Solar and terrestrial radiation dependent on the amount and type of cloud

Ten-year (1964–1973) continuous records at Hamburg of hourly sums of solar and terrestrial, downward and upward radiation flux densities have been evaluated with regard to simultaneous hourly cloud observations. The irradiance at given solar elevation is plotted vs total cloud amount for each season and for the whole year; in the same way, the ratio of the irradiance under clouded to that under cloudless sky is presented. Additional diagrams show the irradiance under cloudless and under overcast sky as function of solar elevation. The ratio of global radiation at total cloud amount N okta, G(N), to global radiation at cloudless sky, G(0), at the same solar elevation γ turned out to be indepenent of γ and can be parameterized by

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. The influence of cloud type is demonstrated by diagrams showing the irradiance under skies overcast by a specific cloud type as function of solar elevation for each season and for the year; also, the corresponding ratios “overcast” to “cloudless” are presented. In the case of global radiation, the ratios which may be interpreted as the transmittances of the specific cloud types for global radiation, turned out to be independent of solar elevation and have the following mean values: Ci, Cc, Cs 0.61; Ac, As 0.27; Sc, Cu 0.25; St 0.18; Ns 0.16.     

The solar radiation climate of Thailand

Geographical, seasonal, and diurnal variations of global solar radiation in Thailand are surveyed. Seasonal effects are shown by separate studies for eight 1.5 month periods of the year defined by standard solar declination values. Detailed maps are given of the geographical distribution of solar radiation prepared from data on cloudiness at 44 stations, duration of sunshine at 18 stations, and linear regressions relating radiation to sunshine at Chiang Mai and Bangkok. The highest mean values are above 19.5 MJ m⁻² d⁻¹ and are widespread in spring. The lowest values are below 15.0 MJ m⁻² d⁻¹ in restricted localities with heavy rainfall in autumn.Rough estimates of diffuse solar radiation and atmospheric turbidity are made from the radiation-sunshine regression parameters. Diffuse radiation averages 8.4 MJ m⁻² d⁻¹. Turbidity at Chiang Mai is high in spring and low in summer and autumn; at Bangkok it is high throughout the year.The diurnal variation of global solar radiation determined from hourly measurements at Chiang Mai and Bangkok is analysed. The mean midday radiation fluxes range from 0.80 kW m⁻² in spring to 0.60 kW m⁻² in autumn. On the average the radiation received in the afternoon is slightly less than that received in the morning.     

Using probabilistic finite automata to simulate hourly series of global radiation

A model to generate synthetic series of hourly exposure of global radiation is proposed. This model has been constructed using a machine learning approach. It is based on the use of a subclass of probabilistic finite automata which can be used for variable-order Markov processes. This model allows us to represent the different relationships and the representative information observed in the hourly series of global radiation; the variable-order Markov process can be used as a natural way to represent different types of days, and to take into account the “variable memory” of cloudiness. A method to generate new series of hourly global radiation, which incorporates the randomness observed in recorded series, is also proposed. As input data this method only uses the mean monthly value of the daily solar global radiation. We examine if the recorded and simulated series are similar. It can be concluded that both series have the same statistical properties.     

Estimation of hourly solar radiation for India

The ASHRAE constants predict high values of the hourly beam radiation and very low values of the hourly diffuse radiation when used to predict radiation at Indian locations. Hence a procedure has been developed for the estimation of direct, diffuse and global hourly solar radiation on a horizontal surface for any location in India. To calculate hourly solar radiation, an exponential curve, similar to the one used by ASHRAE, was fitted to the measured solar radiation data of six cities from different regions of India. The statistical analysis was carried out for the data computed using ASHRAE constants and the set of constants obtained for India using the measured data of four different Indian cities selected randomly. Three statistical indicators were used to compare the accuracy of the developed procedure. The results show that ASHRAE constants are not suitable to estimate hourly solar radiation in India. Hourly solar radiation estimated by constants obtained for India are fairly comparable with measured data. The mean percentage error with Indian constants for these four Indian cities was found as low as 2.27, −6.29 and −6.09% for hourly beam, diffuse and global radiation, respectively.     

Dependence on cloudiness and solar altitude of global solar radiation received at 315 and 545 nm on horizontal surfaces

The study of monthly mean half hourly values of global radiation received at 315 (u.v.) and 545 nm (green) on a horizontal surface at Uccle (Belgium) in 1980 for clear (half hourly sunshine fraction σ = 1) and overcast (σ = 0) skies shows that for any solar altitude, global radiation received at 315 nm is less absorbed by clouds than radiation received at 545 nm. An explanation is given of the dependence on solar altitude for clear skies of the ratio between monthly mean half hourly values of global radiation received at both wavelengths, based on considerations concerning the direct and diffuse components.     

Measured solar radiation in a Nigerian environment compared with predicted data

Diurnal global irradiation was measured with precision pyranometer in Nsukka, Nigeria and compared with values generated from five different empirical models proposed by earlier investigators. Climatological parameters of sunshine hours, relative humidity, and maximum air temperature, as well as geographical declination, latitude and altitude factors are required as the model inputs. The calculated values obtained from the modified empirical formula of Swartman and Ogunlade gave the best agreement with the measured data. Agreement was within ±6 per cent. The analytical results derived from the regression equation of Angstrom agreed to within ±10 per cent with the measured solar radiation intensity. These formulas could be applied with the average best fitted coefficients developed in this investigation to estimate the solar radiation intensity fairly accurately in other parts of Nigeria lacking solar irradiation data.Results are also presented on the effect of dust haze attenuation which characterizes part of the environmental dry season. The period is seen to represent the season of maximum irradiance for the year primarily because of the absence of rain-bearing clouds. The prevailing winds however come north-easterly from the Sahara Desert and the associated dust-laden air results in reduced clearness index and increased diffuse irradiance ratio. The days overcast with dust haze give results that are in close agreement with Canadian cloudy days as presented by Orgill, but the overall dry season correlation follows that of Modi and Sukhatme in India.     

A multivariate qualitative model for the prediction of daily global radiation from three hourly global radiation values

A new model for the prediction of daily global radiation using three hourly radiation values is proposed. This model is obtained by multivariate regression analysis. The hourly clearness index and various qualitative variables are used as independent variables. The hourly values are obtained from net ground measures of hourly global radiation corresponding to the hours in which Meteosat secondary images are available over Europe. The qualitative variables allow us to include additional non-numerical information, specifically, the season of the year. The proposed model is the same for all the locations analysed. This model can be used for the prediction of daily global radiation based on hourly global radiation data obtained from satellite images.     

Monthly ratios of PAR to global solar radiation measured at northern Tibetan Plateau, China

Using narrowband and broadband solar radiation measurements collected at Wudaoliang (WDL) site in northern Tibetan Plateau (NTP) from September 1993 to December 1998, the relationship between monthly photosynthetically active radiation (Q_P) and global solar radiation (R_S) values is analyzed. Temporal variability of the ratio (Q_P/R_S) and its further dependence on several meteorological variables are presented. The narrowband ratio exhibited diurnal and seasonal variability with high values during morning and afternoon hours and low values around noon in winter time, whereas during summer period the ratio was decreased from morning to afternoon. The ratio (Q_P/R_S) was correlated positively with several atmospheric parameters such as water vapor pressure and low-level cloud amount; in contrast, the ratio was negatively correlated with clearness index, relative sunshine duration and atmospheric turbidity. It was also found that both the relative sunshine duration and water vapor pressure are the most influential parameters on the estimations of the spectral PAR ratio. Finally, an empirically derived model is proposed for estimating monthly average PAR values over the northern Tibetan Plateau. Verification results further ensured that the proposed model predicts monthly global PAR values accurately.     

Instantaneous distribution of global and diffuse radiation on horizontal surfaces

The aim of this paper is to obtain a general expression for estimating both the instantaneous global and diffuse radiations on horizontal surfaces from the respective daily values. The proposed expression is a modified Gaussian distribution with two parameters which take into account its width and the asymmetries between morning and afternoon hours. The performance of the method has been tested by comparing the theoretical hourly results with the experimental data of six actinometric stations with different geographical location and climatic conditions. The comparison has shown that the method here proposed is accurate for both the diffuse and global radiation.     

Hourly diffuse fraction correlation at a tropical location

Five years of hourly global and diffuse radiation data on a horizontal surface at a tropical location (Madras, India) were used to establish the relationship between the hourly diffuse fraction and hourly clearness index. Two types of correlations—on a yearly and a seasonal (wet and dry months)—have been established. Piecewise and single polynomial curves have been fitted to the data. These correlations have been compared to those developed by Orgill and Hollands (1977), Erbs et al. (1982), and Reindl et al. (1990), which have been obtained from data of temperate locations. The comparison has been performed in terms of standard deviation and relative standard deviation. The results indicate that the proposed correlations are better. The best fits were obtained when the seasonal effects were taken into account. It is also shown that the hourly diffuse fraction is larger at a tropical location at higher hourly clearness indices.     

Estimation of daily and monthly direct, diffuse and global solar radiation from sunshine duration measurements

An accurate 200 W/m² threshold pyreheliometer instrument for measuring the duration of bright sunshine has been used to derive daily and monthly regressions for direct, diffuse, and global solar radiation component vs sunshine duration. Daily regression for diffuse/global are linear in sunshine duration, while quadratic regression forms are employed for direct normal, direct horizontal, and global/extraterrestrial components. Only the daily direct normal component had regression values which depend on season while all of the monthly regressions depend on season. Linear regression relations for monthly direct normal, diffuse/global and global/extraterrestrial are employed, with a quadratic form being used for direct horizontal. Effects of rainfall, especially in overcast conditions, and of atmospheric turbidity and precipitable water, especially under clear-sky conditions, are observed and documented.     

Evaluation of solar radiation at just in Northern Jordan

Monthly averaged total daily global and direct incident solar radiation are presented. Maximum, averaged, and the minimum values of both global and direct incident radiation are given over the measuring period 1990–1996. The global and direct incident radiation at noon hour are also presented. A mathematical model for maximum total daily GR is given as a function of the number of the month of the year. Two other mathematical regressions were also obtained for the monthly averaged total daily global radiation and for monthly averaged total daily direct incident solar radiation.     

A study of solar ultraviolet radiation at Makkah solar station

Analysis of solar ultraviolet radiation (295–385 nm) and total global radiation (290–3000 nm), continuously recorded at a station in Makkah (21.5°N, 39.8°E) for 17 months in 1987–1988, has shown that the monthly average daily UV was 200 Wh m⁻². The ratio of UV to total global radiation varied from a maximum of 0.043 to a minimum of 0.028. A drop of 25% below the average 0.036, detected in the summer months, is attributed to scattering and absorption by dust and low tropospheric ozone. Comparison with Dhahran and Kuwait has shown that the effect was localised. A study of diurnal variation and clear, midday hourly radiation and the ratio of UV to global radiation, , also revealed an overall depletion in the summer months, despite the relative decrease in attenuation of Iv during cloudy days and at low solar altitudes. Multiple regressions of Hv and Iv on relevant variables with coefficients of determination exceeding 90% have been performed. Frequency distribution of daily UV is briefly discussed.     

Mean daily averages of beam radiation received by tilted surfaces as affected by the atmosphere

A method to compare the values of the monthly average beam radiation tilt factor, , obtained if atmospheric effects are accounted for or not, is presented. It is found that the difference between the two determinations may vary greatly with declination, latitude and ratio of daily averaged diffuse to global irradiation. In cases when this ratio is not obtained via direct measurement and its value is large enough, the accuracy of the “atmospheric” may be seriously affected. By comparison with measured radiation data from Montreal, Canada, the “atmospheric” as calculated by the proposed method appears very accurate for south vertical surfaces, and of acceptable accuracy for east or west vertical surfaces. In the latter case, a part of the discrepancy is attributed to various experimental errors, which are discussed.     

Iterative filtering of ground data for qualifying statistical models for solar irradiance estimation from satellite data

A new technique of filtering solar radiation ground data is proposed for generating models for solar irradiance estimation from geostationary satellite data. The filtering processes consists of an iterative way of selecting the training data set to achieve the best model response. Although in this paper the proposed methodology has been used for solar irradiance modeling, it could be applied to any kind of empirical modeling. The iterative filtering method has proven to have fast convergence and to improve successfully the statistical model response, when applied to hourly global irradiance calculation from satellite-derived irradiances for 13 Spanish locations. Individual statistical models for hourly global irradiance were fitted using the Heliosat I method applied to Meteosat images of 13 Spanish stations for the period 1994–1996.     

A revised empirical model to estimate solar radiation using automated surface weather observations

The transition from manual to automated weather observations at US National Weather Service Offices has compromised the ability to use these data as a means for estimating global horizontal and direct solar radiation. The creation of long term model-derived solar radiation climatologies continues to rely on the in situ cloud data that these observations provide, since homogeneous and readily available satellite data does not span the transition. An existing semi-physical solar radiation model is revised to allow for the estimation of hourly solar radiation based on these observations. Model evaluation reveals that errors in solar radiation estimates are comparable to other contemporary solar radiation models that estimate global horizontal solar radiation on both daily (10–15% mean absolute error) and hourly (15–19% mean absolute error) timescales. Hourly mean absolute errors are similar for different sky conditions, while daily percent errors are similar between seasons. Model updates also allow for accurate estimates of solar radiation in various climate regimes; regional patterns in model bias are not evident.     

A model for calculating hourly global solar radiation from satellite data in the tropics

A model for calculating global solar radiation from geostationary satellite data is presented. The model is designed to calculate the monthly average hourly global radiation in the tropics with high aerosol load. This model represents a physical relation between the earth-atmospheric albedo derived from GMS5 satellite data and the absorption and scattering coefficients of various atmospheric constituents. The absorption of solar radiation by water vapour which is important for the tropics, was calculated from ambient temperature and relative humidity. The relationship between the visibility and solar radiation depletion due to aerosols was developed for a high aerosol load environment. This relationship was used to calculate solar radiation depletion by aerosols in the model. The total column ozone from TOMS/EP satellite was employed for the determination of solar radiation absorbed by ozone. Solar radiation from four pyranometer stations was used to formulate the relationship between the satellite band earth-atmospheric albedo and broadband earth-atmospheric albedo required by the model. To test its performance, the model was used to compute the monthly average hourly global radiation at 25 solar radiation monitoring stations in tropical areas in Thailand. It was found that the values of monthly average of hourly global radiations calculated from the model were in good agreement with those obtained from the measurements, with the root mean square difference of 10%. After the validation the model was employed to generate hourly solar radiation maps of Thailand. These maps reveal the diurnal and season variation of solar radiation over the country.     

Stochastic simulation model of hourly total solar radiation

A stochastic simulation model of hourly global solar radiation is presented in this paper. It is developed by introducing the concept of “time dependent frequency distribution” (TDFD) of hourly insolation values. In this model the two most critical aspects of time series simulation, i.e., the reproduced time series values which have the appropriate time dependent frequency distribution for the parameter being simulated and the correlation between successive values, are taken into account. The elimination of the TDFD of the data and the transformation of the data distribution to a Gaussian distribution (required for the stationary time series analysis) were carried out using a mapping technique. The autocorrelation function of the transformed data showed that the produced time series is stationary. Then, an antimapping coefficient matrix is developed, which provides a simple yet an effective simulation device. The described model has been applied in Athens (Greece) where hourly insolation data covering a period of two years are used. The theoretical results obtained using this simulation model, regarding both the TDFD and the correlation, are in agreement with the measured data.     

Evaluation of a cloud cover based model for estimation of hourly global solar radiation in Western Canada

Cloud cover based solar radiation models are relatively simple and convenient as the models require the input of cloud cover data which are mostly available from the meteorological stations. In this study, the performance of a cloud cover based solar radiation model (Kasten–Czeplak model) with original or locally fitted coefficients was evaluated for estimating the hourly global solar radiation for four different locations in Western Canada. The average value of R², mean bias error, and root mean square error are 0.69, ?61.6, and 157.9?W?m^?2, respectively, for the model with original coefficients, whereas 0.82, 4.4, 107.1?W?m^?2 with locally fitted coefficients. Results show that the Kasten–Czeplak model with locally fitted coefficients satisfactorily estimated the hourly solar radiation of four different locations in Western Canada. Also, the results indicate that the model with original coefficients has very limited accuracy under intermediate cloud cover conditions.     

The determination of hourly insolation on an inclined plane using a diffuse irradiance model based on hourly measured global horizontal insolation

Using only measured hourly values of global insolation on a horizontal surface, a method has been developed for computing the corresponding hourly values of insolation on a surface inclined at any angle and oriented in any direction. The method uses a solar radiation model in which the diffuse component is calculated from global horizontal radiation using three different relationships; the appropriate equation is selected according to the value of the ratio of measured hourly global insolation to hourly global insolation computed for clear sky conditions. The method has been checked using measured hourly values in Melbourne over a 5-yr period of insolation on both a horizontal surface and a plane inclined at 38° to the horizontal facing north. The differences between the computed hourly values and the measured hourly values are found to be approximately normally distributed about zero with a standard deviation of 0.16 MJ m⁻². This method is particularly useful for predicting the heat output of inclined solar flat plate collectors when only measured global horizontal insolation is available, which is often the case. Good agreement was found between the predicted output of a typical collector using measured 38° insolation and the computed hourly values using this method. Since the method has been checked only against Melbourne data it should be applied elsewhere with caution, but it is believed to have general application.