No. 2106
D. G. STEPHENSON
ASHRAE
Member
Solar Radiation on Cloudy Days
S o l a r radiation i s o n e of the most important comp 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 building through t h e windows 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 the building. Therefore, 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 building d e s i g n , particularly in t h e des i g n of t h e air-conditioning s y s t e m . A s s o l a r radiation r e c o r d s a r e a v a i l a b l e for only a very limited
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 find
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 int e n s i t y f o r l o c a t i o n s where r e c o r d s a r e not a v a i l a b l e .
T h e ASHRAE T a s k Group on E n e r g y Requirements 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 developing a procedure for c a l c u l a t i n g energy requirements 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 made 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 amount,
but n o t s o l a r i n t e n s i t y . It i s n e c e s s a r y , therefore,
to try to i n f e r the 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 pilot s t u d y t h a t w a s made 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
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 on a
horizontal 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 horizontal s u r f a c e on cloudy 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 that would 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 int e n s i t y by a factor t h a t d e p e n d s on t h e cloud cover.
T h i s f a c t o r i s c a l l e d the cloud c o v e r f a c t o r (CCF).
T h u s t h e s o l a r radiation o n a horizontal s u r f a c e for
cloudy 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)
where 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 horizont a l s u r f a c e given by t h e formulas a n d d a t a in 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, therefore, is to d e t e r m i n e C C F
a s a function of c l o u d cover. T h i s c a n be d o n e by
u s i n g t h e recorded v a l u e s of the total s o l a r intens i t y on a horizontal 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 with the cloud c o v e r r e c o r d s on
a n hourly b a s i s .
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, Building 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 contribution 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 approval of t h e Director of the D i v i s i o n . T h i s paper was prepared 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.
DATA USED
An a n a l y s i s of t h i s .type w a s made u s i n g t h e s o l a r
radiation 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 ,
Ontario (45' 2 7 ' N , 75' 37'W) t h a t a r e p u b l i s h e d by
the Meteorological 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 horzzon~alsurface
to amount calculated for cloudless day for Srn P:
(a)O.I -0.3, ( b ) 0 . 3 -0.5, (c)O.5 - 0 . 7 , ( d ) 0 . 7 - 0 . 9 ,
and ( e ) 0.9 - 1.0
0
20
40
0
20
40
I rec
60
80
100
(Langleylhr)
LEGEND OF SYMBOLS
IN FIGURES 1 - 2
Symbol
S~np
*
+
o
0
0. 9
0. 7
0.5
0. 3
0. 1
- 1.0
- 0. 9
- 0. 7
- 0.5
- 0. 3
Flg. 2 Correlatzon between calculnted rrldlatlon based
on C C F and recorded radzatzon on horzzontal sur/ace
/or all d n y l ~ g k thours zn ( a ) cblarck 1967, ( b ) l u n e 1967,
( c ) September 1967, and ( d ) Decernber 1967
60
Irec
0
20
40
60
'rec
80
100
(Langleylhr)
80
100
(Langleylhr)
ment of Transport2.3. T h e r a d i a t i o n v a l u e s a r e
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 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 recorder t h a t g i v e s
the total s o l a r radiation incident on a horizontal
s u r f a c e d u r i n g a period of o n e hour e n d i n g o n t h e
hour 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 obs e r v a t i o n s a r e m a d e e v e r y hour (Standard 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 amount 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 the 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
available on punched c a r d s s o the a n a l y s i s could
b e made 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
there 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 (CC).
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 hour 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 by 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
the 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 hour d u r i n g w h i c h I,,, w a s m e a s u r e d . Similarly,
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
Irec/~TH
Was 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 beg 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
made in Standard T i m e rather than in Apparent
Solar Time.
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 rocumulus. 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 very 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
cloud cover. T h e value of C C defined in this way
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
not g i v e n i n t h e r e c o r d s for s t a t i o n s i n t h e U n i t e d
States.
I
I
I
a l t i t u d e but t h e s c a t t e r of the p o i n t s a r e s u b s t a n t i a l l y l o w e r for 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
to b e expected a s the total s o l a r radiation incident
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 altitude a n g l e s and consequently the cloud reflected
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
proportion 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 n P > 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
in the 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 months 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
used to c a l c u l a t e ITHC, the s o l a r intensity that
could 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 condit 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 ITHC 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 graphs show that a l l the points fall in a
band c e n t e r e d o n t h e 4 5 d e g line. T h i s i n d i c a t e s
that the a b s o l u t e error in t h e s o l a r intensity estimated 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 tude 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
the 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 uncommon 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
given by t h e f o r m u l a s i n t h e A S H R A E HANDBOOK
O F F U N D A M E N T A L S a r e n o t overly 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 they
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
the l o a d s that the air-conditioning 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 .
TABLE I
RESULTS
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 differe 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< Sin @<0.3, 0.3< Sin P t 0 . 5 , 0.5< Sin P < 0 . 7 ,
0.7 < S i n P < 0.9 a n d 0.9 < S i n P, 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
C O N S T A N T S IN E Q 2 F O R OTTAWA
sin $3
P
Q
March
June
September
0.5 -0.9
0.5 - 1.0
0.012
0.033
-0.0084
-0.0106
0.5 - 0.9
1.06
0.96
0.95
0.030
-0.0108
December
0.3 - 0.5
1.14
0.003
-0.0082
Month
R
CLOUDLESS-SKY FACTOR
The formulas for calculating solar intensity that
are given in the ASHRAE HANDBOOK O F FUNDAMENTALS are for average cloudless sky conditions. Some localities have a very clean atmosphere and consequently have higher than average
solar intensities when the sky i s cloudless; and
other places with an "industrial" atmosphere have
l e s s than average solar intensities. These local
peculiarities are taken into account by the Cloud
Cover Factor. The value of C C F for a cloud cover
of zero (ie: cloudless sky) can be considered the
Cloudless-Sky Factor for the locality. T h e data
analysis yields values of CCF for cloudy conditions a l s o establishes the value of this factor for
cloudless conditions. This Cloudless-Sky Factor
is just the constant term, P , in the polynomial relating C C F to cloud cover, a s used in Eq 2.
IdH and I D H are diffuse and direct solar radiation
on horizontal surfaces for cloudless sky conditions, respectively.
Thus,
ITH = X + (1 - Y)IDH
(4)
If an * i s added to indicate that P i s other than
unity, and no asterisk indicates P = 1, it follows
that
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
DIRECT AND DIFFUSE INTENSITIES
This study has only been concerned with the total
solar radiation incident on a horizontal surface:
there were no data on the direct or diffuse components separately. I t i s often necessary, however, to be able to estimate the direct and diffuse
components separately. T h i s can be done for the
cloudless sky by using the data of Parmelee.4 The
proportions of direct and sky-diffuse solar radiation given by the formulas in the ASHRAE HANDBOOK OF 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 OF 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 conditions. 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 solar altitude;
Therefore
and a s
-I D
-H -
ITH
s i n ,8
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 sin ,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 of sin P.
It seems reasonable to assume that the direct
component with a partly cloudy sky should be proportional to the fraction of the sky that i s clear, a s
explained in Ref 5. Thus for a partly cloudy sky
and
-
-
-
-
-
-
March
June
September
December
Ottawa
Winnipeg
119671
119661
-.-.-
------ - - - - - - - - - --
L
Fig. 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
and Cl'innip eg
-CLOUD
COVER
(CC)
Fig. 3 Dlrect and 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
Factor ( C C F )
F i g . 3 s h o w s t h e magnitude 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 known for
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
components on any inclined s u r f a c e using the
s t a n d a r d f o r m u l a s as i n Ref 1.
VARIATION 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 months. T h i s i n c r e a s e may
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 ground is
c o v e r e d by 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 part of t h e s o l a r r a d i a t i o n
I
falling 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 toward 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 reflected, and s o contributes to a greater diffuse
s o l a r i n t e n s i t y t h a n would o c c u r o t h e r w i s e . It is
a l s o reasonable to a s s u m e that there are fewer
dust and smoke particles in the atmosphere during
t h e w i n t e r t h a n t h e summer. A l l o w a n c e is made for
t h i s s e a s o n a l v a r i a t i o n by 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 , but 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 pron 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 would b e i n t h e diff 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 turbidity 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
are needed to indicate which one c a u s e s the higher
P during 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
Ottawa results should only be applied to a r e a s that
have a similar climate.
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 Winnipeg, Manitoba (49' 54'
N, 97' 1 4 ' W). In t h i s c a s e , four 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 em o n t h s . T h e res u l t s a r e summzrized in Fig. 4 which s h o w s that
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 four 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
indicate that radiation intensities c a n b e estimated
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 . It 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 proportion of t h e t o t a l
s o l a r radiation falling on a horizontal surface that
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 proportion
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 intensity on a partly cloudy d a y c a n b e higher than
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. Engr., Univ. of
Florida): It s e e m s obvious that to calculate the heati 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 estimate the energy requirements, the s o l a r flux on the
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 method 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
method 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 judgement
factors, the r e s u l t s a g r e e w e l l with measured values.
Rather than depend upon v i s u a l observation and
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 formulas. It would 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 for 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 radiation summary, March, J u n e , September,
December, 1967, Meteorological Branch, Departmenr
of Transport, 315 Bloor St. W. Toronto 5, Ontario,
Canada.
3. Canada-Hourly Surface Observation Records, March,
J u n e , September, December, 1967, hleteorological
Branch, Department of Transport, Toronto, Ontario,
Canada.
4. G. V. P a r m e l e e , Irradiation of Vertical and Horizontal S u r f a c e s by D i f f u s e Solar 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 Publishing Co., Amsterdam, 1966, p. 125.
We would 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 for O t t a w a for o u r a r e a , northern 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 hourly b a s i s a r e
a v a i l a b l e from t h e Weather 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 rec 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
would b e n e c e s s a r y to o b s e r v e a n d record 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 tions could b e extended to include vertical s u r f a c e s
and separation into diffuse and direct.
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 flux
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
been recording solar intensities on a horizontal surf a c e for 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 monthly 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 bureau. S i n c e t h e
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 would
b e necessary t o cover salary c o s t s involved.
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 rep 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 $2,000, 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
many different locations for u s e in energy calculat 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
should preferably b e made in urban d i s t r i c t s where
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
current weather s t a t i o n s which a r e usually located
a t airports.
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 amount.
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
T . KUSUDA (National Bureau of S t a n d a r d s , Washington, D.C.): Drs. 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 their e x c e l l e n t work on t h i s timely
s u b j e c t . A s t h e chairman of the Subcommittee for
H e a t i n g and Cooling L o a d s for t h e ASHRAE T a s k
Group on Energy 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
enough t h e importance of the e f f e c t of radiation t o the
building energy requirement. Current 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 cloudy d a y s where radiation d a t a a r e incomplete. T h e method s u g g e s t e d by t h e paper 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 radiation under cloudy
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
neglected area.
T h e Subcommittee for Heating 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 proposing t o ASHRAE initiation 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 in the United S t a t e s .
T H E AUTHORS: We a r e extremely i n t e r e s t e d t o h e a r
of the Subcommittee's p r o p o s a l concerning i n i t i a t i o n
of a r e s e a r c h project in 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 will b e i n t e r e s t i n g t o see how different
the C C F c u r v e s w i l l b e from t h o s e w e obtained in
our s t u d i e s .
H. B. N O T T A G E (Prof. Eng., UCLA): T h i n g s in e n vironmental r e a l i t i e s a r e inherently 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 need. 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 had in a s t a t i s t i c a l treatment of the 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 regard
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 fitting, for
example, 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 for ext 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 "secondaryimportance" v a r i a b l e s b e introduced 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 order
polynomials where a l l t h e p o i n t s w e r e e q u a l l y
weighted. T h e c u r v e d e r i v e d from t h i s polynomial
d i d not a g r e e w e l l with the d a t a a t higher s o l a r int e n s i t y , probably a s a r e s u l t of fewer d a t a points for
higher s o l a r intensity. C o n s e q u e n t l y higher order
polynomials 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 higher s o l a r i n t e n s i t i e s , however,
s t i l l remained approximately t h e s a m e as with t h e
s e c o n d order 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, however, in s e l e c t i n g t h e s e
weights. 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 height c l o u d s , b u t the 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 think that t h e correlation
c o u l d b e improved i t more of t h e records c o n c e r n i n g
t h e type 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 observation 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 not 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 requirements; therefore r e s u l t s b a s e d o n more e x t e n s i v e
correlation p r o c e d u r e s w e r e not included in t h i s presentation.
R E P R I N T E D F R O M TRANSACTIONS, VOL. 75, P A R T I, 1969, BY
PERMISSION 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.