Abstract:
World energy demand has been outstripping supply since the 1973 Arab/OPEC oil crisis. This has led to a wide
interest in, and development of, renewable and sustainable energy including solar energy. Solar radiation data is an
important input parameter in the design and
implementation of solar energy systems. Only a few scattered
meteorological stations in Kenya measure solar radiation on a continuous basis. The use of models to estimate this
parameter can alleviate the problem. A clear sky model can be easily obtained from measured global solar
radiation on a horizontal surface situate on Earth’s surface. Using solar radiation and duration of sunshine data
from 11 Kenyan meteorological stations, this study tested seven Angstrom
-
Prescott type regression models for their
suitability to estimate clearness index for clear skies
)
(
c
K
. The Angstrom
-
Prescott type models were obtained by
regressing sunshine duration against clearness index and obtaining curves of best fit. Linear, quadratic,
exponential, power and
logarithmic fits were obtained. Model performance was measured using goodness of fit
statistics including Pearson correlation coefficient (r), coefficient of determination (R
2
), Mean Bias Error (MBE),
Root Mean Square Error (RMSE), Students
-
t
-
statistic,
and the t-
test. Out of the 11 stations considered data from
Dagoretti, Eldoret, J K Airport, and Voi meteorological stations showed high R
2
values and these were used to
produce modified Angstrom
-
Prescott models whose long
-
term, short
-
term, and overall per
formances were measured
using MBE, RMSE, and t
-
statistic respectively. For each of the four stations with high R
2
values 10 pairs of
equations, one each for
c
K
presented. These 20 equations are recommended for use in estimating clear
-
sk
y
clearness indices at the four stations (and in the immediate neighbourhood) using measured fraction of duration of
sunshine as the only input. The correlation coefficients for each model were determined and these were found to be
site dependent. For exa
mple the correlation coefficients for the linear model of the Angstrom type for Dagoretti and
Eldoret were 0.316, 0.706 and 0.421, 0.650 respectively while those for the quadratic model for the same two
stations were respectively 0.348, 0.579, 0.118 and 0
.264, 1.175,
-
0.426. A number of recommendations on the use of
these models are given.