High altitude solar radiation

The first step in the development of the ASPG concept is to evaluate how much solar energy is available as a function of altitude. This allows a direct assessment of the potential of the ASPG when compared to an equivalent ground based system.

This section presents a set of calculations to enable this comparison and considers the possible influence of cloud layers at different heights above the ground (up to 12 km). The results obtained are based on existing models for ideal clear sky conditions and are integrated with experimental data acquired by scientific instrumentation at a specific site in the south of the United Kingdom. Although this makes the analysis very location specific, the general conclusions about the potential of high altitude solar collectors can be extended to other countries at similar latitudes and with similar climatic conditions. Moreover it must be noted that the assumptions made in the calculation process are quite conservative in order to avoid a possible overestimate of the potential of the ASPG concept.

The attenuation that a solar beam experiences as it travels through the atmosphere is called extinction and it is mainly due to two different kinds of processes, absorption and scattering, the former being the conversion of photon energy into thermal energy and the latter involving the deflection of the photons after the interaction with atmospheric molecules or larger particles suspended in the air. These two processes cause the radiation falling on a surface to be divided into two components: direct (or beam) and diffuse. The contribution of the diffuse radiation becomes proportionally more important when the collector is located at lower altitudes, in particular under cloudy sky conditions.

Since several models that describe the characteristics of the clear atmosphere at various altitudes have been developed in the past, existing publications can be considered when dealing with these conditions. Some of these models have also been embedded in specific software (such as SMARTS (Donovan & Van Lammeren, 2001) hosted by the National Renewable Energy Laboratory), which are widely used now as design tools in the PV industry. For the present purposes the sky is considered clear above an altitude of 12 km, since it is rare to find clouds at higher layers of the atmosphere and the impact on the final results is assumed to be minimal. Therefore, the clear sky radiation falling on a sun tracking surface at 12 km can be directly determined with the use of SMARTS (Gueymard, 1995) using the site location and time of year as inputs. For the initial calculations only the beam contribution of the solar radiation is included in the analysis.

The influence of clouds is incorporated into the calculation process using the extinction parameter, determined from experimental data. The data used was acquired by radar/lidar systems (www. cloud-net. org) at a station located at Chilbolton Observatory (51.1445 N, 1.4370 W) in the South of the UK. These experimental measurements have been elaborated (see Redi 2009) to provide the extinction parameter profile in actual sky conditions, which relates the attenuation of the solar radiation to its path through the atmosphere, considering the possible presence of cloud layers. The observations were performed almost everyday of the year (from April 2003 to September 2004), 24 hours a day, in the height range between 0 and 12 km. Averaging the data for the different layers of the atmosphere and in different months of the year, it is possible to obtain the extinction parameter profile at various altitudes above the ground. As an example the values obtained for the month of March is presented in Fig. 1.

Having determined the extinction parameter the Lambert-Beers’ attenuation law (Liou, 2002) can be used to calculate the loss of intensity of a solar beam as it travels through the atmosphere. By dividing the atmospheric path along the vertical in segment of length Ah, and defining the extinction parameter for each segment at (m_1), the variation of intensity I (the irradiance in W/m2) can be expressed as:

K»Z )= hum exp|- aMrel (3z )-^(а – Ah]) I (1)

where I12km is defined as the solar irradiance at 12 km estimated with SMARTS and AMrel($z ) is the relative air mass, which describes the path length relative to that at the Zenith and it is therefore a function of the solar Zenith angle 3Z.

Extinction Parameter – Mar


Fig. 1. Daily Mean Extinction (log) for the month of March – Chilbolton Observatory (51.1445 N, 1.4370 W)

Models like MODTRAN (Berk et al., 1989) or LibRadtran (Mayer & Kylling, 2005) that are able to integrate information about the cloud structure with the clear sky data, could be considered as a more accurate alternative to the one proposed here. However these models are quite sophisticated and they are generally more oriented towards atmospheric physics studies rather than engineering ones.

Starting from the irradiance values obtained with SMARTS at 12 km, Eq. 1 is applied to the extinction parameter values in actual sky for different months, in order to get an estimate of the irradiance below an altitude of 12 km in atmospheric conditions including possible clouds. The results obtained for the month of March at 12 km, 6 km and on the ground are presented in Fig. 2.

As a final step, it is necessary to integrate the irradiance values during the day (from sunrise to sunset) to calculate the total beam energy (beam irradiation EB) falling on the high altitude solar collector:


EB (h)=J IB (h)dt (2)


where SS and SR are the time of Sunset and Sunrise.

The total beam energy can now be used to evaluate the potential of the ASPG system when compared to an equivalent ground based PV array.

Considering an altitude of 6 km, and integrating graphs like the ones shown in Fig. 3 gives value of about 3600 kWh/m2 for the energy reaching the sun tracking platform in one year. It must be noticed that due to various conservative assumptions in the calculations this shoud be a rather conservative estimate. A general overview of the beam energy that can be collected by a platform located at an altitude up to 12 km is provided in Table 1.


Comparison Irradiance at 6 km

Fig. 3. Comparison between irradiance at 6km for different monthly means – Chilbolton Observatory (51.1445 N, 1.4370 W)

Altitude [km]

Total Year Beam Irradiation (including possible clouds/) [kWh/mA2]

Total Year Beam Irradiation (clear sky) [kWh/mA2]










Table 1. Year Beam Irradiation at different altitudes – Chilbolton Observatory (51.1445 N, 1.4370 W)

The study has been focused so far on the evaluation of the beam (direct) component of the solar radiation that can reach the surface. However, the contribution of the diffuse part of the radiation can be not negligible. Having considered this, the contribution of the diffuse radiation is estimated at different altitudes, with the use of SMARTS in ideal clear sky conditions. This assumption is expected to be extremely conservative since clouds can increase significantly the amount of this component which can become therefore higher particularly if actual sky conditions are considered.

The ratio between diffuse and global irradiation is estimated to range from about 5% (12 km) to 6% (6 km). This contribution is then summed to the values presented in Table 1, leading to the determination of the total radiation reaching a sun pointing surface located at an altitude up to 12 km which is presented in Table 2. Here, the comparison between the results obtained and the typical irradiation value expected for a PV array based on the ground (facing south and tilted at a fixed angle close to the latitude of its location) is given. The value of the energy collected by the solar power satellite (Glaser et al., 1974) is also included as a limit solution.

In addition to the contribution of the diffuse component of the solar radiation, some considerations about the albedo flux should be made. Considering that the albedo radiation factor can reach a value of 10 % for a satellite in Low Earth Orbit (Jackson, 1996), this component can significantly contribute to the total radiation estimate. In our specific case it is difficult during this preliminary analysis to give an estimate of this component with a sufficient degree of confidence. It must be noticed though, as a caveat, that the values presented in Table 2 are conservative and they are expected to increase when the albedo is included, especially in presence of cloud layers below the platform when the sun is at high zenith angles.

Altitude [km]

Year Global Irradiation including clouds (conservative estimate) [kWh/m2]

Year Global Irradiation (clear sky) [kWh/m2]

Ground Based (Chilbolton)











Solar Power Satellite


Table 2. Comparison between the year global irradiation (including diffuse) values at different altitudes for Chilbolton Observatory (51.1445 N, 1.4370 W)

The results obtained can give a preliminary idea of the gain that a high altitude solar generator could bring in terms of energy collected, if compared to the same generator located on the ground.

Due to the very conservative assumptions the values in the first column can be considered as "minimum" values, and the one in the last column as maximum, although the inclusion of the albedo should give results even higher.

Moreover a collector placed at an altitude of 12km could collect around 45% of what could be collected by the same PV system in a geostationary position (i. e. Solar Power Satellite). The study presented is preliminary and it involves several assumptions that have been made to simplify the analysis and provide useful results to support the following phases of

the project. In particular the extinction parameter data used are acquired in a defined and limited time period and they are relative to a precise location in the south of the UK, which is relatively well placed to collect solar energy on the ground. For this reason and the other discussed previously, the figures presented are conservative and the advantage with respect to ground installations is expected to increase as installations at northern latitude are considered and the values concerning the estimate of the diffuse and albedo contributions are revised.

Updated: August 22, 2015 — 11:29 pm