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.     

Assessment of diffuse solar energy under general sky condition using artificial neural network

In this paper, artificial neural network (ANN) models are developed for estimating monthly mean hourly and daily diffuse solar radiation. Solar radiation data from 10 Indian stations, having different climatic conditions, all over India have been used for training and testing the ANN model. The coefficient of determination (R²) for all the stations are higher than 0.85, indicating strong correlation between diffuse solar radiation and selected input parameters. The feedforward back-propagation algorithm is used in this analysis. Results of ANN models have been compared with the measured data on the basis of percentage root-mean-square error (RMSE) and mean bias error (MBE). It is found that maximum value of RMSE in ANN model is 8.8% (Vishakhapatnam, September) in the prediction of hourly diffuse solar radiation. However, for other stations same error is less than 5.1%. The computation of monthly mean daily diffuse solar radiation is also carried out and the results so obtained have been compared with those of other empirical models. The ANN model shows the maximum RMSE of 4.5% for daily diffuse radiation, while for other empirical models the same error is 37.4%. This shows that ANN model is more accurate and versatile as compared to other models to predict hourly and daily diffuse solar radiation.     

利用神经网络估算太阳辐射

太阳辐射是一项对太阳能利用，建筑能耗分析和农业等十分重要的气象数据，本文建立了日总太阳辐射月均值的神经网络估算模型，在此基础上利用北京市1971年至1995年的气象数据资料对神经网络进行了训练，用1996至2000年的数据对神经网络的估算进行了检验，并与其它经验模型的估算结果进行了对比，结果表明神经网络的估算结果与实测值吻合的较好，并且精度高于其它经验模型。因此利用神经网络来估算太阳辐射具有很好的应用前景。     

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:     

Monthly mean hourly global solar radiation estimation

In this paper, selected empirical models were used to estimate the monthly mean hourly global solar radiation from the daily global radiation at three sites in the east coast of Malaysia. The purpose is to determine the most accurate model to be used for estimating the monthly mean hourly global solar radiation in these sites. The hourly global solar radiation data used for the validation of selected models were obtained from the Malaysian Meteorology Department and University Malaysia Terengganu Renewable Energy Station. In order to indicate the performance of the models, the statistical test methods of the normalized mean bias error, normalized root mean square error, correlation coefficient and t-statistical test were used. The monthly mean hourly global solar radiation values were calculated by using six models and the results were compared with corresponding measured data. All the models fit the data adequately and can be used to estimate the monthly mean hourly global solar radiation. This study finds that the Collares-Pereira and Rabl model performed better than the other models. Therefore the Collares-Pereira and Rabl model is recommended to estimate the monthly mean hourly global radiations for the east coast of Malaysia with humid tropical climate and in elsewhere with similar climatic conditions.     

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.     

Computation of beam solar radiation at normal incidence using artificial neural network

In this paper, an artificial neural network (ANN) model is developed for estimating beam solar radiation. Introducing a newly defined parameter, known as reference clearness index (RCI), computation of monthly mean daily beam solar radiation at normal incidence has been carried out. This RCI is defined as the ratio of measured beam solar radiation at normal incidence to the beam solar radiation as computed by Hottel's clear day model. Solar radiation data from 11 stations having different climatic conditions all over India have been used for training and testing the ANN. The feedforward back-propagation algorithm is used in this analysis. The results of ANN model have been compared with measured data on the basis of root mean square error (RMSE) and mean bias error (MBE). It is found that RMSE in the ANN model varies 1.65–2.79% for Indian region.     

Estimation of monthly average daily global solar irradiation using artificial neural networks

This study explores the possibility of developing a prediction model using artificial neural networks (ANN), which could be used to estimate monthly average daily global solar irradiation on a horizontal surface for locations in Uganda based on weather station data: sunshine duration, maximum temperature, cloud cover and location parameters: latitude, longitude, altitude. Results have shown good agreement between the estimated and measured values of global solar irradiation. A correlation coefficient of 0.974 was obtained with mean bias error of 0.059 MJ/m² and root mean square error of 0.385 MJ/m². The comparison between the ANN and empirical method emphasized the superiority of the proposed ANN prediction model.     

Correlations for estimation of daily global solar radiation with hours of bright sunshine in Turkey

In this study, seven different empirical equations are employed to estimate the monthly average daily global solar radiation on a horizontal surface for provinces in the different regions of Turkey, using only the relative duration of sunshine. Daily global solar radiation and sunshine measurement data collected for the provinces of Turkey are obtained from the Turkish State Meteorological Service. The regression constants of the new models developed in this study are found for the provinces of Turkey, as well as that of some models given in the literature. In order to indicate the performance of the models, the statistical test methods of the mean bias error (MBE), mean absolute bias error (MABE), mean relative error (MRE), root mean square error (RMSE) and correlation coefficient (r) are used.     

A simplified model for generating sequences of global solar radiation data for isolated sites: Using artificial neural network and a library of Markov transition matrices approach

The purpose of this work is to develop a hybrid model which will be used to predict the daily global solar radiation data by combining between an artificial neural network (ANN) and a library of Markov transition matrices (MTM) approach. Developed model can generate a sequence of global solar radiation data using a minimum of input data (latitude, longitude and altitude), especially in isolated sites. A data base of daily global solar radiation data has been collected from 60 meteorological stations in Algeria during 1991–2000. Also a typical meteorological year (TMY) has been built from this database. Firstly, a neural network block has been trained based on 60 known monthly solar radiation data from the TMY. In this way, the network was trained to accept and even handle a number of unusual cases. The neural network can generate the monthly solar radiation data. Secondly, these data have been divided by corresponding extraterrestrial value in order to obtain the monthly clearness index values. Based on these monthly clearness indexes and using a library of MTM block we can generate the sequences of daily clearness indexes. Known data were subsequently used to investigate the accuracy of the prediction. Furthermore, the unknown validation data set produced very accurate prediction; with an RMSE error not exceeding 8% between the measured and predicted data. A correlation coefficient ranging from 90% and 92% have been obtained; also this model has been compared to the traditional models AR, ARMA, Markov chain, MTM and measured data. Results obtained indicate that the proposed model can successfully be used for the estimation of the daily solar radiation data for any locations in Algeria by using as input the altitude, the longitude, and the latitude. Also, the model can be generalized for any location in the world. An application of sizing PV systems in isolated sites has been applied in order to confirm the validity of this model.     

Comparison of artificial intelligence and empirical models for estimation of daily diffuse solar radiation in North China Plain

Accurate diffuse solar radiation (H_d) data is highly crucial for the development and utilization of solar energy technologies. However, due to expensive cost and technology requirements, measurements of H_d are not available in many regions of North China Plain (NCP), where the diffuse and direct solar radiation are affected by severe particulate pollution. Thus, development of models for precisely estimating H_d is indeed essential in NCP. On this account, the present studies proposed four artificial intelligence models, including the extreme learning machine (ELM), backpropagation neural networks optimized by genetic algorithm (GANN), random forests (RF), and generalized regression neural networks (GRNN), for estimating daily H_d at two meteorological stations of NCP. Daily global solar radiation and sunshine duration along with the estimated extraterrestrial radiation and maximum possible sunshine duration were selected as model inputs to train the models. Meanwhile, the proposed AI models were compared with the empirical Iqbal model to test their performance using measured H_d data. The results indicated that the ELM, GANN, RF, and GRNN models all performed much better than the empirical Iqbal model for estimating daily H_d. All the models underestimated H_d for both stations, with average relative error ranging from ?5.8% to ?5.4% for AI models and 19.1% for Iqbal model in Beijing, ?5.9% to ?4.3% and ?26.9% in Zhengzhou, respectively. Generally, GANN model had the best accuracy, and ELM ranked next, followed by RF and GRNN models. The ELM model had a slightly poorer performance but the highest computation speed, and both the GANN and ELM models could be highly recommended to estimate daily H_d in NCP of China.     

Global solar radiation estimation with sunshine duration in Tibet,China

Eight models using only the sunshine duration for estimating the global solar radiation on a horizontal surface are evaluated at Changdu, Geer, Lasa and Naqu stations in Tibet, China against the measured meteorological data during 1994–2008. Based on statistical error tests, results show that the simple linear Ångström–Prescott model is reasonably accurate in practice, and the modifications with complex expression are not necessary in Tibet. Then, two general Ångström–Prescott models for estimating the daily and monthly average daily global solar radiation respectively in Tibet are proposed.     

中国不同气候区日总太阳辐射计算模型适用性分析及通用计算模型优化

利用中国5个气候区96个气象台站的1981—2010年的日值气象数据,对比分析12个基于日照百分率和12个基于温度的日总太阳辐射计算模型在不同气候区的适用性。采用判定系数（R²）、均方根误差（RMSE）、平均绝对误差（MABE）、平均误差（MBE）和全局性能系数（GPI）5个评价指标,确定各气候区最适宜的模型形式。以该模型为基准,建立适用于中国不同气候区的基于日照百分率和基于温度的日总太阳辐射通用计算模型。结果表明,三次方形式的基于日照百分率和基于日较差-平均温度的模型在各气候区计算精度均最高;以该模型为基础,建立适用于中国不同气候区的基于日照百分率和基于温度的日总太阳辐射通用计算模型,其平均R²分别为0.91和0.68。     

Spatial estimation of monthly mean daily sunshine hours and solar radiation across mainland China

Spatial databases of climate data in digital format are required for many agricultural and eco-environmental systems. This study compared 7 approaches for interpolating monthly mean daily sunshine hours and solar radiation over mainland China. The approaches included simple geostatistical approaches to incorporation of Universal Transverse Mercator (UTM) coordinates and elevation. Performance indicators (root mean square error, mean absolute percentage error, and modeling efficiency) showed thin plate smoothing spline with UTM coordinates and elevation (TPS) outperformed other models. Besides, multiple linear regression equations for estimating solar radiation using geographical parameters (UTM coordinates and elevation) and sunshine hours predicted by TPS performed well for the study site. Spatial datasets of annual and monthly mean daily sunshine hours and solar radiation with 1 km resolution were then obtained by the best performance models. Spatial and temporal variability was clearly observed in sunshine hours and solar radiation. For both annual and seasonal scenarios, higher values of sunshine hours and solar radiation existed in north and Tibetan Plateau and lower values were observed in the middle and southern China. Lower values of annual solar radiation were also found in northeastern China. Sunshine hours and solar radiation varied with time, especially from spring to summer and from summer to autumn. The accurate gridded datasets are expected to provide significant information on more efficient use of natural resources.     

Parameterization of a simple model to estimate monthly global solar radiation based on meteorological variables, and evaluation of existing solar radiation models for Tabouk, Saudi Arabia

Using 9 years of solar radiation data, we established a simple model to calculate the monthly mean global solar radiation on a horizontal surface in Tabouk (28.38° N, 36.6° E, Saudi Arabia). The model correlates the global solar radiation with five meteorological parameters. These parameters are the perceptible water vapor, air temperature, relative humidity, atmospheric pressure, and the mean monthly daily fraction of possible sunshine hours. The estimated global radiation from the model was compared with the measured values using the mean bias error (MBE), coefficient of correlation (R), root mean square error (RMSE), and mean percentage error (MPE). The t statistics were also applied as another indication of suitability. The model has a high coefficient of correlation (R = 0.99), MBE = −14 × 10⁻⁴ kW h/m², RMSE = 0.10 kW h/m², and MPE = −0.03%. It is believed that the model developed in this work is applicable for estimating, with great accuracy. The monthly mean daily global radiation at any site having similar conditions to those found in Tabouk.Furthermore, 29 regression models available in the literature were used to estimate the global solar radiation data for Tabouk. The selected models were different in terms of the variables they use and in the number of the variables they contained. The models were compared on the basis of the statistical errors considered above. Apart from Abdall’s model, which showed a reasonable estimate (MPE = −2.04%, MBE = −0.22 kW h/m², and RMSE = 0.59 kW h/m²), all the models under or overestimate the measured solar radiation values. Comparisons between these models and the produced model, from this study, were also considered. According to the statistical results, the model of Abdall showed the prediction closest to those estimated using the developed model.     

城市大气污染对到达地表的太阳辐射的影响研究

在晴空（无云）的条件下,大气污染是影响到达地球表面太阳辐射的重要因素之一。选择中国6个典型城市（北京、沈阳、上海、武汉、广州和成都）,利用2014年1月—2020年12月的空气质量日监测数据以及地面太阳辐射、日照时数等逐日观测数据,定量分析晴空条件下大气污染指数（AQI）与地表太阳总辐射、散射辐射的关系。结果表明：1）大气污染会降低清晰度指数,增加散射系数,对于地表太阳总辐射有衰减作用,对于散射辐射有增强作用。2）2014—2020年,大气污染（AQI>100）使得晴天地表太阳总辐射的年衰减总量和相对衰减量（共7 a）较大的是北京（212.40 MJ/m²,4.01%）、沈阳（184.16 MJ/m²,3.00%）、上海（123.80 MJ/m²,4.37%）和武汉（106.36 MJ/m²,3.04%）,而成都（58.03 MJ/m²,3.82%）和广州（18.76MJ/m²,0.96%）的衰减总量较小。3）大气污染（AQI>100）使得晴天散射辐射的年增加总量和相对衰减量分别是北京256.64 MJ/m²（12.96%）、沈阳134.45 MJ/m²（7.10%）、武汉22.62 MJ/m²（1.36%）、成都43.40 MJ/m²（9.71%）、上海94.74 MJ/m²（8.25%）和广州37.79 MJ/m²（5.90%）。     

An analysis of thermal and solar zone radiation models using an Angstrom–Prescott equation and artificial neural networks

The correlation between the clearness index and sunshine duration is useful in the estimation of the solar radiation for areas where measured solar radiation data are unavailable. Regression techniques and artificial neural networks were used to investigate the correlations between daily global solar radiation (GSR) and sunshine duration for different climates in China. Measurements made during the 30-year period (1971–2000) from 41 measuring stations covering 9 thermal and 7 solar climate zones and sub-zones across China were gathered and analysed. The performance of the regression and the ANN models in the thermal and solar zones was analysed and compared. The coefficient of determination (R²), Nash–Sutcliffe efficiency coefficient (NSEC), mean bias error (MBE) and root-mean-square error (RMSE) were determined. It was found that the regression models in both the thermal and the solar climate zones showed a strong correlation between the clearness index and sunshine duration (R²=0.79–88). There appeared to be an increasing trend of larger MBE and RMSE from colder climates in the north to warmer climates in the south. In terms of the thermal and solar climate zone models, there was very little to choose between the two models.     

Performance of Sayigh''s universal formula for the estimation of global solar radiation in Ghana

The performance of Sayigh's universal formula for the estimation of global solar radiation is tested against that of Angstrom-Black model for 13 stations in Ghana, using monthly mean daily global solar radiation averaged over the years 1957–1981.Sayigh's model is found not to perform as creditably as the Angstrom-Black model in the estimation of monthly global solar radiation in Ghana. Of the 156 values of monthly global solar radiation estimated by Sayigh's model, 123 (or 78.8%) had discrepancies of more than 10% with the measured values. The corresponding value for the Angstrom-Black model was 7 (or 4.5%).     

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.     

Estimating daily global solar radiation by day of year in China

In this study, a new empirical model is proposed for estimating daily global solar radiation on a horizontal surface by the day of the year. The performance of the proposed model is validated by comparing with three trigonometric correlations at nine representative stations of China using statistical error tests such as the mean absolute percentage error (MAPE), mean absolute bias error (MABE), root mean square error (RMSE) and correlation coefficients (r). The results show that the new model provides better estimation and has good adaptability to highly variable weather conditions. Then the application of the methodology is performed for the other 70 meteorological stations across China.