Abstract:
Accurate information on solar radiation at a specific location on the earth’s surface is indispensable for energy applications and atmospheric research. The required data could be obtained from a dense network of solar radiation monitoring stations which is not practicable due to exorbitant costs of equipment and dearth of technical expertise. The available empirical site-independent Hay model, assumed a constant value for clear sky albedo (ρ_a) without taking into account the spatial variation of this parameter. This work was designed to develop a site-independent empirical model which incorporates the parameterisation of the spatial variation of ρ_a.
Monthly averaged daily values of solar radiation〖 (H ̅〗_e), relative humidity, sunshine hours (n ̅), minimum and maximum temperatures, spanning 1984 to 2005, were collected from the National Aeronautics and Space Administration (NASA) and Nigeria Meteorological Agency for eleven locations across Nigeria. Monthly values of ground surface albedo (ρ_g) and surface air pressure were also collected from NASA and optical aerosol thickness at the wavelength of 380 nm from both total ozone mapping spectrometer satellite and Aerosol Robotic Network (AERONET) centre at Ilorin where ground data is available in Nigeria. The ρ_awas parameterised using optical aerosol thickness and the average air mass values. The empirical site-independent Hay model was then modified to accommodate the parameterised ρ_a. New empirical coefficients were derived from field data (sunshine hours and global solar radiation) at Ilorin using regression analyses. The spatial and temporal variations of estimated solar radiation over some locations were investigated using descriptive statistics. Solar radiation values were estimated for five locations (Port-Harcourt, Lagos, Ilorin, Maiduguri and Sokoto) where data were homogenous, using the derived-model, Hay model and six site-dependent models (Angstrom-Prescott, Almoroz-Hontoria, Hargreaves-Samani, Bristow-Campbell, Garcia and Chen-Li). These were analysed using correlation coefficient (r), Mean Bias Error (MBE) and Root Mean Square Error (RMSE) statistics at α_0.05.
Values obtained for ρ_a ranged from 0.09 to 0.12 for the locations as compared to a constant value of 0.25 assumed by Hay. The derived site-independent model was H ̅_e/H ̅_o =(a+b(□(n ̅/N ̅ )))/(1-ρ_g [ρ_a (□(n ̅/N ̅ ))+0.6(1-n ̅/N ̅ ) ] ), where H ̅_o,N ̅ and n ̅ were the monthly averaged daily values of extraterrestrial radiation,day-length and sunshine hours respectively, while a and b were the empirical coefficients with values 0.262 and 0.615, respectively. The r, MBE (MJm^(-2)) and RMSE (MJm^(-2)) obtained with the derived-model were; Port-Harcourt (0.91, -0.99, 1.34), Lagos (0.96, -0.86, 1.03), Ilorin (0.93, -0.01, 0.79), Maiduguri (0.91, 0.99, 1.21) and Sokoto (0.90, 0.58, 0.90) respectively. For Hay model and the six site-dependent models, the range of r, MBE and RMSE were; Port-Harcourt (0.80 – 0.87, -1.53 – 7.87, 2.00 – 7.94), Lagos (0.36 – 0.92, -0.89 – -7.58, 1.69 – -7.64), Ilorin (0.50 – 0.92, -4.44 – 2.68, 1.75 – 4.51), Maiduguri (0.47 – 0.75, -1.80 – 4.11, 1.06 – 4.40) and Sokoto (0.45 – 0.84, -1.26 – 0.71, 0.96 – 2.32) respectively. Values of estimated solar radiation ranged from 16.71 to 23.67MJm^(-2) day^(-1).
The developed site-independent model improved the estimation of solar radiation values over the selected locations.
