Effect of rainfall on the estimation of monthly mean hourly solar radiation for India

~ ) Pergamon Renewable Energy, Vol. 13, No. 4, pp. 505-521, 1998

© 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain

PII: S0960-1481(98)00015-9 0960-1481/98 $19.00+0.00

EFFECT OF R A I N F A L L O N THE E S T I M A T I O N OF M O N T H L Y M E A N

H O U R L Y S O L A R R A D I A T I O N F O R I N D I A

G. V. PARISHWAD,* R. K. BHARDWAJ and V. K. NEMA

Department of Mechanical Engineering, Motilal Nehru Regional Engineering College, Allahabad, 211 004, India

(Received 10 August 1997; accepted 21 January 1998)

Abstract--The constants in the empirical equations to predict hourly solar radiation on a horizontal surface recommended by ASHRAE were modified by the authors [1] for Indian locations. In further studies, India is divided into four regions of rainfall, namely, region of heavy, medium, low and very low rainfall. Using ASHRAE equations with the modified constants, monthly-mean-hourly solar radiation values are estimated for ten cities from different regions of India. From the comparative data analysis of the measured and estimated solar radiation of these cities, empirical correction factors for the four regions of rainfall were obtained. The statistical analysis is carried out for the computed data with and without considering correction factor for rainfall and the measured data for four randomly selected Indian cities. Two statistical indicators, namely, mean percentage error and normalized root mean square error, are used to compare the accuracy of the developed procedure. The results show that the yearly average normalized root mean square error with Indian constants, considering effect of rainfall for these four Indian cities, is found to reduce to 14.86, 12.15 and 7.61% for monthly- mean-hourly beam, diffuse and global radiation respectively on horizontal surface, as against the corresponding values of 23.29, 22.2 and 16% without considering the correction for rainfall. © 1998 Elsevier Science Ltd. All rights reserved.

1. INTRODUCTION

Solar radiation reaching the Earth's surface depends on the local climatic conditions. Information on the availability of solar radiation is needed in many applications dealing with the harnessing of solar energy. A knowledge of monthly-mean values of the hourly radiation enable us to derive very precise information about the performance of solar energy systems [2]. Such data is useful to engineers, architects and designers of solar systems as they endeavour to make effective use of the solar energy.

* To whom all correspondence should be addressed.

505

506 G. V. PARISHWAD et al.

Most locations in India receive abundant solar radiation, and solar energy utilization technology can be profitably applied to these regions. The best solar radiation information of a place is obtained from experimental measurements of the global and diffuse solar radiation at that place. In India, the Meteorological Department measures sunshine duration, global radiation, and diffuse radiation at some selected places. The measured data of 21 years have been compiled and is available in the form of tables [3] giving the monthly average values of hourly global and hourly diffuse values.

For locations where no measurements exist, hourly radiation can be estimated by using empirical correlation developed from the measured data of nearby locations having similar climatological conditions. Various climatic parameters such as humidity, temperature, rainfall, total amount of coverage and in particular, number of sunshine hours, etc., have been used in developing empirical relations, as a substitute for the measurement of solar radiation. Perusal of literature (Threkeld and Jordan [4], Rao and Seshadri [5], and many others) reveals that clear sky solar radiation has been predicted, with reasonable accuracy [6] within + 5%. Attempts have also been made to compute solar radiation under cloudy or overcast conditions. Castagnoli e t al. [7] divided cloud types into four classes defining each of them with its cloudiness degree and found correlations for each of these classes. Similarly, Hoyt [8] considered six different types of clouds and proposed different trans- mission and absorption characteristics for each of them. Such computations are possible only if the cloud conditions at any location are known with the required reliability. Inso- lation and weather data for seventeen Indian cities were analysed and correlated by Modi and Sukhatme [9]. Correlations, based on a citywise regression analysis, indicate tha( daily total insolation correlates best with sunshine duration, cloudiness and precipitation. However, these correlations are not useful for predicting insolation at locations where this data is not measured. Hussain [10-12] developed correlations for estimating monthly-mean- daily beam, diffuse and global radiations from sunshine duration using Indian weather data for eight cities. He considered seasons in India such as pre-monsoon, monsoon, and post- monsoon periods and climatic zones of India such as arid and semi-arid regions, and wet and dry regions, to obtain collective fits for each period. Singh e t al. [13] developed empirical relation to estimate global radiation from hours of sunshine. Reliable data on the duration of sunshine are available [14] for 121 stations in India for periods ranging from 6-28 yrs. Therefore, correlations based on sunshine hours are not useful for places where such data is not available. Reddy [15] proposed an empirical method for computing daily total solar radiation using sunshine hours, humidity and number of rainy days during the month. He tested his equation for only two locations, namely, Pune and Thiruvananthapuram. His equation gave large errors when tested for other locations [9]. Mani and Rangarajan [16] have discussed an empirical method to compute solar radiation parameters under average overcast conditions. They suggested using mean ratio of daily-mean global radiation, measured on overcast sky condition, to that on clear sky condition for 16 stations. The variation in this ratio among the different stations represents variations caused by the characteristics of the cloud types found in different regions of the country. In the present paper, the authors have used a somewhat similar approach so as to estimate monthly- mean-hourly solar radiation at any location in India using only longitude and latitude of the location, and its region of rainfall as input information.

Empirical equations are given in the ASHRAE Handbook [17] to estimate hourly- beam, diffuse and global radiation on clear days. The values of the constants in these equations were derived from the results of research at the University of Minnesota [4]. When these

Effect of rainfall on the estimation of solar radiation 507

equations and constants were used t , predict the solar radiation data for the Indian cities, the predicted values were found to be higher for normal beam radiation and lower for diffuse radiation. Hence, authors have found a new set of values of the constants [1], to be used in these ASHRAE equations, suitable for Indian locations.

It is observed that the estimated solar radiation data closely matches in the dry months, but differs with corresponding measured values due to cloudiness, which is related to rainfall. India is a country with great climatic diversity. It has places like Cherrapunji, in Meghalaya, where total annual average rainfall (TAAR) is above 13,000 mm and places like Leh, in North Kashmir, and Jaisalmer, in West Rajastan, where TAAR is less than 100 mm [18]. Since the hourly solar radiation data is measured by Meteorological Department at only a few selected cities in India, the purpose of the present study is to develop a procedure along with empirical equations for calculating the rainfall correction factor for estimating hourly global (/) and diffuse (Id) radiation on a horizontal surface at any location in India, during both dry and wet months, with reasonable accuracy.

2. ANALYSIS

As recommended by ASHRAE [17], hourly beam radiation in the direction of rays (Ibn) and on the horizontal surface (Ibh) and hourly diffuse radiation (Idh) on the horizontal surface on a clear day are calculated using the following equations :

Ibn = A exp [--B/cosz] (1)

Ibh = Ib. COS Z (2)

Idh = Clbn (3)

where A, B, C are constants whose values are to be determined from the analysis of the solar radiation data and z is the zenith angle, which depends upon latitude of the location (L), hour angle (m) and solar declination (6), and is calculated from the following equation :

cos z = sin L sin 3 + cos L cos 6 cos 09 (4)

Solar declination (6) is calculated by

fi = 23.45 sin [360(284 + N)/365] (5)

where N is the day of the year. The hour angle (09) is an angular measure of time and is equivalent to 15 ° per h. It is measured from noon-based local apparent time (LAT) from the equation given by

09 = 1 5.0(12.0-- LAT) (6)

where the LA T value is obtained from the standard time by using the following equation [19]

EAT -- ST + E T _ 4 ( S T L - LNG) (7)

The equation of time correction(ET) is to consider small perturbations in the Earth's orbit and rate of rotation. The values of ET with respect to the day number (N) are available in graphical and tabular forms [17, 19] and can also be calculated from the following equations [201.

508 G.V. PARISHWAD et al.

ET = 9.87 sin 2 G - 7.53 cos G - 1.5 sin G (8)

where

G = 360(N-- 81)/364 (9)

The value of G is in deg. and that of ET is in minutes. The second correction arises because of the difference between the longitude of location

(LNG) and standard time longitude (STL). As the mainland of India extends between longitude 67.5 E and 97.5 E, standard time in India is based on 82.5 E (STL). The negative sign in this correction is applicable for the eastern hemisphere, while the positive is for the western hemisphere. For India, the negative sign is applicable as it lies in the eastern hemisphere.

2.1. Empirical relations developed for correction factor considering rainfall regions and time Based on climatological data available on rainfall [18], India is broadly divided into four

regions of rainfall (Fig. 1) : (1) region of heavy rainfall (HR) (total annual average rainfall (TAAR) > 1800 mm), (2) region of medium rainfall (MR) (1100 mm < TAAR < 1800 mm), (3) region of low rainfall (LR) (500 mm < TAAR < 1100 mm), and (4) region of very low rainfall (VLR) (TAAR < 500 mm). These limits are not very strict. Therefore, regions have been modified a little by placing cities in a region where TAAR of the city is closer, e.g., New Delhi with total annual average rainfall of 561.1 mm is considered in the region of very low rainfall, and Nagpur, with total annual average rainfall of 1150.7 mm is considered to be in the region of low rainfall.

Ten Indian cities, namely, New Delhi, Mumbai (Bombay), Calcutta, Chennai (Madras), Jodhpur, Nagpur, Goa, Ahmedabad, Bhavnagar and Port Blair, from different regions (Fig. 1) of India, for which measured data was available [3], are selected. Monthly-mean- hourly beam and diffuse radiation are calculated using eqns (1)-(9) and set of constants A, B and C obtained for India (Table 1). Comparative data analysis between measured and calculated values of monthly-mean-hourly beam and diffuse radiation on horizontal surface is made. A polynomial of third order was found suitable as a correction factor for rainfall. Separate empirical constants in these equations are obtained for monthly-mean-hourly beam and diffuse radiation on horizontal surfaces. In order to make the curve-fitting easier [21], the year is divided into two halves, and origin on the month-axis is taken at the middle of the half year in which the month under consideration lies. Accordingly, the month parameter m is modified to p, which is used as the independent parameter in the equation of correction factor of rainfall for beam (2b) and diffuse (2d) radiation on horizontal surfaces and is given by

p = m - 3 . 5 fo rm ~< 6 (10)

p = m - 9 . 5 fo rm > 6 (11)

1. For region of heavy rainfall (HR) (TAAR > 1800 mm) : f o r m ~<6

2b = 0.8631 -- 0.0946p-- 0.0325p 2 -- O.O006p 3 (12)

2d = 1.0 (13)


7~-;E :86°E 88°E ' ' 96'°E

I N D I A

/ r ' " . i

( ' . g

"X.

abac 23 .5°N

Mumbai

- j 6 °N- - ~ .

anantpt

BAr CL-A DESH

Chennai

SRI LANKA

Vishakhapatnam ~ 6 ° N "

~ Port B A Y OF ~ B l a i r B E N G A L

~ . ~ 0 200 400 km

INDIAIN O C E A N 72OE 80°E 88°E

X

,,3¢ o ~--8 N

Fig. 1. Map of India showing locations of the Indian stations selected for the study and regions of rainfalls: (1) Region of Heavy Rainfall (HR) (total annual average rainfall (TAAR) > 1800 mm), (2) Region of Medium Rainfall (MR) (1100 m m < TAAR < 1800 mm), (3) Region of Low Rainfall (LR) (500 m m < TAAR < 1100 ram), and (4) Region of Very Low Rainfall (VLR) (TAAR < 500

mm). Boarders are not sharp but diffuse.


Table 1. Values of Constants A, B and C obtained for predicting hourly solar radiation

in India

Day A ( W / m 2) B C

21 Jan 708.00 0.000 0.192 21 Feb 732.20 0.010 0.209 21 Mar 767.86 0.046 0.229 21 Apr 713.35 0.131 0.385 21 May 798.39 0.150 0.250 21 Jun 440.71 0.398 1.108 21 Jul 222.87 0.171 1.721 21 Aug 240.80 0.148 1.624 21 Sep 396.21 0.074 0.748 21 Oct 644.73 0.020 0.256 21 Nov 666.60 0.008 0.213 21 Dec 692.52 0.000 0.193

f o r m > 6

J-b = 0 . 7 1 2 5 - - 0 . 1 5 8 3 p + 0 . 0 2 1 4 p 2 + 0 . 0 3 3 3 p 3

2d = 1.0563 + 0 . 0 3 6 6 p - - 0 . 0 2 2 8 p 2 - -0 .0117p 3

2. For region of med ium rainfall (MR) (1100 m m < T A A R < 1800 mm) :

f o r m ~ < 6

ftb = 0 . 8 8 8 4 - O . 0 5 4 4 p + O.OO34 p 2 + 0 . 0 0 7 3 p 3

2d = 1 .0459- -0 .0628p+0 .0077p 2 + 0 . 0 0 4 4 p 3

f o r m > 6

2 b = 0 . 9 3 1 9 - 0 . 2 9 2 6 p + 0 . 0 2 9 6 p 2 + 0 . 0 3 1 9 p 3

2d = 1.0663 + O.0948 p + O.O179 p2 --O.OO39 p 3

3. Fo r region of low rainfall (LR) (500 m m < T A A R < 1100 mm) :

f o r m ~< 6

}~b = 1.0791 + 0 . 0 4 4 2 p - - 0 . 0 1 0 5 p 2 - -0 .0123p 3

2d = 0 . 9 0 3 8 - - 0 . 0 2 8 2 p + 0 . 0 0 7 9 p 2 + 0 . 0 0 8 5 p 3

f o r m > 6

•b = 0 . 9 7 9 4 + 0 . 1 6 4 5 p - - 0 . 0 1 1 8 p 2 - -0 .0161p 3

2d = 0.9806-- 0.0702p -- 0.0025 p2 q_ 0.0052p3

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

.

Effect of rainfall on the estimation of solar radiation

F o r region o f very low rainfal l (VLR) ( T A A R < 500 mm) : f o r m ~< 6

2b = 1.0074 + 0.0037 p + 0.0131 p2 -k- 0.0065 p3

2d = 1.0631 + 0 . 0 0 6 2 p - - 0 . 0 0 9 6 p 2 + 0 . 0 0 1 2 p 3

f o r m > 6

511

(24)

(25)

•b ~- 1.3393 - - 0 . 1 1 7 2 p + 0 . 0 0 0 6 p 2 + 0 . 0 0 1 2 p 3 (26)

2d = 0 . 7 6 4 4 - 0 .0566p + 0 .0282p 2 + 0.0041 p3 (27)

Var i a t ion in the ra t io o f measu red to ca lcula ted values for beam and diffuse r ad ia t ion on hor i zon ta l surfaces, with respect to t ime, was s tudied by p lo t t ing g raphs for different cities o f India . I t was observed tha t the ra t io o f measured to ca lcula ted inso la t ion as seen f rom a representa t ive p lo t in Fig. 2 is low for beam and diffuse r ad i a t i on in the morn ing . Then it goes on increas ing up to a r o u n d n o o n time. The ra t io a t ta ins m a x i m a at n o o n for diffuse r ad ia t ion and between 14:00 and 16:00 h for beam rad ia t ion . Thereaf te r it s tar ts

1.4

1.2

1.0

U o.8

ii 0.6 ::i.

0.4

0.2

O,O I I ! I

7 9 11 13 15 17 T i m e in h o u r s

Fig. 2. Variation in the ratio of measured to calculated values for beam and diffuse radiation on horizontal surface with respect to time.


declining. Due to this, the time correction factor for beam (Pb) and diffuse (Pd) radiation is obtained by the following equations :

q = L A T - - 12.0 (28)

Pb = 1.0042 + 0.0693 q-- 0.0090 q2 _ 0.0009 q3 (29)

p~ = 1.2330 + 0.0242 q - 0.0289 q2 -k- 0.0002 q3 (30)

The corrected values of monthly-mean-hourly beam (Ibhc), diffuse (Iahc) and global radiation (/) on horizontal surface are estimated by using the following equations :

Ibhc : I bh '~b#b (31)

Idhc = ldh2d~a (32)

I = Ibhc +Idhc (33)

where Ibh and Iah are estimated using eqns (1) (9).

2.2. Statistical methods used There are numerous statistical methods available in the solar energy literature which deal

with the assessment and comparison of solar radiation estimation models [22, 23]. In the present study statistical indicators namely, normalized root mean square error (NRMSE) and mean percentage error (MPE) are calculated. They are defined as :

( l / n ) ( C i I M i ) 2

N R M S E = × 100 (34) n

(1 In) ~ M, i--I

(Ci--Mi)l X MPE = (l/n) ~=1 ~ M~ J 100 (35/

where Ci and M/are the calculated and measured values of solar radiation respectively, and n is the total number of observations.

The N R M S E provides information on the short-term performance of a model by allowing a term by term comparison of the actual difference between the estimated value and the measured value. This is a true indicator of the magnitude of the error. The MPE provides information on the size of the discrepancy in the measurements. The sign of the error indicates whether the calculated value is higher or lower than the measured value.

2.3. Calculation procedure The exponential curve as described by eqn (1) was fitted to the measured solar radiation

data [3] of six cities, namely, New Delhi, Mumbai (Bombay), Calcutta, Chennai (Madras), Jodhpur and Nagpur from different regions of India, (Fig. 1) and a set of the constants was obtained by the authors [1]. To increase the data-base, four additional cities, namely, Goa, Ahmedabad, Bhavnagar and Port Blair are considered, and the set of constants


obtained for India is slightly modified and given in Table 1. The geographical data of these cities is given in Table 2.

Thereupon, the monthly-mean of the hourly values of each of the beam- and diffuse- radiation are calculated for January to December, separately, using eqns (1)-(9) and a set of constants obtained (Table 1) for the ten cities. It is found from the comparative data analysis that rainfall in different cities is mainly affecting the difference between calculated and measured values. Hence, India is broadly divided into four regions of rainfall (Fig. 1) and empirical relations, eqns (10)-(33), are developed, as explained earlier.

Thereafter, the monthly-mean of the hourly values of each of the beam- and diffuse- radiation are calculated for January to December, separately, using eqns (1)-(9) and a set of constants obtained (Table 1) for four randomly selected Indian cities from different regions Pune, Thi ruvanathapuram (Trivendrum), Shilong and Vishakhapatnam (Fig. 1), with and without considering empirical eqns (10)-(33) for the correction of region of rainfall. These values are compared with the corresponding measured [3] values of the concerned cities. The yearly average of the N R M S E eqn (34) and the MPE eqn (35) obtained for radiation calculated for Pune, Thiruvanathapuram, Shilong and Vishakhapatnam using constants obtained for India with and without considering empirical relations, (10)-(33), as correction factor for rainfall region are given in Tables 3 and 4 respectively.

The locations are selected for evaluation of constants and prediction in such a way that they are fairly distributed over the whole of India, and for which measured data is available. During this study the whole data of monthly-mean-hourly insolation values-~zalculated by Indian constants with and without considering rainfall and time correction and that of measured values- - for direct, diffuse and global radiation for the 14 cities from January to December is processed.

Table 2. Geographical data of the 14 Indian locations of the study

Height Mean above mean annual total

Latitude Longitude sea level rainfall S.N. City (deg.) (deg.) (m) (mm)

1 Ahmedabad 23.07 N 72.63 E 55 741.9 2 Bhavnagar 21.75 N 72.18 E 5 661.5 3 Calcutta 22.65 N 88.45 E 6 1800.0 4 Chennai 13.00 N 80.18 E 16 1268.0 5 Goa 15.48 N 73.82 E 55 2559.1 6 Jodhpur 26.30 N 73.02 E 224 360.9 7 Mumbai 19.12 N 72.85 E 14 808.7 8 Nagpur 21.10 N 79.50 E 310 1150.7 9 New Delhi 28.58 N 77.20 E 216 561.1

10 Pune 18.53 N 73.85 E 559 672.8 11 Port Blair 11.67 N 92.72 E 79 3132.6 12 Shilong 25.57 N 91.88 E 1600 2149.9 13 Thiruvananthapuram 08.48 N 76.95 E 64 1696.5 14 Vishakhapatnam 17.72 N 83.23 E 3 962.4


Table 3. Yearly average normalised root mean square error (NRMSE) for Pune, Thiruvanan- thapuram, Shilong, and Vishakhapatnam

Beam radiation Diffuse radiation Global radiation (%) (%) (%)

LAT 1" 2t 1" 2t 1" 2t

09.0 15.29 12.79 22.22 17.62 09.48 07.12 10.0 20.00 12.69 19.30 14.19 12.32 06.74 11.0 23.40 13.79 24.14 13.30 16.81 07.09 12.0 24.68 13.74 28.09 12.23 19.13 06.61 13.0 25.76 13.04 25.82 10.79 19.65 06.65 14.0 24.94 14.62 21.92 09.49 17.98 07.44 15.0 23.60 16.88 16.23 09.11 14.55 08.73 16.0 28.64 21.36 19.89 11.36 18.09 10.50 Average 23.29 14.86 22.20 12.25 16.00 07.61

* 1-Calculated by only using constants obtained for India without considering the effect of rain ; t 2-Calculated by using constants obtained for India considering the effect of rain.

Table 4. Yearly average mean percentage error (MPE) for Pune, Thiruvananthapuram, Shilong, and Vishakhapatnam

Beam radiation Diffuse radiation Global radiation (%) (%) (%)

LAT 1" 2t 1" 2 t 1" 2t

09.0 0.74 --4.75 18.43 16.46 3.41 2.27 10.0 --4.77 --6.08 --3.88 11.99 --9.05 -0 .94 11.0 --4.23 -- 1.65 -- 14.73 9.20 -- 13.65 0.04 12.0 -- 4.32 1.74 -- 19.92 7.52 -- 15.71 1.12 13.0 --2.99 3.52 --20.11 6.84 - 15.16 2.35 14.0 0.19 6.88 - 16.74 5.59 - 11.34 4.21 15.0 8.01 9.70 -- 7.13 5.20 -- 2.68 6.09 16.0 25.53 12.52 13.77 5.90 15.46 7.46 Average 2.27 2.73 -- 6.29 8.59 - 6.09 2.84

* 1-Calculated by only using constants obtained for India without considering the effect of rain ; t 2-Calculated by using constants obtained for India considering the effect of rain.

3. RESULTS AND DISCUSSION

The result show (Table 3) that the yearly average N R M S E values for beam,, diffuse and global hour ly solar rad ia t ion wi thou t consider ing cor rec t ion factor for rainfall are 23.29,

22.20 and 16.00% respectively, whereas the cor responding values are 14.86, 12.25 and


7.61% respectively when correction factor for rainfall is considered. It is, therefore, obvious that by considering the effect of rainfall NRMSE is reduced. Similarly, Table 4 shows that individual values of MPE, when the effect of rainfall is considered, are reduced as compared to that with the values when the rainfall effect is not considered.

Sets of constants obtained (Table 1) are applicable to all Indian locations in general and are available for different days of the year to calculate the solar radiation. The radiation, so calculated [1], does not consider the effect of rainfall and gives better results during October to April when the sky is clear at most places in India. During May to September, Bay of Bengal Monsoons and Arabian Sea Monsoons cause rainfall in most parts of India. Estimated solar radiation was found to be more than the measured one at the locations of heavy rainfall, and lower than the measured one at the locations of low rainfall, causing an increase in error during May to September. When the effect of rainfall is considered, the error between the estimated and measured values of solar radiation decreases during the rainy months, normally May to September. This leads to an improvement in the overall prediction accuracy.

To make a better comparison the variation of the N RMS E and the MPE of (a) beam, (b) diffuse and (c) global hourly solar radiation for the four cities over the year are shown in Figs 3 and 4 respectively. Figure 3 clearly shows that there is a considerable reduction in NRMSE values of all the three monthly-mean-hourly beam-, diffuse- and global solar radiation on horizontal surfaces when rainfall correction is considered. Figure 4 shows that the variation in MPE is reduced and values are closer to the zero error when rainfall correction is considered as compared to that without considering this factor. There is some variation in NR MSE and MPE values as is seen from the Figs 3 and 4, because here we are considering only total annual average rainfall, albeit the amount of rainfall that varies in day number during the monsoon period. This variation is due to the geographical location of the place such as coastal regions, hilly regions, altitude of the location etc. However, by considering the total annual average rainfall, the N RMS E and MPE are reduced considerably as explained earlier.

Detailed comparative study of the estimation procedure has been reported elsewhere [24].

4. CONCLUSIONS

With the input parameters, the longitude and latitude of the location, the month of the year and the region of rainfall of the location, monthly-mean-hourly beam, diffuse and global radiation on horizontal surfaces can be estimated. The yearly average normalized root mean square error for four randomly selected Indian cities was found to be reduced to 14.86, 12.25 and 7.61% for monthly-mean-hourly beam, diffuse and global radiation respectively, by considering the effect of rainfall, as against the corresponding values of 23.29, 22.2 and 16% without considering the correction factor for rainfall. The improvement in the prediction methodology would lead to a better tool in the hands of general engineers, architects and solar system designers.

The results of this study can be used to estimate solar radiation for any location in India, as the places selected for evaluation of constants and prediction thereof are fairly distributed over the whole of India.

516 G. V. PARISHWAD et al. 50'j --.,-- without considering rainfall I with considering rainfall

40

(a)

rar]

30

10 . . . . . . . . . . . . . . . . . . . . . . . .

O ~ 0 2 4 6 8 10 12

Month of the Year

4 0 • w i thou t cons ide r ing rainfall (b) 35 .... ! .with, c ° n s i d e r i n g r a i n f a ! l . . . . . . . .

30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~ 20 ......

o ..................... , ............... i . . . . . . i . . . . .

0 2 4 6 8 10 12

Month of the Year


30 I • without considering rainfall (C) l, with considering rainfall " •

25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~ 20 . . . . . . . . . . . . . . . . . . . . . . .

~ 1 5 i . E 1 . . . . . . . . . . . . . . . . . . . . . . . . _ "

0 2 4 6 8 l0 12

Month of the Year Fig. 3. Variation of normalised root mean square error (NRMSE) for (a) beam, (b) diffuse and (c) global solar radiation for Pune, Thiruvananthapuram, Shilong, and Vishakhapatnam over the year.

50

40

~ so g ~ 2o

0

-10

G. V. PARISHWAD et al.

----- w!thout considering rainfall (a'l I

-20 0

20 - without considering rainfall (b)

' /

10

o

-10

-20

-30

60

2 4 6 8 10 12

Month of the Year

518

0 I I 1 | [

2 .4 6 8 10 12

Month of the Y e a r


20 [. , without considering rainfal; with considering rainfall

15 . . . . . (c)

101-

5k

o

-10

-15 I-

-20 0 2 4 6 8 10 12

Month of the Year Fig. 4. Variation of mean percentage error (MPE) for (a) beam, (b) diffuse and (c) global solar

radiation for Pune, Thiruvananthapuram, Shilong, and Vishakhapatnarn over the year.


Acknowledgements--One of the authors, G. V. Parishwad, is grateful to the Department of Education, Ministry of Human Resource Development, and Mechanical Engineering Department, Motilal Nehru Regional Engineering College, Allahabad, for providing facili- ties for conducting research towards a doctoral degree under the Quality Improvement Programme.

REFERENCES

1. Parishwad, G. V., Bhardwaj, R. K. and Nema, V. K., Estimation of hourly solar radiation for India. International Journal on Renewable Energy, UK, 1997, 12(3), 303.

2. Gopinathan, K. K., Estimation of hourly global and diffuse solar radiation from hourly sunshine duration. Solar Energy, 1992, 48(1), 3.

3. Mani, A., Handbook of Solar Radiation Data for India. Allied Publishers, New Delhi, India, 1980.

4. Threkeld, J. L. and Jordan, R. C., Direct solar radiation available on clear days. ASHRAE Trans., 1958, 64, 45.

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Effect of rainfall on the estimation of monthly mean hourly solar radiation for India