Evaluation of errors made in solar irradiance estimation due to averaging the Angstrom turbidity coefficient

• Averaging β Angstrom in models for GHI produces errors.
• The magnitude of these errors is evaluated using a parametric model.
• An equation relating GHI variation to β Angstrom variation was established.
• Errors in GHI up to 20% occur if using monthly or yearly mean values of β Angstrom.
• Errors in GHI less than 5% occur if using hourly or daily mean values of β Angstrom.

Even though the monitoring of solar radiation experienced a vast progress in the recent years both in terms of expanding the measurement networks and increasing the data quality, the number of stations is still too small to achieve accurate global coverage. Alternatively, various models for estimating solar radiation are exploited in many applications. Choosing a model is often limited by the availability of the meteorological parameters required for its running. In many cases the current values of the parameters are replaced with daily, monthly or even yearly average values. This paper deals with the evaluation of the error made in estimating global solar irradiance by using an average value of the Angstrom turbidity coefficient instead of its current value. A simple equation relating the relative variation of the global solar irradiance and the relative variation of the Angstrom turbidity coefficient is established. The theoretical result is complemented by a quantitative assessment of the errors made when hourly, daily, monthly or yearly average values of the Angstrom turbidity coefficient are used at the entry of a parametric solar irradiance model. The study was conducted with data recorded in 2012 at two AERONET stations in Romania. It is shown that the relative errors in estimating global solar irradiance (GHI) due to inadequate consideration of Angstrom turbidity coefficient may be very high, even exceeding 20%. However, when an hourly or a daily average value is used instead of the current value of the Angstrom turbidity coefficient, the relative errors are acceptably small, in general less than 5%. All results prove that in order to correctly reproduce GHI for various particular aerosol loadings of the atmosphere, the parametric models should rely on hourly or daily Angstrom turbidity coefficient values rather than on the more usual monthly or yearly average data, if currently measured data is not available.