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| Titel |
Mathematics of the total alkalinity–pH equation – pathway to robust and universal solution algorithms: the SolveSAPHE package v1.0.1 |
| VerfasserIn |
G. Munhoven |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1991-959X
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| Digitales Dokument |
URL |
| Erschienen |
In: Geoscientific Model Development ; 6, no. 4 ; Nr. 6, no. 4 (2013-08-30), S.1367-1388 |
| Datensatznummer |
250084982
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| Publikation (Nr.) |
 copernicus.org/gmd-6-1367-2013.pdf |
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| Zusammenfassung |
| The total alkalinity–pH equation, which relates total alkalinity and pH for
a given set of total concentrations of the acid–base systems that contribute
to total alkalinity in a given water sample, is reviewed and its mathematical
properties established. We prove that the equation function is strictly
monotone and always has exactly one positive root. Different commonly used
approximations are discussed and compared. An original method to derive
appropriate initial values for the iterative solution of the cubic polynomial
equation based upon carbonate-borate-alkalinity is presented. We then review
different methods that have been used to solve the total alkalinity–pH
equation, with a main focus on biogeochemical models. The shortcomings and
limitations of these methods are made out and discussed. We then present two
variants of a new, robust and universally convergent algorithm to solve the
total alkalinity–pH equation. This algorithm does not require any a priori
knowledge of the solution. SolveSAPHE (Solver Suite for Alkalinity-PH
Equations) provides reference implementations of several variants of the new
algorithm in Fortran 90, together with new implementations of other,
previously published solvers. The new iterative procedure is shown to
converge from any starting value to the physical solution. The extra
computational cost for the convergence security is only 10–15% compared
to the fastest algorithm in our test series. |
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