# Development of a Daily Databank of Solar Radiation Components for Moroccan Territory

Authors: Mohammed Benchrifa; Hajar Essalhi; Rachid Tadili; Mohammed N. Bargach; Abdellah Mechaqrane
Journal: International Journal of Photoenergy
 (2019)

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## Abstract

The main objective of this work is to create a daily updated database that includes all components of solar radiation, either energetic or spectral radiation. This will lead us to quantify the Moroccan solar potential and to determine the dimensions of all types of solar thermal and photovoltaic systems. Consequently, the obtained database will be the fundamental support for engineers, designers, and all organizations interested in developing solar systems, in different regions throughout Morocco. It will also be a basic tool for researchers in modelling and simulating the new solar systems. Firstly, we used one year’s worth of measurements of the different components of the solar radiation, provided by the National Meteorological Department, to establish the extrapolation equations between the global radiation at the reference site and the global radiation of twenty-eight other sites. As well as with the same measurements, we developed the correlation equations between the global solar radiation and the other solar radiation components. Secondly, from ten years of Fez station’s daily global radiation measurements and through the extrapolation equations, we were able to estimate the global radiation of all Moroccan cities. Then, by using the obtained global radiation data and the correlation equations, we predicted the other components of solar radiation. Subsequently, with a new measurement campaign carried out on several sites, we validated the estimation models by using the usual statistical indicators. In addition, we compared our results with those obtained by other estimation models. The resulting differences for each solar component display the advantage of our model with errors under 6%. To facilitate the use of our results, we compiled them into maps representing the spread of solar radiation across Morocco.


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## Body

## 1. Introduction

The various applications of solar energy developed in recent years have increased the need for solar radiation component data. However, in most cases, there are not enough stations covering the entire country, and the existing stations do not measure all energetic and spectral components of solar radiation.To remedy this problem, several works using different prediction models have been developed to estimate these solar components around the world. Among these models, we can cite physical models, empirical models [1–3], artificial neural network models [4–7], hybrid models using a combination of several methods [8, 9], and the models based on the satellite images data [10, 11]. Thus, the physical models are based on physical parameters, which estimates the global radiation from insolation duration [12, 13], meteorological variables [14, 15], and spatial variables [16] in different sky conditions [17, 18]. Also, this model predicts the diffuse solar radiation [19] from the global radiation [20], the insolation duration [21], or the clarity index [22, 23] in different climatic zones [21] and in different sky conditions [24, 25]. However, the same parameters have been used to predict the direct [26], inclined [27] solar radiation and spectral solar components [28, 29].This work aims at establishing a solar data bank of energetic components (Hj, Hbj, Hdj, and Hβj) and spectral components (HUVT, HPAR, and HIR) all over Morocco. However, this work will be completed in two main steps as follows:
(i)
First step: we will establish the extrapolation equations to estimate the global solar radiation. Then, we will develop the correlation equations to estimate the other solar radiation components
(ii)
Second step: we will use the obtained extrapolation equations to generate the global solar radiation for twenty-eight sites from reference station data. Then, we will bring together the correlation equations and the estimated global radiation to generate the solar energetic and solar spectral componentThe obtained results will be subject to a validity test, by comparing them with the measurements collected in available stations. In addition, we will compare our results with those obtained by other estimation models [7, 30–34].Finally, all results will be presented in maps [35–38] showing all over Morocco.


## 2. Review of Solar Component Estimation Models

All solar energy conversion systems require knowledge of the solar radiation component measurements. However, in most cases, these measures are not available. For this reason, several studies have been carried out for estimating the components of solar radiation from different variables such as the duration of insolation, the fraction of insolation, and the coefficient of clarity.


### 2.1. Global Solar Radiation Estimation Models

The simplest model for estimating solar radiation is the linear model developed by Angstrom and after revised by Prescott. This model establishes a direct relationship between the global solar radiation and the insolation fraction [39].The Angstrom-Prescott model is as follows:(1)Kt=a+bσ,where a and b are empirically determined regression constants.Based on the linear model, several studies have been performed to predict global solar radiation. Among these models, we can cite the models in Table1.Table 1
Linear models for estimating daily global solar radiation.
Estimation models
Equations
R
Regions
Lemmini’s model [32]
Kt=0.25+0.49 σ
0.92
Beni-Mellal, Morocco
Bargach’s model [31]
Kt=0.27+0.5 σ
0.9
Rabat, Morocco
Nfaoui’s model [33]
Kt=0.26+0.52 σ
0.93
Rabat, Morocco
Zou et al.’s model [7]
Kt=0.208+0.559 σ
0.91
Tengchong, ChinaOther models have been developed such as the quadratic model and cubic model. Among these models, we can mention the models in Table2.Table 2
Quadratic and cubic models for estimating daily global solar radiation.
Estimation models
Equations
R
Region
Ben Kaddour’s model [34]
Kt=0.18+0.83 σ - 0.31 σ2
0.93
Casablanca, Morocco
Zou et al.’s model [7]
Kt=0.185+0.587σ+0.037 σ2 - 0.032 σ3
0.93
Aletai, China


### 2.2. Diffuse Solar Radiation Estimation Models

The value of diffuse solar radiation constitute an important data in the study of solar conversion systems. However, several works have focused on the prediction of this component and this by using different variables such as the clarity indexKt. Among these works, we found the following:
(i)
Ben Kaddour’s model [34]
(2)Kd=0.961+0.456Kt−3.344Kt2+1.67Kt3
(ii)
Nfaoui’s model [33]
(3)Kd=0.98,Kt<0.1,−1.48Kt2+0.15kt+0.98,Kt≥0.1,R=0.93
(iii)
Wang et al.’s model, Injinagaui, China [25]
(4)Kd=14.7924Kt4−23.95Kt3+11.1612Kt2−2.4767Kt+1.1665,R=0.88


## 2.1. Global Solar Radiation Estimation Models

The simplest model for estimating solar radiation is the linear model developed by Angstrom and after revised by Prescott. This model establishes a direct relationship between the global solar radiation and the insolation fraction [39].The Angstrom-Prescott model is as follows:(1)Kt=a+bσ,where a and b are empirically determined regression constants.Based on the linear model, several studies have been performed to predict global solar radiation. Among these models, we can cite the models in Table1.Table 1
Linear models for estimating daily global solar radiation.
Estimation models
Equations
R
Regions
Lemmini’s model [32]
Kt=0.25+0.49 σ
0.92
Beni-Mellal, Morocco
Bargach’s model [31]
Kt=0.27+0.5 σ
0.9
Rabat, Morocco
Nfaoui’s model [33]
Kt=0.26+0.52 σ
0.93
Rabat, Morocco
Zou et al.’s model [7]
Kt=0.208+0.559 σ
0.91
Tengchong, ChinaOther models have been developed such as the quadratic model and cubic model. Among these models, we can mention the models in Table2.Table 2
Quadratic and cubic models for estimating daily global solar radiation.
Estimation models
Equations
R
Region
Ben Kaddour’s model [34]
Kt=0.18+0.83 σ - 0.31 σ2
0.93
Casablanca, Morocco
Zou et al.’s model [7]
Kt=0.185+0.587σ+0.037 σ2 - 0.032 σ3
0.93
Aletai, China


## 2.2. Diffuse Solar Radiation Estimation Models

The value of diffuse solar radiation constitute an important data in the study of solar conversion systems. However, several works have focused on the prediction of this component and this by using different variables such as the clarity indexKt. Among these works, we found the following:
(i)
Ben Kaddour’s model [34]
(2)Kd=0.961+0.456Kt−3.344Kt2+1.67Kt3
(ii)
Nfaoui’s model [33]
(3)Kd=0.98,Kt<0.1,−1.48Kt2+0.15kt+0.98,Kt≥0.1,R=0.93
(iii)
Wang et al.’s model, Injinagaui, China [25]
(4)Kd=14.7924Kt4−23.95Kt3+11.1612Kt2−2.4767Kt+1.1665,R=0.88


## 3. Data Description

### 3.1. Used Data

The Laboratory of Solar Energy and the Environment (LESE) of Mohammed V University of Rabat, Morocco, has, since 2008, a network of five measuring stations installed in Rabat, Fez, Tangier, Tetouan, and Marrakech. These stations measure all components of solar radiation and climatic variables such as the following:(i)
Energy components: global, diffuse, and direct solar radiation, as well as the overall inclined plane
(ii)
Spectral components: ultraviolet, infrared, and synthetically active light solar radiation
(iii)
Climatic variables: ambient temperature, relative humidity, wind speed, wind direction, and precipitationIn addition to these measures, the National Meteorological Department has made available to us one year of climatic variables and solar component measurements for 29 stations of the national network.Table3 represents the geographical data of the measuring stations’ locations.Table 3
The geographical data of the measuring stations’ locations [40].
Measuring station
Latitude (°) Φ
Longitude (°)λ
Altitude (m)
Agadir
30.38
-9.57
18
Al-Hoceima
35.18
-3.83
12
Beni-Mellal
32.37
-6.4
468
Bouarfa
32.52
-1.95
1100
Casa
33.57
-7.67
56
Dakhla
23.77
-15.93
10
El Jadida
33.23
-8.52
27
Essaouira
31.52
-9.78
7
Ifran
33.5
-5.17
1663
Kenitra
34.3
-6.6
5
Laayoun
27.17
-13.22
63
Larache
35.18
-6.13
46
Marrakech
31.62
-8.03
463
Meknes
33.88
-5.53
548
Midelt
32.68
-4.73
1508
Nador
35.15
-2.92
7
Nousar
33.37
-7.57
200
Ouarzazate
30.93
-6.9
1136
Oujda
34.78
-1.93
465
Errachidia
31.93
-4.4
1037
Safi
32.28
-9.23
43
Sidi Ifni
29.37
-10.18
49
Sidi Sliman
34.23
-6.05
51
Tangier
35.72
-5.75
15
Tantan
28.6
-11.08
229
Taza
34.22
-4
509
Tetouan
35.57
-5.33
5
Rabat
34
-6.83
75


### 3.2. Acquisition of Data

For each station, the following instruments record the measurements of the different components of the solar radiation [41]:
(i)
The Kipp & Zonen brand SP-Lite pyranometer for global solar radiation measurements (2% accuracy). The same type of instrument was used to measure the diffuse radiation, but with a sun visor strip to hide the direct radiation
(ii)
Pyrheliometer mounted on a follower type Eppley model NIP 31820 E6 to measure direct solar radiation (accuracy 0.5%)
(iii)
Total Ultraviolet Radiometer (TUVR) model, type Eppley for measuring the total solar ultraviolet radiation (accuracy 2%)
(iv)
Radiometer model NIP 31820 E6, type Eppley, for the measurement of radiation infrared (precision 0.5%)
(v)
Quantum sensor SKP215, type Campbell Scientific for the measurement of photosynthetically active radiation PAR (accuracy 0.5%)
(vi)
Anemometer equipped with a wind vane model wind monitor 05103, type Campbell Scientific, for the measurement of wind speed and direction (accuracy 0.25%)
(vii)
Temperature and relative Humidity Probe HMP45C, manufactured for Campbell Scientific by Vaisala (temperature accuracy 0.2%, humidity accuracy 1%)
(viii)
Rain Gauge ARG100, manufactured by Environmental Measurements for Campbell Scientific, to measure precipitation (accuracy 4%)


### 3.3. Storing Data

All instruments mentioned before are connected to a data acquisition unit (CR10X) with a storage module. Using a computer program, we integrate the measurements collected every 5 seconds over an hour. The obtained hourly values are stored in the raw data files. Then the raw data files are processed and tested to detect and eliminate erroneous values and replace some missing values. In the end, the hourly values are integrated to obtain the daily values.


### 3.4. Characteristics and Description of the Reference Site

The Fez station has been selected as a reference site because of its central geographical location. This city is known as the cultural capital of Morocco (33° 56′N, Longitude 4° 99′W, elevation 579 m) characterized by a seasonal climate, cold and rainy during winter, dry and warm during summer, and mild during spring and autumn [42].The radiometric station was placed at the top of the Faculty of Science and Technology of Fez’s building. The site of the station is completely clear of any shadow effect.Statistical analysis of this station’s data shows a very small percentage of missing or erroneous data (15 erroneous or missing values over 250 390 measured values or 0.006%) throughout the 10-year measurement period (2009-2018).


## 3.1. Used Data

The Laboratory of Solar Energy and the Environment (LESE) of Mohammed V University of Rabat, Morocco, has, since 2008, a network of five measuring stations installed in Rabat, Fez, Tangier, Tetouan, and Marrakech. These stations measure all components of solar radiation and climatic variables such as the following:(i)
Energy components: global, diffuse, and direct solar radiation, as well as the overall inclined plane
(ii)
Spectral components: ultraviolet, infrared, and synthetically active light solar radiation
(iii)
Climatic variables: ambient temperature, relative humidity, wind speed, wind direction, and precipitationIn addition to these measures, the National Meteorological Department has made available to us one year of climatic variables and solar component measurements for 29 stations of the national network.Table3 represents the geographical data of the measuring stations’ locations.Table 3
The geographical data of the measuring stations’ locations [40].
Measuring station
Latitude (°) Φ
Longitude (°)λ
Altitude (m)
Agadir
30.38
-9.57
18
Al-Hoceima
35.18
-3.83
12
Beni-Mellal
32.37
-6.4
468
Bouarfa
32.52
-1.95
1100
Casa
33.57
-7.67
56
Dakhla
23.77
-15.93
10
El Jadida
33.23
-8.52
27
Essaouira
31.52
-9.78
7
Ifran
33.5
-5.17
1663
Kenitra
34.3
-6.6
5
Laayoun
27.17
-13.22
63
Larache
35.18
-6.13
46
Marrakech
31.62
-8.03
463
Meknes
33.88
-5.53
548
Midelt
32.68
-4.73
1508
Nador
35.15
-2.92
7
Nousar
33.37
-7.57
200
Ouarzazate
30.93
-6.9
1136
Oujda
34.78
-1.93
465
Errachidia
31.93
-4.4
1037
Safi
32.28
-9.23
43
Sidi Ifni
29.37
-10.18
49
Sidi Sliman
34.23
-6.05
51
Tangier
35.72
-5.75
15
Tantan
28.6
-11.08
229
Taza
34.22
-4
509
Tetouan
35.57
-5.33
5
Rabat
34
-6.83
75


## 3.2. Acquisition of Data

For each station, the following instruments record the measurements of the different components of the solar radiation [41]:
(i)
The Kipp & Zonen brand SP-Lite pyranometer for global solar radiation measurements (2% accuracy). The same type of instrument was used to measure the diffuse radiation, but with a sun visor strip to hide the direct radiation
(ii)
Pyrheliometer mounted on a follower type Eppley model NIP 31820 E6 to measure direct solar radiation (accuracy 0.5%)
(iii)
Total Ultraviolet Radiometer (TUVR) model, type Eppley for measuring the total solar ultraviolet radiation (accuracy 2%)
(iv)
Radiometer model NIP 31820 E6, type Eppley, for the measurement of radiation infrared (precision 0.5%)
(v)
Quantum sensor SKP215, type Campbell Scientific for the measurement of photosynthetically active radiation PAR (accuracy 0.5%)
(vi)
Anemometer equipped with a wind vane model wind monitor 05103, type Campbell Scientific, for the measurement of wind speed and direction (accuracy 0.25%)
(vii)
Temperature and relative Humidity Probe HMP45C, manufactured for Campbell Scientific by Vaisala (temperature accuracy 0.2%, humidity accuracy 1%)
(viii)
Rain Gauge ARG100, manufactured by Environmental Measurements for Campbell Scientific, to measure precipitation (accuracy 4%)


## 3.3. Storing Data

All instruments mentioned before are connected to a data acquisition unit (CR10X) with a storage module. Using a computer program, we integrate the measurements collected every 5 seconds over an hour. The obtained hourly values are stored in the raw data files. Then the raw data files are processed and tested to detect and eliminate erroneous values and replace some missing values. In the end, the hourly values are integrated to obtain the daily values.


## 3.4. Characteristics and Description of the Reference Site

The Fez station has been selected as a reference site because of its central geographical location. This city is known as the cultural capital of Morocco (33° 56′N, Longitude 4° 99′W, elevation 579 m) characterized by a seasonal climate, cold and rainy during winter, dry and warm during summer, and mild during spring and autumn [42].The radiometric station was placed at the top of the Faculty of Science and Technology of Fez’s building. The site of the station is completely clear of any shadow effect.Statistical analysis of this station’s data shows a very small percentage of missing or erroneous data (15 erroneous or missing values over 250 390 measured values or 0.006%) throughout the 10-year measurement period (2009-2018).


## 4. Presentation of the Method

This work aims at establishing a solar data bank of energetic components (Hj, Hbj, Hdj, and Hβj) and spectral components (HUVT, HPAR, and HIR) all over Morocco. However, this work will be completed in two main steps: firstly, we used one year’s worth of measurements of the different components of the solar radiation, provided by the National Meteorological Department, to establish the extrapolation equations between Fez’s global radiation and the global radiation of twenty-eight other sites. As well as with the same measurements, for each sites, we developed the correlation equations between the global solar radiation and the other solar radiation components. Secondly, from ten years of Fez station’s daily global radiation measurements and through the extrapolation equations, we were able to estimate the global radiation of all Moroccan cities. Then, by using the obtained global radiation data and the correlation equations, we predicted the other components of solar radiation Hj,Hbj,Hdj,Hβj,HUVT,HPAR,andHIR.Thus, we have been able to build a database of different components of solar radiation over ten years for the 29 Moroccan sites. In the end, all the obtained results were tested and validated by using a new series of measurements carried out on the five mentioned stations.


## 5. Extrapolation and Correlation Equations for Daily Solar Components

### 5.1. Extrapolation of the Daily Global Solar Irradiation

The estimation of global solar radiation can be effected by using several methods, such as the empirical model, ANN model, and satellite imagery. However, the use of these models requires knowledge of several variables and the availability of a database that spans several years. On the other hand, databases are not often available, especially for isolated sites. As a result, to remedy this problem, we developed, as part of this work, an extrapolation method to estimate the global solar radiation. Primarily, this method consists of estimating the global radiation at site where we do not have measurements, from the global radiation measured at another site.In the first step of this method, from one year of measurements of global radiation for all Moroccan sites, we looked for to establish correlation equations between the global radiation of the different sites and the global radiation of the reference site. For this, we plotted the global radiation values for each site (Hj) according to the global radiation values of Fez’s site (Hf), chosen as a reference site.The obtained shape of the cloud point led us to linear correlations of the type:(5)Hj=asiteHf+bsite.The coefficients of correlationsasite and bsite depend strongly on the geographical coordinates of the site and the status of the atmosphere [43]. Table 4 gathers the obtained values from these coefficients for all Moroccan sites.Table 4
The equations used for the global radiation extrapolation in Morocco.
Site
asite
bsite
R2
Agadir
0.79
994
0.89
Al-Hoceima
0.94
-181
0.85
Beni-Mellal
0.94
409
0.8
Bouarfa
0.81
780
0.8
Casa
0.91
322
0.82
Dakhla
0.7
1907
0.84
El Jadida
0.95
50
0.89
Essaouira
0.89
539
0.83
Ifran
0.97
-52
0.83
Kenitra
0.97
-15
0.83
Laayoun
0.8
1285
0.85
Larache
1.01
-383
0.87
Marrakech
0.9
672
0.84
Meknes
0.95
-14
0.85
Midelt
0.85
740
0.81
Nador
0.95
-214
0.85
Nousar
0.95
92
0.86
Ouarzazate
0.85
1151
0.83
Oujda
0.96
-81
0.79
Errachidia
0.76
1372
0.78
Safi
0.96
214
0.78
Sidi Ifni
0.63
1341
0.78
Sidi Sliman
0.96
-75
0.85
Tangier
0.97
-114
0.81
Tantan
0.65
1534
0.77
Taza
0.94
-29
0.85
Tetouan
1
429
0.83
Rabat
1.03
-317
0.93


### 5.2. Daily Diffuse Solar Irradiation Estimation

The diffuse component is an important factor for evaluating the performance of solar thermal or solar photovoltaic systems. However, several models, involving the clearness indexKt=Hj/H0 [44], have been made to estimate this component. Among these models, we can cite the Ruth and Chant’s model, the Collares-Pereira and Rabl’s model, and the Liu and Jordan model [45].To find the valid model for Morocco, we compared the estimated diffuse by the mentioned models with the measured diffuse. Then we concluded that the Collares-Pereira and Rabl’s model is the most adequate because it produces a minimal error that does not exceed 5%. This model is illustrated by the following equations [42]:
(6)Kd=0.99;Kt<0.17,14.648Kt4−21.856Kt3+9.473Kt2−2.272Kt+1.188;0.17≤Kt≤0.8.Knowing the diffuse solar irradiation, the direct solar irradiation can easily be inferred by the following equation [46]:
(7)Hbj=Hj−Hdj.


### 5.3. Estimation of Daily Global Solar Irradiations on an Inclined Plane

The solar flux received by an inclined surface consists of three components: a direct component from the solar disk, a diffuse component from the entire celestial vault, and a component reflected by the surrounding soil.The estimation of the direct component is completed by simple geometric transposition of the direct irradiation of a horizontal planeHbj. On the other hand, for the diffuse component, several models have been proposed for its estimation [45, 47, 48]. Consequently, an earlier study showed that the isotropic model of Liu and Jordan is the most valid for our sites [49]. Most of the cases, the reflected component is the lowest of the three components, and it is generally assumed isotropic.The general expression of the inclined daily global solar irradiation with an angleβ is given by [49]:
(8)Hβj=RbHbj+Hdj1+cosβ2+ρH1−cosβ2.directdiffusereflectedRb is the transposition factor of the direct radiation from a horizontal plane to an inclined plane. It was calculated for a south-oriented plane, by the equation as follows:
(9)Rb=cosδj⋅cosφ−β⋅sinωjβ+ωjβ⋅sinδj⋅sinφ−βcosδj⋅cosφφ⋅sinωj+ωj⋅sinδj⋅sinφ,ωjβ=minarcos−tanδj⋅tanϕ,arcos−tanδj⋅tanϕ−β,where ωjβ is the time angle of the sunset on the inclined plane.The values taken by the tilt angleβ, correspond to the characteristic inclinations relative to the latitude of each site: β=φ, β=φ+20, β=φ-20, and β=90 corresponding to the vertical facades.


### 5.4. Estimation of the Spectral Components of Solar Radiation

Some applications of solar energy require knowledge of the spectral components of solar radiation, namely, the ultraviolet component (HUVT) which is involved in the study of the atmosphere and the variations in the ozone layer thickness. The photosynthetically active component noted as HPAR (photosynthetically active radiation) intervenes during the photosynthesis process and plant development; knowing the HPAR value at various sites allows for the appropriate choice of adapted crops. Lastly, the infrared component HIR is used by satellite techniques to determine the total atmospheric column of the water vapor used by meteorology for the climate prediction [50].Based on one year’s worth of measurements of the different components of the solar radiation provided by the National Meteorological Department, we noticed that the variations of the global radiation and the spectral components, functioning in time, have the same rate. As a result, we searched correlation equations connecting the global solar radiation to the spectral solar radiation.For this, we graphed each spectral component according to the global radiation, which gave us linear equations of the formy=ax. To improve the correlation coefficients, we defined three intervals according to the meteorological state of the day characterized by its clearness index Kt [51]. The results are presented in Table 5.Table 5
Correlation equations for the daily values of the spectral components of solar radiation (Wh/m2) in function of global solar radiation H (Wh/m2) for the three sky conditions.
Clarity index intervals
Correlation equations
R2
Kt≤0.35
Huv=0.048H
0.97
HPAR=0.488H
0.99
HIR=0.46H
0.99
0.35<Kt≤0.65
Huv=0.044H
0.97
HPAR=0.484H
0.99
HIR=0.471H
0.99
Kt>0.65
Huv=0.04H
0.98
HPAR=0.478H
0.99
HIR=0.478H
0.99


## 5.1. Extrapolation of the Daily Global Solar Irradiation

The estimation of global solar radiation can be effected by using several methods, such as the empirical model, ANN model, and satellite imagery. However, the use of these models requires knowledge of several variables and the availability of a database that spans several years. On the other hand, databases are not often available, especially for isolated sites. As a result, to remedy this problem, we developed, as part of this work, an extrapolation method to estimate the global solar radiation. Primarily, this method consists of estimating the global radiation at site where we do not have measurements, from the global radiation measured at another site.In the first step of this method, from one year of measurements of global radiation for all Moroccan sites, we looked for to establish correlation equations between the global radiation of the different sites and the global radiation of the reference site. For this, we plotted the global radiation values for each site (Hj) according to the global radiation values of Fez’s site (Hf), chosen as a reference site.The obtained shape of the cloud point led us to linear correlations of the type:(5)Hj=asiteHf+bsite.The coefficients of correlationsasite and bsite depend strongly on the geographical coordinates of the site and the status of the atmosphere [43]. Table 4 gathers the obtained values from these coefficients for all Moroccan sites.Table 4
The equations used for the global radiation extrapolation in Morocco.
Site
asite
bsite
R2
Agadir
0.79
994
0.89
Al-Hoceima
0.94
-181
0.85
Beni-Mellal
0.94
409
0.8
Bouarfa
0.81
780
0.8
Casa
0.91
322
0.82
Dakhla
0.7
1907
0.84
El Jadida
0.95
50
0.89
Essaouira
0.89
539
0.83
Ifran
0.97
-52
0.83
Kenitra
0.97
-15
0.83
Laayoun
0.8
1285
0.85
Larache
1.01
-383
0.87
Marrakech
0.9
672
0.84
Meknes
0.95
-14
0.85
Midelt
0.85
740
0.81
Nador
0.95
-214
0.85
Nousar
0.95
92
0.86
Ouarzazate
0.85
1151
0.83
Oujda
0.96
-81
0.79
Errachidia
0.76
1372
0.78
Safi
0.96
214
0.78
Sidi Ifni
0.63
1341
0.78
Sidi Sliman
0.96
-75
0.85
Tangier
0.97
-114
0.81
Tantan
0.65
1534
0.77
Taza
0.94
-29
0.85
Tetouan
1
429
0.83
Rabat
1.03
-317
0.93


## 5.2. Daily Diffuse Solar Irradiation Estimation

The diffuse component is an important factor for evaluating the performance of solar thermal or solar photovoltaic systems. However, several models, involving the clearness indexKt=Hj/H0 [44], have been made to estimate this component. Among these models, we can cite the Ruth and Chant’s model, the Collares-Pereira and Rabl’s model, and the Liu and Jordan model [45].To find the valid model for Morocco, we compared the estimated diffuse by the mentioned models with the measured diffuse. Then we concluded that the Collares-Pereira and Rabl’s model is the most adequate because it produces a minimal error that does not exceed 5%. This model is illustrated by the following equations [42]:
(6)Kd=0.99;Kt<0.17,14.648Kt4−21.856Kt3+9.473Kt2−2.272Kt+1.188;0.17≤Kt≤0.8.Knowing the diffuse solar irradiation, the direct solar irradiation can easily be inferred by the following equation [46]:
(7)Hbj=Hj−Hdj.


## 5.3. Estimation of Daily Global Solar Irradiations on an Inclined Plane

The solar flux received by an inclined surface consists of three components: a direct component from the solar disk, a diffuse component from the entire celestial vault, and a component reflected by the surrounding soil.The estimation of the direct component is completed by simple geometric transposition of the direct irradiation of a horizontal planeHbj. On the other hand, for the diffuse component, several models have been proposed for its estimation [45, 47, 48]. Consequently, an earlier study showed that the isotropic model of Liu and Jordan is the most valid for our sites [49]. Most of the cases, the reflected component is the lowest of the three components, and it is generally assumed isotropic.The general expression of the inclined daily global solar irradiation with an angleβ is given by [49]:
(8)Hβj=RbHbj+Hdj1+cosβ2+ρH1−cosβ2.directdiffusereflectedRb is the transposition factor of the direct radiation from a horizontal plane to an inclined plane. It was calculated for a south-oriented plane, by the equation as follows:
(9)Rb=cosδj⋅cosφ−β⋅sinωjβ+ωjβ⋅sinδj⋅sinφ−βcosδj⋅cosφφ⋅sinωj+ωj⋅sinδj⋅sinφ,ωjβ=minarcos−tanδj⋅tanϕ,arcos−tanδj⋅tanϕ−β,where ωjβ is the time angle of the sunset on the inclined plane.The values taken by the tilt angleβ, correspond to the characteristic inclinations relative to the latitude of each site: β=φ, β=φ+20, β=φ-20, and β=90 corresponding to the vertical facades.


## 5.4. Estimation of the Spectral Components of Solar Radiation

Some applications of solar energy require knowledge of the spectral components of solar radiation, namely, the ultraviolet component (HUVT) which is involved in the study of the atmosphere and the variations in the ozone layer thickness. The photosynthetically active component noted as HPAR (photosynthetically active radiation) intervenes during the photosynthesis process and plant development; knowing the HPAR value at various sites allows for the appropriate choice of adapted crops. Lastly, the infrared component HIR is used by satellite techniques to determine the total atmospheric column of the water vapor used by meteorology for the climate prediction [50].Based on one year’s worth of measurements of the different components of the solar radiation provided by the National Meteorological Department, we noticed that the variations of the global radiation and the spectral components, functioning in time, have the same rate. As a result, we searched correlation equations connecting the global solar radiation to the spectral solar radiation.For this, we graphed each spectral component according to the global radiation, which gave us linear equations of the formy=ax. To improve the correlation coefficients, we defined three intervals according to the meteorological state of the day characterized by its clearness index Kt [51]. The results are presented in Table 5.Table 5
Correlation equations for the daily values of the spectral components of solar radiation (Wh/m2) in function of global solar radiation H (Wh/m2) for the three sky conditions.
Clarity index intervals
Correlation equations
R2
Kt≤0.35
Huv=0.048H
0.97
HPAR=0.488H
0.99
HIR=0.46H
0.99
0.35<Kt≤0.65
Huv=0.044H
0.97
HPAR=0.484H
0.99
HIR=0.471H
0.99
Kt>0.65
Huv=0.04H
0.98
HPAR=0.478H
0.99
HIR=0.478H
0.99


## 6. Performance Evaluation and Model Validation

To evaluate the quality of the models used to estimate the solar radiation components, we compared the estimated values generated by the different models against the measured values by using the usual statistical indicators such as the relative error (RMBE), the mean absolute error (MAE), the mean absolute percentage error (MAPE), and the mean squared error (RMSE) [34, 38].
(10)RMBE=100∑i=0npi−mi∑i=0nmi,MAE=∑i=0npi−miN,MAPE=1N∑i=0npi−mimi∗100,RMSE=100m¯∑i=0npi−mi2N.


### 6.1. Validation of Energy Component Models

Using the measurements provided by the Solar Energy and Environment Laboratory’s station network, we were able to calculate the statistical indicator and validate the estimation models. However, these calculations were effected for all sites previously mentioned. Table6 and Figures 1–3 are examples of the obtained results for the Rabat Site.Table 6
The performance of models used to estimate daily solar irradiation for the Rabat site.
RMBE
Mean difference
MAPE
RMSE
Number of values
Global radiation
5.42
252
12.14
14.88
290
Diffuse radiation
-3.63
-77
12.71
15.82
257
Direct radiation
1.45
21.6
14.68
17.52
234
Inclined radiation
-6.21
-365
6.35
7.46
323Figure 1
Comparison between measured and estimated values of global radiation.
(a)
(b)Figure 2
Comparison between measured and estimated values of diffuse radiation using the Collares-Pereira and Rabl’s model.
(a)
(b)Figure 3
Comparison between measured and estimated direct radiation values.
(a)
(b)


### 6.2. Validating Spectral Components

The formulas for estimating the spectral components of solar radiation from the measurement of global solar radiation were developed according to the state of the day characterized by itsKt clarity index. The results in Table 7 revealed that the proposed models estimate the spectral components with remarkable accuracy since the maximum deviations obtained do not exceed 4%.Table 7
Errors obtained according to clarity index using Rabat measurements.
HUVT relative error (%)
HPAR relative error (%)
HIR relative error (%)
Kt<0.35
3.8
2.4
2.2
0.35<Kt≤0.65
1.0
1.8
2.1
Kt>0.65
1.0
1.1
1.1For all obtained equations, we found that the conditions of the sky (overcast, moderately covered, and clear) have a significant influence mainly on theHUV/Hj fraction. This result is similarly found to the one in Brazil [52]. An estimate of the ultraviolet component that ignores the state of the sky can induce an error of up to 10%. However, the HPAR/Hj and HIR/Hj fractions are less influenced by cloud cover.


## 6.1. Validation of Energy Component Models

Using the measurements provided by the Solar Energy and Environment Laboratory’s station network, we were able to calculate the statistical indicator and validate the estimation models. However, these calculations were effected for all sites previously mentioned. Table6 and Figures 1–3 are examples of the obtained results for the Rabat Site.Table 6
The performance of models used to estimate daily solar irradiation for the Rabat site.
RMBE
Mean difference
MAPE
RMSE
Number of values
Global radiation
5.42
252
12.14
14.88
290
Diffuse radiation
-3.63
-77
12.71
15.82
257
Direct radiation
1.45
21.6
14.68
17.52
234
Inclined radiation
-6.21
-365
6.35
7.46
323Figure 1
Comparison between measured and estimated values of global radiation.
(a)
(b)Figure 2
Comparison between measured and estimated values of diffuse radiation using the Collares-Pereira and Rabl’s model.
(a)
(b)Figure 3
Comparison between measured and estimated direct radiation values.
(a)
(b)


## 6.2. Validating Spectral Components

The formulas for estimating the spectral components of solar radiation from the measurement of global solar radiation were developed according to the state of the day characterized by itsKt clarity index. The results in Table 7 revealed that the proposed models estimate the spectral components with remarkable accuracy since the maximum deviations obtained do not exceed 4%.Table 7
Errors obtained according to clarity index using Rabat measurements.
HUVT relative error (%)
HPAR relative error (%)
HIR relative error (%)
Kt<0.35
3.8
2.4
2.2
0.35<Kt≤0.65
1.0
1.8
2.1
Kt>0.65
1.0
1.1
1.1For all obtained equations, we found that the conditions of the sky (overcast, moderately covered, and clear) have a significant influence mainly on theHUV/Hj fraction. This result is similarly found to the one in Brazil [52]. An estimate of the ultraviolet component that ignores the state of the sky can induce an error of up to 10%. However, the HPAR/Hj and HIR/Hj fractions are less influenced by cloud cover.


## 7. Application: Building a Ten-Year Database

After having established and validated the extrapolation and correlation equations, we applied them to estimate the different solar radiation components for the different Moroccan sites. The obtained results constitute a solar data bank for all over Morocco for ten years.Figure4 represents the flow-chart summarizing all the steps followed for generating all solar components from the site of the Fez.Figure 4
Flowchart of the building steps of the daily solar data bank for Morocco.


## 8. Representative Year

In preproject studies that aimed at sizing solar systems or characterizing the solar radiation potential, it is often necessary to have a minimum of data. Therefore, it is essential to compact the database. Consequently, after having established, for each site, a database for ten years, we were obliged to select a representative year of this database for facilitating the database exploitation.To determine the representative year, we proceed as follows: for the ten years of estimated values, we calculated an average year. Then, this average year is successively compared to each one of the ten years of estimated values. Consequently, the year with the minimum difference is selected as the representative year.This work was done for all sites and led us to select 2011 as the representative year for the period between 2009 and 2018.


## 9. Results

After having established and validated the various components of solar radiation, we created a solar data bank for all over Morocco. Thus, for each city, the obtained results were grouped in two files easily usable; the first one contains the solar components over ten years between 2009 and 2018, and the second contains the solar components of the representative year. However, this second file has the advantage of providing the maximum of climatic information on a site with a minimum of data. This type of file is requested especially for the preliminary project studies.Table8 represents a sample data file resulting from different estimations.Table 8
Sample data file resulting from different estimations.
Year
Nj (day)
Global
Diffuse
Direct
Inclined (φ+20)
Inclined (φ-20)
Inclined (φ)
Inclined (90)
HUVT
HPAR
HIR
2011
1
2808.4
1164.7
1643.7
4683.6
3552.5
4375
4171.9
123.6
1359.3
1322.8
2011
2
2766.6
1202.5
1564.1
4526.3
3470.8
4246.2
4015.1
121.7
1339
1303.1
2011
3
2435.5
1396.1
1039.4
3499.8
2894.4
3383.5
3018.3
107.2
1178.8
1147.1
2011
4
2515.6
1368.7
1146.9
3710.5
3021.7
3565.1
3217.8
110.7
1217.6
1184.8
2011
5
2629.9
1318.1
1311.8
4028
3208.8
3836.5
3520.3
115.7
1272.9
1238.7
2011
6
2844.2
1192.5
1651.7
4669
3574.9
4378.7
4136.5
125.1
1376.6
1339.6
2011
7
2396
1444.7
951.3
3314.2
2805.5
3235.5
2827.6
105.4
1159.7
1128.5
2011
8
2797.1
1250
1547.1
4458.7
3472.3
4209.8
3922.6
123.1
1353.8
1317.4
2011
9
2608.6
1375
1233.6
3860
3139.2
3708
3341.1
114.8
1262.6
1228.7
2011
10
3083.6
1077.5
2006.1
5291.3
3954.6
4918.1
4715.2
135.7
1492.5
1452.4
2011
11
3201.2
1010.7
2190.5
5617.9
4147.9
5198.1
5022.8
128
1530.2
1530.2
2011
12
2695.6
1368.1
1327.5
4022.1
3256.3
3857.7
3480.8
118.6
1304.7
1269.6
2011
13
3228.4
1024.4
2204
5613.5
4167.3
5206
5002.4
129.1
1543.2
1543.2
2011
14
3130.4
1110.8
2019.6
5265.8
3982.2
4918.6
4660.2
137.7
1515.1
1474.4
2011
15
3253.6
1042.2
2211.4
5595.9
4181
5203.6
4967.9
130.1
1555.2
1555.2
2011
16
3160.8
1126.4
2034.4
5264.7
4005
4930
4642.1
139.1
1529.8
1488.7
2011
17
2880.3
1341.1
1539.2
4373.3
3507.7
4181.2
3783.1
126.7
1394.1
1356.6
2011
18
3239.3
1114.8
2124.5
5395.9
4106.4
5055
4748.2
142.5
1567.8
1525.7
2011
19
2272.2
1593.9
678.3
2748
2531.8
2782.5
2248.4
100
1099.7
1070.2
2011
20
3094.1
1268.5
1825.6
4850.4
3821.8
4606.8
4210.1
136.1
1497.5
1457.3
2011
21
3321.7
1132
2189.7
5464.3
4190.8
5136.6
4781.2
146.2
1607.7
1564.5In addition, to give an overall view of the results, we projected the obtained values of the solar irradiations on the Moroccan map. Furthermore, In order to reduce the number of figures, we chose to represent only the monthly averages of the daily values of the midseason month of the representative year. Thus, for all cities, we obtained twenty-three maps that gather the various solar irradiations. As a result, for each of the four solar components (global, direct, diffuse, and inclined), we have five maps; four of them represent seasonal values and the last one represent the annual cumulative values. The obtained maps are shown in Figures5–12. The three spectral components (HUVT, HPAR, and HIR) are shown in Figure 13.Figure 5
Maps of the monthly average values of daily global irradiations on a horizontal plane, coming from Morocco. Maps of global solar radiation on a horizontal plane (a–d).
(a)
(b)
(c)
(d)Figure 6
Map of annual cumulation of daily global irradiations on a horizontal plane incident in the Moroccan territory. Map of global solar radiation on a horizontal plane.Figure 7
Maps of the monthly average values of daily diffuse irradiations on a horizontal incident plane in Morocco. Maps of diffuse solar radiation on a horizontal plane (a–d).
(a)
(b)
(c)
(d)Figure 8
Map of annual cumulation of daily diffuse irradiations on a horizontal plane incident in the Moroccan territory. Map of diffuse solar radiation on a horizontal plane.Figure 9
Maps of the monthly average daily direct irradiation in the Moroccan territory. Maps of direct solar radiation on a horizontal plane (a–d).
(a)
(b)
(c)
(d)Figure 10
Map of annual cumulation of daily direct irradiations on a horizontal plane incident in the Moroccan territory. Map of direct solar radiation on a horizontal plane.Figure 11
Maps of the monthly average values of the daily global irradiations on inclined planes (β=the site latitude). Maps of the global solar radiation inclined with β = the latitude’s site (a–d).
(a)
(b)
(c)
(d)Figure 12
Map of annual cumulation of daily global irradiations on inclined planes (β=the site latitude) incident in the Moroccan territory. Map of the global solar radiation inclined with β=thelatitude’s site.Figure 13
Maps of the annual cumulation of daily irradiations of the spectral components of solar radiation (HUVT, HPAR, and HIR) on the horizontal plane incident in the Moroccan territory. Maps of solar radiation spectral components (a–c).
(a)
(b)
(c)Finally, in order to evaluate the variation of solar radiation components, we calculated, for each solar component, the monthly averages of the daily values (Table9) and the minimum (Table 10) and maximum (Table 11) daily values for each month of the representative year. Caused by the large number of stations, only the results obtained in Rabat’s station are presented in Tables 9–11 (minimum, maximum, and averages of the daily values for each month of the representative year).Table 9
Representative year monthly averages of various solar radiation component daily values (Wh/m2).
Hj
Hdj
Hbj
Hβj (β=ϕ+20)
Hβj (β=ϕ-20)
Hβj (β=ϕ)
Hβj (β=90)
HUVT
HPAR
HIR
Jan
2552
1302
1250
3772
3072
3627
3252
112
1235
1200
Feb
3881
1471
2409
5271
4556
5223
4247
162
1864
1843
Mar
4493
1966
2527
4718
4848
5075
3273
189
2162
2131
Apr
5382
2401
2981
4704
5511
5409
2822
231
2595
2542
May
5859
2825
3035
4489
5777
5414
2491
251
2825
2769
June
6942
2723
4220
4900
6722
6129
2459
299
3390
3334
Jul
6668
2727
3941
4900
6522
6029
2546
293
3312
3255
Aug
5742
2552
3191
4743
5788
5571
2723
273
3077
3020
Sept
5001
1878
3124
5051
5349
5526
3327
227
2655
2638
Oct
4231
1383
2848
5533
4913
5559
4313
177
2076
2064
Nov
2585
1196
1503
3820
3117
3681
3264
116
1312
1290
Dec
2470
1024
1508
4129
3128
3855
3682
119
1374
1358Table 10
Representative year monthly maximum values.
Hj
Hdj
Hbj
Hβj (β=ϕ+20)
Hβj (β=ϕ-20)
Hβj (β=ϕ)
Hβj (β=90)
HUVT
HPAR
HIR
Jan
3322
1635
2211
5618
4191
5206
5023
146
1608
1565
Feb
5050
2044
3759
6730
5919
6743
5481
206
2414
2414
Mar
6463
2786
4797
6837
6940
7249
5021
259
3090
3090
Apr
7253
3273
5212
6370
7360
7257
3695
298
3467
3467
May
8140
3570
6084
5837
7962
7312
2922
326
3891
3891
June
8192
3575
5999
5556
7895
7115
2684
338
3916
3916
Jul
7832
3652
5563
5522
7612
6944
2887
337
3833
3833
Aug
7072
3320
4551
5452
7018
6600
3069
312
3683
3683
Sept
5883
2981
4175
6065
6185
6416
4235
276
3303
3303
Oct
5285
2424
3907
6523
6034
6688
5344
224
2659
2659
Nov
3688
1843
2669
5953
4630
5638
5109
163
1946
1946
Dec
3061
1459
2151
5530
4016
5083
4984
139
1583
1583Table 11
Representative year monthly minimum values.
Hj
Hdj
Hbj
Hβj (β=ϕ+20)
Hβj (β=ϕ-20)
Hβj (β=ϕ)
Hβj (β=90)
HUVT
HPAR
HIR
Jan
1176
1011
59
1051
1185
1167
776
56
574
541
Feb
1884
1074
179
1712
1911
1893
1258
90
919
867
Mar
1114
1103
11
936
1103
1061
672
54
544
512
Apr
886
877
9
741
876
842
531
43
432
407
may
1843
1825
18
1536
1821
1747
1099
89
900
848
June
3303
2193
316
2693
3254
3101
1856
159
1612
1519
Jul
4885
2052
2109
3620
4758
4403
2039
138
1407
1327
Aug
3996
1815
833
3346
3986
3840
2201
173
1904
1853
Sept
2418
1563
171
2265
2494
2502
1592
89
900
848
Oct
2778
801
823
3052
3003
3189
2371
39
395
372
Nov
931
397
315
734
1049
1003
411
19
196
184
Dec
679
616
1
659
702
712
359
30
304
286


## 10. Discussion

From the obtained results in Tables6 and 7 and the curves in Figures 1–3, we can conclude that the correlation between the estimated and measured solar energy resources has a good level of precision. This was reflected in the following observations:
(i)
The annual average of daily relative errors for energetic components of solar radiation does not exceed 5.42% for global radiation, -3.63% for diffuse radiation, and 2.32% for direct radiation
(ii)
The comparative curves show that the measured and estimated values of solar radiation undergo almost the same variations throughout the year and the differences that do not exceed 12.14% for global radiation, 12.71% for diffuse radiation, and 17% for direct radiation. This result is approved by comparing the cloud of points generated by representing the estimated values in function of the measured values, with the first bisector, which gave almost identical trends
(iii)
For the spectral components, the relative errors do not exceed 3.8% forHUVT, 2.4% for HPAR, and 2.2% for HIRWhen we compared our results with those obtained by other authors’ models, we noticed that our method diminished the differences between estimated and measured values. In brief, the results of this comparison are shown in Table12.Table 12
Relative errors (RMBE) calculated from the values generated by different methods of estimation and the measured values.
Solar components
Our estimation methods
Nfaoui’s methods
Lemmini’s methods
Bargach’s methods
Benkaddour’s methods
Zou et al.’s model
Wang et al.’s model
Global solar radiation
5.42%
-11%
-14.7%
-10.6%
14.13%
-17%
Diffuse solar radiation
-3.63%
12.76%
-8%
11.7%Regarding the maps in Figures5–12, we notice that the Moroccan territory receives a very important sunshine during all seasons. However, there is an unequal distribution of solar resources between regions. This inequality is reflected by maximum values of radiation in the south and south-east regions such as Ouarzazate, Er-Rachidia, Laayoun, and Dakhla and by minimum values of solar radiation in the north regions such as Tangier, Tetouan, and the coastal zone between Agadir and Tan-Tan where there is a microclimate.In addition, the spectral component maps show a similar distribution compared to the global radiation maps, reflected by intense irradiations in the south and south-east regions and low radiations in the north and the microclimate zone. The linear aspect of the estimation equations connecting the spectral components to the global radiation explains this result.


## 11. Conclusion

Through this work, we have been able to create a database that brings together the different components of solar radiation at daily scale over a period of ten years from 2009 to 2018. This database regroups more than one million daily values (1,058,500 values), which divides into 36,500 values for each site.To create this databank, at first, we developed a model to estimate the different components of the solar radiation, and then we validated this model by comparing the estimated values with the measurements provided by installed stations. As a result, the validity tests showed that our model presents minimal errors that do not exceed 5.42% for global radiation, 3.8% forHUVT, 2.4% for HPAR, and 2.2% for HIR. In addition, we compared our results with those obtained by other estimation models developed around the world. The results of this comparison showed the advantage to our model with errors do not exceed 6%.To get the general idea about the solar radiation distribution over all Morocco and considering the large number of data, we chose to present the obtained results in maps. In order to reduce the number of figures, we chose to represent only the monthly averages of the daily values of the midseason month for the representative year and the annual cumulative solar irradiations for the same year. As a result, twenty-three maps of solar radiation were generated. Consequently, we have been able to complete and to update the various works affected in our laboratory, and we have been able to build a complete, clean, and precise database covering all Morocco over a period of ten years. This database covers the basic needs of engineers, installers of solar systems, and especially researchers who often need a long-term database.



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*Source: 6067539-2019-05-16.xml*