Brown, P. N., Byrne, G. D., and Hindmarsh, A. C.: VODE: A variable-coefficient ODE solver, SIAM J. Sci. Stat. Comput., 10, 1038–1051,
https://doi.org/10.1137/0910062, 1989.
a,
b
Burdige, D. J.: Preservation of organic matter in marine sediments: controls, mechanisms, and an imbalance in sediment organic carbon budgets?, Chem. Rev., 107, 467–485,
https://doi.org/10.1021/cr050347q, 2007.
a
Crank, J.: The mathematics of diffusion, Clarendon Press, Oxford, ISBN 13 9780198533078, 1956. a
De Borger, E., Tiano, J., Braeckman, U., Rijnsdorp, A. D., and Soetaert, K.: Impact of bottom trawling on sediment biogeochemistry: a modelling approach, Biogeosciences, 18, 2539–2557,
https://doi.org/10.5194/bg-18-2539-2021, 2021.
a
De Leeuw, J. W. and Largeau, C.: A Review of Macromolecular Organic Compounds That Comprise Living Organisms and Their Role in Kerogen, Coal, and Petroleum Formation, in: Organic Geochemistry: Principles and Applications, edited by: Engel, M. H. and Macko, S. A., Springer US, 23–72,
https://doi.org/10.1007/978-1-4615-2890-6_2, 1993.
a
Deleersnijder, E., Campin, J.-M., and Delhez, E. J.: The concept of age in marine modelling: I. Theory and preliminary model results, J. Marine Syst., 28, 229–267,
https://doi.org/10.1016/S0924-7963(01)00026-4, 2001.
a,
b
Delhez, É. J. and Deleersnijder, É.: The concept of age in marine modelling: II. Concentration distribution function in the English Channel and the North Sea, J. Marine Syst., 31, 279–297,
https://doi.org/10.1016/S0924-7963(01)00066-5, 2002.
a,
b,
c,
d
Forbes, C., Evans, M., Hastings, N., and Peacock, B.: Statistical Distributions, John Wiley & Sons, Inc.,
https://doi.org/10.1002/9780470627242, 2010.
a,
b
Fourier, J. B. J.: Théorie analytique de la chaleur, vol. 504, Didot Paris,
https://gallica.bnf.fr/ark:/12148/bpt6k1045508v (last access: 5 December 2023), 1822. a
Freitas, F. S., Pika, P. A., Kasten, S., Jørgensen, B. B., Rassmann, J., Rabouille, C., Thomas, S., Sass, H., Pancost, R. D., and Arndt, S.: New insights into large-scale trends of apparent organic matter reactivity in marine sediments and patterns of benthic carbon transformation, Biogeosciences, 18, 4651–4679,
https://doi.org/10.5194/bg-18-4651-2021, 2021.
a,
b
Gilbert, P. and Varadhan, R.: numDeriv: Accurate Numerical Derivatives,
https://CRAN.R-project.org/package=numDeriv (last access: 14 October 2023), 2016. a
Hasselman, B.: nleqslv: Solve Systems of Nonlinear Equations,
https://CRAN.R-project.org/package=nleqslv (last access: 14 October 2023), 2023. a
John, V., Angelov, I., Öncül, A., and Thévenin, D.: Techniques for the reconstruction of a distribution from a finite number of its moments, Chem. Eng. Sci., 62, 2890–2904,
https://doi.org/10.1016/j.ces.2007.02.041, 2007.
a
Jørgensen, B. B.: A comparison of methods for the quantification of bacterial sulfate reduction in coastal marine sediments: I. Measurement with radiotracer techniques, Geomicrobiol. J., 1, 11–27,
https://doi.org/10.1080/01490457809377721, 1978.
a,
b,
c
Klingbeil, K., Mohammadi-Aragh, M., Gräwe, U., and Burchard, H.: Quantification of spurious dissipation and mixing – Discrete variance decay in a Finite-Volume framework, Ocean Model., 81, 49–64,
https://doi.org/10.1016/j.ocemod.2014.06.001, 2014.
a
Kuderer, M. J.: How bioturbators perturb the paleo record: From Eulerian to Lagrangian and back, Ph.D. thesis, Utrecht University,
https://doi.org/10.33540/1544, 2022.
a,
b
Meile, C. and Van Cappellen, P.: Particle age distributions and O
2 exposure times: timescales in bioturbated sediments, Global Biogeochem. Cy., 19, GB3013,
https://doi.org/10.1029/2004GB002371, 2005.
a
Meysman, F. J., Boudreau, B. P., and Middelburg, J. J.: Modeling reactive transport in sediments subject to bioturbation and compaction, Geochim. Cosmochim. Ac., 69, 3601–3617,
https://doi.org/10.1016/j.gca.2005.01.004, 2005.
a
Meysman, F. J., Middelburg, J. J., and Heip, C. H.: Bioturbation: a fresh look at Darwin's last idea, Trends Ecol. Evol., 21, 688–695,
https://doi.org/10.1016/j.tree.2006.08.002, 2006.
a
Middelburg, J. J., Soetaert, K., and Herman, P. M.: Empirical relationships for use in global diagenetic models, Deep-Sea Res. Pt. I:, 44, 327–344,
https://doi.org/10.1016/S0967-0637(96)00101-X, 1997.
a
R Core Team: R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria,
https://www.R-project.org/ (last access: 14 October 2023), 2022.
a,
b
Rooze, J.: Application described in paper: A novel Eulerian model based on cen
tral moments to simulate age and reactivity continua interacting with mixing processes, Zenodo [code],
https://doi.org/10.5281/zenodo.10202341, 2023.
a
Rooze, J., Peterson, L., Peterson, R. N., and Meile, C.: Porewater flow patterns in surficial cold seep sediments inferred from conservative tracer profiles and early diagenetic modeling, Chem. Geol., 536, 119468,
https://doi.org/10.1016/j.chemgeo.2020.119468, 2020.
a
Sarmin, E. and Chudov, L.: On the stability of the numerical integration of systems of ordinary differential equations arising in the use of the straight line method, USSR Comp. Math. Math., 3, 1537–1543,
https://doi.org/10.1016/0041-5553(63)90256-8, 1963.
a
Soetaert, K.: rootSolve: Nonlinear root finding, equilibrium and steady-state analysis of ordinary differential equations, r package 1.6, 372 pp., ISBN 978-1-4020-8623-6, 2009. a
Soetaert, K., Petzoldt, T., and Setzer, R. W.: Solving Differential Equations in R: Package deSolve, J. Stat. Softw., 33, 1–25,
https://doi.org/10.18637/jss.v033.i09, 2010.
a
Tromp, T., Van Cappellen, P., and Key, R.: A global model for the early diagenesis of organic carbon and organic phosphorus in marine sediments, Geochim. Cosmochim. Ac., 59, 1259–1284,
https://doi.org/10.1016/0016-7037(95)00042-X, 1995.
a
Vähätalo, A. V., Aarnos, H., and Mäntyniemi, S.: Biodegradability continuum and biodegradation kinetics of natural organic matter described by the beta distribution, Biogeochemistry, 100, 227–240,
https://doi.org/10.1007/s10533-010-9419-4, 2010.
a
Wang, Y. and Van Cappellen, P.: A multicomponent reactive transport model of early diagenesis: Application to redox cycling in coastal marine sediments, Geochim. Cosmochim. Ac., 60, 2993–3014,
https://doi.org/10.1016/0016-7037(96)00140-8, 1996.
a
Xu, S., Liu, B., Arndt, S., Kasten, S., and Wu, Z.: Assessing global-scale organic matter reactivity patterns in marine sediments using a lognormal reactive continuum model, Biogeosciences, 20, 2251–2263,
https://doi.org/10.5194/bg-20-2251-2023, 2023.
a
Zindorf, M., Rooze, J., Meile, C., März, C., Jouet, G., Newton, R., Brandily, C., and Pastor, L.: The evolution of early diagenetic processes at the Mozambique margin during the last glacial-interglacial transition, Geochim. Cosmochim. Ac., 300, 79–94,
https://doi.org/10.1016/j.gca.2021.02.024, 2021.
a
Zonneveld, K. A. F., Versteegh, G. J. M., Kasten, S., Eglinton, T. I., Emeis, K.-C., Huguet, C., Koch, B. P., de Lange, G. J., de Leeuw, J. W., Middelburg, J. J., Mollenhauer, G., Prahl, F. G., Rethemeyer, J., and Wakeham, S. G.: Selective preservation of organic matter in marine environments; processes and impact on the sedimentary record, Biogeosciences, 7, 483–511,
https://doi.org/10.5194/bg-7-483-2010, 2010.
a
