Descriptive and Predictive Growth Curves in Energy System Analysis

Natural Resources Research

Volumn 20, Issue 2, 2011, Pages 103-116

  Höök, Mikael ^a   Li, Junchen ^b   Oba, Noriaki ^a   Snowden, Simon ^c  

^a UPPSALA UNIVERSITY   (Sweden)

^b CHINA UNIVERSITY OF PETROLEUM   (China)

^c UNIVERSITY OF LIVERPOOL MANAGEMENT SCHOOL   (United Kingdom)

Author keywords

curve fitting; Growth curve models; logistic model; resource management

Indexed keywords

EID: 79955936784     PISSN: 15207439     EISSN: 15738981     Source Type: Journal    
DOI: 10.1007/s11053-011-9139-z     Document Type: Review

References (99)

1. Aleklett, K., and Campbell, C., 2003, The peak and decline of world oil and gas production: Miner. Energy, v. 18, no. 1, p. 5-20.
2. Ang, B. W., and Ng, T. T., 1992, The use of growth curves in energy studies: Energy, v. 17, no. 1, p. 25-36.
3. Ayres, R. U., 2006, Turning point: The end of exponential growth?: Technol. Forecast. Soc. Change, v. 73, no. 9, p. 1188-1203.
4. Bardi, U., 2005, The mineral economy: a model for the shape of oil production curves: Energy Policy, v. 33, no. 1, p. 53-61.
5. Bardi, U., 2007, Energy prices and resource depletion: lessons from the case of whaling in the nineteenth century: Energy Sources B Econ. Plann. Policy, v. 2, no. 3, p. 297-304.
6. Bartlett, A. A., 1993, Arithmetic of growth: methods of calculation: Popul. Environ., v. 14, no. 4, p. 359-387.
7. Bartlett, A. A., 1999, Arithmetic of growth: methods of calculation II: Popul. Environ., v. 20, no. 3, p. 215-246.
8. Bartlett, A. A., 2000, An analysis of U. S. and world oil production patterns using Hubbert-style curves: Math. Geol., v. 32, no. 1, p. 1-17.
9. Bartlett, A. A., 2004, The essential exponential! For the future of our planet: Center for Science, Mathematics and Computer Education, University of Nebraska-Lincoln, 302 p.
10. Bass, F., 1969, A new product growth model for consumer durables: Manage. Sci., v. 15, p. 215-227.
11. Bentley, R., and Boyle, G., 2007, Global oil production: forecasts and methodologies: Environ. Plann. B: Plann. Des., v. 35, no. 4, p. 609-626.
12. Bentley, R., Mannan, S. A., and Wheeler, S. J., 2007, Assessing the date of the global oil peak: the need to use 2P reserves: Energy Policy, v. 35, no. 12, p. 6364-6382.
13. Berndes, G., Hoogwijk, M., and van den Broek, R., 2003, The contribution of biomass in the future global energy supply: a review of 17 studies: Biomass Bioenergy, v. 25, no. 1, p. 1-28.
14. Bertalanffy, L. V., 1957, Wachstum, in Helmcke, J. G., Len-Gerken, H. V., and Starck, D., eds., Handbuch der Zoologie: Walter de Gruyter, Berlin, 68 p.
15. Bickel, P. J., Li, B., Tsybakov, A. B., van de Geer, S. A., Yu, B., Valdes, T., Rivero, C., Fan, J., and van der Aart, A., 2006, Regularization in statistics: TEST, v. 15, no. 2, p. 271-344.
16. Billo, E. J., 2007, Excel for scientists and engineers: numerical methods: Wiley Interscience, New Jersey, 454 p.
17. Birch, C. P. D., 1999, A new generalized logistic sigmoid growth equation compared with the Richards growth equation: Ann. Bot., v. 83, p. 713-723.
18. Brandt, A. R., 2007, Testing Hubbert: Energy Policy, v. 35, no. 5, p. 3074-3088.
19. Brody, S., 1945, Bioenergetics and growth: Reinhold Publishing, New York, 1033 p.
20. Brown, D., 2007, World fields study shows trends: giants like stable environments. AAPG Explorer (March 2007), p 36-38.
21. Browne, M. W., 2000, Cross-validation methods: J. Math. Psychol., v. 44, no. 1, p. 108-132.
22. Caithamer, P., 2008, Regression and time series analysis of the world oil peak of production: another look: Math. Geosci., v. 40, no. 6, p. 653-670.
23. Carlson, W. B., 2007, Analysis of world oil production based on the fitting of the logistic function and its derivatives: Energy Sources B Econ. Plann. Policy, v. 2, no. 4, p. 421-428.
24. Cavallo, A. J., 2004, Hubbert's petroleum production model: an evaluation and implications for world oil production forecasts: Nat. Resour. Res., v. 13, no. 4, p. 211-221.
25. Chatfield, C., 2004, The analysis of time series: an introduction (6th edn.): CRC Press, Boca Raton, 333 p.
26. Clark, T. E., 2004, Can out-of-sample forecast comparisons help prevent overfitting?: J. Forecast., v. 23, no. 2, p. 115-139.
27. Cleveland, C. J., and Kaufmann, R. K., 1991, Forecasting ultimate oil recovery and its rate of production: incorporating economic forces into the models of M. King Hubbert: Energy J., v. 12, no. 2, p. 17-46.
28. de Levie, R., 2001, How to use Excel in analytical chemistry and in general scientific data analysis: Cambridge University Press, New York, 487 p.
29. EIA Monthly Energy Review, 2010, Data taken from http://www. eia. doe. gov/emeu/mer/nuclear. html.
30. Energywatch Group, 2007, Coal: resources and future production. See also http://www. energywatchgroup. org/.
31. Feng, L., Junchen, L., and Pang, X., 2008, China's oil reserve forecast and analysis based on peak oil models: Energy Policy, v. 36, no. 11, p. 4149-4153.
32. Fitzpatrick, A., Hitchon, B., and McGregor, J. R., 1973, Long-term growth of the oil industry in the United States: Math. Geol., v. 5, no. 3, p. 237-267.
33. Fylstra, D., Lasdon, L., Warren, A., and Watson, J., 1998, Design and use of the Microsoft Excel Solvers: Interfaces, v. 28, no. 5, p. 29-55.
34. Gompertz, B., 1825, On nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies: Philos. Trans. R. Soc. Lond., v. 115, p. 513-585.
35. Guyon, X., and Yao, J. F., 1999, On the underfitting and overfitting sets of models chosen by order selection criteria: J. Multivar. Anal., v. 70, no. 2, p. 221-249.
36. Hamilton, J. D., 1994, Time series analysis (1st edn.): Princeton University Press, New Jersey, 820 p.
37. Höök, M., and Aleklett, K., 2008, A decline rate study of Norwegian oil production: Energy Policy, v. 36, no. 11, p. 4262-4271.
38. Höök, M., and Aleklett, K., 2009, Historical trends in American coal production and a possible future outlook: Int. J. Coal Geol., v. 78, no. 3, p. 201-216.
39. Höök, M., and Aleklett, K., 2010, Trends in U. S. recoverable coal supply estimates and future production outlooks: Nat. Resour. Res., v. 19, no. 3, p. 189-208.
40. Höök, M., Söderbergh, B., Jakobsson, K., and Aleklett, K., 2009, The evolution of giant oil field production behaviour: Nat. Resour. Res., v. 18, no. 1, p. 39-56.
41. Höök, M., Zittel, W., Schindler, J., and Aleklett, K., 2010a, Global coal production outlooks based on a logistic model: Fuel, v. 89, no. 11, p. 3546-3558.
42. Höök, M., Bardi, U., Feng, L., and Pang, X., 2010b, Development of oil formation theories and their importance for peak oil: Mar. Petrol. Geol., v. 27, no. 9, p. 1995-2004.
43. Hotard, D. G., and Ristroph, J. H., 1984, A regional logistic function model for crude oil production: Energy, v. 9, no. 7, p. 565-570.
44. Hu, J., Chen, Y., and Zhang, S., 1995, A new model for predicting production and reserves of oil and gas fields: Acta Petrolei Sin., v. 16, no. 1, p. 79-86.
45. Hubbert, M. K., 1956, Nuclear energy and the fossil fuels, Presented before the Spring Meeting of the Southern District, American Petroleum Institute, Plaza Hotel, San Antonio, TX, March 7-9, http://www. hubbertpeak. com/Hubbert/1956/1956. pdf.
46. Hubbert, M. K., 1959, Techniques of prediction with application to the petroleum industry, Published in 44th Annual Meeting of the American Association of Petroleum Geologists, Shell Development Company, Dallas, TX, 43 p.
47. Imam, A., Startzman, R. A., and Barrufet, M., 2004, Multicyclic Hubbert model shows global conventional gas output peaking in 2019: Oil Gas J., v. 102, p. 3131-3139.
48. Janoschek, A., 1957, Das reaktionskinetische Grundgesetz und seine Beziehungen zum Wachstums- und Ertragsgesetz: Statistische Vierteljahresschrift, v. 10, p. 25-37.
49. Kaufmann, R. K., 1991, Oil production in the lower 48 states: reconciling curve fitting and econometric models: Resour. Energy, v. 13, no. 1, p. 111-127.
50. Laherrère, J., 1997, Multi-Hubbert modeling, http://www. oilcrisis. com/laherrere/multihub. htm, Accessed 26 May 2010.
51. Laherrère, J., 2000, Distribution of field sizes in a petroleum system: parabolic fractal, lognormal or stretched exponential?: Mar. Petrol. Geol., v. 17, no. 4, p. 539-546.
52. Laherrère, J., 2004, Natural gas future supply, Paper presented at International Energy Workshop jointly organized by the Energy Modeling Forum, International Energy Agency (IEA including ETSAP) and International Institute for Applied Systems Analysis (IIASA), 22-24 June 2004 at the IEA, Paris, France, see also http://www. iiasa. ac. at/Research/ECS/IEW2004/docs/2004P_Laherrere. pdf.
53. Levenberg, K., 1944, A method for the solution of certain non-linear problems in least squares: Q. Appl. Math., v. 2, no. 2, p. 164-168.
54. Lynch, M. C., 2002, Forecasting oil supply: theory and practice: Q. Rev. Econ. Finance, v. 42, no. 2, p. 373-389.
55. Mabel, M. C., and Fernandez, E., 2008, Growth and future trends of wind energy in India: Renew. Sustain. Energy Rev., v. 12, no. 6, p. 1745-1757.
56. Mann, P., Gahagan, L., and Gordon, M. B., 2003, Tectonic setting of the world's giant oil and gas fields, in Halbouty, M. T., ed., AAPG Memoir 78: Giant Oil and Gas Fields of the Decade 1990-1999, p. 15-105.
57. Marquardt, D., 1963, An algorithm for least squares estimation of nonlinear parameters: SIAM J. Appl. Math., v. 11, no. 2, p. 431-441.
58. McArdle, J. J., 2001, Growth curve analysis, in Smelser, N. J., and Baltes, P. B., eds., International Encyclopedia of the Social & Behavioral Sciences: Pergamon, Oxford, p. 6439-6445.
59. Meng, Q. Y., and Bentley, R. W., 2008, Global oil peaking: responding to the case for 'abundant supplies of oil': Energy, v. 33, no. 8, p. 1179-1184.
60. Meyer, P. S., and Ausubel, J. H., 1999, Carrying capacity: a model with logistically varying limits: Technol. Forecast. Soc. Change, v. 61, no. 3, p. 209-214.
61. Milici, R. C., and Campbell, E. V. M., 1997, A predictive production rate life-cycle model for southwestern Virginia coalfields. Geological Survey Circular 1147, http://pubs. usgs. gov/circular/c1147/.
62. Miller, R. G., 1996, Estimating global oil resources and their duration, Norwegian Petroleum Society Special Publications 6, p. 43-56.
63. Modis, T., 2007, Strengths and weaknesses of S-curves: Technol. Forecast. Soc. Change, v. 74, no. 6, p. 866-872.
64. Modis, T., and Debecker, A., 1992, Chaoslike states can be expected before and after logistic growth: Technol. Forecast. Soc. Change, v. 41, no. 2, p. 111-120.
65. Mohamed, Z., and Bodger, P., 2004, Forecasting electricity consumption in New Zealand using economic and demographic variables: Energy, v. 30, no. 10, p. 1833-1843.
66. Mohr, S. H., and Evans, G. M., 2009, Forecasting coal production until 2100: Fuel, v. 88, no. 11, p. 2059-2067.
67. Moore, C. L., 1966, Projections of U. S. petroleum supply to 1980, with annex entitled: the Gompertz curve for analyzing and projecting the historic supply patterns of exhaustible natural resources, Technical Report: Office of Oil and Gas, Washington, DC, 47 p.
68. Moriarty, P., and Honnery, D., 2009, What energy levels can the Earth sustain?: Energy Policy, v. 37, no. 7, p. 2469-2474.
69. Nashawi, I. S., Malallah, A., and Al-Bisharah, M., 2010, Forecasting world crude oil production using multicyclic Hubbert model: Energy Fuels, v. 24, no. 3, p. 1788-1800.
70. Nehring, R., 2006a, Two basins show Hubbert's method underestimates future oil production: Oil Gas J., v. 104, no. 13, p. 37-42.
71. Nehring, R., 2006b, How Hubbert method fails to predict oil production in the Permian Basin: Oil Gas J., v. 104, no. 15, p. 30-35.
72. Nehring, R., 2006c, Post-Hubbert challenge is to find new methods to predict production: Oil Gas J., v. 104, no. 16, p. 43-46.
73. Newton, I., 1726, Philosophiae naturalis principia mathematica, general scholium (3rd edn.), page 943 of I. Bernard Cohen and Anne Whitman's 1999 translation: University of California Press, 974 p.
74. NIST/SEMATECH, 2010, NIST/SEMATECH e-handbook of statistical methods, See also http://www. itl. nist. gov/div898/handbook/.
75. Owen, N. A., Inderwildi, O. R., and King, D. A., 2010, The status of conventional world oil reserves-Hype or cause for concern?: Energy Policy, v. 38, no. 8, p. 4743-4749.
76. Patzek, T. W., 2008, Exponential growth, energetic Hubbert cycles, and the advancement of technology: Arch. Min. Sci., v. 53, no. 2, p. 131-159.
77. Patzek, T. W., and Croft, G. D., 2010, A global coal production forecast with multi-Hubbert cycle analysis: Energy, v. 35, no. 8, p. 3109-3122.
78. Radetzki M, 2007. Råvarumarknaden (in Swedish): SNS Förlag, 312 p.
79. Richards, F. J., 1959, A flexible growth curve for empirical use: J. Exp. Bot., v. 10, no. 2, p. 290-301.
80. Rotty, R. M., 1979, Growth in global energy demand and contribution of alternative supply systems: Energy, v. 4, no. 5, p. 881-890.
81. Silvennoinen, P., and Väänänen, J., 1987, Forecasting technological substitution: the logistic model of energy systems revisited: Technol. Forecast. Soc. Change, v. 32, no. 3, p. 273-280.
82. Simon, J., 1998, The ultimate resource 2. Revised version: Princeton University Press, 778 p.
83. Solow, R., 1974, The economics of resources or the resources of economics: Am. Econ. Rev., v. 64, no. 2, p. 1-14.
84. Sorrell, S., and Speirs, J., 2009, Methods of estimating ultimately recoverable resources, Technical report 5 of the UK Energy Research Centre report on Global Oil Depletion, See also: http://www. ukerc. ac. uk/support/Global%20Oil%20Depletion.
85. Sorrell, S., and Speirs, J., 2010, Hubbert's legacy: a review of curve-fitting methods to estimate ultimately recoverable resources: Nat. Resour. Res., v. 19, no. 3, p. 209-230.
86. Sorrell, S., Speirs, J., Bentley, R. W., Brandt, A. R., and Miller, R. G., 2009, Global oil depletion: an assessment of the evidence for a near-term peak in global oil production: UK Energy Research Centre, London.
87. Sorrell, S., Speirs, J., Bentley, R. W., Brandt, A. R., and Miller, R. G., 2010a, Global oil depletion: a review of the evidence: Energy Policy, v. 38, no. 9, p. 5290-5295.
88. Sorrell, S., Miller, R., Bentley, R., and Speirs, J., 2010b, Oil futures: a comparison of global supply forecasts: Energy Policy, v. 38, no. 9, p. 4990-5003.
89. Sprott, J. C., 2003, Chaos and time-series analysis (1st edn.): Oxford University Press, New York, 507 p.
90. Stone, M., 1978, Cross-validation: a review: Math. Oper. Res. Stat., v. 9, no. 1, p. 127-139.
91. Szklo, A., Machado, G., and Schaeffer, R., 2007, Future oil production in Brazil-estimates based on a Hubbert model: Energy Policy, v. 35, no. 4, p. 2360-2367.
92. Tao, Z., and Li, M., 2007, System dynamics model of Hubbert Peak for China's oil: Energy Policy, v. 35, no. 4, p. 2281-2286.
93. Tsoularis, A., and Wallace, J., 2002, Analysis of logistic growth models: Math. Biosci., v. 179, no. 1, p. 21-55.
94. United States Geological Survey, 2000, World Petroleum Assessment 2000: USGS World Energy Assessment Team, http://pubs. usgs. gov/dds/dds-060/.
95. van Rensburg, W. C. J., 1975, 'Reserves' as a leading indicator to future mineral production: Resour. Policy, v. 1, no. 6, p. 343-356.
96. Verhulst, P. F., 1838, Notice sur la loi que la population suit dans son accroissement: Correspondence Mathematique et Physique, v. 10, p. 113-121.
97. Watkins, G. C., 2006, Oil scarcity: What have the past three decades revealed?: Energy Policy, v. 34, no. 5, p. 508-514.
98. Weibull, W., 1951, A statistical distribution function of wide applicability: J. Appl. Mech., v. 18, no. 3, p. 293-297.
99. Wikipedia, 2009, Wheat and chessboard problem, Available from http://en. wikipedia. org/wiki/Wheat_and_chessboard_problem.