Editing Biogeochemical cycle (section)

==Box models==
{{see also|Climate box models}}
[[File:Simple box model.png|thumb|upright=1|right| Basic one-box model]]

Box models are widely used to model biogeochemical systems.<ref name=Sarmiento1984>{{cite journal| author = Sarmiento, J.L.|author2=Toggweiler, J.R.| year = 1984| title = A new model for the role of the oceans in determining atmospheric P CO 2| journal = Nature| volume = 308| pages = 621–24| doi = 10.1038/308621a0| issue=5960 |bibcode = 1984Natur.308..621S |s2cid=4312683}}</ref><ref name=Bianchi2007>[[Thomas S. Bianchi|Bianchi, Thomas]] (2007) [https://books.google.com/books?id=3no8DwAAQBAJ&q=%22Biogeochemistry+of+Estuaries%22 ''Biogeochemistry of Estuaries''] {{Webarchive|url=https://web.archive.org/web/20210925012739/https://books.google.com/books?id=3no8DwAAQBAJ&printsec=frontcover&dq=%22Biogeochemistry+of+Estuaries%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwixq4PYm_brAhXYILcAHUVzBf0QuwUwAHoECAIQBw#v=onepage&q=%22Biogeochemistry%20of%20Estuaries%22&f=false |date=2021-09-25 }} page 9, Oxford University Press. {{ISBN|9780195160826}}.</ref> Box models are simplified versions of complex systems, reducing them to boxes (or storage [[Thermodynamics#Instrumentation|reservoir]]s) for chemical materials, linked by material [[flux]]es (flows). Simple box models have a small number of boxes with properties, such as volume, that do not change with time. The boxes are assumed to behave as if they were mixed homogeneously.<ref name=Bianchi2007 /> These models are often used to derive analytical formulas describing the dynamics and steady-state abundance of  the chemical species involved.

The diagram at the right shows a basic one-box model. The reservoir contains the amount of material ''M'' under consideration, as defined by chemical, physical or biological properties. The source ''Q'' is the flux of material into the reservoir, and the sink ''S'' is the flux of material out of the reservoir. The budget is the check and balance of the sources and sinks affecting material turnover in a reservoir. The reservoir is in a [[steady state]] if ''Q'' = ''S'', that is, if the sources balance the sinks and there is no change over time.<ref name=Bianchi2007 />

The residence or turnover time is the average time material spends resident in the reservoir. If the reservoir is in a steady state, this is the same as the time it takes to fill or drain the reservoir. Thus, if τ is the turnover time, then τ = ''M''/''S''.<ref name=Bianchi2007 /> The equation describing the rate of change of content in a reservoir is

: <math>\frac{dM}{dt} = Q - S = Q - \frac{M}{\tau}.</math>

When two or more reservoirs are connected, the material can be regarded as cycling between the reservoirs, and there can be predictable patterns to the cyclic flow.<ref name=Bianchi2007 /> More complex [[multi-compartment model|multibox models]] are usually solved using numerical techniques.

[[File:Simplified budget of carbon flows in the ocean.png|thumb|upright=0.9|left| Simple three box model. Simplified budget of ocean carbon flows<ref name=Middelburg2019>Middelburg, J.J.(2019) ''Marine carbon biogeochemistry: a primer for earth system scientists'', page 5, Springer Nature. {{ISBN|9783030108229}}. {{doi|10.1007/978-3-030-10822-9}}. [[File:CC-BY icon.svg|50px]] Material was copied from this source, which is available under a [https://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International License] {{Webarchive|url=https://web.archive.org/web/20171016050101/https://creativecommons.org/licenses/by/4.0/ |date=2017-10-16 }}.</ref>]]

{{Quote box
 |title = Measurement units
 |quote = Global biogeochemical box models usually measure:
* ''reservoir masses'' in [[petagram]]s (Pg)
* ''flow fluxes'' in petagrams per year {{nobr|(Pg yr<sup>−1</sup>)}}
 |source = 
 |align = right
 |width = 30em
}}

The diagram on the left shows a simplified budget of ocean carbon flows. It is composed of three simple interconnected box models, one for the [[euphotic zone]], one for the [[Aphotic zone|ocean interior]] or dark ocean, and one for [[ocean sediment]]s. In the euphotic zone, net [[phytoplankton production]] is about 50 Pg C each year. About 10 Pg is exported to the ocean interior while the other 40 Pg is respired. Organic carbon degradation occurs as [[Particulate organic carbon|particles]] ([[marine snow]]) settle through the ocean interior. Only 2 Pg eventually arrives at the seafloor, while the other 8 Pg is respired in the dark ocean. In sediments, the time scale available for degradation increases by orders of magnitude with the result that 90% of the organic carbon delivered is degraded and only 0.2 Pg C yr<sup>−1</sup> is eventually buried and transferred from the biosphere to the geosphere.<ref name=Middelburg2019 />

[[File:Simplified diagram of the global carbon cycle.jpg|thumb|upright=2.2|right| More complex model with many interacting boxes. Export and burial rates of terrestrial organic carbon in the ocean<ref name=Kandasamy2016 />]]

The diagram on the right shows a more complex model with many interacting boxes. Reservoir masses here represents ''carbon stocks'', measured in Pg C. Carbon exchange fluxes, measured in Pg C yr<sup>−1</sup>, occur between the atmosphere and its two major sinks, the land and the ocean. The black numbers and arrows indicate the reservoir mass and exchange fluxes estimated for the year 1750, just before the [[Industrial Revolution]]. The red arrows (and associated numbers) indicate the annual flux changes due to anthropogenic activities, averaged over the 2000–2009 time period. They represent how the carbon cycle has changed since 1750. Red numbers in the reservoirs represent the cumulative changes in anthropogenic carbon since the start of the Industrial Period, 1750–2011.<ref>{{cite journal |doi = 10.1063/1.1510279|title = Sinks for Anthropogenic Carbon|year = 2002|last1 = Sarmiento|first1 = Jorge L.|last2 = Gruber|first2 = Nicolas|journal = Physics Today|volume = 55|issue = 8|pages = 30–36|bibcode = 2002PhT....55h..30S| s2cid=128553441 |doi-access = free}}</ref><ref>{{cite journal |doi = 10.13140/2.1.1081.8883|year = 2013|last1 = Chhabra|first1 = Abha|title = Carbon and Other Biogeochemical Cycles |journal=Intergovernmental Panel on Climate Change}}</ref><ref name=Kandasamy2016>{{cite journal |doi = 10.3389/fmars.2016.00259|title = Perspectives on the Terrestrial Organic Matter Transport and Burial along the Land-Deep Sea Continuum: Caveats in Our Understanding of Biogeochemical Processes and Future Needs|year = 2016|last1 = Kandasamy|first1 = Selvaraj|last2 = Nagender Nath|first2 = Bejugam|journal = Frontiers in Marine Science|volume = 3| page=259 |s2cid = 30408500|doi-access = free| bibcode=2016FrMaS...3..259K }} [[File:CC-BY icon.svg|50px]] Material was copied from this source, which is available under a [https://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International License] {{Webarchive|url=https://web.archive.org/web/20171016050101/https://creativecommons.org/licenses/by/4.0/ |date=2017-10-16 }}.</ref>

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