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Solar Radiation , Spatial and Temporal Variability

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Definition of the Subject

Solar irradiance is a highly variable and fluctuating resource. This characteristic directly and strongly affects the performance of solar energy systems, such as the electricity production from photovoltaic (PV) systems or solar thermal power plants. This entry describes databases and appropriate methods to characterize spatial and temporal variability in solar radiation. The regional distribution of solar energy depends on the meteorological situation characterized by clouds, aerosols, and water vapor content, but also on topography and ground albedo. Within this entry the focus is laid on cloud-induced fluctuations. The spatial variability caused by the topography of the terrain is not accounted for here, since it is the topic of another entry in this encyclopedia.

Introduction

As fluctuations in solar radiation are directly coupled to the output power and yield of a...

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Abbreviations

Autocorrelation:

The autocorrelation of a random process describes the statistical analogy between values of the process at different points in time, as a function of the two times or of the time difference.

Clearness index:

Ratio of the global irradiance on a horizontal plane (on the earth surface) to the respective irradiance just outside of the atmosphere.

Clear-sky index:

Ratio of the global irradiance on a horizontal plane to the irradiance expected under clear-sky conditions.

DNI:

Direct normal irradiance.

GHI:

Global horizontal irradiance.

Ground albedo:

Measure of how strongly the ground reflects sunlight.

Residual time series:

A time series in which the trends have been removed.

Bibliography

  1. Kemper A, Lorenz E, Hammer A, Heinemann D (2008) Evaluation of a new model to calculate direct normal irradiance based on satellite images of Meteosat Second Generation. In: EUROSUN 2008 – first international conference on solar heating, cooling and buildings, Lisbon, Portugal, 7–10 Oct 2008

    Google Scholar 

  2. Kern SA, Gulachenski EM, Kern GA (1988) Cloud effects on the distributed photovoltaic generation, slow transients at the Gardner Massachusetts photovoltaic experiment. IEEE Trans Energy Convers 4:184–190

    Article  Google Scholar 

  3. Longhetto A, Elisei G, Giraud C (1989) Effect of correlation in time and spatial extent on performance of very large solar conversion systems. Sol Energy 43:77–84

    Article  Google Scholar 

  4. Long CN, Ackerman TP (1995) Surface measurements of solar irradiance: a study of the spatial correlation between simultaneous measurements at separated sites. J Appl Meteorol 34:1039–1046

    Article  Google Scholar 

  5. Glasbey CA, Graham R, Hunter AGM (2001) Spatio-temporal variability of solar energy across a region: a statistical modelling approach. Sol Energy 70:373–381

    Article  Google Scholar 

  6. Luther G (1992) The regional function of solar energy. In: Proceedings of the 11th EC PV solar energy conference, Montreux, Switzerland

    Google Scholar 

  7. Steinberger-Willms R (1993) Analyse der Fluktuationen der Leistungsabgabe großer Wind- und Solarenergiesysteme in Hinblick auf deren Einbindung in elektrische Versorgungsnetze. PhD thesis, University of Oldenburg, Germany

    Google Scholar 

  8. Beyer HG, Hammer A, Luther J, Poplawska J, Stolzenburg K, Wieting P (1994) Analysis and synthesis of cloud pattern for radiation field studies. Sol Energy 52:379–390

    Article  Google Scholar 

  9. Otani K, Minowa J, Kurokawa K (1997) Study on areal solar irradiance for analyzing areally-totalized PV systems. Sol Energy Mater Sol Cells 47:281

    Article  CAS  Google Scholar 

  10. Li Z, Cribb C, Chang FL, Trishchenko AP (2004) Validation of MODIS-retrieved cloud fractions using whole sky imager measurements at three ARM sites. In: Fourteenth ARM science team meeting proceedings, Albuquerque, NM, 22–26 March 2004

    Google Scholar 

  11. Willard JH, Steeves J (1991) Sky-cover correlation within a sky dome. J Appl Meteorol 30:1037–1039

    Article  Google Scholar 

  12. Slater DW, Long CN, Tooman TP (2001) Total sky imager/whole sky imager cloud fraction comparison. In: Eleventh ARM science team meeting proceedings, Atlanta, GA, 19–23 March 2001

    Google Scholar 

  13. Robbins CL, Hunter KC, Cannon T (1984) Mapping sky and surface luminance distribution using a flux mapper. Energy Build 6:247–252

    Article  Google Scholar 

  14. Rosen MA, Hooper FC (1987) A calibration of the three discrete radiance component model. In: Proceedings of the ISES solar world congress, Hamburg, Germany

    Google Scholar 

  15. Brunger AP, Hooper FC (1993) Anisotropic radiance model based on narrow field of view measurements of shortwave radiance. Sol Energy 50:53–64

    Article  Google Scholar 

  16. Perez R, Seals R, Michalsky J (1993) All weather model for sky luminance distribution – preliminary results and validation. Sol Energy 50:235–245

    Article  Google Scholar 

  17. Reinhardt ER, Schwarzmann P, Straub B, Dörrer R (1983) Sky image analysis. Final Report ESF-032-D, Institut für physikalische Elektronik, University of Stuttgart, Germany

    Google Scholar 

  18. Fontoynont M, Dumortier D, Heinemann D, Hammer A, Olseth J, Skartveit A, Ineichen P, Reise C, Page J, Roche L, Beyer HG, Wald L (1998) Satellight: a WWW server which provides high quality daylight and solar radiation data for Western and Central Europe. In: Proceedings of the ninth conference on satellite meteorology and oceanography, Paris

    Google Scholar 

  19. Wald L, Albuisson M, Best C, Delamare C, Dumortier D, Gaboardi E, Hammer A, Heinemann D, Kift R, Kunz S, Lefèvre M, Leroy S, Martinoli M, Ménard L, Page J, Prager T, Ratto C, Reise C, Remund J, Rimoczi-Paal A, Van der Goot E, Vanroy F, Webb A (2004) SoDa: a Web service on solar radiation. In: Proceedings of EUROSUN 2004, vol 3. PSE, Freiburg, pp 921–927. ISBN 3-9809656-4-3

    Google Scholar 

  20. Wilcox S et al (2007) Completing production of the updated National Solar Radiation Database for the United States. In: Solar 2007 conference, Cleveland, OH. ASES

    Google Scholar 

  21. Chandler WS, Stackhouse PW, Whitlock CH, Hoell JM, Westberg D, Zhang T (2010) Near real-time global radiation and meteorology Web services available from NASA. In: Proceedings of ASES annual conference, Phoenix, USA

    Google Scholar 

  22. Stackhouse PW, Kratz DP, McGarragh GR, Gupta SK, Geier EB (2006) Fast Longwave and Shortwave Radiative Flux (FLASHFlux) products from CERES and MODIS measurements. In: Proceedings of the 12th conference on atmospheric radiation, Madison, USA

    Google Scholar 

  23. Anderberg M, Renne D, Stoffel T, Sengupta M, Perez R, Stackhouse P (2010) Evaluating solar resource variability from satellite and ground-based observations. In: Proceedings of ASES annual conference, Phoenix, USA

    Google Scholar 

  24. Lohmann S, Schillings C, Mayer B, Meyer R (2006) Long-term variability of solar direct and global radiation derived from ISCCP data and comparison with reanalysis data. Sol Energy 80:1390–1401

    Article  Google Scholar 

  25. Remund J, Kunz S, Lang R (2003) MeteoNorm. includ. CD-ROM, 5th edn. Meteotest, Bern

    Google Scholar 

  26. Scharmer K, Greif J (2000) ESRA, European Solar Radiation Atlas, 4th edn (includ. CD-ROM). Scientific advisors: Dogniaux R, Page JK. Authors: Wald L, Albuisson M, Czeplak G, Bourges B, Aguiar R, Lund H, Joukoff A, Terzenbach U, Beyer HG, Borisenko EP. Published for the Commission of the European Communities by Presses de l’Ecole, Ecole des Mines de Paris, Paris

    Google Scholar 

  27. Beyer HG, Czeplak G, Terzenbach U, Wald L (1997) Assessment of the method used to construct clearness index maps for the new European Solar Radiation Atlas (ESRA). Sol Energy 61:389–397

    Article  Google Scholar 

  28. Liu BYH, Jordan RC (1960) The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Sol Energy 4:1–19

    Article  Google Scholar 

  29. Hollands KGT, Huget RG (1983) A probability density function for the clearness index, with applications. Sol Energy 30:195–209

    Article  Google Scholar 

  30. Bendt P, Collares-Pereira M, Rabl A (1981) The frequency distribution of daily insolation values. Sol Energy 27:1–5

    Article  Google Scholar 

  31. Saunier GY, Reddy TA, Kumar S (1987) A monthly probability distribution function of daily global irradiation values appropriate for both tropical and temperate locations. Sol Energy 38:169–177

    Article  Google Scholar 

  32. Olseth JA, Skartveit A (1984) A probability density function for daily insolation within the temperate storm belt. Sol Energy 33:533–542

    Article  Google Scholar 

  33. Gordon JM, Reddy TA (1988) Time series analysis of daily horizontal solar radiation. Sol Energy 41:215

    Article  Google Scholar 

  34. Graham VA, Hollands KGT, Unny TE (1987) Stochastic variation of hourly solar radiation over the day. In: Proceedings of ISES solar world congress, Hamburg, Germany

    Google Scholar 

  35. Aguiar R, Collares-Pereira M (1992) TAG: a time dependent autoregressive model for generating synthetic hourly radiation. Sol Energy 49:167

    Article  Google Scholar 

  36. Mejon MJ, Bois P, Lestienne R (1980) Simulation de l'energie solaire directe au pas de temps de la minute. L'exemple de Saint-Chamas (Marseille). Rev Phys Appl 15:113–122

    Article  Google Scholar 

  37. Louche A, Notton G, Poggi P, Simonnot C (1991) Classification of direct irradiation days in view of energetic applications. Sol Energy 46:255–259

    Article  Google Scholar 

  38. Suehrcke H, McCormick PG (1988) The frequency distribution of instantaneous insolation values. Sol Energy 40:413–422

    Article  Google Scholar 

  39. Skartveit A, Olseth JA (1992) The probability density and autocorrelation of short-term global and beam irradiance. Sol Energy 49:477–487

    Article  Google Scholar 

  40. Walkenhorst O, Luther J, Reinhart C, Timmer J (2002) Dynamic annual daylight simulations based on one-hour and one-minute means of irradiance data. Sol Energy 72(5):385–395

    Article  Google Scholar 

  41. Burger B, Rüther R (2006) Inverter sizing of grid-connected photovoltaic systems in the light of local solar resource distribution characteristics and temperature. Sol Energy 80:32–45

    Article  CAS  Google Scholar 

  42. Zehner M, Hartmann M, Weizenbeck J, Gratzl T, Weigl T, Mayer B, Wirth G, Krawczynski M, Betts T, Gottschalg R, Hammer A, Giesler B, Becker G, Mayer O (2010) Systematic analysis of meteorological irradiation effects. In: Twenty-fifth European photovoltaic solar energy conference, Valencia, Spain, 6–9 Sept 2010

    Google Scholar 

  43. Skartveit A, Olseth JA, Tuft ME (1998) An hourly diffuse fraction model with correction for variability and surface albedo. Sol Energy 63:173–183

    Article  Google Scholar 

  44. Brinkworth BJ (1977) Autocorrelation and stochastic modelling of insolation sequences. Sol Energy 19:343–347

    Article  Google Scholar 

  45. Amato U, Andretta A, Bartoli B, Coluzzi B, Cuomo V, Fontanta F, Serio C (1986) Markov processes and Fourier analysis as a tool to describe and simulate daily solar irradiance. Sol Energy 37:179–194

    Article  Google Scholar 

  46. Klein SA, Beckman WA (1987) Loss-of-load probabilities for stand-alone photovoltaic systems. Sol Energy 39:499–512

    Article  Google Scholar 

  47. Graham VA, Hollands KGT, Unny TE (1988) A time series model for Kt with application to global synthetic weather generation. Sol Energy 40:83–92

    Article  Google Scholar 

  48. Aguiar R, Collares-Pereira M, Conde JP (1988) Simple procedure for generating sequences of daily radiation values using a library of Markov transition matrices. Sol Energy 40:269–279

    Article  Google Scholar 

  49. Beyer HG (1988) Zur Bestimmung des energetischen Verhaltens regenerativer Elekrtizitätsversorgungssysteme unter besonderer Berücksichtigung statistischer Eigenschaften des Windes und der Solarstrahlung. PhD thesis, University of Oldenburg, Germany

    Google Scholar 

  50. Manier G, Traup S (1991) Kurzzeitvariation der solaren Bestrahlung. Meteorol Rundsch 43:178–186

    Google Scholar 

  51. Woyte A, Belmans R, Nijs J (2007) Localized spectral analysis of fluctuating power generation from solar energy systems. EURASIP J Adv Signal Process, Article ID 80919, 8 pages. doi:10.1155/2007/80919

    Google Scholar 

  52. Beyer HG, Martinez JP, Suri M, Torres JL, Lorenz E, Müller SC, Hoyer-Klick C, Ineichen P (2009) D 1.1.3 report on benchmarking of radiation products. Technical Report MESOR (Management and Exploitation of Solar Resource Knowledge). http://www.mesor.org/. Accessed May 15, 2010

  53. Zelenka A, Perez P, Seals R, Renné D (1999) Effective accuracy of satellite-derived hourly irradiances. Theor Appl Climatol 62:199–207. doi:10.1007/s007040050084

    Article  Google Scholar 

  54. Beyer HG, Luther J, Steinberger-Willms R (1991) Reduction in fluctuations in lumped power output from distantly spaced PV-arrays. In: Proceedings of ISES solar world conference, Denver, USA

    Google Scholar 

  55. Zelenka A, Czeplak G, D'Agostino V, Weine J, Maxwell E, Perez R (1992) Techniques for supplementing solar radiation network data. Report IEA task 9, vol 2. Report no. IEA-SHCP-9D-1

    Google Scholar 

  56. Sen Z, Sahin AD (2001) Spatial interpolation and estimation of solar irradiance by cumulative semivariograms. Sol Energy 71:11–21

    Article  Google Scholar 

  57. Betcke J, Beyer HG (2004) Accuracy improvement of irradiation data by combining ground and satellite measurements. In: Proceedings of EuroSun2004, Freiburg, Germany, vol 3, pp 764–770

    Google Scholar 

  58. Jewell WT, Ramakumar R (1988) The effect of moving clouds on electric utilities with dispersed photovoltaic generation. IEEE Trans Energy Convers 3:570–576

    Google Scholar 

  59. Garret DL, Jeter SM (1989) A photovoltaic voltage regulation impact investigation technique. Part I – model development. IEEE Trans Energy Convers 4:47–53

    Article  Google Scholar 

  60. Kawasaki N, Takashi O, Otani K, Kurokawa K (2006) An evaluation method of the fluctuation characteristics of photovoltaic systems by using frequency analysis. Sol Energy Mater Sol Cells 90:3356–3363

    Article  CAS  Google Scholar 

  61. Reise C (2003) Entwicklung von Verfahren zur Prognose des Ertrags großflächiger Energieversorgungssysteme auf der Basis von Satelliteninformationen. PhD thesis, University of Oldenburg, Germany

    Google Scholar 

  62. Beyer HG, Costanzo C, Reise C (1995) Multiresolution analysis of satellite-derived irradiance maps – an evaluation of a new tool for the spatial characterization of hourly irradiance fields. Sol Energy 55:9–20

    Article  Google Scholar 

  63. Quaschning V, Geuder N, Ortmanns W (2002) Vergleich und Bewertung verschiedener Verfahren zur Solarstrahlungsbestimmung, 13. In: Internationales Sonnenforum, Berlin, Germany

    Google Scholar 

  64. Meyer R, Lohmann S, Schillings C, Hoyer C (2007) Climate statistics for planning and siting of solar energy systems. In: Solar resource from the local level to global scale in support of the resource management of renewable electricity generation. Nova Science/Earthlink, Nova Science Publisher, New York, 11 pp

    Google Scholar 

  65. Suri M, Huld T, Dunlop ED, Albuisson M, Lefevre M, Wald L (2007) Uncertainties in photovoltaic electricity yield prediction from fluctuations of solar radiation. In: Proceedings of the 22nd EuPVSEC conference, Milano, Italy

    Google Scholar 

  66. Wilcox S, Gueymard CA (2010) Spatial and temporal variability of the solar resource in the United States. In: Proceedings of the ASES annual conference, Phoenix, USA

    Google Scholar 

  67. Meyer R, Butron JT, Marquardt G, Schwandt M, Geuder N, Hoyer-Klick C, Lorenz E, Hammer A, Beyer HG (2008) Combining solar irradiance measurements and various satellite derived products to a site-specific best estimate. In: Fourteenth SolarPACES symposium, Las Vegas, USA

    Google Scholar 

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Hammer, A., Beyer, H.G. (2012). Solar Radiation , Spatial and Temporal Variability . In: Meyers, R.A. (eds) Encyclopedia of Sustainability Science and Technology. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0851-3_449

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