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  Transit-time and age distributions for nonlinear time-dependent compartmental systems

Metzler, H., Mueller, M., & Sierra, C. (2018). Transit-time and age distributions for nonlinear time-dependent compartmental systems. Proceedings of the National Academy of Sciences of the United States of America, 115(6), 1150-1155. doi:10.1073/pnas.1705296115.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0000-33F1-6 Version Permalink: https://hdl.handle.net/21.11116/0000-0002-7C5D-C
Genre: Journal Article

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 Creators:
Metzler, Holger1, 2, Author           
Mueller, Markus1, Author           
Sierra, Carlos1, Author           
Affiliations:
1Theoretical Ecosystem Ecology Group, Dr. Carlos Sierra, Department Biogeochemical Processes, Prof. S. E. Trumbore, Max Planck Institute for Biogeochemistry, Max Planck Society, ou_2074326              
2IMPRS International Max Planck Research School for Global Biogeochemical Cycles, Max Planck Institute for Biogeochemistry, Max Planck Society, Hans-Knöll-Str. 10, 07745 Jena, DE, ou_1497757              

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 Abstract: Many processes in nature are modeled using compartmental systems (reservoir/pool/box systems). Usually, they are expressed as a set of first-order differential equations describing the transfer of matter across a network of compartments. The concepts of age of matter in compartments and the time required for particles to transit the system are important diagnostics of these models with applications to a wide range of scientific questions. Until now, explicit formulas for transit-time and age distributions of nonlinear time-dependent compartmental systems were not available. We compute densities for these types of systems under the assumption of well-mixed compartments. Assuming that a solution of the nonlinear system is available at least numerically, we show how to construct a linear time-dependent system with the same solution trajectory. We demonstrate how to exploit this solution to compute transit-time and age distributions in dependence on given start values and initial age distributions. Furthermore, we derive equations for the time evolution of quantiles and moments of the age distributions. Our results generalize available density formulas for the linear time-independent case and mean-age formulas for the linear time-dependent case. As an example, we apply our formulas to a nonlinear and a linear version of a simple global carbon cycle model driven by a time-dependent input signal which represents fossil fuel additions. We derive time-dependent age distributions for all compartments and calculate the time it takes to remove fossil carbon in a business-as-usual scenario.

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 Dates: 2018-012018-01-222018-02-06
 Publication Status: Issued
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 Rev. Type: -
 Identifiers: Other: BGC2788
DOI: 10.1073/pnas.1705296115
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Title: Proceedings of the National Academy of Sciences of the United States of America
  Other : Proceedings of the National Academy of Sciences of the USA
  Abbreviation : PNAS
Source Genre: Journal
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Publ. Info: Washington, D.C. : National Academy of Sciences
Pages: - Volume / Issue: 115 (6) Sequence Number: - Start / End Page: 1150 - 1155 Identifier: ISSN: 0027-8424
CoNE: https://pure.mpg.de/cone/journals/resource/954925427230