Pergamon

Rem'~*abh, Enerqy. Vol. 4, No. 2. pp. 199 216, 1994

~ Pergamon

Copyright i 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 096() 14~1'94 $6.00 eO.O0

STATISTICAL ANALYSIS OF MEASURED GLOBAL INSOLATION DATA FOR PAKISTAN i. A. RAJA* a n d J. W. TW1DELLt * Department of Physics, University of Balochistan, Quelta, Pakistan: t Energy Studies Unit, University of Strathclyde, Glasgow, U.K.

(Received 26 Fehrlmry 1993 ; acceple,125 June 1993) Abstract--The global insolation data for up to 15 years from six locations m Pakistan are analysed. In addition to simple arithmetic analysis, tables and figures of cumulative frequency distribution and number of consecutive days above certain threshold insolation values are constructed. Results are presented for monthly and annual periods for practical application when planning solar installation. INTRODUCTION Solar energy utilization needs accurate scientific assessment of the resource to establish its potential at a specific location. The financial analysis of the investment in installing a solar system is heavily dependent on accurate inputs of properly organized data. Readily available insolation data, from the observatories all over the world, are in a standard format of tables of hourly, daily or mean values of raw data. Data of this kind find very little direct use in solar application. The data sets are far too large to be applied in design and cost analysis or to calculate the potential efficiency and payback periods. Various forms of reduced data are needed. Therefore, it becomes essential to analyse, process and archive the data for the design of a specific solar system. Organizing and processing the data can make the data more useful and practical for applications of solar energy. For designing an efficient solar system, apart from the simple arithmetic mean, detailed statistics about the distribution of insolation are required. For example, proper sizing of almost all solar systems requires the probability of the expected number of days with insolation above or below certain threshold values. In some specialized applications, the number of consecutive days above or below a given threshold are also needed. The statistical analysis enables the primary data set to be reformed into a manner which is more concise, convenient and informative than the original data. This makes the data easier to comprehend and communicate. This type of descriptive analysis may be found in the work of Barry [1], Liu and Jordan [2], Fritz and MacDonald [3], Bennett [4]. The preparation of the European Solar Radiation Atlas [5] demanded analysis of probably the largest data set of solar radiation ever considered. During the present study both simple arithmetical

descriptions and detailed statistical analysis were carried out with the data for six locations in Pakistan. The work is presented in the form of tables and diagrams. QUALITY CONTROL AND REHABILITATION Much has been written about the poor quality of past insolation data [5,6]. Recent interest in solar energy research and application has created much greater demand for high quality long period data. The choice is either to wait many years for better data sets or to make the best use of past data. Therefore, for present applications we have to rely on past data. However, in order to minimize the errors, it is essential to rehabilitate the historical data before use. Before conducting a detailed analysis, the insolation data from six stations in Pakistan were subjected to quality checks and were rehabilitated. The details of rehabilitation techniques are given by Raja [7]. The suspected erroneous values were removed from the data set. The gaps due to missing record/discarded data were filled with estimated values from empirical relationships. The stations are listed in Table [ with geographical location and period for which the data are used.

STATISTICAL ANALYSIS (a) Simple arithmetic analysis The arithmetic mean is a basic parameter which is most widely used. The accuracy of the arithmetic mean is sensitive to the extreme values. The solar radiation being a highly variable quantity, has a large range between the extreme values. Therefore the simple mean values of the total do not provide the true picture of the solar potential of a location and are quite insufficient for sizing and the cost analysis of 199

1. A. RAJA and J. W. TWIDELL

200

Table 1. I n s o l a t i o n m e a s u r i n g stations in P a k i s t a n Station

Latitude

Longitude

Elevation

Period

lslamabad

33.72 N

73.10 E

510 m

Karachi Lahore Multan Peshawar Quetta

24.90 N 31.55'N 30.20°N 34.00°N 30.18CN

67.13 E 74.3Y E 71.43'E 71.52'E 66.95~E

1985, 1988 89 1975 89 1975 89 1975 89 1975-81 1975 89

(a) Islamabad

g

m m m m m

(b) Karachi

30

"N

21 213 122 358 1672

30

•

Max. [ ] Mean [ ] Min

25 20

20

15 10

1

5 0

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

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

(c) Lahore 35 30

(d)

ImMax.[ ] M e a n

L

[-']Min ]1

35 30

25

25

"~

20

20

=

15

15

10

10

5

5

0

C

(e) Peshawar

(f)

35~

30

"~

I• Max. [ ] Mean [ ]

"

30

20

20

15

15

l0

10

5

5

0

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

Min

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

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

35

Multan

Quetta ill

•

Max. [ ] Mean [ ] Min

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

Months Fig. 1. M e a n m a x i m u m , m i n i m u m and average global i n s o l a t i o n (MJ m 2 d

Months ') over n a m e d locations.

Global insolation data for Pakistan

201

Table 2. Mean minimum and maximum and average insolation over named locations and stated period in MJ m 2 d (a) Islamabad Mean Max.

Months

Min.

Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec.

4.55 4.44 5.71 9.71 13.04 13.45 10.77 10.08 13.41 8.88 7.79 3.84

14.14 17.48 21.91 27.18 28.t4 28.00 27.32 25.31 22.11 18.36 14.50 11.73

(b) Karachi

Months

Min.

10.06 13.59 15.50 22.03 24.32 23.34 21.07 20.47 19.45 15.68 11.57 8.14


9.61 9.96 11.03 15.91 16.98 14.15 10.36 9.75 11.57 14.24 11.50 8.24

(c) Lahore Mean Max.

Months

Min.


4.64 5.66 7.66 10.83 12.39 12.80 8.37 9.35 11.93 10.61 7.15 4.74

14.15 19.05 23.35 26.02 27.73 28.02 26.52 25.90 23.69 19.15 15.03 13.06

Mean Max.

Min.


4.43 5.29 5.80 10.42 IYI7 [6.52 12.58 9.06 3.21 9.14 6.96 4.64

15.62 19.90 24.80 28.03 30.06 31.18 28.71 26.16 23.43 19.21 16.71 13.05

17.73 19.81 23.68 24.96 26.43 27.36 25.57 25.55 24.58 21.44 18.09 15.78

Average 15.34 16.30 20.2l 22.18 23.01 22.52 17.47 16.79 30.07 18.94 15.74 14.08

(d) Multan Mean Max.

Average

Months

Min.

10.53 13.83 17.56 21.59 23.13 23.56 18.87 19.50 19.78 15.96 12.44 10.15


6.02 6.88 8.77 13.45 13.88 13.15 12.36 13.46 14.10 11.88 9.56 5.93

(e) Peshawar

Months

Mean Max.

Average

15.18 18.81 23.23 26.23 27.37 27.10 26.32 25.31 23.18 19.59 15.89 13.57

Average 12.15 14.60 17.98 22.54 23.64 22.80 21.56 21.43 20.17 16.70 13.95 11.05

(f) Quetta Mean Max.

Average

Months

Min.

10.52 14.27 17.40 21.47 24.93 26.52 23.18 20.85 19.16 16.02 13.27 10.51


5.92 7.44 8.99 12.92 15.03 21.15 15.19 14.75 17.92 13.74 8.59 0.16

the solar system. However, if the average data sets are supported by certain other quantities, e.g. mean m a x i m u m and mean m i n i m u m values, these may produce better results. Using the data for six locations in Pakistan for the

17.57 21.66 25.07 29.55 32.06 32.04 29.56 27.59 26.12 22.89 18.76 15.19

Average 13.24 15.95 18.86 24.24 27.43 28.56 24.89 24.11 23.10 19.71 15.31 12.31

period given in Table l, the arithmetic mean of daily global insolation and the mean minimum and mean maximum values per day for each calendar m o n t h were computed. The results are presented in Table 2(a-f) and Fig. l(a f).

202

I. A. RAJA and J. W. TWIDELL

(b) Cumulativefrequency distribution The cumulative frequency distribution provides better estimates of the probability and finds its application in many other areas, apart from planning and sizing solar appliances. For example, better estimates of crop growth rates, energy efficient building designs, water resource assessment and water management (e.g. water evaporation systems, irrigation, snow melt, etc.), are obtained if cumulative distributions of insolation over the area are available. The cumulative distribution is obtained by arranging the data in ascending or descending order, according to the requirements that the estimates of the probabilities of insolation be less than or greater than certain threshold values. For insolation, the values above a given threshold are generally preferred. To construct thc cumulative frequency distribution, the average daily insolation in each month over the period under consideration, for each of the six insolation measuring stations, is arranged in ascending order. With a class interval of I MJ m 2, the range 1--36 MJ m 2is placed in the first column of the frequency table. The next thirteen columns, one for each month and one for annual mean values are filled, by making a count of the number of days d(j) on which the daily insolation falls in the interval, i.e. jMJm

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