Evaluation and improvement of empirical models of global solar irradiation: Case study northern Spain

Abstract

This paper presents a new methodology to build parametric models to estimate global solar
irradiation adjusted to specific on-site characteristics based on the evaluation of variable im-
portance. Thus, those variables higly correlated to solar irradiation on a site are implemented
in the model and therefore, different models might be proposed under different climates. This
methodology is applied in a study case in La Rioja region (northern Spain). A new model is
proposed and evaluated on stability and accuracy against a review of twenty-two already exist-
ing parametric models based on temperatures and rainfall in seventeen meteorological stations
in La Rioja. The methodology of model evaluation is based on bootstrapping, which leads to
achieve a high level of confidence in model calibration and validation from short time series (in
this case five years, from 2007 to 2011).
The model proposed improves the estimates of the other twenty-two models with average
mean absolute error (MAE) of 2.195 MJ/m2 day and average confidence interval width (95%
C.I., n=100) of 0.261 MJ/m2 day. 41.65% of the daily residuals in the case of SIAR and 20.12% in
that of SOS Rioja fall within the uncertainty tolerance of the pyranometers of the two networks
(10% and 5%, respectively). Relative differences between measured and estimated irradiation
on an annual cumulative basis are below 4.82%. Thus, the proposed model might be useful
to estimate annual sums of global solar irradiation, reaching insignificant differences between
measurements from pyranometers.