Solar radiation model for hot dry arid climates

The industrialised countries have well-established solar radiation networks based on detailed observations of solar irradiance data from relatively sophisticated weather stations. However, in many regions of the developing countries the only available data consist of records of sunshine hours. There have been several approaches towards establishing a relationship between sunshine hours and solar irradiance. This paper describes how one particular formula, the Barbaro et al. model, has been modified to determine solar irradiance from sunshine hours for a number of stations located in hot dry arid climates.     

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.     

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.     

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.     

Climatic influences on solar modelling in China

Correlation between clearness index and sunshine duration is useful to the estimation of the solar radiation for areas where measured solar radiation data are not available. Regression techniques were used to investigate the correlations between daily global solar radiation and sunshine duration for different climates in China. Measurements made during the 30-year period (1971–2000) from 40 measuring stations covering major thermal and solar climatic zones across China have been gathered and analysed. The correlations were developed for each individual station as well as for each of the major climates. It was found that the Angstrom–Prescott equation tended to give a good estimation of global solar radiation based on the corresponding measured sunshine hours. A simple two-parameter linear regression equation was proposed for each of the major thermal and solar climatic zones.     

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.     

Empirical relationship of cloud shade to point cloudiness (Canada)

Long-term averages of monthly cloud shade (CS) (based on Campbell-Stokes sunshine records) and point cloudiness (PC) (from weather observer records) for 43 Canadian weather stations show that CS = 0.159PC + 0.837PC². This regression equation is useful for estimating bright sunshine for locations where cloud cover records exist in the absence of sunshine records and can thus be employed to calculate expected solar radiation in solar energy applications. The analysis shows a general decrease of PC-CS with increasing latitude in agreement with similar analyses by other workers. This decrease is explicable in terms of the decrease in average solar elevation with increasing latitude.     

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.     

Estimation of solar radiation over Jordan—predicted tables

As measured solar radiation data for all parts of Jordan are not available, they have to be estimated using correlation relations and models. This paper presents, for the first time, values of solar radiation over Jordan as estimated from these relations. Measurements of global solar irradiance on a horizontal surface and sunshine duration at nine meteorological stations in Jordan are correlated and used for prediction of the regression coefficients of an Angstrom type correlation relation at these stations and others which only have records of sunshine duration. Regional regression coefficients are obtained and used for prediction of global solar irradiance. The agreement with measurements is better than 5% and 1% on monthly and yearly basis respectively. Estimation of diffuse solar irradiance by Page's and also Liu and Jordan's correlations, as well as the direct beam component are also performed and the results are examined and presented. The abundance of solar energy in Jordan is evident from the daily average global solar irradiance which ranges between 5 and 7 kWh/m². A correlation of Angstrom type of the form: H/Ho = 0.448+0.203 S/So is found suitable for Jordan with correlation coefficient r = 0.93.     

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.     

Compilation and evaluation of solar and wind energy resources in Sudan

A number of years worth of data concerning the solar radiation on a horizontal surface, sunshine duration and wind speed in Sudan have been compiled, evaluated and presented in this article.Measurements of global solar radiation on a horizontal surface at 16 stations for several years are compared with predictions made by several independent methods. In the first method the Angstrom formula was used to correlate relative global solar irradiance to the corresponding relative duration of bright sunshine.Regression coefficients are obtained and used for prediction of global solar irradiance. The predicted values were consistent with measured values (± 8.01% variation).In the second method, by Barbaro et al. [Solar Energy, 1978, 20, 431] sunshine duration and minimum air mass were used to drive an empirical correlation for the global radiation. The predicted values compared well with measured values (± 12% variation).The diffuse solar irradiance is estimated. The results of two formulas have close agreement. A radiation map of Sudan was prepared from the estimated radiation values. The annual daily mean global radiation ranges from 3.05 to 7.62 kW h m⁻² per day.Routine wind data from 70 stations were analyzed. Monthly averaged wind speed and average powers were determined for each station. The derived annual average speeds range from 1.53 to 5.07 m s⁻¹. Maximum extractable average wind powers were found to vary between 1.35 and 49.5 W m⁻². A wind map of Sudan was also prepared.Sudan possessed a relatively high abundance of sunshine and moderate wind speed. It is concluded that Sudan is blessed with abundant solar and wind energy.     

Estimation of total solar radiation from cloudiness in Turkey

Using the measured data from six stations in Turkey, two types of correlations are developed to estimate total solar radiation from (i) cloudiness and (ii) a combination of relative sunshine hours and cloudiness. The accuracy of these correlations is compared with previously developed equations based on the bright sunshine data. It has been concluded that the correlation as a function of two parameters, relative sunshine hours and cloudiness, gives more accurate results.     

Mesoscale mapping of available solar energy at the earth's surface by use of satellites

Ground measurements of solar radiation are too sparse to determine important mesoscale differences that can be of major significance in solar power station location and for other purposes. A method is presented for use of cloud images in the visual spectrum from the SMS/GOES geostationary satellites to determine the hourly distribution of sunshine on the mesoscale. Cloud coverage and density as a function of time of day and season are evaluated through the use of digital data processing techniques. Low density cirrus clouds are less detrimental to solar energy collection than other types; and clouds in the morning and evening are less detrimental than those during midday hours of maximum insolation.Seasonal geographic distributions of cloud cover/sunshine are converted to joules of solar radiation received at the earth's surface through relationships developed from long-term measurements of these two parameters at six widely distributed stations. The technique can be used to generate maps showing the geographic distribution of total solar radiation on the mesoscale which is received at the earth's surface.     

基于线性方法的内蒙古地区太阳总辐射月均值估算

探讨了内蒙古地区太阳总辐射月均值与日照百分率的关系,基于5个气象站1996—1998年连续3 a的月日照时数（n）和太阳总辐射值（R_s）。计算得到Angstrom方程的系数a和b,与和清华等拟合得到的中国西部太阳总辐射公式中的a=0.185,b=0.595,比较一致。同时,R_s和n之间的直接线性关系,R与月平均温度（T）之间的直接线性关系也能用来估算太阳总辐射月均值,总均方根误差约为80 MJ·m^-2/month,总百分比误差约为18%。     

Global solar radiation estimation from relative sunshine hours in Yemen

The existing measurements of global solar radiation and sunshine duration for Yemen are examined. The errors of estimating solar radiation from sunshine hour measurements using Angstrom's relation are evaluated. As a simple predictor for global radiation, an average Ansgtrom relations in the form

Full-size image (<1K)

for all stations is evaluated. Other Angstrom correlation relations are also proposed by classifying the stations under into four groups. The estimated results are compared and seem to be satisfactory in the latter case.     

Correlations between monthly average global solar radiation on horizontal surfaces and relative duration of sunshine in Yunnan Province, China

With measured data of global solar radiation and the relevant data of geographic and meteorological parameters at 7 meteorological stations in Yunnan Province, the correlations between monthly average global solar radiation on horizontal surfaces and relative duration of sunshine are developed in this special region which has significantly varying climates. It is believed that the two correlations developed in this work are applicable for estimating monthly global solar radiation on horizontal surfaces at any site in Yunnan Province, China.     

Estimation and prediction of global solar radiation over Greece

A regression analysis of the relative monthly values of global solar radiation ( ) the corresponding values of sunshine (n/N), for the period 1961-75, was performed to determine the constants a and b of the Ångström formula, for Athens. The constants a and b were also determined by a graphical relationship between the average annual relative sunshine (n/N) and these constants, for the same station. The latter method was then used to determine the constants a and b for 33 other stations widely distributed throughout Greece, after making a relative correction to these constants. In this way, monthly and annual values of global solar radiation were estimated for 34 stations over Greece from sunshine measurements. The geographical distribution of the annual totals of global solar radiation over Greece was mapped and some types and sub-types were identified.Further, a stepwise multiple regression analysis of the annual total amounts of global solar radiation and the three factors (latitude, longitude and altitude) was carried out; the validity of the assumption of the linear relationship between the annual totals of global solar radiation and the three factors was examined.     

The importance of maximum air temperature in the parameterisation of solar radiation in Nigeria

Using existing and new empirical model equations to analyse available data for nine stations located in different geographical and climatic zones in Nigeria, it is clearly demonstrated that maximum air temperature is an important climatological parameter which should be used in solar radiation modelling in Nigeria. It is also shown that seasonal variations in the values of the model parameters are significant.Preliminary investigations are also reported which show that (1) a slight modification of the Swartman-Ogunlade formulae improves their applicability to Nigerian stations, and (2) maximum air temperature and relative humidity can be used together (to the exclusion of sunshine duration) to predict solar radiation with satisfactory accuracy.     

Solar radiation climate of India

This paper presents the essential results of solar radiation measurements made at a network of thirteen stations in India during the last ten years. The basic records are of total integral wavelength global solar radiation and sky radiation on a horizontal surface, and of direct solar radiation and its spectral components, defined by the wavelength intervals λ < 525, 525–630, λ < 630, 525–710 and λ < 710 nm. Values of direct solar radiation at normal incidence and on horizontal and vertical surfaces have also been calculated from continuous records of the global and sky radiation on a horizontal surface at all 13 stations. The spatial and seasonal variations of direct solar radiation, global solar, and sky radiation are discussed. Results are also presented of special direct solar observations made at a few high altitude stations in Kashmir in 1969.     

Sensitivity analysis of performance of crop growth simulation models to daily solar radiation estimation methods in Iran

Solar radiation is the single most important environmental factor driving canopy photosynthesis and transpiration. This weather characteristic is measured only in a limited number of weather stations. Hence, in many situations it has to be estimated from other weather characteristics such as sunshine duration and temperature using empirical relations. In this study, the Ångstrom and Hargreaves formulas have been used for solar radiation estimation, based on monthly and annual weather data for three weather stations in Esfahan province, Iran. Deviations of estimated solar radiation from measured values (both absolute and relative) varied with month of the year and with estimation method. Estimated and measured radiation values were used in a crop growth simulation model to explore sensitivity of simulated production with respect to radiation estimation method. Maximum deviation for winter barley and silage maize was around 9%.