21 November 2016

A Generic Law-of-the-Minimum Flux Limiter for Simulating Substrate Limitation in Biogeochemical Models


This paper solves the numerical difficulty in handling multi-substrate co-limitation in all types of biogeochemical models.  We demonstrate the approach for a C, N, and P reaction network


We found:

1.Models like ALM and CLM are suffering from ambiguity in handling substrate limitation

2.The new method is more robust and removes the numerical ambiguity in implementing multi-substrate co-limitation


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 so-lutions to the governing ordinary differential equations. Ap-plication of the flux limiter includes two steps: (1) formula-tion of the biogeochemical processes with a matrix of sto-ichiometric coefficients and (2) application of Liebig’s law of the minimum using the dynamic stoichiometric relation-ship 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 (Accel-erated Climate Modeling for Energy) Land Model (ALM)) of carbon and nutrient interactions, which are error prone when adding new processes, even for experienced model-ers. 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 ap-proaches under non-limiting nutrient conditions, (2) properly resolved the negative solutions under substrate-limited con-ditions where the simple clipping approach failed, (3) suc-cessfully avoided the potential conceptual ambiguities that are implied by those ad hoc down-regulation approaches. We expect our approach will make future biogeochemical mod-els easier to improve and more robust.

William J. Riley
Lawrence Berkeley National Laboratory