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

[摘要] We present a generic flux limiter to account for mass limitations from anarbitrary number of substrates in a biogeochemical reaction network. The fluxlimiter is based on the observation that substrate (e.g., nitrogen,phosphorus) limitation in biogeochemical models can be represented as toensure mass conservative and non-negative numerical solutions to thegoverning ordinary differential equations. Application of the flux limiterincludes two steps: (1) formulation of the biogeochemical processes with a matrixof stoichiometric coefficients and (2) application of Liebig's law of the minimumusing the dynamic stoichiometric relationship of the reactants. This approachcontrasts with the ad hoc down-regulation approaches that are implemented inmany existing models (such as CLM4.5 and the ACME (Accelerated ClimateModeling for Energy) Land Model (ALM)) of carbon and nutrient interactions,which are error prone when adding new processes, even for experiencedmodelers. Through an example implementation with a CENTURY-like decompositionmodel that includes carbon, nitrogen, and phosphorus, we show that ourapproach (1) produced almost identical results to that from the ad hocdown-regulation approaches under non-limiting nutrient conditions,(2) properly resolved the negative solutions under substrate-limitedconditions where the simple clipping approach failed, (3) successfullyavoided the potential conceptual ambiguities that are implied by those ad hocdown-regulation approaches. We expect our approach will make futurebiogeochemical models easier to improve and more robust.

[学科分类] 地球化学与岩石