The quasi-equilibrium framework re-visited: analyzing long-term CO<sub>2</sub>
enrichment responses in plant-soil models
Abstract. Elevated carbon dioxide (CO2) can increase plant growth, but the magnitude of this CO2 fertilization effect is modified by soil nutrient availability. Predicting how nutrient availability affects plant responses to elevated CO2 is a key consideration for ecosystem models, and many modelling groups have moved to, or are moving towards, incorporating nutrient limitation in their models. The choice of assumptions to represent nutrient cycling processes has a major impact on model predictions, but it can be difficult to attribute outcomes to specific assumptions in complex ecosystem simulation models. Here we revisit the quasi-equilibrium (QE) analytical framework introduced by Comins & McMurtrie (1993) and explore the consequences of specific model assumptions for ecosystem net primary productivity. We review the literature applying this framework to plant-soil models, and then examine the effect of several new assumptions on predicted plant responses to elevated CO2. Examination of alternative assumptions for plant nitrogen uptake showed that a linear function of the mineral nitrogen pool or a saturating function of root biomass yield similar CO2 responses over time. In contrast, a saturating function of the mineral nitrogen pool yields no soil nutrient feedback at the very long-term, near-equilibrium timescale, meaning that a full CO2 fertilization effect on production is realized. We show that incorporating a priming effect on slow soil organic matter decomposition attenuates the nutrient feedback effect on production, leading to a strong medium-term CO2 response. Finally, we demonstrate that using a “potential NPP” approach to represent nutrient limitation of growth yields a relatively small CO2 fertilization effect across all timescales. Our results highlight that the QE analytical framework is effective for evaluating both the consequence and the mechanism through which different model assumptions affect predictions. To help constrain predictions of the future terrestrial carbon sink, we recommend use of this framework to analyze likely outcomes of new model assumptions before introducing them to complex model structures.