predicción de la radiación solar global de horas de sol brillante y otros datos meteorológicos

7/27/2019 Prediccin de la radiacin solar global de horas de sol brillante y otros datos meteorolgicos

1/9

Energy Convers. MgmtVol. 23, No. 2, pp. 113-118, 1983 0196-8904/83 $3.00 + 0.00Printed in Great Britain. All rights reserved Copyright 1983 Pergamon Press Ltd

113

PREDICTION OF GLOBAL SOLAR RADIATION FROM

BRIGHT SUNSHINE HOURS AND OTHER

METEOROLOGICAL DATAH. P. GARG and S. N. GARG

Centre of Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi 110 016, India

(Received24April1982)

AbstractThree existing empirical relations which predict global radiation from bright sunshine hoursand meteorological parameters, were tried for 14 Indian stations where all relevant data was available. Alarge amount of error ( 50%') was found. So a new empirical relation was established between globalradiation and meteorological parameters. The new relation predicted the insolation within a 10% errorlimit in most cases. Global radiation dependence on ambient temperature and relative humidity wasintroduced through atmosperic water content per unit volume. The relation is

WAT = RH (4.7923 + 0.3647 x T + 0.0055 x T2 + 0.0003 x T3) G =

Gex, (0.414 + 0.400 x SS0.0055 x WAT)

SSS =

Global radiation Bright sunshine hours Relative humidity Ambient temperature Solarradiation prediction

NOMENCLATURE

G = daily global radiation on a horizontal surfaceL = latitude of the place

S= measured bright sunshine hours

Z= maximum possible bright sunshine hours T,,,maximum temperature of the day CC)

RH = monthly mean relative humidity= sun declination

n =No. of day of the yearG, x, extraterrestrial daily global radiation on a

horizontal surfaceG, = daily global solar radiation on a horizontal

surface observed on earthW, = sunrise hour angle

WAT = atmospheric water content per unit volumenear the earth surface (kg/m3)

SS = fraction of maximum possible bright sunshinehours

1. INTRODUCTION

In a given region, solar energy conversion devices

should be installed only in those places where one gets

sufficient insolation. This necessitates knowledge of

the distribution of insolation over the region. The best

way of knowing it is to install pyranometers at

many loca tions in the given region and look after

their day-to-day maintenance and recording, which

is a very costly exercise. The alternative approach is

to correlate insolation with the meteorological par-

ameters such as sunshine hours, relative humidity,ambient temperature, etc. Daily recordings of these

parameters are available from a lot of stations cov-

ering many years. So, for a few stations, if global

radiation as well as meteorological parameters are

available, and if such a correlation is established, then

one can know global radiation for those stations

where only meteorological parameters are available,

provided these stations also have similar atmospheric

conditions. A basic point, helpful in this correlation

study is that, outside the atmosphere, global radi-ation

on a horizontal surface can be determined very

precisely. Radiation reaching a station depends upon

the atmospheric conditions of that station. The most

important atmospheric condition is the water content

in the atmosphere. From relative humidity and ambi-

ent temperature, water content per unit volume near

the station can be determined. Water content is

important because it highly absorbs solar radiation in

the infrared region. The other meteorological par-

ameter is sunshine hours, which is used as a fraction

of the maximum possible bright sunshine hours.Different authors [1-3] have tried to establish this

correlation. Angstrom [4] has tried to establish a

linear relationship between global radiation and

bright sunshine hours. Page [5] includes extra -

terrestrial radiation also in the computation of global

radiation. In the present study, we have tried to

predict insolation using three commonly used formu -

las, Sayigh formula [1], Reddy's formula [2] and

Swartman's formula [3], and found that, in each case,

there was a large amount of error. Hence, a new

empirical relation was developed which predicted the

global radiation within a 10% error limit in most ofthe cases.

Radiation data, as well as meteorological data, for

14 stations was available from the book compiled by

Mani [6]. The data conforms to the international


2/9

114 GARG and GARG: PREDICTION OF GLOBAL SOLAR RADIATION

L is in degrees. (6)1 +0.1L

G

where(1)

( 3 )

( 4)

Z= -2

cos-I

[ - tan L tan S] 15

= 23.45 sin [(284 + n)36013 6 5 j

i = 1, 2

= 1,2,3 . .. 12

no. of rainy days in a month(10)

total no. of days in the month

where

Table 1. Indian stations used in this study, with daily records of meteorological parameters

StationLatitude (N)

(deg)Longitude (E)

(deg)Global

radiation

Period of recordSunshine Ambienthours temperature

Relativehumidity

New Delhi 28.63 77.20 1957-78 1954-63 1958-67 1958-67Jodhpur 26.30 73.02 1960-78 1954-63 1958-66 1958-65Ahmedabad 23.07 72.63 1962-78 1954-63 1958-67 1958-67

Calcutta 22.65 88.45 1957-78 1954-63 1958-67 1958-67Bhavnagar 21.75 72.18 1967-78 1954-63 1976-78 1976-78

Nagpur 21.10 79.50 1960-78 1954-63 1958-67 1958-67Bombay 19.12 72.85 1969-78 1954-63 1958-67 1958-67Poona 18.53 73.85 1957-78 1954-63 1958-67 1958-67Vizagapatanam 17.72 83.23 1961-78 1962-67 1958-67 1958-67Goa 15.48 73.82 1963-78 1954-67 1964-67 1958-66Madras 13.00 80.18 1957-78 1954-63 1958-69 1958-67Bangalore 12.97 77.58 1978-80 1977-80 1977-80 1977-80Kodai Kanal 10.23 77.47 1962-78 1954-63 1958-67 1958-67

Trivandrum 8.48 76.95 1959-78 1954-63 1958-67 1958-67

meteorological standards as specified by WMO.Table 1 shows the list of stations as well as periods

of data used. Although data periods for different

meteorological parameters, including global radi-

ation parameter, do not coincide, these periods are so

long that one can use them with sufficient accuracy.

Computer programmes were drawn at various stages

of the present study.

2. PREDICTIONS BY THE EXISTINGEMPIRICAL RELATIONS

2.1. Sayigh's formula

Ths formula takes into consideration parameters

like latitude, mean sun declination for the month, and

maximum possible bright sunshine hours in addition

to the main meteorological parameters like measured

bright sunshine hours , relative humidity and max -

imum temperature for the mean day of the month.

The entire range of relative humidity (RH) is divided

into three subranges, viz. RH 65%, RH 70% and 65%

< RH < 70%, and corresponding to each sub-range, a

graph has been drawn between humidity factor, and

12 months of the year. One has to know the annual

mean daily relative humidity for a given station, and

depending upon this annual mean value, one chooses

a particular graph out of the three graphs and

determines the values of ti / for different months of

the year. The complete formula is

K = 100(A Z +111 iicos L) (5)

( 0 . 2 )

In tfrg, i corresponds to the subrange of relative

humidity, and j corresponds to the number of the

month of the year.

Using all these equations, global radiation has been

computed for 14 Indian stations, and the results are

shown only for one station (chosen randomly),

Poona, in Fig. 1. From Fig. 1, it is clear that this

empirical relation does not fit at all during the rainymonths of July and August. During these months, the

error is as high as + 40%. The formula over- estimates

the radiation during rainy months. During the clear

months of December, January and February, this

relation under-estimates the insolation, the error be-

ing as low as -28.2% (December). A similar trend is

also seen in the other 13 stations. The maximum

under-estimation is -52.8% (Kodai Kanal, Decem-

ber ), and the maximum over- estimation is + 60.7%

(Bangalore, July).

2.2. Reddy's formula

This formula does not consider maximum ambient

temperature, rather it considers the number of rainy

days in a month. The

formula is

K(1 + 0.81)(1 - 0.2t)

N/RH

G = NKexP [L s - RH 15 - T1.

N = 1.7 - 0.458 L, L is in radians (2)

K = 100(AZ + O,/ cos L)

0.2

- 1 + O. I L whereL is in degrees


3/9

GARG and GARG: PREDICTION OF GLOBAL SOLAR RADIATION 115

-

E2 8

-a I6

Measu red

2 (S J Reddy)0-

(A A .M Sayigh)

( R.K. Swartman)

re c e

E

o

F = 1.95 x 60.0

x [1 + 0.033 cos

W = cos' tan L tan

(360 x n)1

O , 2 3 / 2

o j 1 : 1 1 1 1 1 1 1

J F M A M J J A S O N D

Months

Fig. 1. Monthly variation of daily average global radiationfor Poona.

trend is observed for other stations also, except for

the two stations, Kodai Kanal and Trivandrum. For

these stations, the formula always under-estimates

the insolation but the common feature is still there,

i.e. under-estimation is high during rainy months and

low during clear months. Partly, it is due to the fact

that Kodai Kanal is a high altitude station. For allthe 14 stations, the maximum over-estimation is

+53.1.0 (New Delhi, December), and the maximum

under-estimation is (Kodai Kanal, June).

3. PRESENT METHODOLOGY

From geometrical considerations, one can deter-

mine the extraterrestrial daily global radiation on a

horizontal surface for a given latitude. The equations

used are

24.0 xFGext= _____ x (cos L cos sin W,

Two values ofi designate whether the station consid-

ered is an inland station or coastal station, and values

of O,/ can be read from the tables for the particular

station. Figure 1 shows the comparison of the pre-

dicted insolation by this formula with the measured

values for Poona. Figure 1 shows that this formula is

good fitting during the rainy months of July and A

ugust. During the clear months of January to April,

the formula over-estimates the radiation, and this

over-estimation is as high as +35% (April). During

rainy months, the over-estimation is as low as +4.0%

(July). The graph shows that this relation over-estimates the radiation during all months of the year.

The same trend is observed for other stations also.

2.3. Swartman's ,formula

This formula predicts global radiation on a hori-

zontal surface from bright sunshine hours and rela-

tive humidity only. Swartman and others have evolved

two empirical equations which are as follows

SG, = 490.0 ( ) 0.357 (RH)-

0262(11)

12

S

G, = 460.0 exp [0.607 (-12RH)]. (12)

Instead of using the sunshine hours parameter as a

fraction of maximum possible bright sunshine hours,

the author uses sunshine hours here as a fraction of 12

only, i.e. mean possible bright sunshine hours, which

is a simplification. For the same values of Sand RH,

both these equations give approximately the same

value ofG. Again, we have tried these two equations

for 14 stations, and results are compared in Fig. 1, for

Poona only. The figure shows that these equations

over-estimate the insolation during clear months andunder-estimate it during rainy months. For Poona, the

maximum under-estimation is 18.53% (July), and

the maximum over-estimation is +30.1`, in the month

of December. A similar type of

+ W, sinL sin )

( W, is in radians) (13)

(14)

(15)

The factor,F, takes into account the variation of earth

sun center-to-center distante from day-to-day. This

formula gives the extraterrestrial radiation in Cal/cm'

day, which can be converted to MJ/m2 day by

multiplying with a factor 0.04183.

On the earth surface, measured values of global

radiation on a horizontal surface are available, and

so by dividing this measured value by G, one

determines the transmission of the atmosphere for

global radiation (in contrast to the direct radiation).

For a given location, hourly values of ambient tem-

perature and relative humidity are known. From

relative humidity and ambient temperature, one can

determine the atmospheric water content per unit

volume. From Fig. 2, at any ambient temperature,

the saturated water amount is known, and as relative

humidity is the ratio of actual water content to thesaturated water content at a given temperature, ac-

tual water content per unit volume is determined.

The analytical way of determining this quantity is

by using the following equation

WAT = RH(4.7923 + 0.3647 x T


4/9

+ 0.0055 x T2 + 0.0003 x T3). (16)

This expression has been determined from Fig. 2

using a least square method. Instead of making

atmospheric transmission (Gob/Ge,) dependent

upon two quantities, relative humidity and ambient

tem-perature, we have made it dependent upon one


5/9


4 8

42

E 36

30

I8

12

Measured

Predicted(present study)

1 1 1 1 1 1 1 1 1 1 1 1J F M A M J J A S O N D

Months

3245)

E

E

2

o2 12

o

o

4

0

1 6

Fig. 4. Monthly variation of daily global radiation forFig. 3. Variation of Gob/Gc, with surface water amount. Poona (calculated from the proposed method).

0 ss=a8oao50 8 o

0 Bp 00o O o

oc'

I 1 1 1 1 1 1 1

0 4 8 1 2 1 6 2 0 2 4 2 8 3 2 3 6 4 0T e m p e r a t u r e ( 0 C )

Fig. 2. Variation of saturated water amount withambient temperature for air.

16 x 10-3 kg/M3 to 22 x 10-3 kg/M3, and trans-mission

vares from 0.45 to 0.35. The scattering of these

points does not show clearly whether the de-pendence

of Gob/Ge, upon water content and fraction of

sunshine hours is linear, exponential or of any other

type. For simplicity, we have assumed linear

dependence. Using a least square technique, thefollowing equation was obtained.

G = Ge,[0.414 + 0.400 x SS 0.0055 x WAT].

(17)

Using this equation, global radiation has been com-

puted for each month for each of the 14 stations, and the

values have been compared with measured values as

shown in Table 2.

4. DISCUSSION OF RESULTS

quantity, water content. It has many advantageous

points, like firstly it is easier to deal with a few

number of variables, and secondly, from morning

until evening, the relative humidity goes on de-

creasing, and ambient temperature goes on increasing

for a clear day, the water content per unit volume

changes very slowly during this period. For each

station, we have calculated hourly values of water

content from 9 a.m. to 5 p.m. and taken the average of

these. These calculations show that, even if one tries

to know water content at 12.00 (L.A.T.), one gets

nearly the same value as the average one. The time

period 9 a.m. to 5 p.m. has been chosen because most

of the radiation is received during this period.Figure 3 shows the variation of Gob/Gex, with water

content. The fraction of maximum possible sunshine

hours, SS, runs as a parameter. Figure 3 shows that, for

low values of SS, water content vares from

0.8

0.7

0.6

0.5

04

C.5

0.3

02

0.1

1

11 1 1 1 i

0 4 8 12 16 20 24 28

Surface water amount (kg /m3) x10-3


6/9

Table 2 shows the observed insolation, predicted

insolation and the corresponding error for all the

stations. It is seen that, in most of the predictions, the

error remains within a 10% limit. Out of a total of

14 x 12 predictions, only 12 predictions have gone

beyond this limit. The maximum over-estimation is +

12.6%, and the maximum under-estimation is 19.6%. So, as far as over-estimation is concerned, it is

also very close to the + 10% limit. In the case of

Poona, just for comparison purposes with other

formulas, results are shown graphically also in Fig. 4.

Figure 4 shows that, during rainy months, the formula

under-estimates the insolation, but during the clear

months, the formula may under-estimate as well as

over-estimate the insolation. The maximum over-

estimation for Poona is 2.8% (May), and the max-

imum under-estimation is 6.4% (October). After

scanning through Table 2, one sees that the trend of

under-estimation during rainy months is observed in

the present study also, but this under-estimation is not

so high as in other studies. Errors


7/9

"rabie 2. Comparison of predicted global radiation with observed values for fourteen Indian stations (M.11m 2day)

StationsMonths

Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

Obs. 14.36 18.01 22.11 24.98 26.25 23.57 19.21 18.20 20.18 19.28 16.29 13.84New Delhi Pred. 14.62 18.59 20.55 23.54 28.33 20.46 18.99 17.79 18.29 18.46 16.39 14.07

"o cr. 1.8 3.1 -7.0 -6.3 7.9 -13.1 -1.1 -2.2 -9.3 -4.3 0.5 1.6Obs. 17.00 20.04 23.59 26.05 27.18 25.46 21.54 18.97 21.98 20.99 17.66 15.96

odhpur Pred. 16.94 20.27 22.19 25.63 31.44 24.42 20.22 18.91 19.37 20.14 17.87 16.08% er. -0.2 1.1 -5.9 -1.6 15.6 -4.0 -6.1 -0.2 -11.8 -4.0 1.1 0.7

Obs. 17.64 20.84 24.26 26.42 27.41 23.01 17.45 16.28 19.97 20.79 18.01 16.53Ahmedabad Pred. 18.42 21.62 23.10 25.39 30.08 22.86 16.95 16.63 17.52 20.29 18.65 17.34

er. 4.4 3.7 -4.7 -3.8 9.7 -0.6 -2.8 2.1 -12.2 -2.3 3.5 4.8Calcutta Obs. 15.21 18.12 20.87 22.77 23.50 17.89 16.72 16.08 16.12 16.41 15.76 14.76

Pred. 16.21 19.14 20.70 21.93 23.87 16.26 15.96 15.39 15.08 16.10 17.13 15.69"o cr. 6.5 5.6 -0.8 -3.6 1.5 -9.0 -4.5 -4.2 -6.4 -1.9 8.6 6.3

Bhavnagar Obs. 18.52 21.47 24.73 26.17 27.38 21.73 16.64 15.51 19.67 21.27 18.80 17.23Pred. 18.91 21.82 23.97 25.44 29.35 20.00 15.59 15.34 18.73 20.52 17.77 17.49

" er. 2.0 1.6 -3.1 -2.8 7.2 -7.9 -6.3 -1.0 -4.8 -3.5 -5.4 1.4Obs. 17.70 20.44 22.73 24.43 24.90 20.32 15.79 14.86 18.42 20.22 18.48 16.80

Nagpur Pred. 18.57 21.88 23.28 25.04 28.04 21.35 15.96 16.33 16.64 19.39 18.78 17.71er. 4.8 7.0 2.4 2.4 12.6 5.0 1.0 9.8 -9.6 -4.0 1.6 5.3

Obs. 18.19 20.73 23.23 25.18 26.16 18.65 14.63 14. 32 17.57 19.60 18.27 17.27Bombay Pred. 19.10 21.56 22.90 23.66 25.36 18.30 14.33 13.97 16.69 19.22 18.66 17.74

er. 4.9 3.9 -1.3 -6.0 -3.0 -1.8 -2.0 -2.4 -5.0 -1.9 2.0 2.7Obs. 19.10 22.23 24.54 25.80 26.30 21.20 16.30 16.50 19.10 20.40 18.90 17.80

Poona Pred. 19.40 22.50 24.20 25.20 27.00 20.00 15.80 16.00 17.90 19.10 18.60 18.10'',, er. 1.4 1.2 -1.2 -2.0 2.8 -5.8 -3.5 -2.9 -6.3 -6.4 -1.5 2.1

Obs. 19.35 21.91 23.44 23.99 24.05 18.64 16.81 17.82 18.60 19.03 18.60 18.25Vizagapatnam Pred. 19.01 21.93 22.67 22.78 24.72 17.51 16.91 18.08 18.01 19.07 18.59 17.94

" er. -1.7 0.0 -3.2 -4.7 2.8 -6.0 0.5 1.4 -3.1 0.2 0.0 -1.6Obs. 20.48 22.97 24.34 24.95 24.26 17.24 14.38 17.14 19.11 20.22 20.22 19.41

Goa Pred. 19.54 22.00 22.88 23.70 24.26 16.97 14.44 16.36 17.85 19.56 19.29 18.03"o er. -4.6 -4.2 -5.9 -5.0 0.0 -1.5 0.4 -4.5 -6.5 -3.2 -4.6 -7.1Obs. 18.85 22.66 24.81 24.93 23.53 20.98 19.46 20.09 20.57 17.46 15.64 15.39

Madras Pred. 18.78 22.13 23.07 23.19 23.28 19.5117.38 18.33

19.37 17.77 16.65 16.80% er. -0.3 -2.3 -6.9 -6.9 -1.0 -6.9 -10.6 -8.7 -5.8 1.7 6.4 9.1Obs. 21.78 21.00 24.28 23.75 22.93 22.05 15.73 15.94 16.99 18.81 16.17 16.07

Bangalore Pred. 21.85 22.30 24.83 24.35 23.18 18.03 16.33 17.63 17.27 19.58 16.48 16.81er. 0.3 6.1 2.2 2.5 1.0 - 18.2 3.8 10.5 1.6 4.0 1.9 4.6

Obs. 22.61 24.16 24.75 23.16 21.04 19.01 16.36 16.92 17.31 15.99 17.08 18.81Kodai Kanal Pred. 19.6 22.05 22.91 21.97 20.04 17.12 16.36 17.43 17.30 16.64 16.40 17.83

er. -13.2 -8.7 -7.4 -5.1 -4.7 -9.9 0.0 3.0 0.0 4.0 -3.9 -5.1Obs. 21.36 22.90 24.07 22.21 19.78 18.91 18.11 20.02 21.40 18.85 17.79 18.48

Trivandrum Pred. 19.98 21.45 22.03 19.94 17.61 15.20 15.72 17.68 18.56 17.27 16.58 18.13

"/ er. -6.4 -6.3 -8.4 -10.2 -10.9 -19.6 -13.1 -11.7 - 13.2 -8.3 -6.8 - 1.8


8/9


are due to several factors. Altitude vares from sea-

level for Bombay, Madras, Calcutta etc. to 921 m

for Bangalore and 2400 m for Kodai Kanal. Atmos-

pheric turbidity also vares highly from station to

station. Jodhpur is a very clear station while

Calcutta has maximum turbidity due to its heavy

industrial-ization. Also, some stations are inlandstations while others are coastal stations.

Atmosphere, which atten-uates the solar radiation

reaching a station, is much different for these two

types of stations. Also on a particular day for

different stations, the zenith angle at solar noon is

different, and so radiation will travel different

depths of the atmosphere for different stations. Thus

the radiation will suffer different amounts of

attenuation. This fact also has not been taken into

consideration in order to make the formula as

useable as possible. If one takes into consideration

all these facts, errors can be further minimised.

5. CONCLUSIONS

From this study, the following conclusions can be

drawn:

1. The three methods discussed in this study are not

able to predict monthly mean global radiation for

these 14 Indian stations within the prescribed error

limits of 10%. The error goes beyond 50% limits

even in some cases.

2. The present study predicts global

radiation within +10% limits in most of the cases.

The max-

imum over-estimation is 12.6;'

,

', and the maximumunder-estimation is19.6%.

3. Dependence on relative humidity and

ambient

temperature can be better shown through water

content per unit volume on the earth surface. It is

more effective and easier to deal with, as it reduces

the number of parameters also.

REFERENCES

1. A. A. M. Sayigh,IVCourse on Solar Energy Conversion,Vol. II, p. 51. International Centre for TheoreticalPhysics, Trieste, Italy (1977).

2. S. J. Reddy, Solar Energy13, 289 (1971).3. R. K. Swartman and O. Ogunlade, Solar Energy 11,

170 (1967).4. A. K. Angstrom, Q. .11 R. met. Soc. 20, 121 (1924).5. J. K. Page, Proc. UN Conf. in New Sources of Energy,

Vol. 4, Paper 5/98, pp. 378-387 (1964).


9/9

6. Handbook of Solar Radiation Data for India, 1980(Compiled by Anna Mani). Allied Publishers Pvt,

New Delhi (1981).

predicción de la radiación solar global de horas de sol brillante y otros datos meteorológicos

Documents