Category Archives: EuroSun2008-13

Artificial Neural Networks

Predictive methods can be divided fundamentally in Numerical Weather Prediction (NWP) models and statistical techniques. Time series prediction belongs to statistical techniques group, which is based on obtaining future values of the variable to predict in function of past observations.

Artificial Neural Networks (ANNs) paradigm was originally an abstract simulation of neural biological systems which tried to synthetic its abilities [3].

Supervised training networks have been the neural network models more developed from the beginning of its design. Training data is constructed by various input and output patterns. Knowing the output is a fact from which the training benefits as a master which supervises and modify its parameters.

Neural network used is backpropagation type; this class of supervised network has a learning algorithm based on error correction method. Learning in backpropagation networks is done in the following way: an input pattern is selected from the set of input patterns, it determines the activations of input nodes, latter, neurons are activated from hidden layers and finally output units are computed. The activation pattern which links the output layer is then compared with output pattern associated to the input pattern to calculate the error [4].

3. Results

The methods described in the previous section are trained with 75% of the data set. Assessment of the models proposed is performed over the 25% of the clearness sky separated sequentially for this purpose.

Neural Network (NN) is essayed with different layer sizes and neurons in each layer with the following architecture:

• One layer and one neuron.

• Two layers with three neurons in input layer and one neuron in output neuron.

• Three layers with five neurons in input layer, three neurons in hidden layer and one neuron in output neuron.

• Four layers with eight neurons in input layer, five and three neurons in hidden layers and one neuron in output neuron.

• Five layers with fifteen neurons in input layer, eight, five and three neurons in hidden layers and one neuron in output neuron.

Training algorithm is Leverage-Marquardt algorithm [3].

image034 Подпись: / RMSD Подпись: (1)

Accuracy of each one of the models presented is studied in terms of relative Mean Bias Deviation (MBD) and Root Mean Squared Deviation (RMSD):

being N the population size, Kt clearness sky index observed and Kt half daily clearness index predicted.

Each one of the models essayed is compared with a basic model, persistence model (PER), which is based on assumption that clearness index for next temporal step is the same as last temporal observation. Comparisons are done in terms of relative RMSD. Improvements over persistence for deviation index (i-error) (in terms of RMSD) defined previously, is obtained from the following expression:

The neural network model, NN(z), has been tested with different input vector size which represents the temporal value of the difference of lost components for half daily lags z=1..10. Fig 4. shows results for percentage of error in term of RMSD for NN model with just one neuron and one layer and with different input vector size. Improvement of the model with lower RMSD (NN(10)) against persistence is shown in Fig. 5. Difference of lost component time series is a signal with high variability which can be seen in the results in the fact that from second time step of prediction the error gets an upper limit of approximately 26% of RMSD.


Fig. 4. RMSE Error: model NN with [1] layer and only lost component as input.


Fig. 5. Improvement NN(10) over Persistence: NN with [1] layer and only lost component as input.

The second model essayed is based on using as input vector the synoptic situation difference for the time step which is being predicted and the difference of lost component for half daily lags z=1..10. Fig 6. shows results for percentage of error in term of RMSD for NN model with four layers and eight,

five, three and one neuron in consecutive layers. Improvement of model with lower RMSD (NN(10)) against persistence is shown in Fig. 7.



Fig. 6. RMSE Error: model NN with [8 5 3 1] layer and lost component and AEMet prediction as input.



Fig. 7. Improvement NN(10) over Persistence: NN with [8 5 3 1] layer and only lost component and AEMet

prediction as input.


3. Conclusion

Properties of ground global solar radiation has been presented based on requirements of statistical prediction techniques. The solar radiation time series has been transformed taking into account gaussian and stationary properties needed by neural network model used to predict future values.

A new model to predict time series of ground global solar radiation based on previous transformation of solar radiation time series has been presented. The error of the model is limited by an upper level which is due to deterministic nonlinear behaviour of the signal that can’t be followed correctly by neural network model. The second model presented is based on using the difference of lost component and the difference of the synoptic situation for the time step of prediction. The error has a lower level of nine percent. The neural network used has a structure more complex than the network used in previous works.


[1] Veziroglu TN and dot a. 21st Century’s energy: Hydrogen energy system. Energy Conversion and Management 2008; 49:1820-1831.

[2] Patlitzianas KD, Ntotas K, Doukas H, and Psarras J. Assessing the renewable energy producers’ environment in EU accession member states. Energy Conversion and Management 2007; 48:890-897.

[3] Haykin S. Neural networks. A comprhensive foundation. New York (USA): 1994.

[4] Palit AK and Popovic D. Computational Intelligence in Time Series Forecasting: Theory and Engineering Applications. 2005.

Statistical methods for correcting forecast of NWP models

Due to its high uncertainties, the performances of the NWP models have to be improved. As stated by Wilks [14], the predictors are the input variables of a statistic black box model, which has the function to predict an output variable, named as predictand that is used for correction. The MOS can be categorized in two distinct methods that differ in its predictors. While the first method, which is applied in [11] and [13], utilizes as predictors the simulated weather variables of the NWP model, except the solar radiation, the second method utilizes as predictors a time series of the measured minus the forecasted variable as presented by Libonati [15]. The second method is thus

enabled for phase and amplitude corrections of a local weather forecast. The Multiple Linear Regression (MLR) as shown in [11] and [13] or an ANN [13] is used as statistic model for the first method and a Kalman Filter for the second method [12]. Correcting the non-hydrostatic model MM5, which has a resolution of (3 x 3) km, the author of [11] obtained for two different years an RMSE of 28 % and 30 % for the prediction of the total daily horizontal solar energy on a site in Germany. Correcting the hydrostatic model ETA, the author of [13] obtained an RMSE of

25.5 % and 25.6 % for the forecast of the same variable for two different sites in Brazil. At a particular day the radiation was predicted with 17 MJ/m2 (107% of the mean value), whereas the measured energy was only 2 MJ/m2. The author selected the used output variables of the ETA model by the application of a significance test based on the MLR. Substituting the MLR with an ANN model the author didn’t observe considerable improvements of the MOS using the selected variables as predictors. The author applied the obtained model to other sites to test the generality of model performance. For two different cases, he obtained 35.6% and 38.9%. The second MOS method, which utilizes the Kalman Filter model [15], wasn’t already applied for the forecast correction of the solar radiation. The Kalman Filter has the disadvantage that it cannot, in its standard version, handle nonlinear problems [16]. Even applied to strictly linear systems, this model has higher uncertainties compared to an ANN, as shown in [17].

Mapping Solar Radiation in Southern Spain using residual kriging


MATRAS Group, Department of Physics, Campus Lagunillas, 23071, University of Jaen, Spain
* Corresponding Author, husain@,uiaen. es


This study presents a comparative analysis of the ordinary and residual kriging methods for mapping, on a 1 km by 1 km grid size, monthly-averaged daily global radiation (H) in the horizontal surface in Andalusia (Southern Spain). The experimental dataset includes four year (2003-2006) of data collected at 166 stations. Overall, the ordinary kriging methods proved to be able to provide fair estimates: RMSE ranging 1.63 MJ m’2day_1 (6.2%) in June to around 1.44 MJ m’2day_1 (11.2%) in October. In the residual kriging procedure, we propose the use of an external explanatory variable that accounts for topographic shadows cast, and that is able to explain between 15% and 45% of the spatial variability. Based in this variable, residual kriging estimates shows a relative improvement in RMSE values ranging from 5% in the summer months to more than 20% in the autumn and winter months. Particularly, RMSE values of the residual kriging estimates ranges from 1.44 MJ m’2day_1 (5.5%) in June to around 1.31 MJ m’2day_1 (10.2 %) in October. It is finally concluded that the proposed residual kriging method is particularly valuable when mapping complex topography areas.

Keywords: GIS, Kriging, Global Solar Radiation, Andalusia (Southern Spain).

1. Introduction

The interpolation techniques were the first methodologies used for mapping climate variables, such as the solar radiation. These techniques allow obtaining spatially continuous databases from isolated-stations measurements based on spatially interpolation methods. The reliability of interpolation techniques are strongly dependent on the sample size [1]. Particularly, ordinary kriging may provide reliable estimates of climate variables, as the solar radiation, in homogeneous terrain with similar climate characteristics. Nevertheless, the reliability of the estimates decreases when the complexity of the topography increases, or when an earth-sea interface is present. In such cases, stochastic interpolation processes may not provide meaningful spatially-continuous estimates, since point-specific measurements can be affected by strong local variation. For the solar radiation, particularly, complex topography areas present a challenge. Variability in elevation, surface orientation (slope and aspect), and shadows cast by topographic features can create strong local gradients in the solar radiation that interpolation processes may not properly account for.

Many techniques have been proposed to overcome this weakness of the kriging interpolation processes. These techniques allows to take into account, prior or during the interpolation process, external variables, that may provide complementary information for the interpolation and, therefore, compensate for the lack of data and the scarce sample size [2]. These external variables may be used locally or in the whole study area and, in most the cases, are related to geographical of

topographical characteristics. There are different ways in which the external variables can be taken into account in the kriging process. For instance, the information coming from the external variables can be considered during the interpolation process. An example of this methodology is the cokriging. This method is advantageous when the external variable is highly correlated to the studied variable, but becomes very complex when more than one covariables are considered [3] Instead of including the external information directly in the kriging process, it is possible to consider it during a first step, prior to the interpolation itself. There are different denominations for this technique, as ‘kriging with a guess field’ [3] or ‘residual kriging’ [4]. We will use this last denomination hereinafter. Basically, in a first step, a multiple linear regression is fitted between the variable of interest and some external explanatory variables. Then, an ordinary kriging procedure is applied to the residuals of this multiple regression analysis. Finally, a map is obtained integrating both the multiple regression and the kriging results. This technique, although relatively simple, is powerful, since allows including in an easy way multiple sources of external information in the interpolation procedure that may compensates for the small sample size. In this work we present an application of the residual kriging methodology for mapping monthly-averaged daily global radiation in horizontal surface in Andalusia (Southern Spain). The ordinary kriging method is also applied, to evaluate the improvement provided by the residual kriging method. The region of study is characterized by a wide range of topographic and climatic characteristic, which allows evaluating the influence of different external variables in the interpolation of the solar radiation.

2. Methodology

Material and methods

The meteorological and climatic features of Galicia are monitored by a network made up by 93 weather stations, located all over the region covering the usual meteorological parameters. Ten — minute averaged data were collected for both monitoring and climatic studies. The network is managed by MeteoGalicia, the Galician weather service (www. meteogalicia. es). Currently, 25 stations provide the solar radiation measurements with Ph. Schenk first class pyranometers (Philipp Schenk GmbH Wien & Co KG, Wien, Austria) and Kipp & Zonen sunshine duration sensors (Kipp & Zonen, Delft, The Netherlands) located in the most representative sites of Galicia. These sensors are periodically cleaned and calibrated by specialized crew, following the manufacturer’s recommendations. Data are collected by dataloggers, sent to a central data server and stored in a database specifically designed for environmental data sets. Here, several filters are applied to ensure the data quality [6, 7].

Подпись: Fig. 1: Geographical location of Galicia in the European continent and localization of the weather stations involved in this work

Since the solar radiation network was gradually set up, eight stations count on a data set longer than five years. The main features of these stations are listed on Table 1, while geographical location is illustrated in Fig. 1.

In this work, the analysis has been focused on the trend of the values of global radiation, sunshine duration and clearness index KT. Other meteorological parameters that are relevant for the solar resource characterization (temperature, relative humidity and precipitation) have also been considered. Finally, monthly and yearly values of global solar irradiation measured in the meteorological stations have been compared with the results obtained by Vazquez et al. [4].

The clearness index has been evaluated by the ratio G/G0, where G is the ground measured irradiation and G0 is the extraterrestrial irradiation. For this purpose, a solar constant value of 1376 Wm-2 was adopted, as recommended by Davies [8]. Astronomical relationships were obtained following Iqbal [9].







Data Record


43.48° N

8.23° W


Subrban, Coastal



42.43° N

8.63° W


Urban, Coastal




43.54° N

7.03° W


Rural, Coastal


Alto do Rodicio

42.30° N

7.59° W


Rural, Interior



42.82° N

6.92° W


Rural, Interior




42.08° N

8.68° W


Rural, Interior



42.56° N

9.03° W


Rural, Coastal



42.82° N

8.46° W


Rural, Interior


Table 1: Main features of the meteorological stations analysed.

3. Results

Lyapunov exponents

Chaotic dynamical systems are predictable for finite time scales, but not for infinite ones. Let consider two initial states of the system with almost identical initial conditions. Their trajectories in the phase space will move apart, given a metric, at an exponential rate while moving on an attractor. This rate is described by the largest Lyapunov exponent in the system, ^max. If any Lyapunov exponent is positive, the system will be chaotic by definition. Yet, should one of them be zero, the system can be described by a set of ordinary differential equations [10].

Figure 6 shows the d Lyapunov exponents for the differenced time series as a function of the number of samples following the suggested algorithm by Sano and Sawada [11]. The main interest in this test is to find Lyapunov exponents greater or equal than zero. The two Lyapunov exponents exhibited by the time series are negative and thus, this time series cannot be considered coming from a chaotic dynamical system neither be described by a set of differential equations.


Fig. 6. Lyapunov exponents against the number of samples.

4. Conclusions

The global solar radiation data were measured at the radiometric station of the University of Almeria (Spain) during eight years. Results have shown the non-existence of any attractor in the phase space for the global irradiance time series. Negative Lyapunov exponents exclude a chaotic behaviour that might allow a better short term prediction than autorregresive models, and the idea of the existence of a nonlinear differential equation system. These results match with those

obtained from applying local linear models for prediction, of which estimations suggest that the data are best described by a linear stochastic process.


This work was supported by the project ENE2007-67849-C02-02 of the Ministerio de Ciencia y Tecnologia of Spain.


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[2] J. Boland, Solar Energy 55 (1995) 377.

[3] H. Morf, Solar Energy 62 (1998) 101.

[4] E. N. Lorenz, J. Atmos. Sci. 20 (1963) 130.

[5] L. Alados-Arboledas, F. J. Batlles, F. J. Olmo, Solar Energy 54 (1995) 183.

[6] F. Takens, (1981). Dynamical Systems and Turbulence, Lecture Notes in Math, Springer-Verlag, Berlin.

[7] A. M. Fraser and H. L. Swinney, Phys. Rev. A, 33 (1986) 1134.

[8] R. Hegger, H. Kantz, and T. Schreiber, Chaos, 9 (1999) 413.

[9] M. B. Kennel, R. Brown, and H. D.I. Abarbanel, Phys. Rev. A, 45 (1992) 3403.

[10] M. Casdagli, J. Roy. Stat. Soc., 54 (1991) 303.

[11] M. Sano and Y. Sawada, Phys. Rev. Lett., 55 (1987) 1082.

[12] J. D. Farmer and J. J. Sidorowich, Phys. Rev. Lett., 59 (1987) 845.

Management and Exploitation of Solar Resource Knowledge

C. Hoyer-Klick1*, H. G. Beyer2, D. Dumortier3, M. Schroedter-Homscheidt4, L. Wald5, M.
Martinoli6, C. Schilings1, B. Gschwind5, L. Menard5, E. Gaboardi6, L. Ramirez-Santigosa7, J.
Polo7, T. Cebecauer8,T. Huld8, M. Suri8, M. de Blas9, E. Lorenz10, R. Pfatischer11, J. Remund12, P.

Ineichen13, A. Tsvetkov14, J. Hofierka15

1 German Aerospace Center (DLR), Institute of Technical Thermodynamics, Pfaffenwaldring 38-40, 70569

Stuttgart, Germany

2 Hochschule Magdeburg-Standal, Germany. 3Ecole Nationale des Travaus Publics de l’Etat (ENTPE), France
4 German Aerospace Center, German Remote Sensing Data Center, Germany 5 Ecole des Mines de Paris, France
6 Icons srl., Italy 7 CIEMAT, Spain 8 European Commission, Joint Research Center, Institute for Energy, Italy
9 Universidad Publica de Navarra, Spain 10 Oldenburg University, Energy — and Semiconductor Research Lab,
Germany 11 meteocontrol GmbH, Germany 12 Meteotest, Switzerland 13 University of Geneva, Switzerland
14 Voeikov Main Geophysical Observatory, World Radiation Data Center, Russia
15 University of Presov, Slovakia

Corresponding Author, carsten. hoyer-klick@dlr. de


Knowledge of the solar energy resource is essential for the planning and operation of solar energy systems. In past years there has been substantial European and national funding to develop information systems on solar radiation data, leading to the situations that several data bases exist in parallel, developed by different approaches, various spatial and temporal coverages and resolutions including those exploiting satellite data. The user of these products may end up with different results for the same requested sites. To better guide the users, a benchmarking exercise is under preparation. A set of reference data has been collected and benchmarking measures and rules have been defined. The results of the benchmarking and the feedback from stakeholders will be integrated into a guide of best practices in the application of solar resource knowledge. Access to data has been quite fragmented. Each service has its own way of access to the data and delivery format. A new broker portal based on the experience of the project Soda aims to unify and ease the access to distributed data sources and applications providing solar resource information.

Keywords: Solar resource information, benchmarking, access to data, user guidance

1. Introduction

Knowledge of the solar energy resource is essential for the planning and operation of solar energy systems. In past years there has been substantial funding from the European Commission to develop information systems on solar radiation data, such as the European Solar Radiation Atlas (ESRA), the projects SoDa, Satel-Light, PVGIS, PVSAT, PVSAT-2 or Heliosat-3 and the Envisolar project of the European Space Agency (ESA). In addition national services were set up as Meteonorm by Meteotest in Switzerland and SOLEMI by DLR in Germany. The information on available databases and
integrated systems has been summarised and later updated in [1,2]. From the regional point of view, the projects focused mainly on Europe or its regions, leading to the situation that several different data bases exist in parallel developed by different approaches, various spatial and temporal coverages and different resolutions including those exploiting satellite data. The users comparing information from different data sources for the requested sites may end up with uncertainty that is difficult to deal with.

Large steps forward have been made for the benefit of research, renewable energy industry, policy making and the environment. Nevertheless, these multiple efforts have led to a fragmentation and uncoordinated access: different sources of information and solar radiation products are now available, but uncertainty about their quality remains. At the same time, communities of users lack common understanding how to exploit the developed knowledge.

The project MESoR started in June 2007 and aims at removing the uncertainty and improving the management of the solar energy resource knowledge. The results of past and present large-scale initiatives in Europe, will be integrated, standardised and disseminated in a harmonised way to facilitate their effective exploitation by stakeholders. The project will contribute to preparation of the future roadmap for R&D and strengthening the European position in the international field.

The project includes activities in user guidance (benchmarking of models and data sets; handbook of best practices), unification of access to information (use of advanced information technologies; offering one-stop-access to several databases), connecting to other initiatives (INSPIRE of the EU, POWER of the NASA, SHC and PVPS of the IEA, GMES/GEO) and to related scientific communities (energy, meteorology, geography, medicine, ecology), and information dissemination (stakeholders involvement, future R&D, communication).

First Steps in the Cross-Comparison of Solar Resource. Spatial Products in Europe

M. Suri1*, J. Remund2, T. Cebecauer1, D. Dumortier3, L. Wald4, T. Huld1 and P. Blanc4

1 European Commission, Joint Research Centre, Institute for Energy,

Renewable Energies Unit, via E. Fermi 2749, TP 450, I-21027 Ispra (VA), Italy
2 Meteotest, Fabrikstrasse 14, CH-3012 Bern, Switzerland
3 Ecole Nationale des Travaux Publics d’Etat, Departement Genie Civil et Batiment,

URA CNRS 1652, Rue Maurice Audin, F-69518 Vaulx-en-Velin, Cedex, France
4 MINES ParisTech, Centre Energetique et Procedes, BP 207, 06904 Sophia Antipolis Cedex, France

* Corresponding Author, marcel. suri@jrc. it


Yearly sum of global irradiation is compared from six spatial (map) databases: ESRA, PVGIS, Meteonorm, Satel-Light, HelioCliom-2, and NASA SSE. This study does not identify the best database, but in a relative cross-comparison it points out to the areas of higher variability of outputs. Two maps are calculated to show an average of the yearly irradiation for horizontal surface together with the standard deviation that illustrates the combined effect of differences between the databases at the regional level. Differences at the local level are analysed on a set of 37 randomly selected points: global irradiation is calculated from subset of databases for southwards inclined (at 34°) and 2-axis tracking surfaces. Differences at the regional level indicate that within 90% of the study area the uncertainty of yearly global irradiation estimates (expressed by standard deviation) does not exceed 7% for horizontal surface, 8.3% for surface inclined at 34°, and 10% for 2-axis tracking surface. Higher differences in the outputs from the studied databases are found in complex climate conditions of mountains, along some coastal zones and in areas where solar radiation modelling cannot rely on sufficient density and quality of input data.

Keywords: solar radiation database, maps, benchmarking

1. Introduction

Solar energy technologies and energy simulation of buildings need high quality climatic data in the phase of localisation (siting), design, financing, and system operation and management. The choice of the best technological option depends among other things on the geographic region, as the performance of solar energy systems is influenced by solar resource and other climate parameters.

Several spatial databases of solar resource information are now available as a result of European and national projects. They have been developed from various data inputs, covering different time periods, where diverse approaches have been applied. Although quality assessments of the individual databases have been performed, no inter-comparison of the outputs was performed. When comparing various data sources, differences show up which is confusing, especially to users who are not fully aware of the uncertainties and the limits of data application. Therefore, better understanding of the geographic distribution and variability of solar resource in Europe is needed.

In this contribution we open a complex issue of benchmarking the solar radiation databases and underlying models for deriving information relevant to energy technology. We focus on a comparison of six spatial databases and integrated systems that offer solar resource and climate

data and energy-related services for Europe: Meteonorm [1], ESRA [2], Satel-Light [3], NASA SSE/RETScreen [4], HelioClim/SoDa [5], and PVGIS [6]. This list is not exhaustive, and in future also other databases may be considered, including those that cover smaller regions. We compare yearly sum of global irradiation as obtained by querying each database. Map analysis compares horizontal irradiation, while on a set of 37 randomly selected points we compare irradiation received by inclined and 2-axis tracking surfaces.

Meteorological data. Meteorological station “Frunze”

The central administrative board on hydrometeorology of the Ministry of Emergencies of the Kyrgyz Republic is entitled to measure meteorological and hydrological data in the Kyrgyz Republic. There are in total 31 weather stations and 75 hydrological stations. One of the weather stations “Frunze” is situated in the west part of Bishkek. The measurement equipment is remained from the USSR period. An actual value of global and diffuse solar radiation is measured 5 times a day at 6.30, 9.30, 12.30, 15.30 and 18.30. Till 1993 daily solar irradiation on horizontal surface was measured by an integrator. This device is, however, absent since 1993 for technical reasons. Therefore, since 1993 daily solar irradiation is estimated by linear interpolation of solar radiation between 5 measured points taking into account the time of sunrise and sunset (the so-called trapezium method). The central administrative board on hydrometeorology claims the accuracy of this method to be in the range of 10% for monthly sums of solar radiation.

Modeling and Analysis of Chinese Exposure to Solar Radiation Based on the Available Meteorological Data at CMA, China

Yu Qiang1* and Wang Zhifeng2

1,2 Institute of Electrical Engineering, CAS P. O.BOX 2703 Beijing 100190, China Corresponding Author, yuqiang1984@mail. iee. ac. cn


The distribution of solar radiation is very important for choosing sites for solar power tower plants. In this paper the observed data which include solar radiation and sunshine duration of eight typical cities of China during the period 1994-2003 are used to establish a correlation equation between monthly average daily values of clearness and relative sunshine. The model is used to estimate the global solar radiation of the whole country. And it is proved to be good results (greater than 94% in most cases). The predictive efficiency of this model is also compared with some other models which are believed to be applicable globally in terms of mean percentage error (MPE), mean bias error (MBE) and root mean square error (RMSE). And the results prove that it is also better than that of those models.

Key Words: global solar radiation, sunshine duration, MBE, MABE, RMSE.

1. Introduction

The design of a solar energy conversion system must always start with a study of solar radiation data at a site. One of the most important requirements in the design is the information on the intensity of solar radiation at a given location [1]. Unfortunately, there are very few meteorological stations that measure global solar radiation. Solar radiation data are still very scarce, especially in developing countries. So we must consider other methods to calculate relative solar data for places where they are not directly measured, many attempts have been made to develop models and empirical correlations that can predict the amount of solar radiation available at a given location from a few input parameters.

While it has been proved that a number of commonly measurable atmospheric and meteorological parameters such as turbidity, relative humidity, degree of cloudiness, temperature and sunshine duration taken severally or jointly, affect the magnitude of the global radiation incident on a given location. And the preponderance of data point to the fact that the greatest influence is exerted by sunshine hours.

There are several correlations [2-7] to have been developed that predict the correlation between the global radiation and the percentage of bright sunshine hours in a simple linear regression form (the Angstrom-Prescott type). And some authors have also developed quadratic correlation [2, 4, 6] model and multiple linear regression. The study of this paper is to establish a linear regression form which uses the data of eight typical cities of China for estimation global solar radiation for the cities where there are no meteorological stations but have similar meteorological conditions.

Materials, methods and models

In the present work the solar radiation is forecasted with the non-hydrostatic model Advanced Regional Prediction System (ARPS). This model is providing its forecast weather variables for a horizontal grid of (0.12 x 0.12)° resolution with a sampling interval of 10 min. The model is simulated at the LEPTEN laboratory (Laboratory of Energy Conversion Process Engineering and Energy Technology), former LABSOLAR, at the Federal University of Santa Catarina. The simulation assimilates the data of the global reanalysis delivered by the National Center for Environmental Prediction (NCEP) [12]. The analysis data characterize the initial condition at every 6 h, necessary to operate ARPS in actual time. The reanalysis data represent improved analysis data of the atmosphere. Both the analysis and reanalysis data are based on atmospheric measurements and their interpolations, as well as on the last forecasts of the GFS, which can accomplish forecasts until a ten days horizon. The operational forecast uncertainty includes both the analysis and the forecast uncertainty. In the present article only the uncertainty based on the reanalysis are verified. Therefore the reanalysis data, based on the GFS model, is assimilated with the regional ARPS model in a 6 h interval. For the uncertainty verification the 24 h mean value of the downward short wave radiation of the ARPS output is compared to the measured mean value of the global radiation. In a second step a statistical correction for the reanalysis uncertainty is accomplished. In the text that follows the daily energy E [Wh/m2] is equal to the daily mean radiation H [W/m2] multiplied by 24 hours.