The global horizontal irradiance

The global horizontal irradiance on the ground is obtained assuming a simple relationship between the cloud index (an estimation of the cloud cover) and the clear sky index :

The clear sky index is the ratio of the global horizontal irradiance for a given atmospheric condition, to the global horizontal irradiance under a cloudless sky condition:

The global horizontal irradiance under cloudless skies is computed as the sum of its direct and diffuse components:

The direct component is given by Page (Page, 1996):

The diffuse component of the global horizontal irradiance is given by Dumortier (Dumortier, 1995):

In these formulae, m is the relative optical air mass, given by Kasten and Young (Kasten-Young, 1989):

is the optical thickness of a Rayleigh atmosphere, given by Kasten (Kasten, 1996). It describes the attenuation of solar radiation in a pure and dry atmosphere:

is the total turbidity factor at a relative optical air mass equal to 2. It describes the attenuation of solar radiation due to water vapor and aerosols in the atmosphere. It is time and site specific. The use of monthly values of the total turbidity factor in the computation of the global horizontal irradiance under cloudless skies improves the accuracy of the satellite estimation, over the use of a constant annual value.

The Satel-Light turbidity model

The total turbidity factor is larger at sea level than in mountainous areas. It increases from the winter to the summer: the larger amount of solar radiation and the growth of the vegetation contribute to an increase of the atmospheric content in water vapor, salt cristals, pollens… It also increases with the level of industrial activities performed at a given site. In spite of these general trends, there is very little information on local variations of the turbidity within Europe. This is the kind of information that cannot be inferred from the analysis of the current generation of Meteosat satellites. The next generation (called Meteosat Second Generation or MSG) fitted with 12 spectral channels will provide enough information to generate maps of turbidity. The MSG is planned to be launched in the year 2000 (more information from EUMETSAT).

For Satel-Light, a model describing the variations of turbidity over Western and Central Europe was developed by Dumortier (Dumortier, 1998). It is based on a database of monthly turbidities in 507 sites, produced in the framework of another European project (the European Solar Radiation Atlas or ESRA).

The Satel-Light turbidity model divides Europe in 13 zones (see the figure below). Within each zone, the variations of the turbidity at sea level are described using a formulation developed by Bourges (Bourges, 1992):

The sea level turbidity is then corrected to take into account the influence of altitude (-0.65 per 1000 m). This model is used by default in the Satel-Light database (maps and site information). However, when requesting site specific information, you are given the ability to overwrite the default values.

The validation procedure

The global horizontal irradiance is computed every half hour, from the cloud index of a given pixel, using the method presented above. 25 test sites spread across Europe have been used to validate the method (see the list below). In the case of IDMP stations, the ground measurements were measured every minute while the satellite provided estimates every 30 minutes. Therefore, the ground data was averaged over a half hour period centered on the time at which the satellite was reading the pixel value.

Two different directions were taken to evaluate the precision of the method.

The first one consisted in comparing every half hour the satellite estimates to the ground measurements. The graph below shows a good correspondence between modeled and measured values under sunny or quasi sunny conditions in Lyon, France. On a yearly basis, in all sites tested, these conditions lead to a MBD (Mean Bias Deviation) ranging from 0% to -6% (the satellite underestimates), and to a RMSD (Root Mean Square Deviation) ranging from 10% to 17%. Intermediate overcast and quasi overcast conditions lead to larger differences. On a yearly basis, they lead to a MBD ranging from 5% to 15% and to a RMSD ranging from 45% to 65%. This is due to the fact that the amount of radiation transmitted by the cloud cover depends on its thickness and its composition. This information cannot be derived just from the knowledge of the radiation reflected by the upper surface of the clouds.

On a yearly basis and for all sky conditions combined, the comparison between the satellite estimates and the ground measurements, lead to a MBD ranging from -1% to 3% and to a RMSD ranging from 20% (South of Europe with a high frequency of sunny skies) to 40% (North of Europe with a high frequency of cloudy skies). These high RMSDs are explained by the fact that we are comparing 30 mn values; they would be smaller, if we were comparing daily or monthly values.

These values should also be compared with the deviations due to extrapolation and interpolation of data between ground stations. Perez (Perez 1997) has shown that for hourly data, the satellite becomes more accurate than a local ground station if the distance from the station exceeds 34 km. Perez has also shown that a RMSD of 15% (for hourly values) persists even between two ground stations located only 4 km away from each other, this is due to the discontinuous nature of hourly radiation spatial structures (i.e. cloud-blue sky).

The second direction taken to evaluate the precision of the method consisted in comparing end user products generated from the satellite estimates to those generated from the ground measurements. The figure below shows that there is a good agreement for a typical end user result such as a cumulative frequency curve. In all test sites, the statiscal characteristics of the solar radiation climate are well reproduced. This is essential for all solar applications.

The diffuse horizontal irradiance

The diffuse horizontal irradiance is computed from the global horizontal irradiance using an updated version of a model developed by Skartveit and Olseth in 1987 (Skartveit, 1987). This model (Skartveit, 1998) is a great improvement over other models used in the past, such as the one from Orgill and Hollands (Orgill, 1977). It assumes that the diffuse fraction depends on the clearness index, on the solar elevation and on the variability index. For a clearness index below a certain threshold, the hourly radiation is expected to be completely diffuse. With increasing clearness index, the diffuse fraction decreases. For high clearness index values, it increases again due to cloud reflection effects. The position of the minimum of diffuse fraction depends on the solar elevation.

The variability index is based on the variations of the clearness index before and after the time considered. It is equal to 0 for a cloudless sky and reaches 0.3 under intermediate skies with broken clouds. Scattered clouds on the sky vault enhance the diffuse solar radiation and leave the beam irradiance unaffected. Therefore, when the variability index increases, the diffuse fraction increases.

As for the global horizontal irradiance, two different directions were taken to evaluate the precision of the method. The first one consisted in comparing every half hour the satellite estimates to the ground measurements. The second one consisted in comparing end user products generated from the satellite estimates to those generated from the ground measurements. This was done for 5 of the 8 IDMP sites and for Bergen, Norway (Olseth, 1998), (Dumortier, 1997).

The tilted irradiances

Irradiances on tilted surfaces are computed from horizontal irradiances. Based on earlier studies and on further validation in Geneva, a version of the Hay's model (Hay, 1979) modified by Skartveit and Olseth (Skartveit, 1986) has been selected. This algorithm assumes Lambertian ground reflectance. Sky radiance anisotropy for cloudless as well as overcast skies is parameterized as follows: one fraction of the horizontal diffuse irradiance (equal to the direct transmittance) is treated as circumsolar radiation, another fraction (decreasing from 0.3 at overcast to zero at direct transmittance = 0.15) is treated as collimated radiation from the zenith. The remaining horizontal diffuse irradiance is treated as isotropic sky radiance. The performance of this model in 4 IDMP sites has been presented by Olseth (Olseth, 1997).