Application of probability models to Malaysian sunshine data

A 10-year Malaysian sunshine data of four stations were fitted to three models, namely the Bendt, Hollands and Huget and Saunier models. Distribution parameters of the models were determined from the values of the observed mean of the sunshine data. The Kolmogorov–Smirnov test was applied to determine the goodness of fit. It was found that the Saunier model was suitable for the Petaling Jaya and Subang stations while the Hollands and Huget model well suited the Bayan Lepas and Kota Bharu stations. The Bendt model did not give a good fit for all stations. It was also found that for the months that have the same observed mean but different observed standard deviations the distribution models were able to fit well only if the estimated standard deviations were close in value to the observed standard deviations. © 1998 John Wiley & Sons, Ltd.     

Global solar radiation estimation using sunshine duration in Spain

Several equations were employed to estimate global solar radiation from sunshine hours for 16 meteorological stations in Spain, using only the relative duration of sunshine. These equations included the original Angström–Prescott linear regression and modified functions (quadratic, third degree, logarithmic and exponential functions). Estimated values were compared with measured values in terms of the coefficient of determination, standard error of the estimate and mean absolute error. All the models fitted the data adequately and can be used to estimate global solar radiation from sunshine hours. This study finds that the third degree models performed better than the other models, but the linear model is preferred due to its greater simplicity and wider application. It is also found that seasonal partitioning does not significantly improve the estimation of global radiation.     

Estimating monthly mean valuesof daily total solar radiation for Australia

Monthly mean values of daily total solar radiation were obtained for the widest possible network acrossAustralia. Bureau of Meteorology sources yielded 11 stations with long term records of both measured daily total solar radiation and sunshine hour values. Monthly modified Angstrom equations were developed from these data and used to estimate radiation values for a further 90 stations in the Bureau of Meteorology network that had sunshine hour data. Measured daily total solar radiation data were obtained from a variety of sources mostly outside the Bureau of Meteorology network for an additional 33 stations. Finally, estimates of solar radiation from detailed cloud cover data were used for a further 12 stations, selected because they filled in significant gaps in coverage. These various sources yielded a total of 146 sets of monthly mean values of daily total solar radiation. For each month optimal surfaces, which were functions of position only, were fitted to this network of values using Laplacian smoothing splines with generalized cross validation. Residuals from the fitted surfaces at the data points were acceptably low. Fitted surfaces which included, in addition to position variables, a cloudiness index based on a transform of mean monthly precipitation further reduced these residuals. The latter fitted surfaces permit estimation of monthly mean values of total daily solar radiation at any point on the continent with a root mean square predictive error of no more than 1.25 MJ m⁻² day⁻¹ (5.2 per cent of the network mean) in summer and 0.74 MJ m⁻² day⁻¹ (5.5 per cent of the network mean) in winter.     

Generation of daily solar irradiation by means of artificial neural net works

The present study proposes the utilization of Artificial Neural Networks (ANN) as an alternative for generating synthetic series of daily solar irradiation. The sequences were generated from the use of daily temporal series of a group of meteorological variables that were measured simultaneously. The data used were measured between the years of 1998 and 2006 in two temperate climate localities of Brazil, Ilha Solteira (São Paulo) and Pelotas (Rio Grande do Sul). The estimates were taken for the months of January, April, July and October, through two models which are distinguished regarding the use or nonuse of measured bright sunshine hours as an input variable. An evaluation of the performance of the 56 months of solar irradiation generated by way of ANN showed that by using the measured bright sunshine hours as an input variable (model 1), the RMSE obtained were less or equal to 23.2% being that of those, although 43 of those months presented RMSE less or equal to 12.3%. In the case of the model that did not use the measured bright sunshine hours but used a daylight length (model 2), RMSE were obtained that varied from 8.5% to 37.5%, although 38 of those months presented RMSE less or equal to 20.0%.A comparison of the monthly series for all of the years, achieved by means of the Kolmogorov–Smirnov test (to a confidence level of 99%), demonstrated that of the 16 series generated by ANN model only two, obtained by model 2 for the months of April and July in Pelotas, presented significant difference in relation to the distributions of the measured series and that all mean deviations obtained were inferior to 0.39 MJ/m².It was also verified that the two ANN models were able to reproduce the principal statistical characteristics of the frequency distributions of the measured series such as: mean, mode, asymmetry and Kurtosis.     

Approach to drawing new global solar irradiation contour maps for Argentina

Given the shortage of solar irradiation measured data accurate enough to fulfill statistical conditions to be considered representative in time and space, there appeared alternatives for estimating them on the basis of the existing meteorological information, and one of the values used was the number of hours of bright sunshine.In this paper a limited number of stations is considered where the daily hours of bright sunshine and of global irradiation were measured simultaneously, thus making it possible to find the constants of the Ångström–Prescott equation for each month. The spatial distribution curves of those constants for the whole country were drawn using the kriging method. From them, and taking into account the data from bright sunshine hours measured in a great number of stations, charts with the distribution of hours relative to bright sunshine were drawn using the above-mentioned interpolation method and the Ångström–Prescott linear equation was applied; mean values for the whole territory were thus found. Using once again the geostatistical interpolation the charts with the space–time distribution of the resource were drawn; the error evaluated is in the order of 10%. The results obtained for the months of January and July are shown for illustration purposes.     

Techniques for the precise estimation of hourly values of global, diffuse and direct solar radiation

The method usually used to compute solar radiation, when no measured data are available, is the well-known regression technique relating mean daily totals of global and diffuse solar radiation with the mean duration of sunshine. Using this method and taking into account the first order multiple reflections between the ground and the atmosphere, regression parameters were obtained from the monthly mean values of daily totals of global solar radiation and sunshine at a network of 16 stations in India. Daily values of global and diffuse solar radiation were then computed for 121 stations, where sunshine data are available for periods of 6–28 yr, using interpolated values of the regression parameters. Where no sunshine data were available, global and diffuse solar radiation were computed from cloud observations, using the inverse relationship between sunshine and cloudiness. Further, using the empirical relationship between daily totals and the corresponding hourly values of global and diffuse solar radiation, two sets of curves were prepared valid for the whole country, using which mean hourly values of global and diffuse radiation could be deduced from the corresponding daily totals, with a high degree of accuracy. The paper discusses the validity of the techniques used for computing daily and hourly values of global and diffuse solar radiation from sunshine and cloud amounts at an extended network of 145 stations in India and stresses the fact that such techniques are successful, only if accurate data on both radiation and sunshine are available at a widely distributed network of stations for a minimum period from at least 5 to 6 yr, using carefully calibrated and well-maintained instruments of the required quality. Theoretical models have also been used to compute clear sky noon values of global, diffuse and direct solar radiation from the solar constant, allowing for attenuation by atmospheric constituents such as ozone, water vapour, dust and aerosols. Using a simple model, calculations of global and diffuse solar radiation on clear days were made for 145 stations from values of the solar constant and measured values of ozone, water vapour and atmospheric turbidity. A method of extending the technique to overcast skies and partly clouded skies is discussed. The values of the mean annual transmission factor for global solar radiation under cloud-free conditions using the two methods show excellent agreement and establishes the soundness of the regression technique on one hand and the reliability of the theoretical model used for computing clear sky radiation, on the other.     

Statistical analysis of solar measurements in Algeria using beta distributions

A method of smoothing solar data by beta probability distributions is implemented in this paper. In the first step, this method has been used to process daily sunshine duration data recorded at thirty-three meteorological stations in Algeria for eleven year periods or more. In the second step, it has been applied to hourly global solar irradiation flux measured in Algiers during the 1987/89 period. For each location and each month of the year, beta probability density functions fitting the monthly frequency distributions of the daily sunshine duration measurements are obtained. Both the parameters characterising the resulting beta distributions are then mapped, enabling us to build the frequency distributions of sunshine duration for every site in Algeria. In the case of solar radiation for Algiers, the recorded data have been processed following two different ways. The first one consists in sorting the hourly global solar irradiation data into eight typical classes of the daily clearness index. The second one is based on the repartition of these data per month. The results of the first classification show that for each class of daily clearness index, the hourly data under consideration are modelled by only one beta distribution. When using the second classification, linear combinations of two beta distributions are found to fit the monthly frequency distributions of the hourly solar radiation data.     

Estimation of height-dependent solar irradiation and application to the solar climate of Iran

An explicitly height-dependent model has been used to estimate the solar irradiation over Iran which has a vast range of altitudes. The parameters of the model have been chosen on general grounds and not by parameters best fitting to any of the available measured irradiation data in Iran. The estimated global solar irradiation on the horizontal surface shows a very good agreement (4.1% deviation) with the 17-year long pyranometric measurements in Tehran, and also, is in good agreement with other, shorter available measured data. The entire data base of the Iranian meteorological stations have been used to establish a simple relation between the sunshine duration records and the cloud cover reports which can be utilized in solar energy estimations for sites with no sunshine duration recorders.Clear sky maps of Iran for direct solar irradiation on tracking, horizontal, and south-facing vertical planes are presented. The global solar irradiation map for horizontal surface with cloudiness is zoned into four irradiation zones. In about four-fifths of the land in Iran, the annual-mean daily global solar irradiation on horizontal surface ranges from 4.5 to 5.4 kWh/m².     

The relationship between global solar radiation and sunshine duration in Vietnam

Two approaches of the well-known modified Angstrom formula were developed from long term records of measured monthly mean daily global solar radiation and sunshine hour values obtained from 12 meteorological stations across Vietnam. These formulae were then used to estimate solar radiation for stations where only sunshine records were available. Three other commonly used correlations between solar irradiation and sunshine duration were also used and their results compared with those of two developed models. The procedure of measurement in Vietnamese weather stations was also indicated.     

Estimation of monthly mean daily diffuse radiation in China

In this study, several equations are employed to estimate monthly mean daily diffuse solar radiation for eight typical meteorological stations in China. Estimated values are compared with measured values in terms of statistical error tests such as mean percentage error (MPE), mean bias error (MBE), root mean square error (RMSE). All the models fit the data adequately and can be used to estimate monthly mean daily diffuse solar radiation from global solar radiation and sunshine hours. This study finds that the quadratic model performed better than the other models:     

Offshore fatigue design turbulence

Fatigue damage on wind turbines is mainly caused by stochastic loading originating from turbulence. While onshore sites display large differences in terrain topology, and thereby also in turbulence conditions, offshore sites are far more homogeneous, as the majority of them are likely to be associated with shallow water areas. However, despite this fact, specific recommendations on offshore turbulence intensities, applicable for fatigue design purposes, are lacking in the present IEC code. This article presents specific guidelines for such loading. These guidelines are based on the statistical analysis of a large number of wind data originating from two Danish shallow water offshore sites. The turbulence standard deviation depends on the mean wind speed, upstream conditions, measuring height and thermal convection. Defining a population of turbulence standard deviations, at a given measuring position, uniquely by the mean wind speed, variations in upstream conditions and atmospheric stability will appear as variability of the turbulence standard deviation. Distributions of such turbulence standard deviations, conditioned on the mean wind speed, are quantified by fitting the measured data to logarithmic Gaussian distributions. By combining a simple heuristic load model with the parametrized conditional probability density functions of the turbulence standard deviations, an empirical offshore design turbulence intensity is determined. For pure stochastic loading (as associated with standstill situations), the design turbulence intensity yields a fatigue damage equal to the average fatigue damage caused by the distributed turbulence intensity. If the stochastic loading is combined with a periodic deterministic loading (as in the normal operating situation), the proposed design turbulence intensity is shown to be conservative. Copyright © 2001 John Wiley & Sons, Ltd.     

Solar radiation maps for Iraq

As measured solar radiation data for all parts of Iraq is not available, it has to be estimated using other weather variables. A number of correlations which use dry bulb temperature, relative humidity and sunshine duration were tried. Finally a correlation using sunshine duration was selected as it gave most accurate estimation of solar radiation. Constants for the correlation for three stations representing three climatic regions in Iraq were determined. Monthly and yearly solar radiation maps were drawn using sunshine duration data from 24 stations from all over the country.     

Assessment of solar and wind energy resources in Ethiopia. I. Solar energy

This paper describes how data from a variety of sources are merged to present new countrywide maps of the solar energy distribution over Ethiopia. The spatial coverage of stations with radiation data was found to be unsatisfactory for the purpose of a countrywide solar energy assessment exercise. Therefore, radiation had to be predicted from sunshine hours by employing empirical models. Using data from seven stations in Ethiopia, linear and quadratic correlation relationships between monthly mean daily solar radiation and sunshine hours per day have been developed. These regional models show a distinct improvement over previously employed countrywide models. To produce a national solar-energy distribution profile, a spatial extension of the radiation/sunshine relationships had to be carried out. To do this, the intercepts (a) and slopes (b) of each of the seven linear regression equations and another six from previous studies, completed in neighbouring Sudan, Kenya and Yemen, were used to interpolate the corresponding values to areas between them. Subsequent to these procedures, 142 stations providing only sunshine data were assigned their “appropriate” a and b values to estimate the amount of solar radiation received, which was then used to produce annual and monthly solar radiation distribution maps for Ethiopia. The results show that in all regions solar energy is an abundant resource.     

Estimates of the Linke turbidity factor over Zimbabwe using ground-measured clear-sky global solar radiation and sunshine records based on a modified ESRA clear-sky model approach

This paper describes a procedure that can be used to calculate values for Linke atmospheric turbidity factors at air mass 2 (TL2) over Zimbabwe. Ground measured daily global solar radiation on clear days over 3years is used to evaluate TL2 for those stations that measure global radiation. The evaluation makes use of the clear-sky model of the European Solar Radiation Atlas (ESRA) combined with a diffuse transmittance model developed in the study. For those stations that do not measure global radiation but have sunshine duration records, global radiation values are generated through Angstrom type regression coefficients between the clearness index and relative sunshine duration. The TL2 values that are generated from the ESRA model are higher than those obtained from the study model (root mean square error (RMSE) up to 1.0 Turbidity Units). When compared to TL2 values from this study, the worldwide database SoDA, give significantly higher TL2 values (RMSE up to 2.2 Turbidity Units), underlining the value addition obtained in using measurement derived values in place of SoDA values.The values obtained from the study may be used to yield better estimates of clear-sky solar radiation for Zimbabwe. A better estimate of the clear-sky solar radiation will in turn improve the accuracy of the global radiation estimates from satellite based methods.     

Test reference year generation from meteorological and simulated solar radiation data

In this paper, a new method for generating test reference year (TRY) from the measured meteorological variables is proposed. Hourly recorded data of air temperature, relative humidity and wind velocity for two stations, Valladolid and Madrid (Spain) were selected to develop the method and a TRY was obtained. Monthly average solar radiation values were calculated taking into account the temperature and solar radiation correlations. Four different methodologies were used to evaluate hourly global solar radiation from hourly weather data of temperature and, as a consequence, four different TRYs with common data sets of temperature, relative humidity and wind velocity were generated for Valladolid and Madrid (Spain) stations. In order to evaluate the four different methodologies, TRYs data were compared with long-term measured data series using statistical estimators such as average, standard deviation, root mean square error (rmse) and mean bias error (mbe). Festa and Ratto and the TAG model, from Aguiar and Collares-Pereira, respectively, turned out to be the best methods for generating hourly solar irradiation data. The best performance was shown by the TRY0 year which was based on the solar radiation models mentioned above. The results show that the best reference year for each site varies with the season and the characteristics of the station.     

Assessing the suitability of wind speed probabilty distribution functions based on wind power density

Three functions have so far predominantly been used for fitting the measured wind speed probability distribution in a given location over a certain period of time, typically monthly or yearly. In the literature, it is common to fit these functions to compare which one fits the measured distribution best in a particular location. During this comparison process, parameters on which the suitability of the fit is judged are required. The parameters that are mostly used are the mean wind speed or the total wind energy output (primary parameters). It is, however, shown in the present study that one cannot judge the suitability of the functions based on the primary parameters alone. Additional parameters (secondary parameters) that complete the primary parameters are required to have a complete assessment of the fit, such as the discrepancy between the measured and fitted distributions, both for the wind speed and wind energy (that is the standard deviation of wind speed and wind energy distributions). Therefore, the secondary statistical parameters have to be known as well as the primary ones to make a judgement about the suitability of the distribution functions analysed. The primary and secondary parameters are calculated from the 12-month of measured hourly wind speed data and detailed analyses of wind speed distributions are undertaken in the present article.     

Solar radiation resource assessment by means of silicon cells

To provide an accurate solar resource assessment, radiometric stations measuring global, diffuse, and direct irradiance must be widespread. Nevertheless, the high capital costs of thermopile instruments, usually used in pyranometry, represent an important obstacle. Therefore, silicon photovoltaic sensors have emerged as a more accessible alternative than standard thermopile sensors. However, their temperature and spectral responses must be taken into account in order to match silicon cells and thermopile responses. Global and diffuse irradiance have been measured from early 1990 to the end of 1992 in Almería, southeastern Spain, by means of thermopile and photovoltaic sensor. Polar axis shadowbands were employed to measure the diffuse irradiance. These 10-minute coincident data sets, covering a complete range of atmospheric conditions, have been used to develop a correction procedure for the silicon detector measurements. Before the correction procedure was applied severe discrepancies were found, especially for the diffuse irradiance measurements performed under clear skies. Results of the correction method applied to an independent data set show a remarkable improvement. After correction, the comparison of silicon cell measurements with those obtained by means of thermopile pyranometers leads to a root mean square deviation of about 4% and 5% over the mean value of global and diffuse horizontal irradiance, respectively.     

The estimation of global and sky radiation in Austria

For obtaining the radiation values necessary for utilization of solar energy at as much possible locations in Austria, the monthly sums of global radiation at the horizontal surface are estimated after Angström from the relative duration of sunshine using the extraterrestrial radiations as maximum values. The thereby needed constants, which were evaluated for 19 stations in Austria with synchronous measurements of global radiation and duration of sunshine, are stated for the seasons as functions of altitude above sea level. The sky radiation is estimated by means of relationships after Liu-Yordan. These relationships were evaluated from the longterm measurements of global- and sky radiation at three stations in Austria for the mean monthly sums and for the mean hourly sums.     

Effect of sunshine and solar declination on the computation of monthly mean daily diffuse solar radiation

Several years of measured data for 17 European locations have been used to develop models for estimating monthly mean daily values of diffuse radiation (Hd) from combinations of the following: clearness index, sunshine fraction, and solar declination. Two models giving the highest correlation coefficients and the lowest standard errors of estimation are tested with data for 10 European locations not used in their development. From consideration of the MBE and RMSE values, a model which estimates Hd values from clearness index, relative sunshine duration and solar declination is found to be the most accurate. Comparison with Hd values predicted with the European Community solar radiation model (ECM) confirms this conclusion.     

Estimation of global solar radiation in Benin

Following Frère and Rietveld's model, correlation constants a and b were determined for many stations in Benin using:

• - a graphical relationship between the average annual relative sunshine SS/SS′o and the constants (Frère's model).

• - a linear relationship between constant a and the appropriate value of sunshine duration and a hyperbolic relationship between constant b and the relative average annual sunshine (Rietveld's model).

Knowledge of constant for a location can be used to predict global solar radiation for other locations using the Angström-Page approach using a statistical relationship between global solar radiation and sunshine duration.The estimated values were compared with measured values.