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The fluctuation of solar irradiance in Hong Kong
Solar Ener~ty Vol. 25, pp. 485~.94 © Pergamon Press Ltd., 1980.
O038-092X/80/1201-O485/S02,00/O
Printed in Great Britain
THE FLUCTUATION OF SOLAR IRRADIANCE IN H O N G KONG C. T. LEUNG Department of Mechanical Engineering, University of Hong Kong, Hong Kong
(Received 29 April 1980; revision accepted 25 July 1980) Abstract--Measurements of the total global solar irradiance on a horizontal surface in Hong Kong during the 10-yr period 1969-78 are analysed. Mean annual, monthly and daily totals and their frequency distributions are computed and examined. The seasonal and climatic effects on the fluctuation of solar irradiance in Hong Kong are discussed. The effect is particularly large during the spring months when the transition from cold to warm weather occurs. The diurnal variation of total global solar irradiance in Hong Kong is also examined and the measured hourly data are observed to be in good agreement with Liu and Jordan's procedure of estimation from daily totals. Results of regression analysis relating total solar irradiance with duration of bright sunshine hours based on data for Hong Kong are summarized. The yearly regression coefficients are found to be varying in an unsystematic manner. Estimation of the Hong Kong monthly average diffuse solar irradiance based on the correlation with the cloudiness index is also performed and the results are found to vary between 7.39 MJ m 2 d- t in the summer and 4.44 MJ m- 2 d- t in the winter.
I. INTRODUCTION Solar insolation data for most parts of the world are now available. However, such information for the region of South East Asia, especially China is scarce. The present study is carried out to provide more detailed solar irradiance information for the designers of solar energy utilization systems under the climatic conditions of Hong Kong. Although. the analysis is based on the data collected in Hong Kong at a station (King's Park) located at 22°19'N, I14°10'E, it may also serve as a useful reference for system designers and users in other subtropical regions of Asia and elsewhere which have the similar climatic conditions. Measurements of the daily total global solar irradiance and duration of bright sunshine have been carried out in Hong Kong by the Royal Observatory for many years since June 1958 up to the present. Daily observations of the duration of sunshine are recorded by the Campbell-Stokes type heliograph and values of the total global solar irradiance are obtained from recordings of a bimetallic actinograph, British Meteorological Office Pattern Mk III, with a wavelength range between 0.3 and 4 pm and accuracy to within 5 per cent. The instrument has been calibrated against a standard recorder at the Kew observatory, and all the measurements presented in this paper are based on the International Pyrheliometric Scale of 1956 (IPS 1956). Unfortunately, continuous and reliable records may not be available for some appreciable long periods due to the malfunctioning of instruments and lack of calibration. Much of the present work is based on the statistical analysis of a continu-
ous set of data available for the 10-yr period between 1969 and 1978. On the other hand, the recordings of the total global solar irradiance on an hourly basis have been obtained only since December 1978. The measurements on hourly data are made by means of a thermo-electric pyranometer of the sealed thermopile dome solarimeter type, manufactured by Kipp and Zonen, Delft, Netherlands. The instrument has a wavelength range of 300nm-2.5pm, and accuracy within 1 per cent. It is calibrated against an Eppley Angstr6m Pyrheliometer and the radiation reference employed is also The International Pyrheliometer Scale (1956). The preliminary analysis on the Hong Kong hourly data presented in this paper is based only on the 12-month period between December 1978 and November 1979. In this paper, the average values of the monthly, yearly daily totals of global solar irradiance in Hong Kong are presented and the seasonal effects on the frequency distribution are discussed. The diurnal variation of solar irradiance and the validity of Liu and J o r d a n ' s [ l ] procedure of estimating hourly totals from daily values in Hong Kong are then examined. The characteristics of the yearly variation of sunshine duration in Hong Kong and its correlation with total solar irradiance are discussed. Finally, the monthly average values of diffuse irradiance in Hong Kong are estimated by two different methods and compared.
485
2. GENERAL CLIMATE OF HONG KONG The territory of Hong Kong which consists of the Hong Kong island proper, the peninsular of Kow-
486
C.T. LE~NG May and September. The wettest month of the year is June when the average rainfall amounts to 457.5 ram. The driest month is December when the average is only 25.9mm. Other climatological information on Hong Kong weather is given in Refs. [2, 3].
loon, New Territories and adjacent islands, has a total area of about 1056 km 2. Climatically, Hong Kong lies within the tropics but, unlike other tropical countries, it experiences distinct seasonal changes in weather due to its position on the southern edge of the Continent of Asia and opposite a vast expanse of ocean. The winter monsoon blows mainly from the North and North East direction and the winter months between November to February are characterized by frequent outbreaks of cold and often dry air originating from the Asian Continental anticyclone from the north. It is not uncommon during January and February for temperatures to drop below 10°C although the mean temperatures from December to March are around 15-18°C. The spring season during March and April is usually short and is characterized by cloudy skies, periods of light rain and sometimes very humid conditions. Also, the temperature tends to fluctuate widely from day to day. In the summer months between May and August, the monsoon blows usually from the South or South East direction. The weather is mainly tropical, hot and humid with occasional showers or thunderstorms. Afternoon temperatures frequently exceed 32°C between June and August with mean temperatures around 27 29°C. In addition, during the months between July and September, tropical cyclones, known as typhoons originating over Pacific Ocean are most common. When these cyclones strike Hong Kong, they bring heavy rain and strong winds of hurricane force which may last for a few consecutive days. The autumn season is rather short and may last from mid September to the beginning of November. The winds become more easterly in direction. The amount of cloud in the sky decreases rapidly at this time of the year and so does the frequency of tropical cyclones. The mean annual rainfall in Hong Kong is 2246.4 mm of which about 80 per cent falls between
3. DALLY TOTAL G L O B A L SOLAR IRRADIANCE
3.1 Monthly and annual totals The Hong Kong monthly and annual values of the total global solar irradiance on a horizontal surface are given in Table i. It can be seen that for the past 10yr, the annual totals range between 4765 and 6030MJm -2 and has a mean value of about 5421 M J m -2. Over the year, the highest monthly mean total occurs in July (584 MJ m-2) and the lowest occurs in February (331 MJm-2t. The highest recorded total for a month was in August 1969 (702MJm -2) and the lowest was in March 1978 (213 MJ m-z). The variability from year to year for the annual totals is quite small, the overall range (maximum to minimum) being only 23.3 per cent of the yearly mean. However, the monthly variability is quite large. March is the month with the greatest variation, having a range of Ill.4 per cent of the monthly mean. This may be mainly due to the unstable climatic condition during the spring season. The steadiest period is at the beginning of summer in the month of May with a range of only 26.8 per cent of the monthly mean. 3.2 Average daily totals Values of the Hong Kong average daily total global solar irradiance on a horizontal surface for each month of the year are shown in Table 2 in which the maximum and minimum monthly average values are
Table 1. Monthly and annual totals of global solar irradiance on a horizontal surface (MJ m-2) J
F
M
A
M
J
J
1969
218
1970
356
259
339
460
568
529
590
439
284
511
495
533
667
1971
468
339
429
459
461
494
544
1972
474
301
625
381
477
648
1973
345
341
443
362
485
1974
374
332
372
420
536
1975
291
340
242
399
1976
410
322
317
388
1977
253
326
438
1978
369
313
213
A
S
O
N
D
Year
702
590
522
465
421
5663
557
471
441
274
421
5449
591
590
599
590
396
5960
648
564
582
561
386
383
6030
468
451
444
417
458
379
455
5048
427
614
577
447
386
367
320
5172
441
431
567
440
513
367
381
353
4765
484
471
543
568
445
429
420
339
5136
406
575
5]3
518
572
460
501
439
356
5357
373
476
60]
698
612
591
485
459
437
5627
Means 356 331 370 416 500 512 584 563 511 475 416 388 542] .................................................................................................................... T~nge 256 180 412 149 134 221 247 262 174 232 316 135 1265 Max-Min .................................................................................................................... Range as % of Mean
71.9
54.4
111.4
35.8
26.8
43.2
42.3
46.5
34,]
48.8
76.0
34.8
23,3
Solar irradiance in Hong Kong
487
Table 2. Average daily totals of global solar irradiance on a horizontal surface (MJ m- 2 d- 1)
J
F
M
A
M
J
J
A
S
©
N
D
Year
11.48
11.76
11.95
13.87
16.13
17.06
18.84
18.16
17.02
15.33
13.87
12,51
14.84
Maximum
15.29
15.68
20.16
17.03
18.55
21,60
22.52
22.65
19.70
19.32
19.67
14.68
16.51
Minimum
7.03
9.25
12.07
14.23
14.23
14.5'3
14.19
13.90
11.84
9.13
10.32
13.05
Mean
6.87
also shown. The average daily total values range from 18.84 MJ m - 2 d-1 in the summer month of July to 11.48 M J m 2 d i in the winter month of January. Over the year, the average daily value is 14.84 MJ m -2 d - 1. The seasonal variation is typical of the subtropical climate in Southern Asia. The exceptionally large fluctuations in the months of March and November are mainly due to the unstable climatic condition during the transition from cold to warm weather and vice versa. 3.3 Frequency distribution of daily totals The percentage frequency distribution of the daily total global solar irradiance for each month of the same 10-yr period is given in Table 3 and intervals of 5.0 MJ m - 2 d - 1 were chosen. Over the year, the highest percentage of occurrences is 28.6 per cent in the interval of 1 5 . ( ~ 2 0 . 0 M J m - Z d 1 and the second highest is 21.8 per cent in the interval of 10.(~15.0 MJ m - 2 d - 1. Generally speaking, much higher percentage frequencies of occurrences with irradiance intensities above 20.0 MJ m - 2 d - 1 are ob-
served in the summer than in the winter. This result is quite typical for countries with distinct seasonal changes over the year. Figure 1 shows the annual curves of the frequency of occurrences in percentage of total number of days when daily global irradiance intensity is below a specified level. In the winter months of December and January, 70 per cent of the days receive less than 1 5 . 0 M J m - 2 d -1. Only a few per cent during this time exceed 2 0 . 0 M J m - 2 d-1 and none above 25.0 MJ m -2 d-1. However, in the summer months between May and September, at least 33 per cent of the days are above 20.0 MJ m - 2 d - 1 and of these a small number of days exceed 30.0 MJ m - 2 d - 1 in the two hottest months of the year. Generally speaking, the yearly frequency distribution is quite symmetrical with respect to the mid-summer month of July in which the frequent occurrences of high irradiance intensities are significant. The gradual decrease in the percentage frequencies of the high irradiance levels in the autumn and spring seasons is rather smooth with little or no discontinuity during the transition.
Table 3. Percentage frequency distribution of daily totals of global irradiance MJ m - 2 d -I
0-5.0
5.0-I0.0
10.0-15.0
15.0-20.0
20.0-25.0
25.0-30.0
Above
JAN
16.2
22.9
29.0
24.9
6.7
-
FEB
17.4
24.1
23.8
29.8
4.6
0.4
MAR
15.2
31.0
18.7
23.6
8.4
3.2
APR
8.3
21.3
25.7
26.0
15.7
3.0
MAY
5.5
15.2
21.6
24.2
25.8
7.7
JUN
3.0
18.3
14.0
28.7
25.0
9.0
2.0
JUL
2.6
12.6
17.1
15.5
29.4
21.3
1.6
AUG
4.2
12.9
13.2
25.8
25.2
18.7
0.3
SEP
3.7
12.3
17.7
32.7
26.7
6.7
0.3
3.6
OCT
9.0
14.2
16.8
35.5
21.0
NOV
10.7
12.3
22.7
45.0
9.3
DEC
7.7
18.4
41.6
31.0
1.3
YEAR
8.6
18.0
21.8
28.6
16.6
-
-
6.1
0.4
30.0
488
C.T. LEUNG r
l
l
l
l
l
l
l
i
[
l
l
tively lower percentage values of the hourly irradiance are received around solar noon. But, in the winter months, a much higher percentage of solar irradiance is received around noon time and comparatively less 8O percentage values of irradiance are received near sunrise and sunset hours. In other words, solar irradiance in Hong Kong is found to be more evenly distributed throughout the summer days than in the winter. Figure 2 presents the isopleth diagram of global ~ 50 solar irradiance at normal incidence in Hong Kong and lines of equal intensity of irradiance ~ 4o 0.50 MJ m - 2 hr- 1 have been drawn. The mean radi3O ation flux at midday is greatest in the month of October, when it exceeds 3.00 MJ m - 2 hr- 1, while the ZO < lowest midday flux occurs in the month of March and is near 0.80 MJ m - 2 hr 1. On the whole, the rise and fall of the mean radiation flux throughout the day is O l l l l l l l f l l l l generally symmetrical with respect to the solar noon JAN FEB MAR APR MAY JUN ]UL AUS SEP OU NOV DEC for all the year around. However, there is a tendency MONTHS OF THE YEAR for the irradiance to be less in the afternoon than it is Fig. l. Percentage~equencyofdailytotalslessthanspeciin the morning for the autumn months of September fled amounts (MJ m 2 d 1). and October. Moreover, a slightly irregular pattern in the diurnal variations is observed to occur in the 4. HOURLY TOTAL GLOBAL month of August which is mainly caused by the effect SOLAR IRRADIANCE of tropical cylcones or typhoons, striking Hong Kong 4.1 Diurnal variation during the summer season. The above analysis based Table 4 gives the Hong Kong monthly mean values on data for only a 12-month period can be regarded of the hourly total solar irradiance received on a hori- as a preliminary one and some of the observations zontal surface within a day for the 12-month period. may have to be confirmed by additional local hourly The annual variation of the mean horizontal solar data measurements for subsequent years in the future. irradiance in percentage values of the daily totals is shown in Table 5. With the exception of the summer 4.2 Comparison with theoretical prediction months, over 14 per cent of the daily total irradiance Methods of estimating hourly irradiance from its is received within the first hour before and after solar daily value have long been established [1,4]. Liu and noon. Likewise, over 12 per cent of the total irra- Jordan had outlined a procedure of determining diance available per day is received in the next hour monthly average hourly total irradiance ] from the before and after the solar noon. In general, the daily total value H. In order to examine whether or seasonal effect on the annual distribution is rather not the Hong Kong data fit Liu and Jordan's proobvious. In the summer months of May-August, rela- cedure, mean values of the pair hours around solar Table 4. Hong Kong monthly average hourly total irradiance received on a horizontal surface (MJ m =hr-1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .H.O.U.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Month 5-6
6-7
7-8
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
Decer~ber
1978
-
0.06
0.36
0.92
I .52
1.93
2.14
2.16
I .95
I .53
I .00
0.44
0.07
-
January
1979
-
0.07
0.33
0.75
I .20
I .55
I .68
I .57
I .40
7 .14
0.72
0,30
0.06
-
0.08
0.33
0.70
I .04
I .30
I .47
1.46
I .35
I .I0
0.72
0.32
0.07
-
0.07
0.21
0.40
0.60
0.79
0.89
0.96
0.92
0.76
0.53
0.27
0.07
0.00
February March
0.01
April
0.03
0.16
0.43
0.77
1.14
1.44
1.56
1.63
1.47
1,13
0.79
0.48
0.18
0.02
May
0.05
0.22
0.51
0.84
I .13
I .41
1.64
I .66
I .60
I .38
I .05
0.59
0.26
0.05
June
0.08
0.33
0.74
I .16
I .57
2.01
2.18
2.08
I .85
I .59
1.23
0.80
0.38
0.09
July
0.10
0.41
0.90
1.50
2.14
2.62
2.82
2.80
2.60
2.17
1.65
1,14
0.56
0.12
August
0.05
0.29
0.71
1.14
1.57
I .82
I .81
I .75
1.71
1.48
I .11
0,70
0.28
0.04
September
0.07
0.37
0.88
I .44
I .89
2.20
2.24
2.10
1.73
1.42
I .02
0.43
0.07
0.00
October
0.01
0.16
0.69
1.43
2.11
2.69
3.02
2.96
2.62
2.09
1.34
0.62
0.09
0.00
0.04
0.29
0.74
I .26
I .61
I .81
I .81
I .58
I .25
0.76
0.28
0.02
November
Solar irradiance in Hong Kong
,
,
,
489
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490
C.T. LEUNG
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Solar irradiance in Hong Kong DEC
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measured duration of sunshine hours occurs in the month of March. This may be again due to the uncertain and variable weather conditions in this month of spring. During the wet and rainy season of summer where typhoons tracking across the South China Sea close to Hong Kong are common, the overall high mean values of the duration of bright sunshine for a given month do not seem to be seriously affected or lowered, although the range of the measured sunshine hours is observed to be slightly higher in the month of August.
I
JAN FEB MAR APR MAY ]UN JUL AUG SEP OCl
NOV DEE
I
I
I
]
I
7
8
9
I0
11
]
I
12 13 HOUR
I
I
I
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IZ,
15
16
17
491
18
5.2 Correlation between total global irradiance and sunshine duration The relationship between the measured total global solar irradiance and the recorded duration of sunshine hours has been studied by a number of investigators[5,6]. The common type of correlation between these two variables is of the linear form [7]. (2 (20
Fig. 2. Diurnal variation of global solar irradiance (MJ m-2 hr-1). Time is true solar time. noon for the ratio of Hong Kong monthly average hourly total to daily total irradiance, ]/H are plotted in Fig. 3 in which the recommended values by Liu and Jordan are shown as solid curves for comparison. Each data point represents the monthly average ratio and the mean sunset angles are calculated on the 15th day of each month. On the whole, it may be said that the hourly irradiance data of Hong Kong fit the solid curves quite well except at sunset hour angles around 94 °, where slightly larger deviations for the expected curves have been observed. Apart from these discrepancies and some noticeable asymmetries in the actual data around solar noon, the Hong Kong hourly radiation values are generally in good agreement with that of theoretical predictions. This confirms that Liu and Jordan's procedure of estimating average hourly horizontal total irradiance based on daily values is applicable in Hong Kong and can be used confidently for future estimates. 5. D U R A T I O N
--=
a + b-
S So
(1)
where (2 is the average daily total global irradiance actually received on a horizontal surface; Qo is the maximum theoretical daily global irradiance that would reach the earth's surface over the same period in the absence of the atmosphere; S is the average measured daily duration of bright sunshine; So is the daily maximum duration of sunshine over the same period; and a, b are local constants depending on latitude and other meteorological parameters. An investigation of the linear regression coefficients in Hong Kong was performed by Sham [8] using earlier monthly mean values of daily total irradiance and recordings of bright sunshine hours for the period
°2°1'\'''
J 0.14J._
~
0A,
HON ,0N0 '
°o~,,. o ~""~o ^o ~o o~,,"
HOURFROMSOLAR NOON
OF BRIGHT SUNSHINE
5.1 Monthly and annual mean values Table 6 gives the Hong Kong monthly and annual average values of the duration of sunshine per day as measured by the Campbell-Stokes type of instrument recorded for the 10-yr period between 1969 and 1978. It can be seen that the month of July has the largest mean value of bright sunshine of 214.7 hr whereas the lowest value of 100.6 hr occurs in March. The figures in Table 6 also confirm that the midsummer months between July and August are the best months for solar radiation in Hong Kong. The effect of seasonal and climatic changes on the yearly distribution of sunshine duration in Hong Kong is also obvious as seen by the relatively longer duration of sunshine hours recorded in the summer months than in the winter. In addition, the largest fluctuation in the
~ -,~ 0.17
a
3~
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~ ° ~ ' °
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~6
i~'o
SUNSEI HOURANGLE,cJs, DEGREE
Fig. 3. Experimental ratio of the hourly total irradiance to the daily total irradiance.
492
C. T. LEUNG Table 7. Yearly variation of regression coefficients
Year
a
b
Correlation Coefficients
1972
0.208
0.692
0.95
1973
0.252
0.429
0.91
1974
0.230
0.450
0.89
1975
0.200
0.503
0.94
1976
0.224
0.468
0.96
1977
0.171
0.540
0.97
between June 1958 and August 1962. The regression coefficients a and b were found to be 0.220 and 0.575 respectively. When data for the recent 6-yr period 1972-77 were used in eqn (1), the regression coefficients a and b for each year were found to vary between the wide ranges of 0.171~0.252 and 0.429q3.692 respectively as seen from Table 7. It is apparent from these results that there seems to be no systematic pattern of variation in these coefficients from year to year. Similar effects have been reported by workers in Singapore [9]. However, a much wider range of variation in the regression coefficients has been observed in the case of Hong Kong. This could be mainly due to the local distinct seasonal weather changes in the subtropical climate of Hong Kong as compared to the little or no seasonal variation
throughout the year in the equatorial climate of Singapore.
6. DIFFUSE SOLAR IRRADIANCE
Solar collectors of the flat-plate type, whether thermal or photovoltaic, can utilize both the direct and diffuse components of the solar irradiance. In the design of such devices, knowledge on the direct and diffuse components of the total irradiance on a horizontal surface is needed and the energy collected by a tilted surface at any angle can then be subsequently calculated [ 10]. Data for total irradiance measurements on horizontal surfaces are known for major parts of the world,
Table 8. Calculation of the Hong Kong monthly average diffuse irradiance on a horizontal surface by the cloudiness correlation methods Page's Liu and Jordan's . . . .Correlation . . . . . . . . . . . . . . . . . . . .Correlation ............. MONTH
Ho
H
[MJm-2d -I ]
[MJm-2d -I ]
KT=(H/H°)
(Hd/~)
Hd
(Ha/~)
[MJm-2d -I ]
Ha [MJm-2d -I ]
JAN
25.21
11.48
0.455
0.486
5.58
0.410
4.71
FEB
29.41
11.76
0.400
0.548
6.44
0.465
5.47
MAR
33.81
11.95
0.353
0.601
7.18
0.521
6.23
APR
37.36
13.87
0.371
0.581
8.06
0.499
6.92
MAY
39.06
16.13
0.413
0.533
8.60
0.451
7.27
JUN
39.58
17.06
0.431
0.513
8.75
0.433
7.39
7.33
JUL
39.30
18.84
0.479
0.459
8.65
0.389
AUG
38.07
18.16
0.477
0.461
8.37
0.390
7.08
SEP
35.30
17.02
0.482
0.455
7.74
0.386
6.57
OCT
31.23
15.33
0.491
0.445
6.82
0.378
5.79
NOV
26.64
13.87
0.521
0.411
5.70
0.354
4.91
DEC
24.12
12.51
0.519
0.414
5.18
0.355
4.44
Solar irradiance in Hong Kong but data on the diffuse irradiance are still not currently available for many locations. Up to the present, there have been no measurements of the diffuse solar irradiance in Hong Kong and one has to rely on theoretical methods for their estimates. A number of investigators have found that the average daily diffuse irradiance fraction of the daily total on a horizontal surface, Ha/Hcan be correlated to the cloudiness index, Kr. The parameter K'r represents the fraction of the mean daily extraterrestrial horizontal irradiance, Ho arriving at the surface of the earth and is defined as
Kr =
(2)
~oo"
The correlation developed by Page [11] was of the linear form: Ha --=
1 . 0 0 - 1.13Kr.
-- 1.390 -- 4.027K"r + 5.531R~ - 3.108K'3r.
(4)
The monthly average values of the daily diffuse solar irradiance in Hong Kong have been calculated by the above two correlations with cloudiness index based on the Hong Kong meteorological data for the 10-yr period between 1969 and 1978 and the results are presented in Table 8. Both methods of correlation indicate that the highest fraction of diffuse solar irradiance occurs in the month of March and the lowest in November. Over the year, the estimated fraction may vary between 0.601 and 0.354 strongly depending on what method of correlation is being used. ZO-O
7
'e
I
l
t
l
t
l
l
l •
18.0 .-
i:zc
l
16'0
.°,
l
l
t
°°.
°°."
"°°
",
•"~OTAL IRRADIANCE,H.".. ..¢ FOR REFERENCE "..,
14.0
," •°
%°
°°°°°°°°
12.0
r DIFFUSE IRR~IANCE.Hd lO.O 0.o 6.o
LIU ANO ]OROAN
4-0
~GE - - - - - -
"= ::i= z
7. CONCLUSION The analysis of the total global solar irradiance measurements in Hong Kong during the 10-yr period 1969-1978 indicates distinct seasonal variation with pattern in line with the climatic changes of the year. The range of variation is especially great in the spring season during the transition period between the cold and the warm weather. In addition, the expected large solar irradiance fluctuation in the summer rainy days and the tropical cyclone periods also suggests the need of relatively large capacity storage systems in Hong Kong solar energy utilization installations to cover periods of days with little or no bright sunshine. Regression equation relating the total global solar irradiance with duration of sunshine has been found to give varying yearly regression coefficients strongly depending on the weather conditions of the particular year. An investigation of the Hong Kong hourly solar irradiance data confirms that Liu and Jordan's procedure of estimating monthly average hourly total horizontal solar irradiance based on daily values is applicable in Hong Kong. Also, predictions on the monthly average diffuse solar irradiance based on the cloudiness index give a maximum value of 7 . 3 9 M J m - 2 d -1 in the summer month of July and 4.44 MJ m - Z d 1 in the winter month of December according to the conservative estimates.
Acknowledgement~The author is indebted to Prof. E. A. Bruges for revising the manuscript, to Drs S. K. Yan and L. Cheung for assistance with some of the computational work and to the Hong Kong Royal Observatory for providing data on solar irradiance measurements.
RRELAIION$ BY:-
w t~
The magnitudes of the monthly average daily diffuse solar irradiance in Hong Kong are presented graphically in Fig. 4 in which the monthly average daily total values are also shown for reference. It is to be noted that both correlations predict a similar pattern of yearly variation though the Liu and Jordan's correlation gives consistently slightly lower estimates. Over the year, the monthly average daily diffuse solar irradiance in Hong Kong is high in the summer and low in the winter. The values range between 7.39 and 4.44 MJ m-2 d 1 based on Liu and Jordan's correlation of estimates. However, since the estimated values differ from method to method and the deviation may be as high as 19 per cent, future experimental data on the local measurements of the daily diffuse horizontal solar irradiance are needed in order to confirm which correlation is the best to use for the Hong Kong climate.
(3)
Liu and Jordan had also presented a different correlation and Klein[10] later developed the following mathematical expression for their correlation: Hd
493
?0
~: 0'0
i
I
I
I
I
I
I
[
I
I
I
NOMENCLATURE
I
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC MONTHS
Fig. 4. Comparison of the monthly variation of the estimated diffuse solar irradiance in Hong Kong.
I H, Q
monthly average hourly total irradiance received on a horizontal surface over 1 hr, MJ m 2 hr monthly average daily total irradiance received on a horizontal surface, MJ m 2 d-
494
C.T. LEUNG
Ho, Qo monthly average of the daily extraterrestrial irradiance on a horizontal surface, MJ m - 2 d - 1 He monthly average daily diffuse irradiance received on a horizontal surface, MJ m - 2 d - 1 So monthly average of the day-length, or the maximum hours of bright sunshine per day, hr S monthly average of the hours of bright sunshine per_day hr ~'r H/Ho
5. 6. 7. 8.
REFERENCES
1. B. Y. H. Liu and R. C. Jordan, The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 4(2), 1-19 (1960). 2. Royal Observatory of Hong Kong, Meteorological Results Part I--Surface Observations (1969-78). 3. Royal Observatory of Hong Kong, Monthly weather summary (1976-79). 4. A. Whillier, The determination of hourly values of total
9. 10. 11.
radiation from daily summations. Arch. Met. Geoph. Biokl. B. 7, 197-244. (1956). A. K. ,~ngstrSm, Solar and terrestrial radiation. Q. J. R. Meteor. Soc. 50, 121 (1924). S. Fritz and T. H. MacDonald, Average solar radiation in the United States. Heating and Ventilating 46(7), 61-64 (1949). J. N. Black, C. W. Bonython and J. M. Prescott, Solar radiation and the duration of sunshine. Q. J. R. Meteor. Soc. 80, 231-235 (1954). P. Sham, Total solar and sky radiation in Hong Kong. Royal Observatory of Hong Kong, Tech. Note 22 (1964). T. N. Goh, Statistical study of solar radiation information in an equatorial region (Singapore). Solar Energy 22, 105 l l l (1979). S. A. Klein, Calculation of monthly average insolation of tilted surfaces. Solar Energy 19, 325-329 (1977). J. K. Page, The estimation of monthly mean values of daily total short-wave radiation on vertical and inclined surfaces from sunshine records for latitudes 40°N~0°S. Proc. UN Conf. New Sources of Energy, Paper S/98 (1961).
O038-092X/80/1201-O485/S02,00/O
Printed in Great Britain
THE FLUCTUATION OF SOLAR IRRADIANCE IN H O N G KONG C. T. LEUNG Department of Mechanical Engineering, University of Hong Kong, Hong Kong
(Received 29 April 1980; revision accepted 25 July 1980) Abstract--Measurements of the total global solar irradiance on a horizontal surface in Hong Kong during the 10-yr period 1969-78 are analysed. Mean annual, monthly and daily totals and their frequency distributions are computed and examined. The seasonal and climatic effects on the fluctuation of solar irradiance in Hong Kong are discussed. The effect is particularly large during the spring months when the transition from cold to warm weather occurs. The diurnal variation of total global solar irradiance in Hong Kong is also examined and the measured hourly data are observed to be in good agreement with Liu and Jordan's procedure of estimation from daily totals. Results of regression analysis relating total solar irradiance with duration of bright sunshine hours based on data for Hong Kong are summarized. The yearly regression coefficients are found to be varying in an unsystematic manner. Estimation of the Hong Kong monthly average diffuse solar irradiance based on the correlation with the cloudiness index is also performed and the results are found to vary between 7.39 MJ m 2 d- t in the summer and 4.44 MJ m- 2 d- t in the winter.
I. INTRODUCTION Solar insolation data for most parts of the world are now available. However, such information for the region of South East Asia, especially China is scarce. The present study is carried out to provide more detailed solar irradiance information for the designers of solar energy utilization systems under the climatic conditions of Hong Kong. Although. the analysis is based on the data collected in Hong Kong at a station (King's Park) located at 22°19'N, I14°10'E, it may also serve as a useful reference for system designers and users in other subtropical regions of Asia and elsewhere which have the similar climatic conditions. Measurements of the daily total global solar irradiance and duration of bright sunshine have been carried out in Hong Kong by the Royal Observatory for many years since June 1958 up to the present. Daily observations of the duration of sunshine are recorded by the Campbell-Stokes type heliograph and values of the total global solar irradiance are obtained from recordings of a bimetallic actinograph, British Meteorological Office Pattern Mk III, with a wavelength range between 0.3 and 4 pm and accuracy to within 5 per cent. The instrument has been calibrated against a standard recorder at the Kew observatory, and all the measurements presented in this paper are based on the International Pyrheliometric Scale of 1956 (IPS 1956). Unfortunately, continuous and reliable records may not be available for some appreciable long periods due to the malfunctioning of instruments and lack of calibration. Much of the present work is based on the statistical analysis of a continu-
ous set of data available for the 10-yr period between 1969 and 1978. On the other hand, the recordings of the total global solar irradiance on an hourly basis have been obtained only since December 1978. The measurements on hourly data are made by means of a thermo-electric pyranometer of the sealed thermopile dome solarimeter type, manufactured by Kipp and Zonen, Delft, Netherlands. The instrument has a wavelength range of 300nm-2.5pm, and accuracy within 1 per cent. It is calibrated against an Eppley Angstr6m Pyrheliometer and the radiation reference employed is also The International Pyrheliometer Scale (1956). The preliminary analysis on the Hong Kong hourly data presented in this paper is based only on the 12-month period between December 1978 and November 1979. In this paper, the average values of the monthly, yearly daily totals of global solar irradiance in Hong Kong are presented and the seasonal effects on the frequency distribution are discussed. The diurnal variation of solar irradiance and the validity of Liu and J o r d a n ' s [ l ] procedure of estimating hourly totals from daily values in Hong Kong are then examined. The characteristics of the yearly variation of sunshine duration in Hong Kong and its correlation with total solar irradiance are discussed. Finally, the monthly average values of diffuse irradiance in Hong Kong are estimated by two different methods and compared.
485
2. GENERAL CLIMATE OF HONG KONG The territory of Hong Kong which consists of the Hong Kong island proper, the peninsular of Kow-
486
C.T. LE~NG May and September. The wettest month of the year is June when the average rainfall amounts to 457.5 ram. The driest month is December when the average is only 25.9mm. Other climatological information on Hong Kong weather is given in Refs. [2, 3].
loon, New Territories and adjacent islands, has a total area of about 1056 km 2. Climatically, Hong Kong lies within the tropics but, unlike other tropical countries, it experiences distinct seasonal changes in weather due to its position on the southern edge of the Continent of Asia and opposite a vast expanse of ocean. The winter monsoon blows mainly from the North and North East direction and the winter months between November to February are characterized by frequent outbreaks of cold and often dry air originating from the Asian Continental anticyclone from the north. It is not uncommon during January and February for temperatures to drop below 10°C although the mean temperatures from December to March are around 15-18°C. The spring season during March and April is usually short and is characterized by cloudy skies, periods of light rain and sometimes very humid conditions. Also, the temperature tends to fluctuate widely from day to day. In the summer months between May and August, the monsoon blows usually from the South or South East direction. The weather is mainly tropical, hot and humid with occasional showers or thunderstorms. Afternoon temperatures frequently exceed 32°C between June and August with mean temperatures around 27 29°C. In addition, during the months between July and September, tropical cyclones, known as typhoons originating over Pacific Ocean are most common. When these cyclones strike Hong Kong, they bring heavy rain and strong winds of hurricane force which may last for a few consecutive days. The autumn season is rather short and may last from mid September to the beginning of November. The winds become more easterly in direction. The amount of cloud in the sky decreases rapidly at this time of the year and so does the frequency of tropical cyclones. The mean annual rainfall in Hong Kong is 2246.4 mm of which about 80 per cent falls between
3. DALLY TOTAL G L O B A L SOLAR IRRADIANCE
3.1 Monthly and annual totals The Hong Kong monthly and annual values of the total global solar irradiance on a horizontal surface are given in Table i. It can be seen that for the past 10yr, the annual totals range between 4765 and 6030MJm -2 and has a mean value of about 5421 M J m -2. Over the year, the highest monthly mean total occurs in July (584 MJ m-2) and the lowest occurs in February (331 MJm-2t. The highest recorded total for a month was in August 1969 (702MJm -2) and the lowest was in March 1978 (213 MJ m-z). The variability from year to year for the annual totals is quite small, the overall range (maximum to minimum) being only 23.3 per cent of the yearly mean. However, the monthly variability is quite large. March is the month with the greatest variation, having a range of Ill.4 per cent of the monthly mean. This may be mainly due to the unstable climatic condition during the spring season. The steadiest period is at the beginning of summer in the month of May with a range of only 26.8 per cent of the monthly mean. 3.2 Average daily totals Values of the Hong Kong average daily total global solar irradiance on a horizontal surface for each month of the year are shown in Table 2 in which the maximum and minimum monthly average values are
Table 1. Monthly and annual totals of global solar irradiance on a horizontal surface (MJ m-2) J
F
M
A
M
J
J
1969
218
1970
356
259
339
460
568
529
590
439
284
511
495
533
667
1971
468
339
429
459
461
494
544
1972
474
301
625
381
477
648
1973
345
341
443
362
485
1974
374
332
372
420
536
1975
291
340
242
399
1976
410
322
317
388
1977
253
326
438
1978
369
313
213
A
S
O
N
D
Year
702
590
522
465
421
5663
557
471
441
274
421
5449
591
590
599
590
396
5960
648
564
582
561
386
383
6030
468
451
444
417
458
379
455
5048
427
614
577
447
386
367
320
5172
441
431
567
440
513
367
381
353
4765
484
471
543
568
445
429
420
339
5136
406
575
5]3
518
572
460
501
439
356
5357
373
476
60]
698
612
591
485
459
437
5627
Means 356 331 370 416 500 512 584 563 511 475 416 388 542] .................................................................................................................... T~nge 256 180 412 149 134 221 247 262 174 232 316 135 1265 Max-Min .................................................................................................................... Range as % of Mean
71.9
54.4
111.4
35.8
26.8
43.2
42.3
46.5
34,]
48.8
76.0
34.8
23,3
Solar irradiance in Hong Kong
487
Table 2. Average daily totals of global solar irradiance on a horizontal surface (MJ m- 2 d- 1)
J
F
M
A
M
J
J
A
S
©
N
D
Year
11.48
11.76
11.95
13.87
16.13
17.06
18.84
18.16
17.02
15.33
13.87
12,51
14.84
Maximum
15.29
15.68
20.16
17.03
18.55
21,60
22.52
22.65
19.70
19.32
19.67
14.68
16.51
Minimum
7.03
9.25
12.07
14.23
14.23
14.5'3
14.19
13.90
11.84
9.13
10.32
13.05
Mean
6.87
also shown. The average daily total values range from 18.84 MJ m - 2 d-1 in the summer month of July to 11.48 M J m 2 d i in the winter month of January. Over the year, the average daily value is 14.84 MJ m -2 d - 1. The seasonal variation is typical of the subtropical climate in Southern Asia. The exceptionally large fluctuations in the months of March and November are mainly due to the unstable climatic condition during the transition from cold to warm weather and vice versa. 3.3 Frequency distribution of daily totals The percentage frequency distribution of the daily total global solar irradiance for each month of the same 10-yr period is given in Table 3 and intervals of 5.0 MJ m - 2 d - 1 were chosen. Over the year, the highest percentage of occurrences is 28.6 per cent in the interval of 1 5 . ( ~ 2 0 . 0 M J m - Z d 1 and the second highest is 21.8 per cent in the interval of 10.(~15.0 MJ m - 2 d - 1. Generally speaking, much higher percentage frequencies of occurrences with irradiance intensities above 20.0 MJ m - 2 d - 1 are ob-
served in the summer than in the winter. This result is quite typical for countries with distinct seasonal changes over the year. Figure 1 shows the annual curves of the frequency of occurrences in percentage of total number of days when daily global irradiance intensity is below a specified level. In the winter months of December and January, 70 per cent of the days receive less than 1 5 . 0 M J m - 2 d -1. Only a few per cent during this time exceed 2 0 . 0 M J m - 2 d-1 and none above 25.0 MJ m -2 d-1. However, in the summer months between May and September, at least 33 per cent of the days are above 20.0 MJ m - 2 d - 1 and of these a small number of days exceed 30.0 MJ m - 2 d - 1 in the two hottest months of the year. Generally speaking, the yearly frequency distribution is quite symmetrical with respect to the mid-summer month of July in which the frequent occurrences of high irradiance intensities are significant. The gradual decrease in the percentage frequencies of the high irradiance levels in the autumn and spring seasons is rather smooth with little or no discontinuity during the transition.
Table 3. Percentage frequency distribution of daily totals of global irradiance MJ m - 2 d -I
0-5.0
5.0-I0.0
10.0-15.0
15.0-20.0
20.0-25.0
25.0-30.0
Above
JAN
16.2
22.9
29.0
24.9
6.7
-
FEB
17.4
24.1
23.8
29.8
4.6
0.4
MAR
15.2
31.0
18.7
23.6
8.4
3.2
APR
8.3
21.3
25.7
26.0
15.7
3.0
MAY
5.5
15.2
21.6
24.2
25.8
7.7
JUN
3.0
18.3
14.0
28.7
25.0
9.0
2.0
JUL
2.6
12.6
17.1
15.5
29.4
21.3
1.6
AUG
4.2
12.9
13.2
25.8
25.2
18.7
0.3
SEP
3.7
12.3
17.7
32.7
26.7
6.7
0.3
3.6
OCT
9.0
14.2
16.8
35.5
21.0
NOV
10.7
12.3
22.7
45.0
9.3
DEC
7.7
18.4
41.6
31.0
1.3
YEAR
8.6
18.0
21.8
28.6
16.6
-
-
6.1
0.4
30.0
488
C.T. LEUNG r
l
l
l
l
l
l
l
i
[
l
l
tively lower percentage values of the hourly irradiance are received around solar noon. But, in the winter months, a much higher percentage of solar irradiance is received around noon time and comparatively less 8O percentage values of irradiance are received near sunrise and sunset hours. In other words, solar irradiance in Hong Kong is found to be more evenly distributed throughout the summer days than in the winter. Figure 2 presents the isopleth diagram of global ~ 50 solar irradiance at normal incidence in Hong Kong and lines of equal intensity of irradiance ~ 4o 0.50 MJ m - 2 hr- 1 have been drawn. The mean radi3O ation flux at midday is greatest in the month of October, when it exceeds 3.00 MJ m - 2 hr- 1, while the ZO < lowest midday flux occurs in the month of March and is near 0.80 MJ m - 2 hr 1. On the whole, the rise and fall of the mean radiation flux throughout the day is O l l l l l l l f l l l l generally symmetrical with respect to the solar noon JAN FEB MAR APR MAY JUN ]UL AUS SEP OU NOV DEC for all the year around. However, there is a tendency MONTHS OF THE YEAR for the irradiance to be less in the afternoon than it is Fig. l. Percentage~equencyofdailytotalslessthanspeciin the morning for the autumn months of September fled amounts (MJ m 2 d 1). and October. Moreover, a slightly irregular pattern in the diurnal variations is observed to occur in the 4. HOURLY TOTAL GLOBAL month of August which is mainly caused by the effect SOLAR IRRADIANCE of tropical cylcones or typhoons, striking Hong Kong 4.1 Diurnal variation during the summer season. The above analysis based Table 4 gives the Hong Kong monthly mean values on data for only a 12-month period can be regarded of the hourly total solar irradiance received on a hori- as a preliminary one and some of the observations zontal surface within a day for the 12-month period. may have to be confirmed by additional local hourly The annual variation of the mean horizontal solar data measurements for subsequent years in the future. irradiance in percentage values of the daily totals is shown in Table 5. With the exception of the summer 4.2 Comparison with theoretical prediction months, over 14 per cent of the daily total irradiance Methods of estimating hourly irradiance from its is received within the first hour before and after solar daily value have long been established [1,4]. Liu and noon. Likewise, over 12 per cent of the total irra- Jordan had outlined a procedure of determining diance available per day is received in the next hour monthly average hourly total irradiance ] from the before and after the solar noon. In general, the daily total value H. In order to examine whether or seasonal effect on the annual distribution is rather not the Hong Kong data fit Liu and Jordan's proobvious. In the summer months of May-August, rela- cedure, mean values of the pair hours around solar Table 4. Hong Kong monthly average hourly total irradiance received on a horizontal surface (MJ m =hr-1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .H.O.U.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Month 5-6
6-7
7-8
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
Decer~ber
1978
-
0.06
0.36
0.92
I .52
1.93
2.14
2.16
I .95
I .53
I .00
0.44
0.07
-
January
1979
-
0.07
0.33
0.75
I .20
I .55
I .68
I .57
I .40
7 .14
0.72
0,30
0.06
-
0.08
0.33
0.70
I .04
I .30
I .47
1.46
I .35
I .I0
0.72
0.32
0.07
-
0.07
0.21
0.40
0.60
0.79
0.89
0.96
0.92
0.76
0.53
0.27
0.07
0.00
February March
0.01
April
0.03
0.16
0.43
0.77
1.14
1.44
1.56
1.63
1.47
1,13
0.79
0.48
0.18
0.02
May
0.05
0.22
0.51
0.84
I .13
I .41
1.64
I .66
I .60
I .38
I .05
0.59
0.26
0.05
June
0.08
0.33
0.74
I .16
I .57
2.01
2.18
2.08
I .85
I .59
1.23
0.80
0.38
0.09
July
0.10
0.41
0.90
1.50
2.14
2.62
2.82
2.80
2.60
2.17
1.65
1,14
0.56
0.12
August
0.05
0.29
0.71
1.14
1.57
I .82
I .81
I .75
1.71
1.48
I .11
0,70
0.28
0.04
September
0.07
0.37
0.88
I .44
I .89
2.20
2.24
2.10
1.73
1.42
I .02
0.43
0.07
0.00
October
0.01
0.16
0.69
1.43
2.11
2.69
3.02
2.96
2.62
2.09
1.34
0.62
0.09
0.00
0.04
0.29
0.74
I .26
I .61
I .81
I .81
I .58
I .25
0.76
0.28
0.02
November
Solar irradiance in Hong Kong
,
,
,
489
~
o
,~
N
g
~
oo
oo
o
o
o
o
o
o
o
o
,
o
o
o
,-~
,~
{w
cw
¢w
,~
o
o
o
o
~
~
~
°~
o
~
~
~
~
~
o
o
~
~
o
~
0~
o
o
~
o
o
oo
o
~
~w
,-~
0~
m
~
m
m
cq
co
m
~o
h-
CO
~D
'~
O~
o
,-4
m
oh
CO
~-
co
co
o~
cq
~D
,-~
m
~
c~
CO
o
0~
0~
0~
o
~
o
0
,o e-,
8
] 0
o
~ o
~
~
~
~
~
~
~
~
~
o
~
°~
~
~
,~
,~
~
o
o
,
,
o~
~
o
~q
,~
~
,~
~,
o
o
o
o
o
o
o
o
8 m,
,
0~
;.~. 2 5 6
0~
,
490
C.T. LEUNG
o
m ;
m
~
e ~
m
b
e~ ~N
p-
c~
m
o
r~
o o r~
Solar irradiance in Hong Kong DEC
I
r
I
I
I
I
~
i
i
measured duration of sunshine hours occurs in the month of March. This may be again due to the uncertain and variable weather conditions in this month of spring. During the wet and rainy season of summer where typhoons tracking across the South China Sea close to Hong Kong are common, the overall high mean values of the duration of bright sunshine for a given month do not seem to be seriously affected or lowered, although the range of the measured sunshine hours is observed to be slightly higher in the month of August.
I
JAN FEB MAR APR MAY ]UN JUL AUG SEP OCl
NOV DEE
I
I
I
]
I
7
8
9
I0
11
]
I
12 13 HOUR
I
I
I
I
IZ,
15
16
17
491
18
5.2 Correlation between total global irradiance and sunshine duration The relationship between the measured total global solar irradiance and the recorded duration of sunshine hours has been studied by a number of investigators[5,6]. The common type of correlation between these two variables is of the linear form [7]. (2 (20
Fig. 2. Diurnal variation of global solar irradiance (MJ m-2 hr-1). Time is true solar time. noon for the ratio of Hong Kong monthly average hourly total to daily total irradiance, ]/H are plotted in Fig. 3 in which the recommended values by Liu and Jordan are shown as solid curves for comparison. Each data point represents the monthly average ratio and the mean sunset angles are calculated on the 15th day of each month. On the whole, it may be said that the hourly irradiance data of Hong Kong fit the solid curves quite well except at sunset hour angles around 94 °, where slightly larger deviations for the expected curves have been observed. Apart from these discrepancies and some noticeable asymmetries in the actual data around solar noon, the Hong Kong hourly radiation values are generally in good agreement with that of theoretical predictions. This confirms that Liu and Jordan's procedure of estimating average hourly horizontal total irradiance based on daily values is applicable in Hong Kong and can be used confidently for future estimates. 5. D U R A T I O N
--=
a + b-
S So
(1)
where (2 is the average daily total global irradiance actually received on a horizontal surface; Qo is the maximum theoretical daily global irradiance that would reach the earth's surface over the same period in the absence of the atmosphere; S is the average measured daily duration of bright sunshine; So is the daily maximum duration of sunshine over the same period; and a, b are local constants depending on latitude and other meteorological parameters. An investigation of the linear regression coefficients in Hong Kong was performed by Sham [8] using earlier monthly mean values of daily total irradiance and recordings of bright sunshine hours for the period
°2°1'\'''
J 0.14J._
~
0A,
HON ,0N0 '
°o~,,. o ~""~o ^o ~o o~,,"
HOURFROMSOLAR NOON
OF BRIGHT SUNSHINE
5.1 Monthly and annual mean values Table 6 gives the Hong Kong monthly and annual average values of the duration of sunshine per day as measured by the Campbell-Stokes type of instrument recorded for the 10-yr period between 1969 and 1978. It can be seen that the month of July has the largest mean value of bright sunshine of 214.7 hr whereas the lowest value of 100.6 hr occurs in March. The figures in Table 6 also confirm that the midsummer months between July and August are the best months for solar radiation in Hong Kong. The effect of seasonal and climatic changes on the yearly distribution of sunshine duration in Hong Kong is also obvious as seen by the relatively longer duration of sunshine hours recorded in the summer months than in the winter. In addition, the largest fluctuation in the
~ -,~ 0.17
a
3~
-Z- 0.06
~ ° ~ ' °
v
° °°~'
_
'
O-OL
O~o" -
0
~a°~
I
60
I g
10
"~ 11
12
~3
6~
~
HOURS ~:RO. SU~R~SE "fO SU,SEI 7~ 9~ 1~s
-
~s
~6
i~'o
SUNSEI HOURANGLE,cJs, DEGREE
Fig. 3. Experimental ratio of the hourly total irradiance to the daily total irradiance.
492
C. T. LEUNG Table 7. Yearly variation of regression coefficients
Year
a
b
Correlation Coefficients
1972
0.208
0.692
0.95
1973
0.252
0.429
0.91
1974
0.230
0.450
0.89
1975
0.200
0.503
0.94
1976
0.224
0.468
0.96
1977
0.171
0.540
0.97
between June 1958 and August 1962. The regression coefficients a and b were found to be 0.220 and 0.575 respectively. When data for the recent 6-yr period 1972-77 were used in eqn (1), the regression coefficients a and b for each year were found to vary between the wide ranges of 0.171~0.252 and 0.429q3.692 respectively as seen from Table 7. It is apparent from these results that there seems to be no systematic pattern of variation in these coefficients from year to year. Similar effects have been reported by workers in Singapore [9]. However, a much wider range of variation in the regression coefficients has been observed in the case of Hong Kong. This could be mainly due to the local distinct seasonal weather changes in the subtropical climate of Hong Kong as compared to the little or no seasonal variation
throughout the year in the equatorial climate of Singapore.
6. DIFFUSE SOLAR IRRADIANCE
Solar collectors of the flat-plate type, whether thermal or photovoltaic, can utilize both the direct and diffuse components of the solar irradiance. In the design of such devices, knowledge on the direct and diffuse components of the total irradiance on a horizontal surface is needed and the energy collected by a tilted surface at any angle can then be subsequently calculated [ 10]. Data for total irradiance measurements on horizontal surfaces are known for major parts of the world,
Table 8. Calculation of the Hong Kong monthly average diffuse irradiance on a horizontal surface by the cloudiness correlation methods Page's Liu and Jordan's . . . .Correlation . . . . . . . . . . . . . . . . . . . .Correlation ............. MONTH
Ho
H
[MJm-2d -I ]
[MJm-2d -I ]
KT=(H/H°)
(Hd/~)
Hd
(Ha/~)
[MJm-2d -I ]
Ha [MJm-2d -I ]
JAN
25.21
11.48
0.455
0.486
5.58
0.410
4.71
FEB
29.41
11.76
0.400
0.548
6.44
0.465
5.47
MAR
33.81
11.95
0.353
0.601
7.18
0.521
6.23
APR
37.36
13.87
0.371
0.581
8.06
0.499
6.92
MAY
39.06
16.13
0.413
0.533
8.60
0.451
7.27
JUN
39.58
17.06
0.431
0.513
8.75
0.433
7.39
7.33
JUL
39.30
18.84
0.479
0.459
8.65
0.389
AUG
38.07
18.16
0.477
0.461
8.37
0.390
7.08
SEP
35.30
17.02
0.482
0.455
7.74
0.386
6.57
OCT
31.23
15.33
0.491
0.445
6.82
0.378
5.79
NOV
26.64
13.87
0.521
0.411
5.70
0.354
4.91
DEC
24.12
12.51
0.519
0.414
5.18
0.355
4.44
Solar irradiance in Hong Kong but data on the diffuse irradiance are still not currently available for many locations. Up to the present, there have been no measurements of the diffuse solar irradiance in Hong Kong and one has to rely on theoretical methods for their estimates. A number of investigators have found that the average daily diffuse irradiance fraction of the daily total on a horizontal surface, Ha/Hcan be correlated to the cloudiness index, Kr. The parameter K'r represents the fraction of the mean daily extraterrestrial horizontal irradiance, Ho arriving at the surface of the earth and is defined as
Kr =
(2)
~oo"
The correlation developed by Page [11] was of the linear form: Ha --=
1 . 0 0 - 1.13Kr.
-- 1.390 -- 4.027K"r + 5.531R~ - 3.108K'3r.
(4)
The monthly average values of the daily diffuse solar irradiance in Hong Kong have been calculated by the above two correlations with cloudiness index based on the Hong Kong meteorological data for the 10-yr period between 1969 and 1978 and the results are presented in Table 8. Both methods of correlation indicate that the highest fraction of diffuse solar irradiance occurs in the month of March and the lowest in November. Over the year, the estimated fraction may vary between 0.601 and 0.354 strongly depending on what method of correlation is being used. ZO-O
7
'e
I
l
t
l
t
l
l
l •
18.0 .-
i:zc
l
16'0
.°,
l
l
t
°°.
°°."
"°°
",
•"~OTAL IRRADIANCE,H.".. ..¢ FOR REFERENCE "..,
14.0
," •°
%°
°°°°°°°°
12.0
r DIFFUSE IRR~IANCE.Hd lO.O 0.o 6.o
LIU ANO ]OROAN
4-0
~GE - - - - - -
"= ::i= z
7. CONCLUSION The analysis of the total global solar irradiance measurements in Hong Kong during the 10-yr period 1969-1978 indicates distinct seasonal variation with pattern in line with the climatic changes of the year. The range of variation is especially great in the spring season during the transition period between the cold and the warm weather. In addition, the expected large solar irradiance fluctuation in the summer rainy days and the tropical cyclone periods also suggests the need of relatively large capacity storage systems in Hong Kong solar energy utilization installations to cover periods of days with little or no bright sunshine. Regression equation relating the total global solar irradiance with duration of sunshine has been found to give varying yearly regression coefficients strongly depending on the weather conditions of the particular year. An investigation of the Hong Kong hourly solar irradiance data confirms that Liu and Jordan's procedure of estimating monthly average hourly total horizontal solar irradiance based on daily values is applicable in Hong Kong. Also, predictions on the monthly average diffuse solar irradiance based on the cloudiness index give a maximum value of 7 . 3 9 M J m - 2 d -1 in the summer month of July and 4.44 MJ m - Z d 1 in the winter month of December according to the conservative estimates.
Acknowledgement~The author is indebted to Prof. E. A. Bruges for revising the manuscript, to Drs S. K. Yan and L. Cheung for assistance with some of the computational work and to the Hong Kong Royal Observatory for providing data on solar irradiance measurements.
RRELAIION$ BY:-
w t~
The magnitudes of the monthly average daily diffuse solar irradiance in Hong Kong are presented graphically in Fig. 4 in which the monthly average daily total values are also shown for reference. It is to be noted that both correlations predict a similar pattern of yearly variation though the Liu and Jordan's correlation gives consistently slightly lower estimates. Over the year, the monthly average daily diffuse solar irradiance in Hong Kong is high in the summer and low in the winter. The values range between 7.39 and 4.44 MJ m-2 d 1 based on Liu and Jordan's correlation of estimates. However, since the estimated values differ from method to method and the deviation may be as high as 19 per cent, future experimental data on the local measurements of the daily diffuse horizontal solar irradiance are needed in order to confirm which correlation is the best to use for the Hong Kong climate.
(3)
Liu and Jordan had also presented a different correlation and Klein[10] later developed the following mathematical expression for their correlation: Hd
493
?0
~: 0'0
i
I
I
I
I
I
I
[
I
I
I
NOMENCLATURE
I
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC MONTHS
Fig. 4. Comparison of the monthly variation of the estimated diffuse solar irradiance in Hong Kong.
I H, Q
monthly average hourly total irradiance received on a horizontal surface over 1 hr, MJ m 2 hr monthly average daily total irradiance received on a horizontal surface, MJ m 2 d-
494
C.T. LEUNG
Ho, Qo monthly average of the daily extraterrestrial irradiance on a horizontal surface, MJ m - 2 d - 1 He monthly average daily diffuse irradiance received on a horizontal surface, MJ m - 2 d - 1 So monthly average of the day-length, or the maximum hours of bright sunshine per day, hr S monthly average of the hours of bright sunshine per_day hr ~'r H/Ho
5. 6. 7. 8.
REFERENCES
1. B. Y. H. Liu and R. C. Jordan, The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 4(2), 1-19 (1960). 2. Royal Observatory of Hong Kong, Meteorological Results Part I--Surface Observations (1969-78). 3. Royal Observatory of Hong Kong, Monthly weather summary (1976-79). 4. A. Whillier, The determination of hourly values of total
9. 10. 11.
radiation from daily summations. Arch. Met. Geoph. Biokl. B. 7, 197-244. (1956). A. K. ,~ngstrSm, Solar and terrestrial radiation. Q. J. R. Meteor. Soc. 50, 121 (1924). S. Fritz and T. H. MacDonald, Average solar radiation in the United States. Heating and Ventilating 46(7), 61-64 (1949). J. N. Black, C. W. Bonython and J. M. Prescott, Solar radiation and the duration of sunshine. Q. J. R. Meteor. Soc. 80, 231-235 (1954). P. Sham, Total solar and sky radiation in Hong Kong. Royal Observatory of Hong Kong, Tech. Note 22 (1964). T. N. Goh, Statistical study of solar radiation information in an equatorial region (Singapore). Solar Energy 22, 105 l l l (1979). S. A. Klein, Calculation of monthly average insolation of tilted surfaces. Solar Energy 19, 325-329 (1977). J. K. Page, The estimation of monthly mean values of daily total short-wave radiation on vertical and inclined surfaces from sunshine records for latitudes 40°N~0°S. Proc. UN Conf. New Sources of Energy, Paper S/98 (1961).