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 simple model for the prediction of yearly energy yields for grid-connected PV systems starting from monthly meteorological data

This paper presents a simple model, called Clear-cloudy sky, which estimates yearly energy yields for PV systems starting from the twelve monthly values of global horizontal solar irradiation, diffuse fraction, Linke turbidity and minimum and maximum ambient temperatures. The proposed model has been included in an online and free-software simulator of PV systems, called SISIFO, which has been used to analyse the performance of the model in comparison with other synthetic models using as reference the typical meteorological years (TMY3) of more than two hundred Class I stations belonging to the NREL American National Solar Radiation database. The results of this comparison show that the model provides yearly predictions on PV system performance parameters that have low bias and uncertainty with respect to the same figures obtained with the original TMY3 hourly time series.     

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.     

Generation of synthetic daily global solar radiation data based on ERA-Interim reanalysis and artificial neural networks

Four variables (total cloud cover, skin temperature, total column water vapour and total column ozone) from meteorological reanalysis were used to generate synthetic daily global solar radiation via artificial neural network (ANN) techniques. The goal of our study was to predict solar radiation values in locations without ground measurements, by using the reanalysis data as an alternative to the use of satellite imagery. The model was validated in Andalusia (Spain), using measured data for nine years from 83 ground stations spread over the region. The geographical location (latitude, longitude), the day of the year, the daily clear sky global radiation, and the four meteorological variables were used as input data, while the daily global solar radiation was the only output of the ANN. Sixty five ground stations were used as training dataset and eighteen stations as independent dataset. The optimum network architecture yielded a root mean square error of 16.4% and a correlation coefficient of 94% for the testing stations. Furthermore, we have successfully tested the forecasting capability of the model with measured radiation values at a later time. These results demonstrate the generalization capability of this approach over unseen data and its ability to produce accurate estimates and forecasts.     

Estimation of solar radiation from Australian meteorological observations

A carefully prepared set of Australian radiation and meteorological data was used to develop a system for estimating hourly or instantaneous broad band direct, diffuse and global radiation from meteorological observations. For clear sky conditions relationships developed elsewhere were adapted to Australian data. For cloudy conditions the clouds were divided into two groups, high clouds and opaque (middle and low) clouds, and corrections were made to compensate for the bias due to reporting practices for almost clear and almost overcast skies. Careful consideration was given to the decrease of visible sky toward the horizon caused by the vertical extent of opaque clouds. Equations relating cloud and other meteorological observations to the direct and diffuse radiation contained four unknown quatities, functions of cloud amount and of solar elevation, which were estimated from the data. These were the proportions of incident solar radiation passed on as direct and as diffuse radiation by high clouds, and as diffuse radiation by opaque clouds, and a factor to describe the elevation dependance of the fraction of sky not obscured by opaque clouds. When the resulting relationships were used to estimate global, direct and diffuse radiation on a horizontal surface, the results were good, especially for global radiation. Some discrepancies between estimates and measurements of diffuse and direct radiation were probably due to erroneously high measurements of diffuse radiation.     

Evaluation of models for predicting insolation on slopes within the Colorado alpine tundra

This empirical study evaluates insolation predictions for the Colorado tundra from models based upon isotropic and anisotropic distribution approximations for diffuse sky and reflected solar radiation. The data set of hourly insolation values was obtained from 40 locations on an alpine ridge by simultaneous measurement of direct beam irradiance and total insolation to the horizontal ridge crest and two nearby sloping surfaces. Six models are used to predict insolation, two based on the isotropic distribution of diffuse solar radiation and four on anisotropic diffuse distribution fields. Three models (one isotropic and two anisotropic) employ measurements of normal direct beam irradiance while the other 3 models incorporate the correlation between the “clearness index” and the ratio of diffuse sky to total insolation. The precision of insolation estimates from models using the correlation method is only slightly less than from other models. Accounting for the increase of diffuse radiation in the circumsolar sky improves insolation predictions. However, inclusion of additional regions of diffuse radiation anisotropy decreases model accuracy. Errors of insolation estimates for the alpine tundra from all models vary in a systematic manner as a function of relative azimuth and ground slope angles.     

Solar radiation over Saudi Arabia and comparisons with empirical models

We present a comparison between models developed by the present authors and 16 other models for different geographical and varied meteorological conditions. The comparisons are made using the mean bias error (MBE), root mean square error (RMSE), mean percentage error (MPE), and mean absolute bias error (MABE). These errors are calculated using monthly-mean, measured daily and estimated values of total solar radiation for 41 locations in Saudi Arabia. We find that our latitude, longitude, altitude, and sunshine-duration-dependent model given in Eq. (1)produced the best estimates for global solar radiation. The second- and third-best estimates were obtained from our linear model and other models given in Eq. (2)and Eq. (11), respectively.     

Calculation of solar radiation using a methodology with worldwide potential

Surface meteorological observations from the DATSAV2 database provide the capability to use the METSTAT (meteorological/statistical) model to calculate hourly values of direct normal, diffuse horizontal, and global horizontal solar radiation for locations throughout the world. Opaque cloud cover, a key input parameter to the METSTAT model, is derived from the DATSAV2 layered cloud cover information. Resulting multiyear data sets include solar radiation and other meteorological data such as dry bulb temperature, dew point temperature, wind speed, and atmospheric pressure. Data filling procedures ensure that the multiyear data sets are serially complete. A minor revision to METSTAT improved solar radiation estimates for conditions of high cloud amounts and low ceiling heights. The methodology was applied to regions of Southern Africa and Saudi Arabia.     

Atmospheric aerosol influence on the Brazilian solar energy assessment: Experiments with different horizontal visibility bases in radiative transfer model

The radiative transfer model BRASIL-SR is used by Brazilian Institute for Space Research for the assessment of the solar irradiation in Brazil. The model parameterizes the influence of aerosols in the solar radiation transmittance using climate averages of horizontal visibility, which does not represent the actual atmospheric condition in Brazil, especially during dry season. In clear sky conditions, aerosols are a major source of bias in solar radiation models. Their concentration have large spatial and temporal variability particularly in the Brazilian Midwestern region from April until October, due to forest fires, and in Southeastern region due to pollution from megacities. In this study, meteorological data from METAR comprising the years of 2006, 2007 and 2008 were analyzed to evaluate the seasonal variability of the horizontal visibility in Brazil to better represent the influence of aerosols on the model estimations of surface solar irradiation. New horizontal visibility values was generated to each month simulated, to provide input data to the BRASIL-SR model and site specific ground data were used to validate the model estimates. The global, direct beam and diffuse solar irradiation estimates obtained by making use of the new horizontal visibility data presented an overall lower BIAS and RMSE deviations.     

Measurements and predictions of solar radiation incident on horizontal surfaces at Santa Fe, Argentina (31° 39′S, 60° 43′W)

Measurements and predictions of solar radiation during a period of 10 years on horizontal surfaces at Santa Fe (31° 39′ S, 60° 43′ W), Argentina, reported as average daily global radiation for each month, are presented. Data are compared to those obtained with a previously published and verified model for computing solar radiation on horizontal planes at the earth's surface for cloudless sky days. Measurements show an important reduction of global radiation with respect to the cloudless sky model predictions for all months of the year. Conversely, averaged daily diffuse solar radiation calculated with Page's formula shows a small increment with respect to the predicted diffuse solar radiation for cloudless sky conditions. When direct solar radiation data, calculated from global and diffuse solar radiation values, are compared to theoretical prediction, a significant decrease is observed. This trend is similar to that obtained for global solar radiation.     

Empirical model development and comparison with existing correlations

This study utilized monthly mean daily values of global solar-radiation and sunshine duration at 41 locations in Saudi Arabia and developed an empirical correlation for the estimation of global solar radiation at locations where it is not measured. The paper also presents the comparison between the present correlation and other models developed under different geographical and varied meteorological conditions. The comparisons are made using standard statistical tests, namely mean bias error (MBE), root mean square error (RMSE), mean percentage error (MPE), and mean absolute bias error (MABE) tests. The errors are calculated using monthly mean daily measured and estimated values of global solar radiation at all 41 locations. The study found that the present correlation produced the best estimates of global solar 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.     

Attenuation of solar radiation in the atmosphere

This paper presents the results of measurements of the solar radiant energy absorbed and scattered in the atmosphere. Since much of the information on solar irradiance at the ground is obtained by computation from extraterrestrial radiation data, it is important to know precisely the actual energy that is absorbed and scattered in its passage through the atmosphere for the accurate estimation of the radiant energy received at the ground. Various models exist for the estimation of daily totals of global solar radiation under clear sky and cloudy conditions, taking these effects into consideration and assuming average values for the ozone and water vapour content and the turbidity of the atmosphere. In the present investigation atmospheric attenuation of solar radiation has been calculated from measured values of ozone and water vapour content and turbidity in the atmosphere, at two stations Bangalore (950 metres above sea level) and Nandi Hills (1479 masl). Direct measurements of direct solar radiation for the whole spectrum and various spectral regions were made at Bangalore and Nandi using Ångström pyrheliometers fitted with broad-band pass filters during the clear months January–May 1979. Global solar radiation and sunshine duration measurements were also made at both stations. Using direct measurements of the total ozone and water vapour content and atmospheric turbidity, direct, diffuse and global solar radiation values at the ground were computed from extraterrestrial values of radiation for clear sky conditions. The results are compared with actual measurements and earlier observations of direct solar radiation at other high-level stations. The importance of atmospheric turbidity measurements in the computation of solar radiation is discussed.     

A grey‐box model of next‐day building thermal load prediction for energy‐efficient control

Accurate building thermal load prediction is essential to many building energy control strategies. To get reliable prediction of the hourly building load of the next day, air temperature/relative humidity and solar radiation prediction modules are integrated with a grey‐box model. The regressive solar radiation module predicts the solar radiation using the forecasted cloud amount, sky condition and extreme temperatures from on‐line weather stations, while the forecasted sky condition is used to correct the cloud amount forecast. The temperature/relative humidity prediction module uses a dynamic grey model (GM), which is specialized in the grey system with incomplete information. Both weather prediction modules are integrated into a building thermal load model for the on‐line prediction of the building thermal load in the next day. The validation of both weather prediction modules and the on‐line building thermal load prediction model are presented. Copyright © 2008 John Wiley & Sons, Ltd.     

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:     

Modeling hourly and daily fractions of UV,PAR and NIR to global solar radiation under various sky conditions at Botucatu,Brazil

In this analysis, using available hourly and daily radiometric data performed at Botucatu, Brazil, several empirical models relating ultraviolet (UV), photosynthetically active (PAR) and near infrared (NIR) solar global components with solar global radiation (G) are established. These models are developed and discussed through clearness index _KT$K_{\text{T}}$ (ratio of the global-to-extraterrestrial solar radiation). Results obtained reveal that the proposed empirical models predict hourly and daily values accurately. Finally, the overall analysis carried out demonstrates that the sky conditions are more important in developing correlation models between the UV component and the global solar radiation. The linear regression models derived to estimate PAR and NIR components may be obtained without sky condition considerations within a maximum variation of 8%. In the case of UV, not taking into consideration the sky condition may cause a discrepancy of up to 18% for hourly values and 15% for daily values.     

Computation of monthly mean daily global solar radiation in China using artificial neural networks and comparison with other empirical models

In this paper, an artificial neural network (ANN) model is developed for estimating monthly mean daily global solar radiation of 8 typical cities in China. The feed-forward back-propagation algorithm is applied in this analysis. The results of the ANN model and other empirical regression models have been compared with measured data on the basis of mean percentage error (MPE), mean bias error (MBE) and root mean square error (RMSE). It is found that the solar radiation estimations by ANN are in good agreement with the measured values and are superior to those of other available empirical models. In addition, ANN model is tested to predict the same components for Kashi, Geermu, Shenyang, Chengdu and Zhengzhou stations over the same period. Data for Kashi, Geermu, Shenyang, Chengdu and Zhengzhou are not used in the training of the networks. Results obtained indicate that the ANN model can successfully be used for the estimation of monthly mean daily global solar radiation for Kashi, Geermu, Shenyang, Chengdu and Zhengzhou. These results testify the generalization capability of the ANN model and its ability to produce accurate estimates in China.     

Methods to estimate global and diffused luminous efficacies based on satellite data

This paper presents universal models and constant values to estimate luminous efficacies for each of global and diffused solar radiation on a horizontal surface. They are applicable to all sky conditions and are based on satellite derived data available via web servers. Solar radiation data from ten locations in Europe and North Africa was used to obtain three global and diffused functions for luminous efficacy (K) against solar altitude (α), cloud amount (C), and sky clearness index (k_t). All were used to estimate illuminance for the ten originating locations; for four locations based on satellite data; and for a further five based on measured data. A statistical assessment showed that the best models are K against α. Comparison between results from the proposed models and those produced using three published models for both cases, indicate that the former produce more accurate estimates of luminous efficacy. Constant values also showed very reliable results, especially for the diffused case. The satellite based approach makes daylight data available in locations remote from current measurement sites.     

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.     

Prediction of monthly mean daily diffuse solar radiation using artificial neural networks and comparison with other empirical models

An artificial neural network (ANN) model for estimating monthly mean daily diffuse solar radiation is presented in this paper. Solar radiation data from 9 stations having different climatic conditions all over China during 1995–2004 are used for training and testing the ANN. Solar radiation data from eight typical cities are used for training the neural networks and data from the remaining one location are used for testing the estimated values. Estimated values are compared with measured values in terms of mean percentage error (MPE), mean bias error (MBE) and root mean square error (RMSE). The results of the ANN model have been compared with other empirical regression models. The solar radiation estimations by ANN are in good agreement with the actual values and are superior to those of other available models. In addition, ANN model is tested to predict the same components for Zhengzhou station over the same period. Results indicate that ANN model predicts the actual values for Zhengzhou with a good accuracy of 94.81%. Data for Zhengzhou are not included as a part of ANN training set. Hence, these results demonstrate the generalization capability of this approach and its ability to produce accurate estimates in China.