Investigation of Atmospheric Turbidity at Ghadaa (Algeria) Using Both Ground Solar Irradiance Measurements and Space Data

Four radiometric models are compared to study the Angström turbidity coefficient β over Ghardaïa (Algeria). Five years of global irradiance measurements and space data recorded with MODIS are used to estimate β . The models are referenced as Dog β for Dogniaux’s method, Louch β for Louche’s method, Pinz β for Pinazo’s method, Gyem β for Gueymard’s method and by modis β for MODIS data. The results showed that Gyem β and Pinz β are very close as the couple Dog β and modis β . Louch β values are between them. Results showed also that all Angström coefficient curves have the same annual trend with maximum and minimum values respectively in summer and winter months. Annual mean values of β increased from 2005 to 2008 with a slight jump in 2007 except for Louch β . The city environment explains it since the urban aerosols predominate over all other types during this period. The jump in 2007 is attributed to the ozone layer thickness that undergoes the same behavior. Some models are then more sensitive to this atmospheric component than others. The occurrence frequency distribution showed that


Introduction
The atmospheric turbidity is responsible of the attenuation of solar radiation reaching a local area of the Earth surface under cloudless sky conditions. Thus, for a given site where implantation of Photovoltaic and thermal energy will be realized, quality and quantity of solar radiation should be estimated and studied [1]. Since good measurement of solar radiation is strongly dependent on Earth atmosphere state, so it is important to quantify the effect of its constituents where solar irradiance is measured. The atmospheric turbidity is associated with aerosols and due to the relationship that exists between them and attenuation of solar radiation reaching the Earth surface, different turbidity factors based on radiometric methods have been defined to evaluate the atmospheric turbidity. Among them, the Angström turbidity coefficient which is commonly used [2]. It was introduced by Angström [
[5] [6] Its zero value refers to a clean atmosphere. Several models may be used to estimate β from broadband measurements of solar irradiance and meteorological data when spectral measurements are not available.
In the present paper, we will investigate the Angström turbidity coefficient of a semi-arid region in Algeria with the widely used broadband models. We will analyse the performance of each model and its sensitivity to the atmosphere components using data recorded at the Applied Research Unit for Renewable Energies (URAER, Ghardaïa) in the south of Algeria from 2005 to 2008 and those obtained from space measurements during the same period.

Turbidity Models
Four radiometric models are used to compute the Angström turbidity coefficient. They have been developed by Dogniaux [7], Louche [8], Pinazo [9] and Gueymard [10]. The four models estimate the turbidity coefficient from broadband solar radiation. Each model uses common and different parameters as input. The availability of local measurements of these parameters conditions which model can be applied. We present in this section a brief description of the four radiometric models used to compute the Angström turbidity coefficient β .
where l T is the Linke turbidity factor, h the Sun elevation angle in degrees and p w the precipitation amount in centimeter. p w is calculated using the following Equation (32): where T is the temperature in Kelvin and φ the relative humidity in fractions of one.
The expression used to evaluate the Linke turbidity factor l T [8] where P is the local pressure in Pascal given by [9]:

Louche's Model
Based on Iqbal C model [8] [17] determine the Angström turbidity coefficient β using the solar irradiance data and the aerosol transmittance a τ .
The aerosol transmittance according to Iqbal Louche's et al. [20] expressed the aerosol transmittance for cloudless sky as: The direct solar irradiance at normal incidence n I in W/m 2 , is directly measured with a pyrheliometer.
The Earth eccentricity correction factor 0 E is given by: where R and 0 R are the same as defined in Equation (5).
The parameter g τ represents the mixing gases absorption transmittance given by: The parameter 0 τ is the ozone absorption transmittance given by: The parameter w τ is the water vapor transmittance expressed as follow:

Pinazo's Model
The approach developed by Pinazo et al. [9] is also based on Iqbal C model and on a coefficient K which is defined as the ratio between the direct beam solar irradiance on a horizontal surface and the global solar irradiance received by the same surface. The aerosol transmittance according to Pinazo et al. is expressed as: The parameter 0 w is the single scattering albedo or the ratio between the scattering and the extinction (scattering plus absorption) coefficients of aerosols that are high above the ground.

1
C and 2 C are given by: c F is the forward scattering parameter defining the radiation fraction scattered in the forward half-space and g ρ is the albedo of the ground.
The Angström coefficient according to this model will be denoted Pinz β and will be calculated using a combination of Equations (10) and (18).

Gueymard's Model
Gueymard and Vignola [10] proposed a method for estimating the Angström coefficient using the relation between the global (or diffuse) and the direct irradiance based on the spectral code SMARTS2 [10] [21]. The Angström coefficient denoted Gyem β is obtained from the following Equation (2): where ab K is the ratio between the diffuse irradiance and the direct beam normal irradiance. It corresponds to a standard value for zero altitude and the total amount of ozone equal to 0.3434 atm-cm. The coefficients i a are function of the zenith Sun angle, the pressure, the perceptible water and the ozone amount. These coefficients and the way they are calculated are detailed in [10].

Site Location and Solar Radiation Data
The data used in the present study is collected at the Applied Research Unit for 2) Ratio between diffuse and global irradiance less than 1/3 3) Perez's clearness index greater than 4.5 4) Data corresponding to solar elevations higher than 5 degrees to avoid cosine response problems of radiometric sensors For the common and the different parameters used as inputs by the four models and how to evaluate them in case where local measurements are not available will be detailed in the following subsections.

Thickness of the Total Vertical Ozone Layer
We take daily mean values of the thickness of the total vertical ozone layer 1 from MODIS satellite data Ichoku 2004 [29] since we have no local measurements for this parameter. Figure

Total Precipitable Water
The total precipitable water is defined as the integrated water vapor in a vertical column extending from the surface to the top of the atmosphere. This parameter is important and its influence in calculation should be studied especially that in most cases we have absence of atmospheric sounding or solar spectral measurements [2]. We have used four algorithms in the present study to estimate the precipitable water: 1) Wright's formula: A linear relationship relates the logarithm of the precipitable water w to the dew point temperature d T [17]:  suitable for estimating instantaneous precipitable water under cloudless skies [31]. Two sources of error affect calculation of d T . They are associated to local parameters a and b and to the calculation method. The parameter d T is calcu- where T is the temperature, Φ the relative humidity and s p the saturation pressure of water vapor calculated with several algorithms among them the commonly used Magnus and Leckner algorithms. The s p , in mbar, is expressed for each algorithm by Equations (25) and (26) where T is in degrees and Φ in fraction of one. M and L letters associted to s p variable stand for Magnus and Leckner respectively.
2) Leckner's formula: This alternative method is often used to calculate the amount of precipitable water L w [32]. It is obtained with the folling Equation: 49.3 3) Gueymard's formula: Gueymard introduced a new formula in 1994 [33] to estimate the precipitable water G w . It is expressed as follow: with G s p and v H are given by Equation (31) and (32) give approximately the same mean values (see Table 1). We will use precipitable water values of each method to estimate the Angström turbidity coefficient with the four broadband models. We notice however, that this parameter obtained from the four methods has not a significant effect on turbidity values for a given broadband model. The difference is about 0.1%.

The Wavelength Exponent
The wavelength exponent α in Equation (1) is related to size distribution of particles. Low values of α correspond to large particles and vice versa.
is suggested by many authors for most natural atmospheres [16]. In our case, we will use MODIS satellite data to obtain the values of this parameter since we did not dispose of photometric ground measurements. The variation of its monthly mean values over Ghardaïa city is shown in the upper side of Figure 3. Its yearly mean value is plotted in the lower side of Figure 3  and it is in agreement with values suggested by many authors.

The Ground Albedo
We also used MODIS data to estimate the ground albedo g ρ at Ghardaïa city.

Single Scattering Albedo and Forward Scattering
The value of 0.8 for the single scattering albedo 0 w is usually chosen for rural-urban sites as advised by Gueymard    suggested by [17] for the forward scattering c F . We preferred here to use modeling techniques to find these parameters and their temporal variations rather than a constant value. In a recent study, [36] assessed the intrinsic performance of 18 broadband radiative models using high-quality data sets from five sites in widely different climates. All these models are able to predict direct, diffuse and of statistical indicators. This model will be considered in our present study to estimate the required parameters since it offers a better accuracy than the others more conventional models [36]. In addition, the model inputs are those that we need, namely the Angstrom coefficient β , the average surface albedo g ρ , the wavelength Angstrom exponent α , the forward scatterance c F and the aerosol single scattering albedo 0 w . Only the last two parameters and the Angstrom coefficient β will be considered since the others are obtained from MODIS data (see Sections 3.3 and 3.4). Before proceeding the estimation of the parameters, we recall hereafter the main equations of this model described in detail in [17].
The direct normal irradiance n I (W/m 2 ) is given by: , a τ α β are respectively the ozone, gas, water, Rayleigh and aerosol scattering transmittances. sc I and 0 E are respectively the solar constant and the eccentricity correction factor.
The aerosol scattering transmittance, which depends on the Angstrom coefficient β and wavelength Angstrom exponent α , is given by Equation (10).
The global solar irradiance ( t I ) measured with our instruments is the contribution of 2 solar irradiance components given by: where a ρ is the albedo of the cloudless sky, which can be computed with: The ( )  We will apply this process to all global solar irradiance of clear days of the recorded data. The clear days are determined using the novel method developed by [37]. Each fit will give us a value of the aerosol single scattering albedo 0 w and a value of the forward scatterance c F . The monthly and the yearly mean values of these two parameters are shown in Figure 6 and

Results and Discussion
All useful parameters described in the previous section are used to calculate the Angstrom coefficient obtained with the four turbidity models. The coefficients   These values are reported in Table 2. We notice from Figure 8    to 100%. We also note that Angström coefficient curves have all the same shape during the period 2005-2008 and along the year where maximum and minimum are respectively during summer and winter months. We can explain it by winds of the south sectors (Sirocco) that characterize the region of Ghardaïa. This kind of winds brings particles of dust and sand with them, which increases the Angström coefficient. It is well observed in Figure 6 where 0 w is higher in summer and consequently contributes to light extinction due to aerosol scattering. The period of winter is characterized by rains (see Figure 2) that wash the atmosphere and diminish turbidity variables.
Annual mean values of β obtained from the models and from space are plotted in Figure 9 and given in Table 3. We can notice three points:    The first point was also reported by [38] when they analyzed the atmospheric turbidity levels at Taichung Harbor near Taiwan Strait. This was observed too by The second point is related to the city environment. The recent study of [39] showed that the urban aerosols during the same period of study predominate the other types of aerosols. It is explained by the presence of many companies of crusher plants and industrial companies installed around the city and agglomeration that increased from year to year.
The third point is probably related to the ozone layer thickness that presents a slight increased in 2007 as shown in Figure 10. The cumulative frequency distribution of Angström turbidity coefficient for each model is calculated and plotted in Figure 12. The various degrees of atmospheric clearness deduced from each cumulative frequency distribution [32] [38] are given in Table 4. We observe from the with the other models. We will then consider its values as those for Ghardaïa and we may conclude that major sky conditions under cloudless days are between clean and turbid for this region.

Conclusions
The Angström turbidity coefficient β is calculated with four broadband models using global solar irradiance measurements recorded during the period      to the ozone layer thickness leading to affirm that these models are sensitive to this atmospheric component. We finally completed the comparison of the models by analyzing the occurrence and cumulative frequency distribution of the Angström turbidity coefficients. Results showed for all models that the frequency distribution is not Gaussian but looks like a Poisson law. The maximum recurrent values for Dog β is found near 0.03, near 0.07 for Louch β , near 0.10 for Pinz β , near 0.09 for Gyem β and near 0.02 for modis β . The cumulative frequency distribution study revealed also that Dog β and modis β yield the maximum "clean to clear conditions" with respect to the other models while Pinz β and Gyem β have the minimum. The opposite was observed on the same pairs of β with regard to the "clear to turbid" and "turbid to very turbid" conditions. The Louche model gave middle values of sky conditions compared to the other models. This result leads us to consider Louche's model values for Ghardaïa city. The major sky conditions under cloudless days for this semi arid region are then between clean and turbid.