Journal cover Journal topic
Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Model evaluation paper
06 Feb 2017
Review status
A revision of this discussion paper was accepted for the journal Geoscientific Model Development (GMD) and is expected to appear here in due course.
Evaluation of the Transport Matrix Method for simulation of ocean biogeochemical tracers
Karin F. Kvale1, Samar Khatiwala2, Heiner Dietze1, Iris Kriest1, and Andreas Oschlies1 1GEOMAR Helmholtz-Zentrum für Ozeanforschung Kiel, Düsternbrooker Weg 20, D-24105 Kiel, Germany
2Department of Earth Sciences, University of Oxford, South Parks Road, Oxford OX1 3AN, UK
Abstract. Conventional integration of earth system and ocean models can accrue considerable computational expenses, particularly for marine biogeochemical applications. Offline numerical schemes in which only the biogeochemical tracers are time-stepped and transported using a pre-computed circulation field can substantially reduce the burden and are thus an attractive alternative. One such scheme is the transport matrix method (TMM), which represents tracer transport as a sequence of sparse matrix-vector products that can be performed efficiently on distributed-memory computers. While the TMM has been used for a variety of geochemical and biogeochemical studies, to date the resulting solutions have not been comprehensively assessed against their online counterparts. Here, we present a detailed comparison of the two. It is based on simulations of the state-of-the-art biogeochemical sub-model embedded within the widely-used University of Victoria Earth System Climate Model (UVic ESCM). Transport matrices were extracted for an equilibrium run of the physical model and subsequently used to integrate the biogeochemical model offline to equilibrium. The identical biogeochemical model was also run online. Our simulations show that offline integration introduces some bias to biogeochemical quantities through the omission of the polar filtering used in UVic ESCM, and in the offline application of time-dependent forcing fields, with high latitudes showing the largest differences with respect to the online model. Differences in other regions and in the seasonality of nutrients and phytoplankton distributions are found to be relatively minor, giving confidence that the TMM is a reliable tool for offline integration of complex biogeochemical models. Moreover, while UVic ESCM is a serial code, the TMM can be run on a parallel machine with no change to the underlying biogeochemical code, thus providing orders of magnitude speed-up over the online model.

Citation: Kvale, K. F., Khatiwala, S., Dietze, H., Kriest, I., and Oschlies, A.: Evaluation of the Transport Matrix Method for simulation of ocean biogeochemical tracers, Geosci. Model Dev. Discuss.,, in review, 2017.
Karin F. Kvale et al.
Karin F. Kvale et al.


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Short summary
Computer models of ocean biology and chemistry are becoming increasingly complex, and thus more expensive, to run. One solution is to approximate the behaviour of the ocean physics and store that information outside of the model. That offline information can then be used to calculate a steady-state solution from the model's biology and chemistry, without waiting for a traditional online integration to complete. We show this offline method reproduces online results, and is 100 times faster.
Computer models of ocean biology and chemistry are becoming increasingly complex, and thus more...