estimating global , direct , diffuse and reflected solar

والتطبيقيةلعلوم الأساسية ا :مجلة الجامعة الأسمرية

م2017(، ديسمبر 2( العدد )2المجلد )

88

Estimating global , direct , diffuse and reflected solar radiation on horizontal

and tilted surfaces in Tripoli , Libya

Ali. S. Al-Nuaimi* Tarig Elmabrouk

Department of physics – Faculty of Science- Omar Al-Mukhtar university – Beida – Libya

E mail ; [email protected] , [email protected]

Keywords: Global radiation ,direct , diffuse radiation , horizontal , tilted surfaces ,Renewable Energy,

Tripoli , Libya

Introduction:

Solar energy occupies one of the most important types of renewable energy sources . It is the

energy provide by the sun .Solar radiation data are fundamental inputs for solar energy applications ,

such as photovoltaic , and solar thermal systems . The design of a solar energy conversion system

requires knowledge regarding the availability of global solar radiation and its component at the location

of interest (1). An accurate knowledge of the solar radiation data for a particular location is a pre

requisite , in estimating the thermal performance and economic efficiency of solar energy systems .The

availability of these data may be of the form of types of total , direct , diffuse , and reflected radiation .

These data may be needed on daily , monthly or yearly time scales . Each of these forms is important

and has particular usage in specific applications. In a recent report(2) Libya is the 16th largest country in

the world in terms of land mass according to OPEC.org. Its economy depends primarily on revenues

from the oil sector , which contribute about 95 percent of export earning .Libya has the potential to

become a renewable energy giant according to Responding to Climate Change .Libya is located on the

cancer orbit line and is exposed to the sun rays through the year with long hours during the day . It

boasts a very high daily solar radiation rate – on a flat coastal plain it is about 7.1 kilowatt hours per

square meter per day , and in the south region it is about 8.1 kWh/m2 /day. If we compare this amount

for instance with the Great Britain we see that Great Britain has half than this amount which is about

2.95 kWh/m2 /day . Libya could generate approximately five times the amount of energy from solar

power than it currently produces in crude oil . If this country which is estimated to be 88 per cent desert

used only 0.1% of its landmass to harness solar power , it could produce the equivalent to almost seven

million barrels of crude oil per day in energy . Renewable energy technology is still in its very early days

in Libya and a clear strategy and timetable is needed to take it forward .In particular , work needs to be

done to develop the skills and knowledge needed to install and maintain renewable energy systems .(3)

Many models have been developed to estimate the amount of global solar radiation on

horizontal surfaces using various climatic parameter, such as sunshine hours Many authors find it is

mailto:[email protected]

mailto:[email protected]



89

rather important to determine the beam ( direct ) , and diffuse components of total radiation incident

on a horizontal surface . Once these components are determined , they can be transported over tilted

surface, and hence , the short as well as the long term performances of tilted flat plate solar collectors ,

photovoltaic , modules and other solar devices can be estimated (4) . Many authors have presented

empirical correlations to estimate the monthly average daily diffuse radiation on a horizontal surface (

5, 6) El-Sebaii and Trabea (7) proposed correlations for estimating horizontal diffuse radiation in Egypt.

Total radiation consists of three components ; beam ( direct ) radiation , diffuse radiation , and ground (

reflected ) radiation . el- Sebaii etal (8) calculated global, direct and diffuse radiation on horizontal and

tilted surfaces in Jeddah , Saudi Arabia . al- Ayed et al (9) proposed empirical correlations for calculating

the monthly average of daily global , direct and diffuse solar radiation on horizontal surfaces in Riyadh

using the data of 1 year .Al-Nuaimi (10) estimated global solar radiation in north Libya . Bannani et al

(11) estimated monthly average solar radiation using data for 11 stations at different locations in Libya.

Al- Dabbas(12) analyzed the characteristics of the solar radiation climate of the daily global radiation

and diffuse radiation in Amman , Jordan .Ueyama (13) estimated hourly and diffuse solar radiation for

the compilation of solar radiation distribution maps in Japan . Gana and Akpootu (14) used an Angstrom

type empirical correlation for estimating global solar radiation in north – eastern Nigeria .Falayi et al

(15) used correlations to estimate monthly mean of daily diffuse solar radiation in some selected cities

in Nigeria . Al-rawahi et al (16) predicted hourly solar radiation on horizontal and inclined surfaces

forMuscat / Oman .Abbasi and Qureshi (17) estimated global , and diffuse solar radiation for

Nawabshah , Sindh , Pakistan using measured data of bright sunshine hours for twenty two years .Bindi

et al (18) used different methods for separating diffuse and direct components of solar radiation and

their application in crop growth models in Italy .

The main objective of this paper is to estimate the various component of solar radiation in

some selected Libyan cities .

Materials and Method :

Data of the sunshine duration hours for Tripoli was e obtained from the national Meteorological

organization in Libya .These data were used to estimate the direct , diffuse and reflected solar radiation

. A model was used to calculate these parameters. A computer programme in Matlab was developed .

The deviation between the estimated and satellite values was determined using the statistical

parameters as given by Nguyen et al [18] as follows :

Mean Bias error (MBE):



90

N

HHMBE Sm

N

i

)(

1

(7)

Root Mean square Error (RMSE):

N

HH

RMSESm

N

i

2

1

)(

(8)

The mean percentage error id calculated using the following formula

100]

)(

[

N

HHH

MPE mcalm

To calculate the various solar parameters.

The model :

In this study the estimation of the monthly average daily global solar radiation on a horizontal surface

is based on a modified version of the original Angstrom – type equation . This equation is a regression

equation that relates monthly average daily solar radiation to clear sky radiation at a location and

average fraction of possible sunshine hours [19], but Page [20] and Duffie and Beckman [21] have made

some modifications on the equation to base it on extraterrestrial radiation on horizontal surface rather

than on clear sky radiation as follows :

)(00 S

Sba

H

H (1)

Where H is the monthly average daily global radiation 0H is the monthly average daily

extraterrestrial radiation , S is the monthly average daily hours of bright sunshine (in hours), 0S is the

monthly average day length (in hours ) , and (a) and (b) are regression empirical coefficients obtained

from the relationship given by Tiwari and Suneja [22] as follows :

)(323.0cos235.0110.00S

Sa



91

)(694.0cos553.0449.10S

Sb (2)

The monthly average daily extraterrestrial radiation on a horizontal surface ( 0H ) can be computed

from the equation given by Duffie and Beckman [21] as follows:

]sinsin180

sincos][cos365

360cos033.01[

240

sssc

nIH (3)

Where scI is the solar constant (= 1367 Wm-2), is the latitude of the city or location , is the solar

declination angle , s is the mean sunrise hour angle for the given month , and n is the number of day

of the year starting from the first of January . The solar declination angle ( ) , and the mean sunrise

hour angle ( s ) can be calculated respectively , as given by Duffie and Beckman [21] as follows:

365

)284(360sin[45.23

n (4)

)tantan(cos 1

s (5)

For a given month , the maximum possible sunshine duration (monthly average day length 0S ) cab be

computed by using the following equation as given by Duffie and Beckman[21] :

sS 15

2)tantan(cos

15

2 1

0 (6)

The monthly average of daily global solar radiation incident on a horizontal surface H is

calculated as follows

)]([0

0S

SbaHH (7)

The clearness index (KT) is defined as the ratio of the measured horizontal terrestrial solar

radiation to the calculated horizontal extraterrestrial solar radiation is calculated from the

following relation



92

0H

HKT (8)

The monthly mean daily diffuse fraction of solar radiation is calculated by the following

equation

T

d KH

H13.100.1

The beam ( direct ) bH solar radiation is calculated from the following relation

db HHH (9)

To calculate the monthly average daily total solar radiation incident on a tilted surface with an

angle facing toward equator , the following steps were followed

1- To calculate the direct ( beam ) incident solar radiation on a tilted surface

bbtb RHH (10)

Where tbH is the total beam solar radiation incident on a tilted surface , and bH is the beam

solar radiation incident on a horizontal surface and bR is the tilt factor which is the ratio of

flux incident on a tilted surface and the flux incident on a horizontal surface and is given by the

following relation

h

bR

cos

cos (11)

Where is the angle of incidence of solar radiation on a tilted surface , and h is the angle of

incidence of solar radiation on a horizontal surface

s

s

h

bR

coscoscossinsin

)cos(coscos)sin(sin

cos

cos

(12)



93

2- To calculate the diffuse solar radiation incident on a tilted surface tdH , the following

relation is used

(13)

Where dR is the tilt factor for diffuse radiation , and is given by

2

cos1 dR (14)

Where is the angle of inclination of the solar collector

3- To calculate the reflected solar radiation from the earth’s surface on the tilted surface of the

solar collector , the following relation is used

rdbtr RHHH )( (15)

Where rR is the tilt factor for reflected solar radiation from the earth , and is calculated from

the following relation

)2

cos1(

rR (16)

Where is the coefficient of reflectivity of the earth’s surface which varies 0.07 for water to

0.75 for ice , and is 0.22 for concrete , and in most cases an average of 0.2 is taken as in our

study

4- Finally the total solar radiation incident on a tilted surface can be calculated using the sum of

the above three steps as follows :

trtdtbt HHHH (17)

Results and Discussion:

Table 1 shows the location of the Tripoli and its elevation above mean sea level .

Table 1 the location of Tripoli

ddtd RHH



94

City Latitude N Longitude E Elevation (m)

Tripoli 32.89 13.18 12.0

Figures 1 shows the comparison between the monthly average daily global radiation on a horizontal

surface as calculated by the model versus the averages as obtained from NASA for Tripoli .

Figure 1. Comparison between the monthly average daily global radiation on a horizontal surface as calculated by the model

versus the averages as obtained from NASA for Tripoli.

It can be seen from this figure that the model works very well during the summer months and there is

a rather little underestimation by the model during the winter season.

Figures 2, shows the scatter plot of the calculated data versus the data measured by NASA for Tripoli

.

0

1

2

3

4

5

6

7

8

9

JAN FEB MAR APR MAY JUNE JULY AUG SEP OCT NOV DEC

Sola

r ra

dia

tio

n (

kw/m

2 )

Month

Tripoli

H(Model)

H(NASA)



95

Figure 2. Scatter plot between calculated and measured monthly average hourly solar radiation for the year 2005 for Tripoli

city

It can be seen from this figure that almost all the values congregate very close to the regression line.

This means the performance of this model seems to be very good in estimating average monthly daily

solar radiation .

Table (2) shows the various parameters as calculated by the model

Month 0H

0SS

H TK

January 5.85 0.65 3.74 0.64

February 7.17 0.69 4.70 0.66

March 8.79 0.65 5.61 0.64

April 10.24 0.65 6.57 0.64

May 11.12 0.75 7.49 0.67

June 11.44 0.75 7.69 0.67

July 11.26 0.88 7.82 0.69

August 10.56 0.87 7.32 0.69

September 9.26 0.74 6.21 0.67

October 7.64 0.70 5.03 0.66

November 6.16 0.80 4.21 0.68

December 5.48 0.87 3.80 0.69

y = 1.2499x - 2.2823

0

5

10

0 2 4 6 8 10

H(M

od

el)

H(NASA)

H(NASA) Vs H(Model)



96

Table (3) shows the calculated global , beam , and diffuse solar radiation for the three cities under

study

Month Global radiation(H) beam radiation(Hb) Diffuse radiation(Hd)

January 3.74 2.70 1.04

February 4.70 3.48 1.22

March 5.61 4.05 1.56

April 6.57 4.77 1.80

May 7.49 5.69 1.79

June 7.69 5.85 1.85

July 7.82 6.13 1.69

August 7.32 5.73 1.59

September 6.21 4.70 1.51

October 5.03 3.74 1.29

November 4.21 3.26 0.96

December 3.80 2.97 0.82



97

Figure 2. Comparison between the monthly Radiation on a horizontal surface as calculated by the model versus the calculated

global , beam , and diffuse solar radiation for Tripoli.

Tables (4, 5, 6 ) show the various solar radiation parameters incident on tilted surfaces for three

selected solar collectors angles ( 300 , 450, 600 )

Table (4) solar radiation parameters on tilted surface for solar collector angle 300

Month Rb Htb Rd Htd Rr Htr Ht

January 1.672 4.52 0.93 0.97 0.01 0.05 5.54

February 1.437 5.00 0.93 1.14 0.01 0.06 6.21

March 1.198 4.86 0.93 1.46 0.01 0.08 6.39

April 0.994 4.74 0.93 1.68 0.01 0.09 6.51

May 0.852 4.85 0.93 1.67 0.01 0.10 6.62

June 0.786 4.60 0.93 1.72 0.01 0.10 6.42

July 0.813 4.99 0.93 1.57 0.01 0.10 6.66

August 0.929 5.32 0.93 1.48 0.01 0.10 6.90

September 1.117 5.25 0.93 1.40 0.01 0.08 6.74

October 1.352 5.06 0.93 1.20 0.01 0.07 6.33

November 1.606 5.23 0.93 0.89 0.01 0.06 6.18

December 1.748 5.20 0.93 0.77 0.01 0.05 6.02

0

1

2

3

4

5

6

7

8

9Ja

n

Feb

Mar

Ap

r

May

Jun

e

July

Au

g

Sep

Oct

No

v

De

c

Sola

r ra

dia

tio

n (

kw/m

2)

Global Radiation(H)

Beam Radiation(Hb)

Diffuse Radiation(Hd)



98

Figure 2. Comparison between the solar radiation parameters on tilted surface

for solar collector angle 300 for Tripoli.



January 1.847 4.99 0.85 0.89 0.03 0.11 5.99

February 1.514 5.27 0.85 1.04 0.03 0.14 6.45

March 1.177 4.77 0.85 1.33 0.03 0.16 6.27

April 0.888 4.24 0.85 1.54 0.03 0.19 5.97

May 0.687 3.91 0.85 1.53 0.03 0.22 5.66

June 0.594 3.48 0.85 1.58 0.03 0.23 5.28

July 0.632 3.88 0.85 1.44 0.03 0.23 5.55

August 0.796 4.56 0.85 1.35 0.03 0.21 6.13

September 1.062 4.99 0.85 1.28 0.03 0.18 6.46

October 1.394 5.22 0.85 1.10 0.03 0.15 6.46

November 1.753 5.71 0.85 0.82 0.03 0.12 6.65

December 1.954 5.81 0.85 0.70 0.03 0.11 6.62

0

1

2

3

4

5

6

7

8

Jan Feb Mar Apr MayJune July Aug Sep Oct Nov Dec

Sola

r ra

dia

tio

n (

kw/m

2)

Chart Title

Htb

Htd

Htr

Ht



99





January 1.896 5.12 0.75 0.78 0.05 0.19 6.09

February 1.488 5.18 0.75 0.91 0.05 0.24 6.33

March 1.075 4.36 0.75 1.17 0.05 0.28 5.81

April 0.721 3.44 0.75 1.35 0.05 0.33 5.12

May 0.475 2.71 0.75 1.34 0.05 0.37 4.42

June 0.362 2.12 0.75 1.38 0.05 0.38 3.89

July 0.409 2.51 0.75 1.26 0.05 0.39 4.16

August 0.608 3.49 0.75 1.19 0.05 0.37 5.04

September 0.934 4.39 0.75 1.13 0.05 0.31 5.83

October 1.342 5.02 0.75 0.97 0.05 0.25 6.24

November 1.781 5.80 0.75 0.72 0.05 0.21 6.73

December 2.027 6.03 0.75 0.62 0.05 0.19 6.84

0

1

2

3

4

5

6

7So

lar

rad

iati

on

(kw

/m2 )

Htb

Htd

Htr

Ht



100



0

1

2

3

4

5

6

7

8

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

Sola

r ra

dia

tio

n (

kw/m

2)

Chart Title

Htb

Htd

Htr

Ht

0

1

2

3

4

5

6

7

8


Sola

r ra

dia

tio

n (

kw/m

2 )

Chart Title

Ht30

Ht45

Ht60



101

Month Ht30 Ht45 Ht60

Jan 5.54 5.99 6.09

Feb 6.21 6.45 6.33

Mar 6.39 6.27 5.81

Apr 6.51 5.97 5.12

May 6.62 5.66 4.42

June 6.42 5.28 3.89

July 6.66 5.55 4.16

Aug 6.9 6.13 5.04

Sep 6.74 6.46 5.83

Oct 6.33 6.46 6.24

Nov 6.18 6.65 6.73

Dec 6.02 6.62 6.84

Average 6.38 6.12 5.54

0

2

4

6

8


Axi

s Ti

tle

Chart Title

Ht30

Ht45

Ht60



102

Table (7) gives the statistical test made on the results

Table 7 gives the statistical test made on the results

City MBE RMSE PE

Tripoli -0.53 0.71 10.69

Conclusion:

It can be concluded from this study that we can use this simple model to estimate the monthly

average daily global radiation on a horizontal surface for Tripoli city in Libya, as there is a rather good

agreement between the calculated values by the model and the measured values as obtained from

NASA. It also gives better estimate for summer months .

0

1

2

3

4

5

6

7

8

Ht30

Ht45

Ht60



103

References:

[1] Datta Debazit and Datta Bimal Kumar ,(2013).empirical model for the estimation of global solar radiation in Dhaka, Bangladesh , international journal of research in Engineering and Technology, volume 2 , issue 11, 649-653

[2] Archangel a. ( 2013 ). Libya solar potential 5X larger than oil reserves , article in a press

[3] Al- habaibeh , (2013), A. Libya could produce more energy in solar power than oil , report by the school of Architecture , design and built environment .

[4]

El- Sebaii , F.S. , Al- Hazmi , A.A., and Al- Ghamdi , S.J, (2009). Global , direct and diffuse solar radiation on horizontal and tilted surfaces in Jeddah , Saudi Arabia .

[5]

Boland j.Ridley (2008) , Model of diffuse solar radiation , Renewable energy , 33 , 575-84

[6]

Iqbal , M. ,(1979) , A study of Canadian diffuse and total solar radiation – II, Monthly average hourly horizontal radiation , Solar Energy , 22 , 87-90

[7] El-Sebaii A.A. and Trabia A.A. ,( 2005 ). Estimation of global solar radiation on horizontal surface over Egypt , Solid, 28, No.1, 163-175

[8] El- Sebaii, A.A. , f.s. al- Hazmi , and Ghamdi S.J. Yaghmour , (2009). Global , direct and diffuse solar radiation on horizontal and tilted surfaces in jeddah , Saudi Arabia , Applied Energy , 87, 568-576

[9] Al-Ayed , M.S. et al ,( 1998 ). Global , direct and diffuse solar irradiance in Riyadh , Saudi Arabia ,renewable Energy , 6, 107-18

[10] Al- Nuaimi a. S. ,( 2015 ). Estimating global solar radiation in North Libya

[11] Bannani , F.K. , T. A. Sharif and A.O.R. Ben- Khalifa ,( 2006 ). Estimation of monthly average solar radiation in Libya , theoretical and Applied Climatology , 83 , 211-215

[12] Al- Dabbas , m.A. ,( 2010 ). The analysis of the characteristics of the solar radiation climate of the daily global radiation and diffuse radiation in Amman , Jordan , International Journal of Renewable Energy , Vol. 5 , No. 3 , 23-38

[13] Ueyama H., (2005). Estimating Hourly Direct and diffuse solar Radiation for the compilation of solar Radiation Distribution Maps , J. agric Meteorology , 61, 940 , 207-



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[14] Gana, N.N. , and Akpootu , D.O., (2013) . Angstrom type empirical correlation for estimating global solar radiation in north – eastern Nigeria , international Journal of engineering and Science , 2 , issue 11 , 78-

[15] Fatayi ,E.O. , Rabiu , A.B. , and Teliat , R.O., ( 2011 ). Correlations to estimate monthly mean of daily diffuse solar radiation in some selected cities in Nigeria , Advanced in Applied Science Research , 2, (4) , 480-490

[16] Al- Rawahi , et al , (2011), predicted hourly solar radiation on horizontal and inclined surfaces for Muscat / Oman , J. of Engineering research , Vol. 8 , No. 2 , 19-31

[17] Abbasi , A. A. , and m.S. , Qureshi, (2012) . Estimation of global and diffuse solar radiation for Nawabshah , Sindh , Pakistan , Quaid – E-Awam university research journal of Engineering science and technology , Vol. 11 , N0. 1, 1- 5

[18] Bindi M. , Francesco Miglietta , and Gaetano Zipopli. (1992), Different methods for separating diffuse and direct components of solar radiation and their application in crop growth models , climate research , Vol. 2, 47-54

[19] Louis e., Aakpabio , I. , and Etuk , E. , (2003) , Relationship between global solar adiation and sunshine duration for Onne , Nigeria , Turk. J. Phys., 27, 161-167

[20] Page, J.K. ,( 1961 ) The estimation of monthly mean values of daily total short wave radiation n vertical and inclined surface from sunshine records for latitudes 40 N – 40 S . Proceedings of UN Conference on New Sources of Energy , 4 , 598 , 378-390

[21] Duffie J.A. ,( 1991 ) and Beckman W.A. , Solar engineering of thermal processes , New York , , Wiley

[22] Tiwari , G.N. , and Suneja S.,( 1997).Solar thermal engineering systems , Narosa Publishing House. Date of Publication

estimating global , direct , diffuse and reflected solar

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