Stochastic approach for daily solar radiation modeling

Mathematical modeling of solar radiation continues to be an important issue in renewable energy applications. In general, existing models are mostly empirical and data dependent. In this paper, a novel approach for solar radiation modeling is proposed and illustrated. The proposed application consists of hidden Markov processes, which are widely used in various signal processing topics including speech modeling with successful results. In the experimental work, mean of hourly measured ambient temperature values are considered as observations of the model, whereas mean of hourly solar radiation values are considered as the hidden events, which constitute the outcomes of the proposed mathematical model. Both solar radiations and temperatures are converted to quantized number of states. Finally, after a training stage that forms the transition probability values of the described states, the hidden Markov model parameters are obtained and tested. The tests are repeated for various numbers of states and observations are presented. Plausible modeling results with distinct properties in terms of accuracy are achieved.     

Measurement of solar energy radiation in Abu Dhabi,UAE

This paper presents data on measurement of actual solar radiation in Abu Dhabi (24.43°N, 54.45°E). Global solar radiation and surface temperatures were measured and analyzed for one complete year. High resolution, real-time solar radiation and other meteorological data were collected and processed. Daily and monthly average solar radiation values were calculated from the one-minute average recorded values. The highest daily and monthly mean solar radiation values were 369 and 290 W/m², respectively. The highest one-minute average daily solar radiation was 1041 W/m². Yearly average daily energy input was 18.48 MJ/m²/day. Besides the global solar radiation, the daily and monthly average clearness indexes along with temperature variations are discussed. When possible, global solar energy radiation and some meteorological data are compared with corresponding data in other Arab state capitals. The data collected indicate that Abu Dhabi has a strong potential for solar energy capture.     

REST2: High-performance solar radiation model for cloudless-sky irradiance, illuminance, and photosynthetically active radiation – Validation with a benchmark dataset

REST2, a high-performance model to predict cloudless-sky broadband irradiance, illuminance and photosynthetically active radiation (PAR) from atmospheric data, is presented. Its derivation uses the same two-band scheme as in the previous CPCR2 model, but with numerous improvements. Great attention is devoted to precisely account for the effect of aerosols, in particular.Detailed research-class measurements from Billings, OK are used to assess the performance of the model for the prediction of direct, diffuse and global broadband irradiance. These measurements were made in May 2003 during a sophisticated radiative closure experiment, which involved the best radiometric instrumentation currently available and many ancillary instruments. As a whole, these exceptional measurements constitute the only known modern benchmark dataset made specifically to test the intrinsic performance of radiation models. Using this dataset as reference, it is shown that REST2 performs better than CPCR2 for irradiance, illuminance or PAR predictions. The availability of the turbidity data required by REST2 or other similar models is also discussed, as well as the effect that turbidity has on each component of broadband irradiance, PAR irradiance and illuminance, and on the diffuse/global PAR ratio.     

Development of a method for generating operational solar radiation maps from satellite data for a tropical environment

Despite a considerable number of publications which use satellite data to map solar radiation, relatively few studies have been undertaken in a tropical environment. In this study, we have developed a method to produce operational solar radiation maps from satellite data for this environment. The method is based on a physical model which relates the satellite-derived earth–atmospheric reflectivity from visible channel of GMS-4 and GMS-5 to the transmissivity of the atmosphere. Cloud reflectivity was determined from satellite data, while radiation absorbed by water vapour, ozone and aerosols and radiation scattered by aerosols were determined from ground-based meteorological data. Techniques for determining the radiation depleted by these atmospheric constituents over a whole country were also presented. Satellite data of a six-year period (1993–1998) with approximately ten thousand satellite images were used to construct the maps. When tested against an independent data set, monthly average of daily global irradiation calculated from this method agree with that obtained from the measurements with the relative root mean square difference of 6.8% with respect to the mean values. Solar radiation is presented as twelve maps showing the monthly average of global irradiation and one map showing the yearly average of global irradiation. Radiation patterns from the maps show a strong influence of the tropical monsoons.     

Validation of short and medium term operational solar radiation forecasts in the US

This paper presents a validation of the short and medium term global irradiance forecasts that are produced as part of the US SolarAnywhere (2010) data set. The short term forecasts that extend up to 6-h ahead are based upon cloud motion derived from consecutive geostationary satellite images. The medium term forecasts extend up to 6-days-ahead and are modeled from gridded cloud cover forecasts from the US National Digital Forecast Database.The forecast algorithms are validated against ground measurements for seven climatically distinct locations in the United States for 1 year. An initial analysis of regional performance using satellite-derived irradiances as a benchmark reference is also presented.     

Direct and indirect uncertainties in the prediction of tilted irradiance for solar engineering applications

Global radiation measured on fixed-tilt, south-facing planes (40° and vertical) and a 2-axis tracker at NREL’s Solar Radiation Research Lab. in Golden, CO is compared to predictions from ten transposition models, in combination with either optimal or suboptimal input data of horizontal irradiance. Suboptimal inputs are typically used in everyday engineering calculations, for which the necessary data are usually unavailable for the site under scrutiny, and must be estimated in some way. The performance of the transposition models is first evaluated for ideal conditions when optimal data are used. In this specific case, it is found that the Gueymard and Perez models provide the best estimates of global tilted irradiance under clear skies in particular.The performance of four direct/diffuse separation models is also evaluated. Their predictions of direct and diffuse radiation appear biased in most cases, with a model-dependent magnitude. Finally, the performance of the resulting combinations of separation and transposition models is analyzed in a variety of situations. When only global irradiance is known, the accuracy of the tilted irradiance predictions degrades significantly, and is mainly conditioned by the local performance of the direct/diffuse separation method. For the south-facing vertical surface, inaccuracies in the ground reflection calculations becomes another key factor and significantly increase the prediction error. The Reindl transposition algorithm appears to perform best in this case. When using suboptimal input data for the prediction of plane-of-array irradiance on a moderately tilted plane (40°S) or a 2-axis tracking plane, the Hay, Reindl and Skartveit models are less penalized than others and tend to perform better. It is concluded that further research should be conducted to improve the overall process of predicting irradiance on tilted planes in realistic situations where no local high-quality irradiance or albedo measurements are available.     

Measuring and evaluating solar radiative properties of plastic shading nets

Plastic shading nets are being used extensively in hot and sunny regions to protect plants from intense solar radiation. Different varieties of these nets are commercially available. However, the choice of net to fulfill specific shading requirements often depends on empirical or economic criteria and not on scientific considerations because essential information used to characterize the different types of nets is not available.In order to replace expensive measuring facilities that use artificial lighting to investigate the radiative properties of plastic shading nets, a simple method was presented to investigate these properties under global, diffuse and direct beam solar radiation conditions. Measurements were performed on clear sunny days, (December 28, 2008-February 10, 2009). Nets with colors and shading factors that are most commonly used in hot regions were selected for the study. The results showed that the behaviors of the plastic nets under solar radiation conditions were similar to those of translucent materials. Accordingly, it is possible to (i) treat plastic nets as translucent materials and (ii) investigate the equivalent optical constants (i.e., refractive indexes and extinction coefficients) for plastic nets as functions of the net solidity, texture type and color. Solidity and color of the net had significant effects on the radiative properties and the effect of color was much more than the effect of solidity. The shading factor of a plastic net, is a function of the daytime, depends on several design and meteorological parameters, so it cannot be used to describe a net. However, the net solidity together with color, and the daily integrals of the shading factor and of the radiative properties are appropriate parameters for describing a net.     

The sun’s total and spectral irradiance for solar energy applications and solar radiation models

Using the most recent composite time series of total solar irradiance spaceborne measurements, a solar constant value of 1366.1 W m⁻² is confirmed, and simple quadratic expressions are proposed to predict its daily value from the Zurich sunspot number, the MgII index, or the 10.7 cm radio flux index. Whenever these three indices are available on a daily basis (since 1978), it is possible to predict the sun’s irradiance within 0.1% on average, as accurately as current measurements.Based on this value of the solar constant, an improved approximation of the extraterrestrial solar spectrum from 0 to 1000 μm is proposed. It is obtained by dividing the spectrum into nine bands and selecting representative (and recent) spectra, as well as appropriate scaling coefficients for each band. Comparisons with frequently used spectra are discussed, confirming previous findings of the literature.This synthetic and composite spectrum is proposed at 0.5-nm intervals in the UV (280–400 nm), 1-nm intervals between 0–280 and 400–1705 nm, 5-nm intervals between 1705 and 4000 nm, and progressively larger intervals beyond 4 μm, for a total of 2460 wavelengths.     

A brief review of models for computing solar radiation on inclined surfaces

Modelling of solar energy systems requires estimation of the hourly radiation incident on surfaces of different tilts and orientations. Most meteorological stations report radiation values on a daily rather than hourly basis. Again, the value of the diffuse component may or may not be reported. Hence, different strategies may be encountered, for each location, with the common goal of computing hourly radiation on inclined surfaces.

In this study, five different schemes are presented to achieve this goal. In each scheme, certain correlations are required which are discussed in detail. The study is divided into five sections, each dealing with a specific type of correlation. These sections are: (i) correlations between daily diffuse and global radiation; (ii) correlations between hourly/daily global radiation; (iii) correlations between hourly/daily diffuse radiation; (iv) correlations between hourly diffuse and global radiation; and (v) models for computing diffuse sky radiation on inclined surfaces. The last section deals extensively with the anisotropic nature of sky diffuse radiation.

The important aspects of all correlation studies are highlighted, and the relative merits and demerits of their results are brought to light.

Mathematical expressions, where available, for models/correlations are provided so that the reader will have access to a comprehensive study. This information should be useful for modelling purposes in which computation of radiation on surfaces of different orientations and tilts is required.     

Solar constant values for estimating solar radiation

There are many solar constant values given and adopted by researchers, leading to confusion in estimating solar radiation. In this study, some solar constant values collected from literature for estimating solar radiation with the Ångström-Prescott correlation are tested in China using the measured data between 1971 and 2000. According to the ranking method based on the t-statistic, a strategy to select the best solar constant value for estimating the monthly average daily global solar radiation with the Ångström-Prescott correlation is proposed.     

Estimation of monthly solar radiation distribution for solar energy system analysis

The concept of probability density frequency, which is successfully used for analyses of wind speed and outdoor temperature distributions, is now modified and proposed for estimating solar radiation distributions for design and analysis of solar energy systems. In this study, global solar radiation distribution is comprehensively analyzed for photovoltaic (PV) panel and thermal collector systems. In this regard, a case study is conducted with actual global solar irradiation data of the last 15 years recorded by the Turkish State Meteorological Service. It is found that intensity of global solar irradiance greatly affects energy and exergy efficiencies and hence the performance of collectors.     

An inexpensive data acquisition system for solar,wind and climatological data recording

A new inexpensive state-of-the-art data-acquisition system, called Suryavijay, for solar radiation, wind and climatological data corresponding to long periods, has been developed and is described in the paper. It acquires data without in situ computers at the field stations. The hourly data are stored in an unpluggable 32 Kbyte EPROM for 24 channel months. The information in the EPROM from a field station is downloaded in a mainframe or personal computer at the mother station. Suryavijay uses a 12 bit analog-to-digital convertor for high resolution and an INTEL 6216 tristat analog multiplexer which accepts differential signals from the sensors and makes the system expandable in integral multiples of 8 channels. It has specially tailor-made signal-conditioning circuits for solar, wind and climatological data channels. In addition, Suryavijay is cost-effective, which makes it possible to have a greater number of field stations in a solar radiation, wind and climatological data network.     

Design,development and testing of an improved multipurpose solar energy device

This paper reports the design, development and testing of an improved multipurpose solar energy device. The novel feature of the device is that it can be used as a solar water heater and solar still simultaneously and, when required, as a solar cabinet dryer by incorporating minor changes.     

A model for managing and evaluating solar radiation for indoor thermal comfort

Thermal comfort of people occupying indoor spaces depends, to a large extent, on the direct component of solar radiation incident on the human body. In turn, even the diffuse component of the solar radiation could affect the thermal sensations of people. Despite this evidence, at the present there is a lack in the availability of simple and reliable methods capable of taking into account the influence of the solar radiation on thermal balance in the human body. In this work a comprehensive method is presented for the computation of the mean radiant temperature of people in thermal moderate indoor environments in the presence of solar radiation. The effects produced on the amount of solar radiation entering rooms in the presence of shadowing devices are also analysed. Finally, an application of the method is provided for a non-parallelepiped room equipped with a south window: results are shown in terms of the mean radiant temperature. A simple evaluation of thermal comfort conditions, referring to the present international standards, is also provided.The model can be easily linked to the computerized methods for analyzing the thermal behaviour of buildings, and is intended as a support for the thermal comfort evaluation methods.     

Global,diffuse and direct solar radiation at the surface in the city of Rio de Janeiro: Observational characterization and empirical modeling

The city of Rio de Janeiro and others 18 cities compose the Metropolitan Area of Rio de Janeiro. The main objective of this work is to characterize observationally the diurnal and seasonal evolution of the solar radiation components in the city of Rio de Janeiro. The measurements of global and diffuse solar radiation and standard meteorological variables at the surface have been carried out regularly at the Geoscience Institute of Federal University of Rio de Janeiro since October of 2011. The microclimatic conditions show that the period 2011–2014 was warmer during most of the year and drier in summer and spring in comparison with climate normal. All solar radiation components present a well defined diurnal cycle with maximum at noon. The estimates of global and direct solar radiation indicate a great potential available for solar energy at the surface, particularly in summer. The behavior of the clearness index and diffuse solar radiation fraction is similar in summer and winter. The Angstrom formula represents properly the estimate of the monthly average daily value of global solar radiation. The sigmoid logistic function is statistically more significant in comparison with others correlation models to represent the diffuse fraction as a function clearness index.     

Models of solar radiation with hours of bright sunshine: A review

In the design and study of solar energy, information on solar radiation and its components at a given location is very essential. Solar radiation data are required by solar engineers, architects, agriculturists and hydrologists for many applications such as solar heating, cooking, drying and interior illumination of buildings. For this purpose, in the past, several empirical correlations have been developed in order to estimate the solar radiation around the world. The main objective of this study is to review the global solar radiation models available in the literature. There are several formulate which relate global radiation to other climatic parameters such as sunshine hours, relative humidity and maximum temperature. The most commonly used parameter for estimating global solar radiation is sunshine duration. Sunshine duration can be easily and reliably measured and data are widely available.     

Comparison between meteorological re-analyses from ERA-Interim and MERRA and measurements of daily solar irradiation at surface

This paper compares the daily solar irradiation available at surface estimated by the MERRA (Modern-Era Retrospective Analysis for Research and Applications) re-analysis of the NASA and the ERA-Interim re-analysis of the European Center for Medium-range Weather Forecasts (ECMWF) against qualified ground measurements made in stations located in Europe, Africa and Atlantic Ocean. Using the clearness index, also known as atmospheric transmissivity or transmittance, this study evidences that the re-analyses often predict clear sky conditions while actual conditions are cloudy. The opposite is also true though less pronounced: actual clear sky conditions are predicted as cloudy. This overestimation of occurrence of clear sky conditions leads to an overestimation of the irradiation and clearness index by MERRA. The overall overestimation is less pronounced for ERA-Interim because the overestimation observed in clear sky conditions is counter-balanced by underestimation in cloudy conditions. The squared correlation coefficient for clearness index ranges between 0.38 and 0.53, showing that a very large part of the variability in irradiation is not captured by the re-analyses. Within an irradiation homogeneous area, the variability of the bias, root mean square error and correlation coefficient are surprisingly large. MERRA and ERA-Interim should only be used in solar energy with proper understanding of the limitations and uncertainties. In regions where clouds are rare, e.g. North Africa, MERRA or ERA-Interim may be used to provide a gross estimate of monthly or yearly irradiation. Satellite-derived data sets offer less uncertainty and should be preferred.     

Towards downscaling of aerosol gridded dataset for improving solar resource assessment,an application to Spain

Solar radiation estimates with clear sky models require estimations of aerosol data. The low spatial resolution of current aerosol datasets, with their remarkable drift from measured data, poses a problem in solar resource estimation. This paper proposes a new downscaling methodology by combining support vector machines for regression (SVR) and kriging with external drift, with data from the MACC reanalysis datasets and temperature and rainfall measurements from 213 meteorological stations in continental Spain.The SVR technique was proven efficient in aerosol variable modeling. The Linke turbidity factor (TL) and the aerosol optical depth at 550 nm (AOD 550) estimated with SVR generated significantly lower errors in AERONET positions than MACC reanalysis estimates. The TL was estimated with relative mean absolute error (rMAE) of 10.2% (compared with AERONET), against the MACC rMAE of 18.5%. A similar behavior was seen with AOD 550, estimated with rMAE of 8.6% (compared with AERONET), against the MACC rMAE of 65.6%.Kriging using MACC data as an external drift was found useful in generating high resolution maps (0.05° × 0.05°) of both aerosol variables. We created high resolution maps of aerosol variables in continental Spain for the year 2008.The proposed methodology was proven to be a valuable tool to create high resolution maps of aerosol variables (TL and AOD 550). This methodology shows meaningful improvements when compared with estimated available databases and therefore, leads to more accurate solar resource estimations. This methodology could also be applied to the prediction of other atmospheric variables, whose datasets are of low resolution.     

Investigation of the impact of atmospheric particles on solar radiation at Nsukka, Nigeria

Using a well-calibrated integrating nephelometer of sensitivity 10⁻⁷/m, we have successfully measured the scattering extinction coefficient of atmospheric fine particles, b_sp at Nsukka, Nigeria, at latitude 6.8°N and longitude 7.35°E and an elevation of 488 m above sea level.

The values of b_sp recorded are 10.0 × 10⁻⁴/m (maximum) and 0.17 × 10⁻⁴/m (minimum). We have also investigated the impact of the scattering extinction coefficient on solar radiation. Results of our investigation reveal that, for high b_sp, mean insolation is generally low, and the reverse is the case for low b_sp. It appears that there is no correlation between instantaneous (hourly) extinction coefficient and insolation for the period covered.     

Quality control of global solar radiation using sunshine duration hours

The aim of this study was to develop a new and automatic method for controlling the quality of daily global solar radiation, G_d, using sunshine duration hours. The new method has three levels of tests: first, G_d is compared against daily extraterrestrial radiation that is received on a horizontal surface (0.03×G_od?G_d<G_od); second, G_d should only exceed by a small amount of the daily clear sky irradiation that is observed under highly transparent clear skies (G_d<1.1G_cd); and third, the method uses a series of persistence checks that utilize the relation between daily global solar radiation and relative sunshine duration hours. The method is capable of identifying systematic and non-systematic errors and its ability has been shown in three different climates including semi-arid, coastal humid and very arid climates.