Pool dynamics of time-dependent compartmental systems with application to the terrestrial carbon cycle.
Author(s)
Chappelle, George
Hastings, Alan
Rasmussen, Martin
Type
Journal Article
Abstract
Compartmental models play an important role to describe the dynamics of systems that involve mass movements between different types of pools. We develop a theory to analyse the average ages of mass in different pools in a linear compartmental system with time-dependent (i.e. non-autonomous) transfer rates, which involves transit times that characterize the average time a particle has spent in a particular pool. We apply our theoretical results to investigate a nine-dimensional compartmental system with time-dependent fluxes between pools modelling the carbon cycle which is a modification of the Carnegie-Ames-Stanford approach model. Knowledge of transit time and mean age allows calculation of carbon storage in a pool as a function of time. The general result that has important implications for understanding and managing carbon storage is that the change in storage in different pools does not change monotonically through time: as rates change monotonically a pool which initially shows a decrease may then show an increase in storage or vice versa. Thus caution is needed in extrapolating even the direction of future changes in storage in carbon storage in different pools with global change.
Date Issued
2023-03
Date Acceptance
2023-02-21
Citation
Journal of the Royal Society Interface, 2023, 20 (200), pp.1-13
ISSN
1742-5662
Publisher
The Royal Society
Start Page
1
End Page
13
Journal / Book Title
Journal of the Royal Society Interface
Volume
20
Issue
200
Copyright Statement
© 2023 The Authors.
Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
License URL
Identifier
https://www.ncbi.nlm.nih.gov/pubmed/36946091
Subjects
Carbon
Carbon Cycle
Carbon Dioxide
carbon cycle
CASA model
compartmental system
McKendrick–von Foerster equation
non-autonomous dynamical system
transit time
Publication Status
Published
Coverage Spatial
England
Date Publish Online
2023-03-22