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Mathematics of Energy and Climate Change: From the Solar Radiation to the Impacts of Regional Projections

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Mathematics of Energy and Climate Change

Part of the book series: CIM Series in Mathematical Sciences ((CIMSMS,volume 2))

Abstract

This chapter focuses on the natural and anthropogenic drivers of climate change and on the assessment of potential impacts of regional projections for different scenarios of future climate. Internal and external forcing factors of climate change are associated to changes in the most important processes of energy transfer with influence on the energy balance of the climate system. The role of the solar activity, regular variations in the orbital parameters of the Earth and the radiative forcing which comprises the changes in the chemical composition of the atmosphere and the characteristics of the radiative processes that occur in the atmosphere and on the surface of the Earth will be discussed. Recent evidences of climate change and the general characteristics of the climate models used in climate projection will be presented. The chapter ends with results of some case studies of potential impacts of regional climate change projections in Portugal, namely in forest fire regime, extreme precipitation intensity and in the design of storm water drainage infrastructures.

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Abbreviations

20C3M:

Twentieth century model simulations

AOGCMs:

Atmosphere–Ocean General Circulation Models

BA:

Burnt area

BAM:

Burned Area Model

BUI:

Buildup Index

CFFBPS:

Canadian Forest Fire Behaviour Prediction System

CFFDRS:

Canadian Forest Fire Danger Rating System

CFFWIS:

Canadian Forest Fire Weather Index System

COSMO-CLM:

COnsortium for Small-scale MOdelling and Climate Limited- area Modelling Community

DMC:

Duff Moisture Code

DC:

Drought Code

DSR:

Daily Severity Rating

ECMWF:

European Centre for Medium-Range Weather Forecasts

FFMC:

Fine Fuel Moisture Code

FWI:

Fire Weather Index

GCM:

General Circulation Model

IDF:

Intensity Duration Frequency Curve

IPCC:

Intergovernmental Panel on Climate Change

IPMA:

Instituto Português do Mar e da Atmosfera

ISI:

Initial Spread Index

LWR:

Long wave radiation

MIROC:

Model for Interdisciplinary Research on Climate

OLR:

Outgoing Long wave radiation

PRFD:

Portuguese Rural Fire Database

RCM:

Regional Climate Model

SWR:

Shortwave radiation

TOA:

Top of the Atmosphere

UNFCCC:

United Nations Framework Convention on Climate Change

WMO:

World Meteorological Organization

References

  1. Ahlfeld, D.P.: Comparison of climate model precipitation forecasts with North American observations. In: Proceedings of the XVI International Conference on Computational Methods in Water Resources (2006)

    Google Scholar 

  2. Aldersley, A., Murray, S.J., Cornell, S.E.: Global and regional analysis of climate and human drivers of wildfire. Sci. Total Environ. 409(18), 3472–3481. (2011)

    Article  Google Scholar 

  3. Amraoui, M., Liberato, M.L., Calado, T.J., DaCamara, C.C., Coelho, L.P., Trigo, R.M., Gouveia, C.M.: Fire activity over Mediterranean Europe based on information from Meteosat-8. For. Ecol. Manag. 294, 62–75 (2013)

    Article  Google Scholar 

  4. Arganis-Juarez, M.L., Mora, R.D., Cisneros-Iturbe, H.L., Fuentes-Mariles, G.E.: Génŕation d’échantillons synthétiques des volumes mensuels écoulés vers deux barrages selon la méthode de Svanidze modifiée/Synthetic sample generation of monthly inflows into two dams using the modified Svanidze method. Hydrol. Sci. J. 53(1), 130–141 (2008)

    Article  Google Scholar 

  5. Barry, L., Craig, G.C., Thuburn, J.: Poleward heat transport by the atmospheric heat engine. Nature 415(6873), 774–777 (2002)

    Article  Google Scholar 

  6. Benestad, R.E.: Solar Activity and Earth’s Climate. Springer, Berlin (2006)

    Google Scholar 

  7. Berger, A.: Milankovitch theory and climate. Rev. Geophys. 26(4), 624–657 (1988)

    Article  Google Scholar 

  8. Bovio, G., Camia, A.: Meteorological indices for large fires danger rating. In: Chuvieco, E. (ed.) A Review of Remote Sensing Methods for the Study of Large Wildland Fires, pp. 73–89. Universidad de Alcalá, Alcalá de Henares Spain (1997)

    Google Scholar 

  9. Bradley, R.S.: Quaternary Palaeoclimatology: Methods of Palaeoclimatic Reconstruction. Unwin Hyman, London (1985)

    Google Scholar 

  10. Brandão, C., Rodrigues, R., Costa, J.P.: Análise de fenómenos extremos, Precipitações intensas em Portugal Continental http://snirh.pt/snirh/download/relatorios/relatorio_prec_intensa.pdf (2001). Accessed 1 Feb 2013

  11. Budyko, M.I.: The effect of solar radiation variations on the climate of the earth. Tellus 21(5), 611–619 (1969)

    Article  Google Scholar 

  12. Campisano, C.J.: Milankovitch cycles, paleoclimatic change, and hominin evolution. Nat. Educ. Knowl. 4(3), 5 (2012)

    Google Scholar 

  13. Coles, S., Bawa, J., Trenner, L., Dorazio, P.: An Introduction to Statistical Modeling of Extreme Values, vol. 208. Springer, New York (2001)

    Book  MATH  Google Scholar 

  14. Costa, L., Thonicke, K., Poulter, B., Badeck, F.W.: Sensitivity of Portuguese forest fires to climatic, human, and landscape variables: subnational differences between fire drivers in extreme fire years and decadal averages. Reg. Environ. Chang. 11(3), 543–551 (2011)

    Article  Google Scholar 

  15. Costa, A.C., Santos, J.A., Pinto, J.G.: Climate change scenarios for precipitation extremes in Portugal. Theor. Appl. Climatol. 108(1–2), 217–234 (2012)

    Article  Google Scholar 

  16. Cubasch, U., Wuebbles, D., Chen, D., Facchini, M.C., Frame, D., Mahowald, N., Winther, J.-G.: Introduction. In: T.F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S.K., Boschung, J., Nauels, A., Xia, Y., Bex, V., Midgley, P.M. (eds.) Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change Stocker. Cambridge University Press, Cambridge (2013)

    Google Scholar 

  17. Diodato, N., Bellocchi, G., Romano, N., Chirico, G.B.: How the aggressiveness of rainfalls in the Mediterranean lands is enhanced by climate change. Clim. Chang. 108(3), 591–599 (2011)

    Article  Google Scholar 

  18. Dissing, D., Verbyla, D.L.: Spatial patterns of lightning strikes in interior Alaska and their relations to elevation and vegetation. Can. J. For. Res. 33, 770–782 (2003)

    Article  Google Scholar 

  19. DR. Decreto Regulamentar n. 23/95 (Regulation-decree n. 23/95). Diário da República, 194/95(I-B). www.dre.pt (1995). Accessed 1 Feb 2013

  20. Drouet, J.C., Sol, B.: Incendies de forêts: Mise au point d’un indice numérique de risqué météorologique d’incendie. Revue Générale de Sécurité, 92 (1990)

    Google Scholar 

  21. Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap, vol. 57. CRC, Boca Raton (1994)

    Google Scholar 

  22. Errasti, I., Ezcurra, A., Sáenz, J., Ibarra-Berastegi, G.: Validation of IPCC AR4 models over the Iberian Peninsula. Theor. Appl. Climatol. 103(1–2), 61–79 (2011)

    Article  Google Scholar 

  23. Flato, G., Marotzke, J., Abiodun, B., Braconnot, P., Chou, S.C., Collins, W., Cox, P., Driouech, F., Emori, S., Eyring, V., Forest, C., Gleckler, P., Guilyardi, E., Jakob, C., Kattsov, V., Reason, C., Rummukainen, M.: Evaluation of climate models. In: T.F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S.K., Boschung, J., Nauels, A., Xia, Y., Bex, V., Midgley, P.M. (eds.) Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge (2013)

    Google Scholar 

  24. Friis-Christensen, E., Lassen, K.: Length of the solar cycle—an indicator of solar activity closely associated with climate. Science 254(5032), 698–700 (1991)

    Article  Google Scholar 

  25. Gonçalves, Z.J., Lourenço, L.: Meteorological index of forest fire risk in the Portuguese mainland territory. In: Proceedings of the International Conference on Forest Fire Research. Coimbra B, vol. 7 (1990)

    Google Scholar 

  26. Guttman, N.B.: Statistical descriptors of climate. Bull. Am. Meteorol. Soc. 70(6), 602–607 (1989)

    Article  Google Scholar 

  27. Haigh, J.D.: The impact of solar variability on climate. Science 272(5264), 981–984 (1996)

    Article  Google Scholar 

  28. Haslinger, K., Anders, I., Hofstätter, M.: Regional climate modelling over complex terrain: an evaluation study of COSMO–CLM hindcast model runs for the Greater Alpine Region. Clim. Dyn. 40(1–2), 511–529 (2013)

    Article  Google Scholar 

  29. Hays, J.D., Imbrie, J., Shackleton, N.J.: Variations in the Earth’s orbit: pacemaker of the ice ages. Science 194(4270), 1121–1132 (1976)

    Article  Google Scholar 

  30. Heikinheimo, M., Venäläinen, A., Tourula, T.: A soil moisture index for the assessment of forest fire risk in the boreal zone. In: COST, vol. 77, No. 79, p. 711 (1998)

    Google Scholar 

  31. Herman, J.R., Goldberg, R.A.: Sun, Weather, and Climate. Dover Publications, Inc., New York (1985)

    Google Scholar 

  32. Holland, P.W., Welsch, R.E.: Robust regression using iteratively reweighted least-squares. Commun. Stat. Theory Methods 6(9), 813–827 (1977)

    Article  Google Scholar 

  33. Huber, P.J.: Robust Statistics, pp. 1248–1251. Springer, Berlin (2011)

    Google Scholar 

  34. Imbrie, J., Boyle, E.A., Clemens, S.C., Duffy, A., Howard, W.R., Kukla, G., et al.: On the structure and origin of major glaciation cycles 1. Linear responses to Milankovitch forcing. Paleoceanography 7(6), 701–738 (1992)

    Google Scholar 

  35. INMG: Nota explicative sobre o Indice de Risco Meteorológico de Incendios Rurais. Divisão de Meteorologia Agrícola, Instituto Nacional de Meteorologia e Geofísica (1988)

    Google Scholar 

  36. IPCC SRES SPM: Summary for Policymakers, Emissions Scenarios: A Special Report of IPCC Working Group III (PDF), IPCC (2000) [ISBN 92-9169-113-5]

    Google Scholar 

  37. IPCC: Summary for policymakers. In: Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K.B., Tignor, M., Miller, H.L. (eds.) Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge (2007)

    Google Scholar 

  38. IPCC: In: Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K.B., Tignor, M., Miller, H.L. (eds.) Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge (2007)

    Google Scholar 

  39. IPCC: In: Field, C.B., Barros, V., Stocker, T.F., Qin, D., Dokken, D.J., Ebi, K.L., Mastrandrea, M.D., Mach, K.J., Plattner, G.-K., Allen, S.K., Tignor, M., Midgley P.M. (eds.) Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation. A Special Report of Working Groups I and II of the Intergovernmental Panel on Climate Change, 582 pp. Cambridge University Press, Cambridge (2012)

    Google Scholar 

  40. IPCC: Annex III: Glossary [Planton, S (ed.)]. In: Stocker, T.F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S.K., Boschung, J., Nauels, A., Xia, Y., Bex, V., Midgley, P.M. (eds.) Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge (2013)

    Google Scholar 

  41. IPCC: Summary for Policymakers. In: Stocker, T.F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S.K., Boschung, J., Nauels, A., Xia, Y., Bex, V., Midgley, P.M. (eds.) Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge (2013)

    Google Scholar 

  42. K-1 model developers: K-1 coupled model (MIROC) description. K-1 technical report 1. In: Hasumi, H., Emori, S. (eds.) Center for Climate System Research. University of Tokyo (2004)

    Google Scholar 

  43. Kloster, S., Mahowald, N.M., Randerson, J.T., Lawrence, P.J.: The impacts of climate, land use, and demography on fires during the 21st century simulated by CLM-CN. Biogeosciences 9(1), 509–525 (2012)

    Article  Google Scholar 

  44. Kotlarski, S., Bosshard, T., Lüthi, D., Pall, P., Schär, C.: Elevation gradients of European climate change in the regional climate model COSMO-CLM. Clim. Chang. 112(2), 189–215 (2012)

    Article  Google Scholar 

  45. Krawchuk, M.A., Moritz, M.A., Parisien, M.A., Van Dorn, J., Hayhoe, K.: Global pyrogeography: the current and future distribution of wildfire. PLoS One 4(4), e5102 (2009)

    Article  Google Scholar 

  46. Kristjánsson, J.E., Kristiansen, J., Kaas, E.: Solar activity, cosmic rays, clouds and climate—an update. Adv. Space Res 34(2), 407–415 (2004)

    Article  Google Scholar 

  47. Laut, P.: Solar activity and terrestrial climate: an analysis of some purported correlations. J. Atmos. Solar Terr. Phys. 65(7), 801–812 (2003)

    Article  Google Scholar 

  48. Lawson, B., Armitage, O.: Weather guide for the Canadian Forest Fire Danger Rating System Natural Resources Canada, Canadian Forest Service, Northern Forestry Centre, Edmonton (2008)

    Google Scholar 

  49. Le Page, Y., Oom, D., Silva, J., Jönsson, P., Pereira, J.: Seasonality of vegetation fires as modified by human action: observing the deviation from eco-climatic fire regimes. Glob. Ecol. Biogeogr. 19(4), 575–588 (2010)

    Google Scholar 

  50. Lean, J., Beer, J., Bradley, R.: Reconstruction of solar irradiance since 1610: implications for climate change. Geophys. Res. Lett. 22(23), 3195–3198 (1995)

    Article  Google Scholar 

  51. Lisiecki, L.E., Raymo, M.E.: A Pliocene-Pleistocene stack of 57 globally distributed benthic δ 18 O records. Paleoceanography 20(1), PA1003 (2005)

    Article  Google Scholar 

  52. Lucarini, V., Calmanti, S., Dell’Aquila, A., Ruti, P.M., Speranza, A.: Intercomparison of the northern hemisphere winter mid-latitude atmospheric variability of the IPCC models. Clim. Dyn. 28(7–8), 829–848 (2007)

    Article  Google Scholar 

  53. Matos, R., Silva, M.: Estudos de precipitação com aplicação no projeto de sistemas de drenagem pluvial. Curvas Intensidade-Duração-Frequência da precipitação em Portugal. ITH24 LNEC, Lisbon (1986)

    Google Scholar 

  54. Maxino, C.C., McAvaney, B.J., Pitman, A.J., Perkins, S.E.: Ranking the AR4 climate models over the Murray-Darling Basin using simulated maximum temperature, minimum temperature and precipitation. Int. J. Climatol. 28(8), 1097–1112 (2008)

    Article  Google Scholar 

  55. Nakicenovic, N., et al.: Special Report on Emissions Scenarios: A Special Report of Working Group III of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  56. Nieto, S., Rodríguez-Puebla, C.: Comparison of precipitation from observed data and general circulation models over the Iberian Peninsula. J. Clim. 19(17), 4254–4275 (2006)

    Article  Google Scholar 

  57. NRC (Natural Resources Canada): Canadian Wildland Fire Information System [Online]. http://www.nrcan.gc.ca/home (2011). Accessed Nov 2011

  58. Pausas, J.G.: Changes in fire and climate in the eastern Iberian Peninsula (Mediterranean basin). Clim. Chang. 63(3), 337–350 (2004)

    Article  Google Scholar 

  59. Pausas, J.G., Bradstock, R.A.: Fire persistence traits of plants along a productivity and disturbance gradient in mediterranean shrublands of south-east Australia. Glob. Ecol. Biogeogr. 16(3), 330–340 (2007)

    Article  Google Scholar 

  60. Peixoto, J.P., Oort, A.H.: Physics of Climate. American Institute of Physics, New York (1992)

    Google Scholar 

  61. Pereira, M.G., Sanches Fernandes, L., Macário, E., Gaspar, S., Pinto, J.G.: Climate change impacts in the design of drainage systems–a case study for Portugal. J. Irrig. Drain. Eng. 141(2), 05014009 (2015)

    Article  Google Scholar 

  62. Pereira, M.G., Malamud, B.D., Trigo, R.M., Alves, P.I., Llasat, M.C.: The history and characteristics of the 1980–2005 Portuguese rural fire database. Nat. Hazards Earth Syst. Sci. 11(12), 3343–3358 (2011)

    Article  Google Scholar 

  63. Pereira, M.G., Calado, T.J., DaCamara, C.C., Calheiros, T.: Effects of regional climate change on rural fires in Portugal. Clim. Res. 57(3), 187–200 (2013)

    Article  Google Scholar 

  64. Pereira M.G., Sanches Fernandes, L., Macário, E., Gaspar, S., Pinto, J.G.: Climate change impacts in the design of drainage systems—a case study for Portugal (2014, accepted)

    Google Scholar 

  65. Prévost, P.: Mémoire sur l’équilibre du feu. J. Phys. 38, 314–322 (1791)

    Google Scholar 

  66. Quinn, T.R., Tremaine, S., Duncan, M.: A three million year integration of the Earth’s orbit. Astron. J. 101, 2287–2305 (1991)

    Article  Google Scholar 

  67. Rockel, B., Will, A., Hense, A.: The regional climate model COSMO-CLM (CCLM). Meteorol. Z. 17(4), 347–348 (2008)

    Article  Google Scholar 

  68. Rosenberg, E.A., Keys, P.W., Booth, D.B., Hartley, D., Burkey, J., Steinemann, A.C., Lettenmaier, D. P.: Precipitation extremes and the impacts of climate change on stormwater infrastructure in Washington State. Clim. Chang. 102(1–2), 319–349 (2010)

    Article  Google Scholar 

  69. Scherrer, S.C.: Present-day interannual variability of surface climate in CMIP3 models and its relation to future warming. Int. J. Climatol. 31(10), 1518–1529 (2011)

    Article  Google Scholar 

  70. Sharif, M., Burn, D.H.: Improved k-nearest neighbor weather generating model. J. Hydraul. Eng. 12(1), 42–51 (2007)

    Article  Google Scholar 

  71. Shetinsky, E.A.: Protection of forests and forest pyrology. Ecology, Moscow, 209 p. (1994)

    Google Scholar 

  72. Street, J.O., Carroll, R.J., Ruppert, D.: A note on computing robust regression estimates via iteratively reweighted least squares. Am. Stat. 42(2), 152–154 (1988)

    Google Scholar 

  73. Svanidse, G.G.: Principles of Estimating River Flow Regulation by the Monte Carlo Method, p. 271. Metsniereba, Tbilisi (1964)

    Google Scholar 

  74. Svanidze, G.G.: Mathematical Modeling of Hydrologic Series for Hydroelectric and Water Resources Computations. Water Resources Publications, Fort Collins (1980)

    Google Scholar 

  75. Tebaldi, C., Hayhoe, K., Arblaster, J.M., Meehl, G.A.: Going to the extremes. Clim. Chang. 79(3–4), 185–211 (2006)

    Article  Google Scholar 

  76. Trigo, R.M., Sousa, P.M., Pereira, M.G., Rasilla, D., Gouveia, C.M.: Modelling wildfire activity in Iberia with different atmospheric circulation weather types. Int. J. Climatol. (2013). http://onlinelibrary.wiley.com/doi/10.1002/joc.3749/full

  77. Van Wagner, C.E., Pickett, T.L.: Equations and FORTRAN Program for the Canadian Forest Fire Weather Index System, vol. 33. Can. For. Serv., Ottawa, Ontario (1985)

    Google Scholar 

  78. Uppala, S.M., Kållberg, P.W., Simmons, A.J., Andrae, U., Bechtold, V., Fiorino, M., et al.: The ERA-40 re-analysis. Q. J. R. Meteorol. Soc. 131(612), 2961–3012 (2005)

    Article  Google Scholar 

  79. Van Wagner, C.E.: Development and Structure of the Canadian Forest Fire Weather Index System. Forestry Technical Report 35, Canadian Forestry Service, Ottawa (1987)

    Google Scholar 

  80. Van Wagner, C.E., Pickett, T.L.: Equations and FORTRAN Program for the Canadian Forest Fire Weather Index System. Forestry Technical Report 33, Canadian Forestry Service, Ottawa (1985)

    Google Scholar 

  81. Viegas, D.X., Bovio, G., Ferreira, A., Nosenzo, A., Sol, B.: Comparative study of various methods of fire danger evaluation in southern Europe. Int. J. Wildland Fire 9(4), 235–246 (2000)

    Article  Google Scholar 

  82. Viegas, D.X., Piñol, J., Viegas, M.T., Ogaya, R.: Estimating live fine fuels moisture content using meteorologically-based indices. Int. J. Wildland Fire 10(2), 223–240 (2001)

    Article  Google Scholar 

  83. Wang, Y., Cheng, H., Edwards, R.L., He, Y., Kong, X., An, Z., et al.: The Holocene Asian monsoon: links to solar changes and North Atlantic climate. Science 308(5723), 854–857 (2005)

    Article  Google Scholar 

  84. Wilks, D.S.: Statistical Methods in the Atmospheric Sciences, vol. 100. Academic, New York (2011)

    Google Scholar 

  85. WMO: World Meteorological Organization: Technical Regulations, vol I. WMO-NO. 49. Geneva, Switzerland (1984)

    Google Scholar 

  86. Wotton, B.M.: Interpreting and using outputs from the Canadian Forest Fire Danger Rating System in research applications. Environ. Ecol. Stat. 16(2), 107–131 (2009)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This was a personal presentation that included results obtained in studies performed in collaboration with other colleagues and, for this reason, the author is grateful to Teresa Calado, Carlos C. DaCamara, and Tomás Calheiros coauthors of [63] as well as Luís Sanches Fernandes, Eduarda Macário, Sónia Gaspar e Joaquim Pinto co-authors of [64]. The author is also thankful to the IPCC (http://www.ipcc.ch/index.htm), the Global Warming Art (http://www.globalwarmingart.com/) and Croatian-English Chemistry Dictionary & Glossary (http://glossary.periodni.com/dictionary.php) for making available and allows the use some of the presented images.

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Pereira, M.G. (2015). Mathematics of Energy and Climate Change: From the Solar Radiation to the Impacts of Regional Projections. In: Bourguignon, JP., Jeltsch, R., Pinto, A., Viana, M. (eds) Mathematics of Energy and Climate Change. CIM Series in Mathematical Sciences, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-16121-1_12

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