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

Rust, Bert W.

doi:10.1109/mcise.2003.1182965

Cited by 8 publications

(2 citation statements)

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“…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: 99%

“…The period of the sinusoid is exactly thê τ in (3), and the phase constant has been set toθ − (τ /2) = −5.85 to make the oscillation exactly one half cycle ahead (or behind) the one for the emissions. Fitting these two models [10] gave the parameter estimates in columns 2 and 3 of Table 1 and the solid and finely dashed curves in Fig. 2.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%