Global insolation (RG) and diffuse solar radiation fraction (KD) reaching the surface of the Earth is altered by atmospheric clarity (based on aerosol concentration) or cloudiness that determines atmospheric transmissivity (KT). Changes in cloud properties, fog, atmospheric aerosol loadings including dust, volcanic or anthropogenic emissions, alter both the KT and KD which also affect plant productivity, and the land carbon sink globally (Mercado et al., 2009). Recent observational findings over diverse plant functional types also established the role of KD on modulating canopy gas exchange processes (Niyogi et al., 2004; Knohl and Baldocchi, 2008; Still et al., 2009; Jing et al., 2010), vegetation, light and water use efficiencies (Rocha et al., 2004; Chen et al., 2009). Studies have also shown the sensitivity of vegetation productivity to the fluctuations in RD and it is more efficiently used by the plants than the direct component (Roderick et al., 2001). Because of its omnidirectional nature (i.e. incident from multiple angles), the diffuse component has the greater capacity to penetrate the light-limited layers of the dense forest canopies, thus stimulating photosynthesis and productivity (Gu et al., 2002; Still et al., 2009).
The main concern of today's world is sustainable development which is directly linked to the utilisation of energy resources. For attaining sustainable development, we need to harness sustainable energy sources, and the use of renewable energy such as ‘solar energy’ will promote sustainability (Dincer and Rosen, 1999). Values of RD and KD are also required for building the solar energy systems. In addition to these, long-term records of RD and KD have significant roles in constructing quantitative information on atmospheric turbidity, aerosol and cloudiness. This, in turn, can be used to study the response-feedback mechanisms between Earth and atmosphere (Barth et al., 2005; Carslaw et al., 2010), for example, atmospherically driven changes in global hydrology and carbon cycles, and the impact of these cycles on the atmospheric properties. Different atmospheric conditions (turbidity and transparency), airmass, content of water vapour in the atmosphere and the cloud cover distribution influence the insolation by absorption, scattering and re?ection (Okogbue et al., 2009). The knowledge of KD can be useful to get an idea of concentration of atmospheric load indirectly, where a low KD will indicate clear sky and more pristine atmosphere, and vice versa. In a developing country like India, RD measurement is sparse because it is expensive and tedious (Veeran and Kumar, 1993; Gopinathan and Soler, 1995; Pandey and Katiyar, 2009). Therefore, a common alternative is to formulate robust correlation models of RD or KD from the observational networks. Many empirical models of KD have been developed in some advanced countries such as Europe and North America (Reindl et al., 1990), US (Erbs et al., 1982), Australia (Spencer, 1982), Canada (Orgill and Hollands, 1977), Italy (Barbora et al., 1981; Jain, 1990), as well as in some developing countries such as Thailand (Janjai et al., 1996), Turkey (Ulgen and Hepbasli, 2009) and Saudi Arabia (Elhadidy and Abdel-Nabi, 1991). These models cannot be straightway extrapolated to a sub-tropical country like India because of differences in the radiative forcing patterns. Besides this, the models of the developed countries are valid for the higher latitudes (above 40°) only. Though Gopinathan and Soler (1995) have developed a KD versus KT relationship taking observations from different parts of the world including two stations of India, yet that relationship suffers from limited climatological information, and the model was not validated over other independent Indian stations. A comprehensive list of correlation models between monthly KD and KT developed earlier is given in Table I (Liu and Jordan, 1960; Erbs et al., 1982; Ulgen and Hepbasli, 2009; and others). No such robust model of KD is available so far for India. This paper aims at developing a monthly model of KD from the time-series measurements of RG and RD. The objectives of the present study are: (1) development of local as well as regional models for monthly average KD using long time-series RG and RD observations over ‘prime’ climates (Section 2) over the Indian sub-tropics; (2) comparison of newly developed KD model outputs with the estimates from existing global models; and (3) validation of the KD model with independent datasets and shorter time series data from 16 different radiometric stations of India.