Further studies on the modulation of fossil fuel production by global temperature variations

Rust, Bert W.; Crosby, Frank J.

doi:10.1016/0160-4120(94)90193-7

Cited by 3 publications

(4 citation statements)

References 17 publications

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“…Bert Rust and collaborators have used VARPRO in a number of applications related to modelling time series in environmental applications [62,[103][104][105]. In their most recent and most comprehensive contribution, they consider the inverse modulation of global fossil fuel production P(t) by variations in northern hemispheric temperatures T (t).…”

Section: Environmental Sciences and Time Series Analysismentioning

confidence: 99%

Separable nonlinear least squares: the variable projection method and its applications

2003

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In this paper we review 30 years of developments and applications of the variable projection method for solving separable nonlinear least-squares problems. These are problems for which the model function is a linear combination of nonlinear functions. Taking advantage of this special structure, the method of variable projections eliminates the linear variables obtaining a somewhat more complicated function that involves only the nonlinear parameters. This procedure not only reduces the dimension of the parameter space but also results in a better-conditioned problem. The same optimization method applied to the original and reduced problems will always converge faster for the latter. We present first a historical account of the basic theoretical work and its various computer implementations, and then report on a variety of applications from electrical engineering, medical and biological imaging, chemistry, robotics, vision, and environmental sciences. An extensive bibliography is included. The method is particularly well suited for solving real and complex exponential model fitting problems, which are pervasive in their applications and are notoriously hard to solve.

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Section: Environmental Sciences and Time Series Analysismentioning

confidence: 99%

Separable nonlinear least squares: the variable projection method and its applications

2003

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“…This temperature cycle was previously noted by Schlesinger and Ramankutty [14], and the inverse correlation between variations in temperature and emissions was previously noted by Rust and Kirk [13]. Their work was extended by Rust and Crosby [12] who argued that the correlation arises from a Gaian feedback by which increasing temperatures reduce the growth in fossil fuel production. (6), the finely dashed curve is the fit of the exponential/sinusoidal model (7), and the coarsely dashed curve is the fit of the atmospheric-CO2-driven/sinusoidal model (10).…”

Section: Introductionmentioning

confidence: 63%

“…With the fit of the CO 2 -driven version (10) of the model (12), in the last exercise above, the analysis has completed a full circle from the purely mathematical representation (2) for the emissions to the dynamical representation (11). The agreement between the two fits, i.e.…”

Section: Exercise 8: For Advanced Studentsmentioning

confidence: 99%

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Student Exercises on Fossil Fuels, Global Warming, and Gaia

Rust

2004

Computational Science - ICCS 2004

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Abstract. In a recent series of tutorial papers, Rust [7,8,9,10] modelled measured time series for global temperatures and fossil fuel CO2 emissions with related combinations of polynomials, exponentials, and sinusoids, using least squares fits that can be done by students well grounded in practical statistics. The analysis suggested that temperatures cycle around a monotonically increasing, accelerating baseline with a period of ≈ 65 years and that the exponential growth rate of CO2 emissions varies inversely with this cycle. The Gaia hypothesis [5] suggests that the biosphere adjusts atmospheric greenhouse gases to maintain an optimal temperature for life. The previous analysis is here extended with a series of fitting exercises designed to demonstrate that the above described inverse relation represents a Gaian feedback.

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Fitting nature's basic functions part IV: the variable projection algorithm

Rust

2003

Comput. Sci. Eng.

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Further studies on the modulation of fossil fuel production by global temperature variations

Cited by 3 publications

References 17 publications

Separable nonlinear least squares: the variable projection method and its applications

Separable nonlinear least squares: the variable projection method and its applications

Student Exercises on Fossil Fuels, Global Warming, and Gaia

Fitting nature's basic functions part IV: the variable projection algorithm

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