Escenas de lectura escolar. La intervención normalista en la formación de la cultura letrada

Renewable Energ.v, Vol. 4. No. 8, pp. 93~ 940, 1994 Copyright ~ 1994 Elsevier Science Ltd Printed in Great Britain, All rights reserved 11960 148194 $ 7 0 0 + 0 . 0 0

Pergamo. 0960-1481(94)00042-5

DATA BANK Solar radiation and sunshine hour maps in Castilla and Le6n region (Spain)

A. DE MIGUEL, J. BILBAO, S. SALSON and A. LAGE Department Fisica Aplicada I, Facultad Ciencias, Universidad de Valladolid, Spain

(Received 8 April 1994; accepted 13 May 1994)

Abstract F r o m global solar radiation and sunshine hour data of Castilla and Le6n region (Spain), six different Angstrom-type correlations have been performed using the least square technique and in each of them the parameters a and b have been calculated. In two of these correlations we have taken into account the optic effects of atmosphere and not burning the sunshine recorder chart. The results have been compared using statistical tests based on MBE, R M S E and CC and from this calculation we have obtained the best correlation for Castilla and Le6n locations. Finally from experimental and calculated data the monthly mean solar global radiation and sunshine isoline maps have been plotted for each m o n t h of the year and for the year as a whole.

1. I N T R O D U C T I O N

N'o ~ [ a r c c o s ( c o s 8 5 - s i n 0 s i n ~ ) / ( c o s 0 c o s r S ) ] / 7 . 5 .

Knowledge of solar radiation values in a region is essential to study and design the economic viability of systems which use solar energy. In order to use solar energy, the most important variable is the mean daily global solar radiation, but measurements of this variable are made in only a few places. This situation can be solved using correlations which estimate solar radiation from more available meteorological parameters, such as sunshine duration. The first correlation proposed for estimating the monthly mean daily solar global radiation was by Prescott [1], who proposed the following relationship :

/7i/7,, = a + b ( n / ~ , , ) ,

N; has been used, in this paper, in the modified methods of Prescott and Hay. Another correlation is McCulloch's, who takes into account the latitude effect : /7//7,, = 0.29 cos 0 + 0.52 (~/,~7,,).

(l)

(2) 2. P L A C E AND M E A S U R E M E N T

This last expression, which has constant coefficients, is applicable anywhere in the world. Hay [3] developed a generalized procedure where the surface albedo plays an important role in determining the magnitude of /7, and he also took into account the modified duration of day length and proposed the following correlations :

/7"/Ho = a+b(n/ffgo),

Castilla and Le6n region is the most extensive region in the EEC; at 94,147 km 2, it comprises a fifth of the Spanish territory. The relief of this region is formed by a 800 m high mesete, surrounded by a number of mountain chains that close it in extreme conditions to the North, East and South ; the West side is limited by the Portuguese Northern m o u n tain range. The average climate is continental, the annual mean temperature is 10~C Y C in winter and 2 4 C in summer. In the middle of the region, the annual mean rainfall ranges from 350 to 500 ram. These values increase in the mountains, up to 2000 ram. Figure 1 shows the geographical location of meteorological stations in Castilla and Le6n and Table 1 shows the characteristics of the measuring stations and the duration of the available recording data used in this analysis. The global radiation and sunshine duration data

(3)

/I' being obtained by the expression

/ 7 - / 7 ' =/Tp[p~(n/N'o)+pc(l-n/N'o)].

(6)

From the previous different correlations, the aim of this paper is to determine solar radiation data and sunshine hour values to find the best correlation to fit the solar radiation values in this region, similar to Halona et al [4] : then, using this correlation, the solar radiation values are estimated in places where solar data are not available; and, finally, the distribution of solar radiation and sunshine hours are shown by means of maps prepared for all m o n t h s of the year. The maps show the level of solar radiation and give an overall view of the distribution of solar radiation and sunshine hours. This method provides much more detail about the solar energy potential in the region than the world solar radiation maps. Similar work has not been done in the Castilla and Leon region with as m u c h record data as this before.

where /7 is the monthly mean daily solar global radiation, /7° is the monthly mean extraterrestrial solar radiation, n is the monthly average sunshine hours, and ~70 is the average day length. Another interesting correlation is Rietveld's [2]. He examined several published values of a and b and noted that the following expression is verified :

/7//7~, = 0.18 + 0.62(~/N,,).

(5)

(4)

p is the surface albedo : p~ is the surface albedo under clear sky ~,. is the cloud albedo, and N~ has the following expression : 933

934

Data Bank

43

43

VILLAFR+IA PALENC+IA 42

42 SORId

ZAlgORA+

+

41

41

40

I

1

t

-6.5

-7.5

I_, -5.5

I

~

--J 40

-4.5

-3.5

-2.5

Fig. 1. G e o g r a p h i c a l l o c a t i o n o f m e t e o r o l o g i c a l stations in Castilla a n d L e 6 n .

T a b l e 1. G e o g r a p h i c a l locations a n d d u r a t i o n o f d a t a r e c o r d s

Province Station

Longitude W

Latitude N

Altitude (m)

R e c o r d used Radiation Sunshine

5°39 ' 6°35 ,

42°35 '

4°43 ' 4°50 ' 4°32 ' 5°45 '

41039 ' 41°42 ' 42°01 ' 41°30 '

667

5°30 '

40°57 '

795

1977-1992

1975-1991

5°38 '

42°22 '

881

1976-1982

1975-1991

4°07 ' 4°00 ' 4°42 '

40°57 ' 40o47 ' 40°39 '

1005

1975-1991

1143

1975-1991

2°28 '

41°46 '

1090

Leon V. C a m i n o Ponferrada

914

1976-1992

740 850

1976-1992

1975-1991

42°33 ,

Valladolid Observatorio Villanubla

Paleneia Zamora Salamanca Matac~in

1975-1991

1975-1991

Burgos Villafrla

Segovia Observatorio Navacerrada Avila

Soria Lubia

1978-1992

1975-1991

-1.5

935

Data Bank used in the analysis were provided by the Meteorological Office of Spain. In the following five stations, Virgen del Camino, Matacfin, Villafria, Sofia and Villanubla, solar radiation data are available for periods ranging from 10 to 16 years, and sunshine hours have been measured at 12 stations for periods ranging from 16 to 30 years.

3. DATA ANALYSIS A N D R E S U L T S Linear regression analysis, using least-square techniques applied to six different correlations, have been made for each of the stations where radiation and sunshine data were measured. Table 2 shows the results ; the magnitude of the parameters a and b varies from station to station and for each m e t h o d ; r, the correlation coefficient, also changes. Following the studies of Jain and Jain [5], the mean #, the standard deviation ~,_ ~ and V, the variation coefficient of the parameters, a, b and r have been calculated to determine the best correlation in the region ; the variation coefficient V is defined as the ratio ~, ~/#; from Table 2 we can see that, for the parameter a, the value of V is 0.106 for the Prescott correlation, and it is higher for Prescott and H a y modified and it is a little lower for the Hay correlation. For parameter b, the values are similar for the three correlations and a little higher for the Prescott one; in relation to the correlation coefficient r, Prescott modified shows the lower value, followed by Prescott's one; from the results we can see that any of them explain completely the deviation a m o n g the regression parameter values. So, to explain that deviation we have also estimated the variation of the R M E and R M S E statistical tests between the estimated and experimental values, and Table 3 shows the results obtained. For each station, the first value is the M B E error and the second is the R M S E (in MJ m ~ day ~). F r o m these results we can say that Prescott's equation gives the smallest error values. The use of the modified duration of daylength does not allow us to obtain better results, but the correlation coefficient is higher. When we use Hay's expressions, the error values do not decrease either when the optic effect is used, or when the modified daylength is used. In conclusion Prescott's correlation has been used to evaluate a and b coefficients in the rest of the stations where only sunshine duration data are available. In these calculations, measurements from seven neighbouring stations belonging to five regions have been used. As a result the m a p s of the a and b values have been plotted, and from them we can obtain a and b for everywhere in the region.

~

~

~

~

~

~ . ~

~

Q~

~Q.~

~

N~

N-=N

• .

QQo--:.

4. C O N S T R U C T I O N O F I S O - R A D I A T I O N AND SUNSHINE HOUR MAPS

Measured and estimated values of monthly and m e a n solar global radiation have been used to draw monthly and yearly solar radiation maps, where the isolines have been traced with intervals of 0.5 MJ m z day 1, similar to Raja and Twidell [6] ; the measurement stations are located with plus signs on the maps. F r o m the experimental values isoline m a p s of sunshine hours have also been plotted with intervals of 0.3 h, and we show only December, July and annual m e a n maps. The results have been compared with the studies of Font [7], who plots the solar radiation and sunshine maps for Spain•

O

2>

>

.

N>

936

Data Bank Table 3. Statistical test results, MBE and RMSE values

Method Prescott Prescott modified McCulloch Rietveld Hay Hay modified

Le6n V. del Camino

Salamanca Matacan

-0.003 0.023 - 0.008 0.029 -0.058 0.063 -0.025 0.080 -0.047 0.052 -0.046 0.052

-0.000 0.022 - 0.001 0.022 -0.011 0.030 0.008 0.038 -0.041 0.046 -0.041 0.046

5. RESULTS AND D I S C U S S I O N In Figs 2 and 3 the monthly mean distribution of solar radiation over the region is shown. Maximum values are received in summer in all places. During this period the distribution is more latitudinal than in winter ; the centre of the region is cloudless and the mountains of the North and South are more cloudy, so there is a gradient from the centre to the North, with a value between 6 and 7 MJ m 2day L; the South gradient increases to 3 MJ m 2 day ~. The maximum values are reached in August, 26.2 MJ m 2 day ~, and the maximum isoline is situated in the Central West. In winter the gradients disappear or become very small; the isoline distribution is more longitudinal in winter and the most frequent value is 5 MJ m z day ~; the global radiation is, in general, more uniform over the centre, and there are small places with maximum values situated in the West of the region. In general, there are low values in December; the isoline of 5.5 MJ m 2 day ~crosses the region and it is the most frequent value. In winter, the values drop to about 25 30% of the radiation available in summer. On the yearly mean radiation map, Fig. 4, we can see a gradient of 3.5 MJ m ~ day ~ from the centre to the North and a gradient of l MJ m ~day ~in the South ; the Central West places receive more radiation than any others the region receives 11--16 MJ m 2 day ~, and the least value occurs in the North; the most frequent value is 15.2 MJ 2 day ~. In conclusion, the region shows an excellent solar climate available for solar conversion systems throughout the year, except in December, when perhaps some days of conventional energy would be required. In Fig. 5 the distribution of sunshine hours is shown. In general the isoline forms change from winter to summer; they are more longitudinal in winter and more latitudinal in summer. The North gradient increases from winter to summer, its maximum is in July, 4.8 h, and the South gradient increases from winter to spring, 1.8 h. The most frequent value ranges from 3.1 h in December to 11.2 h in July. The maximum value ranges from 3.7 h in December to 11.8 h in July. The difference between maximum and minimum increases in summer and diminishes in winter. During winter, sunshine hours are more uniform and lower all over the region and are 30°/,, of the summer available sunshine hours.

Station Burgos Villafria 0.002 0.020 0.000 0.021 -0.054 0.058 -0.040 0.050 -0.044 0.048 0.043 0.047

Soria Lubia

Valladolid Villanubla

0.003 0.017 0.001 0.018 0.036 0.043 -0.018 0.037 -0.044 0.047 -0.041 0.045

0.001 0.019 0.021 0.021 0.020 0.023 0.012 0.040 -0.041 0.047 -0.041 0.046

The results obtained have been compared with Font [7], who published Spanish radiation and sunshine maps, using less data and a smaller period of measurement for our region than*in this paper. His maps were made in 1983 and have less resolution, but again our results are basically in accordance. Comparing the results on sunshine hours, the values in Ref. [7] are higher than the present values in summer and are compatible in spring and autumn ; on solar radiation maps, the values in Ref. [7] are higher in the South of the region, and in the North they show smaller values than our maps, but the differences could be due to the different lengths of the datasets. Finally, taking into account all pairs of values ~/A7o and /7//70, we have obtained the following equation which can be used in all regions: 17//7,, = 0.298 +0.434~/~7o, and Table 4 shows the statistical test error values which are a little bigger than the ones obtained from the Prescott and Prescott modified expressions shown in Table 3. But they are smaller than the ones obtained from the other methods. The advantage of the previous regression is that the coefficients are fixed and available for anywhere in the region.

6. C O N C L U S I O N S The linear regression analysis of the global radiation and sunshine duration data by means of the least-square technique shows that the Prescott correlation is the best for Castilla and Le6n locations. The deviation between the regression parameters is not reduced when the optical effects of the atmosphere and the modified duration ofdaylength (eq. (5)) have been taken into account. Concerning the iso-radiation maps, solar radiation over Castilla and Le6n has an important maximum in summer and a minimum value in December. There is a gradient from the Central region to the North, whose lines are closer in summer and more separated in winter. The gradient could be due to the mountainous nature of the North region. Finally a linear equation which can be used in all regions has been obtained.

Data Bank

937

43

43

42

42

41

41

#

~..

92

40 -7.~

I

I

-6.5

I ~

I

-5.5

I

-4.5

I

-3.5

I

I

-2,5

I

-1,5

40

-7,5

-6.5

-5.5

January

43

.

-%

,,'"-y /

~

2

41

41

-6.5

-5,5

-2.5

-15

-3.5

-2.5

-1.5

•~ - - 42

-7.5

-3.5

43

42

40

-4.5

oj3

February

~

\

~ 2 ,.,.~/

-4.5

-3.5

-2.5

- 1.5

40

-7.5

-6.5

-5.5

March

-4,5

April

43

43

. '1.'5• \\ 43

42

41

41

40 -7.5

-6.5

-5.5

-4.5

May

-35

-2.5

-l.5

40 -7.5

-6.5

-5.5

-4.5

-3.5

June

Fig. 2. Distribution of mean daily global radiation, from January to June (MJ m 2 day ~).

-2.5

-1.5

938

43

Data Bank

-

43

=.....: -

/~.~,

fl

". 42

42

~

41

-7.5

-6.5

41

25

-5.5

-4.5

-3.5

-2.5

- 1.5

40 -7.5

-6.5

-5.5

-4.5

-3.5

-2.5

-1.5

-3.5

-2.5

- 1.5

-3.5

-2.5

-15

August

July

43

43

/~"

.

.

42

42

41

41

40 -7.5

-6.5

-5.5

-4.5

-3.5

-3.5

- 1.5

4O

-6.5

-7.

-5.5

September

-4.5 October

43

43 -/.5

42

42

41

41

40 -7.5

-6.5

-5.5

-4.5 November

-3.5

-2.5

- 1.5

407. 5

I

-6.5

-5.5

-4.5 December

Fig. 3. D i s t r i b u t i o n o f m e a n daily g l o b a l r a d i a t i o n , f r o m July to D e c e m b e r (MJ m z day-~).

D a t a Bank

939

f

T42

/ .~k" 42

41

40 -7.5

-6.5

-5.5

-4.5

-3.5

-2.5

-1,5

Annual Fig. 4. Distribution of m e a n yearly global radiation (MJ m : day l).

43

43

43

42

41

41

40 -7.5

I

I

-6.5

I

I -

-5.5

I

I

-4.5

I

I

I

I

-3.5

I

-2.5

40 -7.5

- 1.5

I

I

-6.5

-5.5

July

-4.5

-3.5

December

43

41

40

-7.5

. ~

%,-, °.~', ".t ~ ' ~ - , . ~ /

ii/ i

I

-6.5

-"

i

I--

-5.5

I

i

-4.5

i

i

-3.5

i

i

-2.5

i

- 1.5

Annual

Fig. 5. Distribution of m e a n daily sunshine hours, in July, December and annual (h).

-2.5

I

- 1.5

940

Data Bank Table 4. Statistical test error of the linear analysis for all data value pairs Station

Leon V. del Camino

Salamanca Matacan

Burgos Villafria

Soria Lubia

Valladolid Villanubla

MBE RMSE

-0.0163 0.028

0.0168 0.027

-0.0121 0.023

-0.0004 0.017

-0.011 0.024

Acknowledgement-- The authors wish to express their thanks to the Meteorological National Institute of Spain for making available the data necessary for this study. The authors gratefully acknowledge the financial support extended by Junta of Castilla and Le6n (Economy and Finance Department, Energy Service).

REFERENCES

1. J. A. Prescott, Evaporation from a water surface in relation to solar radiation. Trans. R. Soc. S. Aust. 64, 114-118 (1940). 2. M. R. Rieltveld, A new method for estimating the regression coefficients in the formula relating solar radiation to sunshine. Ayr. Meteorol. 19, 243-252 (1978).

3. J. E. Hay, Calculation of monthly mean solar radiation for horizontal and inclined surfaces. Solar Energy 23, 301307 (1979). 4. N. Halona, C. T. Nguyen and D. Vo-Ngoc, Calculation of monthly average global solar radiation on horizontal surfaces using daily hours of bright sunshine. Solar Energy 50, 247-258 (1993). 5. S. Jain and P. C. Jain, A comparison of the Angstromtype correlations and the estimation of monthly average daily global irradiation. Solar Energy 40, 93-98 (1988). 6. I. A. Raja and J. W. Twidell, Distribution of global insolation over Pakistan. Solar Energy 44, 63-71 (1990). 7. I. Font, Atlas de la Radiaci6n Solar en Espa~a. Instituto Nacional de Meteorologia, Secci6n de Publicaciones, Madrid (1984).