The generation of a “typical meteorological year” for the city of Athens

Solar Energy Vol. 40, No. 5. pp. 405-411. 1988 Printed in the U.S.A.

0038-092X/88 $3.00 + .00 Cop)right © 1988 Pergamon Press pie

THE GENERATION OF A "TYPICAL METEOROLOGICAL YEAR" FOR THE CITY OF ATHENS D. PISSIMANIS,G. KARRAS, V. NOTARIDOUand K. GAVRA Laboratory for Meteorology, Dept. of Applied Physics, University of Athens, Greece

Abstract--In recent years, the evaluation of the efficiency of the performance of solar energy units is not done by using long-term averages of weather data as input but preferably by using data sets representative of the climatological features of the site that are generated for this purpose. Such data sets, which are usually called "Test Reference Year" or "Short Reference Year," consist mainly of solar radiation data, but they may also include other meteorological data, like temperature wind velocity etc, which may affect the response of the units. In this article, an attempt is made for the generation of such a representative data set for the city of Athens mainly by following a method that has been proposed by Hall et al. This data set, which includes global solar radiation data and six other meteorological parameters referring to temperature, dew point, and wind velocity, has been characterized by Hall as a "Typical Meteorological Year."

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

Due to its typical Mediterranean climate, most of the Greek territory receives considerable annual amounts of solar radiation which, therefore, becomes very important as an energy source for the country. The solar energy income is particularly high at the coastal areas of central and southern Greece as well as in most of the islands where the dry summer period is well pronounced lasting about five months, whereas the sunshine duration in winter remains considerable even in the coldest months. It is, therefore, evident that a complete study of the solar energy income with the help of measurements would be of great interest. Nevertheless, longtime measurements of global solar radiation are available only at the National Observatory of Athens (NOA) and have been statistically elaborated in the past by several authors[I,2]. Measurements are also available at certain other sites of the country but only for short periods in the recent years. The importance of the seasonal distribution of global solar radiation for solar energy designs has led a number of authors to estimate its distribution at different parts of the country. This has been achieved either by using the well-known Angstrom's formula[l,3], or by applying some of the existing solar models that employ astronomical and meteorological data such as those proposed by Budyko[4], Bird and Hulstrom[5], etc.[6,7]. Although the knowledge of the annual march of global solar radiation and its ordinary statistics at a certain site is necessary for the evaluation of the efficiency of the performance of solar energy units, it has recently been realized that the generation of a representative solar climatological database for the site would be more important for the above purpose. Such a representative database has been generated in the past by several authors either with the utilization only of solar radiation data[8,9] or by employing solax and other meteorological data as well[10,1 I]. Pe405

trie[10], for instance, generated what he called a "typical week ~ as representative weather data base for each month, with a duration ranging between 5 and 10 days and consisting of daily readings of solar radiation, temperature, and wind speed. A variety of representative databases of a year's duration, usually referred to as Test Reference Years (TRY) or Short Reference Years, have been developed for a number of European countries[12,13]. Hall[11] has created, for a network of stations in the United States, a representative data base of a year's duration consisting of a series of daily solar radiation and weather readings called a "Typical Meteorological Year" (TMY). In this article, an attempt is made to generate a representative weather database for the city of Athens by employing the method that has been proposed by Hall[l 1] et al. The (TMY) will be generated by using standard meteorological data and data of global solar radiation obtained by measurements at (NOA) for a period of 17 years (1966-1982). It is hoped that in a few years the generation of a (TMY) will become feasible for other stations of the country, when adequate data from solar radiation measurements will be available. 2. M E T H O D A N D D A T A B A S E

In the method proposed by Hall[11], 13 meteorological parameters were examined for a period of 23 years. These parameters were the daily mean, maximum, and minimum values and ranges of temperature, dew point, and wind velocity and the daily values of global solar radiation. Each month was examined separately and the generation of the TMY was done in two stages. At the first stage, five candidate years were selected for every month. This selection was done by comparing the cumulative frequency distribution functions (CDF) of each of the above parameters for every year to their long-term distribution (i.e., for all years). The comparison was

406

D. PISSIMANISet al. m

done by employing the Finkelstein-Schafer[14] statistics (FS). According to this statistic, if a number n of observations of a variable x are available and have been sorted into an increasing order &, x2 . . . . xn, the CDF of this variable is given by a function Sn(x), which is defined as follows.

f

0 f o r x < x(t) Sn(x) = ~ ( k - 0 . 5 ) / n forx(~)-< x < xt, + ,> I I f o r x >- x(~)

Dry Bulb Temp

wj:

WS = X wj FSj

(3)

j=t

(m is the number of parameters). It was found[ 11 ] that 4 of the 13 parameters were of very little importance so zero weights were given to them. These parameters were the three ranges and the minimum wind velocity. The remaining parameters were given the following weights

(1)

Dew Point

Wind Vel.

Solar Rad.

Max

Min

Mean

Max

Min

Mean

Max

Mean

1/24

1/24

2/24

1/24

1/24

2/24

2/24

2/24

From its definition, Sn(x) is a monotonically increasing step function with steps of sizes 1/n occuring at xk and is bounded by 0 and 1. The FS by which the comparison between the long-term CDF of each month and the short-term C D F for each individual year of the same month was done is given by the equation n

FS = ( I / n ) 2

(2)

8'

i=1

where 8i is the absolute difference between the longterm CDF of the month and one year C D F for the same month at xi(i = 1,2 . . . . n), n being the number of daily readings of the month. For each month, the function FS was computed for every year and for all of the 13 parameters that have been considered. Since the above-mentioned parameters were not found to be of equal importance, weights were given to their FS statistic and a weighted sum (WS) was produced,

12/24

The candidate years selected for each month were the five years with the smallest values of WS. According to Hall[ 11 ], the final selection of the most representative year for each month was done in a second stage by examining a number of statistics of the daily values of global solar radiation and mean daily temperature. These statistics were the differences between the long- and short-range means annd medians and the FS statistics. Also, the persistence of the daily values of global radiation and the mean daily temperature was taken into account by examining the frequencies and run lengths above and below fixed longterm percentiles. Thus the frequencies and run lengths above the 67th and below 33rd long-term percentile for temperature and the frequency and run length below the 33rd long-term percentile for daily global radiation was examined. By applying the above procedure for all months a composite year was finally formed (i.e., the TMY), consisting of the selected most representative years

Table 1. Weighted sums of the FS statistics (WS). Underlined numbers correspond to the five candidate years of each month. Asterisks denote the TMY for each month Year

I

F

M

A

M

J

J

A

S

O

N

D

1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982

0.061 0.070 0.064 0.111 0.073 0.095 0.085 0.042 0.091 0.082 0.116 0,.061 0.057* 0.060 0.073 0.081 0.061

0,165 0.052 0.080 0.089 0,129 0.081 0.089 0,037 0.049* 0,098 0,077 O. 155 0.084 0.057 0.075 .0.,070 0.098

0.047 0.042 0.054 O. 144 0.036* 0.057 0.060 0.093 0.065 0.091 0.077 0.078 0.096 0.108 0.056 0.124 0.069

0.062 0.073 0.085 0.101 0.062 0#043 0.073 0.084 0.094 0.095 0.057* 0.082 0.082 0.042 0.071 0.059 0.090

0.064 0.092 0.171 0.080 0.092 0.087 0.089 0.094 0.078 0.119 0.060* 0.090 0.109 0.114 0.066 0.104 0.084

0.111 0.150 0.199 0.086 0.067 0.097 0.135 0.047 0.049 0.124 0.080 0.065 0.194 0.104 0.049* 0.103 0.194

0.115 0.162 0.185 0.099 0.063 O. 129 0.103 O. 107 0.108 0.102 0.087 0.096 0.144 0.066* 0.092 0.096 0.142

0.112 0.169 0.202 0.094 0.062 O. 117 0.127 0.087 0.077* 0.193 0.120 O. 126 0.101 0.073 0.079 0.123 0.157

0.106 O. 137 0.143 0.052 0.068 O. 135 0.078* 0.056 0.084 0.104 0.153 0.057 0.087 0.101 0.114 0.085 0.174

0.152 O. 111 0.141 0.091 0.115 0.087 0.075 0.034 0.077 0.037* 0.067 O. 136 0.049 0.080 0.071 0.143 0.103

0.104 0.089 0.162 0.093 0.093 0.067 0.131 0.079 0.099 0.087 0.058 0.082 0.103 0.047* 0.094 0.144 0.106

0.042* 0.073 0.123 0.076 0.060 0.092 0.097 0.067 0.099 0.091 0.059 O. 110 0.084 0.051 0.046 0.132 0.117

Generation of a ~typical meteorological year"

407

Table 2. FS statistics of global solar radiation Year 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 . 1981 1982

I

F

M

A

M

J

J

A

S

O

N

0.08 0.09 0.04 0.17 0.04 0.08 0.13 0.04 0.10 0.07 O. 19 0.06 0.04 0.06 0.09 0.07 0.07

0.16 0.02 0.08 0.09 O. 19 0.08 0.14 0.02 0.04 0.07 0.07 0.15 0.07 0.05 0.07 0.08 0.06

0.05 0.03 0.05 0.22 0.04 0.05 0.07 0.09 0.07 0.08 0.07 0.10 0.08 0.09 0.05 0.11 0.06

0.04 0.10 0.09 0.09 0.05 0.04 0.05 0.10 0.10 0.09 0.03 0.10 0.05 0.03 0.04 0.06 0.10

0.03 0.11 0.21 0.07 0.08 0.10 0.10 0.12 0.08 0.12 0.06 0.12 0.08 O. 14 0.03 0.11 0.11

0.15 0.17 0.32 0.12 0.08 0.12 0.19 0.03 0.05 0.18 0.11 0.08 0.23 O. 14 0.03 0.11 0.31

0.15 0.21 0.27 0.08 0.07 0.17 0.06 0.07 0.14 0.16 0.04 0.10 0.20 0.05 0.06 0.13 0.23

0.13 0.24 0.31 0.11 0.05 0.17 0.18 0.08 0.06 0.26 0.04 0.17 0.10 0.08 O. 10 0.13 0.21

0.14 0.19 0.21 0.05 0.06 0.20 0.04 0.07 0.10 0.11 0.17 0.04 0.06 0.13 0.07 0.10 0.24

0.13 0.16 0.17 0.04 O. 14 0.08 0.04 0.03 0.04 0.04 0.07 0.14 0.04 O. 11 0.05 0.14 0.17

0.11 0.10 0.21 0.05 O. 14 0.10 0.20 0.09 0.07 0.09 0.05 0.06 0.05 0.04 0.04 0.18 0.10

D 0.05 0.07 0.19 . 0.09 0.07 0.09 0.10 0.04 0.07 O. 10 0.07 0.07 0.07 0.05 0.05 0.14 0.15

Table 3. FS statistics of temperature Year

I

F

M

A

M

J

J

A

S

O

N

D

1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982

0.08 0.06 0.06 0.10 0.18 0.17 0.03 0.07 0.13 0.I0 0.05 0.04 0.04 0.09 0.08 0.18 0.05

0.27 0.13 0.08 0.13 0.12 0.14 0.07 0.07 0.05 0.21 0.16 0.27 O. 11 0.07 0.13 0.09 0.25

0.04 0.07 0.07 0.11 0.04 0.14 0.05 0.17 0.06 0.17 0.10 0.11 0.09 O. 19 0.07 0.18 0.17

0.16 0.04 0.15 0.17 0.16 0.07 0.10 0.11 0.15 0.13 0.06 0.07 0.06 0.07 0.15 0.07 0.10

0.17 0.09 0.27 0.13 0.15 0.16 0.07 0.08 0.13 0.06 0.08 0.12 0.05 0.04 0.20 0.15 0.06

0.08 0.17 0.10 0.04 0.07 0.05 0.08 0.07 0.07 0.04 0.10 0.08 0.08 0.11 0.06 0.09 0.05

0.11 0.04 0.07 0.20 0.07 0.14 0.10 0.07 0.04 0.08 0.17 0.18 0.08 0.05 0.11 0.06 0.09

0.23 0.17 0.14 0.06 0.13 0.07 0.09 0.15 0.05 0.16 0.29 0.15 O. 14 0.05 0.04 0.05 0.10

0.11 0. i 0 0.04 0.07 0.10 0.11 0.05 0.06 0.05 0.20 0.12 0.06 0.22 0.06 0.12 0.07 0.15

0.30 0.09 0.13 0.18 0.12 0.13 0.18 0.07 0.18 0.03 0.07 0.18 0.08 0.07 0.07 0.26 0.06

0.17 0.09 0.05 0.17 0.05 0.03 0.05 0.11 0.15 0.11 0.06 0.17 0.29 0.06 0.22 0.16 O. ! 2

0.03 0.10 0.09 0.08 0.07 0.12 0.15 O. 13 0.13 0.14 0.05 0.19 0.13 0.08 0.02 0.22 0.04

Table 4. Root mean square differences (RMSD) of the mean hourly values of global solar radiation ( M J / m - 2 / h o u r -z) for the five candidate years of each month Year 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982

I

F

M

--0.059 -0.033 0.062 --0.042 . . . . --0.056* ---. . . . 0.034 0.039 --0.030* -. . . . ---0.065 --. -0.030* . . 0.083 0.061 ~ --0.123 -0.103 -0.063 . .

A

M

J

J

A

0.093 . . . . . . . . . . . . . . O. 101 -----0.076 0.072 0.056 0.054 . . . . . . . . . --0.052 -0.070 -0.067 0.051 -0.036* . . . . . 0.074* 0.069* -0.037 ---0.066 --. . . . . . 0.098 --0.043* 0.050 ~ 0.080 0.045* 0.056 0.072 0.162 --0.091 . . . . . . .

S

0.057 . .

O

. . . 0.057 0.110 . 0.022* 0.077 . -0.100 --.

. .

. . .

N

0.029* . . ---

-0.043 .

D

. 0.043* 0.088 -0.033 ~ 0.037 . . .

--0.050 -0.085 . -0.049 0.047 -0.033* ~ .

-0.050 ---0.078 --0.067 0.055

408

D. I::qSS[MANISet

28 2~ 24 22

2C la

'o

/i/IILl 1C

8

"'... 4 2 C

Fig. I. Annual variation of global solar radiation for the TMY (solid line) and for the period 1966-1982 (dashed line). Dotted line indicates variation for 1968, which was chosen as a most unfavorable year. for the 12 months. The author admits, however, that the final selection at the second stage was somewhat subjective, probably due to the large number of statistical parameters that had to be taken into account simultaneously. The generation of the TMY for the city of Athens was done by using standard meteorological data and data of global solar radiation from the continuous measurements at NOA and for a 17year period (1966-1982). Data were not available for two of the nine meteorological parameters mentioned

r

al.

above (i.e., the maximum and minimum dew point values), but since their weighting factors were only of the order of 1/24, they should not be considered as vital for the selection of the TMY. The weighting functions were produced according to the method stated above and the five candidate years with the smallest values of WS were found. This was accomplished with the help of a computer program constructed for this purpose. In Table 1 the values of WS for the 17 years examined are given for all months and the 5 selected years with the smallest values of WS are underlined. Also, in Tables 2 and 3 the FS statistics for daily global solar radiation and for mean daily temperature are given for all months of the 17year period. In the second stage, a restriction of the number of statistical parameters, which were finally examined for the selection of the most representative year of each month, was done so that the results would be more easily reproduceable. Thus, the selection of the most representative of the 5 candidate years for each month was done by examining the following three parameters. First, the deviations of the short-range mean daily values of global solar radiation in each month for every one of the five candidate years were examined with respect to the long-range values. Second, the FS statistic of the daily values of global solar radiation and finally the FS statistic of the mean daily temperature was examined. As far as the first parameter is concerned, since hourly values of global solar radiation were also available, the deviations were found by estimating the Root Mean Square Differences (RMSD)[15] of the mean hourly distribution of the global solar radiation for each of the five candidate years of each month with respect to the mean long-range hourly distribution. The RMSD is defined as follows.

JANUARY

APRIL

JULY

OCTOBER

3-

2-

O J¢

E 2

i

f

I

I

I

I

8

10

12

14

16

I 18

i

6

8

10

12

1,4

16 m

18

hour's

Fig. 2. Mean hourly values of global solar radiation for the TMY (solid line) and for the period 1966-1982 (dashed line) for four representative months. Dotted lines indicate the same values for January 1976, April 1974, and July and October 1968, which have been chosen as most unfavorable for these months.

Generation of a "typical meteorological year"

RMSD =

(x~t - ~t)2/N

}'

409

each month are given in Table 4. From this table, the smallest values were chosen within a range of 0.02 M J / m " / h o u r (i.e., less than 4% of the mean hourly values of global solar radiation of the 12 months). From the selected years, those with the best FS radiation statistics were retained with a range of 0.03 and finally the FS of temperature was taken into account by choosing the year with lowest FS statistics

(4)

where the indices k and l denote the year and hour of the day respectively and N is the number of hours of the day with global radiation not being zero. The values of the R M S D for the five candidate years for 2e

JANUARY 26 2,4 22

20 18 16

I[ 1C

•

i!a-

.........7t^

I

4

2! O,

i

t

!

i

APRIL 28 26 2a

20

°°

' /!J

~14

-

:

~" 1 2

".:

.."

~

i;

"~

7"'""

:

,,

i

"

"

.

~0

i •

8 "

o

:: ::::

::::

:.

6

0

~ 1

3

5

~ 7

9

11

~ 13

15

17

19

21

23

25

27

29

3"1

--------- d o ) , Fig. 3. Sequences of daily values of global solar radiation for the TMY (solid line) for January and April. The same sequences for the unfavorable years of Fig. 2 are shown by dotted lines. Continuous solid straight line indicates the mean monthly values.

D. PISSIMANIS et al.

410

if more than one candidate year was still left for the final choice. The final selected years for all months are indicated by stars (*) in Tables 1 and 4. In Fig. 1, the mean monthly values of global solar radiation are given for the TMY for the 17-year period and for the year of 1968, which exhibits quite unfavorable values of WS for most of the months. Also, in Fig. 2 the mean hourly values of global solar radiation for four rep-

resentative months of the TMY (i.e., January, April, July, and October) are given together with the mean hourly values for the 17-year period. In the same figure, the mean hourly values are given for the years with the most unfavorable (large) values of FS radiation statistics. If the maximum value of FS appeared in more than one year for the same month, the year with the largest value of WS was chosen. It can be verified that the values of global solar radia-

30

28 26 24 22 20 18

~j

"0 ~

I[

14

I[ 10 8 6 4

2 0 OCTOBER 24

22 20 18 16 0

1,4

•""/

"~.....',..."A ': /"",..X/ A

.,.,. . . \/

~ IE 10

.-":.

•

8 6

4 2

0

'

1

.....

3

5

7

;--~'

13

;

5

'~--,'~

1

'

23

'

b

2.5 ~- d a y

Fig. 4. Same as in Fig. 3 but for the months of July and October.

2'9

Generation of a "typical meteorological year" tion in unfavorable years show considerable deviations from the long-range mean values as well as from the values of the TMY. Finally in Figs. 3 and 4 the sequences of daily values of global solar radiation for the TMY are given in four representative months together with the daily values for the same unfavorable years as in Fig, 2. It can be seen that the daily values of global solar radiation for the years that belong to the T M Y are more normally distributed with respect to the corresponding mean monthly values (straight lines). It can be also noticed from the above figures that the maximum variation of global solar radiation appears in spring. This should be attributed to the fact that in April the mean daily value of global solar radiation under clear sky in Athens is relatively high, whereas cloudiness shows a considerable variation having a mean value 4.5 in October. It must be noted that since data were taken from measurements at NOA, which is sited in the interior of the city of Athens, the values of global solar radiation may have been influenced to a certain degree by the air pollution which, at times, has become considerably high in the period examined according to existing measurements[ 16]. Since this subject has not been investigated adequately we may only assume that the real mean longrange monthly values as well as the T M Y monthly values might have been somewhat higher in the absence of the influence of the city. REFERENCES

1. B. D. Katsoulis and C. E. Papachristopoulos, Analysis of solar radiation measurements at Athens observatory and estimates of solar radiation in Greece. Solar Energy 21, 217-226 (1978). 2. D. A. Kouremenos, K. A. Antonopoulos and E. S. Domazakis, Solar radiation correlations for the Athens-Greece area. Solar Energy 35, 259-269 (1985). 3. A. A. Flocas, Estimation and prediction of global solar

411

radiation over Greece. Solar Energy 24, 63-70 (1980). 4. M. I. Budyko, Atlas of the heat balance of the earth. Leningrad, (1963). 5. R. Bird and R. L. Hulstrom, Direct insolation models. U.S. Solar Energy Research Institute SERI/TR, 33534-4 (1980). 6. V. A. Notaridou and D. P. Lalas, The distribution of global and net radiation over Greece. Solar Energy 22, 505-514 (1979). 7. D. P. Lalas, D. K. Pissimanis and V. A. Notaridou, Methods of estimation of the intensity of solar radiation on a tilted surface and tabulated data for 30 °, 45 ° and 60° in Greece. Technica Chronica, Scientific Journal of the Technical Chamber of Greece-Section B. 2, 129-178 (1982). 8. X. Benseman and Y. Cook, Solar radiation in New Zealand--The standard year, N. Zeal. J. Sci. 12, 698708 (1969). 9. D. Feuermann, J. M. Gordon and Y. Zarmi, A typical Meteorological day (TMD) approach for predicting the long-term performance of Solar Energy systems. Solar Energy 35(1), 63-69 (1985). I0. R. P. William and M. McClintock, Determining typical weather for use in Solar Energy simulations. Solar Energy 21, 55-59 (1978). 11. I. J. Hall, Generation of a Typical Meteorological Year. Proceedings of the 1978 annual meeting of AS of ISES. Denver CO, 2.2 (1978). 12. Test Reference years (TRY), Weather Data Sets for Computer Simulations of Solar Energy Systems and Energy Consumption in Buildings. Commission of the European Communities Directorate General XII for Science, Research and Development (1985). 13. R. Dogniaux and R. Sneyers, Mrthodologie d'analyse statistique des donnres mrtrorologiques en vue de la constitution de "prriodes-types" pour l'application h des probl~,mes sprcifiques. Rapport des joumres nationales d'rtudes sur le chauffage solaire dans le bfitiment. AIM Lirge, Belgique (1977). 14. J. M. Finkelstein and R. E. Schafer, Improved goodness of fit tests, Biometrika 58, 641-645 (1971). 15. C. C. Y. Ma and M. lqbal, Statistical comparison of solar radiation correlations--Monthly average global and diffuse radiation on horizontal surfaces. Solar Energy 33(2), 143-148 (1984). 16. National Observatory of Athens Meteorological Institute. Bulletin of air pollution.