Solar Radiation Time Series Research Articles

Solar Radiation forecasting using neural networks and Wavelet Transform

In this paper, a model has been developed which can estimate solar irradiation values from meteorological parameters like temperature, humidity, wind speed etc. This model is based on the Wavelet Transform and Recurrent Neural Network. It includes wavelet decomposition of solar radiation time series into approximate and detail components. The meteorological parameters are then mapped to these components separately using different recurrent neural network models. The final result is obtained by adding the results of each recurrent network. The use of wavelet transform helps in proper training of the recurrent network. For evaluation, results of the model used is compared against the results of normal recurrent network. Later, the developed model is used to perform 7 day hourly solar radiation forecast.

A fast and accurate model for forecasting wind speed and solar radiation time series based on extreme learning machines and principal components analysis

Precise forecasting of renewable energies such as solar and wind is becoming one of the very important concerns in developing modern electrical grids. Hence, establishing appropriate tools of weather forecasting with satisfactory accuracy becomes an essential preoccupation in today's changing power world. In this paper, an approach based on Principal Component Analysis (PCA) and Extreme Learning Machines (ELM) is proposed for the forecasting of time series. The PCA maps the data into a smaller subspace in which the components accounts for as much of the variability in the input space as possible. The variables extracted by the PCA are then introduced to the extreme learning machines, a learning algorithm much faster than the traditional gradient-based learning algorithms. The experiments carried out on three time series lead to: (i) The PCA as variable selection method shows a positive impact on the accuracy of the forecasting process. (ii) ELM model is significantly faster than Multi-Layer Perceptron Network, Radial Basis Function Networks, and Least Squares Support Vector Machines, while preserving the same accuracy level.

日射量変動予測シナリオ群に基づく蓄電池運転計画の最適化

日射量変動予測シナリオ群に基づく蓄電池運転計画の最適化

A New Method for Fusion of Measured and Model-derived Solar Radiation Time-series

When planning solar plants project developers and financers consider the long-term average of solar radiation and its uncertainty as the most important site selection criteria. Accurate time series of at least 10 years length are needed to calculate realistic estimates of such long-term averages. Ground-based measurements usually are not available for long time periods, but satellite- derived data may show significant differences compared to more accurate ground-measured values with respect to instantaneous values and frequency distribution. To overcome these shortcomings a new method for adaption of satellite-derived solar radiation values to ground measured time-series is developed. One year of overlapping time period is used for training the adaption. A weighted polynomial fit with additional constraints is then applied to the remaining satellite-derived solar radiation values. The method is tested at two sites for four satellite data models. The results show improvements for all data sets. After applying the adaption also during periods where no ground-based measurements are available the bias on average is nearing 0% for most models. This requires that the satellite-derived data realistically represent the interannual variability. Frequency distributions are also matching better. Especially this is the case for maxima, which can be critical for design purposes.

Satellite image analysis and a hybrid ESSS/ANN model to forecast solar irradiance in the tropics

We forecast hourly solar irradiance time series using satellite image analysis and a hybrid exponential smoothing state space (ESSS) model together with artificial neural networks (ANN). Since cloud cover is the major factor affecting solar irradiance, cloud detection and classification are crucial to forecast solar irradiance. Geostationary satellite images provide cloud information, allowing a cloud cover index to be derived and analysed using self-organizing maps (SOM). Owing to the stochastic nature of cloud generation in tropical regions, the ESSS model is used to forecast cloud cover index. Among different models applied in ANN, we favour the multi-layer perceptron (MLP) to derive solar irradiance based on the cloud cover index. This hybrid model has been used to forecast hourly solar irradiance in Singapore and the technique is found to outperform traditional forecasting models.

Prediction of solar radiation with genetic approach combing multi-model framework

In this paper, a genetic approach combing multi-model framework for solar radiation time series prediction is proposed. The framework starts with the assumption that there exists several different patterns in the stochastic component of the solar radiation series. To uncover the underlying pattern, a genetic algorithm is used to segment the solar series dynamically, and the subsequences are further grouped into different clusters. For each cluster, a prediction model is trained to represent that specific pattern. In the prediction phase, identifying the pattern for current period is of great importance. Thus a procedure for the pattern identification is performed to identify the proper pattern for the series belong to. The prediction result of the proposed framework is then compared to other algorithms. It shows that the proposed framework could provide superior performance compared to others.

A comparison of data sources for creating a long-term time series of daily gridded solar radiation for Europe

Satellite-derived surface solar radiation estimates are an alternative to the solar radiation measured at weather stations or modelled from other measured meteorological variables. The advantage of satellite-derived solar radiation is its high spatial and temporal resolution in comparison with solar radiation derived from weather stations, which has to be spatially interpolated. Solar radiation estimates at approximately 3–5km resolution derived from geostationary Meteosat satellites are available for Europe through the EUMETSAT Satellite Application Facilities (SAFs). The SAF responsible for land monitoring (LSA-SAF) has been providing daily solar radiation estimates in near real-time since 2005. The SAF on climate monitoring (CM-SAF) provided a 23-year long (1983–2005) consistent dataset of daily solar radiation. In this study we examine if these two solar radiation datasets may effectively be merged to generate a long-term gridded solar radiation time series for Europe. Further, we evaluate whether the ERA-Interim reanalysis or interpolated measured solar radiation (JRC-MARS) can be used as a replacement for existing and possible future data gaps in the satellite-based dataset. We show that the root mean square error and mean absolute error of LSA-SAF’s and the CM-SAF’s solar radiation estimates are similar (p<0.05), calculated against measured solar radiation data. A grid-based comparison of LSA-SAF’s and CM-SAF’s datasets showed an average root mean square difference over Europe of 2MJm−2 and a mean difference of 0.37MJm−2. For replacing data gaps in satellite-based radiation, we recommend the use of the ERA-Interim reanalysis data; they correspond better to both the ground reference and satellite-derived solar radiation data as compared to interpolated JRC-MARS. We conclude that both satellite-based products can be concatenated to create long-term gridded time series of solar radiation for Europe.

SVR-based prediction of evaporation combined with chaotic approach

Evaporation, temperature, wind speed, solar radiation and relative humidity time series are used to predict water losses. Prediction of evaporation amounts is performed using Support Vector Regression (SVR) originated from Support Vector Machine (SVM). To prepare the input data for SVR, phase space reconstructions are realized using both univariate and multivariate time series embedding methods. The idea behind SVR is based on the computation of a linear regression in a multidimensional feature space. Observations vector in the input space are transformed to feature space by way of a kernel function. In this study, Radial Basis Function (RBF) is preferred as a kernel function due to its flexibility to observations from many divers fields. It is widely accepted that SVR is the most effective method for prediction when compared to other classical and modern methods like Artificial Neural Network (ANN), Autoregressive Integrated Moving Average (ARIMA), Group Method of Data Handling (GMDH) (Samsudin et al., 2011). Thus SVR has been chosen to predict evaporation amounts because of its good generalization capability. The results show that SVR-based predictions are very successful with high determination coefficients as 83% and 97% for univariate and multivariate time series embeddings, respectively.

Empirical evidences for a planetary modulation of total solar irradiance and the TSI signature of the 1.09-year Earth-Jupiter conjunction cycle

The time series of total solar irradiance (TSI) satellite observations since 1978 provided by ACRIM and PMOD TSI composites are studied. We find empirical evidence for planetary-induced forcing and modulation of solar activity. Power spectra and direct data pattern analysis reveal a clear signature of the 1.09-year Earth-Jupiter conjunction cycle, in particular during solar cycle 23 maximum. This appears to suggest that the Jupiter side of the Sun is slightly brighter during solar maxima. The effect is observed when the Earth crosses the Sun-Jupiter conjunction line every 1.09 years. Multiple spectral peaks are observed in the TSI records that are coherent with known planetary harmonics such as the spring, orbital and synodic periods among Mercury, Venus, Earth and Jupiter: the Mercury-Venus spring-tidal cycle (0.20 year); the Mercury orbital cycle (0.24 year); the Venus-Jupiter spring-tidal cycle (0.32 year); the Venus-Mercury synodic cycle (0.40 year); the Venus-Jupiter synodic cycle (0.65 year); and the Venus-Earth spring tidal cycle (0.80 year). Strong evidence is also found for a 0.5-year TSI cycle that could be driven by the Earth’s crossing the solar equatorial plane twice a year and may indicate a latitudinal solar-luminosity asymmetry. Because both spring and synodic planetary cycles appear to be present and the amplitudes of their TSI signatures appear enhanced during sunspot cycle maxima, we conjecture that on annual and sub-annual scales both gravitational and electro-magnetic planet-sun interactions and internal non-linear feedbacks may be modulating solar activity. Gravitational tidal forces should mostly stress spring cycles while electro-magnetic forces could be linked to the solar wobbling dynamics, and would mostly stress the synodic cycles. The observed statistical coherence between the TSI records and the planetary harmonics is confirmed by three alternative tests.

Solar irradiance forecasting using spatial-temporal covariance structures and time-forward kriging

Electricity power grid operations require information about demand and supply on a variety of timescales and areas. The advent of significant generation contributions by time variable renewable energy sources means that forecasting methods are increasingly required. Some of the earliest requirements will be for spatial-temporal estimation of solar irradiance and the resulting photovoltaic-generated electricity. Accurate forecasts represent an important step towards building a smart grid for renewable energy driven cities or regions, and to this end we develop forecasting tools that use data from ground-based irradiance sensors.Spatial-temporal datasets that enjoy the properties of stationarity, full symmetry and separability are in general more amenable to forecasting using time-forward kriging algorithms. Usually, none of these properties obtain in meteorological data such as wind velocity fields and solar irradiance distributions. In this paper, we construct a statistical forecast system to mitigate this problem. We first achieve temporal stationarity by detrending solar irradiance time series at individual monitoring stations. We then approximate spatial stationarity through deformations of the geographic coordinates. Various spatial-temporal variance-covariance structures are formed to explore full symmetry and separability. Finally, time-forward kriging is used to forecast the hourly spatial-temporal solar irradiance data from 10 Singapore weather stations. The aim of the proposed system is to forecast irradiance and PV electricity generation at arbitrary spatial locations within a monitored area.

Calibrated digital images of Campbell–Stokes recorder card archives for direct solar irradiance studies

Abstract. A systematic, semi-automatic method for imaging the cards from the widely used Campbell–Stokes sunshine recorder is described. We show how the application of inexpensive commercial equipment and practices can simply and robustly build an archive of high-quality card images and manipulate them into a form suitable for easy further analysis. Rectified and registered digital images are produced, with the card's midday marker in the middle of the longest side, and with a temporal scaling of 150 pixels per hour. The method improves on previous, mostly manual, analyses by simplifying and automating steps into a process capable of handling thousands of cards in a practical timescale. A prototype method of extraction of data from this archive is then tested by comparison with records from a co-located pyrheliometer at a resolution of the order of minutes. The comparison demonstrates that the Campbell–Stokes recorder archive contains a time series of downwelling solar-irradiance-related data with similar characteristics to that of benchmark pyrheliometer data from the Baseline Surface Radiation Network. A universal transfer function for card burn to direct downwelling short-wave radiation is still some way off and is the subject of ongoing research. Until such time as a universal transfer function is available, specific functions for extracting data in particular circumstances offer a useful way forward. The new image-capture method offers a practical way to exploit the worldwide sets of long-term Campbell–Stokes recorder data to create a time series of solar irradiance and atmospheric aerosol loading metrics reaching back over 100 yr from the present day.

Short-term solar irradiance forecasting using exponential smoothing state space model

We forecast high-resolution solar irradiance time series using an exponential smoothing state space (ESSS) model. To stationarize the irradiance data before applying linear time series models, we propose a novel Fourier trend model and compare the performance with other popular trend models using residual analysis and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) stationarity test. Using the optimized Fourier trend, an ESSS model is implemented to forecast the stationary residual series of datasets from Singapore and Colorado, USA. To compare the performance with other time series models, autoregressive integrated moving average (ARIMA), linear exponential smoothing (LES), simple exponential smoothing (SES) and random walk (RW) models are tested using the same data. The simulation results show that the ESSS model has generally better performance than other time series forecasting models. To assess the reliability of the forecasting model in real-time applications, a complementary study of the forecasting 95% confidence interval and forecasting horizon of the ESSS model has been conducted.

Recent variability of the solar spectral irradiance and its impact on climate modelling

Abstract. The lack of long and reliable time series of solar spectral irradiance (SSI) measurements makes an accurate quantification of solar contributions to recent climate change difficult. Whereas earlier SSI observations and models provided a qualitatively consistent picture of the SSI variability, recent measurements by the SORCE (SOlar Radiation and Climate Experiment) satellite suggest a significantly stronger variability in the ultraviolet (UV) spectral range and changes in the visible and near-infrared (NIR) bands in anti-phase with the solar cycle. A number of recent chemistry-climate model (CCM) simulations have shown that this might have significant implications on the Earth's atmosphere. Motivated by these results, we summarize here our current knowledge of SSI variability and its impact on Earth's climate. We present a detailed overview of existing SSI measurements and provide thorough comparison of models available to date. SSI changes influence the Earth's atmosphere, both directly, through changes in shortwave (SW) heating and therefore, temperature and ozone distributions in the stratosphere, and indirectly, through dynamical feedbacks. We investigate these direct and indirect effects using several state-of-the art CCM simulations forced with measured and modelled SSI changes. A unique asset of this study is the use of a common comprehensive approach for an issue that is usually addressed separately by different communities. We show that the SORCE measurements are difficult to reconcile with earlier observations and with SSI models. Of the five SSI models discussed here, specifically NRLSSI (Naval Research Laboratory Solar Spectral Irradiance), SATIRE-S (Spectral And Total Irradiance REconstructions for the Satellite era), COSI (COde for Solar Irradiance), SRPM (Solar Radiation Physical Modelling), and OAR (Osservatorio Astronomico di Roma), only one shows a behaviour of the UV and visible irradiance qualitatively resembling that of the recent SORCE measurements. However, the integral of the SSI computed with this model over the entire spectral range does not reproduce the measured cyclical changes of the total solar irradiance, which is an essential requisite for realistic evaluations of solar effects on the Earth's climate in CCMs. We show that within the range provided by the recent SSI observations and semi-empirical models discussed here, the NRLSSI model and SORCE observations represent the lower and upper limits in the magnitude of the SSI solar cycle variation. The results of the CCM simulations, forced with the SSI solar cycle variations estimated from the NRLSSI model and from SORCE measurements, show that the direct solar response in the stratosphere is larger for the SORCE than for the NRLSSI data. Correspondingly, larger UV forcing also leads to a larger surface response. Finally, we discuss the reliability of the available data and we propose additional coordinated work, first to build composite SSI data sets out of scattered observations and to refine current SSI models, and second, to run coordinated CCM experiments.

Use of a clear-day solar radiation model to homogenize solar radiation measurements in Hawai‘i

The reliability of solar irradiance measurements is dependent on the calibration of the pyranometer used to make them. Internationally recognized standards for pyranometer calibrations require resources that may not be available to all observers. To fill this gap, we propose a method of homogenizing hourly solar radiation time series based on comparison of clear-sky radiation observations against estimates derived from a clear-sky radiation model. Inhomogeneities in the record are identified based on shifts in pyranometer response in relation to the model estimates, and corrected to produce a homogeneous time series. This method was applied to the ∼23year record of hourly solar irradiance measurements recorded at three climate stations along a 870m elevation gradient (2120–2990m) on the slopes of Haleakalā Volcano, Maui, Hawai‘i. Corrections resulted in changes in monthly solar radiation of as much as 6.8–7.4% among the three stations.

Analyzing the impact of environmental variables on the repayment time for solar farms under feed-in tariff

BackgroundEnvironmental concerns have promoted the rise of low emissions “green” power technologies such as solar power. In part to make these technologies of economic interest to investors, many green energy policies have been proposed, and a wide variety of green energy developments have been launched which take advantage of these policies. This paper studies the impact of the unpredictable solar insolation on two variables of key interest to solar plant developers: the repayment time and the cash flow at risk.ResultsUsing a bootstrap analysis of solar irradiation time series, we model solar farms which sell their power output at a Feed-In Tariff (FIT) rate motivated by one used in the province of Ontario, Canada. We show that the feed-in tariff level which existed in Ontario in March 2012 was more than sufficient to remove the financial risks inherent in financing a solar PV plant.ConclusionsWe conclude that the Ontario Canada FIT 2012 program was an effective tool to encourage investment in solar PV plants. We also find that repayment time is strongly sensitive to FIT rates. So FIT is a very efficient tool to impact/control the volume risk.

Hourly solar irradiance time series forecasting using cloud cover index

We apply time series analysis to forecast next hour solar irradiance including cloud cover effects. Three forecasting methods are proposed using different types of meteorological data as input parameters, namely, global horizontal irradiance (GHI), diffuse horizontal irradiance (DHI), direct normal irradiance (DNI) and cloud cover. The first method directly uses GHI to forecast next hour GHI through additive seasonal decomposition followed by an Auto-Regressive Integrated Moving Average (ARIMA) model. The second method forecasts DHI and DNI separately using additive seasonal decomposition followed by an ARIMA model and then combines the two forecasts to predict GHI using an atmospheric model. The third method considers cloud cover effects. An ARIMA model is used to predict cloud transients. GHI at different zenith angles and under different cloud cover conditions is constructed using nonlinear regression, i.e., we create a look-up table of GHI regression models for different cloud cover conditions. All three methods are tested using data from two weather stations in the USA: Miami and Orlando. It is found that forecasts using cloud cover information can improve the forecast accuracy.

An investigation on the relationship between solar irradiance signal from ERBS and 8B solar neutrino flux signals from SNO

In the present work an attempt has been made to investigate statistical association between solar neutrino flux data (both D2O and Salt data) collected from Sudbury Neutrino Observatory and solar irradiance data detected by Earth Radiation Budget Satellite. To serve the present purpose we have used the Multifractal Detrended Cross Correlation Analysis (MF-DCCA) based on Detrended Fluctuation Analysis (MF-X-DFA) method and the Detrending Moving Average Analysis (MF-X-DMA) which explores the long term power-law cross correlations between above two pairs of data sets. Investigation also has been made to find the frequency and time dependent local phase relationship in each pair of data sets using continuous wavelet transform (CWT) based Semblance Analysis. The Semblance Analysis reveals that there exists positive phase correlation as well as negative phase correlation between solar irradiance and D2O data at different time sub-intervals. This type of mixed phase correlation is also experienced between solar irradiance and Salt data at different time sub-intervals. The causal relationship between the D2O and the solar irradiance time series and that between Salt and solar irradiance time series have been revealed using Singular Spectral Analysis (SSA). Calculations indicate that possibly the present solar neutrino flux data (both D2O and Salt data) is supportive to predict the solar irradiance data but may not the vice versa which in turn suggests that the variability of nuclear energy generation process inside the Sun may influence the solar activity.

Testing for nonlinearity in solar radiation time series by a fast surrogate data test method

Recently, various time series models have been proposed to predict solar radiation, for instance the ARIMA (autoregressive integrated moving average) model and neural networks. Before building a model for the data, however, it is advisable to check whether the data suggest this type of modeling. More specifically, a nonlinearity test is suggested before further analysis with the linear or nonlinear tools are to be applied. In this paper, we test the presence of nonlinearity in the solar radiation time series by the method of surrogate data. The surrogate test method used in this paper is based on evaluation of the differences between the original time series and the linear model that best approximates it. Nonlinearity tests are carried out for four data sets including 5-min, hourly, daily and monthly global solar radiation time series from the UO (University of Oregon) Solar Radiation Monitoring Laboratory. The test statistics show that the 5-min, hourly, daily global solar radiation time series exhibit apparently nonlinearity while the monthly time series does not.

Correlation Between the Sunspot Number, the Total Solar Irradiance, and the Terrestrial Insolation

Our study deals with the correlations between the solar activity on the one hand and the solar irradiance above the Earth’s atmosphere and at ground level on the other. We analyzed the combined ACRIM I+II time series of the total solar irradiance (TSI), the Mauna Loa time series of terrestrial insolation data, and data of terrestrial cosmic ray fluxes. We find that the correlation between the TSI and the sunspot number is strongly non-linear. We interpret this as the net balance between brightening by faculae and darkening by sunspots where faculae dominate at low activity and sunspots dominate at high activity. Such a behavior is hitherto known from stellar analogs of the Sun in a statistical manner. We perform the same analysis for the Mauna Loa data of terrestrial insolation. Here we find that the linear relation between sunspot number and insolation shows more than 1% rise in insolation by sunspot number variations which is much stronger than for the TSI. Our conclusion is that the Earth atmosphere acts as an amplifier between space and ground, and that the amplification is probably controlled by solar activity. We suspect the cosmic rays intensity as the link between solar activity and atmospheric transparency. A Fourier analysis of the time series of insolation shows three dominant peaks: 10.5, 20.4, and 14.0 years. As a matter of fact, the cosmic rays data show the same pattern of significant peaks: 10.7, 22.4, and 14.9 years. This analogy supports our idea that the cosmic rays variation has influence on the transparency of the Earth atmosphere.

Application of Neuro-Fuzzy Techniques for Solar Radiation

Problem statement: The prediction is very useful in solar energy applications because it permits to estimate solar data for locations where measurements are not available. The developed artificial intelligence models predict the solar radiation time series more effectively compared to the conventional procedures based on the clearness index. Approach: The forecasting ability of some models could be further enhanced with the use of additional meteorological parameters. After having simulated many different structures of neural networks and trained using measurements as training data, the best structures were selected in order to evaluate their performance in relation with the performance of a neuro-fuzzy system. As the alternative system, ANFIS neuro-fuzzy system was considered, because it combines fuzzy logic and neural network techniques that are used in order to gain more efficiency. ANFIS is trained with the same data. Results: The comparison and the evaluation of both of the systems were done according to their predictions, using several error metrics. Fuzzy model was trained using data of daily solar radiation recorded on a horizontal surface in National Research Institute of Astronomy and Geophysics, Helwan, Egypt (NARIG) at ten years (1991-2000). Conclusion: The predicting conclusion indicated that the TS fuzzy model gave a good accuracy of approximately 96% and a root mean square error lower than 6%.