Models for obtaining daily global solar irradiation from air temperature data

The study presents a critical assessment of the possibility of global solar irradiation computation by using air temperature instead of sunshine duration with the classical Ångström equations. The reason for this approach comes from the fact that, although the air temperature is a worldwide measured meteorological parameter, this is rarely used in solar radiation estimation techniques. More than that, the literature is very silent concerning the testing of such models in Eastern Europe. Two new global solar irradiation models (to be called AEAT) related to solar irradiation under clear sky conditions and having the minimum and maximum daily air temperature as input parameters were tested and compared with others from the literature against data measured at five stations in Romania in the year 2000. The accuracy of AEAT is acceptable and comparable to that of the models which use sunshine duration or cloud amount as input parameters. Since temperature-based Ångström correlations are strongly sensitive to origin, the approach for AEAT as a tool for potential users is presented in detail. Additionally reported is a new method to increase the generality of AEAT concerning the extension of the geographical application area. Based on overall results it was concluded that air temperature successfully substitutes sunshine duration in the estimation of the available solar energy.     

Ultraviolet sky radiance distributions of translucent overcast skies

Summary The diffuse sky radiation component in the ultraviolet wavelengths is often at least 50% of the global irradiance under clear skies, and is the dominant component of ultraviolet global radiation under translucent overcast skies. The distribution of sky radiance was measured in a rural area and modeled for wavelength bands of ultraviolet-B (UVB, 280–320 nm) and ultraviolet-A (UVA, 320–400 nm). Sky radiance measurements were made during the summer of 1993 over a wide range of solar zenith angles using radiance sensors mounted on a hand-operated hemispherical rotation mount. UVB irradiance measurements were also made during each scan. Since the ratio of measured irradiance under overcast skies and that predicted for clear skies was not correlated with cloud base height, opaque cloud fraction, or solar zenith angle, it was concluded that the scattering from the clouds dominated the global irradiance, and this scattering was relatively unaffected by the scattering off opaque clouds in the translucent atmosphere.Analysis of the translucent overcast sky UVA and UVB radiance measurements using a semi-empirical distribution model showed that the spectral influences on multiple scattering, single scattering, and horizon brightening components of the distributions agreed with basic atmospheric radiation theory. The best model used solar zenith, the sky zenith, and the scattering angle with resultant coefficient of determination values of 0.62 and 0.25 for the UVA and UVB respectively. The developed equations can be applied directly to the diffuse sky irradiance on the horizontal to provide radiance distributions for the sky.With 6 Figures     

Effect of clouds on UV and total irradiance at Paradise Bay, Antarctic Peninsula, from a summer 2000 campaign

Summary ?The analysis of ground-based measurements of solar erythemal ultraviolet (UV) irradiance with a Solar Light 501 biometer, and total (300–3000 nm) irradiance with an Eppley B&W pyranometer at the Argentine Antarctic Base “Almirante Brown”, Paradise Bay (64.9° S, 62.9° W, 10 m a.s.l.) is presented. Measurement period extends from February 16 to March 28 2000. A relatively high mean albedo and a very clean atmosphere characterise the place. Sky conditions were of generally high cloud cover percentage. Clear-sky irradiance for each day was estimated with model calculations, and the effect of the cloudiness was studied through the ratio of measured to clear-sky value (r). Two particular cases were analysed: overcast sky without precipitation and overcast sky with rain or slight snowfall, the last one presenting frequently dense fog. Total irradiance was more attenuated than UV by the homogeneous cloudiness, obtaining mean r values of 0.54 for erythemal irradiance and 0.30 for total irradiance in the first case (without precipitation) and 0.27 and 0.17 respectively in the second case (with precipitation). Mean r values for the complete period were 0.58 for erythemal irradiance and 0.43 for total irradiance. Erythemal and total daily insolations reduce quickly at this epoch due to the increase of the noon solar zenith angle and the decrease of daylight time. Additionally, they were strongly modulated by cloudiness. Measured maxima were 2.71 kJ/m² and 18.42 MJ/m² respectively. Measurements were compared with satellite data. TOMS-inferred erythemal daily insolation shows the typical underestimation with respect to ground measurements at regions of high mean albedo. Measured mean total daily insolation agrees with climatological satellite data for the months of the campaign. Received August 9, 2002; revised January 4, 2003; accepted January 28, 2003 Published online May 20, 2003     

A new kind of cloudy sky model to compute instantaneous values of diffuse and global solar irradiance

Summary A model that uses two parameters to describe the state of the sky is presented. The parameters are the total cloud amount and a new two-value parameter – the sunshine number – stating whether the sun is covered or uncovered by clouds. Regression formulae to compute instantaneous cloudy sky global and diffuse irradiance on a horizontal surface are proposed. Fitting these relationships to Romanian data shows low bias errors for global radiation but larger errors for diffuse radiation. The model’s accuracy is significantly higher than one based on total cloud amount alone. The model is used to generate time-series of solar radiation data. A first approximate relationship, neglecting auto-correlation of the sunshine number, is used in the computations. Received July 17, 2001 Revised November 7, 2001     

Procedure of embedding biological action functions into the atmospheric transmittance

In order to perform calculations of biologically effective irradiance, the usual procedure is to modulate the ground-measured spectral solar irradiance with a specific biological action function. The inconvenience is that only a few meteorological stations worldwide are equipped to measure the spectral solar irradiance in the ultraviolet range. This motivates the search for a numerical substitute, which constitutes the subject of this report. An innovative approach based on generalized mean is used to infer the effective atmospheric transmittance. Its illustration resulted in a new parametric model for computing the biological dose under clear sky. The action spectrum for the growth response of plants, as a carrier of biological effects, is encapsulated into the atmospheric transmittance, leading to the calculation of the effective irradiance by simple algebra. The overall results indicate that the new parametric model performs accurately enough to be routinely used in practice. The procedure is general; therefore, it is described in detail to guide potential users in developing similar models incorporating other biological action spectra as needed. For speed-intensive applications, an executable file intended to run on any PC, which computes the effective irradiance with the proposed model, is provided.     

The albedo of snow for partially cloudy skies

The albedo of snow for different cloudiness conditions is an important parameter in the Earth's radiation budget analysis and in the study of snowpack's thermal conditions. In this study an efficient approximate method is derived to calculate the incident spectral solar flux and snow-cover albedo in terms of different atmospheric, cloud, and snow parameters. The global flux under partially cloudy skies is expressed in terms of the clear sky flux and a coefficient which models the effect of scattering and absorption by cloud patches and multiple reflections between the cloud base and snowcover. The direct and the diffuse components of the clear sky flux are obtained using the spectral flux outside the atmosphere and the spectral transmission coefficients for absorption and scattering by molecules and aerosols.The spectral snow reflectance model considers both specular surface reflection and volumetric multiple scattering. The surface reflection is calculated by using a crystal-shape-dependent bidirectional reflectance distribution function; the volumetric multiple scattering is calculated by using a crystal-size-dependent approximate solution in the radiative transfer equation. The input parameters to the model are atmospheric precipitable water, ozone content, turbidity, cloud optical thickness, the size and shape of ice crystals of snow and surface pressure. The model yields spectral and integrated solar flux and snow reflectance as a function of solar elevation and fractional cloudcover.The model is illustrated using representative parameters for the Antarctic coastal regions. The albedo for a clear sky depends inversely on the solar elevation. At high elevations the albedo depends primarily upon the grain size; at low elevation the albedo depends on grain size and shape. The gradient of the albedo-elevation curve increases as the grains become larger and faceted. The albedo for a densely overcast sky is a few percent higher than the clear-sky albedo at high elevations. A simple relationship between grain size and the overcast albedo is obtained. For a set of grain size and shape, the albedo as a function of solar elevation and fractional cloud cover is tabulated.     

Generation of daylight reference years for two European cities with different climate: Athens, Greece and Bratislava, Slovakia

In this work, daylight reference years (DRYs), based on daylight and solar radiation measurements, are designed for two European cities, Athens, Greece and Bratislava, Slovakia, by using the Danish method, the Festa–Ratto technique and the Modified Sandia National Laboratories methodology. The data basis consists of 5-minute values of global and diffuse horizontal illuminance, global and diffuse horizontal irradiance, zenith luminance and solar altitude as well as of daily values of sunshine duration for 5 years for Athens and 8 years for Bratislava. Moreover, Linke's turbidity factor, luminous turbidity factor and relative sunshine duration are calculated and utilized. Then, for each DRY, the predominant sky-luminance distributions over Athens and Bratislava are identified, by using the methodology of Kittler et al., who corresponded the main sky conditions to 15 theoretical sky standards in diagrams of the ratio of zenith luminance to diffuse horizontal illuminance against solar altitude.For both cities the three aforementioned methods do not create identical DRYs. Despite the differences, the sky types defined for each of the two places seem not to depend on the choice of DRY. The predominant sky standard, for all of them, is a cloudless, polluted sky with a broad solar corona for Athens and an overcast sky with slight brightening towards the sun as well as very clear sky with low atmospheric turbidity for Bratislava. However, the selection of the DRY, which represents best the daylight conditions, is necessary for studies in saving energy in buildings. The DRY, which is created by the Modified Sandia National Laboratories method, is chosen for most cases, while the one created by the Danish method is also useful on certain occasions.     

Generation of daylight reference years for two European cities with different climate: Athens,Greece and Bratislava,Slovakia

In this work, daylight reference years (DRYs), based on daylight and solar radiation measurements, are designed for two European cities, Athens, Greece and Bratislava, Slovakia, by using the Danish method, the Festa–Ratto technique and the Modified Sandia National Laboratories methodology. The data basis consists of 5-minute values of global and diffuse horizontal illuminance, global and diffuse horizontal irradiance, zenith luminance and solar altitude as well as of daily values of sunshine duration for 5 years for Athens and 8 years for Bratislava. Moreover, Linke's turbidity factor, luminous turbidity factor and relative sunshine duration are calculated and utilized. Then, for each DRY, the predominant sky-luminance distributions over Athens and Bratislava are identified, by using the methodology of Kittler et al., who corresponded the main sky conditions to 15 theoretical sky standards in diagrams of the ratio of zenith luminance to diffuse horizontal illuminance against solar altitude.For both cities the three aforementioned methods do not create identical DRYs. Despite the differences, the sky types defined for each of the two places seem not to depend on the choice of DRY. The predominant sky standard, for all of them, is a cloudless, polluted sky with a broad solar corona for Athens and an overcast sky with slight brightening towards the sun as well as very clear sky with low atmospheric turbidity for Bratislava. However, the selection of the DRY, which represents best the daylight conditions, is necessary for studies in saving energy in buildings. The DRY, which is created by the Modified Sandia National Laboratories method, is chosen for most cases, while the one created by the Danish method is also useful on certain occasions.     

A new approach to identify the sensitivity and importance of physical parameters combination within numerical models using the Lund–Potsdam–Jena (LPJ) model as an example

Daily global solar irradiation (R _s) is one of the main inputs in environmental modeling. Because of the lack of its measuring facilities, high-quality and long-term data are limited. In this research, R _s values were estimated based on measured sunshine duration and cloud cover of our synoptic meteorological stations in central and southern Iran during 2008, 2009, and 2011. Clear sky solar irradiation was estimated from linear regression using extraterrestrial solar irradiation as the independent variable with normalized root mean square error (NRMSE) of 4.69 %. Daily R _s was calibrated using measured sunshine duration and cloud cover data under different sky conditions during 2008 and 2009. The 2011 data were used for model validation. According to the results, in the presence of clouds, the R _s model using sunshine duration data was more accurate when compared with the model using cloud cover data (NRMSE = 11. 69 %). In both models, with increasing sky cloudiness, the accuracy decreased. In the study region, more than 92 % of sunshine durations were clear or partly cloudy, which received close to 95 % of total solar irradiation. Hence, it was possible to estimate solar irradiation with a good accuracy in most days with the measurements of sunshine duration.     

A new algorithm to estimate sky condition based on 5 minutes-averaged values of clearness index and relative optical air mass

Summary This work describes a new algorithm to characterize sky condition in intervals of 5 min using four categories of sun exposition: apparent sun with cloud reflection effects; apparent sun without cloud effects; sun partially concealed by clouds; and sun totally concealed by clouds. The algorithm can also be applied to estimate hourly and daily sky condition in terms of the traditional three categories: clear, partially cloudy and cloudy day. It identifies sky conditions within a confidence interval of 95% by minimizing local climate and measurement effects. This is accomplished by using a logistic cumulative probability function to characterize clear sky and Weibull cumulative probability function to represent cloudy sky. Both probability functions are derived from frequency distributions of clearness index, based on 5 minutes-averaged values of global solar irradiance observed at the surface during a period of 6 years in Botucatu, Southeastern of Brazil. The relative sunshine estimated from the new algorithm is statistically comparable to the one derived from Campbell-Stocks sunshine recorder for both daily and monthly values. The new method indicates that the highest frequency of clear sky days occurs in Botucatu during winter (66%) and the lowest during the summer (38%). Partially cloudy condition is the dominant feature during all months of the year.     

Modelling daily global radiation at the forest floor

A simple model is developed which estimates daily global radiation at the floor of a non-homogeneous Eucalyptus forest. Model input parameters are easily derived from field measurements and consist of individual tree location, tree height, maximum canopy width and its corresponding height, height of the lowest branch and trunk thickness. In addition, the model requires values for global and diffuse irradiance in the open. The tree canopy is represented as a series of spheres containing leaves which are homogeneously spaced but are oriented in the vertical plane. This configuration closely approaches that of actual eucalyptus trees. A Monte-Carlo approach is used to estimate the albedo of the unit sphere as a function of solar zenith angle. At a given combination of solar zenith and azimuth angle, the model estimates the solar irradiance at a specific forest floor location.The model, when tested against pyranometer measurements, predicted daily solar irradiance with a correlation of 0.98 and a standard error of 0.98 MJ m^-2 day^-1. This good performance is attributed to the spatial averaging of the radiation fluxes over the entire day, and the relatively low sensitivity of the calculated solar irradiance to sphere albedo.     

Modelling frequency distributions of 5 minute-averaged solar radiation indexes using Beta probability functions

Summary ¶Five minute-averaged values of sky clearness, direct and diffuse indices, were used to model the frequency distributions of these variables in terms of optical air mass. From more than four years of solar radiation observations it was found that variations in the frequency distributions of the three indices of optical air mass for Botucatu, Brazil, are similar to those in other places, as published in the literature. The proposed models were obtained by linear combination of normalized Beta probability functions, using the observed distributions derived from three years of data. The versatility of these functions allows modelling of all three irradiance indexes to similar levels of accuracy. A comparison with the observed distributions obtained from one year of observations indicate that the models are able to reproduce the observed frequency distributions of all three indices at the 95% confidence level.Received September 2, 2002; revised February 28, 2003; accepted March 16, 2003 Published online September 10, 2003     

敦煌地区晴空散射辐射影响因子的统计特征

利用敦煌地区1981—1983年全年及1984年与1985年1～2月的日射观测资料,统计分析了敦煌地区晴空下散射辐射与太阳高度角、大气柱气溶胶垂直光学厚度等影响因子的关系,用最小二乘法拟合得到了相应的函数关系式。拟合结果表明：晴空下散射辐射与太阳高度角符合幂函数关系;晴空下散射辐射随大气柱气溶胶光学厚度线性增长。     

基于EC细网格数值预报产品的太阳辐照度订正技术

太阳辐照度与光伏电站发电功率密切相关,其预报的准确性直接影响发电功率预报的准确性。根据光伏电站太阳辐照度实况、气象站实况、WRF(Weather Research and Forecast Model)模式辐照度预报、EC细网格数值预报以及太阳理论辐照度,利用逐步回归法开展太阳辐照度预报订正研究,得到以下结论:①太阳辐照度实况与太阳理论辐照度的比值与EC细网格数值预报中气象要素的相关性优于太阳辐照度实况与气象要素的相关性;②不同时刻影响太阳辐照度的气象因子存在差异,通过逐步回归法建立不同时刻太阳辐照度预报模型;③在非晴天情况下,回归预报辐照度相对均方根误差比WRF模式预报辐照度降低10%左右,减小了辐照度预报误差。该研究成果在光伏电站的新能源数值预报服务中有一定的应用价值。     

Derivation of Cloud Index from Geostationary Satellites and Application to the Production of Solar Irradiance and Daylight Illuminance Data

Summary  We investigate in the present paper the relationship between satellite count, global irradiance and other solar and illumination resource components, bringing a particular attention to low solar elevation situations (below 20 °) which are very important in northern latitudes. Our investigation is based on data from two geostationary satellites, METEOSAT and GOES, backed by ground measurements in Switzerland and the northeastern USA. The study of different clear sky normalizations lead to the conclusion that a linear correlation between the global clearness index and the irradiance (like the heliosat method) would be inaccurate for low solar elevations, and therefore for high latitude regions. We developed a model that directly relates an elevation dependent clearness index to the could index. This methodology presents a definite advantage because it can be generalized to address the clearness index of other solar radiation components, besides global irradiance, such as direct irradiance, diffuse illuminance, etc. The correlations described in this paper were developed on the data from Geneva (in the frame of the EC program “Satellight”) and evaluated on two other independent data sets (Albany, USA and Lausanne, Switzerland). Their precisions, on a hourly basis, are respectively 30%, 40% and 60% for the global, diffuse and beam components) (90,55 and 95 W/m²). The use of independent data for thederivation and the validation of the models shows thatthose can be used in a wide range of locations, even if the applicability has to be assessed for very different climates. Received June 27, 1998 Revised February 26, 1999     

Fengyun-4 Geostationary Satellite-Based Solar Energy Nowcasting System and Its Application in North China

Surface solar irradiance (SSI) nowcasting (0–3 h) is an effective way to overcome the intermittency of solar energy and to ensure the safe operation of grid-connected solar power plants. In this study, an SSI estimate and nowcasting system was established using the near-infrared channel of Fengyun-4A (FY-4A) geostationary satellite. The system is composed of two key components: The first is a hybrid SSI estimation method combining a physical clear-sky model and an empirical cloudy-sky model. The second component is the SSI nowcasting model, the core of which is the derivation of the cloud motion vector (CMV) using the block-matching method. The goal of simultaneous estimation and nowcasting of global horizontal irradiance (GHI) and direct normal irradiance (DNI) is fulfilled. The system was evaluated under different sky conditions using SSI measurements at Xianghe, a radiation station in the North China Plain. The results show that the accuracy of GHI estimation is higher than that of DNI estimation, with a normalized root-mean-square error (nRMSE) of 22.4% relative to 45.4%. The nRMSE of forecasting GHI and DNI at 30–180 min ahead varied within 25.1%–30.8% and 48.1%–53.4%, respectively. The discrepancy of SSI estimation depends on cloud occurrence frequency and shows a seasonal pattern, being lower in spring–summer and higher in autumn–winter. The FY-4A has great potential in supporting SSI nowcasting, which promotes the development of photovoltaic energy and the reduction of carbon emissions in China. The system can be improved further if calibration of the empirical method is improved.     

Classification of daily solar irradiation by fractional analysis of 10-min-means of solar irradiance

Summary This paper deals with fractal analysis of daily solar irradiances measured with a time step of 10 minutes at Golden and Boulder located in Colorado. The aim is to estimate the fractal dimensions in order to perform classification of daily solar irradiances. The estimated fractal dimension and the clearness index KT are used as classification criteria. The results show that these criteria lead to three classes: clear sky, partially covered sky and overcast sky. The results also show that the evaluation of the fractal dimension of the irradiance signal based on a data set with 10 minutes time step is possible.     

Value-Added Products Derived from 15 Years of High-Quality Surface Solar Radiation Measurements at Xianghe,a Suburban Site in the North China Plain

Surface solar radiation(SSR) is a key component of the energy budget of the Earth’s surface, and it varies at different spatial and temporal scales. Considerable knowledge of how and why SSR varies is crucial to a better understanding of climate change, which surely requires long-term measurements of high quality. The objective of this study is to introduce a value-added SSR dataset from Oct 2004 to Oct 2019 based on measurements taken at Xianghe, a suburban site in the North China Plain; two va...     

Global photosynthetically active radiation and its relationship with global solar radiation in the Eastern Mediterranean basin

Summary ?The relationship between global photosynthetically active radiation (PAR) and global solar radiation is studied with a 2-year data archive of hourly values H_PAR and H_SW of these irradiances obtained at Athalassa, Cyprus. These data are used to determine the temporal variability of H_PAR and its dependence on sky conditions. The seasonal variation of the ratio H_PAR/H_SW obtained from daily data ranges from 0.456 (during summer) to 0.451 (during winter) with an annual mean value of 0.454. The ratio increases from 0.454 to 0.467 (daily values) or from 0.460 to 0.501 (hourly values), as sky conditions change from clear to overcast. Finally, the effect of aerosol content on the H_PAR/H_SW ratio is found to incur substantial changes in the PAR fraction. Received June 27, 2001; revised April 17, 2002; accepted May 18, 2002     

Fuzzy modelling of solar irradiation using air temperature data

Summary Fuzzy sets theory is applied to relate global solar irradiation to both the daily average and the daily amplitude of air temperature. In addition to the presentation of a new mapping technique, from the input to the output of the model, an innovative approach for the tuning of the fuzzy algorithm to fit a local meteo-climate is proposed. Since air temperature-based solar radiation models are strongly dependent on the origin location, the adaptive method presented here is designed as a tool for potential users to either increase the application area or to devise more precise local models. A critical assessment of fuzzy model performances and limitations has been conducted. Results reported here demonstrate the potential of modelling solar irradiation using fuzzy sets approach. Authors’ address: E. Tulcan-Paulescu, M. Paulescu, Physics Department, West University of Timisoara, V. Parvan 4, 300223 Timisoara, Romania.