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Solar radiation in peninsular Malaysia—Statistical presentations
Eneroy Coneers. M qmt Vol. 22, pp. 71 to 84, 1982
0196-8904/82/010071-14503.00/0 Pergamon Press Ltd
Printed in Great Britain
SOLAR RADIATION IN P E N I N S U L A R MALAYSIA--STATISTICAL PRESENTATIONS D O N A L D G . S. C H U A H a n d S. L. LEE School of Physics and School of Mathematical Science, Universiti Sains Malaysia, Penang, Malaysia (Received 20 July 1981)
Abstract--Statistical presentations of solar radiation data from three major stations in Peninsular Malaysia are given. These data are presented in several ways that will be useful in the design and performance study of solar energy conversion devices. Solar radiation Statistical presentations Solar energy utilisation radiation Transitions persistence Radiation classes
Design performance
Daily total
coast while Kota Baru is in the east coast. The stations in Penang and Kota Baru are situated near the sea, while the stations in Kuala Lumpur are situated in the land mass (see Map 1).
INTRODUCTION Information on solar radiation is essential in the design and study of solar energy utilization systems. In this paper statistical presentations of radiation data from three major cities in Peninsular Malaysia, viz Kuala Lumpur (3c07'N, 101 ~ 3YE). Penang (5: 18'N, 10ft 16'E) and Kota Baru (6: 10'N, 102 ~ 17'E) are given. These data are presented in several ways that will be useful in the design and performance study of solar energy utilization systems for implementation under local conditions. These presentations include frequencies of periods of successive days of daily total radiation below arbitrarily fixed values, the expected number of days in which the total radiation falls within arbitrarily fixed intervals and probabilities of transitions and persistence in radiation classes. Similar studies have been carried out for Thailand [5] and Singapore I-6].
R E L A T I O N S B E T W E E N SOLAR RADIATION AND DURATION OF SUNSHINE The simplest relationship between the daily total radiation Q and the daily duration of sunshine S is the linear relation
Q
--
Q•
s
(1)
= a + b --
S.
GEOGRAPHICAL FEATURES Peninsular Malaysia is a peninsular stretching from latitude 1: 20'N to 6: 40'N, and longitude 99 ~ 35'E to 10= 20'E, and has a tropical type, wet and dry climate. The land mass is divided into the east and" west coasts by the main range running from north to south. The South-West Monsoon brings rain and cloud to the west coast from June to early October while the North-East Monsoon brings rain and cloud to the east coast from November to March. Ther~ore, the west coast is dry from November to March while the east coast is dry from June to September. During the dry season, the climate is hot and sunny (the average monthly temperatures are shown in Table 7) with intermittent breaks of cloud formation and hence rainfalls in t h e l a t e afternoons due to convection currents. The three cities where data are available are situated in regions of different geographical conditions. Penang and Kuala Lumpur are in the west r,(.~l. 2 2 I
r
KUALA TI~N~ I
IPOH• • (;AIdl litON HIGHLAND
LWAN
KDANTAN • KUALA LUIdPUR
t
m
SINGAPORE
MOp I I_ocolions of $1oli0n$. • ROdiohOn ~ Sun|hl~ DOIO Aveik~011m • Sunshiml DOra AVOillble o Cloudiness Doto Avoifoble
71
72
C H U A H AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
developed by A n g s t r o m [ I ] , where Q = a m o u n t of radiation received per day o n the earth surface at a particular location, Q,, = a m o u n t o f radiation available per day at the same location in the a b s e n c e o f a t m o s p h e r i c effect,
S,. = m a x i m u m n u m b e r o f h o u r s o f sunshine that are possible at the site on the s a m e day. T h e c o n s t a n t s a and b for the three stations are c o m p u t e d in [3], w h e r e radiation a m o u n t s for t o w n s without radiation d a t a are also o b t a i n e d by extrapo-
Table 1. Frequencies and expected frequencies (occurrences per year) of periods of successive days of total radiation Q (mWh cm-2) below specified values (a) Station: Penang, Lat. 5 c 18'N Long. 100 16'E Ht. 3 m above S.L. Length of occurrences (No. of days)
Radiation Q ~<
1975
1976
1977
1978
Mean .¥
95°0 confidence interval
I 2 3 1 2 3 4
200 200 200 300 300 300 300
1 2 0 17 5 0 0
7 0 0 17 3 1 0
3 1 0 10 5 0 0
8 0 0 17 5 1 0
4.75 0.75 0 15.25 4.5 0.5 0
(0, 10.00t (0, 2.27) (0, 0t (9.69, 20.81) (2.91, 6.09} (0.21, 0.79) (0, 0)
1 2 3 4 5 6
400 400 400 400 400 400
33 12 4 0 1 0
27 10 4 1 0 0
36 2 2 0 2 0
25 15 5 1 0 0
30.25 9.75 3.75 0.5 0.75 0
(22.10, 38.40) (0.91, 18.59) (1.76, 5.74) (0.21, 0.79} (0, 2.27) (0, O)
(b) Station: Kota Baru, Lat. 6 10'N Long. 102 17'E Ht. 5 m above S.L. Length of occurrences (No. of days)
Radiation Q ~<
1975
1976
1977
1978
Mean .~
95°0 confidence interval
1 2 3 4 5 6 7 1 2 3 4 5 6 7 8
200 200 200 200 200 200 200 300 300 300 300 300 300 300 300
18 3 1 0 1 0 0 16 5 0 3 1 1 1 0
7 2 1 0 1 1 0 10 4 2 0 1 1 0 0
8 3 0 0 0 0 0 18 6 1 1 0 0 0 0
3 0 3 1 0 0 0 10 8 2 1 0 0 0 0
9.0 2.0 1.25 0.25 0.5 0.25 0 13.5 5.75 1.25 1.25 0.5 0.5 0.25 0
(0, 19.141 (0, 4.25) (0, 3.25) (0, 1.051 (0.21, 0.791 10, 1.05) (0, 0) (6.94, 20.06) (0, 8.471 {0.52, 1.981 (0, 3.25) (0.21, 0.79) (0.2 !, 0.791 (0, 1.051 (0, O)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
28 5 2 0 2 0 2 0 0 0 0 1 0 0 1
28 11 4 3 0 0 0 1 0 0 0 0 0 1 0
24 10 6 3 1 1 1 0 0 0 0 0 0 0 0
36 12 2 3 1 0 0 0 0 0 0 0 0 0" 0
29.00 9.5 3.5 2.25 1.0 0.25 0.75 0.25 0 0 0 0.25 0 0.25 0.25
(21.00, 37.00) (4.56, 14.44) (0.46, 6.54) (0, 4.64) (0, 2.30) (0, 1.05) C0, 1.80) {0. 1.05) (0, 0) (0, 0) (0, 0) {0, 1.05) {0, 0) CO, 1.05) (0, 1.05)
CHUAH AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
73
(c) Station: Kuala Lumpur, Lat. 3° 07'N Long. 101 33'E Ht. 19 rn above S.L. Length of occurrences (No. of days)
Radiation Q ~<
1975
1976
1977
1978
Mean .~
95';~ confidence interval
1 2 3 1 2 3 4 5 1 2 3 4 5 6 7
200 200 200 300 300 300 300 300 400 400 400 400 400 400 400
5 1 0 15 1 0 0 0 37 9 3 2 0 0 0
8 0 0 26 2 0 0 0 45 10 4 2 0 I 0
5 0 0 16 1 0 0 0 43 13 2 3 1 0 0
4 0 0 14 1 1 0 0 53 13 9 1 1 0 0
5.50 0.25 0 17.75 1.25 0.25 0 0 44.50 11.25 4.50 2.00 0.5 0.25 0
(2.75, 8.25) (0, 1.05) (0, O) (14.31, 21.19) (0.45, 2.05) (0, 1.05) (0, O) (0, O) (33.99, 55.01) (7.97, 14.53) (0, 9.44) (0.70, 3.30) (0.21, 0.79) (0, 1.05) (0, O)
lations a n d interpolations. Regression analysis using cubic spline functions is presented in [4]. However these studies yield only the monthly means and totals of solar radiation available at the regions under consideration, and the stochastic components are not taken into account, and therefore these results are not enough for effective design and study of solar utilization systems, and the presentation in this paper supplements the results of our earlier papers [3, 4]. EXPECTED FREQUENCIES OF O C C U R R E N C E O F S U C C E S S I V E DAYS O F
TOTAL RADIATION BELOW (ABOVE) ARBITRARILY FIXED VALUES Knowledge of the frequencies of occurrence of periods of successive days with low radiation is
required for the performance study of solar installations and also such calculations as storage requirements [2, 7]. Such information, based on daily records of 1975-1978 for Penang, Kota Baru and Kuala Lumpur is presented in Tables l(a), l(b), l(c), 2(a), 2(b) and 2(c) and the results of Tables l(a), l(b) and l(c) are also presented graphically. For the sake of discussion, we shall call the n u m b e r of days in an occurrence of a period of successive days with radiations b61ow (or above) specified values, the length of the occurrence. Tables l(a), l(b), l(c) show a year=to-year analysis of the frequencies of occurrence of various length in which the daily radiations are below the energy levels of 2 0 0 m W h c m - 2 , 300 m W h c m - 2 and 400 m W h cm -2 for the stations in Penang, Kota Baru and Kuala L u m p u r respectively. The sample mean for the frequencies of occur-
Table 2. Frequencies and expected frequencies (occurrences per year) of periods of successive days of total radiation Q (mWh cm-2) below specified values* Ca) Station: Penang, Lat. 5: 18'N Long. 10ft 16'E Hr. 3 m above S.L. Length of occurrences (No. of days)
Radiation Q ~<
1975
1976
1977
1978
Mean ~
95'~Jhconfidence interval
1 2 3 1 2 3 4 1 2 3 4 5 6
200 200 200 300 300 300 300 400 400 400 400 400 400
5 2 0 27 5 0 0 74 24 7 2 1 0
7 0 0 26 5 1 0 63 21 6 1 0 0
5 1 0 20 5 0 0 56 14 8 4 2 0
8 0 0 30 7 1 0 74 28 7 1 0 0
6.25 0.75 0 25.75 5.50 0.50 0 66.75 21.75 7.00 ZOO 0.75 0
(3.87, 8.63) (0, 2.27) (0, 0) C19.0K 32.42) (3.91, 7.09) (0.21, 0.79) (0, 0) (52.70, 80.80) (12,36, 31.14) (6.08, 7.92) ( 1.29.2.71 ) C0, 2.27) (0, 0)
* Frequency counts involve also occurrences obtained from those of bigger lengths.
74
C H U A H AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
(b) Station: Kota Baru, Lat. 6 10'N Long. 102 17'E Ht. 5 m above S.L. Length of occurrences (No. of days)
Radiation Q ~<
1975
1976
1977
1978
Mean ~
1 2 3 4 5 6 7 I 2 3 4 5 6 7 8
200 200 200 200 200 200 200 300 300 300 300 300 300 300 300
32 9 4 2 I 0 0 56 29 18 12 6 3 1 0
25 13 8 5 3 1 0 35 17 9 5 3 1 0 0
14 3 0 0 0 0 0 37 11 3 ! 0 0 0 0
16 9 5 1 0 0 0 36 15 4 1 0 0 0 0
21.75 8.50 4.25 2.00 1.00 0.25 0.00 41.00 18.00 8.50 4.75 2.25 1.00 0.25 0.00
(8.49, 35.01) (1.95, 15.06) (0, 9.50) (0, 5.43) (0, 3.25) (0, 1.05) (0, 0) (25.05, 56.95) (5.68.30.32) (0, 19.40) (0, 13.00) (0, 6.82) (0, 3.27) (0, 1.05) (0, 0)
I 2 3 4 5 6 7 8 9 10 11 12 13 14 15
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
95 54 41 33 27 21 17 13 11 9 7 5 3 2 1
96 48 28 19 14 12 10 8 6 5 4 3 2 1 0
92 46 24 12 6 3 I 0 0 0 0 0 0 0 0
83 29 11 5 1 0 0 0 0 0 0 0 0 0 0
91.50 44.25 26.00 17.25 12.00 9.00 7.00 5.25 4.25 3.50 2.75 2.00 1.25 0.75 0.25
(82.09, 100.91) (27.21, 61.29) (6.35, 45.65) (0, 36.26) (0,31.12) (0, 24.08) (0. 19.79) (0, 15.42) (0, 12.70) (0, 10.43) (0, 8.16) (0, 5.89) (0, 3.63) (0, 2.18) (0, 1.05)
95?,0 confidence interval
(C) Station: Kuala Lumpur, Lat. 3 07'N Long. 101 33'E Hr. 19 m above S.L. Length of occurrences (No. of days)
Radiation Q ~<
1975
1976
1977
1978
Mean .~
1 2 3
200 200 200
7 1 0
8 0 0
5 0 0
4 0 0
5.75 0.25 0
1 2 3 4 5 I 2 3 4 5 6 7
300 300 300 300 300 400 400 400 400 400 400 400
21 4 2 1 0 72 21 7 2 0 0 0
30 2 0 0 0 91 29 12 5 2 I 0
18 1 0 0 0 92 30 11 5 1 0 0
19 3 1 0 0 " 115 38 14 3 1 0 0
17.5 2.5 0.75 0.25 0.00 92.5 29.5 11.00 3.75 1.00 0.25 0.00
rence for each length below each energy level is also given, and a 95°o confidence interval for the m e a n is c o m p u t e d . This provides useful i n f o r m a t i o n for the p e r f o r m a n c e prediction o f solar energy utilization systems. F o r easy reference Tables 2(a), 2(b) a n d 2(c) give the frequency counts which involve occurrences o b t a i n e d from those o f bigger lengths. F o r instance for each
95°0 confidence interval (2.82, 8.69) (0, 1.051 (0, 0) (8.15.29.49) (0.45, 4.55) (0, 2.27) (0, 1.05) (0, 0) (64.52, 120.48) (18.45.40.55) (6.32, 15.68) (1.99, 5.51) (0, 2.30) (0, 1.05) (0, 0)
o c c u r r e n c e of length I, there are two occurrences o f length 1 - 1, three occurrences o f I - 2 a n d so on. Tables 3(a), 3(b), 3(c) give the year-to-year analysis o f the frequencies o f o c c u r r e n c e o f periods o f successive days o f total daily radiation a b o v e the energy level o f 4 0 0 m W h c m 2 a n d 500 m W h c m - 2 . This inform a t i o n will also be helpful in the design o f solar energy utilization systems.
CHUAH AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
40
30
o
~20
1975
?
1976
1977
1978
MEAN
La
;o
o
5
1o
o
~
;o
o
~
,o
o ~
,o
o
~
;o
Number of succtssive days.
Histograms of frequencies (occurrences per year) of periods of successive days of total radiation below 2 0 0 m W h c m -2. Table l(a), Penang.
40
30
b
20 1975
i
1976
1977
1978
M EA N
:)
g o I0--
O--
0
5
I0
0
5
I'0
o
s,o
0
5
I0
5
IO
Nu'~bef Of SUCCeSSive OQy$
Histograms of frequencies (occurrences per year) of periods of successive days of total radiation below 300mW hcm -2. Table I(a). Penang.
75
76
CHUAH AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
401975
1976
19 77
1978
M[AN
30
o 2O
u
~ ~o
Illl
fl 5
5
io
I0
0
5
o I0
0
5
Number of
I0
0
successive
5
I0
clays
Histograms of frequencies (occurrences per year) of periods of successive days of total radiation below 4 0 0 m W h c m -2. Table l(a), Penang.
40
30
1975
o
1976
1977
1978
MEAN
2o
~o
o
5
io
o ;
i'o
o ~,;
o
~ ;o
o s ,'o
Number of ,%ccese~ve Days
Histograms of frequencies (occurrences per year) of periods of successive days of total radiation below 200row h cm -2. Table l(b), Kota Bharu.
CHUAH AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
I .11 a 20
1975
1976
1977
1979
MEAN
u I0
I ,
0
5
IO
0
5
i0
0
5
I'O
o
~ 1'o
o
s ,o
Number of successive doys
Histograms of frequencies (occurrences per year) of periods of successive days of total radiation below 3 0 0 m W h c m -2, Table l(b). Kota Bharu.
401975
1976
1977
1978
MEAN
30 I
o b=
8
o
I0
0
5
I0
15
0
S
I0 I |
0
§
I0
15 0
i
I0 15
0
Number of successive
5
I'0
15
doys'
Histograms of frequencies (occurrences per y e a r ) o f pel'iods of successive days of total radiation below 3 0 0 m W h c m -2. Table lib). Kota Bharu.
77
78
CHUAH AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
40--
30
b o b
20
=) e.,
I0
1975
0
1976
5
I0
0
1977
5
I0
0
19711
5
I0
0
MEA N
.5
I0
0
S
I0
Number of Successive
O0ys.
Histograms of frequencies (occurrences per year) of periods of successive days of total radiation below 2 0 0 m W h c m -2, Table l(c). Kuala Lumpur.
40--
50
1975
1976
1977
1978
MEAN
20 b
b
I0
in 0
l S
, I0
0
, S
i I0
,
0
'5
I0
i
S
I0
Number of successive
0
5
i
IO
d0ys
Histograms of frequencies {occurrences per year) of periods of successive days of total radiation below 3 0 0 m W h c m -2, Table l(c), Kuala Lumpur.
CHUAH AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
79
60-
1975
1976
1977
MEAN
1978
50
40
30
20
:) u
I0
Itn i
0
5
I0
0
S
I0
0
S
I0
0
5
I0
0
5
I0
Nun~bQ¢ O| Su(:¢e&$ive doyl
Histograms of frequencies (occurrences per year) of periods of successive days of total radiation below 400mW hem -2. Table l(c). Kuala Lumpur.
E X P E C T E D N U M B E R O F DAYS IN A M O N T H IN WHICTI R A D I A T I O N F A L L S W I T H I N S P E C I F I E D VALUES The variation of daily radiation from month-tomonth is shown in Tables 4(a), 4(b) and 4(c) for the stations in Penang, Kota Baru and Kuala Lumpur respectively. Solar radiation amounts ranging from 0 to 7 5 0 m W h c m -2 are divided into intervals of 50 mWh cm -2, and the expected number of days in a month and year in which daily total falls within each interval are computed. M O N T H L Y ANALYSIS O F PERSISTENCE AND TRANSITION IN SOLAR R A D I A T I O N Solar radiation amounts ranging from 0 to 750 are divided into three classes. Class A contains daily total
radiations greater than 500 mWh c m - 2 class B contains daily total radiations between 300 and 500 mWh c m - 2 and class C contains daily total radiation less than 300 mWh cm -2. The event of transition of daily total radiation from class A to class A is denoted by AA. from class A to class B is denoted by AB and so on. The probability of a daily total radiation falling within each class for each month for the stations in Penang. Kota Baru and Kuala Lumpur are given in Tables 5(al. 5(b) and 5(c) respectively. Tables 6(a), 6(b) and 6(c) give the probabilities for the events of transition from class to class. CONCLUSION Statistical presentations of solar radiation data useful for the performance study and design of solar installation system are given. The analysis shows that
80
C H U A H AND LEE:
SOLAR R A D I A T I O N IN P E N I N S U L A R MALAYSIA
Table 3. Frequencies and expected frequencies (occurrences per year) of periods of successive days of total radiation Q (mWh cm -2) above specified values (a) Station: Penang, Lat. 5 ° 18'N Long. 100 ~ 16'E Ht. 3 m above S.L. Length of occurrences (No. of days)
Radiation Q i>
1975
1976
1977
1978
Mean ~
1 2 3 4 5 6 7 8 9
400 400 400 400 400 400 400 400 400
10 5 7 9 5 0 4 4 0
11 3 4 3 2 3 2 2 1
11 3 6 5 3 2 0 0 1
13 8 2 2 2 2 '1 2 0
11.25 4.75 4.75 4.75 3.00 1.75 1.75 2.00 0.5
(9.25, 73.25) (0.99, 8.51) (1.22, 8.28) (0, 9.67) (0.75, 5.25) (0, 3.75) (0, 4.47) (0,6.11) (0.21, 0.79)
~< 20 ~< 50 ~< 100 ~< 150
400 400 400 400 400
3 2 3 0 0
0 9 2 0 0
2 5 3 1 0
0 11 2 0 0
1.25 6.75 2.50 0.25 0
(0, 3.00) (0, 13.16) (1.58, 3.42) (0, 1.05j (0,0)
~< 20 ~< 50 ~< 100 ~< 150
500 500 500 500 500 500 500 500 500 500 500 500 500 500
23 17 8 6 5 1 2 2 0 1 2 1 0 0
21 9 8 8 2 1 1 1 1 0 4 2 0 0
24 9 12 8 3 1 0 2 3 0 2 2 0 0
22 15 6 8 2 3 2 3 I 0 3 0 0 0
22.50 12.50 8.50 7.50 3.00 1.50 1.25 2.00 1.25 0.25 2.75 1.25 0 0
10 x x x x
10 20 50 100
< < < <
10 20 50 100
1 2 3 4 5 6 7 8 9 10 < x < x < x < x
95% confidence interval
(20.45, 24.55) (5.94, 19.06) (4.50, 12.50) (5.91, 9.09) (0.75, 5.25) (0, 3.09) (0.25, 2.25) (0.7, 3.30) (0, 2.89) (0.21, 0.79) (1.23, 4.27) (0, 2.77) (0, 0) (0,0)
(bt Station: Kota Baru, Lat. 6 ~ 10'N Long. 102 ° 17'E Ht. 5 m above S.L. Length of occurrences (No. of days)
10 20 50 100
1 2 3 4 5 6 7 8 9 10 < x < x < x < x
10 20 50 100
1 2 3 4 5 6 7 8 9 10 < x < x < x < x
Radiation Q~>
1975
1976
1977
1978
Mean .~
95% confidence interval
~< 20 ~< 50 <~ 100 ~< 150
400 400 400 400 400 400 400 400 400 400 400 400 400 400
12 4 6 6 4 1 0 1 1 1 6 2 0 0
3 3 1 4 2 4 1 1 1 1 6 1 1 0
13 6 7 4 2 3 2 0 2 0 4 3 0 0
10 13 8 2 3 6 2 6 1 0 5 1 0 0
9.5 6.56 5.50 4.00 2.75 .3.50 1.25 2.00 1.25 0.5 5.25 1.75 0.25 0
(2.36316.64) (0, 13.73) (0.56, 10.44} (0, 6.60) ( 1.23, 4.27) (0,19, 6.81) (0, 2.77) (0,6.31) (0.45, 2.05) (0;21, 0.79) (3.73, 6.771 (0.23, 3.27) (0. 1.05) (0,0)
~< 20 ~< 50 ~< 100 ~< 150
500 500 500 500 500 500 500 500 500 500 500 500 500 500
18 13 12 6 4 1 1 1 0 0 2 1 0 0
14 10 5 3 4 1 0 2 2 0 6 1 0 0
16 16 7 3 1 3 2 1 2 0 1 1 0 0
31 21 4 6 1 3 1 3 0 1 0 0 0 0
19.75 10.25 7.00 4.50 2.50 2.00 1.00 1.75 1.00 0.25 2.25 0,75 0 0
(7.55, 31.95) (0, 21.72) (1.34, 12.66) (1.75, 7.25) (0, 5.25~ (0.16, 3.84) (0, 2.30) (0.23, 3.27) (0, 2.84) (0, 1.05) (0, 4.73) (0, 1.80) (0, 0) (0,0)
C H U A H AND LEE:
SOLAR R A D I A T I O N IN P E N I N S U L A R MALAYSIA
(c) Station: Kuala Lumpur, Lat. 3 .=07'N Long. 101 3YE Ht. 19 m above S.L. Length of Radiation Q>~
1975
1976
1977
1978
Mean .~
95°o confidence interval
<~ 20 ~< 50 <~ 100 ~< 150
400 400 400 400 400 400 400 400 400 400 400 400 400 400
8 8 6 6 2 2 1 3 3 0 8 1 0 0
24 8 5 4 4 5 3 1 1 2 3 1 0 0
20 10 10 7 3 2 3 1 1 2 5 0 0 0
29 17 5 9 7 1 1 I 3 0 3 0 0 0
20.25 10.75 6.50 6.50 4.00 2.50 2.00 1.50 2.00 1.00 4.75 0.5 0 0
(6.01, 34.49} (3.96, 17.54) (2.72, 10.281 13.19,9.81) (0.57, 7.43} (0, 5.251 10.16, 3.841 (0, 3,091 (0.16, 3.84} (0, 2.841 10.99, 8.511 (0.21,0.79}
~< 20 ~< 50 ~< 100 ~< 150
500 500 500 500 500 500 500 500 500 500 500 500 500 500
31 14 9 7 2 3 I 1 1 0 0 0 0 0
35 8 8 3 2 0 1 0 2 0 1 0 0 0
34 21 6 3 0 1 0 1 0 I 0 0 0 0
38 13 5 3 0 1 0 0 0 0 0 0 0 0
34.50 14.00 7.00 4.00 1.00 1.25 0.5 0.5 0.75 0.25 0.25 0 0 0
occurrences (No. of days) 1 2 3 4 5 6 7 8 9 10 10 < x 20 < x 50
10 20 50 100
1 2 3 4 5 6 7 8 9 10 < x < x
(0,O) (0.O) (29.91, 39.09) (5.49, 22.51) (4.10, 9.9) 10.82, 7.18) 10, 2.84) (0, 2.00)
(0.21,0.79) (0.21.0.79) (0. 2.27) (0.21, 0.79) (0.2I,0.79) (0, O) (0, O) (0,0)
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C H U A H AND LEE:
SOLAR R A D I A T I O N IN P E N I N S U L A R MALAYSIA
Table 4. Expected No. of days in a m o n t h in which radiation Q falls with specified values (a) Station: Penang, Lat. 5 ' 18'N, Long. 100 ICE, Ht. 3 m above S.L. Radiation classes ( m W h c m - 2)
Jan.
Feb.
Mar.
April
May
Jun.
July
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
0-50 50-100 100-150 150-200 200-250 250-300 300-350 350-400 400-450 500-550 550-600 600-650 650-700 700-750 Total
0 0 0 0 0 0 1.25 1.00 0.50 4.00 5.50 8.50 8.00 0 31
0 0 0 0 0.5 0.74 0.25 1.24 1.00 2.97 3.72 6.44 8.18 1.24 28
0 0 0 0 0 0.75 0.25 1.25 1.50 4.75 5.00 6.50 " 7.00 2.00 31
0 0 0 0 0 0.75 0.75 1.25 0.50 2.25 8.25 7.25 6.25 1.5 30
0 0 0 0 0.50 0.75 1.25. 3.00 3.75 3.75 6.25 4.25 3.00 0.25 31
0 0 0 0.75 1.00 1.25 2.25 2.50 2.75 4.50 6.25 4.25 1.25 0 30
0 0 0.25 0.75 0.50 0.50 1.00 2.25 3.50 5.50 5,50 5.25 2.00 0 31
0 0 0.25 0.75 1.00 1.25 2.50 3.00 3.25 3.75 5.00 3.25 3.25 0 31
0 0 0.25 1.25 1.25 1.50 2.50 3.00 3.75 3.25 3.75 3,50 1.00 1,75 30
0 0 0.50 0.50 0.75 2.25 2.50 2.75 1.75 4.00 6.75 3.75 1.50 0.50 31
0 .0 0.25 0.75 0.75 1.50 0.75 2.25 3.50 5.00 5.50 3.75 2.00 0 30
0 0.25 0 0.75 0.25 0.25 0.75 2.00 2.50 5.50 6.50 5.75 1.50 0 31
0 0.75 1.50 5.50 6.50 11.49 16.00 25.49 28.25 49.22 67.97 62.44 44.93 7.24 365
(b) Station: Kota Baru, Lat. 6 ~ 10'N, Long. 102 17'E, Ht. 5 m above S.L. Radiation classes (mWhcm-2)
Jan.
Feb.
Mar.
April
May
Jun.
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
0-50 50-100 100-150 150-200 200-250 250-300 300-350 350-400 40(050 450-500 500-550 550-600 600-650 650-700 700-750 Total
0.50 0.25 0.75 0.75 0.50 0.75 1.00 1.50 4.50 5.75 7.50 4.75 2.50 0 0 31
0 0 0.25 0 0.74 0.25 0.99 1.73 2.73 5.45 4.71 5.70 3.47 1.98 0 28
0 0 0.25 0 0.50 0.25 0.50 1.00 0.50 2.50 6.00 6.00 5.50 5.75 2.25 31
0 0 0 0 0 0 0.50 1.25 1.25 1.25 3.25 3.75 9.75 6,75 2,25 30
0 0 0 1.00 0.25 0.25 0.75 2.00 2.25 3.50 5.50 6.00 8.25 1.00 0.25 31
0 0 0.50 0 1.00 1.50 1.50 2.00 2.75 3.75 7.75 5.25 3.00 1.00 0 30
0 0 0 0.25 0.75 0.50 1.50 3.00 3.50 4.25 6.75 8,25 2,25 0 0 31
0 0 0 0.25 0.75 0.75 2.25 1.50 1.75 5.5 6.75 5.25 4.5 1.50 0.25 31
0 0 0 0.25 0 1.00 1.25 2.00 4.25 4.00 5.50 4.75 5.25 1.00 0.75 30
0 0 0.75 1.25 1.00 1.25 2.50 2.25 3.00 4.75 4.50 5.00 3.75 1.00 0 31
1.50 1.75 1.75 2.25 2.50 2.75 2.75 2.75 2.25 2.50 3.50 2.75 0.75 0.25 0 30
1.50 1.50 1.25 1.50 1.50 2.25 2.75 3.25 5.25 6.00 2.50 1.25 0.25 0.25 0 31
3.50 3.50 5.50 7.50 9.49 11.50 18.24 24.23 33.98 49.20 64.21 58.70 49.22 20.48 5.75 365
(c) Station: Kuala Lumpur, Lat. 3~ 07'N, Long. 101= 33'E, Hr. 1 9 m above S,L. Radiation classes (mWh c m - 2 )
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
0-50 50-100 100--150 150-200 200-250 250-300 300-350 350-400 400-450 450-500 500-550 550-600 600-650 650-700 700-750 Total
0 0 0 0.25 0.25 0.75 1.25 4.00 5.00 5.75 5.50 5.25 2.25 0.50 0.25 31
0 0.25 0 0.25 0 0.74 1.98 2.23 4.46 5.45 5.95 3.22 1.98 0.99 0.50 28
0 0 0 0.25 0 0.25 0.75 2.25 3.75 4.75 9.00 6.25 3.00 0.50 0.25 31
0 0 0 0.25 0 0.75 1.50 2.25 2.50 6.25 8.25 6.00 1.25 1.00 0 30
0 0 0.25 0.50 1.00 0.25 1.50 3.75 4.00 7.00 7.50 2.50 2.50 0.25 0 31
0 0 0 0.50 0.25 0.50 2.50 4.25 7.50 6.25 4.75 3.00 0.50 0 0 30
0 0 0 0 0.75 1.00 2.00 4.25 6.50 6.00 6.00 4.00 0.50 0 0 31
0 0 0 0.75 1.25 0.50 4.50 2.75 4.00 4.75 5.00 3.75 3.25 0.50 0 31
0 0 0 0.25 0.75 1.00 2.50 3.00 6.50 6.00 5.00 3.75 0.75 0.50 0 30
0 0 0 0 0.25 1.00 4.00 5.50 5.00 5.00 4.25 3.75 2.00 0.25 0 31
0 0 0 1.25 1.25 1.50 4.00 5.00 7.00 5.50 2.75 1.50 0.25 0 0 30
0 0 0.25 0.75 0.75 0.75 3.00 4.75 8.00 5.00 5.00 2.50 0.25 0 0 31
0 0.25 0.50 5.00 6.50 8.99 29.48 43.98 64.21 67.70 68.95 45.47 18.48 4.49 1.00 365
C H U A H AND LEE:
83
SOLAR R A D I A T I O N IN P E N I N S U L A R MALAYSIA
Table 5. Probabilities of solar radiation classes (a) Station: Penang, Lat. 5 18'N, Long. 100 16'E, HT. 3 m above S.L. Radiation classes (mWhcm-2) A(500 <~ Q) B(300 ~< Q < 500) CtQ < 300)
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
0.84 0.16 0
0,81 0.15 0.04
0.81 0.16 0.03
0.84 0.13 0.03
0.57 0.39 0.04
0.54 0.36 0.10
0.59 0.35 0.06
0.50 0.40 0.10
0.44 0.40 0.16
0.53 0.34 0.13
0.54 0.35 0.11
0.62 0.33 0.05
0.64 0.29 0.07
(b) Station Kota Baru, Lat. 6 ~ 10'N, Long. 102 17'E, Hr. 5 m above S.L. Radiation classes (mWhcm-2) A(500 ~< QI B(300 ~< Q < 5001 CIQ < 3001
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sept,
Oct.
Nov.
Dec.
Annual
0.48 0.41 0.11
0.57 0.39 0.04
0.82 0.15 0.03
0.86 0.14 0
0.68 0.27 0.05
0.57 0.33 0.10
0.56 0.40 0.04
0.59 0.35 0.06
0.58 0.38 0.04
0.46 0.40 0.14
0.24 0.34 0.42
0.14 0.55 0.31
0.54 0.34 0.12
(c) Station: Kuala Lumpur, Lat. 3 07'N, Long. 101 33'E, Ht. 19 m above S.L. Radiation classes (mWh c m - 2 ) A(500 ~< Q) B(300 ~< Q < 500) C(Q < 300)
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
0.44 0.52 0.04
0.45 0.51 0.04
0.61 0.37 0.02
0.55 0.42 0.03
0.41 0.52 0.07
0.26 0.68 0.04
0.34 0.60 0.06
0.40 0.52 0.08
0.33 0.60 0.07
0.33 0.63 0.04
0.15 0.72 0.13
0.25 0.67 0.08
0.38 0.56 0.06
Table 6. Probabilities of transitions between solar radiation classes on successive days lal Station: Penang, Lat. 5' 18'N, Long. 10ft 16'E, Hr. 3 m above S.L. Event AB means radiation Q changes from class A to class B Events
Jan.
Feb.
Mar.
Apr.
May
Jun,
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
AA AB AC BA BB BC CA CB CC
0.74 0.10 0 0.09 0.06 0 0.01 0 0
0.71 0.08 0.03 0.07 0.07 0 0.03 0 0.01
0.72 0.09 0.01 0.09 0.05 0.02 0.01 0.01 0
0.76 0.09 0.02 0.07 0.02 0.01 0.02 0.01 0
0.32 0.20 0.03 0.21 0.19 0.01 0.02 0.02 0
0.33 0.18 0.06 0.18 0.15 0.02 0.05 0.02 0.01
0.30 0,18 0,02 0,16 0.17 0.07 0.02 0.06 0.02
0.30 0.18 0.02 0.16 0.17 0.07 0.02 0.06 0.02
0.23 0.14 0.05 0.13 0.22 0.07 0.07 0.07 0.02
0.34 0.14 0.06 0.15 0.14 0.03 0.05 0.05 0.04
0.33 0.17 0.03 0.16 0.16 0.05 0.06 0.02 0.03
0.47 0.19 0.01 0.12 0.14 0.03 0.03 0 0.01
0.47 0.15 0.03 0.14 0.12 0.03 0.04 0.01 0.01
Ib) Station: Kota Baru, Lat. 6: 10'N, Long. 102: 17'E, Hr. 5 m above S.L. Events
Jan.
Feb.
Mar.
Apr.
May
Jun.
July
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
AA AB AC BA BB BC CA CB CC
0.33 0.12 0.01 0.14 0.21 0.04 0.02 0.06 0.07
0.42 0.16 0 0.15 0.20 0.02 0 0.03 0.02
0.73 0.08 0.01 0.08 0.05 0.02 0.01 0.01 0.01
0.76 0.10 0 0.11 0.03 0 0 0 0
0.50 0.16 0.02 0.13 0.12 0.02 0.04 0 0.01
0.39 0.14 0.04 0.12 0.16 0.05 0.07 0.03 0
0.32 0.18 0.04 0.21 0.19 0.01 0.03 0.02 0
0.37 0.18 0.02 0.15 0.21 0.04 0.01 0.02 0
0.38 0.16 0.02 0.17 0.21 0.02 0.02 0.02 0
0.26 0.19 0.03 0.15 0.19 0.06 0.06 0.02 0.04
0.14 0.08 0.05 0.09 0.07 0.10 0.03 0.13 0.31
0.06 0.08 0.01 0.06 0.36 0.15 0.02 0.11 0.15
0.39 0.13 0.02 0.13 0.17 0.04 0.03 0.04 0.05
84
CHUAH AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA Table 6. (contd.)
(c) Station: Kuala Lumpur, Lat. 3 07'N, Long. 101 3YE, Ht. 19 m above S.L. Events
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
AA AB AC BA BB BC CA CB CC
0.26 0.!5 0 0.17 0.35 0.02 0.01 0.02 0.02
0.25 0.17 0.02 0.22 0.28 0.02 0.02 0.02 0
0.41 0.18 0,02 0.19 0.18 0 0 0.02 0
0.28 0.24 0.02 0.24 0.19 0.01 0.02 0 0
0.19 0.18 0.04 0.16 0.34 0.02 0.06 0.01 0
0.10 0.16 0 0.18 0.48 0.03 0.01 0.04 0
0.14 0.19 0.02 0.20 0.36 0.03 0.02 0.03 0.01
0.10 0.17 0.03 0.15 0.39 0.05 0.03 0.07 0.01
0.12 0.20 0.02 0.20 0.34 0.04 0.03 0.05 0
0.13 0.19 0.02 0.19 0.43 0.01 0.02 0.01 0
0.05 0.09 0.01 0.09 0.54 0.09 0.04 0.06 0.03
0.10 0.13 0.01 0.12 0.51 0.05 0.01 0.05 0.02
0.18 0.18 0.02 0.18 0.35 0.03 0.02 0.03 0.01
Table 7. Monthly average temperature Station Penang Kuala Lumpur Kota Baru
Period
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug. Sept.
Oct.
Nov.
Dec.
Annual
1959-1972
80.2
81.0
81.3
81.7
81.6
81.0
80.4
8 0 . 1 79.7
79.4
79.5
79.8
80.5
1966-1972 1959-1972
78.5 78.0
79.3 78.9
79.9 80.2
80.0 81.8
80.7 82.3
79.9 81.3
79.4 80.7
79.3 80.2
79.3 78.9 8 0 . 1 79.6
78.6 78.5
78.3 78.3
79.3 80.0
days with low daily total radiations occur scarcely in Penang and Kuala Lumpur. In Penang, days with high radiation occur more frequently than in Kuala Lumpur. However, Kota Baru experiences a larger variability of daily total radiation. Extreme low radiations for long periods occur frequently during the N o r t h - E a s t M o n s o o n period, while high radiations for long periods occur during the dry season.
Acknowledqemem--The authors wish to thank the Malaysian Meteorological Service for making available the data for this work.
REFERENCES [-1] A. Angstrom. Q.J.R. Meteor. Soc. 50, 121 (1924). [2] J. N. Black, Some aspects of the climatology of solar radiation. New Sources of Energy 4, 311, U.N. Publication Sales No. 6 63.2.38 (1964). [:3] Donald G. S. Chuah and S. L. Lee, Solar Energy 26, 33 (1981). [4] Donald G. S. Chuah. S. L. Lee and R. E. Childs, Analysis of solar radiation data using cubic splines. In press. [5] R. H. B. Exell, Solar Energy 18, 549 (1976). [6] T. N. Goh. Solar Energy 22, 105 (1979). [7] L. Machta, Monitoring solar radiation for solar energy, UNESCO/WHO Solar Energy Symp., Geneva (1976).
0196-8904/82/010071-14503.00/0 Pergamon Press Ltd
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SOLAR RADIATION IN P E N I N S U L A R MALAYSIA--STATISTICAL PRESENTATIONS D O N A L D G . S. C H U A H a n d S. L. LEE School of Physics and School of Mathematical Science, Universiti Sains Malaysia, Penang, Malaysia (Received 20 July 1981)
Abstract--Statistical presentations of solar radiation data from three major stations in Peninsular Malaysia are given. These data are presented in several ways that will be useful in the design and performance study of solar energy conversion devices. Solar radiation Statistical presentations Solar energy utilisation radiation Transitions persistence Radiation classes
Design performance
Daily total
coast while Kota Baru is in the east coast. The stations in Penang and Kota Baru are situated near the sea, while the stations in Kuala Lumpur are situated in the land mass (see Map 1).
INTRODUCTION Information on solar radiation is essential in the design and study of solar energy utilization systems. In this paper statistical presentations of radiation data from three major cities in Peninsular Malaysia, viz Kuala Lumpur (3c07'N, 101 ~ 3YE). Penang (5: 18'N, 10ft 16'E) and Kota Baru (6: 10'N, 102 ~ 17'E) are given. These data are presented in several ways that will be useful in the design and performance study of solar energy utilization systems for implementation under local conditions. These presentations include frequencies of periods of successive days of daily total radiation below arbitrarily fixed values, the expected number of days in which the total radiation falls within arbitrarily fixed intervals and probabilities of transitions and persistence in radiation classes. Similar studies have been carried out for Thailand [5] and Singapore I-6].
R E L A T I O N S B E T W E E N SOLAR RADIATION AND DURATION OF SUNSHINE The simplest relationship between the daily total radiation Q and the daily duration of sunshine S is the linear relation
Q
--
Q•
s
(1)
= a + b --
S.
GEOGRAPHICAL FEATURES Peninsular Malaysia is a peninsular stretching from latitude 1: 20'N to 6: 40'N, and longitude 99 ~ 35'E to 10= 20'E, and has a tropical type, wet and dry climate. The land mass is divided into the east and" west coasts by the main range running from north to south. The South-West Monsoon brings rain and cloud to the west coast from June to early October while the North-East Monsoon brings rain and cloud to the east coast from November to March. Ther~ore, the west coast is dry from November to March while the east coast is dry from June to September. During the dry season, the climate is hot and sunny (the average monthly temperatures are shown in Table 7) with intermittent breaks of cloud formation and hence rainfalls in t h e l a t e afternoons due to convection currents. The three cities where data are available are situated in regions of different geographical conditions. Penang and Kuala Lumpur are in the west r,(.~l. 2 2 I
r
KUALA TI~N~ I
IPOH• • (;AIdl litON HIGHLAND
LWAN
KDANTAN • KUALA LUIdPUR
t
m
SINGAPORE
MOp I I_ocolions of $1oli0n$. • ROdiohOn ~ Sun|hl~ DOIO Aveik~011m • Sunshiml DOra AVOillble o Cloudiness Doto Avoifoble
71
72
C H U A H AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
developed by A n g s t r o m [ I ] , where Q = a m o u n t of radiation received per day o n the earth surface at a particular location, Q,, = a m o u n t o f radiation available per day at the same location in the a b s e n c e o f a t m o s p h e r i c effect,
S,. = m a x i m u m n u m b e r o f h o u r s o f sunshine that are possible at the site on the s a m e day. T h e c o n s t a n t s a and b for the three stations are c o m p u t e d in [3], w h e r e radiation a m o u n t s for t o w n s without radiation d a t a are also o b t a i n e d by extrapo-
Table 1. Frequencies and expected frequencies (occurrences per year) of periods of successive days of total radiation Q (mWh cm-2) below specified values (a) Station: Penang, Lat. 5 c 18'N Long. 100 16'E Ht. 3 m above S.L. Length of occurrences (No. of days)
Radiation Q ~<
1975
1976
1977
1978
Mean .¥
95°0 confidence interval
I 2 3 1 2 3 4
200 200 200 300 300 300 300
1 2 0 17 5 0 0
7 0 0 17 3 1 0
3 1 0 10 5 0 0
8 0 0 17 5 1 0
4.75 0.75 0 15.25 4.5 0.5 0
(0, 10.00t (0, 2.27) (0, 0t (9.69, 20.81) (2.91, 6.09} (0.21, 0.79) (0, 0)
1 2 3 4 5 6
400 400 400 400 400 400
33 12 4 0 1 0
27 10 4 1 0 0
36 2 2 0 2 0
25 15 5 1 0 0
30.25 9.75 3.75 0.5 0.75 0
(22.10, 38.40) (0.91, 18.59) (1.76, 5.74) (0.21, 0.79} (0, 2.27) (0, O)
(b) Station: Kota Baru, Lat. 6 10'N Long. 102 17'E Ht. 5 m above S.L. Length of occurrences (No. of days)
Radiation Q ~<
1975
1976
1977
1978
Mean .~
95°0 confidence interval
1 2 3 4 5 6 7 1 2 3 4 5 6 7 8
200 200 200 200 200 200 200 300 300 300 300 300 300 300 300
18 3 1 0 1 0 0 16 5 0 3 1 1 1 0
7 2 1 0 1 1 0 10 4 2 0 1 1 0 0
8 3 0 0 0 0 0 18 6 1 1 0 0 0 0
3 0 3 1 0 0 0 10 8 2 1 0 0 0 0
9.0 2.0 1.25 0.25 0.5 0.25 0 13.5 5.75 1.25 1.25 0.5 0.5 0.25 0
(0, 19.141 (0, 4.25) (0, 3.25) (0, 1.051 (0.21, 0.791 10, 1.05) (0, 0) (6.94, 20.06) (0, 8.471 {0.52, 1.981 (0, 3.25) (0.21, 0.79) (0.2 !, 0.791 (0, 1.051 (0, O)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
28 5 2 0 2 0 2 0 0 0 0 1 0 0 1
28 11 4 3 0 0 0 1 0 0 0 0 0 1 0
24 10 6 3 1 1 1 0 0 0 0 0 0 0 0
36 12 2 3 1 0 0 0 0 0 0 0 0 0" 0
29.00 9.5 3.5 2.25 1.0 0.25 0.75 0.25 0 0 0 0.25 0 0.25 0.25
(21.00, 37.00) (4.56, 14.44) (0.46, 6.54) (0, 4.64) (0, 2.30) (0, 1.05) C0, 1.80) {0. 1.05) (0, 0) (0, 0) (0, 0) {0, 1.05) {0, 0) CO, 1.05) (0, 1.05)
CHUAH AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
73
(c) Station: Kuala Lumpur, Lat. 3° 07'N Long. 101 33'E Ht. 19 rn above S.L. Length of occurrences (No. of days)
Radiation Q ~<
1975
1976
1977
1978
Mean .~
95';~ confidence interval
1 2 3 1 2 3 4 5 1 2 3 4 5 6 7
200 200 200 300 300 300 300 300 400 400 400 400 400 400 400
5 1 0 15 1 0 0 0 37 9 3 2 0 0 0
8 0 0 26 2 0 0 0 45 10 4 2 0 I 0
5 0 0 16 1 0 0 0 43 13 2 3 1 0 0
4 0 0 14 1 1 0 0 53 13 9 1 1 0 0
5.50 0.25 0 17.75 1.25 0.25 0 0 44.50 11.25 4.50 2.00 0.5 0.25 0
(2.75, 8.25) (0, 1.05) (0, O) (14.31, 21.19) (0.45, 2.05) (0, 1.05) (0, O) (0, O) (33.99, 55.01) (7.97, 14.53) (0, 9.44) (0.70, 3.30) (0.21, 0.79) (0, 1.05) (0, O)
lations a n d interpolations. Regression analysis using cubic spline functions is presented in [4]. However these studies yield only the monthly means and totals of solar radiation available at the regions under consideration, and the stochastic components are not taken into account, and therefore these results are not enough for effective design and study of solar utilization systems, and the presentation in this paper supplements the results of our earlier papers [3, 4]. EXPECTED FREQUENCIES OF O C C U R R E N C E O F S U C C E S S I V E DAYS O F
TOTAL RADIATION BELOW (ABOVE) ARBITRARILY FIXED VALUES Knowledge of the frequencies of occurrence of periods of successive days with low radiation is
required for the performance study of solar installations and also such calculations as storage requirements [2, 7]. Such information, based on daily records of 1975-1978 for Penang, Kota Baru and Kuala Lumpur is presented in Tables l(a), l(b), l(c), 2(a), 2(b) and 2(c) and the results of Tables l(a), l(b) and l(c) are also presented graphically. For the sake of discussion, we shall call the n u m b e r of days in an occurrence of a period of successive days with radiations b61ow (or above) specified values, the length of the occurrence. Tables l(a), l(b), l(c) show a year=to-year analysis of the frequencies of occurrence of various length in which the daily radiations are below the energy levels of 2 0 0 m W h c m - 2 , 300 m W h c m - 2 and 400 m W h cm -2 for the stations in Penang, Kota Baru and Kuala L u m p u r respectively. The sample mean for the frequencies of occur-
Table 2. Frequencies and expected frequencies (occurrences per year) of periods of successive days of total radiation Q (mWh cm-2) below specified values* Ca) Station: Penang, Lat. 5: 18'N Long. 10ft 16'E Hr. 3 m above S.L. Length of occurrences (No. of days)
Radiation Q ~<
1975
1976
1977
1978
Mean ~
95'~Jhconfidence interval
1 2 3 1 2 3 4 1 2 3 4 5 6
200 200 200 300 300 300 300 400 400 400 400 400 400
5 2 0 27 5 0 0 74 24 7 2 1 0
7 0 0 26 5 1 0 63 21 6 1 0 0
5 1 0 20 5 0 0 56 14 8 4 2 0
8 0 0 30 7 1 0 74 28 7 1 0 0
6.25 0.75 0 25.75 5.50 0.50 0 66.75 21.75 7.00 ZOO 0.75 0
(3.87, 8.63) (0, 2.27) (0, 0) C19.0K 32.42) (3.91, 7.09) (0.21, 0.79) (0, 0) (52.70, 80.80) (12,36, 31.14) (6.08, 7.92) ( 1.29.2.71 ) C0, 2.27) (0, 0)
* Frequency counts involve also occurrences obtained from those of bigger lengths.
74
C H U A H AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
(b) Station: Kota Baru, Lat. 6 10'N Long. 102 17'E Ht. 5 m above S.L. Length of occurrences (No. of days)
Radiation Q ~<
1975
1976
1977
1978
Mean ~
1 2 3 4 5 6 7 I 2 3 4 5 6 7 8
200 200 200 200 200 200 200 300 300 300 300 300 300 300 300
32 9 4 2 I 0 0 56 29 18 12 6 3 1 0
25 13 8 5 3 1 0 35 17 9 5 3 1 0 0
14 3 0 0 0 0 0 37 11 3 ! 0 0 0 0
16 9 5 1 0 0 0 36 15 4 1 0 0 0 0
21.75 8.50 4.25 2.00 1.00 0.25 0.00 41.00 18.00 8.50 4.75 2.25 1.00 0.25 0.00
(8.49, 35.01) (1.95, 15.06) (0, 9.50) (0, 5.43) (0, 3.25) (0, 1.05) (0, 0) (25.05, 56.95) (5.68.30.32) (0, 19.40) (0, 13.00) (0, 6.82) (0, 3.27) (0, 1.05) (0, 0)
I 2 3 4 5 6 7 8 9 10 11 12 13 14 15
400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
95 54 41 33 27 21 17 13 11 9 7 5 3 2 1
96 48 28 19 14 12 10 8 6 5 4 3 2 1 0
92 46 24 12 6 3 I 0 0 0 0 0 0 0 0
83 29 11 5 1 0 0 0 0 0 0 0 0 0 0
91.50 44.25 26.00 17.25 12.00 9.00 7.00 5.25 4.25 3.50 2.75 2.00 1.25 0.75 0.25
(82.09, 100.91) (27.21, 61.29) (6.35, 45.65) (0, 36.26) (0,31.12) (0, 24.08) (0. 19.79) (0, 15.42) (0, 12.70) (0, 10.43) (0, 8.16) (0, 5.89) (0, 3.63) (0, 2.18) (0, 1.05)
95?,0 confidence interval
(C) Station: Kuala Lumpur, Lat. 3 07'N Long. 101 33'E Hr. 19 m above S.L. Length of occurrences (No. of days)
Radiation Q ~<
1975
1976
1977
1978
Mean .~
1 2 3
200 200 200
7 1 0
8 0 0
5 0 0
4 0 0
5.75 0.25 0
1 2 3 4 5 I 2 3 4 5 6 7
300 300 300 300 300 400 400 400 400 400 400 400
21 4 2 1 0 72 21 7 2 0 0 0
30 2 0 0 0 91 29 12 5 2 I 0
18 1 0 0 0 92 30 11 5 1 0 0
19 3 1 0 0 " 115 38 14 3 1 0 0
17.5 2.5 0.75 0.25 0.00 92.5 29.5 11.00 3.75 1.00 0.25 0.00
rence for each length below each energy level is also given, and a 95°o confidence interval for the m e a n is c o m p u t e d . This provides useful i n f o r m a t i o n for the p e r f o r m a n c e prediction o f solar energy utilization systems. F o r easy reference Tables 2(a), 2(b) a n d 2(c) give the frequency counts which involve occurrences o b t a i n e d from those o f bigger lengths. F o r instance for each
95°0 confidence interval (2.82, 8.69) (0, 1.051 (0, 0) (8.15.29.49) (0.45, 4.55) (0, 2.27) (0, 1.05) (0, 0) (64.52, 120.48) (18.45.40.55) (6.32, 15.68) (1.99, 5.51) (0, 2.30) (0, 1.05) (0, 0)
o c c u r r e n c e of length I, there are two occurrences o f length 1 - 1, three occurrences o f I - 2 a n d so on. Tables 3(a), 3(b), 3(c) give the year-to-year analysis o f the frequencies o f o c c u r r e n c e o f periods o f successive days o f total daily radiation a b o v e the energy level o f 4 0 0 m W h c m 2 a n d 500 m W h c m - 2 . This inform a t i o n will also be helpful in the design o f solar energy utilization systems.
CHUAH AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
40
30
o
~20
1975
?
1976
1977
1978
MEAN
La
;o
o
5
1o
o
~
;o
o
~
,o
o ~
,o
o
~
;o
Number of succtssive days.
Histograms of frequencies (occurrences per year) of periods of successive days of total radiation below 2 0 0 m W h c m -2. Table l(a), Penang.
40
30
b
20 1975
i
1976
1977
1978
M EA N
:)
g o I0--
O--
0
5
I0
0
5
I'0
o
s,o
0
5
I0
5
IO
Nu'~bef Of SUCCeSSive OQy$
Histograms of frequencies (occurrences per year) of periods of successive days of total radiation below 300mW hcm -2. Table I(a). Penang.
75
76
CHUAH AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
401975
1976
19 77
1978
M[AN
30
o 2O
u
~ ~o
Illl
fl 5
5
io
I0
0
5
o I0
0
5
Number of
I0
0
successive
5
I0
clays
Histograms of frequencies (occurrences per year) of periods of successive days of total radiation below 4 0 0 m W h c m -2. Table l(a), Penang.
40
30
1975
o
1976
1977
1978
MEAN
2o
~o
o
5
io
o ;
i'o
o ~,;
o
~ ;o
o s ,'o
Number of ,%ccese~ve Days
Histograms of frequencies (occurrences per year) of periods of successive days of total radiation below 200row h cm -2. Table l(b), Kota Bharu.
CHUAH AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
I .11 a 20
1975
1976
1977
1979
MEAN
u I0
I ,
0
5
IO
0
5
i0
0
5
I'O
o
~ 1'o
o
s ,o
Number of successive doys
Histograms of frequencies (occurrences per year) of periods of successive days of total radiation below 3 0 0 m W h c m -2, Table l(b). Kota Bharu.
401975
1976
1977
1978
MEAN
30 I
o b=
8
o
I0
0
5
I0
15
0
S
I0 I |
0
§
I0
15 0
i
I0 15
0
Number of successive
5
I'0
15
doys'
Histograms of frequencies (occurrences per y e a r ) o f pel'iods of successive days of total radiation below 3 0 0 m W h c m -2. Table lib). Kota Bharu.
77
78
CHUAH AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
40--
30
b o b
20
=) e.,
I0
1975
0
1976
5
I0
0
1977
5
I0
0
19711
5
I0
0
MEA N
.5
I0
0
S
I0
Number of Successive
O0ys.
Histograms of frequencies (occurrences per year) of periods of successive days of total radiation below 2 0 0 m W h c m -2, Table l(c). Kuala Lumpur.
40--
50
1975
1976
1977
1978
MEAN
20 b
b
I0
in 0
l S
, I0
0
, S
i I0
,
0
'5
I0
i
S
I0
Number of successive
0
5
i
IO
d0ys
Histograms of frequencies {occurrences per year) of periods of successive days of total radiation below 3 0 0 m W h c m -2, Table l(c), Kuala Lumpur.
CHUAH AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA
79
60-
1975
1976
1977
MEAN
1978
50
40
30
20
:) u
I0
Itn i
0
5
I0
0
S
I0
0
S
I0
0
5
I0
0
5
I0
Nun~bQ¢ O| Su(:¢e&$ive doyl
Histograms of frequencies (occurrences per year) of periods of successive days of total radiation below 400mW hem -2. Table l(c). Kuala Lumpur.
E X P E C T E D N U M B E R O F DAYS IN A M O N T H IN WHICTI R A D I A T I O N F A L L S W I T H I N S P E C I F I E D VALUES The variation of daily radiation from month-tomonth is shown in Tables 4(a), 4(b) and 4(c) for the stations in Penang, Kota Baru and Kuala Lumpur respectively. Solar radiation amounts ranging from 0 to 7 5 0 m W h c m -2 are divided into intervals of 50 mWh cm -2, and the expected number of days in a month and year in which daily total falls within each interval are computed. M O N T H L Y ANALYSIS O F PERSISTENCE AND TRANSITION IN SOLAR R A D I A T I O N Solar radiation amounts ranging from 0 to 750 are divided into three classes. Class A contains daily total
radiations greater than 500 mWh c m - 2 class B contains daily total radiations between 300 and 500 mWh c m - 2 and class C contains daily total radiation less than 300 mWh cm -2. The event of transition of daily total radiation from class A to class A is denoted by AA. from class A to class B is denoted by AB and so on. The probability of a daily total radiation falling within each class for each month for the stations in Penang. Kota Baru and Kuala Lumpur are given in Tables 5(al. 5(b) and 5(c) respectively. Tables 6(a), 6(b) and 6(c) give the probabilities for the events of transition from class to class. CONCLUSION Statistical presentations of solar radiation data useful for the performance study and design of solar installation system are given. The analysis shows that
80
C H U A H AND LEE:
SOLAR R A D I A T I O N IN P E N I N S U L A R MALAYSIA
Table 3. Frequencies and expected frequencies (occurrences per year) of periods of successive days of total radiation Q (mWh cm -2) above specified values (a) Station: Penang, Lat. 5 ° 18'N Long. 100 ~ 16'E Ht. 3 m above S.L. Length of occurrences (No. of days)
Radiation Q i>
1975
1976
1977
1978
Mean ~
1 2 3 4 5 6 7 8 9
400 400 400 400 400 400 400 400 400
10 5 7 9 5 0 4 4 0
11 3 4 3 2 3 2 2 1
11 3 6 5 3 2 0 0 1
13 8 2 2 2 2 '1 2 0
11.25 4.75 4.75 4.75 3.00 1.75 1.75 2.00 0.5
(9.25, 73.25) (0.99, 8.51) (1.22, 8.28) (0, 9.67) (0.75, 5.25) (0, 3.75) (0, 4.47) (0,6.11) (0.21, 0.79)
~< 20 ~< 50 ~< 100 ~< 150
400 400 400 400 400
3 2 3 0 0
0 9 2 0 0
2 5 3 1 0
0 11 2 0 0
1.25 6.75 2.50 0.25 0
(0, 3.00) (0, 13.16) (1.58, 3.42) (0, 1.05j (0,0)
~< 20 ~< 50 ~< 100 ~< 150
500 500 500 500 500 500 500 500 500 500 500 500 500 500
23 17 8 6 5 1 2 2 0 1 2 1 0 0
21 9 8 8 2 1 1 1 1 0 4 2 0 0
24 9 12 8 3 1 0 2 3 0 2 2 0 0
22 15 6 8 2 3 2 3 I 0 3 0 0 0
22.50 12.50 8.50 7.50 3.00 1.50 1.25 2.00 1.25 0.25 2.75 1.25 0 0
10 x x x x
10 20 50 100
< < < <
10 20 50 100
1 2 3 4 5 6 7 8 9 10 < x < x < x < x
95% confidence interval
(20.45, 24.55) (5.94, 19.06) (4.50, 12.50) (5.91, 9.09) (0.75, 5.25) (0, 3.09) (0.25, 2.25) (0.7, 3.30) (0, 2.89) (0.21, 0.79) (1.23, 4.27) (0, 2.77) (0, 0) (0,0)
(bt Station: Kota Baru, Lat. 6 ~ 10'N Long. 102 ° 17'E Ht. 5 m above S.L. Length of occurrences (No. of days)
10 20 50 100
1 2 3 4 5 6 7 8 9 10 < x < x < x < x
10 20 50 100
1 2 3 4 5 6 7 8 9 10 < x < x < x < x
Radiation Q~>
1975
1976
1977
1978
Mean .~
95% confidence interval
~< 20 ~< 50 <~ 100 ~< 150
400 400 400 400 400 400 400 400 400 400 400 400 400 400
12 4 6 6 4 1 0 1 1 1 6 2 0 0
3 3 1 4 2 4 1 1 1 1 6 1 1 0
13 6 7 4 2 3 2 0 2 0 4 3 0 0
10 13 8 2 3 6 2 6 1 0 5 1 0 0
9.5 6.56 5.50 4.00 2.75 .3.50 1.25 2.00 1.25 0.5 5.25 1.75 0.25 0
(2.36316.64) (0, 13.73) (0.56, 10.44} (0, 6.60) ( 1.23, 4.27) (0,19, 6.81) (0, 2.77) (0,6.31) (0.45, 2.05) (0;21, 0.79) (3.73, 6.771 (0.23, 3.27) (0. 1.05) (0,0)
~< 20 ~< 50 ~< 100 ~< 150
500 500 500 500 500 500 500 500 500 500 500 500 500 500
18 13 12 6 4 1 1 1 0 0 2 1 0 0
14 10 5 3 4 1 0 2 2 0 6 1 0 0
16 16 7 3 1 3 2 1 2 0 1 1 0 0
31 21 4 6 1 3 1 3 0 1 0 0 0 0
19.75 10.25 7.00 4.50 2.50 2.00 1.00 1.75 1.00 0.25 2.25 0,75 0 0
(7.55, 31.95) (0, 21.72) (1.34, 12.66) (1.75, 7.25) (0, 5.25~ (0.16, 3.84) (0, 2.30) (0.23, 3.27) (0, 2.84) (0, 1.05) (0, 4.73) (0, 1.80) (0, 0) (0,0)
C H U A H AND LEE:
SOLAR R A D I A T I O N IN P E N I N S U L A R MALAYSIA
(c) Station: Kuala Lumpur, Lat. 3 .=07'N Long. 101 3YE Ht. 19 m above S.L. Length of Radiation Q>~
1975
1976
1977
1978
Mean .~
95°o confidence interval
<~ 20 ~< 50 <~ 100 ~< 150
400 400 400 400 400 400 400 400 400 400 400 400 400 400
8 8 6 6 2 2 1 3 3 0 8 1 0 0
24 8 5 4 4 5 3 1 1 2 3 1 0 0
20 10 10 7 3 2 3 1 1 2 5 0 0 0
29 17 5 9 7 1 1 I 3 0 3 0 0 0
20.25 10.75 6.50 6.50 4.00 2.50 2.00 1.50 2.00 1.00 4.75 0.5 0 0
(6.01, 34.49} (3.96, 17.54) (2.72, 10.281 13.19,9.81) (0.57, 7.43} (0, 5.251 10.16, 3.841 (0, 3,091 (0.16, 3.84} (0, 2.841 10.99, 8.511 (0.21,0.79}
~< 20 ~< 50 ~< 100 ~< 150
500 500 500 500 500 500 500 500 500 500 500 500 500 500
31 14 9 7 2 3 I 1 1 0 0 0 0 0
35 8 8 3 2 0 1 0 2 0 1 0 0 0
34 21 6 3 0 1 0 1 0 I 0 0 0 0
38 13 5 3 0 1 0 0 0 0 0 0 0 0
34.50 14.00 7.00 4.00 1.00 1.25 0.5 0.5 0.75 0.25 0.25 0 0 0
occurrences (No. of days) 1 2 3 4 5 6 7 8 9 10 10 < x 20 < x 50
10 20 50 100
1 2 3 4 5 6 7 8 9 10 < x < x
(0,O) (0.O) (29.91, 39.09) (5.49, 22.51) (4.10, 9.9) 10.82, 7.18) 10, 2.84) (0, 2.00)
(0.21,0.79) (0.21.0.79) (0. 2.27) (0.21, 0.79) (0.2I,0.79) (0, O) (0, O) (0,0)
81
82
C H U A H AND LEE:
SOLAR R A D I A T I O N IN P E N I N S U L A R MALAYSIA
Table 4. Expected No. of days in a m o n t h in which radiation Q falls with specified values (a) Station: Penang, Lat. 5 ' 18'N, Long. 100 ICE, Ht. 3 m above S.L. Radiation classes ( m W h c m - 2)
Jan.
Feb.
Mar.
April
May
Jun.
July
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
0-50 50-100 100-150 150-200 200-250 250-300 300-350 350-400 400-450 500-550 550-600 600-650 650-700 700-750 Total
0 0 0 0 0 0 1.25 1.00 0.50 4.00 5.50 8.50 8.00 0 31
0 0 0 0 0.5 0.74 0.25 1.24 1.00 2.97 3.72 6.44 8.18 1.24 28
0 0 0 0 0 0.75 0.25 1.25 1.50 4.75 5.00 6.50 " 7.00 2.00 31
0 0 0 0 0 0.75 0.75 1.25 0.50 2.25 8.25 7.25 6.25 1.5 30
0 0 0 0 0.50 0.75 1.25. 3.00 3.75 3.75 6.25 4.25 3.00 0.25 31
0 0 0 0.75 1.00 1.25 2.25 2.50 2.75 4.50 6.25 4.25 1.25 0 30
0 0 0.25 0.75 0.50 0.50 1.00 2.25 3.50 5.50 5,50 5.25 2.00 0 31
0 0 0.25 0.75 1.00 1.25 2.50 3.00 3.25 3.75 5.00 3.25 3.25 0 31
0 0 0.25 1.25 1.25 1.50 2.50 3.00 3.75 3.25 3.75 3,50 1.00 1,75 30
0 0 0.50 0.50 0.75 2.25 2.50 2.75 1.75 4.00 6.75 3.75 1.50 0.50 31
0 .0 0.25 0.75 0.75 1.50 0.75 2.25 3.50 5.00 5.50 3.75 2.00 0 30
0 0.25 0 0.75 0.25 0.25 0.75 2.00 2.50 5.50 6.50 5.75 1.50 0 31
0 0.75 1.50 5.50 6.50 11.49 16.00 25.49 28.25 49.22 67.97 62.44 44.93 7.24 365
(b) Station: Kota Baru, Lat. 6 ~ 10'N, Long. 102 17'E, Ht. 5 m above S.L. Radiation classes (mWhcm-2)
Jan.
Feb.
Mar.
April
May
Jun.
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
0-50 50-100 100-150 150-200 200-250 250-300 300-350 350-400 40(050 450-500 500-550 550-600 600-650 650-700 700-750 Total
0.50 0.25 0.75 0.75 0.50 0.75 1.00 1.50 4.50 5.75 7.50 4.75 2.50 0 0 31
0 0 0.25 0 0.74 0.25 0.99 1.73 2.73 5.45 4.71 5.70 3.47 1.98 0 28
0 0 0.25 0 0.50 0.25 0.50 1.00 0.50 2.50 6.00 6.00 5.50 5.75 2.25 31
0 0 0 0 0 0 0.50 1.25 1.25 1.25 3.25 3.75 9.75 6,75 2,25 30
0 0 0 1.00 0.25 0.25 0.75 2.00 2.25 3.50 5.50 6.00 8.25 1.00 0.25 31
0 0 0.50 0 1.00 1.50 1.50 2.00 2.75 3.75 7.75 5.25 3.00 1.00 0 30
0 0 0 0.25 0.75 0.50 1.50 3.00 3.50 4.25 6.75 8,25 2,25 0 0 31
0 0 0 0.25 0.75 0.75 2.25 1.50 1.75 5.5 6.75 5.25 4.5 1.50 0.25 31
0 0 0 0.25 0 1.00 1.25 2.00 4.25 4.00 5.50 4.75 5.25 1.00 0.75 30
0 0 0.75 1.25 1.00 1.25 2.50 2.25 3.00 4.75 4.50 5.00 3.75 1.00 0 31
1.50 1.75 1.75 2.25 2.50 2.75 2.75 2.75 2.25 2.50 3.50 2.75 0.75 0.25 0 30
1.50 1.50 1.25 1.50 1.50 2.25 2.75 3.25 5.25 6.00 2.50 1.25 0.25 0.25 0 31
3.50 3.50 5.50 7.50 9.49 11.50 18.24 24.23 33.98 49.20 64.21 58.70 49.22 20.48 5.75 365
(c) Station: Kuala Lumpur, Lat. 3~ 07'N, Long. 101= 33'E, Hr. 1 9 m above S,L. Radiation classes (mWh c m - 2 )
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
0-50 50-100 100--150 150-200 200-250 250-300 300-350 350-400 400-450 450-500 500-550 550-600 600-650 650-700 700-750 Total
0 0 0 0.25 0.25 0.75 1.25 4.00 5.00 5.75 5.50 5.25 2.25 0.50 0.25 31
0 0.25 0 0.25 0 0.74 1.98 2.23 4.46 5.45 5.95 3.22 1.98 0.99 0.50 28
0 0 0 0.25 0 0.25 0.75 2.25 3.75 4.75 9.00 6.25 3.00 0.50 0.25 31
0 0 0 0.25 0 0.75 1.50 2.25 2.50 6.25 8.25 6.00 1.25 1.00 0 30
0 0 0.25 0.50 1.00 0.25 1.50 3.75 4.00 7.00 7.50 2.50 2.50 0.25 0 31
0 0 0 0.50 0.25 0.50 2.50 4.25 7.50 6.25 4.75 3.00 0.50 0 0 30
0 0 0 0 0.75 1.00 2.00 4.25 6.50 6.00 6.00 4.00 0.50 0 0 31
0 0 0 0.75 1.25 0.50 4.50 2.75 4.00 4.75 5.00 3.75 3.25 0.50 0 31
0 0 0 0.25 0.75 1.00 2.50 3.00 6.50 6.00 5.00 3.75 0.75 0.50 0 30
0 0 0 0 0.25 1.00 4.00 5.50 5.00 5.00 4.25 3.75 2.00 0.25 0 31
0 0 0 1.25 1.25 1.50 4.00 5.00 7.00 5.50 2.75 1.50 0.25 0 0 30
0 0 0.25 0.75 0.75 0.75 3.00 4.75 8.00 5.00 5.00 2.50 0.25 0 0 31
0 0.25 0.50 5.00 6.50 8.99 29.48 43.98 64.21 67.70 68.95 45.47 18.48 4.49 1.00 365
C H U A H AND LEE:
83
SOLAR R A D I A T I O N IN P E N I N S U L A R MALAYSIA
Table 5. Probabilities of solar radiation classes (a) Station: Penang, Lat. 5 18'N, Long. 100 16'E, HT. 3 m above S.L. Radiation classes (mWhcm-2) A(500 <~ Q) B(300 ~< Q < 500) CtQ < 300)
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
0.84 0.16 0
0,81 0.15 0.04
0.81 0.16 0.03
0.84 0.13 0.03
0.57 0.39 0.04
0.54 0.36 0.10
0.59 0.35 0.06
0.50 0.40 0.10
0.44 0.40 0.16
0.53 0.34 0.13
0.54 0.35 0.11
0.62 0.33 0.05
0.64 0.29 0.07
(b) Station Kota Baru, Lat. 6 ~ 10'N, Long. 102 17'E, Hr. 5 m above S.L. Radiation classes (mWhcm-2) A(500 ~< QI B(300 ~< Q < 5001 CIQ < 3001
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sept,
Oct.
Nov.
Dec.
Annual
0.48 0.41 0.11
0.57 0.39 0.04
0.82 0.15 0.03
0.86 0.14 0
0.68 0.27 0.05
0.57 0.33 0.10
0.56 0.40 0.04
0.59 0.35 0.06
0.58 0.38 0.04
0.46 0.40 0.14
0.24 0.34 0.42
0.14 0.55 0.31
0.54 0.34 0.12
(c) Station: Kuala Lumpur, Lat. 3 07'N, Long. 101 33'E, Ht. 19 m above S.L. Radiation classes (mWh c m - 2 ) A(500 ~< Q) B(300 ~< Q < 500) C(Q < 300)
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
0.44 0.52 0.04
0.45 0.51 0.04
0.61 0.37 0.02
0.55 0.42 0.03
0.41 0.52 0.07
0.26 0.68 0.04
0.34 0.60 0.06
0.40 0.52 0.08
0.33 0.60 0.07
0.33 0.63 0.04
0.15 0.72 0.13
0.25 0.67 0.08
0.38 0.56 0.06
Table 6. Probabilities of transitions between solar radiation classes on successive days lal Station: Penang, Lat. 5' 18'N, Long. 10ft 16'E, Hr. 3 m above S.L. Event AB means radiation Q changes from class A to class B Events
Jan.
Feb.
Mar.
Apr.
May
Jun,
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
AA AB AC BA BB BC CA CB CC
0.74 0.10 0 0.09 0.06 0 0.01 0 0
0.71 0.08 0.03 0.07 0.07 0 0.03 0 0.01
0.72 0.09 0.01 0.09 0.05 0.02 0.01 0.01 0
0.76 0.09 0.02 0.07 0.02 0.01 0.02 0.01 0
0.32 0.20 0.03 0.21 0.19 0.01 0.02 0.02 0
0.33 0.18 0.06 0.18 0.15 0.02 0.05 0.02 0.01
0.30 0,18 0,02 0,16 0.17 0.07 0.02 0.06 0.02
0.30 0.18 0.02 0.16 0.17 0.07 0.02 0.06 0.02
0.23 0.14 0.05 0.13 0.22 0.07 0.07 0.07 0.02
0.34 0.14 0.06 0.15 0.14 0.03 0.05 0.05 0.04
0.33 0.17 0.03 0.16 0.16 0.05 0.06 0.02 0.03
0.47 0.19 0.01 0.12 0.14 0.03 0.03 0 0.01
0.47 0.15 0.03 0.14 0.12 0.03 0.04 0.01 0.01
Ib) Station: Kota Baru, Lat. 6: 10'N, Long. 102: 17'E, Hr. 5 m above S.L. Events
Jan.
Feb.
Mar.
Apr.
May
Jun.
July
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
AA AB AC BA BB BC CA CB CC
0.33 0.12 0.01 0.14 0.21 0.04 0.02 0.06 0.07
0.42 0.16 0 0.15 0.20 0.02 0 0.03 0.02
0.73 0.08 0.01 0.08 0.05 0.02 0.01 0.01 0.01
0.76 0.10 0 0.11 0.03 0 0 0 0
0.50 0.16 0.02 0.13 0.12 0.02 0.04 0 0.01
0.39 0.14 0.04 0.12 0.16 0.05 0.07 0.03 0
0.32 0.18 0.04 0.21 0.19 0.01 0.03 0.02 0
0.37 0.18 0.02 0.15 0.21 0.04 0.01 0.02 0
0.38 0.16 0.02 0.17 0.21 0.02 0.02 0.02 0
0.26 0.19 0.03 0.15 0.19 0.06 0.06 0.02 0.04
0.14 0.08 0.05 0.09 0.07 0.10 0.03 0.13 0.31
0.06 0.08 0.01 0.06 0.36 0.15 0.02 0.11 0.15
0.39 0.13 0.02 0.13 0.17 0.04 0.03 0.04 0.05
84
CHUAH AND LEE:
SOLAR RADIATION IN PENINSULAR MALAYSIA Table 6. (contd.)
(c) Station: Kuala Lumpur, Lat. 3 07'N, Long. 101 3YE, Ht. 19 m above S.L. Events
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sept.
Oct.
Nov.
Dec.
Annual
AA AB AC BA BB BC CA CB CC
0.26 0.!5 0 0.17 0.35 0.02 0.01 0.02 0.02
0.25 0.17 0.02 0.22 0.28 0.02 0.02 0.02 0
0.41 0.18 0,02 0.19 0.18 0 0 0.02 0
0.28 0.24 0.02 0.24 0.19 0.01 0.02 0 0
0.19 0.18 0.04 0.16 0.34 0.02 0.06 0.01 0
0.10 0.16 0 0.18 0.48 0.03 0.01 0.04 0
0.14 0.19 0.02 0.20 0.36 0.03 0.02 0.03 0.01
0.10 0.17 0.03 0.15 0.39 0.05 0.03 0.07 0.01
0.12 0.20 0.02 0.20 0.34 0.04 0.03 0.05 0
0.13 0.19 0.02 0.19 0.43 0.01 0.02 0.01 0
0.05 0.09 0.01 0.09 0.54 0.09 0.04 0.06 0.03
0.10 0.13 0.01 0.12 0.51 0.05 0.01 0.05 0.02
0.18 0.18 0.02 0.18 0.35 0.03 0.02 0.03 0.01
Table 7. Monthly average temperature Station Penang Kuala Lumpur Kota Baru
Period
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug. Sept.
Oct.
Nov.
Dec.
Annual
1959-1972
80.2
81.0
81.3
81.7
81.6
81.0
80.4
8 0 . 1 79.7
79.4
79.5
79.8
80.5
1966-1972 1959-1972
78.5 78.0
79.3 78.9
79.9 80.2
80.0 81.8
80.7 82.3
79.9 81.3
79.4 80.7
79.3 80.2
79.3 78.9 8 0 . 1 79.6
78.6 78.5
78.3 78.3
79.3 80.0
days with low daily total radiations occur scarcely in Penang and Kuala Lumpur. In Penang, days with high radiation occur more frequently than in Kuala Lumpur. However, Kota Baru experiences a larger variability of daily total radiation. Extreme low radiations for long periods occur frequently during the N o r t h - E a s t M o n s o o n period, while high radiations for long periods occur during the dry season.
Acknowledqemem--The authors wish to thank the Malaysian Meteorological Service for making available the data for this work.
REFERENCES [-1] A. Angstrom. Q.J.R. Meteor. Soc. 50, 121 (1924). [2] J. N. Black, Some aspects of the climatology of solar radiation. New Sources of Energy 4, 311, U.N. Publication Sales No. 6 63.2.38 (1964). [:3] Donald G. S. Chuah and S. L. Lee, Solar Energy 26, 33 (1981). [4] Donald G. S. Chuah. S. L. Lee and R. E. Childs, Analysis of solar radiation data using cubic splines. In press. [5] R. H. B. Exell, Solar Energy 18, 549 (1976). [6] T. N. Goh. Solar Energy 22, 105 (1979). [7] L. Machta, Monitoring solar radiation for solar energy, UNESCO/WHO Solar Energy Symp., Geneva (1976).