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
7/27/2019 Prediccin de la radiacin solar global de horas de sol brillante y otros datos meteorolgicos
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
7/27/2019 Prediccin de la radiacin solar global de horas de sol brillante y otros datos meteorolgicos
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
7/27/2019 Prediccin de la radiacin solar global de horas de sol brillante y otros datos meteorolgicos
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
7/27/2019 Prediccin de la radiacin solar global de horas de sol brillante y otros datos meteorolgicos
5/9
116 GARG and GARG: PREDICTION OF GLOBAL SOLAR RADIATION
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
7/27/2019 Prediccin de la radiacin solar global de horas de sol brillante y otros datos meteorolgicos
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
7/27/2019 Prediccin de la radiacin solar global de horas de sol brillante y otros datos meteorolgicos
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
7/27/2019 Prediccin de la radiacin solar global de horas de sol brillante y otros datos meteorolgicos
8/9
118 GARG and GARG: PREDICTION OF GLOBAL SOLAR RADIATION
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).
7/27/2019 Prediccin de la radiacin solar global de horas de sol brillante y otros datos meteorolgicos
9/9
6. Handbook of Solar Radiation Data for India, 1980(Compiled by Anna Mani). Allied Publishers Pvt,
New Delhi (1981).
Top Related