Category Archives: EuroSun2008-13

. Locally linear prediction

The easiest nonlinear method of local prediction was developed by Lorenz [4] and called method of analogies. Let be xt a point within the d-dimensional phase space, the predicted value a time T later, xt+T, will belong to some kind of interpolation between known points xt1+T, …, xtr+T, where x;7, …, xtr are the nearest r points to xt. Farmer and Sidorowich [12] propose an enhanced method by making a least-squared fit of a local linear map of xt into xt+T. Doing T = 1, we can obtain the predicted value as x’t+1 = atxt + bt by minimising:

W = SI lx+i- atxt — bt |2 (1)

XtGNi

in regard to at and bt. Nt is the s-neighborhood of xt.

Подпись: E2 Подпись: < E2 > Подпись: <[xt - xt]2 > <[xt -< xt >]2 > Подпись: (2)

Casdagli [10] suggests to use these models as a test for nonlinearity prediction, obtaining the average forecast error given by:

where <•> is the arithmetic average. If E = 0 then the prediction is perfect, and if E = 1, the prediction is no better than a constant predictor in the time series average. If E is calculated for different s-values, occurring the optimum for large neighbourhood sizes, this will indicate that the data are better described by a linear stochastic process in this embedding space. On the other hand, an optimum at rather small sizes will point out the existence of a nonlinear equation of motion.

The average forecast error of local linear models is plotted as a function of the neighbourhood size s in Fig. 5. Note the high value of E and how the minimum value of E occurs at higher neighborhood sizes. This result is associated with stochastic processes.

image126

Fig. 5. Average forecast error of the local linear modelas a function of the neighborhood size fot the

differenced time series.

Solar Climate of Azores:. results of monitoring at Faial and Terceira islands

Ricardo Aguiar *, Antonio Rocha e Silva and Ricardo Coelho

INETI, Department of Renewable Energies
Lisbon, Portugal

* Tel: +351 210 924 602, E-Mail: ricardo. aguiar@ineti. pt

1. Introduction

The North Atlantic archipelago of Azores (Portugal) consists of nine islands, located about 1,500 km from mainland Europe. Currently the Azores has about 243,000 inhabitants, which depend heavily on imported fossil fuel for their energy supply. This is a concern for the regional Government and its Agency for Energy and Environment, ARENA, which naturally support energy efficiency and use of renewable energies. The Azores are rich in several renewable resources, and have even pioneered Portuguese exploitation of wind, wave, and high enthalpy geothermal energy for electricity generation. However, so far solar energy has not been a priority in the renewable energy panorama, probably because the Azores climate has been considered too cloudy. Nevertheless, this is true only in comparison with the Portuguese mainland, as the radiation levels are probably similar or even better than those of Northern Europe.

In this context ARENA is developing efforts for increasing the use of solar systems. A collaboration, partly financed by an INTERREG III B Project of the European Community, has been established with INETI, the Portuguese Public Laboratory for the area of Energy, to improve the solar climatology of the Azores. This climatology is indeed quite incomplete. It consists mainly on daily measurements for two sites only at the S. Miguel and Terceira islands. Some sunshine records are available from Campbell-Stokes heliographs. Satellite data exists but their quality is uncertain due to the small size of the islands and the shallow view angle.

2. Methods

A measuring campaign was established to gather data on solar radiation, having in mind the data needs for sizing solar thermal and photovoltaic systems in the first place, but also for thermal simulation of buildings. Four meteorological stations were equipped to measure horizontal global solar radiation, ambient temperature and relative humidity. Unfortunately the financial and human resources available did not allow for diffuse radiation sensors.

The first phase of the work addressed the two islands of the eastern group, Sta. Maria and S. Miguel. The current work describes preliminary results for the second phase of the work, which concerned two of the five islands of the central group, Faial and Terceira, see Figure 1 and Table 1. Other efforts are now addressing a third island of this central group, Graciosa.

image016

Figure 1 — Location of monitoring stations.

Station sites were selected according to criteria that included island coverage, representation of microclimatic conditions, safety and reliance of the stations, low horizon obstructions, and placement near populated areas, i. e. those with potential solar energy users. Typical vistas can be appreciated in Fig. 2.

The equipment installed includes Rotronic Hygroclip S3 thermohygrometers, Huksefulx LP 02 pyranometers and Campbell Scientific CR510 dataloggers. The pyranometers were calibrated by early 2005 against a secondary standard (Kipp & Zonnen CM 11) held by the Laboratory for Solar Collector Testing at the INETI Campus, Lisbon.

Tabela 1 — Station sites.

Island

Zone

Site

Longitude

(W)

Latitude (N)

height

(m)

Terceira

Angra

Basic School Padre Jeronimo Emilio Andrade

27° 12′ 52.0»

38° 39′ 21.9»

80

Terceira

Biscoitos

Basic School of Biscoitos

27° 15′ 58.0»

38° 47′ 35.4»

100

Faial

Horta

Secondary School Doutor Manuel de Arriaga

28° 37′ 39.6»

38° 31′ 50.4»

50

Faial

Cedros

Basic School

Prof. Constantino Magno Amaral Jdnior

28° 41′ 34.2»

38° 38′ 9.4»

50

image017

Fig. 2 — Typical mounting of instruments and vistas around the stations.

3. Results

Measurements started by November 2005 and still continue, but the work reports only on the results obtained up to October 2007 (thus about two years).

Figure 3 shows recorded data at Angra, for the year of 2006, as an example. For solar radiation, the extraterrestrial values and clear-sky estimates are also shown. Clear-sky estimates were obtained with the ESRA model (ESRA, 2000) assuming a value of 2 for the Linke turbidity for airmass 2, TLK(2). Figure 4. shows monthly data for the 4 stations.

It is remarked that sequences of clear sky days — and even single clear sky days — are rare situations. On the contrary there are numerous overcast days. The seasonality of radiation data is low compared with continental sites. This feature is especially visible when the clearness index data is analysed: most of the daily values remain in a narrow range of 0.4 to 0.5, complemented with lower values during the Winter and higher values during the Summer, so at the seasonal level, the oscillation is from 0.2 to 0.55 (Fig. 4).

Temperature series show the well known characteristics for relatively small islands, of low thermal amplitude at daily (see Fig. 5) and seasonal levels. Also relative humidity levels are, as expected, quite high and show little variability.

image018

image019

image020

Fig. 3 — Daily records of solar radiation (top, kWh/m2), ambient temperature (middle, °C), and

relative humidity (bottom, %)

In Figure 5 it can be appreciated that the daily mean profiles of hourly solar radiation are almost symmetrical in respect to solar noon. This is somewhat different from the pattern for continental stations. For the later, it is usual that the afternoon values are a bit smaller than the corresponding morning values, due to larger cloud sizes brought about by the accelerated temperature related convection.

image021image022

image023 Подпись: (2005-2007)

Monthly Global Horizontal Solar Radiation (kWh/m2)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

image025 image026 Подпись: 2005-2007

Monthly Clearness Index

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

12

10

8

6

Fig. 5 — Typical mean daily profiles for 2 stations (May 2006-2007).

4. Climatology

Long term records of sunshine hours are available for some classic meteorological stations operated by the Portuguese Weather Services. It is possible to estimate long term solar radiation data using the well known relationships of relative sunshine and clearness index at the monthly scale.

As simultaneous radiation and sunshine data was not available throughout the Azores region, the usual Angstrom relationship is difficult to apply. The approach taken was instead the one proposed by Suehrcke (e. g. Suehrcke, 2000; Tiba et al., 2002)

Подпись: [1](<Gm> /<Gcm>)2 = <Sm> / <S()m>

where <> denotes long term averages, index m a monthly mean, G is global horizontal solar radiation, Gc the corresponding clear sky value, S is bright sunshine hours and S0 the daylength.

Подпись: Fig. 6 - Adjusting the Linke turbidity for the Angra site.

A clear sky must be implemented to use the method. Figure 6 illustrates the approach used to obtain a Linke turbidity to feed in the ERA model. Maxima for each Julian day where computed from the data and these where fitted by adjusting the Linke turbidity. For many days and the short monitoring period, only cloudy values where available, so the method is not fully objective in this conditions. Nevertheless an estimate of TLK(2)=4 was obtained. This is higher than for continental unpolluted stations, which typically display values around 3.

Using these turbidity estimates and the recorded sunshine data for 1951-80 (IM, 2003), the climatology obtained is the one presented in Table 2.

The differences of the estimated climatology to the short-term monitoring mean data are surprisingly small. The Suehrcke approach points to long term data a bit above the short-term monitoring 2005-2007. The main difference appears for June, and it seems quite possible that this was because of atypical weather at the region, in particular for the Summer 2005.

Table 2 — Solar radiation climatology at Angra do Heroismo estimated from sunhsine records.

Tlk(2)

<Sm>

(hours/month)

<Gm>

(kWh/m2.day)

Л

E

V

Estimated

2005-07

Estimated

2005-07

Jan

4

83

2.08

1.81

0.33

0.28

Feb

4

87

2.67

2.67

0.35

0.35

Mar

4

114

3.44

3.28

0.38

0.36

Apr

4

134

4.27

4.20

0.42

0.40

May

4

168

4.96

5.54

0.45

0.50

Jun

4

170

5.13

4.79

0.45

0.42

Jul

4

201

5.45

5.66

0.49

0.51

Aug

4

227

5.56

5.10

0.53

0.49

Sep

4

167

4.42

4.24

0.47

0.45

Oct

4

133

3.31

2.96

0.42

0.36

Nov

4

93

2.34

2.09

0.35

0.31

Dec

4

80

1.93

1.59

0.32

0.26

Year

3.80

3.66

0.41

0.39

5. Conclusions

Preliminary results of monitoring for 2005-2007 reveal that the climate at the four stations — and therefore at the two islands — is very similar. Daily thermal amplitude is low and relative humidity levels are high, features already expected taking into account the nearby ocean. Atmospheric turbidity apparently suffers from high levels of humidity and marine aerosols.

Some morning-afternoon asymmetry exists but it is small. The findings at the Azores islands suggest that most of the nebulosity there is related to macroscale eddies (the Azores Anticyclone in particular). This would also explain why the data at the northern and southern sites of the islands, and at various islands, are so similar. Indeed average yearly global horizontal irradiation at Terceira island was about 3.65 kWh/m2 per day, slightly less than for Faial island, 3.75 kWh/m2 per day.

Daily radiation sequences do not display long runs of overcast or sunny conditions, but frequent oscillations, reflected in low autocorrelation values of the detrended sequences. However, the most striking aspect is the small seasonality of the various parameters. This was expected for temperature and humidity due to the presence of the ocean and the small size of the islands, but is also true for solar radiation, especially when viewed from a clearness index perspective.

As a result of the monitoring, a clear sly model and a methodology to obtain long term climatic values could be obtained for these islands.

6. Further work

The meteorological records are now being processed to yield Reference Meteorological Years, with the objective of providing better meteorological data for the Portuguese governmental schemes supporting solar energy as well as for the Portuguese building regulation codes (subsidiary to the EU Directive on Energy Efficiency in Buildings). These require that both the summer thermal energy balance of buildings and a mandatory contribution of solar energy be computed through detailed numerical simulation with hourly data — currently obtained from stochastic models not yet tuned for these mid-Atlantic climates.

Acknowledgements — This work was partly supported by Project ERAMAC — Maximizagao da Penetragao das Energias Renovaveis e Utilizagao Racional da Energia nas Ilhas da Macaronesia, integrated in Programme INTERREG III-B, also supported by the Regional Government of Azores, and implemented by the Azores Regional Energy and Environment Agency, ARENA.

References

ESRA (2000). The European Solar Radiation Atlas. Scharmer, K. and J. Greif, Eds. ISBN 2-911762-21­5, 110 pp. Presses de l’Ecole des Mines de Paris, Chapter 3: Basics of Solar Radiation. J. Page and R. Aguiar.

IM (2003). Normais Climatologicas para 1961-90 publicadas pelo Institute de Meteorologia, obtidas via Projecto CLIMAAT, INTERREG_3B — Mac 2.3/A3.

Suehrcke, H. (2000) On the relationship betweeen duration of sunshine and solar radiation on the earth’s surface: Angstrom’s equation revisited, Solar Energy, 68, 5, 417-425.

Tiba, C., N. Fraidenraich e R. Aguiar (2002). Valor Acrescentado do Modelo de Suerhcke para a

Radiagao Global Mensal Avaliado com Dados Brasileiros. Actas do XI Congresso Iberico e VI Ibero Americano de Energia Solar, 29 Set. a 2 Out. 2002, Vilamoura. Edigao SPES, Lisboa.

Yearly Sum and Frequency distribution of DNI

The accuracy of the proposed method to derive DNI was evaluated for the year 2005 for six stations of the Spanish Meteorological Service INM, see table 1. The evaluation was performed for all hourly values with the sun above horizon.

Table 1: INM stations with measurements of direct normal irradiance DNI.

Id

Site

Latitude

Longitude

1

Santander

43.49°N

3.80°W

2

Oviedo

43.35°N

5.87°W

3

A Coruna

43.37°N

8.42°W

4

Valladolid

41.65°N

4.77°W

5

Murcia

38.00°N

1.17°W

6

Madrid

40.45°N

3.27°W

Special focus of the evaluation was on the accuracy of yearly sums and on the investigation of frequency distributions of the time series, as these are relevant for yield estimates. Beside this, the relative bias rBIAS and the relative root mean square error rRMSE are used for quantitative comparisons.

For hourly values an rRMSE of 14.7% for global irradiance and of 31% for direct normal irradiance was found for the Spanish stations. The rBIAS is 1.5% for global irradiance and 1.1% for direct irradiance respectively.

Figure 4 displays rBIAS and rRMSE of DNI for the Spanish stations. The rBIAS for one year and one station is equivalent to the relative deviation of the annual sum for one station. In addition the rBIAS for clear sky situations rBIASclearsky is provided. Hours are assigned as clear sky situations, if two criteria match: The clear sky index lies within 0.9<=k*< =1.1 and the variability of the cloud index in a small region of 3×5 pixel is small.

The comparison of rBIAS and rBIASciearsky illustrates the strong influence of the quality of the clear sky model and the atmospheric input parameters on the quality of the annual sums. The deviation of annual satellite derived irradiance sums from the respective ground measured sums between -2% and 8.5% for DNI.

In table 2 the accuracy information is given on different time scales which are relevant for solar energy applications. The deviation of annual satellite derived irradiance sums from the respective ground measured sums is between -2% and 4.5% for GHI and between -2% and 8.5% for DNI.

Table 2: Accuracy of satellite derived global horizontal irradiance GHI and direct normal irradiance DNI for

Подпись: Fig. 5: Frequency distribution of calculated and measured direct normal irradiance (left) and of global irradiance (right) for the 6 spanish stations.

different time scales.

GHI

DNI

hourly mean

335 W/m2

366 W/m:

rRMSE hourly

14.5%

31.1%

rRMSE daily

7.5%

18.5%

rRMSE monthly

3.6%

6.3%

rBIAS

1.5%

1.1%

For energy conversion systems with non-linear response to the irradiance input a correct representation of the frequency distribution is of special importance. Figure 5 displays the frequency distribution of calculated and measured DNI and GHI for the Spanish stations; a fairly good agreement is achieved.

3. Conclusion

We developed a method to derive direct normal irradiance from MSG data. The influence of clouds on the direct normal irradiance is derived from MSG data with high quality. The quality for clear skies is determined by the accuracy of the aerosol climatology.

4. Acknowledgements

Thanks are due to the Spanish Meteorological Service INM for the supply of ground data.

References

[1] Hammer A., Heinemann D., Hoyer C., Kuhlemann R., Lorenz E., Muller R., Beyer H. G. (2003): Solar energy assessment using remote sensing technologies. Remote Sensing of Environment, 86, 423-432.

[2] Fontoynont, M., Dumortier, D., Heinemann, D., Hammer, A., Olseth, J. A., Skartveit, A., Ineichen, P., Reise, C., Page, J., Roche, L., Beyer, H. G. and Wald, L.: 1998, ‘Satellight: A WWW Server Which Provides High Quality Daylight and Solar Radiation Data for Western and Central Europe’, Proceeding of the 9th Conference on Satellite Meteorology and Oceanography, Paris, France, 25.-29.05.1998, 434-437

[3] Muller, R. W., Dagestad, K. F., Ineichen, P., Schroedter, M., Cros, S., Dumortier, D., Kuhlemann, R., Olseth, J. A., Piernavieja, C., Reise, C., Wald, L., Heinemann, D. (2004): Rethinking satellite based solar irradiance modelling — The SOLIS clear-sky module. Remote Sensing of the Environment, Volume 91, Issue 2, 160-174

[4] Mayer, B. and Kylling, A. (2005): Technical Note: The libRadtran software package for radiative transfer calculations: Description and examples of use. Atmos. Chem. Phys., 5:1855-1877, 2005

[5] Kinne et al. (2005): An AeroCom Initial Assessment — Optical Properties in Aerosol Component Modules of Global Models. In: Atmospheric Chemistry and Physics Discussions, 5, 8285-8330.

[6] Kalnay, E. et al. (1996): The NMC/NCAR 40-year reanalysis project. Bull. Am. Meteorol. Soc. 77 (3), 437­472.

[7] Kemper A. (2007): Bestimmung der Diffusstrahlung unter Wolken aus Daten des Satelliten MSG. Diploma thesis, Oldenburg Unversity, Germany.

Comparison of meteorological data from different sources. for Bishkek city, Kyrgyzstan

Ruslan Botpaev[2]*, Alaibek Obozov1,

Janybek Orozaliev2, Christian Budig2, Klaus Vajen2,

1 Kyrgyz State Technical University, Department for Renewable Energies, Bishkek (Kyrgyzstan)
2 Kassel University, Institute of Thermal Energy Engineering, Kassel (Germany)
Corresponding Author, botpaev@inbox. ru

Abstract

Meteorological data from different sources (a local weather station, Meteonorm 5.1 and 6.0 as well as own measurements) have been compared with each other for Bishkek, Kyrgyzstan. It was identified that Bishkek city in Meteonorm 5.1 and 6.0 has wrong altitude (2111 m instead of 760 m), which leads to significantly lower ambient temperatures. Therefore, it is necessary to define Bishkek manually as a new site with the correct coordinates. In this case the ambient temperatures are in agreement with those measured by the weather station Frunze. Annual global solar irradiation from own measurements («1500 kWh/m2a) and weather station Frunze (1572 kWh/m2a) are in a good agreement, while its values from Meteonorm 5.1 and 6.0 are approx. 20% lower. Furthermore, monthly sums of global solar irradiation generated with Meteonorm 5.1 have an untypical trend in summer, having two local maximum points. This is inconsistent with irradiation data from other sources and with the sunshine duration in the relevant period. The data from Meteonorm should be proved on plausibility, particularly for sites or stations in developing countries.

1. Introduction

For designing and dimensioning of solar plants and prediction of solar gains it is important to have precise meteorological data, i. e. data of solar radiation, ambient temperatures and wind velocity. Meteorological data for different places can be taken from own measurements, reference books, weather stations or generated with special software (e. g. Meteonorm1).

For Bishkek, the capital of the Kyrgyz Republic in Central Asia, basically, three sources of meteorological data are available: a local weather station Frunze, a software Meteonorm (only versions 5.1 and 6.0 are considered in this study) and own measurement data (only radiation). Geographical coordinates of Bishkek are 74.5°E longitude, 42.8°N latitude (comparable with Rome) and 760 m altitude. The climate is strong continental (hot summer, cold winter, high number of sunny days).

The objective of this investigation is to compare these sources of meteorological data with each other regarding average annual ambient temperatures and solar radiation data.

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)
image037

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.

image038

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

image039

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.

 

image040

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

 

image041

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.

References

[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].