A new modelling approach intended to develop maps of annual solar irradiation and comparative study using satellite data of M. R. Yaiche, A. Bouhanik, S. M. A. Bekkouche, and T. Benouaz

Citation: Journal of Renewable and Sustainable Energy 8, 043702 (2016); doi: 10.1063/1.4958993 View online: http://dx.doi.org/10.1063/1.4958993 View Table of Contents: http://scitation.aip.org/content/aip/journal/jrse/8/4?ver=pdfcov Published by the AIP Publishing

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A new modelling approach intended to develop maps of annual solar irradiation and comparative study using satellite data of Algeria M. R. Yaiche,1 A. Bouhanik,1 S. M. A. Bekkouche,2,a) and T. Benouaz3 1Centre de Developement des Energies Renouvelable CDER, Route de l’observatoire, Bouzareah, 16340 , Algeria 2Unite de Recherche Appliquee en Energies Renouvelables, URAER, Centre de Developpement des Energies Renouvelables, CDER, 47133 Gharda€ıa, Algeria 3Laboratory of Automatic, University of , BP. 119, R.p. 13000 Tlemcen, Algeria (Received 30 October 2015; accepted 2 July 2016; published online 15 July 2016)

Solar irradiation is the main potential energy source used in various processes. An accurate estimation of solar irradiation becomes a challenge due to the unavailability of weather data in Algeria. Therefore, an operated model can offer an important alternative for calculating the solar irradiation including the minimum of the input data. The present study derives a simple model from a review of our previously published work. It aims to develop a new approach for the estimation of the global irradiation on the horizontal plane only based on the measured sunshine duration. Maps of solar energy are required by many system designs; for this reason, it is mandatory to draw the global solar irradiation maps for Algeria for all types of sky. Algebraic relative errors were used as indicators of the agreement between the experimental and the calculated global irradiation. It has been proved that the highest intensity of the solar irradiation is located around the area of and , whereas the less intense area extends from zone to , and more exactly in around 7 longitude. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4958993]

I. INTRODUCTION Solar irradiation research is an interesting field due to its various applications in the solar field. It is worthy to mention that in many different areas of the world, the most commonly en- countered examples are: solar thermal power plant, thermal engineering for buildings, solar electric power generation, solar lighting and solar pumping systems. The optimum start-up of these installations is directly connected to the ideal choice of the solar field location, which plays a crucial role for the success of these technologies. However, solar resource assessment is the difficult task, faced by all the fields of the solar industry, either photovoltaic or thermal so- lar. In some industrial and commercial fields, solar energy applications require an accurate esti- mation of solar irradiation using various climatic parameters.1 Climate conditions in Algeria are favourable for the development of solar energy due to the abundant sunshine throughout the year, especially in the region.2 As a first approximation, the intensity of the direct irradiation evolves during the passage through the atmosphere as a decreasing exponential atmospheric mass. In fact, this law is rea- sonably checked if each irradiation wavelength will be taken separately. To determine the solar irradiation relative to an atmosphere, it remains to introduce a parameter named Linke turbidity factor that is related to the sunshine duration.3–5

a)Author to whom correspondence should be addressed. Electronic mail: [email protected]. Present address: URAER, B.P. 88, ZI, Gart Taam, Gharda€ıa 47000, Algeria. Tel.: 213 661 31 76 29. Fax: 213 29 87 01 52.

1941-7012/2016/8(4)/043702/18/$30.008, 043702-1 Published by AIP Publishing.

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The intensity of the solar irradiation at a given location depends on the latitude, terrain, sea- son, time of day, and atmospheric conditions. A literature review on relevant research works conducted to conclude that several techniques have been developed to estimate solar irradiation from the measured sunshine duration data. Estimation of global solar irradiation from sunshine duration is a common procedure used in solar energy engineering. The results obtained in Ref. 6 show the useful relationship of solar maps for concentrating solar power and for grid-connected photovoltaic technology in Vietnam. In the same context, Park et al.7 conducted a study on the spatial distribution of solar irradiation in South Korea, an empirical model is developed to calcu- late the solar irradiation from topographic characteristics and sunshine durations data. However, Behar et al.8 have introduced an additional accuracy factor for predicting solar irradiation in Algeria, this method provides satisfactory results and was considered as one of the most suitable for estimating the global solar irradiation. Another relevant work carried out by Chelbi et al.,9 shows the utility of linear and nonlinear regression models for the calculation of the monthly and annual mean daily global solar irradiation in Tunisia. They found that by approaching the south, it reaches maximum values in the vicinity of the Gulf of Gabes. After that, Mecibah el al.10 have devoted a part of their research work to indicate the excellent fitting between the glob- al solar irradiation and sunshine duration. They have been selected and generalized a best model for global solar irradiation estimation on a horizontal surface for solar applications usages in the absence of the measured solar data. Indeed, Messen has drawn descriptive maps of Algeria from the computed solar irradiations. The study shows that the annual average solar irradiation is more marked by the astronomical factors whereas the monthly irradiation is rather dependent on the meteorological phenomena.11 Another paper12 provides an investigational study to estimate the solar irradiation by an another empirical model based on a soft computing technique, named support vector regression. As expected in Refs. 13–19, in order to inspect the effective correla- tion of solar irradiation, a series of simulations were performed and several factors were studied such as the relationship between direct and anisotropic diffuse irradiation and the apparent radi- ance of cloud. This contribution is an extension of different relevant works published last year, attempted to draw global solar irradiation maps for Algeria for all types of sky. The incident solar irradia- tion on a horizontal surface was determined using a new modelling approach based only on the measured sunshine duration. The originality of this work is the calculation of the solar radiation received on a horizontal surface for clear skies without calculating the direct and diffuse solar radiation (new approach). The adopted approach for determining cloud cover according to the insolation fraction “to calculate the global solar radiation received on a horizontal surface for different types of sky” is a simple method that allows anyone to draw solar map of his own country, even if the country belongs to the Northern hemisphere. The predicted results will be compared to the measured data in the goal to validate the modelling approach, once validated, these data can then be used to draw the solar map covering the entire Algerian territory.

II. ESTIMATION OF GLOBAL SOLAR IRRADIATION UNDER CLEAR-SKY This section is devoted to the determination of the solar irradiation in various , officially the People’s Democratic Republic of Algeria. It is a country in Northern Africa on the Mediterranean coast. Algeria ranges in latitude from 18.96 to 37.09 north, and in longitude from 8.68 west to 11.95 east. Its capital and most populous city is Algiers. It consists of 48 provinces and 1541 communes. With a population exceeding 37 million, it is the 34th most populated country on Earth.20 The Algerian climate is influenced by two preponder- ant seasonal factors. The first factor concerns the important solar irradiation on a great part of the country which leads to a thermal depression in the desert zone. The second factor is related to the intertropical front which creates an edge of nebulosity at the south of the country when this front goes up northwards.21 Referring to its geographical situation, Algeria is located in the highest solar reservoir region in the world. The insolation time over the quasi-totality of the na- tional territory exceeds 2000 h annually and may reach 3900 h (high plains and Sahara). The daily obtained energy on a horizontal surface of 1 m2 is of 5 kW h over the major part of the

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national territory, or about 1700 kW h/m2/year for the North and 2263 kW h/m2 year for the South of the country.20 For these reasons, the solar irradiation is an ample source of energy in Algeria which could be developed. The solar irradiation analysis tools are commonly based on the calculation of the solar irra- diation outside the atmosphere, its intensity before entering the atmosphere and the various con- stituents thereof. We also present the various changes undergone by this irradiation across the atmosphere.

A. Determining equations The solar constant is the amount of energy flow received by a unit surface. In our case, the 2 value that was selected is 1980 I0 ¼ 1367 W/m . The distance Earth-Sun is flexible due to the elliptical path of the sun; for this consequence, it is assumed that the correction in Earth-Sun distance is given by the following equation:22  360 C ¼ 1 þ 0:034 cos ðÞj 2 : (1) ts 365

The corrected solar constant is defined as

I ¼ I0 Cts; (2)

Ct-s is the Earth–sun distance correction and j is the Day number ranging from 0 to 365. Throughout the atmosphere, the solar irradiation is attenuated by the atmosphere through absorption, scattering, and reflection. These phenomena are caused by gas molecules, water va- por, and solid or liquid atmospheric particles known as “aerosols.” This attenuation depends on the number, size, and nature of molecules and encountered particles. It also varies with the path length of the solar irradiation through the Earth’s atmosphere (is defined as the air mass). This length is characterized by what is called the atmospheric mass or the optical air mass. After un- dergoing various extinctions during the entering, the atmosphere solar irradiations reach the ground as beam and diffuse irradiation whose total components constitute the total global irradiation. In our approach, we will calculate the horizontal daily global irradiation without using di- rect and diffuse irradiation. The calculation of solar irradiation outside the atmosphere at 12 TSV is given by the following equation:23

G0hj12h ¼ I sinðhÞj12h: (3)

The general equation to calculate the sinðhÞj12h is as follows:

sinðhÞ¼sinðuÞ sinðdÞþcosðuÞ cosðdÞ cosðAHÞ: (4)

In our case, we are interested only in calculating sinðhÞ at 12 TSV (TSV: apparent solar time (hour)). For Algeria:

TSV ¼ TU þ Et þ Cl; (5)

TU ¼ TL–1; (6)

where TU is the universal time (h), TL is the local time (h), Et is the equation of time (min), and Cl is the longitude correction (min). At 12 TSV, AH ¼ 0 therefore cos(AH) ¼ 1

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Equation (4) becomes

sinðhÞj12h ¼ sinðuÞ sinðdÞþcosðuÞ cosðdÞ; (7)

where sinðhÞj12h is the height of the sun at 12 TSV, u is the latitude in degrees, and d is the declination of the sun in degrees  360 d ¼ 23:45 sin ðÞ284 þ j : (8) 365

The daily solar irradiation outside atmosphere is calculated by the following equations:23,24

Gout d ¼ 1:09 G0hj12h ð0:5SS0 þ 1Þ; (9)  2 SS0 ¼ a cos – tanðÞu tanðÞd ; (10) 15

where SS0 is the sunshine duration (measured in hours). The daily global irradiation received on a horizontal surface under clear-sky is calculated as follows:22–24

0:86 Ghcc ¼ Gout d–ðT Gout d Þ: (11)

Perrin de Brichambaut is based on the calculation of T due to the absorption by atmospheric gases (O2,CO2, and O3) and molecular diffusion of Rayleigh given by the following approach:22

T ¼ 0:89 Z: (12)

In our case, according to the previous equations and following a very recent database (from 2008 to 2014), we found that we can have better results for Algeria if we use the following approach: T ¼ 0:79 Z: (13)

This new approach can provide better results than previous works.23,24 Z is the altitude in kilo- metres and T is the atmospheric trouble due to the absorption by atmospheric gases (O2,CO2, and O3) and molecular diffusion of Rayleigh.

B. Comparison of results In order to verify our approach entrusted to the calculation of the global irradiation incident on a horizontal surface for clear skies, our results were compared to those concluded by Perrin Brichambaut.23,24 The Linke turbidity factor is a key point in this model, equations have been used in a research work published in 2010 (Refs. 23–26) dealing with the estimation of the global irradiation at any inclination and orientation of different types of skies. It allows to calculate the direct and diffuse components of the incident global radiation. Absorption and diffusion caused by constituents of the atmosphere may be expressed by this factor. The atmospheric turbidity coeffi- cient was decomposed into three auxiliary trouble factors: the trouble due to absorption by water vapor, the trouble due to the Rayleigh molecular diffusion, and the trouble due to the aerosol dif- fusion. The validated model has yielded good results especially for a horizontal plane. However, the approach used in this work is based on a very easy method estimating the daily solar irradia- tion on any plane at any given time. The model based on the Linke turbidity factor was calibrated by the measured points; these points are defined according to the climatic zones of the region. The mesh (or grid) points are spaced at 10 km. The test of this approach will be carried out by deter- mining the corresponding algebraic relative error, which is given by

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j G –G j Err ¼ hc PB hc AP ; (14) Ghc AP

Ghc_PB is the daily global irradiation incident on a horizontal surface which is obtained through the theoretical approach of Perrin Brichambaut and Ghc_AP is the daily global irradiation inci- dent on a horizontal surface calculated with the proposed model. The daily and annual global irradiation incidents on a horizontal surface for Gharda€ıa, Tamanrasset, Bechar, Bouzareah, National Meteorology Office (ONM) Algiers, and sta- tion are presented in Tables I and II The maximum and minimum values of the relative algebraic error on the daily global irradia- tion incident on a horizontal surface are indicated with dark and light shading, respectively. For all stations, the reported results can be used with a monthly annual average error less than 1.62% and an average error ranging from 0.06% until 5.75%. The theoretical approach of Perrin Brichambaut has been validated in the previous work;23–25 accordingly, from these obtained results, we once again confirm the reliability of this approach especially for a horizontal surface.

III. ESTIMATION OF SOLAR IRRADIATION FOR ALL TYPES OF SKY A. Methodology To calculate the total solar irradiation on a horizontal surface for different types of skies, we will first determine the cloud cover according to the sunshine fraction. We can write the sunshine fraction given by Equation (11) in the form below26

SS r ¼ ; (15) SS0

SS is the measured sunshine duration (hours) and SS0 is the calculated sunshine duration in TSV (hours). The usefulness of using cloud cover, in conjunction with sunshine duration, in predicting total solar irradiation and plotting solar maps has been demonstrated.26

Cn ¼ 1 – r; (16)

where Cn is the cloud cover. Then, we determine the direct and diffuse solar irradiation received on a horizontal surface for a completely clear sky. To calculate the daily horizontal direct irradiation under a clear sky, the following new formula has been used:23–25 0:9 Shcc ¼ Gout d – ðTGout d Þ: (17)

B. Comparison of results To check the quality of our approach devoted to the estimation of the horizontal direct irradi- ation valid for a clear sky, we will adopt the same approach used for the horizontal global irradia- tion. Perrin Brichambaut model will remain as the reference model. The algebraic relative error is a valuable index in this case to test the proposed approach applied to Algerian sites as follows: j S –S j Err ¼ hc PB hc AP ; (18) Shc AP

Shc_PB is the daily direct irradiation received on a horizontal surface calculated by the theoreti- cal approach of Perrin Brichambaut and Shc_AP is the daily direct irradiation received on a hori- zontal surface calculated by the appropriate model. The daily direct irradiation incident on a horizontal surface, calculated by both the theoreti- cal approach of Perrin Brichambaut and the proposed model for the same stations is given in Tables III and IV.

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TABLE I. Representing the daily global irradiation incident on a horizontal surface and the calculation of the relative alge- braic error for the following Saharan provinces: Gharda€ıa, Tamanrasset, and Bechar. (The maximum and minimum values of the relative algebraic error on the daily global irradiation incident on a horizontal surface are indicated by dark and light shading, respectively.)

Site

Latitude Longitude Altitude Month Ghc_PB Ghc_AP Err

Gharda€ıa 32.38 3.81 450 January 3976 4038 0.0156 February 5186 5114 0.0139 Mars 6513 6373 0.0215 April 7738 7605 0.0172 May 8397 8380 0.0020 June 8556 8693 0.0160 July 8337 8547 0.0252 August 7746 7945 0.0257 September 6714 6911 0.0293 October 5464 5633 0.0309 November 4228 4398 0.0402 December 3632 3768 0.0374 Annual average 6374 6450 0.0120

Tamanrasset 22.78 5.51 1378 January 5567 5571 0.0007 February 6620 6527 0.0140 Mars 7655 7541 0.0149 April 8470 8388 0.0097 May 8788 8799 0.0013 June 8780 8909 0.0147 July 8648 8834 0.0215 August 8347 8537 0.0228 September 7711 7891 0.0233 October 6799 6932 0.0196 November 5776 5885 0.0189 December 5235 5315 0.0153 Annual average 7366 7427 0.0083

Bechar 31.63 2.25 806 January 4221 4269 0.0114 February 5439 5356 0.0153 Mars 6760 6617 0.0212 April 7970 7835 0.0169 May 8615 8588 0.0031 June 8763 8887 0.0142 July 8557 8745 0.0220 August 7984 8163 0.0224 September 6968 7147 0.0257 October 5727 5875 0.0258 November 4482 4632 0.0335 December 3870 3995 0.0323 Annual average 6613 6676 0.0095

We also note that the algebraic relative error on the daily irradiation is generally small. The numbers in dark and light shading, respectively, are the maximum and minimum values of Err with relative errors in the range of 0.15%–6.67%. The annual average daily direct irradia- tion can be used with an error less than 0.53% and an average error ranging from 0.08% to

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TABLE II. Representing the daily global irradiation incident on a horizontal surface and the calculation of the relative alge- braic error for the following coastal regions: Oran and Algiers. (The maximum and minimum values of the relative algebra- ic error on the daily global irradiation incident on a horizontal surface are indicated by dark and light shading, respectively.)

Site

Latitude Longitude Altitude Month Ghc_PB Ghc_AP Err

Bouzareah Algiers 36.8 3 345 January 3366 3436 0.0208 February 4608 4557 0.0111 Mars 6057 5920 0.0226 April 7470 7328 0.0190 May 8288 8276 0.0014 June 8556 8689 0.0155 July 8293 8507 0.0258 August 7550 7757 0.0274 September 6337 6541 0.0322 October 4941 5123 0.0368 November 3622 3812 0.0525 December 3022 3163 0.0467 Annual average 6009 6092 0.0139

ONM Algiers 36.68 3.22 25 January 3268 3346 0.0239 February 4485 4437 0.0107 Mars 5902 5767 0.0229 April 7276 7138 0.0190 May 8065 8060 0.0006 June 8316 8462 0.0176 July 8055 8285 0.0286 August 7330 7555 0.0307 September 6150 6371 0.0359 October 4790 4989 0.0415 November 3510 3712 0.0575 December 2928 3080 0.0519 Annual average 5840 5934 0.0161

Oran 35.63 0.60 90 January 3429 3499 0.0204 February 4639 4585 0.0116 Mars 6032 5895 0.0227 April 7368 7230 0.0187 May 8123 8115 0.0010 June 8350 8494 0.0172 July 8098 8324 0.0279 August 7408 7628 0.0297 September 6266 6483 0.0346 October 4935 5129 0.0393 November 3667 3863 0.0534 December 3085 3232 0.0476 Annual average 5950 6040 0.0151

0.52%. In this setup, we are interested in calculating the annual direct irradiation. After this process, we deduct the annual average daily diffuse irradiation received on a horizontal surface; which is given by the following expression:

Dhcc ¼ Ghcc – Shcc: (19)

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IV. RELEVANT FACTORS OF TYPES OF SKY Sky cover gives the amount of cloud cover at a particular time, it is expressed in octas. Our classification method uses the octas unit as a basic criterion to achieve the classification of the solar irradiance and to yield different types of days. The fraction of the sky that is obscured by clouds is in eighths: one octa means that one eighth of the sky is obscured, two octas that

TABLE III. Indicative table representing the daily direct irradiation incident on a horizontal surface and the calculation of the relative algebraic error for the following Saharan provinces: Gharda€ıa, Tamanrasset, and Bechar. (The numbers in dark and light shading represent, respectively, the maximum and minimum values of Err with relative errors in the range of 0.15–6.67 %.)

Site

Latitude Longitude Altitude Month Shc_PB Shc_AP Err

Gharda€ıa 32.38 3.81 450 January 3481 3429 0.0149 February 4588 4353 0.0512 Mars 5779 5436 0.0594 April 6808 6497 0.0457 May 7299 7165 0.0184 June 7343 7435 0.0125 July 7097 7309 0.0299 August 6571 6790 0.0333 September 5713 5898 0.0324 October 4662 4799 0.0294 November 3620 3738 0.0326 December 3136 3198 0.0198 Annual average 5508 5504 0.0008

Tamanrasset 22.78 5.51 1378 January 5058 4941 0.0231 February 6048 5795 0.0418 Mars 6995 6700 0.0422 April 7688 7457 0.0300 May 7907 7824 0.0105 June 7834 7923 0.0114 July 7676 7856 0.0234 August 7405 7590 0.0250 September 6867 7013 0.0213 October 6079 6156 0.0127 November 5183 5222 0.0075 December 4721 4714 0.0015 Annual average 6622 6599 0.0034

Bechar 31.63 2.25 806 January 3747 3692 0.0147 February 4871 4640 0.0474 Mars 6070 5742 0.0540 April 7106 6807 0.0421 May 7603 7467 0.0179 June 7654 7729 0.0098 July 7421 7604 0.0247 August 6906 7094 0.0272 September 6044 6205 0.0266 October 4979 5094 0.0231 November 3908 4009 0.0258 December 3398 3454 0.0165 Annual average 5809 5795 0.0024

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TABLE IV. Indicative table representing the daily direct irradiation incident on a horizontal surface and the calculation of the relative algebraic error for the following coastal regions: Oran and Algiers. (The numbers in dark and light shading rep- resent, respectively, the maximum and minimum values of Err with relative errors in the range of 0.15–6.67 %.)

Site

Latitude Longitude Altitude Month Shc_PB Shc_AP Err

Bouzareah Algiers 36.8 3 345 January 2908 2893 0.0052 February 4038 3847 0.0473 Mars 5335 5011 0.0607 April 6529 6216 0.0479 May 7161 7028 0.0186 June 7283 7383 0.0137 July 6998 7226 0.0326 August 6348 6584 0.0372 September 5335 5542 0.0388 October 4160 4330 0.0409 November 3053 3213 0.0524 December 2564 2661 0.0378 Annual average 5143 5161 0.0036

ONM Algiers 36.68 3.22 25 January 2778 2757 0.0076 February 3875 3670 0.0529 Mars 5127 4785 0.0667 April 6261 5938 0.0516 May 6844 6715 0.0188 June 6934 7054 0.0173 July 6646 6904 0.0388 August 6022 6289 0.0443 September 5061 5293 0.0458 October 3945 4132 0.0474 November 2900 3063 0.0562 December 2437 2536 0.0406 Annual average 4903 4928 0.0052

Oran 35.63 0.60 90 January 2929 2898 0.0106 February 4026 3811 0.0534 Mars 5260 4914 0.0658 April 6364 6041 0.0508 May 6921 6788 0.0192 June 6996 7106 0.0157 July 6717 6966 0.0371 August 6120 6377 0.0420 September 5187 5409 0.0428 October 4091 4268 0.0433 November 3051 3204 0.0501 December 2586 2675 0.0344 Annual average 5021 5038 0.0035

one quarter is obscured, and so on. The purpose, therefore, is to present the sky by a circle di- vided into eight equal parts. It is an approximate value given by eye judgement. In the case of our work, we need the extreme case of cloudiness. We denote by Ni the di- rect cloudiness factor and by Nd the diffuse cloudiness factor. The values of the cloudiness fac- tor are summarised26 in Table V.

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TABLE V. Cloudiness factor corresponding to the different types of skies.

Octas Type of sky NI ND Octas Type of sky NI ND

0 Completely clear sky 1 1 4 Moderately cloudy sky 0.5000 2.0000 4/5 0.4792 2.0208 0/1 Clear sky 0.9792 1.0208 4/5 Cloudy sky 0.4583 2.0417 0/1 0.9583 1.0417 4/5 0.4375 2.0625 0/1 0.9375 1.0625 4/5 0.4167 2.0833 0/1 0.9167 1.0833 4/5 0.3958 2.1042 0/1 Partly cloudy sky 0.8958 1.1042 5 0.3750 2.1250 1 0.8750 1.1429 5/6 0.3542 2.1458 1/2 0.8542 1.1637 5/6 0.3333 2.1667 1/2 0.8333 1.1845 5/6 0.3125 2.1875 1/2 0.8125 1.2054 5/6 0.2917 2.2083 1/2 0.7917 1.2262 5/6 0.2708 2.2292 1/2 0.7708 1.2470 6 0.2500 2.2500 2 0.7500 1.3333 6/7 0.2292 2.2708 2/3 0.7292 1.3542 6/7 0.2083 2.2917 2/3 0.7083 1.3750 6/7 0.1875 2.3125 2/3 0.6875 1.3958 6/7 0.1667 2.3333 2/3 0.6667 1.4167 6/7 0.1458 2.3542 2/3 0.6458 1.4375 7 Very cloudy sky 0.1250 2.3750 3 0.6250 1.6000 7/8 0.1042 2.3958 3/4 0.6042 1.6208 7/8 0.0833 2.4167 3/4 0.5833 1.6417 7/8 0.0625 2.4375 3/4 0.5625 1.6625 7/8 0.0417 2.4583 3/4 0.5417 1.6833 7/8 0.0208 2.4792 3/4 0.5208 1.7042 8 Covered sky 0 2.5

The daily global irradiation incident on a horizontal surface for a completely covered sky corresponds to a cloudiness of 8 octas. The equations have been used in a research work published in Refs. 25 and 26 dealing with the estimation of the daily global irradiation (at any inclination and orientation) of differ- ent types of skies. Shcc and Dhcc represent, respectively, the daily direct and diffuse irradiation received on a horizontal plane for a completely clear sky. The global irradiation received on a horizontal plane is represented by the following equation:

Ghcouv ¼ Shcc Ni þ Dhcc Nd: (20)

Knowing that for a completely covered sky, Ni ¼ 0 and Nd ¼ 2.5, the relationship below is pre- sented as follows:

Ghcouv ¼ 2:5Dhcc: (21) The daily global irradiation received on a horizontal plane for different types of skies given by Equation (18) is calculated as

Ghttc ¼ð1 – CnÞðGhcc – GhcouvÞþ Ghcouv: (22)

V. ANNUAL SOLAR IRRADIATION MAP OF ALGERIA We first estimate the annual average of daily global irradiation received on a horizontal surface using the annual average of the measured daily sunshine duration. The question relates to the identification of a typical day to calculate the annual and monthly average daily global

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irradiation received on a horizontal surface for a completely clear sky. We then calculate the al- gebraic relative error for each month according to the annual global irradiation,

j G – G j Err ¼ hc ha ; (23) Gha

2 Ghc is the monthly average of daily global irradiation received on a horizontal plane (Wh/m ) and Gha is the annual average of daily global irradiation received on a horizontal plane for a to- tally clear sky (Wh/m2).

TABLE VI. Estimation of the nearest average monthly global irradiation compared to the average annual global irradiation for Gharda€ıa, Tamanrasset, and Bechar province. (Shaded values indicate the monthly error value that corresponds most closely to the annual error value.)

Site

Latitude Longitude Altitude Month Ghc Gha Err

Gharda€ıa 32.38 3.81 450 January 4038 6450 0.3740 February 5114 0.2072 Mars 6373 0.0120 April 7605 0.1790 May 8380 0.2991 June 8693 0.3477 July 8547 0.3250 August 7945 0.2317 September 6911 0.0714 October 5633 0.1267 November 4398 0.3182 December 3768 0.4159

Tamanrasset 22.78 5.51 1378 January 5571 7427 0.2499 February 6527 0.1212 Mars 7541 0.0153 April 8388 0.1293 May 8799 0.1847 June 8909 0.1995 July 8834 0.1894 August 8537 0.1494 September 7891 0.0624 October 6932 0.0667 November 5885 0.2077 December 5315 0.2844

Bechar 31.63 2.25 806 January 4269 6676 0.3605 February 5356 0.1977 Mars 6617 0.0088 April 7835 0.1737 May 8588 0.2864 June 8887 0.3312 July 8745 0.3100 August 8163 0.2228 September 7147 0.0706 October 5875 0.1199 November 4632 0.3061 December 3995 0.4016

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TABLE VII. Estimation of the nearest average monthly global irradiation compared to the average annual global irradia- tion for Oran and Algiers. (Shaded values indicate the monthly error value that corresponds most closely to the annual error value.)

Site

Latitude Longitude Altitude Month Ghc Gha Err

Bouzareah Algiers 36.8 3 345 January 3436 6092 0.4360 February 4557 0.2520 Mars 5920 0.0283 April 7328 0.2028 May 8276 0.3584 June 8689 0.4262 July 8507 0.3963 August 7757 0.2732 September 6541 0.0736 October 5123 0.1591 November 3812 0.3743 December 3163 0.4808

ONM Algiers 36.68 3.22 25 January 3346 5934 0.4361 February 4437 0.2522 Mars 5767 0.0281 April 7138 0.2030 May 8060 0.3584 June 8462 0.4261 July 8285 0.3963 August 7555 0.2733 September 6371 0.0737 October 4989 0.1592 November 3712 0.3744 December 3080 0.4809

Oran 35.63 0.60 90 January 3499 6040 0.4207 February 4585 0.2409 Mars 5895 0.0240 April 7230 0.1971 May 8115 0.3436 June 8494 0.4063 July 8324 0.3782 August 7628 0.2630 September 6483 0.0734 October 5129 0.1508 November 3863 0.3604 December 3232 0.4649

Tables VI and VII summarize the astronomical coordinates of these six stations as well as the annual and monthly averages of the daily global irradiation on a horizontal plane. The smallest relative error is found in March for any given site. To calculate the average annual global irradiation received on a horizontal surface, we retain the 15th of each month as a typical day for a clear sky.26 Table VIII summarises the results for the stations of Tamanrasset, Bouzareah CDER- Algiers, Dar El Beida ONM-Algiers, Bechar, URAER-Ghardaia, and Oran-Senia and reports some examples to test the effectiveness of our approach. We designed by:

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TABLE VIII. Indicative table representing: latitude, longitude, altitude, annual average of the measured daily sunshine du- ration, annual average of the daily global irradiation and their relative error values.

Altitude SS Ghm Ghc Site Latitude Longitude (m) Years (h) (Wh/m2) (Wh/m2) Err

Tamanrasset 22.78 Nord 5.51 Est 1378 1976–1983 9.12 6457 6584 0.0193 Tamanrasset 22.78 Nord 5.51 Est 1378 1973–1974 9.56 7073 6800 0.0401 CDER-Bouzareah 36.80 Nord 3.00 Est 345 1986–1989 7.19 4352 4702 0.0744 CDER-Bouzareah 36.80 Nord 3.00 Est 345 2011–2012 7.20 4459 4705 0.0523 ONM Dar El Beida 36.68 Nord 3.22 Est 25 1972–1974 7.35 4838 4706 0.0280 Bechar 31.50 Nord 2.25 Ouest 809 1972–1974 9.56 6369 6224 0.0233 URAER-Ghardaia 32.40 Nord 3.80 Est 468 2009–2010 9.13 5949 5723 0.0395 Oran-Senia 35.63 Nord 0.60 Ouest 90 1982–1984 7.89 4952 5024 0.0143

SS is the annual average of the measured daily sunshine duration (hours). Ghm is the annual average of the measured daily global irradiation received on a horizontal surface (Wh/m2). Ghc is the annual average of the daily global irradiation on a horizontal surface, calculated using our proposed model (Wh/m2). Err is the algebraic relative error. For several years, we found that the agreement between the results and the measured results is acceptable; the relative error is less than 7.45%. The principle aim of this work is to develop the annual solar map of the global irradiation received on a horizontal surface using the annual average of the measured daily sunshine dura- tion. To do this, the interval between latitude contours is 0.2 and it is also fixed at 0.5 for the longitude (Fig. 1). It is well known that the National Meteorology Office (ONM) has only 64 astronomical sta- tions measuring this parameter (sunshine duration). The methodology consists, first, of exploiting positions of these stations, and then drawing the map of Algeria. The idea is to use the average of the sunshine duration according to the area color and by swiping the map of Algeria from 19.00 to 37.00 for discretized latitude with an interval of 0.2 and from 8.50 to 11.50 for discretized longitude with an interval of 0.5. As a result, we could have 2137 points instead of 64. From these geographical coordinates, we calculate the annual average of the global irradiation received on a horizontal surface, while taking into account the altitudes for each geographical point. By follow- ing this reasoning, we then will compare our results with satellite data: “SOLAR-MED-ATLAS,” “Meteotest Global dataset 8 km,” and “Global NASA SSE 1 Degree 2008.”27 In order to draw the solar irradiation map for Algeria, this previous method was imple- mented for calculating the mean annual global irradiation on the horizontal plane and their rela- tive error values. Solar maps allow to generate quantifiable outputs that can modify the deci- sions made by official governments and the general public. In this context, Table IX is a database that defines latitude, longitude, altitude, and average annual sunshine duration mea- sured during the period from 2002 to 2011 for 64 stations. It can be translated into solar map

FIG. 1. Extreme case of cloudiness: (a) completely clear sky and (b) completely covered sky.

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TABLE IX. Database-values for: latitude, longitude, altitude, and average annual sunshine duration measured within the period from 2002 to 2011.

SS SS No. Sites Latitude Longitude Altitude measured No. Sites Latitude Longitude Altitude measured

01 Dellys Afir 36.92 3.95 8 7.60 33 Mascara Gh. 35.22 0.15 511 8.57 02 Skikda 36.88 6.90 2 7.29 34 Tlemcen Z. 35.20 1.47 246 8.20 03 Annaba 36.83 7.80 3 7.80 35 S.B.Abbes 35.20 0.62 475 8.40 04 port 36.82 5.88 6 7.65 36 Chellala 35.17 2.32 800 8.09 05 Jijel Airport 36.80 5.88 8 7.53 37 Saida 34.87 0.15 750 8.14 06 Bejaia aer. 36.72 5.07 2 7.43 38 Maghnia 34.82 1.78 427 8.34 07 36.70 4.05 188 7.25 39 34.80 5.73 82 9.11 08 B. Bouarrerridj 36.70 4.77 928 8.29 40 Mechria 34.52 0.28 1149 8.25 09 Alger D.E.B 36.68 3.22 25 7.69 41 34.33 3.38 1180 8.07 10 Bouharoun 36.67 2.63 5 7.06 42 El Kheiter 34.15 0.07 1000 8.08 11 Tenes 36.50 1.33 17 7.45 43 33.70 6.08 87 9.32 12 36.47 7.47 227 7.62 44 33.67 1.00 1341 8.26 13 Bouira 36.38 3.88 555 7.65 45 33.50 6.78 64 9.07 14 Ain Bessem 36.32 3.53 748 8.03 46 Naama 33.27 0.30 1166 8.34 15 Miliana 36.30 2.23 715 7.95 47 Hassi Rmel 32.93 3.30 764 9.47 16 Constantine 36.28 6.62 693 7.59 48 IN SAFRA 32.77 0.60 1058 8.75 17 36.28 7.97 680 7.67 49 Ghardaia 32.40 3.80 468 9.50 18 Medea 36.28 2.73 1030 7.87 50 31.93 5.40 144 8.90 19 36.20 1.33 143 8.25 51 H.Messaoud 31.67 6.15 142 9.63 20 Setif 36.17 5.32 1007 8.14 52 Bechar 31.50 2.25 809 9.52 21 35.88 0.12 137 8.23 53 El GOLEA 30.57 2.87 397 9.12 22 O.E.Bouaghi 35.87 7.12 889 7.80 54 Beni Abbes 30.13 2.17 550 9.53 23 Arzew 35.82 0.27 3 7.19 55 29.25 0.28 312 9.72 24 Batna 35.75 6.32 822 7.96 56 28.50 9.63 561 9.48 25 35.73 0.53 95 7.49 57 Adrar 27.82 0.18 279 9.26 26 Msila 35.67 4.50 441 8.38 58 27.70 8.17 443 9.51 27 Oran Senia 35.63 0.60 90 8.30 59 27.23 2.50 268 9.63 28 Khenchella 35.47 7.08 983 6.96 60 26.50 8.42 558 9.44 29 Tebessa 35.42 8.12 821 8.02 61 Djanet 24.27 9.47 968 9.77 30 35.35 1.47 977 8.15 62 Tamanrasset 22.80 5.43 1362 8.92 31 Barika 35.33 5.33 460 7.94 63 B.B.Mokhtar 21.33 0.95 397 7.75 32 Beni Saf 35.30 1.35 68 8.11 64 19.57 5.77 400 7.75

of Algeria that defines the distribution of the measured average annual sunshine duration (Figure 2). For all maps and in order to perform different interpolations, we use SURFER software. In areas with marked relief, it is possible to observe a forming fog along the slopes, there- by leaving an unobstructed valley. This occurs when a low wind pushes the warm moist air from the valley to the assault relief. Cloud formations grow from the moisture evaporation of the earth’s surface and then concentrate on relief according to the instability of the air mass. Cloudiness helps to differentiate heights, mid-slopes, and down landscapes. The importance of hanging clouds confers one part of characteristics of high landscapes, bright in early morning and then veiled in clouds rest of the day. The role of the relief map is to give mainly a felt im- pression for solar potential at all scales (see Figure 3). Solar maps have a considerable importance in the field of design of solar power systems. With these maps, we can adopt an optimum solar installation. In Figure 4, we managed to de- velop solar irradiation map which means the creation of illustrations revealing the geographical distribution of solar irradiation.

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FIG. 2. The average annual of the measured daily sunshine duration, the period from 2002 to 2011.

FIG. 3. Relief map (altitudes) for Algeria.

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FIG. 4. Estimation of the mean annual global irradiation on the horizontal plane.

It has been concluded that the highest intensity of the solar irradiation is generally located around the area of Djanet and Tamanrasset. In parallel, the less intense area is generally located between Skikda and Annaba. We confirm the same remarks reported in the article published previously in 2014;26 these results are strongly agreed with the measured sunshine duration. Table X is a database that defines latitude, longitude, altitude, the mean annual global irra- diation on the horizontal plane and relative error. Therefore, in accordance with the method de- scribed above and based on the calculation of the relative algebraic error, we can compare the results with the satellite data denoted by GHI(1) is the predicted value of the mean annual global irradiation on a horizontal plane from Meteotest Global dataset 8 km satellite. GHI(2) is the predicted value of the mean annual global irradiation on a horizontal plane from SOLAR-MED-ATLAS satellite. GHI(3) is the predicted value of the mean annual global irradiation on a horizontal plane from Global NASA SSE 1Degree 2008 satellite. GHI is the value of the mean annual global irradiation calculated on a horizontal plane by our approach. Erri is the algebraic relative error

j GHIi–GHI j Erri ¼ : (24) GHI The best way to identify the amount of solar irradiation at a given site is to install pyranome- ters. Therefore, providing an intensive swiping of Algerian solar map which includes 2137 sta- tions requires heavy investment because the operation is very expensive. The solar potential study through the sky modelling allowed us to know better the solar map of Algeria and conse- quently presents a preferred solution.

VI. CONCLUSION This work deals with a semi-empirical model, derived to estimate the mean annual global irradiation on the horizontal plane and contains two main important results.

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TABLE X. Database-values for: latitude, longitude, the mean annual global irradiation on the horizontal plane within the period from 2002 to 2011, and the calculated relative error.

Latitude Longitude GHI GHI (1) Relative GHI (2) Relative GHI (3) Relative 2 2 2 2 degrees degrees kWh/m kWh/m error Err1% kWh/m error Err2% kWh/m error Err3%

36.6 3.0 1767 1750 1.0 1761 0.3 1770 0.2 36.8 8.0 1741 1700 2.4 1726 0.9 1799 3.3 35.6 0.5 1883 1900 0.9 1861 1.2 1770 6.0 35.0 2.0 1974 2000 1.3 2050 3.9 1719 12.9 33.4 7.0 2004 2150 7.3 1923 4.0 1901 5.1 33.6 1.0 2042 2100 2.8 2126 4.1 1887 7.6 32.4 4.0 2097 2250 7.3 2029 3.2 1956 6.7 31.6 2.0 2272 2200 3.2 2140 5.8 1964 13.6 27.8 0.0 2229 2300 3.2 2149 3.6 2081 6.6 26.4 8.5 2234 2300 3.0 2253 0.9 2110 5.6 21.2 1.5 2074 2250 8.5 2253 8.6 2234 7.7 19.6 5.5 2148 2300 7.1 2304 7.3 2332 8.6 22.8 5.5 2337 2250 3.7 2423 3.7 2256 3.5 24.2 9.5 2393 2300 3.9 2285 4.5 2245 6.2 27.6 8.0 2315 2300 0.6 2202 4.9 2077 10.3 29.0 5.0 2167 2300 6.1 2110 2.6 2128 1.8 23.4 2.5 2180 2300 5.5 2262 3.8 2128 2.4 25.2 0.5 2221 2250 1.3 2180 1.8 2099 5.5 34.8 1.5 1976 2000 1.2 1948 1.4 1938 1.9 32.6 0.5 2127 2200 3.4 2124 0.1 1891 11.1

• A new modelling approach including simplified equations has been proposed to calculate the global solar irradiation received on a horizontal plane for any type of sky, taking into account only the measured sunshine duration. The correlation may then be used for any stations for dif- ferent geographical characteristics where the solar data are not available. These results allow also to draw global solar irradiation maps which can be used as a database for future invest- ments in the solar sector in Algeria. • With these simple calculations, anyone who wants to draw the solar map of his country can do it easily even if it belongs into the northern hemisphere. Overall, the comparison between the measured and the computed results was very satisfac- tory, the agreement is acceptable; values of the relative error summarised in tables reflect these findings. Through this study and the literatures, several research works have revealed that Algeria is covered by a highest solar potential. Our results fit with the preliminary annual Algerian solar map for the horizontal global irradiation set out in Refs. 27–29. The south region of Algeria has a greater solar potential than other regions, the highest intensity of the solar irradiation is located around the area of Djanet and Tamanrasset, whereas the less intense area extends from Skikda zone to Annaba, and more exactly in around 7 of longitude.

ACKNOWLEDGMENTS The authors thank Dr. S. M. Boudia (Researcher at CDER) for providing an altitudes database for each geographic point and his support.

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