NONLINEAR SUBSTANCE FLOW MODELS FOR DISCOVERING SYSTEM BEHAVIOR

Two model approaches, one mechanistic and the other empirical, are described for the development of quantitative substance flow models (SFMs). Nonlinear models enable quantification of interactions and variable sensitivities... [ view full abstract ]

Two model approaches, one mechanistic and the other empirical, are described for the development of quantitative substance flow models (SFMs). Nonlinear models enable quantification of interactions and variable sensitivities among the flows and other parameters, with implications for management of the resources.

The mechanistic approach is illustrated with a mechanistic model of global phosphorus flows based on the substance flow analysis data of Cordell, et al (2009) and a conceptual model of the individual flows. Most phosphorus used in agriculture is mined, and is thus inherently unsustainable. There is no substitute for its use in agriculture, and thus is a critical resource for producing food. The SFM is configured as demand-driven, and includes several conservation interventions as parameters so the system sensitivity to those parameters can be explored. Example parameters include recycle rates for various substances (food, manure, human wastes) or utilization efficiencies (agricultural use, food production). Population is also included as a driver to determine its sensitivity as well as the “planetary boundary,” the level that could be supported by natural sources alone. The single most sensitive parameter was the fraction of meat in the diet; however reducing this quantity quickly resulted in an optimum, beyond which mine production increased due to reduced dependence on natural (grazing) sources.

The second model is an empirical model of tungsten flow in the United States. It uses the Stepwise Response Surface Method (S-RSM) to develop nonlinear vector time-series models of the flows. The main advantage of the empirical approach is that the resulting model is entirely data-driven, does not require a conceptual model of individual flows, and is relatively free of a priori assumptions (such as residence time distributions for substance stocks).

We find that for both of these approaches, the resulting nonlinear models are capable of identifying complex (and even chaotic) relationships among material flows and exogenous variables. These kinds of relationships cannot be discovered by use of linear models, greatly reducing the possibility of model mis-specification and bias.