Articles | Volume 13, issue 3
Technical note
05 Feb 2016
Technical note |  | 05 Feb 2016

Technical Note: A generic law-of-the-minimum flux limiter for simulating substrate limitation in biogeochemical models

J. Y. Tang and W. J. Riley

Abstract. We present a generic flux limiter to account for mass limitations from an arbitrary number of substrates in a biogeochemical reaction network. The flux limiter is based on the observation that substrate (e.g., nitrogen, phosphorus) limitation in biogeochemical models can be represented as to ensure mass conservative and non-negative numerical solutions to the governing ordinary differential equations. Application of the flux limiter includes two steps: (1) formulation of the biogeochemical processes with a matrix of stoichiometric coefficients and (2) application of Liebig's law of the minimum using the dynamic stoichiometric relationship of the reactants. This approach contrasts with the ad hoc down-regulation approaches that are implemented in many existing models (such as CLM4.5 and the ACME (Accelerated Climate Modeling for Energy) Land Model (ALM)) of carbon and nutrient interactions, which are error prone when adding new processes, even for experienced modelers. Through an example implementation with a CENTURY-like decomposition model that includes carbon, nitrogen, and phosphorus, we show that our approach (1) produced almost identical results to that from the ad hoc down-regulation approaches under non-limiting nutrient conditions, (2) properly resolved the negative solutions under substrate-limited conditions where the simple clipping approach failed, (3) successfully avoided the potential conceptual ambiguities that are implied by those ad hoc down-regulation approaches. We expect our approach will make future biogeochemical models easier to improve and more robust.

Short summary
We present a generic flux-limiting approach to simultaneously handle the availability limitation from many substrates, a problem common in all biogeochemical models. Our approach does not have the ordering problem like a few existing ad hoc approaches, and is straightforward to implement. Our results imply that significant uncertainties could have occurred in many biogeochemical models because of the improper handling of the substrate co-limitation problem.
Final-revised paper