Solar radiation and heat models
Long-term surface solar radiation records have been kept at only a few sites worldwide . Solar radiation is conceptually simple and its attenuation through the atmosphere can be modeled with a fair degree of accuracy. The greatest uncertainty in estimating surface solar radiation is due to the effect of overlying clouds. Satellite observations of reflected solar radiation help to remove this uncertainty, and with the aid of radiation model or correlative relationships they are used to estimate the global distribution of surface radiation.
In general, modeling the solar radiation arriving at the top of atmosphere can simply be considered as the product of the solar constant Scs and the astronomical factor, f (R), of annual average 1.0, proportional to R~2, where R is the distance of the earth from the sun. Passing through the atmosphere, the solar beam undergoes wavelength and direction dependent adsorption and scattering by atmospheric gases, aerosols, and cloud droplets. The scattered radiation reaching the earth’s surface is referred to as diffuse radiation. On any clear day, the diffuse component from the Rayleigh and aerosol scattering is about 10-30% of the total incident radiation, whereas when the solar beam passes through a cloud essentially all the surface radiation is of
diffuse type. This radiation consists of solar photons arriving from all directions of the sky with intensities depending on the incoming direction.
However, for the modeling of solar radiation at the earth’s land surfaces, it is usually adequate to assume that the diffuse radiation is isotropic (has the same intensity in all directions from the sky). If Ig is the intensity of radiation arriving at the surface from a given direction, then the amount incident per unit surface area is Ig cos Z, where Z is the angle between the normal to the surface and the direction of the beam (Fig. 15). In the simplest modeling efforts, land is assumed to be horizontal. However, in hilly and mountainous terrains the distribution of slopes has major effects on surface climate and radiation amounts. Surface radiation may change widely according to the frequency and optical thickness of clouds. Modeling these cloud properties successfully is important for the treatment of surface energy balance.
Solar irradiation on the earth surface has many implications in hydrology, climatology, agriculture, heat engineering and many other human activities. Hence, it is an essential task to estimate by some simple and practical means the natural variation of solar irradiation at the earth’s surface depending on the locations in terms of longitudes and latitudes, in addition to the atmospheric effects on the extraterrestrial irradiation arrival through the troposphere at any desired location. Among the effective atmospheric agents on the irradiation are the aerosols and particulate matter concentrations as well as the humidity, temperature, cloud cover and sunshine duration. Theoretically, one can express in an implicit mathematical manner the amount of incident solar irradiation in terms of these agents. However, in practical studies more preferable is the relevance of simply applicable formulations. Estimation of solar
irradiation has direct uses in the solar energy received at the earth surface, which represents a fundamental parameter in various disciplines, like climatology, agriculture, building agriculture and solar systems. Unfortunately, measurement networks do not provide solar radiation data with sufficient spatial and temporal resolutions. For this reason, it is necessary to develop models that are needed to fill spatial and temporal gaps for various regions in the world. Furthermore, model estimations are also necessary for onsite solar irradiation amounts on the basis of measured agents. Starting with the original contribution of Angstrom  up to date, there appeared many models for the estimation of the solar irradiation data from various geographical, meteorological and climatologic variables such as sunshine duration, cloud cover, humidity, temperature, pressure, altitude, etc. A critical review of recent solar irradiation methods has been provided by Gueymard et al. . Apart from the linear Angstrom method others have been developed with various modifications by
different researches. Several major studies are performed by different researchers [30,31,47,93,104,107,113,120,130]. However, after the critical assessments by Guemard et al. , few new models are presented into the literature [70,94,121,126,131-133].
Monthly average daily radiation on a horizontal surface is summed from daily measurements for many sites in the world. However, there are a large number of areas particularly in developing countries, where there are no measurements or the measurements are available only for limited periods of time. It is, therefore, of practical interest whenever possible to calculate monthly average daily radiation from other meteorological variables. For both historical and practical reasons, the most significant basic meteorological variables must be used in modeling the solar irradiation. This variable, as the number of sunshine hours per month, is indeed a natural choice, since both radiation and sunshine depend on earth-sun geometry and on the condition of the atmosphere . Solar radiation information is needed for numerous applications including agriculture, water resources, day lighting and architectural design, solar thermal and photovoltaic devices, and climate change studies. Since irradiation data are scarce, many different models have been suggested and used to estimate irradiation from sunshine duration records the latter is more readily available.