Pergamon

Renewable Energy, Vol. 11, No. i, pp. 47--60, 1997 ~) 1997 Elsevier Science Ltd

Printed in Great Britain. All fights reserved Pl I : S0960-14gl (96)00122--X 0960-1481/97 $17.00+0.00

D A T A B A N K

The relationship between global solar radiation and sunshine duration in Vietnam

BAO T. N G U Y E N and TREVOR L. PRYOR Murdoch University Energy Research Institute, Murdoch University, WA 6150,

Australia

(Received 10 September 1996; accepted 17 September 1996)

Abstract--Two approaches of the well-known modified Angstrom formula were developed from long term records of measured monthly mean daily global solar radiation and sunshine hour values obtained from 12 meteorological stations across Vietnam. These formulae were then used to estimate solar radiation for stations where only sunshine records were available. Three other commonly used correlations between solar irradiation and sunshine duration were also used and their results compared with those of two developed models. The procedure of measurement in Vietnamese weather stations was also indicated. © 1997 Elsevier Science Ltd. All rights reserved.

1. INTRODUCTION

Information on solar radiation received at any site is essential in the design and study of solar energy applications. Obviously, measured data are the best sources of this information. Unfortunately, the measurement of this parameter is made only in a few meteorological stations, especially in developing countries, for both historical and economical reasons.

Therefore, there have been numerous investigations on the examination of the relationship between global radiation and sunshine duration for which data are available in a greater number of meteoro- logical stations. A global study of the world distribution of solar radiation has been carried out by Lof et al. [1], while there have been many attempts to find common models apphcable anywhere in the world [2], or large regions such as Europe [3] and humid tropical countries [4]. Besides those, this relationship has also been examined nationally in many countries throughout the world, e.g. Australia [5] and Canada [6, 7] ; Caribbean countries including Guatemala [8], the West Indies [9], Venezuela [10] ; Middle East countries like Kuwait [1 I], Iraq [12] and Egypt [13] ; South Asian countries such as Sri Lanka [14], India [15] and Pakistan [16] ; and Nigeria [17], Sudan [18] and Lesotho [19] on the African continent. In South East Asia, studies have been done in Hong Kong [20], Maeau [21], Thailand [22], Malaysia [23] and Singapore [24].

To fill one of the gaps in the South East Asian area, this paper will present an analysis of the relationship between global radiation and sunshine hours for Vietnam. First, the current situation with solar radiation data in Vietnam will be discussed. Next, the common correlations between global radiation and sunshine duration in the country will be developed. These correlations will then be used to estimate solar radiation for places where only sunshine records are available. The results of these correlations are also compared to the results of three other commonly used correlations.

2. SOLAR RADIATION DATA IN VIETNAM

For historical reasons, all radiation instruments used in Vietnamese meteorological stations were imported from the former Soviet Union, as follows [25-27] :

47

48 Data Bank

• Savinov-Yanishevsky pyrheliometers, models AT-50, AP-1 and M3, for measuring direct solar radiation flux.

• Yanishevsky pyranometers, models M80, PP-1 and M-115M, for monitoring shortwave, diffuse and reflected radiation. A shadow band was used for the diffuse measurements, and the pyran- ometer was inverted for the reflected radiation measurements.

• Albedometers, model AP-33, for measuring the albedo of the underlying surface. • Balancemeters (or radiometers), models M-10 and M-10M, for monitoring radiation balance. • Campbell-Stokes sunshine recorders for recording sunshine duration.

In all Vietnamese weather stations, where solar radiation was measured, observations were made every 3 h (i.e. 6h30, 9h30, 12h30, 15h30 and 18h30). The data were not integrated over hourly intervals as in the case of many other countries [28]. The measurement procedure at each observation time was as follows :

(1) Three readings of the diffuse radiation (called ldl) were taken 10-15 s apart. In between these readings, the direct radiation (Ib0 was measured and the status of the sun, in terms of, cloud cover, was observed and recorded.

(2) Three readings of the radiation balance (called B~) were taken with measurements of the direct radiation (IbB) and the status of the sun being taken in between these measurements.

(3) Three readings of the reflected radiation (called R~), with two readings of the direct radiation (IbO in between, were then taken by inverting the diffuse radiation pyranometer.

(4) The first step was then repeated to give a further three readings of diffuse radiation (Id2)" and two readings of direct radiation (Ib2).

(5) Depending on the stability of the values of direct solar radiation flux and the observed status of the sun, the average values of diffuse and beam radiation in one of the above steps would be chosen to calculate values of global radiation. E.g. when the beam flux was stable (i.e. the differences of beam flux values measured in steps (1)-(4) did not exceed 0.05 cal/cm2/min) and if the status of the sun did not change between steps (2)-(4), the global radiation would be set to : I = lbr + ld2. If the status of the sun in step (4) differed from those in the first three steps, the global radiation was given by: I = lb~ +Id2" In case the beam flux was not stable, if the beam value in step (3) was similar to that of step (4), but higher than the value in step (1), the global radiation was: I = lbr+I~; otherwise: I = Ibl +Idl" Finally, if all the above conditions were not satisfied, the global value would be derived from: I = lb2 + I a [27].

At the end of the day, the above global, beam and diffuse radiation measurements were used to calculate the daily and monthly global, beam and diffuse radiation values by using the trapezoidal model, assuming that these values varied linearly between two consecutive observations [27]. Accord- ing to the National Bureau of Meteorology in Vietnam, the errors of this method did not exceed 10% compared with the measured values [27, p. 48]. More detailed discussion on this method can be found in Refs [29, 30]. Table 1 shows the difference between monthly mean daily global radiation calculated by the trapezoidal model, Hcalctdatea, and monthly mean measured global radiation, Hm~,d , for three particular stations in Vietnam. The H ~ u ~ values for these stations were measured by Robitzsch bimetallic pyranographs.

The data used in this paper were supplied by the National Bureau of Basic Investigation [31] from the meteorological station network, as shown in Table 2. Figure 1 shows the location of these stations in Vietnam. These data have been collected over a period of 5-10 yr. Of the 25 stations considered, 12 have records of both sunshine duration and global radiation data (Group 1), and the rest only have sunshine duration records (Group 2).

3. METHODOLOGY

Based on Trewartha's climatic classification [32], Vietnam is divided into three types of climate : the northern part (region 3) stretching from latitude 23.25'N to 18.30'N has a humid subtropical climate of type Caw; the east coast (region 2), between latitudes 18.30'N and 12.30'N, belongs to a tropical wet climate of type Af; while a tropical wet and dry climate of type A~ occurs in the areas south of 12.30'N (region 1). Figures 2-4 show the measured monthly average daily global radiation

Data Bank 49

Table 1. The differences between monthly mean daily global radiation calculated by the trapezoidal model, H ~ , t , ~ and daily measured global radiation, H~,~,,~ for three particular stations in Vietnam

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Station: Cantho [33]

H ~ 396 481 510 520 387 392 378 344 332 372 352 412 Hm,as,,~ 417 456 508 501 356 369 379 358 356 332 343 450 a(cal/cm 2) - 2 1 25 2 19 25 23 - 1 - 1 4 - 2 4 40 9 - 3 8 e(%) 5.0 5.5 0.4 3.8 7.0 6.2 0.3 3.9 6.7 12.0 2.6 8.4

Station : Tan Son Nhut [33]

Healoulat~l 404 499 543 503 453 370 431 368 366 364 309 353 H m ~ 397 482 557 485 438 401 423 367 361 361 324 329 a(cal/cm 2) 7 17 - 1 4 23 15 - 3 1 8 19 5 3 - 1 5 ' 24 e(%) 1.8 3.5 2.5 4.7 3.4 7.7 1.9 5.2 1.4 0.8 4.6 7.3

Station: Lang [34]

H~lo~a,,~ 209 138 213 220 475 452 549 475 441 349 301 245 Hm,~,~ 206 140 207 204 483 465 574 492 467 356 313 253 a(cal/cm 2) 3 - 2 6 16 --8 --13 - 2 5 - 1 7 - 5 --7 - 1 2 - 8 e(%) 1.5 1.4 2.9 7.6 5.4 2.8 4.4 1.4 5.6 2.0 3.8 3.2

Note : a(cal/cm 2) = H~j~a~t~-Hmwu~a ; e(%) = a / H ~ _ ~ s u ~ .

values for the 12 stations in Group 1 while Figs 5-7 plot the measured monthly average daily sunshine hours for these stations.

In both sets of plots, one figure is used for each climatic region in order to assess the similarity, or otherwise, of the data in these regions.

As shown in these figures, all stations in a particular region have similar annual trends, in both global radiation and sunshine duration records, while the forms of the curves in the three regions are significantly different. In region 1, both global radiation and sunshine duration have peak values in March and April, then decrease to their lowest values in the August-October period. Meanwhile, regions 2 and 3 have the highest values of global radiation and sunshine duration between July and September. The difference between these two regions is that the curves of stations in region 2 are quite flat, whereas those in region 3 have very low values in the first months of the year and then increase quite sharply. Therefore, it is reasonable to classify all stations in the country into the three regions, as per Trewartha's classification.

In this paper, a generally accepted modified form of the formula first introduced by Angstrom is used to relate average daily global radiation with average daily sunshine hours [28] :

17o - a + b , (1)

where /7 is the monthly mean daily global radiation on a horizontal surface and/70 is the average daily extraterrestrial insolation on a horizontal surface. It is approximated by the value of H0 for an average day in the month (in MJ m-2), given as [28] :

= G~¢ 360n FIog, /7o 24x3"6x10-3II 1 + 0 . 0 3 3 - ~ - cos ~b cos 6 sin cos + 1-~s in~bs in6 , (2)

where n' is the average day of the month, G,~ = 1367 W/m 2 is the solar constant, ~b is the latitude of the place, 6 is the declination angle, derived from :

50 Data Bank

Table 2. Geographical location of stations and record length

Location

Station Province Latitude Longitude Height Radiation

record Sunshine

record

Group 1 Son La Son La 21.19"N 103.53'E 675.9 m Lai Chau Lai Chau 22.04'N 103.09'E 244.0 m Cao Bang Cao Bang 22.39'N 106.15'E 244.6 m Phu Ho Vinh Phu 21.29'N 105.13'E 054.8 m Phu Lien Hai Phong 20.48'N 106.38'E 116.2 m Lang Ha Noi 21.02'N 105.51'E 005.2 m Yen Dinh Thanh Hoa 19.59'N 105.40'E 009.4 m Vinh Nghe An 18.40'N 105.40'E 005.5 m Da Nang Da Nang 16.02'N 108.11'E 005.8 m Pleiku Gia Lai 13.59'N 108.00'E 800.0 m Tan Son Nhut Hochiminh City 10.49'N 105.13'E 054.8 m Can Tho Can Tho 10.02'N 105.47'E 003.0 m Group 2 Ca Mau Kien Giang 09.10'N 105.10'E 003.0 m Chau Doc Kien Giang 10.46'N 105.08'E 005.0 m Tay Ninh Tay Ninh l l .19 'N 106.04'E 010.0 m Phan Thiet Phu Khanh 10.56'N 108.06'E 009.0 m Nha Trang Phu Khanh 11.57'N 109.10'E 020.0 m Quy Nhon Nghia Binh 13.36'N 109.13'E 005.0 m Buon Me Thuot Nghia Binh 12.41'N 108.03'E 490.0 m Dong Ha Quang Tri 16.50'N 107.05'E 004.0 m Ba Don Quang Binh 17.45'N 106.25'E 008.0 m Quy Chau Nghe An 19.33'N 105.07'E 087.0 m Tien Yen Quang Ninh 21.20'N 107.24'E 014.0 m Pho Rang Yen Bai 22.14'N 104.28'E 098.0 m Ha Giang Ha Giang 22.49'N 104.59'E 118.0 m

89-93 89-93 89-93 89-93 89-93 84-93 89-93 89-93 84-93 89-93 71-82 84-93

m

m

89-93 89-93 89-93 89-93 89-93 84-93 89-93 89-93 84-93 89-93 78-82 84-93

84-93 84-93 84-93 84-93 84-93 84-93 84-93 84-93 84-93 84-93 89-93 84-93 84-93

si {~. 284+n'\ t$ = 23.45 n ~ J ~ o ~ ) (3)

and cos is the sunset hour angle

o~ = cos - 1 ( _ tan ~b tan 6), (4)

a is the monthly average daily hours of bright sunshine, 37 is the maximum possible number of bright sunshine hours, or the number of daylight hours, approximated for the average day, given by [28],

2 l 37 = ]-~ cos - (tan q~ tan 6). (5)

a and b are constants to be determined. To use eq. (1) for locations with sunshine data only, a and b must be known. In this case, a and b

can be found from the available global radiation and sunshine data for the 12 stations in Group 1, and then applied to compute global radiation for the 13 stations in Group 2, given the sunshine data for those locations.

Two approaches were used in this paper: the region model and the country model. In the region model, the 12 stations in Group 1 were grouped into three regions depending on their locations, and the a and b values were determined for each region. In the country model, all locations were grouped

102 ° 104 ° 106 ° + + +

D a t a Bank

108 ° +

!10 ° +

112 ° +

51

Ha Giang Lai Chau

• + Pho Rang + °

Son La Phu Ho

Lang

:hau

Lien

+

+ 22 °

+ 20 °

t Ba Don + + 1 8 °

Dong Ha

~Da Nang + + 16 °

x x x

x x

+ x +

Pleiku " , ¢ uy Nhon x

+ 14 °

oT•ay N i + nh Phan Thiet o Tan.Soy

Chau Doc Can Tho

• O + +

Nha Trang

+ + 12 °

+ + I0 °

Fig. 1. Solar r ad ia t ion s ta t ions in V i e t n a m : • s t a t ions wi th rad ia t ion a n d sunsh ine da ta ; 0 s ta t ions wi th sunsh ine da t a only.

52 Data Bank

2O 8

n. lO

(11 o 5 0

0 I I I ~ I I I I I I

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

- - 0 - - - Can Tho l I - .o - Pleiku

L-- ~ - Tan Son l,a'~

Fig. 2. Monthly average daily global radiation for region 1.

~, 15 ~ , , ' ' ~ - ' - °

- - o - Da Nang tY >.

r,, o l

= Jan Feb Mar Apt May Jun Jul Aug Sep Oct Nov Dec

Month

Fig. 3. Monthly average daily global radiation for region 2.

25

2o

.~ 15

>. 10 Q ® 5 o )

0

Jan

. o - , ~ ' t t : : = . : : . A . .

~ a . ~:"~"-":-o ~ ' " "~- - - x : " " +' " . ' Y ' ~ : - ' ~ - -

I I [ I I i I i ' ( ' I

Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

Fig. 4. Monthly radiation for region 3.

Cao Bang

- - ~- -- Lang

- -x- - Phu Ho - -x- - Phu Lien

- .o -- Son La -- -4- -- Vinh

- -o - Yen Dinh

together, and countrywide a and b values were derived. The results from these two approaches were then compared to determine which approach was better for the Vietnamese data.

For each of the 12 stations,/7o and K r were computed for each month by using eqs (2) and (5), respectively. Next, with average values over 5 or 10 yr of measured data o f /7 and t~, the monthly average daily values of////7o and t~/N for each station were obtained. After being grouped together in either the region or country model, these/7//70 and fl/ATvalues were used to compute the regression coefficients a and b of eq. (1) by a least squares curve fit process. In this process, the equations for a and b were as follows [1] :

Data Bank 53

o ~ 10;

8,2

. t o o

F I I I I I I I I I

- - - o - - Can 111o

- . o - Pleiku

-. ~ - -Tan Son Nhut

Jan Feb Mar Apt May Jun Jul /~g Sep Oct Nov Dec

Monlh

Fig. 5. Monthly average daily sunshine duration for region 1.

e " v

O " 1 "

O )

m t ' ~

10

6

4

2

0

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

Fig. 6. Monthly average daily sunshine duration for region 2.

- o - Da Nang ]

A

8 7

: 1 :

s == 4 o~ >, 3

8 , 1

]

o - - - * . . . . ~*: : - " * -~-" "*': '" " ' * l • . . ~ . : y , ,~ ._ . x . , . o - - - 1

. -

. s / ~ f + .... * i

I . . . .

0 i I I I I I I t J I [ Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

Fig. 7. Monthly average daily sunshine duration for region 3.

Cao Bang . . . & . . . Lang

- . x . - P h u Ho

- . x - - Phu Lien

_ . o _ _ Son La

_ . + . _ V inh

- - o - - Yen Dinh

a -

-

b -

(6a)

(6b)

where M was the number of points.

54 Data Bank

The resulting a and b values were then used in eq. (1) to compute calculated values o f / 7 (called est imated/7) . Results obtained from the two models were compared to the corresponding measured values of the global solar radiation at each of the 12 stations o f Group 1, as shown in Table 3. The deviations between the estimated and measured values were summarised by the following statistical parameters [6] :

1 1 Ei Mean BiasError , M B E ( % ) = 00 (~ - - '~m) (~ ) (7)

/ 1 \ / E~2\ °5 Root Mean Square Error, R M S E ( % ) = lO0|-~--|[~-~|\n~/\_ / ' (8)

where, Ei = ~J~cstiraat~l-- t~measured, i = 1, 2 , . . . , M ; M was the total number of observation points and Am was the arithmetic mean value of M measured values of the global solar radiation.

Correlat ion coefficients r between estimated and measured radiation values are also shown in Table 3. The coefficient r was defined by :

~'~(Jl~tmtimatcd - - ~¢)(~me.aaured - - /T in ) r = (9)

, / ( x ( a . , ~ . , ~ - a ~ ) ~ ) ( x ( a ~ = ~ . ~ - am) ~)

w h e r e / 7 e is the arithmetic mean value of M estimated values of the global solar radiation. The results o f these models were compared with three previously reported models which were

considered most likely to be appropriate for Vietnam. The three models were :

Table 3. The results o f two models applied for Vietnam

Region model Country model a = 0.14 b = 0.60

Station M B E ( % ) R M S E ( % ) r M B E ( % ) R M S E ( % ) r

Region 1 a = 0.26 b = 0.36

Cantho - 3.74 6.88 0.97 - 1.88 4.32 0.98 Pleiku 3.73 9.12 0.96 8.76 9.41 0.99 Tan Son Nhut 0.06 2.90 0.96 6.18 9.61 0.95

Region 2 a = 0.08 b = 0.66

Danang - 0.05 3.52 0.99 7.35 8.11 0.99

Reg ion3 a = 0 . 1 5 b = 0 . 6 6

Caobang - 4.83 6.99 0.99 - 10.41 12.49 0.99 Laichau --3.71 14.73 0.73 - 9 . 6 3 16.81 0.73 Lang - 8.72 9.03 1.00 - 14.10 16.64 0.99 Phuho 5.74 6.82 1.00 - 0.44 4.16 0.99 Phulien 16.97 20.58 0.98 9.97 13.40 0.98 Sonla 0.85 6.42 0.93 - 5.54 8.28 0.93 Vinh 0.07 6.58 0.99 - 6 . 0 1 10.55 0.99 Yendinh - 0.51 4.70 0.99 - 6.42 8.40 0.99

Data Bank 55

Turton's model Turton [4] evaluated the relationship between the duration of bright sunshine and global radiation

for humid tropical countries by using long term monthly average data from 25 stations around the world, both in the northern and southern hemispheres, and found that the regression constants a and b ofeq. (1) are 0.30 and 0.40, respectively.

Rietveld's model Rietveld [2] has used measured data collected from 42 stations in different countries. A unified

correlation was derived to calculate the global solar radiation, which was believed to be applicable anywhere in the world. This correlation was as follows :

~00 = 0.18+0.62 . (t0)

This correlation has been applied successfully in some previous studies [3, 7, 20].

Fre're model Samuel [t4] quoted Fre 're curves of the values of a and b versus the corresponding average values

of (n/N) in the equation forms, as :

a = - -0 .27+ 1.75(n/AT)- 1.34(n/N) 2 (1 la)

b = 1 .32- 2.93(n/N) + 2.30(ti/N) 2. (1 lb)

Then, he modified these equations to fit with Sri Lankan conditions. In this paper, a trial and error process was used to develop a modified pair of parabolas to apply to Vietnamese climatological conditions :

a = - -0 .27+ 1.75 (n/N)-- 1.34 (~/N)2 (12a)

b -- 1.32-2.95 (~/N) +2.26 (a/N) 2. (12b)

These three models were applied to the sunshine data from the Vietnamese locations in Group 1, and the calculated and measured values of average daily global horizontal radiation were compared. The results, together with those from the Vietnam countrywide model, are shown in Table 4.

4. RESULTS AND DISCUSSION

As can be seen in Table 4, Turton's model overestimates solar radiation values for all stations in Vietnam. However, the obtained coefficients a and b for stations" in region 1 with the climatic type of A~, as shown in Table 3, agree reasonably well with Turton's model [4]. The Fre're model produces underestimates for most of the stations in region 3 and overestimates for the region I and 2 stations. Rietveld's model gives good results for region 3 having the chmate type of Caw. This is in agreement with the results in Macau [21] where the climate type is the same. Meanwhile, this model gives overestimates for regions 1 and 2. In some stations in region 3, such as Caobang, Laichau and Lang, Rietveld's model gives better MBE and RMSE values compared with those from the countrywide model. However, the countrywide model still gives consistently better results than the other three models, in general.

The regression coefficients a and b obtained from the region model (Table 2) for regions 1 and 3 are reasonably acceptable if compared with Turton's model and Rietveld's model, correspondingly. The a and b values for region 2 are incomparable. However, it is difficult to criticise this result because only one station in this region, where both H and n records have been available, was used to obtain a and b.

As shown in Table 3, the results of the region models are clearly not better than those of the country model. Therefore, for simplicity, the country model is chosen to apply for all stations in the country.

The common a and b values for the whole country were then used to compute the monthly average daily global radiation values for the 13 stations in Group 2. These stations, if considered in terms of

56 Data Bank

o~ 0~

O

03 D .

O L~

03

O

8 ~

¢-q

~e

gfl

t--q t-~ [-~

~ D c q

o o ~ o o

~D o o t-~

I ~ Ox t ~

od c~ ~q

o o ,-~ he3

w'~ t--- ,~-

o ~ ~ re3

i 717 i i i

z

03 "~o~ " ~ o . u ~ ~ . ~ o~ ~ 0J 03 ~ 03 03 0 3 . . ~

Data Bank 57

geographical location and climatic type, can also be divided into three regions. Figures 8-10 plot the monthly average daily sunshine hours of these stations. In each figure one representative location from Group 1 is used to show the common trend of curve in every region. It can be seen that these new stations follow the same regional trends in sunshine hour data as those identified earlier.

Table 5 gives annual average fractions of ~/N and the estimated annual average daily global radiation for these 13 stations. As can be seen in this table, the annual average daily global radiation values in Vietnam lie between 11.5 and 19 MJ m -2. This agrees with the estimated range of 12-17 MJ m -2 d-1 for this country, suggested by Lof et al. [1]. As shown in Tables 3 and 4, the correlation coefficients of all models for all stations are quite high. This demonstrates that the well-known modified Angstrom's formula (1) can be applied successfully for stations in Vietnam.

"c e-

o .1-

p.

t l i

O )

ca

10

"'l~'" .... ~,":'::.A .... ~" "'x .._

4

2

0 I I I I I I I I I I

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

_ ._o~ Tan Son Nhut ( for comp~son)

_..o__ Buon Me Tht~

.. . , , . . . CaMau

_ .x ._Chau Doc

- . x - . Nha Trar~

_ ..o_ _ Pha~ "fleet

. . . + . . Tay Nir~

Fig. 8. Monthly average daily sunshine duration for region 1 (Group 2).

E o

i

¢1 Q ¢D

9 8 7 6 5 4 3 2 1 0

. . . O . S

I ° " ? Q

I I ) ] I I I I I I

- - o - - - Da Nang (for comparison)

_..o__ Ba Don

...A... Dong Ha

- . o- - Quy Nhon

Jan Feb Mar Apt May Jun Jul Aug Sep Oct Nov Dec

Month

Fig. 9. Monthly average daily sunshine duration for region 2 (Group 2).

J ~

- l -

&

x . , x. ,-..,1 "~--m-~L~.~_ "~,

, . ' / t~_ '~ .~ -:,':,:~ o.

,..-.;~," '~--:~.:~. o o~

) I 1 I I I I I I I

Lang ( for comparison)

- -.o- - Ha Giang

...,,... Pho Rang

- . x . - Quy Chau

- . o - . "lien Yen

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

Fig. 10. Monthly average daily sunshine duration for region 3 (Group 2).

58 Data Bank

Furthermore, Table 6 shows one example of the comparison between estimated and measured global solar radiation in Phu Ho station in region 3. Once again, this table indicates that the chosen model can be applied very well to estimate monthly average daily global radiation from monthly average daily sunshine hours, which were available in many stations across the country.

5. CONCLUSION

Two versions of the modified Angstrom formula were studied in this paper. From the comparison of the results of these models and for reasons of simplicity, the country model was chosen to apply for all stations in Vietnam.

Table 5. Estimates of global radiation for stations in Viet- nam

Annual Annua l /7 Station Location •/57 (MJ/m 2 day)

Region 1 Ca Man 09.10'N 0.56 16.98 Chau Doc 10.46'N 0.61 17.90 Phan Thiet 10.56'N 0.68 19.08 Tay Ninh l l .19 'N 0.64 18.37 Nha Trang 11.57'N 0.60 17.73 Buon Me Thuot 12.41'N 0.62 17.84 Region 2 Quy Nhon 13.36'N 0.56 16.94 Dong Ha 16.50'N 0.44 14.25 Ba Don 17.45'N 0.42 13.76 Region 3 Quy Chau 19.33'N 0.38 12.76 Tien Yen 21.20'N 0.35 11.90 Pho Rang 22.14'N 0.33 11.57 Ha Giang 22.49'N 0.33 11.51

Table 6. Comparison of estimated and measured global radiation for Phu Ho station

Estimated radiation Measured radiation Error Month (MJ/m 2 day) (MJ/m 2 day) (MJ/m 2 day)

Jan 5.79 5.78 0.01 Feb 6.94 6.85 0.09 Mar 7.16 6.84 0.32 Apr 10.26 9.85 0.41 May 14.81 14.91 - 0 . 1 0 Jun 15.50 15.80 - 0 . 3 0 Jul 16.02 15.80 0.22 Aug 18.24 18.75 -0 .51 Sep 16.60 17.31 -0 .71 Oct 12.37 13.34 -0 .97 Nov 10.35 10.97 - 0.62 Dec 9.15 9.56 -0 .41

Annual 11.93 12.15 - 0.22

Data Bank 59

Three other models from previous investigations were also applied to the Vietnamese data and compared with the two models of this work. The countrywide model gave consistently better results than the other three models, although in specific locations one of the three models gave better results.

Finally, this study showed that until more precise instruments and measurement methods are available, or solar radiation is measured in more stations, the modified Angstrom formula :

~-o - a+b

can be applied to any site in Vietnam, with the use of common a and b values for the whole country. The global radiation values produced by this approach can be used in the design and estimation of performance of solar applications, which are gaining increasing attention in Vietnam. Furthermore, this correlation will be used to supply the basic data for our further work in generating daily and hourly global radiation values, the essential data required for using simulation packages for assessing the potential of solar energy systems in this country.

REFERENCES

1. G. O. G. Lof, J. A. Duffle and C. O. Smith, World distribution of solar radiation. Solar Energy 10, 27-37 (1966).

2. M. R. Rietveld, A new method for estimating the regression coefficients in the formula relating solar radiation to sunshine. Agricultural Meteorology 19, 243-252 (1978).

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