T H O R S : I t w o u l d c e r t a i n l y b e of g r e a t u s e t o h a v e a v a i l a b l e m e a s u r e m e n t s of s o l a r r a d i a t i o n a t m a n y d i f f e r e n t l o c a t i o n s f o r u s e i n e n e r g y c a l c u l a - t i o n s . If t h i s is u n d e r t a k e n t h e s e m e a s u r e m e n t s s h o u l d p r e f e r a b l y b e m a d e i n u r b a n d i s t r i c t s w h e r e t h e a t m o s p h e r e is q u i t e d i f f e r e n t from t h a t a t t h e c u r r e n t w e a t h e r s t a t i o n s w h i c h a r e u s u a l l y l o c a t e d a t a i r p o r t s .
T . KUSUDA ( N a t i o n a l B u r e a u of S t a n d a r d s , Washing- ton, D.C.): D r s . Kimura a n d S t e p h e n s o n s h o u l d be c o n g r a t u l a t e d for t h e i r e x c e l l e n t work o n t h i s timely s u b j e c t . A s t h e c h a i r m a n of t h e S u b c o m m i t t e e for H e a t i n g a n d C o o l i n g L o a d s for t h e ASHRAE T a s k
Group on E n e r g y R e q u i r e m e n t s , I c a n n o t e m p h a s i z e e n o u g h t h e i m p o r t a n c e of t h e e f f e c t of r a d i a t i o n t o t h e building e n e r g y requirement. C u r r e n t d a t a in the ASHRAE HANDBOOK O F FUNDAMENTALS a r e only for the c l o u d l e s s d a y s , a n d y e t most of t h e d a y s in t h e y e a r a r e c l o u d y d a y s w h e r e r a d i a t i o n d a t a a r e in- c o m p l e t e . T h e method s u g g e s t e d by t h e p a p e r for e s t i - mating t h e d i r e c t a n d d i f f u s e r a d i a t i o n under c l o u d y s k i e s s h o u l d be a n important f i r s t s t e p for t h i s most n e g l e c t e d a r e a . T h e S u b c o m m i t t e e for H e a t i n g a n d C o o l i n g L o a d C a l c u l a t i o n s i s p r o p o s i n g t o ASHRAE i n i t i a t i o n of r e s e a r c h p r o j e c t s for s i m i l a r s t u d i e s b a s e d upon t h e s o l a r d a t a i n t h e United S t a t e s . T H E AUTHORS: We a r e e x t r e m e l y i n t e r e s t e d t o h e a r o f t h e S u b c o m m i t t e e ' s p r o p o s a l c o n c e r n i n g i n i t i a t i o n o f a r e s e a r c h p r o j e c t i n t h e U n i t e d S t a t e s s i m i l a r t o our s t u d y . It w i l l b e i n t e r e s t i n g t o s e e how d i f f e r e n t t h e C C F c u r v e s w i l l b e from t h o s e w e o b t a i n e d i n our s t u d i e s . H. B. N O T T A G E (Prof. E n g . , U C L A ) : T h i n g s i n e n - v i r o n m e n t a l r e a l i t i e s a r e i n h e r e n t l y s t o c h a s t i c . T h e u s e of s t o c h a s t i c i n p u t s for d e s i g n a n a l y s e s i s a n important p r a c t i c a l n e e d . What e x p e r i e n c e s h a v e t h e a u t h o r s h a d in a s t a t i s t i c a l t r e a t m e n t of t h e d a t a ?
What p r a c t i c a l s i g n i f i c a n c e may b e inferred in r e g a r d to s t a t i s t i c a l a s p e c t s ? If l e a s t s q u a r e s f i t t i n g , for e x a m p l e , p r o v e s to be d i s c o u r a g i n g , w h a t s o r t of a p p r o a c h might be c o n s i d e r e d ? A s t h e n e e d f o r ex- t e n s i v e d a t a i s e m p h a s i z e d , might o t h e r " s e c o n d a r y - importance" v a r i a b l e s b e i n t r o d u c e d a n d m e a s u r e d ? T H E AUTHORS: T h e l e a s t s q u a r e s method w a s f i r s t u s e d to c a l c u l a t e the c o e f f i c i e n t s of s e c o n d o r d e r p o l y n o m i a l s w h e r e a l l t h e p o i n t s w e r e e q u a l l y w e i g h t e d . T h e c u r v e d e r i v e d from t h i s polynomial d i d n o t a g r e e w e l l with t h e d a t a a t higher s o l a r in- t e n s i t y , probably a s a r e s u l t of f e w e r d a t a p o i n t s f o r h i g h e r s o l a r i n t e n s i t y . C o n s e q u e n t l y h i g h e r order p o l y n o m i a l s were c a l c u l a t e d u s i n g t h e l e a s t s q u a r e s method. T h e error a t h i g h e r s o l a r i n t e n s i t i e s , h o w e v e r , s t i l l r e m a i n e d a p p r o x i m a t e l y t h e s a m e as w i t h t h e s e c o n d o r d e r polynomials. Weighting of t h e d a t a p o i n t s w a s c o n s i d e r e d . T h i s would h a v e involved s u b j e c t i v e judgement, h o w e v e r , i n s e l e c t i n g t h e s e w e i g h t s . An a t t e m p t w a s then made t o t a k e a c c o u n t of medium h e i g h t c l o u d s , b u t t h e c o r r e l a t i o n did n o t improve s i g n i f i c a n t l y . We t h i n k that t h e c o r r e l a t i o n c o u l d b e improved i t more of t h e r e c o r d s c o n c e r n i n g t h e t y p e a n d h e i g h t of c l o u d s w e r e t a k e n i n t o a c c o u n t . T h e c l o u d o b s e r v a t i o n d a t a as e x p r e s s e d by 1 t o 10 s c a l e d o n o t s e e m s u f f i c i e n t l y a c c u r a t e t o u s e a s a b a s i s for e x a c t r e l a t i o n s h i p s . In a d d i t i o n , w e b e l i e v e t h a t s i m p l i c i t y of method i s o n e of the primary re- q u i r e m e n t s ; t h e r e f o r e r e s u l t s b a s e d o n more e x t e n s i v e c o r r e l a t i o n p r o c e d u r e s w e r e n o t i n c l u d e d i n t h i s p r e s - e n t a t i o n .
R E P R I N T E D F R O M TRANSACTIONS, VOL. 75, P A R T I,
1969,
BYPERMISSION O F T H E AMERICAN SOCIETY O F HEATING, REFRIGERATING AND AIR-CONDITIONING ENGINEERS, INC. ASHRAE DOES NOT NECESSARILY A G R E E WITH T H E S T A T E - MENTS OR OPINIONS ADVANCED A T MEETINGS OR P R I N T E D IN ITS PUBLICATION.
