




































Asian Review of Environmental 

and Earth Sciences 
ISSN: 2313-8173 
Vol. 1, No. 2, 43-50, 2014 

http://www.asianonlinejournals.com/index.php/AREES 

 
 

 

 

 

 

 

43 

 

Estimation of Hourly Photo synthetically- Active Radiation 

(PAR) From Hourly Global Solar Radiation (GSR) In Jos, 

Nigeria 
 

Anjorin, O.F.
1
 --- Utah, E.U.

2
 --- Likita

,
 M.S.

3
 

 
1
Department of Science Laboratory Technology, University of Jos. Plateau State, Nigeria 

2
Department of Physics, University of Uyo, Uyo, Akwa Ibom State, Nigeria 

3
Federal College of Forestry Mechanization, Afaka, Kaduna State, Nigeria 

 

Abstract 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
This work is licensed under a Creative Commons Attribution 3.0 License 

Asian Online Journal Publishing Group 

 

1. Introduction 
Solar radiation is the principal energy source for physical, biological and chemical processes, such as, snow melt, 

plant photosynthesis, evapotranspiration, crop growth and is also a variable needed for biophysical models to 

evaluate risk of forest fires, hydrological simulation models and mathematical models of natural processes [1]. Jun, 

et al. [2] identified that the spectral portion of the solar spectrum that is used by plant biochemical processes in 

photosynthesis (light energy conversion to biomass) extends from 400 to 700 nm.  This portion of the solar spectrum 

is called the photo synthetically- active radiation (PAR). 

Photo synthetically-active radiation (PAR) is a necessary input in applications dealing with plant physiology, 

biomass production and natural illumination in greenhouses. Unfortunately, in Africa and the larger part of the 

world, a routine network for the measurement of photo synthetically-active radiation (PAR) is not yet established and 

it is often calculated as a constant ratio of the broadband solar radiation.  

PAR can be measured basically by two methods; one is to measure these values directly with instruments [3], 

and the other is to estimate them from other data [4, 5]. These are respectively referred to as direct method and 

indirect method. The direct method is not too commonly adopted in tropical region of Africa due to its reliability 

problems for various reasons such as maintenance, instrument type, information on calibration, local environment, 

and data recording, hence the common application of indirect method. Jun, et al. [2] further categorized the indirect 

method into two categories: satellite-based methods [6, 7] and site-based methods [8]. A satellite-based method uses 

remote sensing signals to retrieve information on the atmosphere, applies the retrieve [9].These parameters are used 

to drive an irradiative transfer model (or search a lookup table based on the irradiative transfer model), and 

eventually obtains PAR estimates at Earth’s surface. A site-based method, on the other hand, takes routine 

meteorological data collected at weather stations as inputs to estimate PAR values. Some schemes of this type are 

based on empirical relationships between the global solar radiation (GSR) and the PAR that are constructed 

In this work, an hourly model was used in estimating the values of Photo-synthetically Active Radiation 

(PAR); a parameter closely related to plant growth in Jos, Nigeria (Latitude 9
0 
57’ N, Longitude 8

0
53’E ) 

and Altitude 1153m asl.) from hourly Global Solar Radiation Rs and to predict its  hourly (PAR) daily 

seasonal trend. For this purpose, three years (2003, 2004 and 2005) data recorded using Gunn-Bellani 

Radiation Integrator at the weather observatory station of Geography and Planning Department of the 

University of Jos was used. The trend of variation of the mean hourly PAR PQ  shows that the maximum 

was obtained at 12.00p.m. PQ for the raining season months of June, July and August for year 2003 are 

respectively 3.176 EmJ
-1

, 2.900 EmJ
-1

 and 2.960 EmJ
-1

 while that of the dry season months of 

November, December and January for the same year are respectively 3.871EmJ
-1

, 3.997 EmJ
-1

 and 

3.655EmJ
-1

. Also, there exists seasonal variation in the average predicted value of the hourly global 

PAR; two maxima occurred- major at February and March and the minor at November and December. 

The trend of variation of hourly QP/RS (μEJ
-1

) for the year 2003, 2004, and 2005 with local time shows 

maximum values at noon for the months considered. The ratio is lower and more variable in wet season 

than in dry season, and is usually higher at noon. 
 

      Keywords: Global solar radiation, Photo synthetically- active radiation, Second kt model. 

http://creativecommons.org/licenses/by/3.0/


Asian Review of Environmental and Earth Sciences, 2014, 1(2): 43-50 

 

 

 

 

 

44 

 

according to certain meteorological variables (e.g., near-surface air pressure, temperature, or humidity) [10, 11]. In 

this paper, an empirical model developed by Alados, et al. [12] and applied in Southeastern Spain is used in 

estimating the values of photo synthetically-active radiation, QP for Jos, a town in the North- central zone of Nigeria. 

This model is used in this work because at its development, its goal was to provide a model that is transferable to 

those locations where broad band solar radiation and appropriate meteorological parameters are routinely measured. 

This paper aims at obtaining an hourly baseline data of the values of PAR (Qp) and its ratio to global (broadband) 

solar radiation (Rs) for Jos. Also the daily seasonal characteristics of Qp in different integration intervals, daily and 

hourly values are described. 

 

2. Geography of the Site 
Nigeria is a tropical country in West Africa. Jos, the town in which this project is carried out is the Plateau State 

capital. This state is situated in the middle belt of Nigeria. Its coordinates are: Latitude; 09
0
 57N Longitude; 08

0
 53E   

and altitude; 1153m above sea level.  Jos is located in the transition zone between deciduous forest of the south and 

the Savannah of the North. The monthly average temperature is almost uniform through out the year with its mean 

average value for 2003, 2004 and 2005 being 24.5
0
C. For 2003, 2004 and 2005 respectively, the total annual rainfalls 

are 1038.6mm, 1308.4mm and 1025.6mm.  

The prevailing winds in Nigeria, and of course, Jos are the south-westerly (SW) and North- Easterly (NE) trade 

winds. The SW wind blows from the Atlantic and brings rain to the West African coast, including Nigeria from 

about April to October- this is the raining season period. The NE wind, a very dry wind, blows across the country 

between November and March bringing the harmattan dust with it- this is the dry season period. 

The project site is on a flat platform at the observatory station of Geography and Planning Department, 

University of Jos. In this site, the instruments for measuring solar radiation are the radiometer and Gunn- Bellani 

radiation integrator. The observatory provides maximum exposure to the instrument sensors without much obstacle 

to incoming radiation. 

 

3. Method 
In this paper, a site-based method is adopted in which routine meteorological data were collected at the 

observatory station of Geography and Planning Department of University of Jos as inputs to estimate PAR values for 

the period of three years (2003, 2004 and 2005). The data of GSR obtained were in milliliters. These were converted 

to MJm
-2

 day
-1

 by using the calibration equation. 

1ml= 1.26x 10
6
Jm

-2
 of Gunn- Bellani (GB) [13].                                               (1) 

The average values are tabulated in table 1  

 
Table-1. The Data of Average Monthly Global Solar Radiation ml and Their Conversion in MJm-2 day-1 

 

4. Method of Prediction 
The monthly averages of daily global solar insolation data were obtained from the observatory unit of Geography 

and Planning Department of University of Jos. These data were then reduced to the daily average hourly clearness 

index (kt) by taking the ratio of  hourly global solar insolation to the calculated hourly extra-terrestrial horizontal 

insolation from their respective monthly average daily values using the ratio of the hourly total to daily irradiation r t.  

An empirical model developed by Alados, et al. [12] and applied in Southeastern Spain is then used in estimating the 

hourly values of photosynthetically- active radiation, QP. This empirical model otherwise known as the second kt 

model is expressed as: 

 
 

P

S

Q

R
= 1.832 – 0.191 lin kt +0.099 sin α                                                                                                                 (2)    

Qp = hourly global “PAR” 

RS = I, hourly global solar radiation 

where α (degrees) is the solar altitude and is related to the zenith angle ѲZ by the 

equation 3; [14] 

sin α=cos ѲZ               (3) 

The angle of incidence θz is the zenith angle of the Sun: [15]  

cos ѳz =sinδ sinϕ + cosδ cosϕ cosω                                 (4)                                      

 2003 2004 2005 

MONTH   mL MJm-
2
day

-1
 ml MJm-

2
day

-1
 ml MJm-

2
day

-1
 

JAN. 16.0 20.2 19.7 24.8 12.4 15.6 

FEB. 19.2 24.2 19.0 23.9 17.6 22.2 

MAR. 19.0 23.9 19.0 23.9 16.2 20.4 

APRIL 13.1 16.5 18.7 23.6 15.6 19.7 

MAY 18.2 22.9 13.6 17.1 11.7 14.7 

JUNE 14.0 17.6 15.3 19.7 11.2 14.1 

JULY 12.9 16.3 14.2 18.8 8.8 11.1 

AUG. 12.2 16.2 12.2 15.4 7.9 10.0 

SEPT. 15.6 19.7 15.9 20.0 11.5 14.5 

OCT. 17.9 22.6 17.4 21.9 15.4 19.4 

NOV. 17.2 21.7 17.9 22.6 15.8 19.9 

DEC. 17.9 22.6 18.8 23.7 15.6 19.7 



Asian Review of Environmental and Earth Sciences, 2014, 1(2): 43-50 

 

 

 

 

 

45 

 

 

P

S

Q

R
 = 1.832 – 0.191 lin kt +0.099 cos ѲZ                               (5)  

This model excludes the dew point and temperature dependence. 

 To avoid cosine response problems, solar zenith angle of less than 87
0 
were used.  

The hourly clearness index is given as 

kt=

0I

I
,                            (6)                                                                                                                             

where I= hourly global solar radiation measured in MJm
-2

hr
-1

      

I0= hourly extraterrestrial solar radiation measured in MJm
-2

hr
-1

 
 

                                                                                                                                            

H0 is evaluated from the equation [16]:      

H0=
24


IscE0[(

180


)ωS(sinδsinϕ)+(cosδcosϕsinωs)]                (7)                                                                    

where Isc is the Solar constant = 1367W/m
2
.  

Eo (dimensionless) is the eccentricity correction-factor of the Earth’s orbit and is given by Spencer [17] as 

Eo = 1.00011+ 0.034221cos Г+ 0:00128sin Г+ 0.000719cos2 Г+ 0.000077sin2 Г     (8) 

The extraterrestrial hourly radiation measured in MJm
-2

 hr
-1

 can be evaluated from the equation [14]; 

I0=IscE0 (sinδsinϕ + 0.9972cosδcosϕcosω1)                  (9) 

where Isc is the solar constant measured in MJm
-2

hr
-1

 (Isc= 4.92MJm
-2

hr
-1

), δ, ϕ and ω1  are the declination, 

latitude and hour angle respectively at the middle of an hour in degrees.       

 The day angle Г is    

Г = 2π (
1

365

N 
)                    (10) 

In this relation, the angles are expressed in radians.  

The ratio of the hourly total to daily irradiation rt is expressed by Wong and Chow, 2001 as  

tr
24


  ( 1 s

s s s

cos cos

sin cos
180

 


  





)(a +bcosω1)                                                             (11) 

where ω1 is the hour angle at the middle of the hour measured in degrees. This is calculated from  

ω1=  
1

4
 (number of minutes from noon).                (12) 

  ωs ,the sunrise (or sunset) hour angle is evaluated using: [18]; 

 ωs = cos 
1 
(- tan ø tan δ)                             (13) 

where ø = latitude of the location and  

δ= the solar declination. 

δ can be obtain from the equation 14; [19] 

δ= 23.45sin (
2 ( 80)

365

N 
)                                                                                         (14) 

where N is the day of the year (N=1 on January 1st and N=365 on December 31st, February 29
th
 is ignored)  

The coefficients a and b expressed as function of ωs  by Collares-Pereira and Rabl [20] are:   

a =0.409+0.5016 sin (ω-60)                                                                                        (15) 

b=0.6609+0.4767 sin (ω- 60)                                                                                       (16) 

In terms of the hourly global solar radiation I and the monthly global solar radiation H,  

the expression for rt  presented by Collares-Pereira and Rabl [20] is: 

rt=
I

H
= 0

0

I

H
(a+bcosω1)           (17) 

Hence the hourly global radiation can be obtained from the 

rtH=I              (18)                                                                                                                                

where I= Rs (hourly global solar radiation)                                                                                    (19) 

 

5. Results Analysis 
5.1. Estimation of Hourly Photo Synthetically Active Radiation (PAR) From Hourly Global Solar 

Radiation (GSR).  
Computing the average hourly values of PAR (QP) from average hourly global solar radiation by using the 

second kt model in equation 5 gives the values of QP as presented in Table 2.  The tables show approximately 

identical seasonal variation with maximum daily value of hourly QP obtained at 12pm for January of the years 2003, 

2004 and 2005 under consideration. The parameters required for estimating QP (hourly PAR) such as; the hourly 

global solar radiation, I, the hourly horizontal extraterrestrial global radiation I0, rt (which is the ratio of the hourly 

total to daily irradiation), the hour angle ωs, the extraterrestrial monthly horizontal global solar irradiation H0, the 

hourly clearness index kt, and the cosine of the zenith angle cos θz were calculated and presented in the tables 2 and 

3. These values show a seasonal variation with the local time. It is clear from table 2 that Qp and RS have a similar 

trend. The graph showing the variations with local time is shown in figure 1. Each curve depicts a peak as maximum 

value of hourly PAR. From this graph, the variation of QP for 2003, 2004 and 2005 are seen to have a similar trend. 



Asian Review of Environmental and Earth Sciences, 2014, 1(2): 43-50 

 

 

 

 

 

46 

 

Also, the estimated values of mean hourly PAR, PQ for 2003, 2004 and 2005 are presented in table 3. It is obvious 

from table 3 that higher values of  PQ  are predicted for the dry season months and lower values for wet season 

months. Table 4 shows a more detailed variation of the estimated PQ for the dry season months of January and 

December and the wet season months of June and August averaged over 2003, 2004 and 2005.This also reveals 

higher hourly values for dry season months and lower values for wet season months. However, the maximum  PQ
   

was obtained at noon around 12pm for all seasons. Figure 2 shows that in 2003, 2004 and 2005, there were two 

maxima (major and minor) and one minimum. The major maximum occurred between February-March and the 

minor maximum occurred between October and November. The minimum occurred between August and September. 

From figure 2, the variation of QP is similar to the mean monthly global solar radiation, H in figure 4. 
    

 

  Figure 5 shows cosine of zenith angle, cos Ѳz as an indispensible parameter in obtaining QP with the variation 

depicting similarity in behaviour with figure 1.  Furthermore, in an attempt to reach a deeper knowledge of the ratio 

of photo synthetically-active radiation to broadband solar radiation we have analysed the hourly values. The hourly 

pattern of the ratio photo synthetically-active photon density flux to broadband solar irradiance hourly values (Qp/Rs), 

are shown in Tables 5 and 6 for the dry and wet seasons respectively. The trend of variation of diurnal hourly QP/RS 

(μEJ
-1

) for the years reveals maximum value around noon. It is found that this ratio also has seasonal and daily 

variations which are greater in the wet season months than in the dry season months. From these tables, the ratio is 

higher and more variable in wet season than in dry season, and is usually higher at noon. From figure 6, it is obvious 

that the lowest value occurred during the dry season months of November, December, January, February and March 

while the highest occurred during wet season months of May, June, July, August and September. T 

 
Table-2. Estimated Values of Hourly Par for the Month of January of 2003, 2004 And 2005. 

 

Table-3. Estimated Values of the Ratio Of Average Hourly Par To Hourly Global Radiation,

 

p

s

Q

R
 And Average Hourly Par, Qp 2003, 2004 

And 2005. 

 
 

Table-4. Average Estimated Values of Hourly Par, Qp for January, June, August and June of 2003, 2004 and 2005. 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LOCAL TIME 
P(JANUARY)Q  

MJm
-2

h
-1

 

P( )Q JUNE  

MJm
-2

h
-1

 

P( )Q AUGUST  

MJm
-2

h
-1

 

P( )Q DECEMBER  

MJm
-2

h
-1

 

7.00a.m 0.843 0.764 0.628 0.908 

8.00a.m 2.166 1.915 1.379 2.339 

9.00a.m 3.566 3.128 2.590 3.853 

10.00a.m 4.770 4.171 3.458 5.156 

11.00a.m 5.614 4.899 4.065 6.091 

12.00p.m 5.898 5.145 4.268 6.374 

1.00p.m 5.614 4.899 4.065 6.091 

2.00p.m 4.770 4.171 3.458 5.156 

3.00p.m 3.566 3.128 2.590 3.853 

4.00p.m 2.166 1.915 1.379 2.339 

5.00p.m 0.843 0.764 0.628 0.908 



Asian Review of Environmental and Earth Sciences, 2014, 1(2): 43-50 

 

 

 

 

 

47 

 

Table-5. Estimated Values of the Ratio of Hourly Par to Hourly Global radiation for January, February and March of 2003, 2004 and 2005. 

 QP/RS 2003 (μE J
-1

) QP/RS 2004 (μE J
-1

) QP/RS 2005 (μE J
-1

) 

 JAN FEB MAR JAN FEB MAR JAN FEB MAR 

7.00a.m 1.937 1.922 1.940 1.900 1.924 1.940 1.987 1.938 1.970 

8.00a.m 1.960 1.945 1.964 1.920 1.947 1.964 2.009 1.961 1.994 

9.00a.m 1.978 1.964 1.984 1.940 1.967 1.984 2.028 1.981 2.014 

10.00a.m 1.993 1.979 1.999 1.953 1.982 1.999 2.042 1.996 2.030 

11.00a.m 2.002 1.989 2.009 1.962 1.991 2.009 2.051 1.989 2.039 

12.00p.m 2.005 1.992 2.012 1.965 1.994 2.012 2.054 2.009 2.043 

1.00p.m 2.002 1.989 2.009 1.962 1.991 2.009 2.051 1.989 2.039 

2.00p.m 1.993 1.979 1.999 1.953 1.982 1.999 2.042 1.996 2.030 

3.00p.m 1.978 1.964 1.984 1.940 1.967 1.984 2.028 1.981 2.014 

4.00p.m 1.960 1.945 1.964 1.920 1.947 1.964 2.009 1.961 1.994 

5.00p.m 1.937 1.922 1.160 1.900 1.924 1.940 1.987 1.938 1.970 

 
Table-6. Estimated Values of the Ratio of Hourly Par to Hourly Global Radiation for July, August and September of 2003, 2004 and 2005. 

 QP/RS 2003 (μE J
-1

) QP/RS 2004 (μE J
-1

) QP/RS 2005 (μE J
-1

) 

 JULY AUG SEPT JULY AUG SEPT JULY AUG SEPT 

7.00a.m 2.019 2.016 1.978 1.990 2.026 1.975 2.092 2.108 2.036 

8.00a.m 2.040 2.040 2.001 2.013 2.049 1.999 2.114 2.131 2.060 

9.00a.m 2.059 2.059 2.020 2.032 2.068 2.019 2.133 2.151 2.080 

10.00a.m 2.074 2.074 2.037 2.046 2.083 2.034 2.147 2.166 2.096 

11.00a.m 2.083 2.083 2.047 2.056 2.093 2.044 2.156 2.175 2.105 

12.00p.m 2.086 2.085 2.050 2.059 2.095 2.047 2.159 2.177 2.109 

1.00p.m 2.083 2.083 2.047 2.056 2.093 2.044 2.156 2.175 2.105 

2.00p.m 2.074 2.074 2.037 2.046 2.083 2.034 2.147 2.166 2.096 

3.00p.m 2.059 2.059 2.020 2.032 2.068 2.019 2.133 2.151 2.080 

4.00p.m 2.040 2.040 2.001 2.013 2.049 1.999 2.114 2.131 2.060 

5.00p.m 2.019 2.016 1.978 1.990 2.026 1.975 2.092 2.108 2.036 

 
Table-7. Ratio of Par Photon Irradiation to Global Solar Irradiation on Monthly, Annual and Seasonal Groupings [21]. 

 

 

 

 

 

 

 

 

 
Fig-1. Variation of Hourly Par with Local Time for January of 2003, 2004 and 2005. 

 

0

1

2

3

4

5

6

7

8

 LOCAL TIME 

PQ

PERIOD fp(=∑( PAR/H)/n(EMJ
-1

) Standard deviation Energy ratio 

January 1993 1.92 0.036 0.42 

February 1993 2.06 0.040 0.45 

March 1993 2.10 0.065 0.46 

April 1993 2.14 0.032 0.47 

May 1993 2.15 0.029 0.47 

June 1993 2.14 0.026 0.47 

July 1993 2.11 0.029 0.46 

August 1993 2.09 0.036 0.46 

September 1992 2.11 0.043 0.46 

October 1992 2.13 0.022 0.47 

November 1992 2.06 0.077 0.45 

December 1992 1.96 0.043 0.43 

Year 2.08 0.040 0.46 

Q2005 

Q2003 

Q2004 



Asian Review of Environmental and Earth Sciences, 2014, 1(2): 43-50 

 

 

 

 

 

48 

 

 

Figure-2. Variation of Average Monthly Par ( PQ ) for 2003, 2004 and 2005. 

 

 
Figure-3. Variation of Daily Hourly Extraterrestrial Solar Radiation, I0 and Daily Hourly Global Solar Radiation, I with Local Time. 

 

 
Figure-4.  Variation of Monthly Extraterrestrial Solar Radiation, H0 and Measured Monthly Global Solar Radiation, H . 

 

0

2

4

6

8

10

12

14

Q
P

 

MONTH 

I 

Io 

 

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

I O
  M

J
/m

2
/h

r,
 I

 M
J/

m
2 /

h
r 

TIME OF DAY (GMT +1) 

I

Io

0

5

10

15

20

25

30

35

40

H
,H

o
 

MONTH 

H

H0

QP 2005 

QP 2004 

QP 2003 

H0 

H 



Asian Review of Environmental and Earth Sciences, 2014, 1(2): 43-50 

 

 

 

 

 

49 

 

 
Figure-5. Variation of Estimated Par, Qp for December 2003, 2004 and 2005 with cosine of Zenith Angle, Cos Ѳz 

                    

 
Fig-6. Variation of Mean Monthly Ratio of Hourly Par, Qp to Hourly Global Solar Radiation, Rs. 

 

6. Discussion 
Photo-synthetically Active Radiation (PAR) is the amount of light available for photosynthesis, which is light in 

the 400 to 700 nanometer wavelength range. PAR changes seasonally and varies depending on the latitude and time 

of day. PQ  is low for the wet and raining season months as compared to the months of dry and harmattan season. For 

example, PQ  for the raining season months of June, July and August for year 2003 are respectively 3.176 EmJ
-1

, 

2.900 EmJ
-1

 and 2.960 EmJ
-1

 while that of the dry season months of November, December and January for the same 

year are respectively 3.871EmJ
-1

, 3.997 EmJ
-1

 and 3.655EmJ
-1

. It is obvious from these results that the PQ is higher 

during the dry season months of the year. This could be attributed to sky clearness and low cloudiness. The results in 

Table 2 show that high values of  PQ  are predicted for the months with lower atmospheric cloudiness and much 

reduced harmattan dust. This occurs in February, March, May and November. The months of December and January 

in the harmattan have lower values of  PQ  compare to other dry season months due to high dust concentration from 

harmattan and high scattering aerosols in the atmosphere due to bush burning. 

A careful analysis of table 2 reveals that the dry season months have mean hourly  QP/RS (μEJ-
1
) of 1.900 QP/RS 

(μEJ-
1
) while the wet season months have mean hourly QP/RS (μEJ-

1
) of 2.000 QP/RS (μEJ-

1
). Also the tables show 

the annual pattern of the daily monthly means of the ratio of photo synthetically-active radiation to broadband solar 

irradiation, Qp/Rs, suggests the existence of a seasonal dependence of this term. In this sense we found higher values 

associated with raining season months and lower values from November to March. Water vapour is important 

because of its absorption effects. This absorption takes place in the infra-red region of the spectrum and will 

therefore decrease the hourly global solar radiation, Rs to a much greater extent than Qp. On the other hand, scattering 

by aerosols that have enhanced atmospheric water vapour content acts primarily in the visible region and will affect 

the hourly global photo synthetically- active radiation, Qp, more than the hourly global (broadband) solar radiation, 

Rs.  Also, in January and December, it could be observed that the atmosphere is very hazy with harmattan dust 

coming into the town from the Sahara desert and aerosols due to high level of bush burning, hence the low predicted 

value of hourly mean QP/RS . It is to be noted that harmattan dust is known to have no waveband attenuation of the 

global solar radiation which is evident in the near whitish sky always prevalent during these months [21].  

In March, the dust arising from harmattan clears off paving way for the onset of rainy season while in November, 

the dry season is about to set in. Hence February and November are transition months for the mean value of the ratio 

0

1

2

3

4

5

6

7

8

0.165 0.383 0.571 0.714 0.805 0.835 0.805 0.714 0.571 0.383 0.165

Q
2

0
0

3
, Q

2
0

0
4

, Q
2

0
0

5 

COS  ѲZ 

Q1

Q2

Q3

2003 

2004 

2005 

1.8

1.85

1.9

1.95

2

2.05

2.1

2.15

2.2

MONTH 

Q/I 03

Q/I 04

Q/I 05

p

s

Q

R



Asian Review of Environmental and Earth Sciences, 2014, 1(2): 43-50 

 

 

 

 

 

50 

 

of hourly PAR to hourly global solar radiation. However, the effects are not always so noticeable on a daily basis. 

However, during the raining season the moisture content of the atmosphere affect the results.  

 Furthermore, from figure 4, it is clear that that the monthly variation of global extraterrestrial solar radiation, H0 

does not follow a fairly periodic pattern as the monthly global solar radiation, H. This is due to the fact that the 

calculated extra-terrestrial horizontal insolation per day at a given place, which is the insolation on a horizontal 

surface, is without any atmospheric effects. It can be seen from equation (7) that the extra-terrestrial horizontal 

insolation is a function of latitude and the day of year only. Hence, it can be calculated for any location for any given 

day. However, the calculated insolation does not take any atmospheric effects into account. According to Wong and 

Chow [14], the clearness index, kt gives a measure of the atmospheric effects at a place on the insolation which is the 

measure of the climatic condition at a geographical location. 

 The independent set of data obtained from the second kt model can be compared with the data generated by Udo 

and Aro [21] from some linear regression equations. Table 7 presents the result by Udo and Aro [21]. It is clear that 

the values of 
PAR

H
 given in this table are comparable to the values of P

S

Q

R
 obtained in this work as listed in table 2. 

Hence the values of the mean ratio of hourly photo synthetically- Active Radiation (PAR) to the hourly global  

(broadband) solar radiation(Rs) predicted by the second kt model are in close agreement with those predicted by Udo 

and Aro [21]. 

 

7. Conclusion 
The analyses of data of photo synthetically-active radiation and broadband solar radiation registered from 

January 2003 to December 2005 in Jos, North- central Nigeria have showed the seasonal dependence of the ratio of 

photo synthetically-active radiation to broadband solar radiation. The higher values are for the raining season, while 

in the dry season are lower and more variable. The hourly values of QP for this period show that; the higher values 

were obtained during the dry season months of December, January, February, March and April, while the lower 

values occurred during the raining season months of June, July, August, September and October. However, the 

hourly pattern of the ratio photo synthetically-active photon density flux to broadband solar irradiance hourly values 

(Qp/Rs) for these periods show higher values around noon for all seasons.  
 

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