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Solar Platform













Two themes are considered this year:

-         Enhancing the accuracy of the SIMv.1 clear sky solar irradiance model by better accounting for the aerosol influence on the atmospheric transmittance

-         Modeling the diffuse fraction





The relationship between solar irradiance and sunshine duration was investigated from the very beginning of solar radiation measurements. Many studies were devoted to this topic aiming to include the complex influence of clouds on solar irradiation into equations. The main topic of the seminar was focused on the famous Ångström-Prescott equation, which was investigated from different perspectives: (1) physical basis (mathematical derivation, physical meaning), (2) accuracy of the empirical models and (3) sensitivity to various astronomical and geographical factors; (4) Intrinsic limitations and the possibility to find a formula with general applicability.



Paulescu M, Stefu N, Calinoiu D, Paulescu E, Pop N, Boata R, Mares O (2016) Ångström – Prescott equation: Physical basis, empirical models and sensitivity analysis. Renewable and Sustainable Energy Reviews 62: 495-506.


In this paper the Ångström-Prescott equation is reviewed from three different perspectives: (1) the physical basis, (2) the accuracy of the empirical models and (3) the sensitivity to various astronomical and geographical factors. A mathematical derivation of the Ångström-Prescott equation is performed, showing the approximations behind it and the physical meaning of the coefficients. A number of 33 empirical Ångström-Prescott equations of different degrees of complexity and originated from different location around the world are being analyzed and tested against data recorded at 59 European stations. No model is ranked as the best, but the specific situations when a model performs better than others are discussed. A comparative study on the influence of different parameters (latitude, altitude, season, local climatology) on the performance of the Ångström-Prescott equations is presented. It is shown that an Ångström-Prescott equation having relative sunshine, altitude and the month index as input parameters can explain roughly 90% of the variability in the data from the entire database considered in this paper.   


Stefu N, Paulescu M, Blaga R, Calinoiu D, Pop N, Boata R, Paulescu E (2016) A theoretical framework for Ångström equation. Its virtues and liabilities in solar energy estimation. Energy Conversion and Management, 112, 236-245


This study is focused on the linear relationship between the clear sky index and the relative sunshine proposed by the pioneering work of Ångström. A full semi-empirical derivation of the equation, highlighting its virtues and liabilities, is presented. Specific Ångström – type equations for beam and diffuse solar irradiation were derived separately. The sum of the two components recovers the traditional form of the Ångström equation.  The physical meaning of the Ångström parameter, as the average of the clouds transmittance, emerges naturally. The theoretical results on the Ångström equation performance are well supported by the tests against measured data. Using long-term records of global solar irradiation and sunshine duration from thirteen European radiometric stations, the influence of the Ångström constraint (slope equals one minus intercept) on the accuracy of the estimates is analyzed. Another focus is on the assessment of the degradation of the equation calibration. The temporal variability in cloud transmittance (both long-term trend and fluctuations) is a major source of uncertainty for Ångström equation estimates. 



2013 - 2014



The main topic of the seminar was focused on the evaluation of the aerosol influence on the solar energy collected at the ground level. Within these studies a parametric model for solar irradiance components (SIMv.1) was developed. Also a part of the seminaries was devoted to forecasting solar irradiance. Significant results:


Calinoiu D, Paulescu M, Ionel I, Stefu N, Pop N, Boata R, Pacurar A, Gravila P, Paulescu E, Trif-Tordai G. (2013) Influence of aerosols pollution on the amount of collectable solar energy. Energy Conversion and Management 70, 76-82.


The solar energy loss due to the atmospheric pollution with aerosols is assessed in this paper. For this, a parametric clear sky solar irradiance model has been built and validated. For applying the model, a set of four meteorological parameters (surface air pressure, ozone column content, nitrogen dioxide column content and the Ångström turbidity coefficient) are required at input.

Eight episodes of pollution in Timisoara, Romania during 2011 have been identified. The energy loss in a pollution episode was evaluated as the difference between the clear sky solar irradiation computed in two situations: (1) using measured values for all inputs and (2) using measured values for all inputs excepting the Ångström turbidity coefficient, for which a climatological reference value has been assumed. The calculations show that the aerosol pollution can lead to a significant loss of collectable solar energy, of over 20%. Such very high values of losses are irregular in time and difficult to anticipate. However, such a reduction of collected energy should be taken into account when calculating the solar resource for sizing or operating a photovoltaic system. A practical simple equation which connects the collectable energy losses due to aerosols pollution to the Ångström turbidity coefficient has been established.


Calinoiu D, Stefu N, Paulescu M, Trif-Tordai G, Mares O, Paulescu E, Boata R, Pop N, Pacurar A. (2014) Evaluation of errors made in solar irradiance estimation due to averaging the Angstrom turbidity coefficient. Atmospheric Research, 150. 69-78.


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 Ångström 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 Ångström 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 Ångström 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 Ångström turbidity coefficient may be very high, even exceeding 20%. However, when instead of the current value of the Ångström turbidity coefficient an hourly or a daily average value is used, 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 Ångström turbidity coefficient values rather than on the more usual monthly or yearly average data, if currently measured data is not available.




2010 -2012



The topic of the seminar was focused on modeling the UV solar radiation.

The main results were reported in two papers:


Paulescu M, Stefu N, Tulcan-Paulescu E, Caliniu D, Neculae A, Gravila P (2010) UV solar irradiance from broadband radiation and other meteorological data. Atmospheric Research 96, 141-148.


Two original models for estimating UV solar irradiance are reported in this paper. The first, UV4PM, evaluates UV solar irradiance using four surface parameters: air pressure, the ozone column content, the nitrogen dioxide column content and the Ångström turbidity coefficient. As demonstrated in the paper, UV4PM is able to trace exactly the atmospheric transmittances calculated by integrating the original spectral transmittances. The second model, UV2G, correlates the UV solar irradiance components with the broadband ones. UV2G is derived from UV4PM aiming to remove the ozone and nitrogen dioxide column content from the list of the input parameters. The model can be used in any sky conditions since broadband solar irradiance measurements carry within the information concerning the actual state of the sky. Comparison with other models and measurements shows a fair level of accuracy of UV4PM and UV2G models.

The models presented in this study can be regarded as starting points to develop other parametric models able to evaluate the biological effects of UV radiation. This goal can be achieved by just adding appropriate spectral weighting functions in the first step of the parameterization algorithm.



Paulescu E, Stefu N, Gravila P, Boata RS, Pop N, Paulescu M (2012) Procedure of embedding biological action functions into the atmospheric transmittance. Theoretical and Applied Climatology 109, 323-332.


The method may be adapted to construct other parametric models able to evaluate the required biological effective irradiance. This goal can be achieved by simply putting in the appropriate spectral weighting function in the first step of the parameterization algorithm. The user should then verify if using the weighted average in the parametric model is fit enough to approximate the original spectral one, otherwise we indicate a solution based on the generalized mean. To our knowledge, this is the first study using generalized instead of weighted average to enhance the accuracy of effective parametric transmittances. In order to guide potential users to derive models according to their own requirements, the procedures for elaborating an effective atmospheric transmittance parametric model has been described in detail. For users interested in speed-intensive computation of the effective solar irradiance, a PC program based on the parametric equations above along with a user guide is posted online at (, section download_software). The application runs with celerity and is very easy to be exploited.   




Last update 22.02.2017