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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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 1, Issue 1, January 219, pp , Article ID: IJCIET_1_1_152 Available online at ISSN Print: and ISSN Online: 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 Department of Process Engineering, Mohammadia School of Engineers, Mohammed V University of Rabat, Morocco 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 (198) 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 (2) model using atmospheric transmittance for the determination of the atmosphere turbidity, the transmittance values will be calculated using the Schillings et al. (4) model. Comparing the two models applied to the case of Morocco resulted in the decision that the model of Ineichen and Perez (2) 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:, 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) 1(1), 219, pp 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 editor@iaeme.com

2 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.1 at.5µm. For turbidity near.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 (.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.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 (198) takes into consideration the solar constant, zenith angle, surface pressure, ground albedo, precipitable water vapor, total ozone, turbidity at.5µm and/or.38µm, aerosols forward scattering ratio (.84 recommended) [7]. King and Buckius (1981) used a model of cloudy sky tested in Ibadan with two values of cloudiness coefficient k (=1. and.75) with the case of.75 being superior and for which the deviations from the data do not exceed 15% [8]. Kasten el al (198) 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 editor@iaeme.com

3 Contribution to the Study of Two Methods for Estimating Direct and Diffuse Solar Radiation in Morocco at the Fès-Saïs Site 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 [1]. Perez et al (2) 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. (198) model for the determination of the Linke turbidity factor. The second model differs from the first by using the Ineichen and Perez (2) model [19], using atmospheric transmittance for the determination of atmospheric turbidity parameter, the transmittance values will be calculated using the Schillings et al. (4) [15]. the year 1 is chosen as a reference year for calculating radiation components, the year 1 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 (33.158N, 4.159W), the climate of the city is characterized by a dry and hot summer and a cold winter, the summer temperature may exceed 4 C and reached less than C in winter. Fez was chosen for this study because of the availability of experimental data conducted in 1 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 1%. 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]: editor@iaeme.com

4 ( ( )) 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 2 [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. (198) 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 =.2 for a place in the mountains B =.5 for a rural location (case of Fez-Saïs station). B =.1 for an urban place. B =.2 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 (2) [19] with: editor@iaeme.com

5 Contribution to the Study of Two Methods for Estimating Direct and Diffuse Solar Radiation in Morocco at the Fès-Saïs Site ( ( ) ) ( ) 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) [2] [21] [22]. 4. RESULTS AND DISCUSSION The results analyzed below (figures 1 and 2) correspond to the evolution during the day of 6/8/1 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 R²=,97 RMSE=124 NRMSE=15% Kasten Figure 1 Evolution of direct solar radiation on a measured and simulated horizontal surface of 6/8/1 in the synoptic station of Fez-Saïs R²=,93 RMSE=28,7 NRMSE=17% Kasten Model Figure 2 Evolution of diffuse solar radiation on a measured and simulated horizontal surface of 6/8/1 in the synoptic station of Fez-Saïs editor@iaeme.com

6 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 1 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 = 2.2%) for direct radiation. The Kasten model gives an average error of almost 24% for both components R²=,75 RMSE=178,5 NRMSE=2,2% Kasten Model Figure 3 Annual variation of measured and simulated horizontal direct radiation during the year 1 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 1 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 (2) is used for the calculation of the atmospheric turbidity parameter (Linke). Simulated and measured results presented in editor@iaeme.com

7 Contribution to the Study of Two Methods for Estimating Direct and Diffuse Solar Radiation in Morocco at the Fès-Saïs Site 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. 35 R²=,77 RMSE= 51 Kasten Model Figure 4 Annual change in the horizontal diffuse radiation measured and simulated during 1 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. 35 R²=,95 RMSE=55 NRMSE=6% Perez Model Figure 5 Annual variation of measured and simulated horizontal diffuse radiation during 1 using the advanced model (Ineichen and Perez 2) editor@iaeme.com

8 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 1. The model has a good consistency with the experiment, with a RMSE of 32W / m² and a normalized squared error of 8% R²=,95 RMSE=32 NRMSE=8% Perez Model 6 5 Figure 6 Annual variation of measured and simulated horizontal direct radiation during 1 using the advanced model (Ineichen and Perez 2) 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 2 Kasten 198 Direct radiation 8% 2,2% 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. (198)), this method has led to an average annual mean squared error of 27% and 2% 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 editor@iaeme.com

9 Contribution to the Study of Two Methods for Estimating Direct and Diffuse Solar Radiation in Morocco at the Fès-Saïs Site The second method is based on a semi-empirical technique for calculating the parameter of atmospheric turbidity (Perez et al. 2), 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]. REFERENCES [1] Atwater, M. A.; Ball, J. T. "A Numerical Solar Radiation Model Based on Standard Meteorological Observations" Solar Energy. Vol. 21: pp [2] Atwater, M. A.; Ball, J. T. Solar Energy. Vol. 23: p [3] Davies, J. A.; Hay, J. E. "Calculation of the Solar Radiation Incident on a Horizontal Surface." Proceedings, First Canadian Solar Radiation Data Workshop. [4] Watt, D. On the Nature and Distribution of Solar Radiation. HCP/T U.S. Department of Energy. [5] Hoyt, D. V. "A Model for the Calculation of Solar Global Insolation." Solar Energy. Vol. 21: pp, [6] Lacis, A. L.; Hansen, J. E. "A Parameterization for Absorption of Solar Radiation in the Earth's Atmosphere. " J. Atmospheric Science. Vol. 31: pp, [7] Bird, R. E.; Hulstrom, R. E. Direct Insolation Models. SERI! TR Golden, CO: Solar Energy Research Institute. [8] F.J.K. Ideriah, 'A Model for Calculating Direct and Diffuse Solar Radiation', Solar Energy, Vol. 26, pp , [9] Iziomon M.G., Mayer H. Performance of solar radiation model4s-a case study. Agric. For. Meteorol. 1;11:1 11. [1] Viorel Badescu, Alexandru Dumitrescu. New models to compute solar global hourly irradiation from point cloudiness. Energy Conversion and Management, Volume 67, March 213, Pages [11] Dazhi Yang, Zhen Ye, André M. Nobre, Hui Du,... Thomas Reindl. Bidirectional irradiance transposition based on the Perez model. Solar Energy, Volume 11, December 214, Pages [12] A New Airmass Independant formulation for the Linke Turbidity Coefficient. Perez, P. Ineichen and R , s.l. : Solar Energy, 2, Vol. 73(3). [13] An atmospheric model for computing direct and diffuse solar radiation. Barbaro, S. et al. 35 4, s.l. : Solar Energy, 1977, Vol. 6 (1). [14] Estimating global solar radiation. Davies, J.A., Schertzer, W., Nunez, M., , s.l. : Boundary-Layer Meteorol, 1975, Vol. 9 (1) editor@iaeme.com

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