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.