Laplace transform analysis of the carbon cycle |
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| Affiliation: | 1. Department of Natural Resources and Environmental Science, MS 186, University of Nevada-Reno, Reno, NV 89557, US;2. School of Science and Technology, University of Washington-Bothell, 18115 Campus Way NE, Bothell, Washington, US;3. Department of Chemistry, Saint Mary''s College of California, Moraga, CA 94575-4527, US;1. CTS-UNINOVA, Department of Electrical Engineering, Faculty of Science and Technology, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal;2. Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal;3. Universidad de La Laguna, Departamento de Análisis Matemático, 38271 La Laguna, Tenerife, Spain |
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| Abstract: | A Laplace transform representation is used to describe the changes in atmospheric CO2 in response to emissions. The formalism gives an explicit representation of generic relations that are less clear when model results are presented as numerical integrations with particular parameter values. In particular, the Laplace transform formalism clarifies some issues involved in inversion of ice-core data and analysis of geosequestration. The airborne fraction is expressed as the emission growth rate multiplied by the Laplace transform of the atmospheric response function, evaluated at the growth rate. This representation emphasises that historical data only capture carbon cycle dynamics over a limited range of time-scales. The Laplace transform formalism provides a basis for expressing uncertainties in the response function in terms of the Padé–Laplace transformation used for fitting sums of exponentials. |
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