Editing Geochemistry (section)

== Cycles ==
{{Main|Geochemical cycle}}
{{See also|Climate model#Box models}}
Through a variety of physical and chemical processes, chemical elements change in concentration and move around in what are called ''geochemical cycles''. An understanding of these changes requires both detailed observation and theoretical models. Each chemical compound, element or isotope has a concentration that is a function {{math|''C''('''r''',''t'')}} of position and time, but it is impractical to model the full variability. Instead, in an approach borrowed from [[chemical engineering]],<ref name=Albarede/>{{rp|81}} geochemists average the concentration over regions of the Earth called ''geochemical reservoirs''. The choice of reservoir depends on the problem; for example, the ocean may be a single reservoir or be split into multiple reservoirs.<ref name=Lasaga>{{cite journal|last1=Lasaga|first1=Antonio C.|last2=Berner|first2=Robert A.|title=Fundamental aspects of quantitative models for geochemical cycles|journal=Chemical Geology|date=April 1998|volume=145|issue=3–4|pages=161–175|doi=10.1016/S0009-2541(97)00142-3|bibcode=1998ChGeo.145..161L|doi-access=free}}</ref> In a type of model called a ''box model'', a reservoir is represented by a box with inputs and outputs.<ref name=Albarede/>{{rp|81}}<ref name=Lasaga/>

Geochemical models generally involve feedback. In the simplest case of a linear cycle, either the input or the output from a reservoir is proportional to the concentration. For example, [[salt]] is removed from the ocean by formation of [[evaporite]]s, and given a constant rate of evaporation in evaporite basins, the rate of removal of salt should be proportional to its concentration. For a given component {{math|''C''}}, if the input to a reservoir is a constant {{math|''a''}} and the output is {{math|''kC''}} for some constant {{math|''k''}}, then the ''[[mass balance]]'' equation is
{{NumBlk2|:|<math>\frac{d C}{d t} = a - kC.</math>|1}}
This expresses the fact that any change in mass must be balanced by changes in the input or output. On a time scale of {{math|''t'' {{=}} 1/k}}, the system approaches a [[steady state]] in which {{math|''C''<sup>steady</sup> {{=}} ''a''/''k''}}. The ''[[residence time]]'' is defined as
:<math>\tau_\mathrm{res} = C^\text{steady}/I = C^\text{steady}/O,</math>
where {{math|''I''}} and {{math|''O''}} are the input and output rates. In the above example, the steady-state input and output rates are both equal to {{math|''a''}}, so {{math|&tau;<sub>res</sub> {{=}} 1/''k''}}.<ref name=Lasaga/>

If the input and output rates are nonlinear functions of {{math|'' C''}}, they may still be closely balanced over time scales much greater than the residence time; otherwise, there will be large fluctuations in {{math|'' C''}}. In that case, the system is always close to a steady-state and the lowest order expansion of the mass balance equation will lead to a linear equation like Equation ({{EquationNote|1}}). In most systems, one or both of the input and output depend on {{math|''C''}}, resulting in feedback that tends to maintain the steady-state. If an external forcing perturbs the system, it will return to the steady-state on a time scale of {{math|1/''k''}}.<ref name=Lasaga/>