Monthly Average Daily Global Radiation Research Articles

NEW MODELS FOR ESTIMATION OF DIFFUSE SOLAR RADIATION USING METEOROLOGICAL PARAMETERS FOR BENIN, NIGERIA

In this comprehensive study, an extensive 22-year dataset (2001-2022) for Benin (Latitude 6.32 oN, Longitude 5.10 oE and 77.80 m above sea level) were obtained from the National Aeronautic Space Administration (NASA) website. The datasets comprises of the monthly average daily global solar radiation, diffuse solar radiation, relative humidity, atmospheric pressure, wind speed, and mean temperature, was utilized to develop 19 new models for estimating diffuse solar radiation. These models were categorized into five distinct groups: modified Page, Liu and Jordan models; clearness index and one-variable models; two-variable models; three-variable models, and a four-variable model. These models were statistically evaluated using a set of five validation indices—Mean Bias Error (MBE), Root Mean Square Error (RMSE), Mean Percentage Error (MPE), t-test, and the coefficient of determination (R²). The study identified the most effective models in each category. Equation 28b from the modified Page, Liu and Jordan category, Equation 28f from the clearness index and one-variable models, Equation 28j from the two-variable models, and Equation 28o from the three-variable models category were found to be the best-performing models. A comparative assessment of these performed models revealed that the quadratic regression model (Equation 28b) stood out as the most suitable for accurately estimating diffuse solar radiation in Benin. This implies that the developed model equation 28b can be used to estimate the diffuse solar radiation for Benin and locations with similar climatic conditions

Sunshine and Temperature Based Models for Estimating Global Solar Radiation in Maiduguri, Nigeria

Nine existing sunshine based models and three existing temperature based models were evaluated and compared to ascertain the most suitable models for estimating global solar radiation in Maiduguri; the most suitable sunshine based and most suitable temperature based models were also compared. The measured monthly average daily global solar radiation, sunshine hours, maximum and minimum temperature meteorological parameters during the period of thirty one years (1980 – 2010) was utilized and the evaluated models were tested statistically using validation indicators of coefficient of determination, Mean Bias Error, Root Mean Square Error, Mean Percentage Error, t – test, Nash – Sutcliffe Equation and Index of Agreement. The results indicated that the linear exponential sunshine based model and the logarithmic temperature based model were found more accurate for global solar radiation estimation in Maiduguri as compared to other evaluated models. Furthermore, the logarithmic temperature based model was found more accurate for estimating global solar radiation as compared to the linear exponential sunshine based model, and this was testified from the figure showing the comparison between the recommended sunshine based and temperature based models in which the recommended temperature based model depicts the best fitting with the measured global solar radiation data.

Empirical Model for Estimating Measured Monthly Average Global Solar Radiation in Lawra using TMY Data

In this study, simple and multiple regression models were developed to estimate the monthly average daily global solar radiation in Lawra, Ghana using ground measurement of global horizontal irradiance (Nov 2020–May 2022) and typical meteorological year (TMY) data (Jan 2017–Dec 2019). Various predictor variables such as sunshine ratio, minimum relative humidity and maximum relative humidity ratio, minimum and maximum temperature ratio, etc. were correlated from the TMY data. Many model equations were developed with the variables ranging from one to eight. The best model from each category was chosen and compared using statistical indices to determine the overall best model. We used the JMP statistical software’s ‘All Possible Models’ functionality to select the best model from each category. The selected models where then compared using the adjusted R-squared, mean absolute percentage error, and the root mean square error statistical indices. The best model equation correlated with eight independent variables with adjusted R-squared of 0.99. The equation can be used to estimate monthly global solar radiation in Lawra and in locations with similar climatic conditions where ground measurement of radiation data is unavailable but have access to the National Solar Radiation Database’s (NSRDB) TMY data.

A generalized approach for the determination of optimum tilt angle for solar photovoltaic modules with selected locations in Ethiopia as illustration examples

The amount of total solar energy that strikes the photovoltaic module's surface directly affects how much power is generated. On the other hand, solar energy is influenced by the solar module's location, tilt angle, and orientation. The models presented in this study can be used to determine the seasonal and annual optimal tilt angles of photovoltaic modules at any location in Ethiopia as a function of the location's latitude and elevation without the need for solar radiation data. Both isotropic and anisotropic diffuse solar radiation models were used to determine the monthly, seasonal, and annual optimal tilt angles. The monthly average daily global horizontal solar radiation for a total of 44 study sites, 32 for training and 12 for testing, were retrieved from the National Aeronautical and Space Administration database. The optimal tilt angle and regression models were determined by developing and applying algorithms in the programming languages MATLAB and R. The proposed model estimates the optimal tilt angle with the fewest statistical validation errors. By using the proposed monthly optimal tilt angles, solar radiation gains of 6.76% - 8.48% (for isotropic models) and 10.16% - 26.97% (anisotropic models) were obtained for Bahir Dar city. The solar radiation gains for the cities of Adigrat, Butajira, and Gode were found to be 7.18–9.02% (isotropic) and 10.90%–28.06% (anisotropic), 5.43%–7.05% (isotropic) and 8.48%–25.99% (anisotropic), and 4.33%–5.79% (isotropic) and 6.96%–23.03% (anisotropic), respectively. The results of this study were further confirmed by comparing them to previously published papers and online PVGIS and NREL's PVWatt software tools.

Performance Evaluation and Statistical Analysis of Solar Energy Modeling: A Review and Case Study

The main target of this research is a quantitative review of literature on global solar radiation (GSR) models available for different stations around the world. The statistical analysis of 400 existing sunshine-based GSR models on a horizontal surface is compared using 40-year meteorological data in the selected locations in Egypt. The measured data is divided into two sets. The first sub-data set from 1980 to 2019 was used to develop empirical correlation models between the monthly average daily global solar radiation fraction (H/H0) and the monthly average of desired meteorological parameters. The second sub-data set from 2015–2019 was used to validate and evaluate the derived models and correlations. The developed models were compared with each other and with the experimental data of the second subset based on the statistical error indicators such as RMSE, MBE, MABE, MPE, and correlation coefficient (R). The statistical test of the correlation, coefficient (R), for all models gives very good results (above 0.92). The smallest values of t-Test occur around the models (M 272, M 261, M 251, and M 238). The accuracy of each model is tested using ten different statistical indicator tests. The Global Performance Indicator (GPI) is used to rank the selected GSR models. According to the results, the Rietveld model (Model 272) has shown the best capability to predict the GSR on horizontal surfaces, followed by the Katiyar et al. model (Model 251) and the Aras et al. model (Model 261).

Development of Optimal Tilt Angle Models of a Photovoltaic Module for Maximum Power Production: Ethiopia

The power generated from the photovoltaic module is directly related to the magnitude of total incident solar radiation on the surface of the solar module. The total incident solar radiation depends on the location, tilt angle, and orientation of the solar module. In this paper, generic models were developed that determine the seasonal and annual optimal tilt angle of the Photovoltaic module at any location in Ethiopia without using meteorological data. Both isotropic and anisotropic diffuse solar radiation models were used to estimate monthly, seasonal, and annual optimal tilt angles. The monthly average daily global horizontal solar radiation for a total of 44 cities -32 for training and 12 for testing were obtained from the National Aeronautical and Space Administration database, and algorithms were developed and implemented using MATLAB and R programming software to obtain optimum tilt angle and regression models. The study showed that the developed model accurately estimates the optimal tilt angle with the minimum statistical validation errors. It is also found that 5.11% to 6.275% (isotropic) and 5.72% to 6.346% (anisotropic models) solar radiation energy is lost when using the yearly average fixed optimal tilt angle as compared with the monthly optimal tilt angle. The result of this study was also validated by comparing it with the previously published works, PVGIS and PVWatt online software. The graphical abstract is included in the supplementary file.

Novel Assessment and Classification of Monthly Average Daily Global Solar Radiation Models Through a Figure of Merit Called Irradiation Time Equivalence: Analysis of 70 Regression Models Based on Air Temperature and Sunshine Hours Predictors

Abstract Irradiation time equivalence pioneers the classification of models that predict monthly average daily global solar radiation on a horizontal surface based on their double cross-validation performances. By exploiting indigenous irradiation data, novel irradiation-based models can be created and used to classify prediction models, thereby facilitating a deeper understanding of model performance beyond routine summary statistics. The concept was demonstrated by formulating novel 1-hour and 2-hour irradiation-based models to predict monthly average daily global horizontal irradiation. Double cross-validations of the two irradiation-based models and 70 existing regression models were performed using a pair of 5-year subsets. The 70 models used the measured meteorological predictors of air temperature and sunshine hours, either alone or combined. The irradiation time equivalence of a model evaluated under double cross-validation has been defined as the minimum number of hours of measured irradiation needed to predict the monthly average daily irradiation in an average year, with a root mean square error less than or equal to that of the model. Despite their intracompetitiveness, all 44 temperature-based models had an irradiation time equivalence of 1 h, while the remaining 26 models that contained the sunshine-hours predictor were classified with a higher-performance rank of 2 h. An irradiation time equivalence scale extending to 13 h was also developed to cater to the classification of higher-performance models. This fresh perspective on model performance directs future investigations toward determining whether prediction models exhibit global classification constancy.

ESTIMATION OF GLOBAL SOLAR RADIATION USING SUNSHINE HOURS IN SOKOTO NIGERIA

Inadequate installations of materials such as solar water heater, solar still, solar dryer, and solar cooker etc. Which required solar radiation and maximally, in the area location of is a major problem and this hinders the abundant utilization of solar energy as it can be harnessed directly without any requirement of external energy such as electricity. It is the lack of the information that limits the number of installations in the study area. Therefore, it is compulsory to study and analyzed the solar radiation of our environment to get better view of monitoring the performance of solar energy conversion system in Sokoto State, so that companies and government should know what period or seasons can therefore utilize the abundant solar energy. A new model was developed for estimation the monthly average daily global solar radiation. In this research a modified angstrom model for estimation of global solar radiation in Sokoto, Nigeria using sunshine duration based on meteorological data were used. However, solar radiation estimates are too local since they rely on weather stations or have a resolution that is too satellites. In this work, a model was developed for estimation of global solar radiation on horizontal surface for Sokoto at latitude of m13 13.00E and longitude of 5.250N. Global solar radiation and maximum temperature data for Sokoto were used to fit the Angstrom model, Regression coefficient a, b, and c. 1.12, 0.65, and 0.32 respectively were obtained from the models base on sunshine duration respectively. In order to evaluate the results, three statistical methods have been used namely: mean bias, root mean square, and percentage errors of values -6.47, 6.47 and 41.20% respectively. It was found from statistical model’s performance indicators that the model provides reasonably high degree of precision in the estimation of average global solar radiation on horizontal surfaces.

Estimating Global Solar Radiation from Empirical Models: An Application

Solar radiation data are required for many applications and many areas of research. In order to achieve this, several empirical models have been suggested to predict the global solar radiation in Turkey and other countries. The different meteorological data as the global solar radiation, the sunshine duration, the temperature, the atmospheric pressure, the wind speed and the relative humidity were measured by Eskisehir Osmangazi University during the period between 01 January 2011 and 31 December 2014. These data were used to develop the empirical models in order to estimate the monthly average daily global solar radiation on the horizontal surface over Eskisehir City of Turkey. The developed empirical models were analyzed with the widely used nine statistical methods, namely; the relative percentage error (E), the mean percentage error (MPE), the mean absolute percentage error (MAPE), the sum of squares of relative errors (SSRE), the relative standard error (RSE), the mean bias error (MBE), the root mean square error (RMSE), the t-statistic method (t-stat) and coefficient of determination (R2). It is expected that the new model will be beneficial to everyone who is the solar engineers, architects, agriculturists, and hydrologists involved or interested in the design and study of solar energy applications such as solar furnaces, wood drying, stoves, concentrating collectors, interior illumination and thermal load analyzing of buildings, and photovoltaics, agricultural and meteorological forecasting.

Correlating clearness index with cloud cover and other meteorological parameters for forecasting the global solar radiation over Morocco

In this study, new correlations between clearness index and cloud cover without and/or with other meteorological parameters were proposed for estimating the monthly average daily global solar radiation (MADGSR) on a horizontal surface. By using a long-term of continuously observed meteorological data at fourteen cities over Morocco, seventeen new correlation models were established, evaluated and compared with the other seven cloud-based models selected from the literature. The statistical analysis was done based on the coefficient of determination (R²), mean bias error (MBE), mean square error (MSE), root mean square error (RMSE), standard deviation (σ) and performance score (φ). Results revealed that the new proposed model, which combines the clearness index with the cloud cover and all other meteorological parameters, has a good prediction level of the MADGSR for the considered Moroccan cities. The accuracy of the newly developed model may recommend it to be employed in the future design and assessment of the performance of different solar energy applications in Morocco and in other locations with similar climatic conditions.

Off-grid rural electrification using integrated renewable energy sources

Presented in this study is an economic and technical evaluation to determine the optimal system combination for off-grid power generation based on solar, wind and biodiesel renewable energy resource. Nsukka being endowed with high intensity solar radiation, adequate wind speed and sufficient bioresource is a prospective candidate for a hybrid system. The monthly average daily global radiation ranges from 3.91kWh/m2 to 5.74kWh/m2 and the average wind speed is about 2.64m/s. This system was designed to meet the load requirement of the school with annual electrical demand of 10,163 MWh. Sensitivity analysis was carried out based on the effect of change in biodiesel fuel price and interest rates on the economic performance criteria of the optimal configuration. The optimum hybrid system is composed of 1kW capacity PV system, auto sized biodiesel generator and battery bank of 820h of autonomy. The Levelized Cost of Energy from the optimal system was found to be $0.0898/kWh based on sensitivity results. These results obtained shows that an integrated system with combination of PV, biodiesel generator and battery bank is a cost-effective alternative to grid extension which cost $0.126/kWh. The system life span is for 25years and it is sustainable, economical, technically feasible and environmentally friendly.

Sunshine-based Global Solar Radiation Modelling: Case Study of Putrajaya, Malaysia

Electricity demands are on the rise and with it, carbon dioxide emissions from many conventional power plants are increasing. In the efforts to mitigate such phenomena, the Malaysian government seeks to implement Building Integrated Photovoltaic (BIPV) projects. Early stage studies on Global Solar Radiation (GSR) have been carried out in several states in Malaysia including Penang, Kuala Lumpur and Kota Bharu. Afterward, data from the Malaysia Meteorological Department and the Malaysia National University have been used to estimate the monthly average daily global radiation in various locations in Malaysia. Putrajaya, a location which is implementing Malaysian Building Integrated Photovoltaic (MBIPV) is among the locations where a GSR study is currently absent. Conventional methods exist for GSR estimation with the aid of pyranometer. However, this method of GSR estimation is time consuming and not cost-effective practice. The main objective of this study is to estimate the GSR in Putrajaya. This is achieved in this study by utilizing sunshine-based data with calculated monthly average daily extraterrestrial radiation on a horizontal surface and monthly average maximum possible daily sunshine to plot a linearly fitted graph. Coefficients in the Angstrom-Prescott (A-P) model was generated from the plotted graph and was used for GSR estimation where a = 0.5 and b = 0.11. The mean percentage error (MPE) of the GSR estimation was found to be 3.4. Therefore, the estimation of GSR in Putrajaya have been successful for the first-time using sunshine-based data from dual locations method. The GSR estimation of Putrajaya in this study could benefit stakeholders in civil development sectors, policy and energy authorities.

Estimating Daily Global Solar Radiation with No Meteorological Data in Poland

The aim of the study was to calibrate coefficients and evaluate performance of simple, day-of-the-year, global solar radiation (H) models nominated from the literature. Day-of-the-year models enable estimation of global solar radiation when no meteorological data is available. The study used 16-year-long data series of daily H, taken at 15 actinometric stations located in various parts of Poland. The goodness-of-fit of the models to the actual long-term monthly average daily global solar radiation data expressed by determination coefficient (R2) ranges from 0.94 to 0.97. Depending on statistical indicators analysis (root mean square error—RMSE, mean absolute bias error—MABE, mean average percentage error—MAPE) the best model was selected. The averaged values of H computed by the recommended model deviate from those measured by 4.16% to 8.71%. Locally calibrated, day-of-the-year model provides satisfactory accuracy and—where meteorological data is unavailable—can be used to estimate mean monthly daily global solar radiation in Poland and similar climate conditions.

Empirical Models for Estimating Tropospheric Radio Refractivity Over Osogbo, Nigeria

Background:Estimation of tropospheric radio refractivity is significant in the planning and design of terrestrial communication links.Methods:In this study, the monthly average daily atmospheric pressure, relative humidity and temperature data obtained from the National Aeronautics and Space Administration (NASA) during the period of twenty two years (July 1983 - June 2005) for Osogbo (Latitude 7.470N, Longitude 4.290E, and 302.0 m above sea level) were used to estimate the monthly tropospheric radio refractivity. The monthly average daily global solar radiation with other meteorological parameters was used to developed one, two, three and four variable correlation(s) tropospheric radio refractivity models for the location. The accuracy of the proposed models are validated using statistical indicator of coefficient of determination (R2), Mean Bias Error (MBE), Root Mean Square Error (RMSE), Mean Percentage Error (MPE), Nash - Sutcliffe Equation (NSE) and Index of Agreement (IA).Results:In each case one empirical model was recommended based on their exceptional performances after ranking, except for the two variation correlations with two empirical models. The recommended models were further subjected to ranking from which the three variable correlations model that relates the radio refractivity with the absolute temperature, relative humidity and global solar radiation was found more suitable for estimating tropospheric radio refractivity for Osogbo with R2= 100.0%, MBE = -0.2913 N-units, RMSE = 0.3869 N-units, MPE = 0.0811%, NSE = 99.9999% and IA = 100.00%.Conclusion:The newly developed recommended models (Equations 16c, 17d, 17f, 18d and 19) can be used for estimating daily and monthly values of tropospheric radio refractivity with higher accuracy and has good compliance to highly varying climatic conditions for Osogbo and regions of similar climatic information.

Empirical Models for Estimating Tropospheric Radio Refractivity Over Osogbo, Nigeria

Background:Estimation of tropospheric radio refractivity is significant in the planning and design of terrestrial communication links.Methods:In this study, the monthly average daily atmospheric pressure, relative humidity and temperature data obtained from the National Aeronautics and Space Administration (NASA) during the period of twenty two years (July 1983 - June 2005) for Osogbo (Latitude 7.470N, Longitude 4.290E, and 302.0 m above sea level) were used to estimate the monthly tropospheric radio refractivity. The monthly average daily global solar radiation with other meteorological parameters was used to developed one, two, three and four variable correlation(s) tropospheric radio refractivity models for the location. The accuracy of the proposed models are validated using statistical indicator of coefficient of determination (R2), Mean Bias Error (MBE), Root Mean Square Error (RMSE), Mean Percentage Error (MPE), Nash - Sutcliffe Equation (NSE) and Index of Agreement (IA).Results:In each case one empirical model was recommended based on their exceptional performances after ranking, except for the two variation correlations with two empirical models. The recommended models were further subjected to ranking from which the three variable correlations model that relates the radio refractivity with the absolute temperature, relative humidity and global solar radiation was found more suitable for estimating tropospheric radio refractivity for Osogbo with R2= 100.0%, MBE = -0.2913 N-units, RMSE = 0.3869 N-units, MPE = 0.0811%, NSE = 99.9999% and IA = 100.00%.Conclusion:The newly developed recommended models (Equations 16c, 17d, 17f, 18d and 19) can be used for estimating daily and monthly values of tropospheric radio refractivity with higher accuracy and has good compliance to highly varying climatic conditions for Osogbo and regions of similar climatic information.

Developing of the new models in solar radiation estimation with curve fitting based on moving least-squares approximation

Recently, serious progress has been made in solar energy applications in developed and developing countries. Solar radiation on a horizontal surface is the basic parameter required for the design of solar energy systems and for evaluating the system performance. Therefore, solar radiation the exact determination of the amount of land in different latitudes on the earth's surface is of great importance in many solar energy applications. In this study, Angstorm coefficients were determined by Moving Least Squares Approximation (MLSA). Three different models were obtained by using the moving least squares method. In this study, new empirical models were developed for determining the monthly average daily global solar radiation on a horizontal surface for Antalya. The developed models were compared with the models in the literature by using different error analysis methods. The statistical compatibility of the investigated models was tested and the model closest to the measurements was determined. Although, this study concluded that the suggested methods are applicable to estimate the monthly average daily diffuse radiation on a horizontal surface for selected region, it has been observed that the performance of these models varies according to years and the error analysis test used. If the results are generally evaluated the developed linear model showed the best performance to estimate the global solar radiation on a horizontal surface for Antalya. Also, among the models used in the literature, the Togrul model showed the best performance for selected region.

Estimating the global solar radiation in Putrajaya using the Angstrom-Prescott model

Global solar radiation (GSR) studies are essential in enhancing the use of solar PV systems especially for Building Integrated PV system (BIPV). Various studies on GSR had been carried out in Malaysia including Penang, Kuala Lumpur and Kota Bharu at the earlier stage. Afterward, data from the Malaysian Meteorological Department (MET) and the Malaysian National University were used to estimate the monthly average daily global radiation for various locations in Malaysia including Kuala Lumpur, Kuala Lumpur, Petaling Jaya, Bandar Baru Bangi, Kota Baru, Senai, Bayan Lepas, Kuching and Kota Kinabalu. GSR in Putrajaya, a location which has identified to implement Malaysian Building Integrated Photovoltaic (MBIPV) projects has yet to be estimated. The conventional method to obtain the amount of GSR at a location is to install a measuring device like a pyranometer at the site to observe and document its day-to-day recordings. However, this is a time-consuming and costly practice. The models used to estimate the GSR are usually based on astronomical factors, geometrical factors, physical factors and meteorological factors. There are numerous models used to predict GSR which can be categorized based on sunshine, cloud, temperature and other meteorological parameters. Additionally, the global solar energy models can be grouped by its modelling techniques such as linear, nonlinear, artificial intelligence and fuzzy logic modelling techniques. The reviews discovered that the models used to estimate GSR were mostly correlated to sunshine duration (SD), air temperature, relative humidity and geographical parameters like latitude, longitude and altitude. In this paper, the GSR in Putrajaya is estimated from the hourly solar radiation and daily sunshine hours data from the Malaysian Meteorological Department. The data, along with the calculated monthly average daily extraterrestrial radiation on a horizontal surface and monthly average maximum possible daily sunshine is used to plot a scatter graph that is linearly fitted. The gradient and vertical axis cut-off from the linear fit is used to obtain the coefficients in the Angstrom-Prescott (A-P) model. Subsequently, the coefficients were used to estimate the GSR in Putrajaya. In line with the government’s initiative, this study will provide an estimation of the GSR in Putrajaya where the finding will be beneficial to the stakeholders, policy maker, developer and investor and energy authority. The average monthly GSR was obtained for nine out of twelve months with highest at 21.18 MJ/m2 in March and lowest at 18.34 MJ/m2 in June.

Sunshine and Temperature Dependent Models for Estimating Global Solar Radiation Across the Guinea Savannah Climatic Zone of Nigeria

This study investigates the most accurate sunshine and temperature dependent models for estimating global solar radiation over Makurdi and Ibadan situated in the Guinea savannah of Nigeria by comparing nine (9) different existing sunshine dependent models. The study also proposed two temperature dependent models that took the form of quadratic logarithmic and quadratic exponential and were compared to three existing temperature dependent models (Chen, Hargreaves and Samani (HS) and Garcia). The measured monthly average daily global solar radiation, sunshine hours, maximum and minimum temperature meteorological parameters during the period of thirty one (1980-2010) years was utilized and the accuracy of the sunshine and temperature dependent models to ascertain the most suitable models in each location were tested using seven various statistical validation indicators of coefficient of determination (R²), Mean Bias Error (MBE), Root Mean Square Error (RMSE), Mean Percentage Error (MPE), t-test, Nash-Sutcliffe Equation (NSE) and Index of Agreement (IA). The results revealed that the exponent sunshine dependent model proposed by Bakirci and the linear exponential sunshine dependent model proposed by Bakirci were found more accurate for estimating global solar radiation in Makurdi and Ibadan respectively. The proposed quadratic logarithmic and quadratic exponential temperature dependent models were found more suitable for estimating global solar radiation in Makurdi and Ibadan respectively. These recommended models can be found appropriate, if properly calibrated in regions with similar climatic information. The HS temperature dependent model evaluated in this study for Ibadan was compared with those available in literatures and was found more suitable. Furthermore, the most suitable sunshine dependent model was found more suitable for global solar radiation estimation when compared to the most suitable temperature dependent model in each of the studied locations and this was testified from the figures of the comparison between the measured and estimated sunshine and temperature dependent models as the sunshine dependent models depicts the best fitting with the measured global solar radiation data.

Developing Empirical Models for Estimating Photo synthetically Active Radiation overAkure, South Western, Nigeria

In this study, the measured monthly average daily global solar radiation and extraterrestrial solar radiation using the generalized 45% and 40% dataset was utilized to estimate the photosynthetically active radiation (PAR) and extraterrestrial photosynthetically active radiation (PAR0) for Akure (Latitude 7.170N, Longitude 5.180E, and 375.0 m above sea level) Ondo State located in South Western, Nigeria. The monthly average daily sunshine hours, maximum and minimum temperature data were used to develop nine (9) new PAR sunshine based models and three (3) PAR temperature-based models. The meteorological parameters used in this study covered a period of thirty-one years (1980 – 2010). The newly developed models were tested using statistical indicators of the coefficient of determination (R2), Mean Bias Error (MBE), Root Mean Square Error (RMSE), Mean Percentage Error (MPE), t-test, Nash – Sutcliffe Equation (NSE) and Index of Agreement (IA). The PAR sunshine based models that took a quadratic form and the linear logarithmic PAR temperature-based models were found more suitable for estimating PAR for the location under study. Comparing the PAR sunshine based and temperature-based models indicated that the PAR sunshine based model is more suitable for PAR estimation in Akure. Furthermore, the results showed that PAR is high during the dry season and low during the rainy season. Based on the measured and estimated PAR models; the minimum values were found in July and August while the maximum values in February, March and November. The descriptive statistical analysis shows that the PAR and all the estimated sunshine based PAR data spread out more to the left of their mean value (negatively skewed). Similarly, they have negative kurtosis which indicates a relatively flat distribution and the possibility of platykurtic distribution. The PAR and the PAR logarithmic temperature-based model (equation 17a) data spread out more to the left of their mean value (negatively skewed), while the PAR linear exponent and linear temperature-based models (equation 17b and 17c) data spread out more to the right of their mean value (positively skewed). The PAR and all the estimated PAR temperature-based data have negative kurtosis which indicates a relatively flat distribution and the possibility of platykurtic distribution.

Empirical models for estimating global solar radiation in Wuhan City, China

Seven existing models and four proposed models were calibrated and evaluated to calculate the monthly average daily global solar radiation (GSR) on a horizontal surface in Wuhan city, China, using meteorological data measured from 2006 to 2011. The results show that the sunshine duration (n) is an important parameter for estimating the GSR and adding the dew point temperature (DP) is a significant effect in humid regions especially in Wuhan. Notably, all the tested models that used only the sunshine ratio or the sunshine ratio combined with other parameters exhibited satisfactory estimation performance. Adding the maximum and minimum air temperatures to the sunshine ratio in the Chen and Li model yielded a considerable improvement over the existing models, and adding the DP in the new model resulted in the most accurate estimations of solar radiation. Additionally, using the simple linear Angstrom-Prescott model was better than using the more complex Bahel model or the Ododo model. Models based on the maximum, minimum and average air temperature (Li Huashan model) and DP (Li model) exhibited poor performance. The worst performance was displayed by the Badescu model, which uses only cloud cover as a key input. Finally, we propose a strategy for selecting the most appropriate model for estimating the GSR.