In this work, we have developed a comparison between solar radiation values measured in Morocco and values estimated by two theoretical models proposed in the literature by various researchers. The selected site is the synoptic station of the city of Fez in Morocco, in which meteorological and radiometric data are continuously collected. For the two chosen theoretical models, the first model is the Barbaro et al (1977) and Davies el al (1975) model for direct and diffuse rays respectively, based on the kasten (1980) model for the determination of the Linke turbidity values as an atmospheric turbidity parameter. The second model differs from the first by using the Ineichen and Perez (2002) model using atmospheric transmittance for the determination of the atmosphere turbidity, the transmittance values will be calculated using the Schillings et al. (2004) model. Comparing the two models applied to the case of Morocco resulted in the decision that the model of Ineichen and Perez (2002) is best suited to the climatic conditions in Morocco with the lowest normalized square error of 7%, taking into account the locals climatic conditions of the site investigated

1. http://www.iaeme.com/IJCIET/index.asp 1664 editor@iaeme.com
International Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 01, January 2019, pp. 1664–1673, Article ID: IJCIET_10_01_152
Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=10&IType=1
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
©IAEME Publication Scopus Indexed
CONTRIBUTION TO THE STUDY OF TWO
METHODS FOR ESTIMATING DIRECT AND
DIFFUSE SOLAR RADIATION IN MOROCCO
AT THE FÈS-SAÏS SITE
Alaoui Sosse Jihad, Mohamed Tahiri
Department of Process Engineering,
Mohammadia School of Engineers, Mohammed V – University of Rabat 10000, Morocco
Email: sys.energie@gmail.com, mhmtahiri@gmail.com
ABSTRACT
In this work, we have developed a comparison between solar radiation values
measured in Morocco and values estimated by two theoretical models proposed in the
literature by various researchers. The selected site is the synoptic station of the city of
Fez in Morocco, in which meteorological and radiometric data are continuously
collected. For the two chosen theoretical models, the first model is the Barbaro et al
(1977) and Davies el al (1975) model for direct and diffuse rays respectively, based
on the kasten (1980) model for the determination of the Linke turbidity values as an
atmospheric turbidity parameter. The second model differs from the first by using the
Ineichen and Perez (2002) model using atmospheric transmittance for the
determination of the atmosphere turbidity, the transmittance values will be calculated
using the Schillings et al. (2004) model. Comparing the two models applied to the case
of Morocco resulted in the decision that the model of Ineichen and Perez (2002) is
best suited to the climatic conditions in Morocco with the lowest normalized square
error of 7%, taking into account the locals climatic conditions of the site investigated.
Key words: Direct and diffuse Solar Radiation; Atmospheric turbidity; Linke Factor;
Fes-Saïs synoptic station.
Cite this Article: Alaoui Sosse Jihad, Mohamed Tahiri, Contribution to the Study of
Two Methods for Estimating Direct and Diffuse Solar Radiation in Morocco at the
Fès-Saïs Site, International Journal of Civil Engineering and Technology (IJCIET)
10(1), 2019, pp. 1664–1673.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=10&IType=1
1. INTRODUCTION
Energy is the basis of all human activity. Nowadays, a large part of the global energy demand
is provided from fossil resources. However, the reserves of fossil fuels are limited. Some
developed countries are directed at nuclear power, while the latter is not within the reach of
all States, and especially of the developing countries and present a risk of serious accidents.

2. Alaoui Sosse Jihad, Mohamed Tahiri
http://www.iaeme.com/IJCIET/index.asp 1665 editor@iaeme.com
Indeed, the growth of global energy demand, the inevitable exhaustion of fossil resources,
more or less long-term, and the deterioration of the environment caused by these types of
energies, led to the development of new sources of energy, renewable, sustainable and
protection of the environment which has become a very important point.
The use of photovoltaic and thermal solar energy seems to be a necessity for the future.
Indeed, the solar radiation is the most abundant source of energy on Earth. The amount of
energy released by the Sun (captured by the planet Earth) during an hour could be sufficient
to cover the world's energy needs for a year. In order to better harness this energy and
optimize its collection by photovoltaic collectors, it is necessary to know the distribution of
solar irradiation on the place of implantation designed for photovoltaic and thermal solar
installations, under different orientations and inclinations. However, the solar irradiation is
one of weather parameters’ most difficult to estimate because it is a function of several
geographical and astronomical parameters and is dependent on weather and atmospheric
conditions. That did not the development of several models of estimation on different
temporary scales (hour, day and month) from weather data most readily available. Besides,
radiative models of predictions have attracted the attention of a large number of researchers in
the field of renewable energy and in particular for the prediction of weather data such as solar
irradiation. Many research demonstrates several models capable of predicting the weather
data and the prediction of solar irradiation.
Atwater and Ball (1978) used a model with the following input parameters: solar constant,
zenith angle, surface pressure, ground albedo, precipitable water vapor, total ozone,
broadband turbidity. This model is applicable to extremely clear atmospheric conditions with
an atmospheric turbidity near 0.1 at 0.5µm. For turbidity near 0.27, this model underestimated
the global irradiance by approximately 8% for air mass equal to 1. This model is extremely
simple but does not have a good method of treating aerosol transmittance [1] [2]. Davies and
Hay (1978) used a model where the input parameters are: solar constant, zenith angle, surface
pressure, ground albedo, precipitable water vapor, total ozone, aerosol single scattering ratio
(0.85 recommended), and broadband aerosol transmittance. The model uses a look-up table
for the Rayleigh scattering transmittance term and does not have a good method for treating
aerosol transmittance [3]. Watt (1978) takes into consideration the parameters: solar constant,
zenith angle, surface pressure, ground albedo, precipitable water vapor, total ozone, turbidity
at 0.5µm and the upper layer turbidity. The Watt model is relatively complicated and appears
to overestimate the global insolation conditions, for an air mass equal to 1, by approximately
7%. This is a complete model based on meteorological parameters. However, the upper air
turbidity required in this model is not readily available [4]. Hoyt (1978) uses the solar
constant, zenith angle, surface pressure, ground albedo, precipitable water vapor, total ozone,
turbidity at one wavelength. This model’s use of look-up tables and the requirement to
recalculate transmittance and absorption parameters for modified air mass values causes this
model to be relatively difficult to use [5]. Lacis and Hansen (1974) use in their model: solar
constant, zenith angle, surface pressure, surface temperature, ground albedo, precipitable
water vapor, total ozone. This model is extremely simple. It tends to overestimate the global
irradiance by approximately 8% at an air mass equal to 1, and it has no provisions for
calculating direct irradiance [6]. Bird et al (1980) takes into consideration the solar constant,
zenith angle, surface pressure, ground albedo, precipitable water vapor, total ozone, turbidity
at 0.5µm and/or 0.38µm, aerosols forward scattering ratio (0.84 recommended) [7]. King and
Buckius (1981) used a model of cloudy sky tested in Ibadan with two values of cloudiness
coefficient k (=1.0 and 0.75) with the case of 0.75 being superior and for which the deviations
from the data do not exceed 15% [8]. Kasten el al (1980) used a cloud-based empirical solar
radiation model which results had an error of 2.5% for the lowland sites and of 13% for the
mountain sites [9]. Angstrom-Prescott, Garg and Garg and Sivkov a sunshine-based solar

3. Contribution to the Study of Two Methods for Estimating Direct and Diffuse Solar Radiation in
Morocco at the Fès-Saïs Site
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radiation model whose empirical results had an error of 2.5% for lowland sites and of 3.4%
for the mountain sites [9]. Kasten and Czeplak used a very simple cloudy sky models based
on atmospheric transmission factors. Transmission factors are nonlinear functions of the
cosine of the zenith angle, test results in Germany presented an error of 2.5% (Bremgarten)
for lowland sites and 13% (Feldberg) for mountain sites. The model’s performance is good
for low and intermediate cloudy skies [10]. Perez et al (2002) irradiance model offers a
practical representation of solar irradiance by considering the sky hemisphere as a three-part
geometrical framework, namely, the circumsolar disc, the horizon band and the isotropic
background. This Model’s test done by Solar Energy Research Institute of Singapore « SERIS
» provides a degree of trust of 95% (error of 5%) [11][12].
We have chosen to study two different models of direct and diffuse radiation estimation;
the first model is the Barbaro et al (1977) and Davies el al (1975) model for direct and diffuse
rays respectively [13] [14], based on the kasten et al. (1980) model for the determination of
the Linke turbidity factor. The second model differs from the first by using the Ineichen and
Perez (2002) model [19], using atmospheric transmittance for the determination of
atmospheric turbidity parameter, the transmittance values will be calculated using the
Schillings et al. (2004) [15]. the year 2001 is chosen as a reference year for calculating
radiation components, the year 2001 was chosen because of the availability of meteorological
data of direct and diffuse radiation during this period.
2. THE MEASUREMENT SITE
The city of Fez is situated in the northern of Morocco (33.1580N, 4.1590W), the climate of
the city is characterized by a dry and hot summer and a cold winter, the summer temperature
may exceed 40 °C and reached less than 0 °C in winter.
Fez was chosen for this study because of the availability of experimental data conducted
in 2001 by the Moroccan direction of the weather. The data were taken from the
meteorological station of Fes-Saïs with the following coordinates (33.93°N, 4.98°O). The
uncertainty of the measuring equipment is variable according to the intensity of the incident
radiation, it varies between 1% and 10%.
3. METHODOLOGY
The direct solar radiation received on a horizontal plane is determined by the formula of
Barbaro et al (1977):
As is the normal incident radiation and the incidence coefficient, in our case we are
interested in direct radiation on a horizontal surface ( ) which leads to:
Direct solar radiation on a normal receiving plane to this radiation can be evaluated by
(Linke 1922 [16]):
As is the solar constant almost equal to 1367W / m². The value of this parameter can be
more precise by taking into account the distance of the earth away from the sun which is a
function of the order number of the day in the year with [17]:

4. Alaoui Sosse Jihad, Mohamed Tahiri
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( ( ))
J being the order number of the day in the year (1 for January 1st).
: Defined by Linke [16] as the optical Rayleigh thickness of a cloudless atmosphere,
without water vapor and without aerosols, it is determined by the following formula:
am is the relative optical air mass. The Rayleigh optical thickness is used to
determine the attenuation due to scattering only.
The simplest definition of the air mass is the relative path of a solar light beam through
the atmosphere, Kasten et Young (1989) [18] have found a precise formula of the relative air
mass and which has been widely used (Perez and Ineichen 2002 [19]).
As h is the height of the sun and z the altitude of the location.
TRL is the Linke's turbidity. We chose the method proposed by Kasten et al. (1980) which
has the advantage of being simple especially for the determination of the atmospheric
turbidity of LINKE.
The method uses as main parameter the coefficient B "Angstrom cloud coefficient" of
atmospheric turbidity which takes a value of:
• B = 0.02 for a place in the mountains
• B = 0.05 for a rural location (case of Fez-Saïs station).
• B = 0.10 for an urban place.
• B = 0.20 for an industrial site (polluted atmosphere)
Pv is the partial pressure of the water vapor (mmHg) which can be estimated by:
With Pvs is saturation vapor pressure, HR is the average relative humidity and:
Where T is the air temperature in ° C derived from the data measured by the station.
For diffuse solar radiation on a horizontal surface it is calculated with the empirical
equation of Barbaro et al (1977):
√ [ √ ]
With h the height of the sun in degree and TRL the Linke turbidity calculated with the
empirical equation proposed by Kasten without dependence of the air mass.
The second method of this work consists in determining the values of the turbidity TRL
according to the data of the atmospheric components (ozone, water vapor and aerosol)
expressed in the form of atmospheric transmittance. To calculate TRL from atmospheric data,
we use the following formulation described by Ineichen and Perez (2002) [19] with:

5. Contribution to the Study of Two Methods for Estimating Direct and Diffuse Solar Radiation in
Morocco at the Fès-Saïs Site
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( ( ) )
( )
And normal direct radiation to clear sky:
The calculation of the transmission coefficients and the atmospheric input data used are
described below. Each atmospheric transmission coefficient is calculated separately using
the atmospheric input data. All equations for calculating clear sky transmittances are
described in Iqbal (1983) [20] [21] [22].
4. RESULTS AND DISCUSSION
The results analyzed below (figures 1 and 2) correspond to the evolution during the day of
06/08/2001 of the direct radiation is diffuse "measured by the synoptic station and simulated
by the empirical formulas proposed in the first case of the model of Kasten "in true solar time
on a horizontal surface of the station.
Figure 1 Evolution of direct solar radiation on a measured and simulated horizontal surface of
06/08/2001 in the synoptic station of Fez-Saïs.
Figure 2 Evolution of diffuse solar radiation on a measured and simulated horizontal surface of
06/08/2001 in the synoptic station of Fez-Saïs.
0
100
200
300
400
500
600
700
800
900
0 2 4 6 8 10 12 14 16 18 20 22 24
W/m²
Solar Time
R²=0,97
RMSE=124
W/m²
NRMSE=15%
Kasten
0
50
100
150
200
250
300
350
400
0 2 4 6 8 10 12 14 16 18 20 22 24
W/m²
Solar Time
R²=0,93
RMSE=28,7 W/m²
NRMSE=17%
Kasten
Model

6. Alaoui Sosse Jihad, Mohamed Tahiri
http://www.iaeme.com/IJCIET/index.asp 1669 editor@iaeme.com
The simulated and measured results shown in Figures 1 and 2 show good agreement for
both direct and diffuse radiation, with an average squared error [RMSE] of 28.7W / m²
(NRMSE [normalized squared error]= 17%) for diffuse radiation and 124W / m² (NRMSE =
15%) for direct radiation. The adequacy of the results at almost 16% of error for the two
components comes in particular from the constant value of the atmospheric turbidity during
the day (TRL = 4.8) knowing that such a constraint varies according to the meteorological
conditions (cloud, temperature, aerosol ...) which also justifies the underestimates and
overestimations at the beginning and end of the period. We can also observe a difference
between the simulated and measured results. This shift is caused by the non-inclusion in the
Kasten model [6] of the masks due to the reliefs present on the measurement site. These
masks significantly affect the profile of the radiation especially at the beginning and end of
the day when the sun's height is very low. From the results previously presented, the Kasten
model determines to almost 84% accuracy direct and diffuse solar radiation.
The results of the evolution during the year 2001 of the direct and diffuse "measured and
simulated" radiation in true solar time on a horizontal surface of the Fes-Saïs synoptic station
are presented in both figures 3 and 4. significant difference between the measured direct and
diffuse horizontal radiation and those simulated by the Kasten simplifier model is noted. The
mean squared error is 51W / m² (NRMSE = 27.4%) for diffuse radiation and 178.7W / m²
(NRMSE = 20.2%) for direct radiation. The Kasten model gives an average error of almost
24% for both components.
Figure 3 Annual variation of measured and simulated horizontal direct radiation during the year 2001
using the Kasten model.
During the winter period there is a large difference between measurements and simulation
results, this difference is due to the nature of the model of Kasten, which is determined in
clear sky conditions, unsuitable for the winter period. For the summer period the results are in
good order according to the low atmospheric turbulence "clear sky model: no cloud" over this
period. The following figure presents the annual variation of diffuse radiation during the year
2001 for the synoptic station of Fez-Saïs and data simulated by the simplified formula of
Kasten.
It should be noted that the agreement is less in comparison to that obtained for direct
radiation. This is an indication that diffuse radiation is at the origin of atmospheric turbidity in
the Kasten model. In order to improve the performance of the radiative model for the winter
period, the most advanced model of Ineichen and Perez (2002) is used for the calculation of
the atmospheric turbidity parameter (Linke). Simulated and measured results presented in
0
100
200
300
400
500
600
700
800
900
1000
1
256
511
766
1021
1276
1531
1786
2041
2296
2551
2806
3061
3316
3571
3826
4081
4336
4591
4846
5101
5356
5611
5866
6121
6376
6631
6886
7141
7396
7651
7906
8161
8416
8671
W/m²
Solar Time
R²=0,75
RMSE=178,5
W/m²
NRMSE=20,2%
Kasten Model

7. Contribution to the Study of Two Methods for Estimating Direct and Diffuse Solar Radiation in
Morocco at the Fès-Saïs Site
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Figures 5 and 6 show good agreement for both direct and diffuse radiation during all
simulated year with a standard deviation of 32W / m² (NRMSE = 8%) for diffuse radiation
and 55W / m² (NRMSE = 6%) for direct radiation. The adequacy of the results to almost 7%
of error for the two components comes in particular from the precision of the experimental
forcing data used as the entry of the model representing the various meteorological factors
(cloud, temperature, aerosol ...) leading to the variable atmospheric turbidity during the year.
Figure 4 Annual change in the horizontal diffuse radiation measured and simulated during 2001 by
using the simplified model of Kasten
An overestimation of the two direct and diffuse radiation explained by the monthly mean
value taken into account for the four atmospheric parameters, the optical thickness, the
aerosol and the ozone layer, the water vapor and the cloud index. From the results previously
presented, the model then determines to almost 93% of accuracy the measured data of direct
and diffuse solar radiation.
Figure 5 Annual variation of measured and simulated horizontal diffuse radiation during 2001 using
the advanced model (Ineichen and Perez 2002).
0
50
100
150
200
250
300
350
400
1
256
511
766
1021
1276
1531
1786
2041
2296
2551
2806
3061
3316
3571
3826
4081
4336
4591
4846
5101
5356
5611
5866
6121
6376
6631
6886
7141
7396
7651
7906
8161
8416
8671
W/m²
Solar Time
R²=0,77
RMSE= 51
W/m²
Kasten Model
0
50
100
150
200
250
300
350
400
1
256
511
766
1021
1276
1531
1786
2041
2296
2551
2806
3061
3316
3571
3826
4081
4336
4591
4846
5101
5356
5611
5866
6121
6376
6631
6886
7141
7396
7651
7906
8161
8416
8671
W/m²
Solar Time
R²=0,95
RMSE=55W/m²
NRMSE=6%
Perez Model

8. Alaoui Sosse Jihad, Mohamed Tahiri
http://www.iaeme.com/IJCIET/index.asp 1671 editor@iaeme.com
The model shows good consistency with the experience, except for some days where the
difference becomes important , given the average monthly value of the transmittance used.
The following figure shows the variation of the horizontal direct radiation measured and
simulated throughout the year 2001. The model has a good consistency with the experiment,
with a RMSE of 32W / m² and a normalized squared error of 8%.
Figure 6 Annual variation of measured and simulated horizontal direct radiation during 2001 using the
advanced model (Ineichen and Perez 2002)
The model has a good consistency with the experiment, except for some days because of
the average value of transmittance for the ozone layer and the aerosol. For the summer period
the results are in good agreement with the low atmospheric turbulence during this period and
the accuracy of the model by the integration of forcing parameters.
The above results allow us to conclude on the validity of the approach used to calculate
the components of direct and diffuse solar radiation. However, the method used requires the
integration of several satellite data in order to improve the performance of the calculations by
forcing parameters, better describing the optical character of the atmosphere.
The next table shows the summary of the results obtained for the both methods :
Table 1 Normalized error (NRMSE) for the both model (Kasten and perez) and for both the diffuse
and direct radiation.
Perez et al 2002 Kasten 1980
Direct radiation 8% 20,2%
Diffuse radiation 6% 27,4%
5. CONCLUSION AND PERSPECTIVE
In this work, two different methods of estimating the two direct and diffuse components of
solar radiation are studied. The first method is based on a perfectly empirical technique for
calculating the parameter of atmospheric turbidity (Kasten et al. (1980)), this method has led
to an average annual mean squared error of 27% and 20% for diffuse and direct radiation
respectively, the latter method represents the disadvantage of not to reconcile the state of the
local atmosphere of the site.
0
100
200
300
400
500
600
700
800
900
1000
1
252
503
754
1005
1256
1507
1758
2009
2260
2511
2762
3013
3264
3515
3766
4017
4268
4519
4770
5021
5272
5523
5774
6025
6276
6527
6778
7029
7280
7531
7782
8033
8284
8535
W/m²
Solar Time
R²=0,95
RMSE=32W/m²
NRMSE=8%
Perez Model

9. Contribution to the Study of Two Methods for Estimating Direct and Diffuse Solar Radiation in
Morocco at the Fès-Saïs Site
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The second method is based on a semi-empirical technique for calculating the parameter
of atmospheric turbidity (Perez et al. 2002), while integrating atmospheric forcing data, this
method led to normalized mean squared errors of latter method represents the advantage of
7% and 8% for the diffuse and direct rays respectively, and the advantage of considering the
state of the local atmosphere of the investigated site.
The Perez model is therefore the most practical in the modeling of solar irradiation with
an average error of 7.5% between the two direct and diffuse components, it proves to be the
best model to use for Morocco to model the solar irradiation. Overall solar exposure in the
country. The chosen model will also be used for the realization of urban scale predictions and
will play the role of an input radiative model for microclimate simulations carried out in
Morocco [23] [24] as well as thermodynamic simulations of buildings [25].
As a work perspective, it would be important for the next studies to make a comparison
between a wide range of radiative models such as the Gaussian, sunshine duration and cosine
models [26] [27].
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