The quantification of the
aerosol influence on solar resources is the main topic of the seminar.
The seminar was focused on studying
the ability of the clear-sky solar irradiance models to accurately
partition the global solar irradiance (GHI) into beam and diffuse
components. Diverging from the traditional perspective, the diffuse
fraction was assessed as an appropriate quantifier for the fractional
part of GHI estimated by a clear-sky solar irradiance model as being
diffuse. Acting as a quantifier, the diffuse fraction has the merit of
isolating the uncertainty induced by aerosols in estimating the diffuse
The main results are collected
in a manuscript submitted to Meteorology and Atmospheric Physics:
Blaga R, Calinoiu D, Stefu
N, Boata R, Sabadus A, Paulescu E, Pop N, Mares O, Bojin S, Paulescu M (2020)
Quantification of the aerosol-induced errors in solar irradiance modeling.
2017 - 2018
seminar was focused on enhancing the accuracy of clear-sky solar
irradiance models, by a better capturing the aerosol influence on the
atmospheric transmittance. A key result is SIMv.2 model, an upgraded
version of our parametric clear-sky solar irradiance model (Energy
Conversion and Management 70 (2013) 76-82), aiming to improve the
estimates accuracy in arid environment.
Calinoiu D, Stefu N,
Boata R, Blaga R, Pop N, Paulescu E, Sabadus A, Paulescu M (2018)
Parametric modeling: A simple and versatile route to solar irradiance.
Energy Conversion and Management 164, 175-187.
ABSTRACT. A clear-sky solar
irradiance model is certainly a basic tool in the estimation of solar
resources. With all the abundance of such models, there is plenty of room
for searching a clear-sky solar irradiance model with general
applicability, i.e. to be able to provide high-accurate estimates in most
places around the world. This paper reports an upgraded version (further
referred to as SIMv.2) of our parametric clear-sky solar irradiance model
SIMv.1, aiming to improve the accuracy of estimates in arid environment.
The new elements of SIMv.2, such as new equations for aerosol absorption
and downward fraction, have been introduced targeting a better capture of
the peculiarities of the solar radiation extinction by aerosols. Overall,
the results of testing SIMv.2 at twelve stations located in regions with
temperate, arid and tropical climate show that SIMv.2 performs much better
than SIMv.1, an improvement in nRMSE of 37.1% for global solar irradiance
and of 24.7% for the diffuse component being noticed. The comparison with
other fourteen clear-sky solar irradiance models at five stations located
in arid climate places SIMv.2 in the class of the best performing models.
The limitation of the SIMv.2 performance in extreme weather conditions is
discussed in two cases.
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.
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:
ABSTRACT. 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
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,
ABSTRACT. 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:
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,
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.
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.
ABSTRACT. 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.
The topic of the seminar
was focused on modeling the UV solar radiation.
The main results were
reported in two papers:
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.
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 (http://solar.physics.uvt.ro/srms,
section download_software). The application runs with celerity and is
very easy to be exploited.