Category Archives: EuroSun2008-13

Data basis and verification

The performance of the NWP model ARPS and the proposed MOS procedure is verified for the site Florianopolis, localized in the south of Brazil with 48° 3ri5’’W longitude and 27° 36’ 76’’S latitude. The measured global horizontal radiation within the period from January 2000 to June 2006 was used to calculate the daily mean values. For daily mean values, the utilized pyranometer CM11 has a measurement uncertainty of 1 % for 95 % confidence as stated in [31]. For the quality control [32], [33] the measured radiation vales have to appear in the measurement range of (0 to 1367) W/m2. If this criterion was not fulfilled for a time interval larger than 10 min, the daily mean value was rejected as recommended in [33]. From the training-validation of 6.5 years, 119 days were excluded by the quality criterion, leading to the remaining data, which appears in 53 consistent time series. To facilitate the implementation, the data blocks of the training data set were chained, rather than is accomplished a specific DWT of each block, obtaining three equal length vectors with synchronized day numbers. The vector of residuals {sA} is obtained by subtraction of the measured {H} from the forecasted daily solar radiation means {HA}. The obtained predictors sAsi_1 to sAsi-k and predictands sAsi (eqn. 3), selected from the partially reconstructed sub-signals (eqn. 2, {sAS}), have to consider the limitations of each of the data blocks to avoid uncharacteristic modification of the ANN input pattern. As to see in eqn. 3, the data of the first k days of each block are used exclusively as predictors, thus a time series with the length nj provide (n-k) training samples for the ANN. Each sample has an input vector with the pattern length k, the predictors, and one output variable, the observed predictand, of the forecast at the considered time scale. The total number of training-validation samples ntv is obtained with expression (5).

ntv = YU (nj — k ) (5)

Where j = 1…nb defines the number of data blocks obtained by the data qualification, with block individual number of training samples nj. The resulting data set is subdivided in two subsets, the training and the validation set. As recommended in Kaastra [34], the validation set, which is independent from the training set has to represent (10 … 30) % of the data. This set may be selected randomly from the data or it follows immediately the training set [34]. From the data the last year, representing a validation set of 18 % was separated. Due to hardware improvements of the measurement system [35], the validation set was not exposed to system outages, which leads to its consistence.

image113

4. Results

The average of the selected daily mean values of the measured solar radiation is 182.36 W/m2. For ARPS model simulations, based on the reanalysis dada, was obtained a RMSE of 70 W/m2 that corresponds to 38.4% of the measured average value. The maximal error of the daily mean solar radiation simulation is with 264.3 W/m2 higher than the measured average value (compare figure 3 — third chart and figure 4). If the correction is build up with data of twelve subsequent previous days (k = 12), a set of 1356 predictor vectors (sAs, (i-1) … sAs, (i-k) ) were selected. With the proposed MOS method the RMSE of the ARPS model reduces to 18.92 W/m2 for the training data set, which corresponds to 10.37 % of the measured average value of 182.36 W/m2. For the independent validation data set was obtained 9.06 % (see figure 3, fourth chart and figure 5). Worst performances were observed for the sub-signal di which contains the details of the higher frequency band (RMSE = 9.08 W/m2) and for the approximation sub-signal a1 (RMSE = 6.82 W/m2). The generalization performance of the ANN was verified with the validation data set. By arbitrary configured number of neurons in each layer with (k = 12), the best performance of the d1 sub-signal correction was observed, for 22 neurons at the first, and 12 neurons at the second hidden layer. This configuration of the neurons was used also for the other three ANN, whereby the one used for the approximation signal was configured as RNN, due to slight improvement in its performance. To access the probably higher boundary uncertainties under operation of the prediction model, it is necessary to accomplish ntv times (equation 5) the DWT for the data set having ntv predictor/predictand samples (see discussion in section 3.2). Avoiding numerical effort, the present article release only the results based on a single DWT of the data set as accomplished in

[9] .

Figure 3 — Daily mean values of the solar radiation — charts from the top to the bottom: (1) measured solar radiation H; (2) forecasted solar radiation with the ARPS model HA; (3) (H — HA); (4) (H — HA, corr), where HA, con — is the corrected ARPS forecast. The validation set appears from 2000 to 2500 days.

Models evaluation

The ordinary and residual kriging models were obtained based on the training dataset. After that, the validation dataset were used to evaluate these models. Particularly, model estimates were evaluates in terms of the ME, MAE, RMSE and the correlation coefficient.

Reference values for ground reflectivity

In order to calculate the ground reflectivity pg, in an iterative procedure values larger than the mean value of the distribution plus ag are filtered out, until convergence is achieved. The mean value of the new distribution is assigned to pg.

In the original Heliosat method a constant value ag was used, ag = 27 is a suitable value for MSG. But an approach that accounts for the dependency of ag on the sun-satellite geometry leads to even better results. The bias of the clear sky irradiance is used as a measure to quantify the influence of ag. For clear sky situations, the quality of the ground reflectivity can be evaluated directly and there is little super imposition with other effects. If ag is chosen too small, the corresponding values of the ground reflectivity will be too small as well. This results in an underestimation of the irradiance. On the other hand, if CTg is too high, an overestimation of the irradiance is the consequence. Best results were found for 15<=CTg<= 50 for different classes of solar and satellite zenith angles and the azimuth angle between sun and satellite.

Parameters influencing SSI

Clouds regularly cover about 50 % of the earth and represent the most important modulators of radiation in the earth-atmosphere system (Liou 1976). A cloud in libRadtran is characterized by its optical thickness (tc), type (cloud water or ice cloud), height of cloud top (ztop) and bottom (zbot) and the effective radius (ref) particles.

Many radiative transfer codes contain the same six atmospheric profiles corresponding to geographical and seasonal averages (Mayer, Kylling 2005; Vermote et al. 1997): Midlatitude Summer (afglms), Midlatitude Winter (afglmw), Subarctic Summer (afglss), Subarctic Winter (afglsw), Tropical (afglt) and U. S. Standard (afglus). “afgl” means Air Force Geophysics Laboratory.

The gas whose variation have a major influence on the SSI are water vapour (H2O), ozone (O3), carbon dioxide (CO2), oxygen (O2), methane (CH4), and nitrous oxide (N2O) (Vermote et al. 1997).

The attenuation of radiation by aerosols varies with its nature, density and size distribution. Following Shettle (1989), required parameters in libRadtran are: aerosol type from 0 km to 2 km altitude (haze), aerosol type above 2 km altitude (vulcan), season, and visibility (vis). The visibility is closely linked to the aerosol optical thickness (iaer) (Vermote et al. 1997). Taer represents the total extinction induced by aerosols of the medium for a given wavelength. It is sensitive to micro-physical properties of aerosols. Because these properties are difficult to assess accurately, the spectral variation of the aerosol optical thickness is usually calculated using a simplified method:

Taer A = в (Я/ Ям/" (1)

where AM = 1000 nm, в is the aerosol optical thickness at the wavelength 1000 nm and a is the Angstrom coefficient (Perrin de Brichambaut and Vauge, 1982).

When radiation reaches the earth’s surface, it can be absorbed or reflected. The intensity of the reflected radiation varies with the value of the incident radiation and the reflectance of the receiving surface. The ground reflectance is the function of the illuminating and emitting angles; the albedo is its hemispherical average. Both change with soil type and wavelength. A portion of this reflected radiation is then backscattered by the atmosphere and increases the value of the diffuse component of the SSI.

Unifying Access

The second major objective of the MESoR project is to unify and ease access to solar resource information. This builds upon experiences made within the SoDa portal, adopting mapping features from PVGIS web system. SoDa was build with proprietary software and communication protocols. As the World Wide Web evolved over recent years, the new MESoR portal builds upon open source software with a larger development community and standard web services. This will make the new portal more sustainable in terms of software development and the connection to the portal more easy and open as only widely accepted standards have to be followed.

The portal will serve as a broker to solar resource information and services. It does not contain and maintain data for itself. It just links data bases and services with a single point of entry and a common user interface. Databases and services have to be hosted by the providers. They keep control over their data and applications.

Metadata are essential to exchange knowledge between applications. They describe objects to be exchanged (e. g. a time series of irradiance, a geographical location, a date…). After a series of consultations with several bodies involved in standards, such as ISO, GEOSS (Global Earth Observation System of Systems), INSPIRE (Infrastructure for Spatial Information in Europe) and national meteorological offices, a thesaurus has been defined which is specific to solar resource. A thesaurus is a set of terms that describe the solar resource.

A prototype of the broker will be set up during the project. A new user interface has been designed. It utilises the API (application programming interface) of Google Maps. Users can therefore use the full capabilities (geographical search, maps and images) of Google to identify their sites and select the right locations or regions. As this interface is easy to use and applied already in many other applications it the user feels familiar with it. The front page of a service gives the site selection window and some descriptive information of the service, as a general description, property rights and credits, inputs and outputs descriptions. The results can be written to the browser window or saved in a specific format (e. g. spreadsheet-compatible). The available data bases can be selected by the menu on top of the page. Fig. 2 shows two sample screenshots of the current prototype (see http://project. mesor. net).

image031
Conclusions

The project MESoR together with the IEA Task 36 “Solar Resource Knowledge Management” aim at developing better guidance about the energy application of solar resource information. The benchmarking exercise will ease the comparison of different data sources and the standardised rules will make accuracy evaluations more transparent and comparable. The guide will help users in the choice of data sources and how to use the data for their specific needs.

The new broker portal aims to ease the access to solar resource data and online applications by serving as single point of entry to a variety of data sources all with a similar look and feel and common data formats. More information about the project can be found at http://www. mesor. net.

References

[1] L. Wald, (2006). Available databases, products and services. In Dunlop E. D., Wald L., Suri M. (Eds.), Solar Energy Resource Management for Electricity Generation from Local to Global Scale. Nova Science Publishers, New York, pp. 29-41.

[2] M. Suri (2007). Solar resource data and tools for an assessment of photovoltaic systems. In Jager-Waldau A. (editor), Status Report 2006, Office for Official Publications of the European Communities, Luxembourg, pp. 96-102.

[3] B. McArthur, (2004). Baseline Surface Radiation Network. Operations Manual Version 2.1.

[4] Iqbal, M., 1983. An Introduction to Solar Radiation. Academic Press, New York

[5] C. N. Long, E. G. Dutton (without year). BSRN Global Network recommended QC tests, V2.0 (available at BSRN website http://bsrn. eth. ch).

[6] B. Espinar, L. Ramirez, A. Drews, H. G. Beyer, L. F. Zarzalejo, J. Polo, L. Martin. Analysis of different comparison parameters applied to solar radiation data from satellite and German radiometric stations, Solar Energy (2008) In Press.

WRF Analysis Results

The Weather Research and Forecasting (WRF) system was developed by the National Oceanic and Atmospheric Adminstration (NOAA) National Centers for Environmental Prediction (NCEP). The current release is Version 2.2. The WRF modelling system software is in the public domain and is freely available for community use. The WRF is designed to be a flexible, state-of-the-art atmospheric simulation system that is portable and efficient on available parallel computing platforms. The WRF is suitable for use in a broad range of applications across scales ranging from meters to thousands of kilometres, including:

• Real-time NWP

• Forecast research

• Parameterization research

• Coupled-model applications

• Teaching

The WRF model is run over Europe with 3 nesting levels and using NCEP boundary conditions data. The variable validated is global solar radiation which is a direct output from WRF model. The period of data studied is the year 2005. The spatial resolution of the domain over Spain is 27km.

WRF model has been executed in analysis mode for the domain of the whole Europe with special resolution of 27km approximately and hourly temporal resolution. Three nested domain where used and the model was fed with data from NCEP global model. The period of simulation goes from 1/1/2005 to 28/2/2005.

The validation is done comparing with ground measurements from 40 stations from AEMet and variable direct output downward global solar radiation of WRF model. Normalized results of MBD and RMSD for hourly and daily resolution are presented in Fig. 6-4. The graphic shows all the stations ordered from lower latitude to higher latitude. Stations with lower latitude present a predominance of clear sky situations which results in small errors.

MBE Hourly Solar Radiation Forecasting

20

image107

25 L______________ [_________________ [_________________ Г________________ Г________________ [_______________ [_________________ [_________________ [

36 37 38 39 40 41 42 43 44

Latitude

Подпись: RMSE Hourly Solar Radiation Forecasting 0 36 37 38 39 40 41 42 43 44 Latitude

Fig. 6. Normalized MBD for hourly global solar radiation

Подпись: 20

MBE Daily Solar Radiation Forecasting

-30

36 37 38 39 40 41 42 43 44

Latitude

Fig. 8. Normaliazed MBd for daily global solar radiation

RMSE Daily Solar Radiation Forecasting

 

90

 

36 37 38 39 40 41 42 43 44

Latitude

 

image110

image111 image112

Overall the model is able to reproduce clear sky synoptic conditions. Errors are presents mainly in situations where fronts and huge cloud movements need to be reproduced. Fig. 10-13 presents a synoptic situation from the date 22/2/2005. Fig. 10. is the measurements from the satellite which represents the real situation. Fig. 12 is an instantaneous map of the global irradiance modelled. We can see as the model is missing a lot of small clouds. Fig. 11 and 12 represents measured and WRF modelled hourly global irradiance for two stations, Granada in the South of Spain and Oviedo in the north. In this date the model is getting a contradictory prediction with measurements. In Granada (lower middle part of Fig. 10.) the model is getting an overcast situation in the firs half of the day and clearsky in the other half, although measurements are the other way. In Oviedo (higher middle part of Fig. 10.) it is clearly an overcast situation and the WRF model predicts a clear sky situation.

2. Conclusion

WRF model has been validated for a whole year over Spain. The comparison has been done with ground solar global radiation measurements. Errors are from 30-98% in terms of RMSD for hourly global radiation and from 23-89% in terms of RMSD for daily global radiation. Different synoptic situations have been studied and the WRF model fed with NCEP data is not reproducing them quite well, however ECMWF model reproduce them in a much nicer way. Using ECMWF data as boundary conditions and testing other cloud parameterizations could improve results from WRF model in the future.

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.

Young have developed a good, practical formula which is well suited for use with small solar elevation angles [8]

. _ ms ga а gtnv-i (2)

_ з tк* V 4 sin^V-t (S. ffiLGS 9&a ri tT V 4 GJGGCaca?

This equation approaches the simple expression 1/sin V asymptotically for angles greater than 250. (The reader may wish to try using the angle V = 900 in the Kasten-Young equation. Note that L = 1 with the sun directly overhead.

2.4 Enhanced global irradiance model

One would expect the diffuse contribution IF to the global irradiance to increase with increasing atmo­spheric turbidity (increasing values of a) and that these two quantities are related to one another and to the solar elevation angle. This connection has been examined in earlier work, and the graphical result is shown in Figure 3. The Linke turbidity factor TL enters the analysis in the term for the direct irradiance and is equal to unity for a pure Rayleigh atmosphere (no aerosols — only molecular scattering). The term aL is in this formulation replaced by:

a1 = «ф [-0.B662 ■ Тя ■ L ■ (3)

where Dr(L) is the Rayleigh optical depth as a function of the air mass L. A very useful empirical equation for 1/Dr has been developed by Louche, Peri and Iqbal and modified by Fritz Kasten [8]:

Подпись: Figure 3: The observed diffuse irradiance on a horizontal surface depends upon the value of the Linke turbidity factor TL and the solar elevation angle.

-7T = 6J&296+ 1.7 515 ■ L — 0.12Є2 ■ — (ШВ65 ■ £a — 0JD0Q13 ■ L4 <4)

The data of Figure 3 has been used to find an expression for the diffuse irradiance on a horizontal surface IF as a function of the elevation angle V and the turbidity factor TL:

£r = (4ВД4 ■ Г, — Ш2)- (1-ехр[аі — Г, — 0.P905- Y]’) (5)

2.5 Equation for finding TL from observations

In view of the foregoing remarks it is now possible to write an algorithm for the determination of the Linke turbidity factor from observations of the global solar irradiance on a horizontal surface and with knowledge of the solar elevation angle. The elevation angle is readily computed when the latitude, longitude and time of day are known.

tc = 2» ■ Щ — sinF ■ дС-азьи-*!. — l-вд + (4^4,^ _ 4^33) ■ (1 — (6)

IG is the global irradiance measured, and V can be found from the time and position data. Knowledge of V yields the air mass L which in turn permits the optical depth DR to be determined. The only unknown parameter in the equation is the Linke turbidity factor TL which can then be calculated. This program has been carried out for clear days at a wide range of locations during the voyage from the Arctic to the Antarctic.

2.6 Results

image006

For all of the good, clear days during the eight month expedition the Linke turbidity factor was computed using the algorithm described above. For these same days the mid day temperature and relative humidity were obtained by examination of the Galathea III database. From the temperature and humidity data it is straightforward to compute the amount of water present in a cubic meter of surface air. These calculations were performed with the data shown in Figure 4 as the result. The regression shows that a moisture content close to zero should yield a Linke turbidity factor near unity as expected. The value 1,19 may reflect the fact that some aerosols will typically be present in the maritime environments from which data is available in addition to water vapor.

This analysis permits the estimation of the Linke turbidity factor in maritime environments based upon knowledge of the temperature and relative humidity. Compute the water content of a cubic meter of surface air, and apply the equation shown in Figure 4 to find TL. With TL in hand a good prediction of the global irradiance on the horizontal on a clear day, including the distribution of direct and diffuse irradiance, can be made using Equation 6. As local temperature and relative humidity are standard meteorological parameters, no special equipment or data is needed to do the calculations. Visibility conditions are also derivable from knowledge of the turbidity factor as discussed elsewhere [7]. This method does not take account of other aerosol which may be present, but it can be applied in typical maritime conditions without a modest amount of dry atmospheric aerosol particles.

References:

[1] Galathea 3 Expedition portal in English: http://galathea3.emu. dk/eng/index. html

[2] Frank Bason; Solar Irradiance Measurements from the Danish Galathea 3 Expedition, ISES Solar World Conference Beijing 2007, Proceedings.

[3] Pierre Ineichen, Richard Perez; A new airmass independent formulation for the Linke turbidity coef­

ficient, Solar Energy 73, no. 3, pp 151-157, 2002.

[4] Linke, F.; Transmissions-Koeffizient und Trubungsfaktor, Beitr. Phys. fr. Atmos. 10, 91-103 (1922).

[5] Frank Bason; Solar Radiation Measurements from Greenland to Antarctica — Optics Table Data from the Danish Galathea III Expedition (2006-2007) , North Sun Conference 2007, Riga,

Latvia, May 2007

[6] John Duffie, William Beckman, Solar Engineering of Thermal Processes, Wiley & Sons, New York, 1991.

[7] Frank Bason; Diffuse Solar Irradiance and Atmospheric Turbidity, EuroSun 2004 Conference

Proceedings, Freiburg, Germany, June 2004.

[8] F. Kasten, A. T. Young; Revised optical air mass tables and approximation formula, Applied Optics,

28, no. 22, pp 4735-4738, 15 Nov 1989.

Materials 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. Moreover, 40 silicon cell sensor pyranometres (Skye Instruments LTD, UK), are installed in as many stations. 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 [10, 11].

image059

Fig. 1: Names and locations of the meteorological stations considered in this work, and location of the two pyranometers (at A Coruna and Vigo) used by Vazquez et al. [7].

As a part of the Solar Radiation subject’s programme, each student was required to choose one station between the 65 equipped with pyranometers and to analyse data between September 2006 and August 2007. The main features of these stations are listed on Table 1.

Data proceeding from every selected meteorological station have been processed to obtain monthly-averaged daily values of global irradiation, sunshine duration and clearness index. Measurements of precipitation, temperature and relative humidity have also been processed in order to complete the dataset for analysis.

Table 1: Main features of the meteorological stations applied in the analysis.

Code

Station

Latitude

Longitude

Altitude (m)

Environment

Manufacturer

C1

CIS Ferrol

43.49° N

8.2°

W

34

Suburban, Coastal

Schenk

C2

Sergude

42.82° N

8.46°

W

230

Rural, Inland

N. A.

C3

Rio do Sol

43.1° N

8.69°

W

540

Rural, Inland

Skye

C4

Marco Curra

43.34° N

7.89°

W

649

Rural, Inland

Schenk

C5

EOAS Santiago

42.87° N

8.57°

W

255

Urban, Inland

Schenk

C6

Olas

43.13° N

8.28°

W

401

Rural, Inland

Skye

C7

Serra Faladoira

43.59° N

7.79°

W

576

Rural, Coastal

Skye

C8

Fontecada

42.97° N

8.87°

W

369

Rural, Inland

Schenk

C9

Malpica

43.34° N

8.82°

W

161

Rural, Coastal

Schenk

L1

Courel

42.6° N

7.19°

W

777

Rural, Inland

Skye

L2

Foz

43.56° N

7.28°

W

73

Rural, Inland

Skye

L3

Penedo Galo

43.66° N

7.56°

W

545

Rural, Coastal

Schenk

L4

Burela

43.65° N

7.37°

W

421

Rural, Coastal

Skye

L5

Ancares

42.82° N

6.92°

W

1364

Rural, Inland

Schenk

L6

Boveda

42.65° N

7.47°

W

432

Rural, Inland

Schenk

L7

Pedro Murias

43.54° N

7.08°

W

51

Rural, Coastal

Schenk

L8

Abradelo

42.75° N

7.25°

W

826

Rural, Inland

Skye

L9

Portomarin

41.81° N

7.62°

W

447

Rural, Inland

Skye

P1

Cies

42.22° N

8.9°

W

25

Rural, Coastal

Skye

P10

Queimadelos

42.23° N

8.43°

W

371

Rural, Inland

Schenk

P11

Corrubedo

42.56° N

9.03°

W

30

Rural, Coastal

Schenk

P2

Coron

42.58° N

8.8°

W

14

Rural, Coastal

Schenk

P3

Pereira

42.63° N

8.32°

W

717

Rural, Inland

Skye

P4

Monte Aloia

42.08° N

8.68°

W

484

Rural, Inland

Schenk

P6

Lourizan

42.41° N

О

SO

SO

00

W

57

Urban, Coastal

Schenk

P7

Castro Vicaludo

42° N

8.86°

W

473

Rural, Coastal

Skye

P8

Serra do Faro

42.58° N

7.93°

W

991

Rural, Inland

Skye

P9

Rebordelo

42.47° N

8.5°

W

367

Rural, Inland

N. A.

R1

Baltar

41.95° N

7.71°

W

807

Rural, Inland

Skye

R2

Ourense

42.35° N

7.85°

W

167

Urban, Inland

Skye

R3

Invernadeiro

42.12° N

7.34°

W

1026

Rural, Inland

Schenk

R4

Monte Medo

42.23° N

7.63°

W

608

Rural, Inland

Skye

R5

Amiudal

42.42° N

8.24°

W

553

Rural, Inland

N. A.

R6

Xures

41.9° N

7.9°

W

1059

Rural, Inland

Schenk

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. [7].

The clearness index, KT, 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

Подпись: C9 Подпись: C3 image062 Подпись: P3 Подпись: C7, Подпись: -7.5 Подпись: R3 Подпись: I

1376 Wm-2 was adopted, as recommended by Davies [12]. Astronomical relationships were obtained following Iqbal [13].

image068 Подпись: 3100 3000 2900 2800 2700 2600 2500 2400 2300 2200 2100 2000 1900 1800 1700 1600 1500 1400 1300 1200 1100 1000 900 800 700 600 500 image070 Подпись: -9 image072 image073 Подпись: -7.5 Подпись: -7 Подпись: 7 3

Fig. 2: Annual mean values of daily global solar irradiation (kJm-2) distribution over the region. Squares show the locations of the stations selected by the students and applied in this analysis.

image077image078Fig. 3: Annual values of (a) precipitation (mm) and (b) mean relative humidity (%) over the region.

Data for every station were collected, joined together and interpolated using Kriging technique, in order to get appropriate maps for analysis. Software package SURFER (http://www. ssg- surfer. com/) provided graphical representation of these results.

2. Results

Discussion of the results, conclusions and future activities

As shown in figures 3 to 5 the presented MOS model improves considerably the output of the ARPS model simulation. Small amount of performance improvement may be obtained by the single convolution of each data block, instead of chaining, to avoid the boundary uncertainties at the borders of each of the data block on the training set (se section 4). However, to evaluate the operation of the statistical correction, the uncertainties under continuous boundary conditions have to be evaluated (see sections 3.2 and 5).

Furthermore, as the presented results are only based on simulated reanalysis data, they have to be still compared with the statistical corrections of ARPS simulations based on data of analysis, and forecast global simulations. The former is important to verify the performance loss for the analysis data. The latter is important to verify the statistical correction of both the analysis and the forecast uncertainties, since they appear in a combined form within the forecast results. Furthermore, actualizations of the NWP model may lead to additional uncertainties in the analysis and forecast corrections. With a forecast based on the reanalysis data, also named reforecast, these actualizations are avoided [12]. Additional performance improvement may be obtained by the inclusion of time series of other variables forecasted by the NWP [36]. Comparable to the MOS in [12], the presented MOS method DWT-ANN is only able to improve the forecasts at sites where measurements of the simulated variable are available. A solution for this problem is proposed in [36] with a site unspecific time series MOS, based on a wavelet model. This model may be applied with low uncertainties for the NWP output corrections of a limited region, as e. g. a city, where CSDHWS installations can be find in different locations.

Acknowledgements

The authors are indebted to the CAPES — Coordenagao de Aperfeigoamento de Pessoal de Nivel Superior for support to the present work and to Dr. Reinaldo Haas to place at disposal the simulated data using the ARPS model.

References

[1] Eletrobras, Programa National de Conservagao de Energia Eletrica (PROCEL) apresenta pesquisa sobre posse e uso de equipamentos eletricos. 2007, Noticias da Eletrobras, 18. 04. 2007 ,http://www. eletrobras. com. br/elb/portal/main. asp.

[2] Salazar, J. P., Economia de energia e redugao do pico da curva de demanda para consumidores de baixa renda por agregagao de energia solar termica, Dissertagao. Departamento de Engenharia Mecanica, Laboratorio de Energia Solar. 2004, Florianopolis: Universidade Federal de Santa Catarina.

[3] Colle, S., Glitz, K., Salazar, J. P., and S. L. Abreu. Cost Optimization of Low-Cost Solar Domestic Hot Water Systems Assisted by Electric Energy. in ISES Solar World Congress 2003. Goteburg, Sweden: ISES — International Solar Energy Society.

[4] Colle, S., Abreu, S. L., Glitz, K., and F. Colle. Optimization of the auxiliary heating and water storage insulation of a low cost domestic hot water heating system with an electric shower. in ISES — Solar World Congress. 2001. Adelaide — Australia.

[5] Salazar, J. P., Abreu S. L., Borges T. P. F, Colle S. Optimization of a compact solar domestic hot water system for low-income families with peak demand and total cost constraints. in Solar World Congress 2003. Goteborg, Sweden: ISES — International Solar Energy Society.

[6] Duffie, J. A. and W. A. Beckman, Solar engineering of thermal processes. 3rd ed. 2006, Hoboken, N. J.: Wiley Interscience, New York. 908.

[7] Mellit, A., M. Benghanem, and S. A. Kalogirou, An adaptive wavelet-network model for forecasting daily total solar-radiation. J. Applied Energy, 2006. 83(7): p. 705-722.

[8] Cao, J. and L. Xingchun, Study of hourly and daily solar irradiation forecast using diagonal recurrent wavelet neural networks. Energy & Conversion Management, 2008. 49: p. 1396-1406.

[9] Cao, S. and Cao J., Forecast of solar irradiance using recurrent neural networks combined with wavelet analysis. Applied Thermal Engineering, 2004. 25: p. 161-172.

[10] Lorenz, E., Methoden zur Beschreibung der Wolkenentwicklung in Satellitenbildern und ihre Anwendung zur Solarstrahlungsvorhersage, Ph. D. thesis. 2004, Carl von Ossietzky University, Faculty of Mathematics and Natural Sciences: Oldenburg, Germany. p. 111.

[11] Girodo, M., ed. Solarstrahlungsvorhersage auf der Basis numerischer Wettermodelle, Ph. D. thesis. ed. E. a.S. R.L. Faculty of Mathematics and Natural Sciences. 2006, Carl von Ossietzky University:

Oldenburg, Germany. 159 p.

[12] Hamill, T. M., Whitaker, J. S., Mullen S. L., Reforecasts, an important data set for improving weather predictions. Bulletin of the American Meteorological Society, 2005: p. 43.

[13] Guarnieri, R. A., Emprego de Redes Neurais Artificials e Regressao Linear Mhltipla no Refinamento das Previsoes de Radiagao Solar do Modelo Eta, Dissertagao. CPTEC-INPE. 2006, Sao Jose dos Campos (SP).

[14] Wilks, D. S., Statistical methods in the atmospheric sciences, in International Geophysics Series, Dep. of Earth and Atmospheric Sciences. 2006, Academic Press: Cornell University. p. 179-548.

[15] Libonati R., Trigo I., and C. C. DaCamara, Correction of 2 m-temperature forecasts using Kalman Filtering technique. Atmospheric Research, 2008. 87: p. 183-197.

[16] Julier, S. J., Uhlmann, J. K., A new extension of the Kalman Filter to nonlinear systems, in The Robotics Research Grou, Department of Engineering Science. 1997, University of Oxford: Oxford U. K.

[17] DeCruyenaere J. P. and H. M. Hafez. A comparison between Kalman filters and recurrent neural networks. in Neural Networks — IJCNN conference. 1992. Baltimore, MD, USA.

[18] Todini, E., Using phase-state modeling for inferring forecasting uncertainty in nonlinear stochastic decision schemes. J. Hydroinformatics, 1999. 1(2): p. 75-82.

[19] Addison, P. S., The illustrated wavelet transform handbook: Introductory theory and applications in science, engineering, medicine and finance. 2002, Institute of Physics Publ.: Bristol U. S.A. p. 353.

[20] Nanavati, S. P., Panigrahi, P. K., Wavelet transform: A new mathematical microscope. J. Resonance, 2004. 9(3): p. 50-64.

[20]Cohen, A., I. Daubechies, and J. C. Feauveau, Biorthogonal bases of compactly supported wavelets. J. Communications on Pure and Applied Mathematics, 1992. 55: p. 458-560.

[22] Souza, E. M., et al., Comparagao das Bases de Wavelets Ortonormais e Biortogonais: Implementagao, Vantagens e Desvantagens no Posicionamento com GPS. J. Mat. Apl. Comput., 2007. 8(1): p. 149-158.

[23] Renaud, O., J. C. Starck, and Murtagh F., Wavelet-based combined signal filtering and prediction. J. IEEE — Transactions on Systems, MAN and Cybernetics, 2005. 36(6): p. 1241-1251.

[24] Xia, X., D. Huang, and Jin Y. Nonlinear adaptive predictive control based on orthogonal wavelet networks. in Proceedings of the 4th World Congress on Intelligeut Control and Automation. 2002. Shanghai, China IEEE.

[25] Goswami, J. C. and C. A. K., Fundamentals of Wavelets ed. I. John Wiley & Sons. 1999, New York. 319.

[26] Daubechies, I. Ten lectures on wavelets. 1992. Philadelphia,: Regional Conferences Series in Applied Mathematics SIAM.

[27] Alsberg, B. K., et al., Variable selection in wavelet regression models. Analytica Chimica Acta, 1998. 368(1): p. 29-44.

[28] Tsay, R. S., Analysis of financial time series — Financial econometrics. 2002, John Wiley & Sons, INC. p. 457p.

[29] Kratzenberg, M. G. and C. S. Selegao da transformada de wavelet para a corregao estatistica da previsao da radiagao sola. in II Congresso Brasileiro de Energia Solar e III Conferencia Regional Latino- Americana da ISES. 2008 b. Florianopolis — Brazil.

[30] Haykin, S. S., Neural networks: A comprehensive foundation. 1994, New York, Toronto: Maxwell Macmillan International. xix, 696 p.

[31] Kipp&Zonen, Instruction manual — CM11 pyranometer. 1999, Delft, Holland. 63.

[32] Younes, S., R. Claywell, and T. Muneer, Quality control of solar radiation data: Present status and proposed new approaches. J. Energy, 2005. 30(9): p. 1533-1549.

[33] Abreu, S. L., Colle, S., and A. P. Almeida, Mantelli, S. L.N. Qualificagao e recuperagao de dados de radiagao solar medidos em Florianopolis — SC. in ENCIT — VIII, Encontro Nacional de Ciencias Termicas. 2000. Porto Alegre, Brazil.

[34] Kaastra, I. and M. Boyd, Designing a Neural Network for Forecasting, Financial and Economic Time Series. Neurocomputing, 1996. 10: p. 215-236.

[35] Mantelli, S. L.N., E. B. Pereira, and C. Thomaz. J. C. J., S. Sistema de Organizagao Nacional de Dados Ambientais para o setor de energia. in SNPTEE Seminario Nacional de Produgao e Transmissao de Energia Eletrica, Grupo de estudo de impactos ambientais. 2007. Rio de Janeiro, Brazil.

[36] Kratzenberg, M. G., Corregao estatistica a base da transformada wavelet para previsao de energia solar atraves de modelo numerico meteorologico, Exame de Qualificacgao de Doutorado, D. d.E. M. Universidade Federal de Santa Catarina, Editor. 2008 a: Florianopolis. p. 69.

Ordinary kriging model evaluation

Подпись: Fig. 3. June and October H maps based on the ordinary kriging method on a 1 km x 1 km grid.

Validation dataset results showed, overall, that the ordinary kriging is able to provide fair estimates. Error values present a seasonal pattern: the summer months shows the lowest RMSE values (in percentage) and the winter months the highest ones. For instance, in October RMSE is 1.44 MJ m-2day-1 (11.21%) and for June RMSE is 1.63 MJ m-2day-1 (6.20%). The MAE values ranges from 0.26 MJ m-2day-1 (2.6%) in February to 0.78 MJ m-2day-1 (6%) in October. Additionally, the ordinary kriging estimates shows scarce bias, being the ME values almost negligible for almost all the months. Only for November, a slight overestimation is found. Values of R2 range from 0.9 in December to 0.96 in June. Figure 3 shows the estimated H maps of June and October based on the ordinary kriging procedure.